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Sample records for nonlinear fokker planck

  1. Nonlinear Fokker-Planck Equations Fundamentals and Applications

    CERN Document Server

    Frank, Till Daniel

    2005-01-01

    Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stationary solutions, emphasizing the stability analysis of stationary solutions by means of self-consistency equations, linear stability analysis, and Lyapunov's direct method. Also treated are Langevin equations and correlation functions. Nonlinear Fokker-Planck Equations addresses various phenomena such as phase transitions, multistability of systems, synchronization, anomalous diffusion, cut-off solutions, travelling-wave solutions and the emergence of power law solutions. A nonlinear Fokker-Planck perspective to quantum statistics, generalized thermodynamics, and linear nonequilibrium thermodynamics is given. Theoretical concepts are illustrated where possible by simple examples. The book also reviews several applications in the fields of condensed matter physics, the physics of porous media and liquid crystals, accelerator physics, neurophysics, social sciences, popul...

  2. Numerical method for the nonlinear Fokker-Planck equation

    International Nuclear Information System (INIS)

    Zhang, D.S.; Wei, G.W.; Kouri, D.J.; Hoffman, D.K.

    1997-01-01

    A practical method based on distributed approximating functionals (DAFs) is proposed for numerically solving a general class of nonlinear time-dependent Fokker-Planck equations. The method relies on a numerical scheme that couples the usual path-integral concept to the DAF idea. The high accuracy and reliability of the method are illustrated by applying it to an exactly solvable nonlinear Fokker-Planck equation, and the method is compared with the accurate K-point Stirling interpolation formula finite-difference method. The approach is also used successfully to solve a nonlinear self-consistent dynamic mean-field problem for which both the cumulant expansion and scaling theory have been found by Drozdov and Morillo [Phys. Rev. E 54, 931 (1996)] to be inadequate to describe the occurrence of a long-lived transient bimodality. The standard interpretation of the transient bimodality in terms of the flat region in the kinetic potential fails for the present case. An alternative analysis based on the effective potential of the Schroedinger-like Fokker-Planck equation is suggested. Our analysis of the transient bimodality is strongly supported by two examples that are numerically much more challenging than other examples that have been previously reported for this problem. copyright 1997 The American Physical Society

  3. Massively parallel Fokker-Planck calculations

    International Nuclear Information System (INIS)

    Mirin, A.A.

    1990-01-01

    This paper reports that the Fokker-Planck package FPPAC, which solves the complete nonlinear multispecies Fokker-Planck collision operator for a plasma in two-dimensional velocity space, has been rewritten for the Connection Machine 2. This has involved allocation of variables either to the front end or the CM2, minimization of data flow, and replacement of Cray-optimized algorithms with ones suitable for a massively parallel architecture. Calculations have been carried out on various Connection Machines throughout the country. Results and timings on these machines have been compared to each other and to those on the static memory Cray-2. For large problem size, the Connection Machine 2 is found to be cost-efficient

  4. From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag

    Science.gov (United States)

    Plastino, A. R.; Curado, E. M. F.; Nobre, F. D.; Tsallis, C.

    2018-02-01

    Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these evolution equations can be interpreted as providing an effective description of a system of particles interacting via short-range forces while performing overdamped motion under the effect of an external confining potential. This point of view has been recently applied to the study of thermodynamical features of interacting vortices in type II superconductors. In the present work we explore an embedding of the nonlinear Fokker-Planck equation within a Vlasov equation, thus incorporating inertial effects to the concomitant particle dynamics. Exact time-dependent solutions of the q -Gaussian form (with compact support) are obtained for the Vlasov equation in the case of quadratic confining potentials.

  5. One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

    Science.gov (United States)

    Shapovalov, A. V.

    2018-04-01

    The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

  6. Vectorized Fokker-Planck package for the CRAY-1

    International Nuclear Information System (INIS)

    McCoy, M.G.; Mirin, A.A.; Killeen, J.

    1979-08-01

    A program for the solution of the time-dependent, two dimensional, nonlinear, multi-species Fokker-Planck equation is described. The programming is written such that the loop structure is highly vectorizable on the CRAY FORTRAN Compiler. A brief discussion of the Fokker-Planck equation itself is followed by a description of the procedure developed to solve the equation efficiently. The Fokker-Planck equation is a second order partial differential equation whose coefficients depend upon moments of the distribution functions. Both the procedure for the calculation of these coefficients and the procedure for the time advancement of the equation itself must be done efficiently if significant overall time saving is to result. The coefficients are calculated in a series of nested loops, while time advancement is accomplished by a choice of either a splitting or an ADI technique. Overall, timing tests show that the vectorized CRAY program realizes up to a factor of 12 advantage over an optimized CDC-7600 program and up to a factor of 365 over a non-vectorized version of the same program on the CRAY

  7. On the linear discrepancy model and risky shifts in group behavior: a nonlinear Fokker-Planck perspective

    International Nuclear Information System (INIS)

    Frank, T D

    2009-01-01

    Using a nonlinear Fokker-Planck perspective we re-formulate the linear discrepancy model proposed by Boster and colleagues that describes the emergence of risky shifts during group decision making. Analytical expressions for the stationary case are derived and risky shifts are obtained by Monte Carlo simulations. Striking similarities with the Kuramoto model for group synchronization are pointed out

  8. Expansion of the relativistic Fokker-Planck equation including non-linear terms and a non-Maxwellian background

    International Nuclear Information System (INIS)

    Shkarofsky, I.P.

    1997-01-01

    The relativistic Fokker-Planck collision term in Braams and Karney [Phys. Fluids B 1, 1355 (1989)] is expanded using Cartesian tensors (equivalent to associated Legendre spherical harmonics) retaining all non-linear terms and an arbitrary zeroth order distribution background. Expressions are given for collision terms between all harmonics and the background distribution in terms of the j and y functions in Braams and Karney. The results reduce to Braams and Karney for the first order harmonic term with a Maxwellian background and to those given by Shkarofsky [Can. J. Phys. 41, 1753 (1963)] in the non-relativistic limit. Expressions for the energy and momentum transfer associated with relativistic Coulomb collisions are given. The fast two dimensional Fokker-Planck solver in Shoucri and Shkarofsky [Comput. Phys. Commun. 82, 287 (1994)] has been extended to include the second order harmonic term. copyright 1997 American Institute of Physics

  9. A Lie-admissible method of integration of Fokker-Planck equations with non-linear coefficients (exact and numerical solutions)

    International Nuclear Information System (INIS)

    Fronteau, J.; Combis, P.

    1984-08-01

    A Lagrangian method is introduced for the integration of non-linear Fokker-Planck equations. Examples of exact solutions obtained in this way are given, and also the explicit scheme used for the computation of numerical solutions. The method is, in addition, shown to be of a Lie-admissible type

  10. Maximum Path Information and Fokker Planck Equation

    Science.gov (United States)

    Li, Wei; Wang A., Q.; LeMehaute, A.

    2008-04-01

    We present a rigorous method to derive the nonlinear Fokker-Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang [Chaos, Solitons & Fractals 23 (2005) 1253] for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q (the index of Tsallis entropy [J. Stat. Phys. 52 (1988) 479] and the time t.

  11. Proof of the path integral representation of the nonlinear Fokker-Planck equation by means of Fourier series

    International Nuclear Information System (INIS)

    Dekker, H.

    1978-01-01

    The lagrangian for the action occurring in the path integral solution of the nonlinear Fokker-Planck equation with constant diffusion function is derived by means of a straightforward Fourier series analysis. In this manner the path between the prepoint and the postpoint in the short time propagator is not restricted a priori to the usually considered straight line. Earlier results by Graham, Stratonovich, Horsthemke and Back, and the author's are recovered and thus put on much safer ground. (Auth.)

  12. Stochastic reliability analysis using Fokker Planck equations

    International Nuclear Information System (INIS)

    Hari Prasad, M.; Rami Reddy, G.; Srividya, A.; Verma, A.K.

    2011-01-01

    The Fokker-Planck equation describes the time evolution of the probability density function of the velocity of a particle, and can be generalized to other observables as well. It is also known as the Kolmogorov forward equation (diffusion). Hence, for any process, which evolves with time, the probability density function as a function of time can be represented with Fokker-Planck equation. In stochastic reliability analysis one is more interested in finding out the reliability or failure probability of the components or structures as a function of time rather than instantaneous failure probabilities. In this analysis the variables are represented with random processes instead of random variables. A random processes can be either stationary or non stationary. If the random process is stationary then the failure probability doesn't change with time where as in the case of non stationary processes the failure probability changes with time. In the present paper Fokker Planck equations have been used to find out the probability density function of the non stationary random processes. In this paper a flow chart has been provided which describes step by step process for carrying out stochastic reliability analysis using Fokker-Planck equations. As a first step one has to identify the failure function as a function of random processes. Then one has to solve the Fokker-Planck equation for each random process. In this paper the Fokker-Planck equation has been solved by using Finite difference method. As a result one gets the probability density values of the random process in the sample space as well as time space. Later at each time step appropriate probability distribution has to be identified based on the available probability density values. For checking the better fitness of the data Kolmogorov-Smirnov Goodness of fit test has been performed. In this way one can find out the distribution of the random process at each time step. Once one has the probability distribution

  13. Fokker-Planck equation resolution for N variables-Application examples

    International Nuclear Information System (INIS)

    Munoz Roldan, A.; Garcia-Olivares, A.

    1994-01-01

    A set of problems which are reducible to Fokker-Planck equations are presented. Those problems have been solved by using the CHAPKOL library. This library of programs solves stochastic ''Fokker-Planck'' equations in one or several dimensions by using the Chapman-Kolmogorov integral. This method calculates the probability distribution at a time t+dt from a distribution given at time t through a convolution integral in which the integrant is the product of the distribution function at time t and the Green function of the Fokker-Planck equation. The method have some numerical advantages when compared with finite differences algorithms. The accuracy of the method is analysed in several specific cases

  14. A Fokker-Planck-Landau collision equation solver on two-dimensional velocity grid and its application to particle-in-cell simulation

    Energy Technology Data Exchange (ETDEWEB)

    Yoon, E. S.; Chang, C. S., E-mail: cschang@pppl.gov [Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Korea Advanced Institute of Science and Technology, Yuseong-gu, DaeJeon 305-701 (Korea, Republic of)

    2014-03-15

    An approximate two-dimensional solver of the nonlinear Fokker-Planck-Landau collision operator has been developed using the assumption that the particle probability distribution function is independent of gyroangle in the limit of strong magnetic field. The isotropic one-dimensional scheme developed for nonlinear Fokker-Planck-Landau equation by Buet and Cordier [J. Comput. Phys. 179, 43 (2002)] and for linear Fokker-Planck-Landau equation by Chang and Cooper [J. Comput. Phys. 6, 1 (1970)] have been modified and extended to two-dimensional nonlinear equation. In addition, a method is suggested to apply the new velocity-grid based collision solver to Lagrangian particle-in-cell simulation by adjusting the weights of marker particles and is applied to a five dimensional particle-in-cell code to calculate the neoclassical ion thermal conductivity in a tokamak plasma. Error verifications show practical aspects of the present scheme for both grid-based and particle-based kinetic codes.

  15. A nonlinear Fokker-Planck equation approach for interacting systems: Anomalous diffusion and Tsallis statistics

    Science.gov (United States)

    Marin, D.; Ribeiro, M. A.; Ribeiro, H. V.; Lenzi, E. K.

    2018-07-01

    We investigate the solutions for a set of coupled nonlinear Fokker-Planck equations coupled by the diffusion coefficient in presence of external forces. The coupling by the diffusion coefficient implies that the diffusion of each species is influenced by the other and vice versa due to this term, which represents an interaction among them. The solutions for the stationary case are given in terms of the Tsallis distributions, when arbitrary external forces are considered. We also use the Tsallis distributions to obtain a time dependent solution for a linear external force. The results obtained from this analysis show a rich class of behavior related to anomalous diffusion, which can be characterized by compact or long-tailed distributions.

  16. Fokker-Planck and quasilinear codes

    International Nuclear Information System (INIS)

    Karney, C.F.F.

    1985-11-01

    The interaction of radio-frequency waves with a plasma is described by a Fokker-Planck equation with an added quasilinear term. Methods for solving this equation on a computer are discussed. 40 refs., 12 figs., 3 tabs

  17. Solving the Fokker-Planck equation on a massively parallel computer

    International Nuclear Information System (INIS)

    Mirin, A.A.

    1990-01-01

    The Fokker-Planck package FPPAC had been converted to the Connection Machine 2 (CM2). For fine mesh cases the CM2 outperforms the Cray-2 when it comes to time-integrating the difference equations. For long Legendre expansions the CM2 is also faster at computing the Fokker-Planck coefficients. 3 refs

  18. Integral solution for the spherically symmetric Fokker-Planck equation

    International Nuclear Information System (INIS)

    Donoso, J.M.; Soler, M.

    1993-01-01

    We propose an integral method to deal with the spherically symmetric non-linear Fokker-Planck equation appearing in plasma physics. A probability transition expression is obtained, which takes into account the proper domain for the radial velocity component. The analytical and computational results are new, and the time evolution is completely satisfactory. The main achievement of the method is conservation of both the initial norm and energy for unlimited times, which has not been attained in the differential approach to the problem. (orig.)

  19. A multigroup flux-limited asymptotic diffusion Fokker-Planck equation

    International Nuclear Information System (INIS)

    Liu Chengan

    1987-01-01

    A more perfrect flux-limited method is applied to combine with asymptotic diffusion theory of the radiation transpore, and the high peaked component in the scattering angle is treated with Fokker-Planck methods, thus the flux-limited asymptotic diffusion Fokker-Planck equation has been founded. Since the equation is of diffusion form, it retains the simplity and the convenience of the classical diffusion theory, and improves precision in describing radiation transport problems

  20. Fermi-Dirac-Fokker-Planck equation : well-posedness & long-time asymptotics

    OpenAIRE

    Carrillo , José A.; Laurençot , Philippe; Rosado , Jesús

    2009-01-01

    International audience; A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments are finite, we can show the global existence of weak solutions for this problem. The natural associated entropy of the equation is the main tool to derive uniform in time a priori estimates for the kinetic energy and entropy. As a con...

  1. Boltzmann-Fokker-Planck calculations using standard discrete-ordinates codes

    International Nuclear Information System (INIS)

    Morel, J.E.

    1987-01-01

    The Boltzmann-Fokker-Planck (BFP) equation can be used to describe both neutral and charged-particle transport. Over the past several years, the author and several collaborators have developed methods for representing Fokker-Planck operators with standard multigroup-Legendre cross-section data. When these data are input to a standard S/sub n/ code such as ONETRAN, the code actually solves the Boltzmann-Fokker-Planck equation rather than the Boltzmann equation. This is achieved wihout any modification to the S/sub n/ codes. Because BFP calculations can be more demanding from a numerical viewpoint than standard neutronics calculations, we have found it useful to implement new quadrature methods ad convergence acceleration methods in the standard discrete-ordinates code, ONETRAN. We discuss our BFP cross-section representation techniques, our improved quadrature and acceleration techniques, and present results from BFP coupled electron-photon transport calculations performed with ONETRAN. 19 refs., 7 figs

  2. Contribution to the study of the Fokker-planck equation; Contribution a l'etude de l'equation de Fokker-planck

    Energy Technology Data Exchange (ETDEWEB)

    Blaquiere, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1963-07-01

    In the first paragraphs of this report, the Fokker-Planck equation is presented using the presentation method due to S. Chandrasekhar. Certain conventional resolution methods are given, and then a consideration of the physical interpretation of its various terms leads to a new study method based on the use of Campbell's theorems. This gives a solution to the equation in an integral form. The integral kernel of the solution is a normal centred distribution. Finally, the use of the Laplace transformation leads to a simple determination of the parameters of this integral kernel and connects the present theory to the characteristic function method used in particular in the field of nuclear reactors. The method also makes it possible to calculate the moments of the different orders of the probability distribution without the necessity of solving the Fokker-Planck equation. (author) [French] Dans les premiers paragraphes de ce rapport, l'equation de FOKKER-PLANCK est introduite en utilisant le mode d'expose de S. CHANDRASEKHAR. Puis, apres avoir rappele certaines methodes classiques de resolution, l'interpretation physique de ses differents termes nous conduit a une nouvelle methode d'etude qui repose sur l'utilisation des theoremes de CAMPBELL. On est ainsi conduit a la solution de l'equation sous forme integrale. Le noyau integral de la solution est une distribution normale centree. Enfin l'emploi de la transformation de LAPLACE conduit a une determination simple des parametres de ce noyau integral, et relie la theorie actuelle a la methode de la fonction caracteristique associee, utilisee en particulier dans le domaine des reacteurs nucleaires. Finalement cette methode permet le calcul des moments des differents ordres de la distribution de probabilites, sans passer par la resolution souvent laborieuse de l'equation de FOKKER-PLANCK. (auteur)

  3. Fokker-Planck modeling of current penetration during electron cyclotron current drive

    International Nuclear Information System (INIS)

    Merkulov, A.; Westerhof, E.; Schueller, F. C.

    2007-01-01

    The current penetration during electron cyclotron current drive (ECCD) on the resistive time scale is studied with a Fokker-Planck simulation, which includes a model for the magnetic diffusion that determines the parallel electric field evolution. The existence of the synergy between the inductive electric field and EC driven current complicates the process of the current penetration and invalidates the standard method of calculation in which Ohm's law is simply approximated by j-j cd =σE. Here it is proposed to obtain at every time step a self-consistent approximation to the plasma resistivity from the Fokker-Planck code, which is then used in a concurrent calculation of the magnetic diffusion equation in order to obtain the inductive electric field at the next time step. A series of Fokker-Planck calculations including a self-consistent evolution of the inductive electric field has been performed. Both the ECCD power and the electron density have been varied, thus varying the well known nonlinearity parameter for ECCD P rf [MW/m -3 ]/n e 2 [10 19 m -3 ] [R. W. Harvey et al., Phys. Rev. Lett 62, 426 (1989)]. This parameter turns out also to be a good predictor of the synergetic effects. The results are then compared with the standard method of calculations of the current penetration using a transport code. At low values of the Harvey parameter, the standard method is in quantitative agreement with Fokker-Planck calculations. However, at high values of the Harvey parameter, synergy between ECCD and E parallel is found. In the case of cocurrent drive, this synergy leads to the generation of large amounts of nonthermal electrons and a concomitant increase of the electrical conductivity and current penetration time. In the case of countercurrent drive, the ECCD efficiency is suppressed by the synergy with E parallel while only a small amount of nonthermal electrons is produced

  4. Fokker-Planck equation resolution for N variables. Application examples

    International Nuclear Information System (INIS)

    Munoz, A.; Garcia-Olivares, A.

    1994-01-01

    A set of problems which are reducible to Fokker-Planck equations are presented. Those problems have been solved by using the CHAPKOL library. This library of programs solves stochastic Fokker-Plank equations in one or several dimensions by using the Chapman- Kolmogorov integral. This method calculates the probability distribution at a time t + dt from a distribution given at time t through a convolution integral in which the integration is the product of the distribution function at time t and the Green function of the Fokker-Planck equation. The method have some numerical advantages when compared with finite differences algorithms. The accuracy of the method is analysed in several specific cases. (Author) 9 refs

  5. Generalized Fokker-Planck equations for coloured, multiplicative Gaussian noise

    International Nuclear Information System (INIS)

    Cetto, A.M.; Pena, L. de la; Velasco, R.M.

    1984-01-01

    With the help of Novikov's theorem, it is possible to derive a master equation for a coloured, multiplicative, Gaussian random process; the coefficients of this master equation satisfy a complicated auxiliary integro-differential equation. For small values of the Kubo number, the master equation reduces to an approximate generalized Fokker-Planck equation. The diffusion coefficient is explicitly written in terms of correlation functions. Finally, a straightforward and elementary second order perturbative treatment is proposed to derive the same approximate Fokker-Planck equation. (author)

  6. Fokker-Planck equation resolution for N variables. Application examples; Aplicaciones del programa CHAPKOL para la resolucion de ecuaciones Fokker-Planck en N variables

    Energy Technology Data Exchange (ETDEWEB)

    Munoz, A; Garcia-Olivares, A

    1993-07-01

    A set of problems which are reducible to Fokker-Planck equations are presented. Those problems have been solved by using the CHAPKOL library. This library of programs solves stochastic Fokker-Plank equations in one or several dimensions by using the Chapman- Kolmogorov integral. This method calculates the probability distribution at a time t + dt from a distribution given at time t through a convolution integral in which the integration is the product of the distribution function at time t and the Green function of the Fokker-Planck equation. The method have some numerical advantages when compared with finite differences algorithms. The accuracy of the method is analysed in several specific cases. (Author) 9 refs.

  7. Fermi-Dirac-Fokker-Planck equation: well-posedness and long-time asymptotics

    OpenAIRE

    Carrillo, José A.; Laurençot, Philippe; Rosado, Jesús

    2008-01-01

    A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments are finite, we can show the global existence of weak solutions for this problem. The natural associated entropy of the equation is the main tool to derive uniform in time a priori estimates for the kinetic energy and entropy. As a consequence, long-time asym...

  8. Exact solutions of the Fokker-Planck equation from an nth order supersymmetric quantum mechanics approach

    Energy Technology Data Exchange (ETDEWEB)

    Schulze-Halberg, Axel [Escuela Superior de Fisica y Matematicas, IPN, Unidad Profesional Adolfo Lopez Mateos, Col. San Pedro Zacatenco, Edificio 9, 07738 Mexico D.F. (Mexico)], E-mail: xbataxel@gmail.com; Rivas, Jesus Morales [Universidad Autonoma Metropolitana - Azcapotzalco, CBI - Area de Fisica Atomica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 Mexico D.F. (Mexico)], E-mail: jmr@correo.azc.uam.mx; Pena Gil, Jose Juan [Universidad Autonoma Metropolitana - Azcapotzalco, CBI - Area de Fisica Atomica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 Mexico D.F. (Mexico)], E-mail: jjpg@correo.azc.uam.mx; Garcia-Ravelo, Jesus [Escuela Superior de Fisica y Matematicas, IPN, Unidad Profesional Adolfo Lopez Mateos, Col. San Pedro Zacatenco, Edificio 9, 07738 Mexico D.F. (Mexico)], E-mail: ravelo@esfm.ipn.mx; Roy, Pinaki [Physics and Applied Mathematics Unit, Indian Statistical Institute, Calcutta-700108 (India)], E-mail: pinaki@isical.ac.in

    2009-04-20

    We generalize the formalism of nth order Supersymmetric Quantum Mechanics (n-SUSY) to the Fokker-Planck equation for constant diffusion coefficient and stationary drift potential. The SUSY partner drift potentials and the corresponding solutions of the Fokker-Planck equation are given explicitly. As an application, we generate new solutions of the Fokker-Planck equation by means of our first- and second-order transformation.

  9. Exact solutions of the Fokker-Planck equation from an nth order supersymmetric quantum mechanics approach

    International Nuclear Information System (INIS)

    Schulze-Halberg, Axel; Rivas, Jesus Morales; Pena Gil, Jose Juan; Garcia-Ravelo, Jesus; Roy, Pinaki

    2009-01-01

    We generalize the formalism of nth order Supersymmetric Quantum Mechanics (n-SUSY) to the Fokker-Planck equation for constant diffusion coefficient and stationary drift potential. The SUSY partner drift potentials and the corresponding solutions of the Fokker-Planck equation are given explicitly. As an application, we generate new solutions of the Fokker-Planck equation by means of our first- and second-order transformation.

  10. Derivation of a Fokker-Planck equation for bunched beams

    International Nuclear Information System (INIS)

    Ruggiero, A.G.

    1993-01-01

    This report investigates the derivation of the Fokker-Planck equation which is commonly used to evaluate the evolution with time of an ensemble of particles under the effect of external rf forces, cooling and forces of stochastic nature like intrabeam scattering. The conventional approach based on the classical work by Chandrasekhar is first exposed, where the phase delay and the momentum error of the particle are used. The method is then extended to the case the distribution function is expressed in terms of the amplitude of motion instead of the original rectilinear variables. The new Fokker-Planck equation is obtained with an averaging process over the phase distribution instead of the time-averaging as it was usually performed earlier, to avoid the appearance of a singularity behavior. The solution of the Fokker-Planck equation is chosen in the proper form which makes easier the evaluation of the beam lifetime in the presence of the separatrix of the rf buckets. Finally the numerical applications apply the Relativistic Heavy Ion Collider (RHIC)

  11. Darboux transformations for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix

    International Nuclear Information System (INIS)

    Schulze-Halberg, Axel

    2012-01-01

    We construct a Darboux transformation for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix. Our transformation is based on the two-dimensional supersymmetry formalism for the Schrödinger equation. The transformed Fokker-Planck equation and its solutions are obtained in explicit form.

  12. An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations

    KAUST Repository

    Festa, Adriano; Gomes, Diogo A.; Machado Velho, Roberto

    2017-01-01

    Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.

  13. An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations

    KAUST Repository

    Festa, Adriano

    2017-03-22

    Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.

  14. Linear analysis of the momentum cooling Fokker-Planck equation

    International Nuclear Information System (INIS)

    Rosenzweig, J.B.

    1989-01-01

    In order to optimize the extraction scheme used to take antiprotons out of the accumulator, it is necessary to understand the basic processes involved. At present, six antiproton bunches per Tevatron store are removed sequentially by RF unstacking from the accumulator. The phase space dynamics of this process, with its accompanying phase displacement deceleration and phase space dilution of portions of the stack, can be modelled by numerical solution of the longitudinal equations of motion for a large number of particles. We have employed the tracking code ESME for this purpose. In between RF extractions, however, the stochastic cooling system is turned on for a short time, and we must take into account the effect of momentum stochastic cooling on the antiproton energy spectrum. This process is described by the Fokker-Planck equation, which models the evolution of the antiproton stack energy distribution by accounting for the cooling through an applied coherent drag force and the competing heating of the stack due to diffusion, which can arise from intra-beam scattering, amplifier noise and coherent (Schottky) effects. In this note we examine the aspects of the Fokker-Planck in the regime where the nonlinear terms due to Schottky effects are small. This discussion ultimately leads to solution of the equation in terms of an orthonormal set of functions which are closely related to the quantum simple-harmonic oscillator wave-functions. 5 refs

  15. Fokker-Planck equation in the presence of a uniform magnetic field

    International Nuclear Information System (INIS)

    Dong, Chao; Zhang, Wenlu; Li, Ding

    2016-01-01

    The Fokker-Planck equation in the presence of a uniform magnetic field is derived which has the same form as the case of no magnetic field but with different Fokker-Planck coefficients. The coefficients are calculated explicitly within the binary collision model, which are free from infinite sums of Bessel functions. They can be used to investigate relaxation and transport phenomena conveniently. The kinetic equation is also manipulated into the Landau form from which it is straightforward to compare with previous results and prove the conservation laws.

  16. Fokker-Planck equation in the presence of a uniform magnetic field

    Energy Technology Data Exchange (ETDEWEB)

    Dong, Chao, E-mail: chaodong@iphy.ac.cn [Center for Plasma Theory and Computation, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Department of Nuclear Engineering, Seoul National University, Seoul 151-744 (Korea, Republic of); Zhang, Wenlu [Center for Plasma Theory and Computation, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Li, Ding, E-mail: dli@ustc.edu.cn [Center for Plasma Theory and Computation, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Department of Modern Physics, University of Science and Technology of China, Anhui Hefei 230026 (China)

    2016-08-15

    The Fokker-Planck equation in the presence of a uniform magnetic field is derived which has the same form as the case of no magnetic field but with different Fokker-Planck coefficients. The coefficients are calculated explicitly within the binary collision model, which are free from infinite sums of Bessel functions. They can be used to investigate relaxation and transport phenomena conveniently. The kinetic equation is also manipulated into the Landau form from which it is straightforward to compare with previous results and prove the conservation laws.

  17. Application of Fokker-Planck equation in positron diffusion trapping model

    International Nuclear Information System (INIS)

    Bartosova, I.; Ballo, P.

    2015-01-01

    This paper is a theoretical prelude to future work involving positron diffusion in solids for the purpose of positron annihilation lifetime spectroscopy (PALS). PALS is a powerful tool used to study defects present in materials. However, the behavior of positrons in solids is a process hard to describe. Various models have been established to undertake this task. Our preliminary model is based on the Diffusion Trapping Model (DTM) described by partial differential Fokker-Planck equation and is solved via time discretization. Fokker-Planck equation describes the time evolution of the probability density function of velocity of a particle under the influence of various forces. (authors)

  18. Automatic mesh refinement and parallel load balancing for Fokker-Planck-DSMC algorithm

    Science.gov (United States)

    Küchlin, Stephan; Jenny, Patrick

    2018-06-01

    Recently, a parallel Fokker-Planck-DSMC algorithm for rarefied gas flow simulation in complex domains at all Knudsen numbers was developed by the authors. Fokker-Planck-DSMC (FP-DSMC) is an augmentation of the classical DSMC algorithm, which mitigates the near-continuum deficiencies in terms of computational cost of pure DSMC. At each time step, based on a local Knudsen number criterion, the discrete DSMC collision operator is dynamically switched to the Fokker-Planck operator, which is based on the integration of continuous stochastic processes in time, and has fixed computational cost per particle, rather than per collision. In this contribution, we present an extension of the previous implementation with automatic local mesh refinement and parallel load-balancing. In particular, we show how the properties of discrete approximations to space-filling curves enable an efficient implementation. Exemplary numerical studies highlight the capabilities of the new code.

  19. An adaptive, implicit, conservative, 1D-2V multi-species Vlasov-Fokker-Planck multi-scale solver in planar geometry

    Science.gov (United States)

    Taitano, W. T.; Chacón, L.; Simakov, A. N.

    2018-07-01

    We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we extend the conservative adaptive velocity-space discretization scheme proposed in [Taitano et al., J. Comput. Phys., 318, 391-420, (2016)] to a spatially inhomogeneous system. In this approach, we normalize the velocity-space coordinate to a temporally and spatially varying local characteristic speed per species. We explicitly consider the resulting inertial terms in the Vlasov equation, and derive a discrete formulation that conserves mass, momentum, and energy up to a prescribed nonlinear tolerance upon convergence. Our conservation strategy employs nonlinear constraints to enforce these properties discretely for both the Vlasov operator and the Fokker-Planck collision operator. Numerical examples of varying degrees of complexity, including shock-wave propagation, demonstrate the favorable efficiency and accuracy properties of the scheme.

  20. Fokker-Planck transport in solid state accelerator concepts

    International Nuclear Information System (INIS)

    Newberger, B.; Tajima, T.

    1989-01-01

    Particle transport in a crystalline solid under channeling conditions is considered by means of a Fokker-Planck description. The model includes electron multiple scattering, radiation damping and an accelerating electric field. Analytic solutions have been obtained using a harmonic potential model to describe the channeling forces. These solutions will be described

  1. Generalized multivariate Fokker-Planck equations derived from kinetic transport theory and linear nonequilibrium thermodynamics

    International Nuclear Information System (INIS)

    Frank, T.D.

    2002-01-01

    We study many particle systems in the context of mean field forces, concentration-dependent diffusion coefficients, generalized equilibrium distributions, and quantum statistics. Using kinetic transport theory and linear nonequilibrium thermodynamics we derive for these systems a generalized multivariate Fokker-Planck equation. It is shown that this Fokker-Planck equation describes relaxation processes, has stationary maximum entropy distributions, can have multiple stationary solutions and stationary solutions that differ from Boltzmann distributions

  2. On the Fokker-Planck theory of electron three-body recombination

    International Nuclear Information System (INIS)

    Sayasov, Yu. S.

    1977-01-01

    The Fokker-Planck theory of electron three-body recombination based on the concept of electron diffusion along the energy scale in the excited hydrogen-like atoms formed in the recombining plasmas, is extended in several respects. 1) An universal formula for population distribution of the excited atoms in strongly ionized plasmas was found under a sole assumption, that the cross-sections for the inelastic atom-electron collisions are governed by the classical impulse approximation. 2) A general Fokker-Planck theory of the recombination in a slightly ionized, two-temperature plasmas was formulated. The recombination coefficients for such plasmas were shown to possess some peculiar properties in case the electronic temperature differs appreciable from the atomic one. A few limitations of the existing schemas for calculation of the recombination kinetics are briefly discussed. (orig.) [de

  3. FIFPC, a fast ion Fokker--Planck code

    International Nuclear Information System (INIS)

    Fowler, R.H.; Callen, J.D.; Rome, J.A.; Smith, J.

    1976-07-01

    A computer code is described which solves the Fokker--Planck equation for the velocity space distribution of fast ions injected into a tokamak plasma. The numerical techniques are described and use of the code is outlined. The program is written in FORTRAN IV and is modularized in order to provide greater flexibility to the user. A program listing is provided and the results of sample cases are presented

  4. The Fokker-Planck equation for coupled Brown-Néel-rotation.

    Science.gov (United States)

    Weizenecker, Jürgen

    2018-01-22

    Calculating the dynamic properties of magnetization of single-domain particles is of great importance for the tomographic imaging modality known as magnetic particle imaging (MPI). Although the assumption of instantaneous thermodynamic equilibrium (Langevin function) after application of time-dependent magnetic fields is sufficient for understanding the fundamental behavior, it is essential to consider the finite response times of magnetic particles for optimizing or analyzing various aspects, e.g. interpreting spectra, optimizing MPI sequences, developing new contrasts, and evaluating simplified models. The change in magnetization following the application of the fields is caused by two different movements: the geometric rotation of the particle and the rotation of magnetization with respect to the fixed particle axes. These individual rotations can be well described using the Langevin equations or the Fokker-Planck equation. However, because the two rotations generally exhibit interdependence, it is necessary to consider coupling between the two equations. This article shows how a coupled Fokker-Planck equation can be derived on the basis of coupled Langevin equations. Two physically equivalent Fokker-Planck equations are derived and transformed by means of an appropriate series expansion into a system of ordinary differential equations, which can be solved numerically. Finally, this system is also used to specify a system of differential equations for various limiting cases (Néel, Brown, uniaxial symmetry). Generally, the system exhibits a sparsely populated matrix and can therefore be handled well numerically.

  5. The Fokker-Planck equation for coupled Brown-Néel-rotation

    Science.gov (United States)

    Weizenecker, Jürgen

    2018-02-01

    Calculating the dynamic properties of magnetization of single-domain particles is of great importance for the tomographic imaging modality known as magnetic particle imaging (MPI). Although the assumption of instantaneous thermodynamic equilibrium (Langevin function) after application of time-dependent magnetic fields is sufficient for understanding the fundamental behavior, it is essential to consider the finite response times of magnetic particles for optimizing or analyzing various aspects, e.g. interpreting spectra, optimizing MPI sequences, developing new contrasts, and evaluating simplified models. The change in magnetization following the application of the fields is caused by two different movements: the geometric rotation of the particle and the rotation of magnetization with respect to the fixed particle axes. These individual rotations can be well described using the Langevin equations or the Fokker-Planck equation. However, because the two rotations generally exhibit interdependence, it is necessary to consider coupling between the two equations. This article shows how a coupled Fokker-Planck equation can be derived on the basis of coupled Langevin equations. Two physically equivalent Fokker-Planck equations are derived and transformed by means of an appropriate series expansion into a system of ordinary differential equations, which can be solved numerically. Finally, this system is also used to specify a system of differential equations for various limiting cases (Néel, Brown, uniaxial symmetry). Generally, the system exhibits a sparsely populated matrix and can therefore be handled well numerically.

  6. FOKKER-PLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS

    Energy Technology Data Exchange (ETDEWEB)

    Lindberg, R. R.

    2017-06-25

    We analyze single bunch transverse instabilities due to wakefields using a Fokker-Planck model. We expand on the work of Suzuki [1], writing out the linear matrix equation including chromaticity, both dipolar and quadrupolar transverse wakefields, and the effects of damping and diffusion due to the synchrotron radiation. The eigenvalues and eigenvectors determine the collective stability of the beam, and we show that the predicted threshold current for transverse instability and the profile of the unstable agree well with tracking simulations. In particular, we find that predicting collective stability for high energy electron beams at moderate to large values of chromaticity requires the full Fokker-Planck analysis to properly account for the effects of damping and diffusion due to synchrotron radiation.

  7. Massively parallel Fokker-Planck code ALLAp

    International Nuclear Information System (INIS)

    Batishcheva, A.A.; Krasheninnikov, S.I.; Craddock, G.G.; Djordjevic, V.

    1996-01-01

    The recently developed for workstations Fokker-Planck code ALLA simulates the temporal evolution of 1V, 2V and 1D2V collisional edge plasmas. In this work we present the results of code parallelization on the CRI T3D massively parallel platform (ALLAp version). Simultaneously we benchmark the 1D2V parallel vesion against an analytic self-similar solution of the collisional kinetic equation. This test is not trivial as it demands a very strong spatial temperature and density variation within the simulation domain. (orig.)

  8. Fokker-Planck modeling of pitting corrosion in underground pipelines

    Energy Technology Data Exchange (ETDEWEB)

    Camacho, Eliana Nogueira [Risco Ambiental Engenharia, Rio de Janeiro, RJ (Brazil); Melo, Paulo F. Frutuoso e [Coordenacao dos Programas de Pos-Graduacao de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear; Saldanha, Pedro Luiz C. [Comissao Nacional de Energia Nuclear (CGRC/CNEN), Rio de Janeiro, RJ (Brazil). Coordenacao Geral de Reatores e Ciclo do Combustivel; Silva, Edson de Pinho da [Universidade Federal Rural do Rio de Janeiro (UFRRJ), Seropedica, RJ (Brazil). Dept. of Physics

    2011-07-01

    Full text: The stochastic nature of pitting corrosion has been recognized since the 1930s. It has been learned that this damage retains no memory of its past. Instead, the future state is determined only by the knowledge of its present state. This Markovian property that underlies the stochastic process governing pitting corrosion has been explored as a discrete Markovian process by many authors since the beginning of the 1990s for underground pipelines of the oil and gas industries and nuclear power plants. Corrosion is a genuine continuous time and space state Markovian process, so to model it as a discrete time and/or state space is an approximation to the problem. Markovian chains approaches, with an increasing number of states, could involve a large number of parameters, the transition rates between states, to be experimentally determined. Besides, such an increase in the number of states produces matrices with huge dimensions leading to time-consuming computational solutions. Recent approaches involving Markovian discrete process have overcome those difficulties but, on the other hand, a large number of soil and pipe stochastic variables have to be known. In this work we propose a continuous time and space state approach to the evolution of pit corrosion depths in underground pipelines. In order to illustrate the application of the model for defect depth growth a combination of real life data and Monte Carlo simulation was used. The process is described by a Fokker-Planck equation. The Fokker-Planck equation is completely determined by the knowledge of two functions known as the drift and diffusion coefficients. In this work we also show that those functions can be estimated from corrosion depth data from in-line inspections. Some particular forms of drift and diffusion coefficients lead to particular Fokker-Planck equations for which analytical solutions are known, as is the case for the Wiener process, the Ornstein-Uhlenbeck process and the Brownian motion

  9. Integral propagator solvers for Vlasov-Fokker-Planck equations

    International Nuclear Information System (INIS)

    Donoso, J M; Rio, E del

    2007-01-01

    We briefly discuss the use of short-time integral propagators on solving the so-called Vlasov-Fokker-Planck equation for the dynamics of a distribution function. For this equation, the diffusion tensor is singular and the usual Gaussian representation of the short-time propagator is no longer valid. However, we prove that the path-integral approach on solving the equation is, in fact, reliable by means of our generalized propagator, which is obtained through the construction of an auxiliary solvable Fokker-Planck equation. The new representation of the grid-free advancing scheme describes the inherent cross- and self-diffusion processes, in both velocity and configuration spaces, in a natural manner, although these processes are not explicitly depicted in the differential equation. We also show that some splitting methods, as well as some finite-difference schemes, could fail in describing the aforementioned diffusion processes, governed in the whole phase space only by the velocity diffusion tensor. The short-time transition probability offers a stable and robust numerical algorithm that preserves the distribution positiveness and its norm, ensuring the smoothness of the evolving solution at any time step. (fast track communication)

  10. Boundary conditions and subelliptic estimates for geometric Kramers-Fokker-Planck operators on manifolds with boundaries

    CERN Document Server

    Nier, Francis

    2018-01-01

    This article is concerned with the maximal accretive realizations of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup. Admissible boundary conditions cover a wide range of applications for the usual scalar Kramer-Fokker-Planck equation or Bismut's hypoelliptic laplacian.

  11. Kappa and other nonequilibrium distributions from the Fokker-Planck equation and the relationship to Tsallis entropy

    Science.gov (United States)

    Shizgal, Bernie D.

    2018-05-01

    This paper considers two nonequilibrium model systems described by linear Fokker-Planck equations for the time-dependent velocity distribution functions that yield steady state Kappa distributions for specific system parameters. The first system describes the time evolution of a charged test particle in a constant temperature heat bath of a second charged particle. The time dependence of the distribution function of the test particle is given by a Fokker-Planck equation with drift and diffusion coefficients for Coulomb collisions as well as a diffusion coefficient for wave-particle interactions. A second system involves the Fokker-Planck equation for electrons dilutely dispersed in a constant temperature heat bath of atoms or ions and subject to an external time-independent uniform electric field. The momentum transfer cross section for collisions between the two components is assumed to be a power law in reduced speed. The time-dependent Fokker-Planck equations for both model systems are solved with a numerical finite difference method and the approach to equilibrium is rationalized with the Kullback-Leibler relative entropy. For particular choices of the system parameters for both models, the steady distribution is found to be a Kappa distribution. Kappa distributions were introduced as an empirical fitting function that well describe the nonequilibrium features of the distribution functions of electrons and ions in space science as measured by satellite instruments. The calculation of the Kappa distribution from the Fokker-Planck equations provides a direct physically based dynamical approach in contrast to the nonextensive entropy formalism by Tsallis [J. Stat. Phys. 53, 479 (1988), 10.1007/BF01016429].

  12. Reduced Fokker-Planck models for fast particle distribution across a transition layer of disparate plasma temperatures

    Science.gov (United States)

    Tang, Xian-Zhu; Berk, H. L.; Guo, Zehua; McDevitt, C. J.

    2014-03-01

    Across a transition layer of disparate plasma temperatures, the high energy tail of the plasma distribution can have appreciable deviations from the local Maxwellian distribution due to the Knudson layer effect. The Fokker-Planck equation for the tail particle population can be simplified in a series of practically useful limiting cases. The first is the approximation of background Maxwellian distribution for linearizing the collision operator. The second is the supra-thermal particle speed ordering of vTi ≪ v ≪ vTe for the tail ions and vTi ≪ vTe ≪ v for the tail electrons. Keeping both the collisional drag and energy scattering is essential for the collision operator to produce a Maxwellian tail distribution. The Fokker-Planck model for following the tail ion distribution for a given background plasma profile is explicitly worked out for systems of one spatial dimension, in both slab and spherical geometry. A third simplification is an expansion of the tail particle distribution using the spherical harmonics, which are eigenfunctions of the pitch angle scattering operator. This produces a set of coupled Fokker-Planck equations that contain energy-dependent spatial diffusion terms in two coordinates (position and energy), which originate from pitch angle scattering in the original Fokker-Planck equation. It is shown that the well-known diffusive Fokker-Planck model is a poor approximation of the two-mode truncation model, which itself has fundamental deficiency compared with the three-mode truncation model. The cause is the lack of even-symmetry representation in pitch dependence in the two-mode truncation model.

  13. Chaotic universe dynamics using a Fokker-Planck equation

    International Nuclear Information System (INIS)

    Coule, D.H.; Olynyk, K.O.

    1987-07-01

    A Fokker-Planck equation that accounts for fluctuations in field and its conjugate momentum is solved numerically for the case of a λ phi 4 potential. Although the amount of inflation agrees closely with that expected classically, in certain cases (large initial fields or large dispersions),the ''slow rolling'' approximation appears invalid. In such cases inflation would stop prematurely before possibly restarting. 18 refs., 2 figs

  14. Space distribution and energy straggling of charged particles via Fokker-Planck equation

    International Nuclear Information System (INIS)

    Manservisi, S.; Molinari, V.; Nespoli, A.

    1996-01-01

    The Fokker-Planck equation describing a beam of charged particles entering a homogeneous medium is solved here for a stationary case. Interactions are taken into account through Coulomb cross-section. Starting from the charged-particle distribution as a function of velocity and penetration depth, some important kinetic quantities are calculated, like mean velocity, range and the loss of energy per unit space. In such quantities the energy straggling is taken into account. This phenomenon is not considered in the continuous slowing-down approximation that is commonly used to obtain the range and the stopping power. Finally the well-know Bohr of Bethe formula is found as a first-order approximation of the Fokker-Planck equation

  15. On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

    KAUST Repository

    Annunziato, Mario

    2014-09-01

    In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assumptions it is shown that the two strategies are equivalent in the case of expected cost functionals, while the FokkerPlanck formalism allows considering a larger class of objectives. To illustrate the connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.

  16. Fractional Fokker-Planck equation and oscillatory behavior of cumulant moments

    International Nuclear Information System (INIS)

    Suzuki, N.; Biyajima, M.

    2002-01-01

    The Fokker-Planck equation is considered, which is connected to the birth and death process with immigration by the Poisson transform. The fractional derivative in time variable is introduced into the Fokker-Planck equation in order to investigate an origin of oscillatory behavior of cumulant moments. From its solution (the probability density function), the generating function (GF) for the corresponding probability distribution is derived. We consider the case when the GF reduces to that of the negative binomial distribution (NBD), if the fractional derivative is replaced to the ordinary one. The H j moment derived from the GF of the NBD decreases monotonically as the rank j increases. However, the H j moment derived in our approach oscillates, which is contrasted with the case of the NBD. Calculated H j moments are compared with those of charged multiplicities observed in pp-bar, e + e - , and e + p collisions. A phenomenological meaning of introducing the fractional derivative in time variable is discussed

  17. Fokker-Planck equation in mirror research

    International Nuclear Information System (INIS)

    Post, R.F.

    1983-01-01

    Open confinement systems based on the magnetic mirror principle depend on the maintenance of particle distributions that may deviate substantially from Maxwellian distributions. Mirror research has therefore from the beginning relied on theoretical predictions of non-equilibrium rate processes obtained from solutions to the Fokker-Planck equation. The F-P equation plays three roles: Design of experiments, creation of classical standards against which to compare experiment, and predictions concerning mirror based fusion power systems. Analytical and computational approaches to solving the F-P equation for mirror systems will be reviewed, together with results and examples that apply to specific mirror systems, such as the tandem mirror

  18. Simulating transient dynamics of the time-dependent time fractional Fokker-Planck systems

    Science.gov (United States)

    Kang, Yan-Mei

    2016-09-01

    For a physically realistic type of time-dependent time fractional Fokker-Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker-Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed.

  19. Fully non-linear multi-species Fokker-Planck-Landau collisions for gyrokinetic particle-in-cell simulations of fusion plasma

    Science.gov (United States)

    Hager, Robert; Yoon, E. S.; Ku, S.; D'Azevedo, E. F.; Worley, P. H.; Chang, C. S.

    2015-11-01

    We describe the implementation, and application of a time-dependent, fully nonlinear multi-species Fokker-Planck-Landau collision operator based on the single-species work of Yoon and Chang [Phys. Plasmas 21, 032503 (2014)] in the full-function gyrokinetic particle-in-cell codes XGC1 [Ku et al., Nucl. Fusion 49, 115021 (2009)] and XGCa. XGC simulations include the pedestal and scrape-off layer, where significant deviations of the particle distribution function from a Maxwellian can occur. Thus, in order to describe collisional effects on neoclassical and turbulence physics accurately, the use of a non-linear collision operator is a necessity. Our collision operator is based on a finite volume method using the velocity-space distribution functions sampled from the marker particles. Since the same fine configuration space mesh is used for collisions and the Poisson solver, the workload due to collisions can be comparable to or larger than the workload due to particle motion. We demonstrate that computing time spent on collisions can be kept affordable by applying advanced parallelization strategies while conserving mass, momentum, and energy to reasonable accuracy. We also show results of production scale XGCa simulations in the H-mode pedestal and compare to conventional theory. Work supported by US DOE OFES and OASCR.

  20. Numerical solution of modified fokker-planck equation with poissonian input

    Czech Academy of Sciences Publication Activity Database

    Náprstek, Jiří; Král, Radomil

    2010-01-01

    Roč. 17, 3/4 (2010), s. 251-268 ISSN 1802-1484 R&D Projects: GA AV ČR(CZ) IAA200710805; GA ČR(CZ) GA103/09/0094 Institutional research plan: CEZ:AV0Z20710524 Keywords : Fokker-Planck equation * poisson ian exciation * numerical solution * transition effects Subject RIV: JN - Civil Engineering

  1. The Fokker-Planck equation for ray dispersion in gyrotropic stratified media

    NARCIS (Netherlands)

    Golynski, S.M.

    1984-01-01

    The Hamilton equations of geometrical optics determine the rays of the relevant wave field in the short wavelength. We give a systematic derivation of the Fokker-Planck equation for the joint probability density of the position and unit direction vector of rays propagating in a gyrotropic stratified

  2. Hypersonic expansion of the Fokker--Planck equation

    International Nuclear Information System (INIS)

    Fernandez-Feria, R.

    1989-01-01

    A systematic study of the hypersonic limit of a heavy species diluted in a much lighter gas is made via the Fokker--Planck equation governing its velocity distribution function. In particular, two different hypersonic expansions of the Fokker--Planck equation are considered, differing from each other in the momentum equation of the heavy gas used as the basis of the expansion: in the first of them, the pressure tensor is neglected in that equation while, in the second expansion, the pressure tensor term is retained. The expansions are valid when the light gas Mach number is O(1) or larger and the difference between the mean velocities of light and heavy components is small compared to the light gas thermal speed. They can be applied away from regions where the spatial gradient of the distribution function is very large, but it is not restricted with respect to the temporal derivative of the distribution function. The hydrodynamic equations corresponding to the lowest order of both expansions constitute two different hypersonic closures of the moment equations. For the subsequent orders in the expansions, closed sets of moment equations (hydrodynamic equations) are given. Special emphasis is made on the order of magnitude of the errors of the lowest-order hydrodynamic quantities. It is shown that if the heat flux vanishes initially, these errors are smaller than one might have expected from the ordinary scaling of the hypersonic closure. Also it is found that the normal solution of both expansions is a Gaussian distribution at the lowest order

  3. A purely Lagrangian method for the numerical integration of Fokker-Planck equations

    International Nuclear Information System (INIS)

    Combis, P.; Fronteau, J.

    1986-01-01

    A new numerical approach to Fokker-Planck equations is presented, in which the integration grid moves according to the solution of a differential system. The method is purely Lagrangian, the mean effect of the diffusion being inserted into the differential system itself

  4. High energy ion range and deposited energy calculation using the Boltzmann-Fokker-Planck splitting of the Boltzmann transport equation

    International Nuclear Information System (INIS)

    Mozolevski, I.E.

    2001-01-01

    We consider the splitting of the straight-ahead Boltzmann transport equation in the Boltzmann-Fokker-Planck equation, decomposing the differential cross-section into a singular part, corresponding to small energy transfer events, and in a regular one, which corresponds to large energy transfer. The convergence of implantation profile, nuclear and electronic energy depositions, calculated from the Boltzmann-Fokker-Planck equation, to the respective exact distributions, calculated from Monte-Carlo method, was exanimate in a large-energy interval for various values of splitting parameter and for different ion-target mass relations. It is shown that for the universal potential there exists an optimal value of splitting parameter, for which range and deposited energy distributions, calculated from the Boltzmann-Fokker-Planck equation, accurately approximate the exact distributions and which minimizes the computational expenses

  5. A fractional Fokker-Planck model for anomalous diffusion

    Energy Technology Data Exchange (ETDEWEB)

    Anderson, Johan, E-mail: anderson.johan@gmail.com [Department of Earth and Space Sciences, Chalmers University of Technology, SE-412 96 Göteborg (Sweden); Kim, Eun-jin [Department of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Moradi, Sara [Ecole Polytechnique, CNRS UMR7648, LPP, F-91128 Palaiseau (France)

    2014-12-15

    In this paper, we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.

  6. Collective motions and non-polynomial lagrangians in Fokker-Planck dynamics

    International Nuclear Information System (INIS)

    Spina, A.; Vucetich, H.

    1986-04-01

    A method based on the ideas of collective motion is applied to Fokker-Planck dynamics. The usual diagramatic techniques used in stochastic dynamics are enlarged in order to deal with the non-polynomial Lagrangians that appear in the theory. The technique is tested and applied to the case of a self-sustained sinusoidal oscillator whose statistical behaviour is well understood: the Poincare oscillator. (author)

  7. Cusping, transport and variance of solutions to generalized Fokker-Planck equations

    Science.gov (United States)

    Carnaffan, Sean; Kawai, Reiichiro

    2017-06-01

    We study properties of solutions to generalized Fokker-Planck equations through the lens of the probability density functions of anomalous diffusion processes. In particular, we examine solutions in terms of their cusping, travelling wave behaviours, and variance, within the framework of stochastic representations of generalized Fokker-Planck equations. We give our analysis in the cases of anomalous diffusion driven by the inverses of the stable, tempered stable and gamma subordinators, demonstrating the impact of changing the distribution of waiting times in the underlying anomalous diffusion model. We also analyse the cases where the underlying anomalous diffusion contains a Lévy jump component in the parent process, and when a diffusion process is time changed by an uninverted Lévy subordinator. On the whole, we present a combination of four criteria which serve as a theoretical basis for model selection, statistical inference and predictions for physical experiments on anomalously diffusing systems. We discuss possible applications in physical experiments, including, with reference to specific examples, the potential for model misclassification and how combinations of our four criteria may be used to overcome this issue.

  8. Solving Fokker-Planck Equations on Cantor Sets Using Local Fractional Decomposition Method

    Directory of Open Access Journals (Sweden)

    Shao-Hong Yan

    2014-01-01

    Full Text Available The local fractional decomposition method is applied to approximate the solutions for Fokker-Planck equations on Cantor sets with local fractional derivative. The obtained results give the present method that is very effective and simple for solving the differential equations on Cantor set.

  9. Efficient statistically accurate algorithms for the Fokker-Planck equation in large dimensions

    Science.gov (United States)

    Chen, Nan; Majda, Andrew J.

    2018-02-01

    Solving the Fokker-Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional methods suffer from the curse of dimensionality and have difficulties in capturing the fat tailed highly intermittent probability density functions (PDFs) of complex systems in turbulence, neuroscience and excitable media. In this article, efficient statistically accurate algorithms are developed for solving both the transient and the equilibrium solutions of Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures. The algorithms involve a hybrid strategy that requires only a small number of ensembles. Here, a conditional Gaussian mixture in a high-dimensional subspace via an extremely efficient parametric method is combined with a judicious non-parametric Gaussian kernel density estimation in the remaining low-dimensional subspace. Particularly, the parametric method provides closed analytical formulae for determining the conditional Gaussian distributions in the high-dimensional subspace and is therefore computationally efficient and accurate. The full non-Gaussian PDF of the system is then given by a Gaussian mixture. Different from traditional particle methods, each conditional Gaussian distribution here covers a significant portion of the high-dimensional PDF. Therefore a small number of ensembles is sufficient to recover the full PDF, which overcomes the curse of dimensionality. Notably, the mixture distribution has significant skill in capturing the transient behavior with fat tails of the high-dimensional non-Gaussian PDFs, and this facilitates the algorithms in accurately describing the intermittency and extreme events in complex turbulent systems. It is shown in a stringent set of test problems that the method only requires an order of O (100) ensembles to successfully recover the highly non-Gaussian transient PDFs in up to 6

  10. Solution of the Fokker-Planck equation for axially-channeled relativistic electrons

    International Nuclear Information System (INIS)

    Muralev, V.A.; Telegin, V.I.

    1981-01-01

    A method of the two dimensional kinetic equation of the Fokker-Planck type for axially-channeled electrons is proposed. This equation has been obtained recently by Beloshitsky and Kumakhov to describe the diffusion of channeling negative particles over the transverse energy and angular momentum. The results of computation of the dechanneling function of 1 GeV electrons in tungsten are presented. (author)

  11. LLE-LLNL progress report on studies in nonlocal heat transport in spherical plasmas using the Fokker-Planck code SPARK

    International Nuclear Information System (INIS)

    Epperlein, E.M.

    1992-01-01

    Preliminary 1-D studies of nonlocal heat transport in spherical plasmas based on the Fokker-Planck code SPARK indicate significant levels of electron preheat and radial heat flux across a spherical heat sink surface kept at fixed temperature. However, the diffusive approximation to the Fokker-Planck equation is shown to be particularly sensitive to the nature of the inner surface boundary condition chosen. A suggested remedy is the inclusion of a target capsule in future simulations studies with SPARK

  12. Single particle dynamics of many-body systems described by Vlasov-Fokker-Planck equations

    International Nuclear Information System (INIS)

    Frank, T.D.

    2003-01-01

    Using Langevin equations we describe the random walk of single particles that belong to particle systems satisfying Vlasov-Fokker-Planck equations. In doing so, we show that Haissinski distributions of bunched particles in electron storage rings can be derived from a particle dynamics model

  13. On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

    KAUST Repository

    Annunziato, Mario; Borzì , Alfio; Nobile, Fabio; Tempone, Raul

    2014-01-01

    appropriate assumptions it is shown that the two strategies are equivalent in the case of expected cost functionals, while the FokkerPlanck formalism allows considering a larger class of objectives. To illustrate the connection between the two control

  14. A Simple Map Between Fokker-Planck Equation and its Fractional form

    International Nuclear Information System (INIS)

    Zahran, M.A.; El-Shewy, E.K.

    2008-01-01

    A simple map between Fokker-Planck Equation (FPE) and its fractional form (FFPE), which recently formulates to describe sub diffusive processes, has been suggested. This connection based on a relation between k-orders for moments of ordinary time domain of FPE and the moments associated with fractional time domain of FFPE . Two classes of special interest of FFPE has been considered to outline this map

  15. Modelling of thermal transport using Fokker-Planck equations in laser produced plasma

    International Nuclear Information System (INIS)

    Nakarmi, J.J.; Jha, L.N.

    1996-12-01

    The kinetic equation with Fokker-Planck collision term has been presented to obtain the distribution function in the corona of inertial confinement fusion, in the presence of the self generated magnetic field. The resulting distribution has non-local form with the convolution in Maxwellian. An expression for thermal flux with self generated magnetic field is obtained. (author). 22 refs

  16. Invalidity of the spectral Fokker-Planck equation forCauchy noise driven Langevin equation

    DEFF Research Database (Denmark)

    Ditlevsen, Ove Dalager

    2004-01-01

    -called alpha-stable noise (or Levy noise) the Fokker-Planck equation no longer exists as a partial differential equation for the probability density because the property of finite variance is lost. In stead it has been attempted to formulate an equation for the characteristic function (the Fourier transform...

  17. Fokker-Planck description for the queue dynamics of large tick stocks

    Science.gov (United States)

    Garèche, A.; Disdier, G.; Kockelkoren, J.; Bouchaud, J.-P.

    2013-09-01

    Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation. Our description explicitly includes state dependence, i.e., the fact that the drift and diffusion depend on the volume present on both sides of the spread. “Jump” events, corresponding to sudden changes of the best limit price, must also be included as birth-death terms in the Fokker-Planck equation. All quantities involved in the equation can be calibrated using high-frequency data on the best quotes. One of our central findings is that the dynamical process is approximately scale invariant, i.e., the only relevant variable is the ratio of the current volume in the queue to its average value. While the latter shows intraday seasonalities and strong variability across stocks and time periods, the dynamics of the rescaled volumes is universal. In terms of rescaled volumes, we found that the drift has a complex two-dimensional structure, which is a sum of a gradient contribution and a rotational contribution, both stable across stocks and time. This drift term is entirely responsible for the dynamical correlations between the ask queue and the bid queue.

  18. Fokker-Planck simulation study of Alfven eigenmode burst

    International Nuclear Information System (INIS)

    Todo, Y.; Watanabe, T.; Park, Hyoung-Bin; Sato, T.

    2001-01-01

    Recurrent bursts of toroidicity-induced Alfven eigenmodes (TAEs) are reproduced with a Fokker-Planck-magnetohydrodynamic simulation where a fast-ion source and slowing down are incorporated self-consistently. The bursts take place at regular time intervals and the behaviors of all the TAEs are synchronized. The fast-ion transport due to TAE activity spatially broadens the classical fast-ion distribution and significantly reduces its peak value. Only a small change of the distribution takes place with each burst, leading to loss of a small fraction of the fast ions. The system stays close to the marginal stability state established through the interplay of the fast-ion source, slowing down, and TAE activity. (author)

  19. Time dependent solutions of the Fokker-Planck equation for fast fusion ions

    International Nuclear Information System (INIS)

    Gnavi, G.; Gratton, F.T.; Heyn, M.

    1990-01-01

    Approximate time dependent solutions for the Fokker-Planck equation for fast fusion ions from an isotropic, monoenergetic source are presented, for the problem of D - T - He 3 reactions. The equations include the effect of diffusion, which is particularly noticeable in the distribution of particles of lower energy and in the formation of a tail of particles with energy higher than that of the source. (Author)

  20. Generalized Fokker-Planck theory for electron and photon transport in biological tissues: application to radiotherapy.

    Science.gov (United States)

    Olbrant, Edgar; Frank, Martin

    2010-12-01

    In this paper, we study a deterministic method for particle transport in biological tissues. The method is specifically developed for dose calculations in cancer therapy and for radiological imaging. Generalized Fokker-Planck (GFP) theory [Leakeas and Larsen, Nucl. Sci. Eng. 137 (2001), pp. 236-250] has been developed to improve the Fokker-Planck (FP) equation in cases where scattering is forward-peaked and where there is a sufficient amount of large-angle scattering. We compare grid-based numerical solutions to FP and GFP in realistic medical applications. First, electron dose calculations in heterogeneous parts of the human body are performed. Therefore, accurate electron scattering cross sections are included and their incorporation into our model is extensively described. Second, we solve GFP approximations of the radiative transport equation to investigate reflectance and transmittance of light in biological tissues. All results are compared with either Monte Carlo or discrete-ordinates transport solutions.

  1. Quasilinear simulation of auroral kilometric radiation by a relativistic Fokker-Planck code

    International Nuclear Information System (INIS)

    Matsuda, Y.

    1991-01-01

    An intense terrestrial radiation called the auroral kilometric radiation (AKR) is believed to be generated by cyclotron maser instability. We study a quasilinear evolution of this instability by means of a two-dimensional relativistic Fokker-Planck code which treats waves and distributions self-consistently, including radiation loss and electron source and sink. We compare the distributions and wave amplitude with spacecraft observations to elucidate physical processes involved. 3 refs., 1 fig

  2. Generalized study of the return to equilibrium of a particle in a plasma (Fokker-Planck formalism) (1961); Etude generale du retour a l'equilibre d'une particule au sein d'un plasma (formalisme de Fokker-Planck) (1961)

    Energy Technology Data Exchange (ETDEWEB)

    Salmon, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires; Faculte des Sciences de Caen, 14 (France)

    1961-07-01

    The author examines the problem of the return to equilibrium of a particle in a plasma and completely explains Fokker-Planck equation. After that, he studies the possibility of interpreting the return of the test particle to Maxwellian distribution, using the development - which is obtained. He discusses the validity limits of the Rosenbluth, MacDonald and Judd approximation. (author) [French] Examinant le probleme du retour a l'equilibre d'une particule test au sein d'un plasma en equilibre, l'auteur cherche a expliciter completement l'expression de l'operateur de Fokker-Planck. Il etudie ensuite les conditions de coherence, c'est-a-dire la possibilite pour le developpement obtenu de traduire le retour de la particule test a l'etat maxwellien et discute des limites de validite de la formule de 'Rosenbluth, Mac Donald et Judd'. (auteur)

  3. Applicability of the Fokker-Planck equation to the description of diffusion effects on nucleation

    Science.gov (United States)

    Sorokin, M. V.; Dubinko, V. I.; Borodin, V. A.

    2017-01-01

    The nucleation of islands in a supersaturated solution of surface adatoms is considered taking into account the possibility of diffusion profile formation in the island vicinity. It is shown that the treatment of diffusion-controlled cluster growth in terms of the Fokker-Planck equation is justified only provided certain restrictions are satisfied. First of all, the standard requirement that diffusion profiles of adatoms quickly adjust themselves to the actual island sizes (adiabatic principle) can be realized only for sufficiently high island concentration. The adiabatic principle is essential for the probabilities of adatom attachment to and detachment from island edges to be independent of the adatom diffusion profile establishment kinetics, justifying the island nucleation treatment as the Markovian stochastic process. Second, it is shown that the commonly used definition of the "diffusion" coefficient in the Fokker-Planck equation in terms of adatom attachment and detachment rates is justified only provided the attachment and detachment are statistically independent, which is generally not the case for the diffusion-limited growth of islands. We suggest a particular way to define the attachment and detachment rates that allows us to satisfy this requirement as well. When applied to the problem of surface island nucleation, our treatment predicts the steady-state nucleation barrier, which coincides with the conventional thermodynamic expression, even though no thermodynamic equilibrium is assumed and the adatom diffusion is treated explicitly. The effect of adatom diffusional profiles on the nucleation rate preexponential factor is also discussed. Monte Carlo simulation is employed to analyze the applicability domain of the Fokker-Planck equation and the diffusion effect beyond it. It is demonstrated that a diffusional cloud is slowing down the nucleation process for a given monomer interaction with the nucleus edge.

  4. Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

    International Nuclear Information System (INIS)

    Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

    2009-01-01

    The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

  5. Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

    Energy Technology Data Exchange (ETDEWEB)

    Densmore, Jeffery D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Lowrie, Robert B [Los Alamos National Laboratory; Morel, Jim E [TEXAS A& M UNIV

    2008-01-01

    The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

  6. Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

    Science.gov (United States)

    Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

    2009-09-01

    The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

  7. An application of the ideas of collective motion to Fokker-Planck dynamics

    International Nuclear Information System (INIS)

    Spina, A.

    1985-08-01

    The implementation of ideas and techniques of field theory to statistical physics have proved invaluable both in deepening our understanding in this second area and as a powerful computational tool. In this paper we analyze some aspects of the application to Fokker-Planck dynamics for the case of self-sustained oscillators driven by white noise of a concept that has been found fruitful in quantum field theory, namely the collective coordinate method. (author)

  8. Fokker-Planck-Rosenbluth-type equations for self-gravitating systems in the 1PN approximation

    International Nuclear Information System (INIS)

    Ramos-Caro, Javier; Gonzalez, Guillermo A

    2008-01-01

    We present two formulations of Fokker-Planck-Rosenbluth-type (FPR) equations for many-particle self-gravitating systems, with first-order relativistic corrections in the post-Newtonian approach (1PN). The first starts from a covariant Fokker-Planck equation for a simple gas, introduced recently by Chacon-Acosta and Kremer (2007 Phys. Rev. E 76 021201). The second derivation is based on the establishment of an 1PN-BBGKY hierarchy, developed systematically from the 1PN microscopic law of force and using the Klimontovich-Dupree (KD) method. We close the hierarchy by the introduction of a two-point correlation function that describes adequately the relaxation process. This picture reveals an aspect that is not considered in the first formulation: the contribution of ternary correlation patterns to the diffusion coefficients, as a consequence of the nature of 1PN interaction. Both formulations can be considered as a generalization of the equation derived by Rezania and Sobouti (2000 Astron. Astrophys. 354 1110), to stellar systems where the relativistic effects of gravitation play a significant role

  9. Remarks on the chemical Fokker-Planck and Langevin equations: Nonphysical currents at equilibrium.

    Science.gov (United States)

    Ceccato, Alessandro; Frezzato, Diego

    2018-02-14

    The chemical Langevin equation and the associated chemical Fokker-Planck equation are well-known continuous approximations of the discrete stochastic evolution of reaction networks. In this work, we show that these approximations suffer from a physical inconsistency, namely, the presence of nonphysical probability currents at the thermal equilibrium even for closed and fully detailed-balanced kinetic schemes. An illustration is given for a model case.

  10. Green function of the double-fractional Fokker-Planck equation: Path integral and stochastic differential equations

    Science.gov (United States)

    Kleinert, H.; Zatloukal, V.

    2013-11-01

    The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.

  11. Analytic solution of the two-dimensional Fokker-Planck equation governing stochastic ion heating by a lower hybrid wave

    International Nuclear Information System (INIS)

    Malescio, G.

    1981-04-01

    The two-dimensional Fokker-Planck equation describing the ion motion in a coherent lower hybrid wave above the stochasticity threshold is analytically solved. An expression is given for the steady state power dissipation

  12. Solution of the Boltzmann-Fokker-Planck transport equation using exponential nodal schemes; Solucion de la ecuacion de transporte de Boltzmann-Fokker-Planck usando esquemas nodales exponenciales

    Energy Technology Data Exchange (ETDEWEB)

    Ortega J, R.; Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: roj@correo.azc.uam.mx

    2003-07-01

    There are carried out charge and energy calculations deposited due to the interaction of electrons with a plate of a certain material, solving numerically the electron transport equation for the Boltzmann-Fokker-Planck approach of first order in plate geometry with a computer program denominated TEOD-NodExp (Transport of Electrons in Discreet Ordinates, Nodal Exponentials), using the proposed method by the Dr. J. E. Morel to carry out the discretization of the variable energy and several spatial discretization schemes, denominated exponentials nodal. It is used the Fokker-Planck equation since it represents an approach of the Boltzmann transport equation that is been worth whenever it is predominant the dispersion of small angles, that is to say, resulting dispersion in small dispersion angles and small losses of energy in the transport of charged particles. Such electrons could be those that they face with a braking plate in a device of thermonuclear fusion. In the present work its are considered electrons of 1 MeV that impact isotropically on an aluminum plate. They were considered three different thickness of plate that its were designated as problems 1, 2 and 3. In the calculations it was used the discrete ordinate method S{sub 4} with expansions of the dispersion cross sections until P{sub 3} order. They were considered 25 energy groups of uniform size between the minimum energy of 0.1 MeV and the maximum of 1.0 MeV; the one spatial intervals number it was considered variable and it was assigned the values of 10, 20 and 30. (Author)

  13. New Approaches for Solving Fokker Planck Equation on Cantor Sets within Local Fractional Operators

    Directory of Open Access Journals (Sweden)

    Hassan Kamil Jassim

    2015-01-01

    Full Text Available We discuss new approaches to handling Fokker Planck equation on Cantor sets within local fractional operators by using the local fractional Laplace decomposition and Laplace variational iteration methods based on the local fractional calculus. The new approaches maintain the efficiency and accuracy of the analytical methods for solving local fractional differential equations. Illustrative examples are given to show the accuracy and reliable results.

  14. A Fokker-Planck based kinetic model for diatomic rarefied gas flows

    Science.gov (United States)

    Gorji, M. Hossein; Jenny, Patrick

    2013-06-01

    A Fokker-Planck based kinetic model is presented here, which also accounts for internal energy modes characteristic for diatomic gas molecules. The model is based on a Fokker-Planck approximation of the Boltzmann equation for monatomic molecules, whereas phenomenological principles were employed for the derivation. It is shown that the model honors the equipartition theorem in equilibrium and fulfills the Landau-Teller relaxation equations for internal degrees of freedom. The objective behind this approximate kinetic model is accuracy at reasonably low computational cost. This can be achieved due to the fact that the resulting stochastic differential equations are continuous in time; therefore, no collisions between the simulated particles have to be calculated. Besides, because of the devised energy conserving time integration scheme, it is not required to resolve the collisional scales, i.e., the mean collision time and the mean free path of molecules. This, of course, gives rise to much more efficient simulations with respect to other particle methods, especially the conventional direct simulation Monte Carlo (DSMC), for small and moderate Knudsen numbers. To examine the new approach, first the computational cost of the model was compared with respect to DSMC, where significant speed up could be obtained for small Knudsen numbers. Second, the structure of a high Mach shock (in nitrogen) was studied, and the good performance of the model for such out of equilibrium conditions could be demonstrated. At last, a hypersonic flow of nitrogen over a wedge was studied, where good agreement with respect to DSMC (with level to level transition model) for vibrational and translational temperatures is shown.

  15. On self-consistent ray-tracing and Fokker-Planck modeling of the hard X-ray emission during lower-hybrid current driven in Tokamaks

    International Nuclear Information System (INIS)

    Bizarro, J.P.; Peysson, Y.; Bonoli, P.T.; Carrasco, J.; Dudok de Wit, T.; Fuchs, V.; Hoang, G.T.; Litaudon, X.; Moreau, D.; Pocheau, C.; Shkarofsky, I.P.

    1993-04-01

    A detailed investigation is presented on the ability of combined ray-tracing and Fokker-Planck calculations to predict the hard x-ray (HXR) emission during lower-hybrid (LH) current drive in tokamaks when toroidally induced-ray-stochasticity is important. A large number of rays is used and the electron distribution function is obtained by self-consistently iterating the appropriate LH power deposition and Fokker-Planck calculations. Most of the experimentally observed features of the HXR emission are correctly predicted. It is found that corrections due to radial diffusion of suprathermal electrons and to radiation scattering by the inner wall can be significant

  16. Computing generalized Langevin equations and generalized Fokker-Planck equations.

    Science.gov (United States)

    Darve, Eric; Solomon, Jose; Kia, Amirali

    2009-07-07

    The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

  17. Numerical Resolution of N-dimensional Fokker-Planck stochastic equations; Resolucion Numerica de Ecuaciones Estocasticas de tipo Fokker-Planck en Varias Dimensiones

    Energy Technology Data Exchange (ETDEWEB)

    Garcia-Olivares, R A; Munoz Roldan, A

    1992-07-01

    This document describes the use of a library of programs able to solve stochastic Fokker-Planck equations in a N-dimensional space. The input data are essentially: (i) the initial distribution of the stochastic variable, (ii) the drift and fluctuation coefficients as a function of the state (which can be obtained from the transition probabilities between neighboring states) and (iii) some parameters controlling the run. A last version of the library accepts sources and sinks defined in the states space. The output is the temporal evolution of the probability distribution in the space defined by a N-dimensional grid. Some applications and readings in Synergetic, Self-Organization, transport phenomena, Ecology and other fields are suggested. If the probability distribution is interpreted as a distribution of particles then the codes can be used to solve the N-dimensional problem of advection-diffusion. (Author) 16 refs.

  18. Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

    Science.gov (United States)

    Frank, T. D.

    2008-02-01

    We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

  19. Solution of the Boltzmann-Fokker-Planck transport equation using exponential nodal schemes

    International Nuclear Information System (INIS)

    Ortega J, R.; Valle G, E. del

    2003-01-01

    There are carried out charge and energy calculations deposited due to the interaction of electrons with a plate of a certain material, solving numerically the electron transport equation for the Boltzmann-Fokker-Planck approach of first order in plate geometry with a computer program denominated TEOD-NodExp (Transport of Electrons in Discreet Ordinates, Nodal Exponentials), using the proposed method by the Dr. J. E. Morel to carry out the discretization of the variable energy and several spatial discretization schemes, denominated exponentials nodal. It is used the Fokker-Planck equation since it represents an approach of the Boltzmann transport equation that is been worth whenever it is predominant the dispersion of small angles, that is to say, resulting dispersion in small dispersion angles and small losses of energy in the transport of charged particles. Such electrons could be those that they face with a braking plate in a device of thermonuclear fusion. In the present work its are considered electrons of 1 MeV that impact isotropically on an aluminum plate. They were considered three different thickness of plate that its were designated as problems 1, 2 and 3. In the calculations it was used the discrete ordinate method S 4 with expansions of the dispersion cross sections until P 3 order. They were considered 25 energy groups of uniform size between the minimum energy of 0.1 MeV and the maximum of 1.0 MeV; the one spatial intervals number it was considered variable and it was assigned the values of 10, 20 and 30. (Author)

  20. Some exact solutions for a unidimensional fokker-planck equation by using lie symmetries

    Directory of Open Access Journals (Sweden)

    Hugo Hernán Ortíz-Álvarez

    2015-01-01

    Full Text Available The Fokker Planck equation appears in the study of diffusion phenomena, stochastics processes and quantum and classical mechanics. A particular case fromthis equation, ut − uxx − xux − u=0, is examined by the Lie group method approach. From the invariant condition it was possible to obtain the infinitesimal generators or vectors associated to this equation, identifying the corresponding symmetry groups. Exact solution were found for each one of this generators and new solution were constructed by using symmetry properties.

  1. Multi-dimensional Fokker-Planck equation analysis using the modified finite element method

    Czech Academy of Sciences Publication Activity Database

    Náprstek, Jiří; Král, Radomil

    2016-01-01

    Roč. 744, č. 1 (2016), č. článku 012177. ISSN 1742-6588. [International Conference on Motion and Vibration Control (MOVIC 2016) /13./ and International Conference on Recent Advances in Structural Dynamics (RASD 2016) /12./. Southampton, 04.07.2016-06.07.2016] R&D Projects: GA ČR(CZ) GP14-34467P; GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : Fokker-Planck equation * finite element method * single degree of freedom systems (SDOF) Subject RIV: JM - Building Engineering http://iopscience.iop.org/article/10.1088/1742-6596/744/1/012177

  2. Fokker--Planck/transport analyses of fusion plasmas in contemporary beam-driven tokamaks

    International Nuclear Information System (INIS)

    Mirin, A.A.; McCoy, M.G.; Killeen, J.; Rensink, M.E.; Shumaker, D.E.; Jassby, D.L.; Post, D.E.

    1978-04-01

    The properties of deuterium plasmas in experimental tokamaks heated and fueled by intense neutral-beam injection are evaluated with a Fokker-Planck/radial transport code coupled with a Monte Carlo neutrals treatment. Illustrative results are presented for the Poloidal Divertor Experiment at PPPL as a function of beam power and plasma recycling coefficient, R/sub c/. When P/sub beam/ = 8 MW at E/sub b/ = 60 keV, and R/sub c/ = 0.2, then approximately 0.5, [ 2 / 3 ] = 22 keV approximately 6 , and the D-D neutron intensity is 10 16 n/sec

  3. A New Fokker-Planck Approach for the Relaxation-driven Evolution of Galactic Nuclei

    Science.gov (United States)

    Vasiliev, Eugene

    2017-10-01

    We present an approach for simulating the collisional evolution of spherical isotropic stellar systems based on the one-dimensional Fokker-Planck equation. A novel aspect is that we use the phase volume as the argument of the distribution function instead of the traditionally used energy, which facilitates the solution. The publicly available code PhaseFlow implements a high-accuracy finite-element method for the Fokker-Planck equation, and can handle multiple-component systems, optionally with the central black hole and taking into account loss-cone effects and star formation. We discuss the energy balance in the general setting, and in application to the Bahcall-Wolf cusp around a central black hole, for which we derive a perturbative solution. We stress that the cusp is not a steady-state structure, but rather evolves in amplitude while retaining an approximately ρ \\propto {r}-7/4 density profile. Finally, we apply the method to the nuclear star cluster of the milky Way, and illustrate a possible evolutionary scenario in which a two-component system of lighter main-sequence stars and stellar-mass black holes develops a Bahcall-Wolf cusp in the heavier component and a weaker ρ \\propto {r}-3/2 cusp in the lighter, visible component, over the period of several Gyr. The present-day density profile is consistent with the recently detected mild cusp inside the central parsec, and is weakly sensitive to initial conditions.

  4. FOKN: a relativistic Fokker-Planck code with large angle scattering and radiation losses

    International Nuclear Information System (INIS)

    Zimmerman, G.; Scharlemann, T.; Wood, L.; Weaver, T.; Chu, T.; Lee, G.

    1976-07-01

    FOKN is a computer code which employs a relativistic Fokker-Planck algorithm to evolve the distribution functions of the various mutually interacting components of a multi-species plasma forward in time, with the optional addition of high angle, large energy and momentum transfer interactions between the various charged species of the plasma. As a computational expediency, the latter processes are handled by transfer matrices which are generated separately by another code, RNUX, so that once specific transfer matrices are generated, they can be used over and over by FOKN provided the group structures are compatible

  5. New Fokker-Planck derivation of heavy gas models for neutron thermalization

    International Nuclear Information System (INIS)

    Larsen, E.W.; Williams, M.M.R.

    1990-01-01

    This paper is concerned with the derivation of new generalized heavy gas models for the infinite medium neutron energy spectrum equation. Our approach is general and can be used to derive improved Fokker-Planck approximations for other types of kinetic equations. In this paper we obtain two distinct heavy gas models, together with estimates for the corresponding errors. The models are shown in a special case to reduce to modified heavy gas models proposed earlier by Corngold (1962). The error estimates show that both of the new models should be more accurate than Corngold's modified heavy gas model, and that the first of the two new models should generally be more accurate than the second. (author)

  6. Numerical Resolution of N-dimensional Fokker-Planck stochastic equations

    International Nuclear Information System (INIS)

    Garcia-Olivares, R. A.; Munoz Roldan, A.

    1992-01-01

    This document describes the use of a library of programs able to solve stochastic Fokker-Planck equations in a N-dimensional space. The input data are essentially: (i) the initial distribution of the stochastic variable, (ii) the drift and fluctuation coefficients as a function of the state (which can be obtained from the transition probabilities between neighboring states) and (iii) some parameters controlling the run. A last version of the library accepts sources and sinks defined in the states space. The output is the temporal evolution of the probability distribution in the space defined by a N-dimensional grid. Some applications and readings in Synergetic, Self-Organization, transport phenomena, Ecology and other fields are suggested. If the probability distribution is interpreted as a distribution of particles then the codes can be used to solve the N-dimensional problem of advection-diffusion. (Author) 16 refs

  7. Efficient positive, conservative, Maxwellian preserving and implicit difference schemes for the 1-D isotropic Fokker-Planck-Landau equation; Schemas positifs, implicites, conservant l'energie et les etats d'equilibre pour l'equation de Fokker-Planck-Landau isotrope

    Energy Technology Data Exchange (ETDEWEB)

    Buet, Ch. [CEA Bruyeres-le-Chatel, Dept. Sciences de la Simulation et de l' Information, Service Numerique Environnement et Constantes, 91 (France); Le Thanh, K.C. [CEA Bruyeres-le-Chatel, Service Physique des Plasmas et Electromagnetisme, 91 (France). Dept. de Physique Theorique et Appliquee

    2008-07-01

    The aim of this paper is to describe the discretization of the Fokker-Planck-Landau (FPL) collision term in the isotropic case, which models the self-collision for the electrons when they are totally isotropized by heavy particles background such as ions. The discussion focuses on schemes, which could preserve positivity, mass, energy and Maxwellian equilibrium. The Chang and Cooper method is widely used by plasma's physicists for the FPL equation (and for Fokker-Planck type equations). We present a new variant that is both positive and conservative contrary to the existing one's. We propose also a non Chang and Cooper 'type scheme on non-uniform grid, which is also both positive, conservative and equilibrium state preserving contrary to existing one's. The case of Coulombian potential is emphasized. We address also the problem of the time discretization. In particular we show how to recast some implicit methods to get band diagonal system and to solve it by direct method with a linear cost. (authors)

  8. Fokker-Planck Modelling of Delayed Loss of Charged Fusion Products in TFTR

    International Nuclear Information System (INIS)

    Edenstrasser, J.W.; Goloborod'ko, V.Ya.; Reznik, S.N.; Yavorskij, V.A.; Zweben, S.

    1998-01-01

    The results of a Fokker-Planck simulation of the ripple-induced loss of charged fusion products in the Tokamak Fusion Test Reactor (TFTR) are presented. It is shown that the main features of the measured ''delayed loss'' of partially thermalized fusion products, such as the differences between deuterium-deuterium and deuterium-tritium discharges, the plasma current and major radius dependencies, etc., are in satisfactory agreement with the classical collisional ripple transport mechanism. The inclusion of the inward shift of the vacuum flux surfaces turns out to be necessary for an adequate and consistent explanation of the origin of the partially thermalized fusion product loss to the bottom of TFTR

  9. Large-Time Behavior of Solutions to Vlasov-Poisson-Fokker-Planck Equations: From Evanescent Collisions to Diffusive Limit

    Science.gov (United States)

    Herda, Maxime; Rodrigues, L. Miguel

    2018-03-01

    The present contribution investigates the dynamics generated by the two-dimensional Vlasov-Poisson-Fokker-Planck equation for charged particles in a steady inhomogeneous background of opposite charges. We provide global in time estimates that are uniform with respect to initial data taken in a bounded set of a weighted L^2 space, and where dependencies on the mean-free path τ and the Debye length δ are made explicit. In our analysis the mean free path covers the full range of possible values: from the regime of evanescent collisions τ → ∞ to the strongly collisional regime τ → 0. As a counterpart, the largeness of the Debye length, that enforces a weakly nonlinear regime, is used to close our nonlinear estimates. Accordingly we pay a special attention to relax as much as possible the τ -dependent constraint on δ ensuring exponential decay with explicit τ -dependent rates towards the stationary solution. In the strongly collisional limit τ → 0, we also examine all possible asymptotic regimes selected by a choice of observation time scale. Here also, our emphasis is on strong convergence, uniformity with respect to time and to initial data in bounded sets of a L^2 space. Our proofs rely on a detailed study of the nonlinear elliptic equation defining stationary solutions and a careful tracking and optimization of parameter dependencies of hypocoercive/hypoelliptic estimates.

  10. Development of parallel Fokker-Planck code ALLAp

    International Nuclear Information System (INIS)

    Batishcheva, A.A.; Sigmar, D.J.; Koniges, A.E.

    1996-01-01

    We report on our ongoing development of the 3D Fokker-Planck code ALLA for a highly collisional scrape-off-layer (SOL) plasma. A SOL with strong gradients of density and temperature in the spatial dimension is modeled. Our method is based on a 3-D adaptive grid (in space, magnitude of the velocity, and cosine of the pitch angle) and a second order conservative scheme. Note that the grid size is typically 100 x 257 x 65 nodes. It was shown in our previous work that only these capabilities make it possible to benchmark a 3D code against a spatially-dependent self-similar solution of a kinetic equation with the Landau collision term. In the present work we show results of a more precise benchmarking against the exact solutions of the kinetic equation using a new parallel code ALLAp with an improved method of parallelization and a modified boundary condition at the plasma edge. We also report first results from the code parallelization using Message Passing Interface for a Massively Parallel CRI T3D platform. We evaluate the ALLAp code performance versus the number of T3D processors used and compare its efficiency against a Work/Data Sharing parallelization scheme and a workstation version

  11. Theoretical background and implementation of the finite element method for multi-dimensional Fokker-Planck equation analysis

    Czech Academy of Sciences Publication Activity Database

    Král, Radomil; Náprstek, Jiří

    2017-01-01

    Roč. 113, November (2017), s. 54-75 ISSN 0965-9978 R&D Projects: GA ČR(CZ) GP14-34467P; GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : Fokker-Planck equation * finite element method * simplex element * multi-dimensional problem * non-symmetric operator Subject RIV: JM - Building Engineering OBOR OECD: Mechanical engineering Impact factor: 3.000, year: 2016 https://www.sciencedirect.com/science/ article /pii/S0965997817301904

  12. Steady state solution of the Fokker-Planck equation combined with unidirectional quasilinear diffusion under detailed balance conditions

    International Nuclear Information System (INIS)

    Hizanidis, K.

    1984-04-01

    The relativistic collisional Fokker-Planck equation combined with an externally imposed unidirectional quasilinear (rf) diffusion is solved for arbitrary values of rf diffusion coefficient under conditions of detailed balance of the staionary joint distribution involved. The detailed balance condition imposes a restriction on the functional form of the quasilinear diffusion coefficient which might be associated with the existence of a saturated spectrum of fluctuation in a quasilinearly rf-driven plasma

  13. Diffusion coefficients of Fokker-Planck equation for rotating dust grains in a fusion plasma

    Science.gov (United States)

    Bakhtiyari-Ramezani, M.; Mahmoodi, J.; Alinejad, N.

    2015-11-01

    In the fusion devices, ions, H atoms, and H2 molecules collide with dust grains and exert stochastic torques which lead to small variations in angular momentum of the grain. By considering adsorption of the colliding particles, thermal desorption of H atoms and normal H2 molecules, and desorption of the recombined H2 molecules from the surface of an oblate spheroidal grain, we obtain diffusion coefficients of the Fokker-Planck equation for the distribution function of fluctuating angular momentum. Torque coefficients corresponding to the recombination mechanism show that the nonspherical dust grains may rotate with a suprathermal angular velocity.

  14. A transformed path integral approach for solution of the Fokker-Planck equation

    Science.gov (United States)

    Subramaniam, Gnana M.; Vedula, Prakash

    2017-10-01

    A novel path integral (PI) based method for solution of the Fokker-Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.

  15. Vlasov-Fokker-Planck modeling of magnetized plasma

    Energy Technology Data Exchange (ETDEWEB)

    Thomas, Alexander [Univ. of Michigan, Ann Arbor, MI (United States)

    2016-08-01

    Understanding the magnetic fields that can develop in high-power-laser interactions with solid-density plasma is important because such fields significantly modify both the magnitude and direction of electron heat fluxes. The dynamics of such fields evidently have consequences for inertial fusion energy applications, as the coupling of the laser beams with the walls or pellet and the development of temperature inhomogeneities are critical to the uniformity of the implosion and potentially the success of, for example, the National Ignition Facility. To study these effects, we used the code Impacta, a two-dimensional, fully implicit, Vlasov-Fokker-Planck code with self-consistent magnetic fields and a hydrodynamic ion model, designed for nanosecond time-scale laser-plasma interactions. Heat-flux effects in Ohm’s law under non-local conditions was investigated; physics that is not well captured by standard numerical models but is nevertheless important in fusion-related scenarios. Under such conditions there are numerous interesting physical effects, such as collisional magnetic instabilities, amplification of magnetic fields, re-emergence of non-locality through magnetic convection, and reconnection of magnetic field lines and redistribution of thermal energy. In this project highlights included the first full-scale kinetic simulations of a magnetized hohlraum and the discovery of a new magnetic reconnection mechanism, as well as a completed PhD thesis and the production of a new code for Inertial Fusion research.

  16. Vlasov-Fokker-Planck modeling of magnetized plasma

    International Nuclear Information System (INIS)

    Thomas, Alexander

    2016-01-01

    Understanding the magnetic fields that can develop in high-power-laser interactions with solid-density plasma is important because such fields significantly modify both the magnitude and direction of electron heat fluxes. The dynamics of such fields evidently have consequences for inertial fusion energy applications, as the coupling of the laser beams with the walls or pellet and the development of temperature inhomogeneities are critical to the uniformity of the implosion and potentially the success of, for example, the National Ignition Facility. To study these effects, we used the code Impacta, a two-dimensional, fully implicit, Vlasov-Fokker-Planck code with self-consistent magnetic fields and a hydrodynamic ion model, designed for nanosecond time-scale laser-plasma interactions. Heat-flux effects in Ohm's law under non-local conditions was investigated; physics that is not well captured by standard numerical models but is nevertheless important in fusion-related scenarios. Under such conditions there are numerous interesting physical effects, such as collisional magnetic instabilities, amplification of magnetic fields, re-emergence of non-locality through magnetic convection, and reconnection of magnetic field lines and redistribution of thermal energy. In this project highlights included the first full-scale kinetic simulations of a magnetized hohlraum and the discovery of a new magnetic reconnection mechanism, as well as a completed PhD thesis and the production of a new code for Inertial Fusion research.

  17. Multi-diffusive nonlinear Fokker–Planck equation

    International Nuclear Information System (INIS)

    Ribeiro, Mauricio S; Casas, Gabriela A; Nobre, Fernando D

    2017-01-01

    Nonlinear Fokker–Planck equations, characterized by more than one diffusion term, have appeared recently in literature. Here, it is shown that these equations may be derived either from approximations in a master equation, or from a Langevin-type approach. An H-theorem is proven, relating these Fokker–Planck equations to an entropy composed by a sum of contributions, each of them associated with a given diffusion term. Moreover, the stationary state of the Fokker–Planck equation is shown to coincide with the equilibrium state, obtained by extremization of the entropy, in the sense that both procedures yield precisely the same equation. Due to the nonlinear character of this equation, the equilibrium probability may be obtained, in most cases, only by means of numerical approaches. Some examples are worked out, where the equilibrium probability distribution is computed for nonlinear Fokker–Planck equations presenting two diffusion terms, corresponding to an entropy characterized by a sum of two contributions. It is shown that the resulting equilibrium distribution, in general, presents a form that differs from a sum of the equilibrium distributions that maximizes each entropic contribution separately, although in some cases one may construct such a linear combination as a good approximation for the equilibrium distribution. (paper)

  18. An approximate factorization procedure for solving nine-point elliptic difference equations. Application for a fast 2-D relativistic Fokker-Planck solver

    Energy Technology Data Exchange (ETDEWEB)

    Peysson, Y. [Association Euratom-CEA, CEA Grenoble, 38 (France). Dept. de Recherches sur la Fusion Controlee; Choucri, M. [Centre Canadien de Fusion Magnetique, Varennes, PQ (Canada)

    1997-09-01

    A full implicit numerical procedure based on the use of a nine-point difference operator is presented to solve the two dimensional (2{sub D}) relativistic Fokker-Planck equation for the current drive problem and synergetic effects between the lower hybrid and the electron cyclotron waves in tokamaks. As compared to the standard approach based on the use of a five-point difference operator [M. Shoucri, I. Shkarofsky, Comput. Phys. Comm. 82 (1994) 287], the convergence rate towards the steady state solution may be significantly enhanced with no loss of accuracy on the distribution function. Moreover, it is shown that the numerical stability may be strongly improved without a large degradation of the CPU time consumption as in the five-point scheme, making this approach very attractive for a fast solution of the 2-D Fokker-Planck equation on a fine grid in conjunction with other numerical codes for realistic plasma simulations. This new algorithm, based on an approximate matrix factorization technique, may be applied to all numerical problems with large sets of equations which involve nine-point difference operators. (author) 21 refs.

  19. An approximate factorization procedure for solving nine-point elliptic difference equations. Application for a fast 2-D relativistic Fokker-Planck solver

    International Nuclear Information System (INIS)

    Peysson, Y.

    1997-09-01

    A full implicit numerical procedure based on the use of a nine-point difference operator is presented to solve the two dimensional (2 D ) relativistic Fokker-Planck equation for the current drive problem and synergetic effects between the lower hybrid and the electron cyclotron waves in tokamaks. As compared to the standard approach based on the use of a five-point difference operator [M. Shoucri, I. Shkarofsky, Comput. Phys. Comm. 82 (1994) 287], the convergence rate towards the steady state solution may be significantly enhanced with no loss of accuracy on the distribution function. Moreover, it is shown that the numerical stability may be strongly improved without a large degradation of the CPU time consumption as in the five-point scheme, making this approach very attractive for a fast solution of the 2-D Fokker-Planck equation on a fine grid in conjunction with other numerical codes for realistic plasma simulations. This new algorithm, based on an approximate matrix factorization technique, may be applied to all numerical problems with large sets of equations which involve nine-point difference operators. (author)

  20. Finite element method analysis of Fokker-Plank equation in stationary and evolutionary versions

    Czech Academy of Sciences Publication Activity Database

    Náprstek, Jiří; Král, Radomil

    2014-01-01

    Roč. 72, June (2014), s. 28-38 ISSN 0965-9978 R&D Projects: GA ČR(CZ) GA103/09/0094; GA AV ČR(CZ) IAA200710902 Institutional support: RVO:68378297 Keywords : Fokker-Planck equation * numerical solution * transition effects * stochastic mechanics * probability density function * non-linear dynamic systems Subject RIV: JM - Building Engineering Impact factor: 1.402, year: 2014 http://www.sciencedirect.com/science/article/pii/S0965997813001142

  1. Quantal Brownian Motion from RPA dynamics: The master and Fokker-Planck equations

    International Nuclear Information System (INIS)

    Yannouleas, C.

    1984-05-01

    From the purely quantal RPA description of the damped harmonic oscillator and of the corresponding Brownian Motion within the full space (phonon subspace plus reservoir), a master equation (as well as a Fokker-Planck equation) for the reduced density matrix (for the reduced Wigner function, respectively) within the phonon subspace is extracted. The RPA master equation agrees with the master equation derived by the time-dependent perturbative approaches which utilize Tamm-Dancoff Hilbert spaces and invoke the rotating wave approximation. Since the RPA yields a full, as well as a contracted description, it can account for both the kinetic and the unperturbed oscillator momenta. The RPA description of the quantal Brownian Motion contrasts with the descriptions provided by the time perturbative approaches whether they invoke or not the rotating wave approximation. The RPA description also contrasts with the phenomenological phase space quantization. (orig.)

  2. Fokker-Planck theory of electron cyclotron assisted startup and breakdown in Tokamaks

    International Nuclear Information System (INIS)

    Fidone, I.; Granata, G.

    1993-04-01

    The kinetic theory of plasma startup in a tokamak in the presence of electron cyclotron resonance heating is discussed. The linear theory of the X-mode and the upper-hybrid converted mode damping in low density and temperature plasmas are first reviewed. Then, the kinetic equation for the electron velocity distribution is considered, which is determined by the perpendicular electron cyclotron quasilinear diffusion operator, the parallel electric field, elastic and inelastic electron-neutral collisions and various losses. Two different time scales, namely the elastic electron-neutral collision time and the much longer ionization time, are identified. Thus a two time scale ordering procedure is legitimated for which the velocity distribution is determined by the quasilinear diffusion and the electron-neutral collision frequency; the ionization rate is computed using the Fokker-Planck solution for the electron velocity distribution

  3. Studies of parallel algorithms for the solution of a Fokker-Planck equation

    International Nuclear Information System (INIS)

    Deck, D.; Samba, G.

    1995-11-01

    The study of laser-created plasmas often requires the use of a kinetic model rather than a hydrodynamic one. This model change occurs, for example, in the hot spot formation in an ICF experiment or during the relaxation of colliding plasmas. When the gradients scalelengths or the size of a given system are not small compared to the characteristic mean-free-path, we have to deal with non-equilibrium situations, which can be described by the distribution functions of every species in the system. We present here a numerical method in plane or spherical 1-D geometry, for the solution of a Fokker-Planck equation that describes the evolution of stich functions in the phase space. The size and the time scale of kinetic simulations require the use of Massively Parallel Computers (MPP). We have adopted a message-passing strategy using Parallel Virtual Machine (PVM)

  4. On the quantum-mechanical Fokker-Planck and Kramers-Chandrasekhar equation

    International Nuclear Information System (INIS)

    Balazs, N.L.

    1978-01-01

    In the classical theory of Brownian motion the Langevin equation can be considered as an infinitesimal transformation between the coordinates and momenta of a Brownian particle, given probabilistically, since the impulse appearing is characterized by a Gaussian random process. This probabilistic infinitesimal transformation generates a streaming on the distribution function, expressed by the classical Fokker-Planck and Kramers-Chandrasekhar equations. If the laws obeyed by the Brownian particle are quantum mechanical, the Langevin equation can be reinterpreted as an operator relation expressing an infinitesimal transformation of these operators. Since the impulses are independent of the coordinates and momenta one can think of them as c numbers described by a Gaussian random process. The so resulting infinitesimal operator transformation induces a streaming on the density matrix. One may associate, according to Weyl, functions with operators. The function associated with the density matrix is the Wigner function. Expressing, then, these operator relations in terms of these functions the streaming can be expressed as a continuity equation of the Wigner function. It is found that in this parametrization the extra terms which appear are the same as in the classical theory, augmenting the usual Wigner equation. (Auth.)

  5. Fokker-Planck simulations of knock-on electron runaway avalanche and bursts in tokamaks

    International Nuclear Information System (INIS)

    Chiu, S.C.; Rosenbluth, M.N.; Harvey, R.W.; Chan, V.S.

    1998-01-01

    The avalanche of runaway electrons in an ohmic tokamak plasma triggered by knock-on collisions of traces of energetic electrons with the bulk electrons is simulated by the bounce averaged Fokker-Planck code, CQL3D. It is shown that even when the electric field is small for the production of Dreicer runaways, the knock-on collisions can produce significant runaway electrons in a fraction of a second at typical reactor parameters. The energy spectrum of these knock-on runaways has a characteristic temperature. The growth rate and temperature of the runaway distribution are determined and compared with theory. In simulations of pellet injection into high temperature plasmas, it is shown that a burst of Dreicer runaways may also occur depending on the cooling rate due to the pellet injection. Implications of these phenomena on disruption control in reactor plasmas are discussed. (author)

  6. Solution of the relativistic 2-D Fokker-Planck equation for LH current drive

    International Nuclear Information System (INIS)

    Hizanidis, K.; Hewett, D.W.; Bers, A.

    1984-03-01

    We solve numerically the steady-state two-dimensional relativistic Fokker-Planck equation with strong rf diffusion using spectra relevant to recent experiments in ALCATOR-C. The results (current generated, power dissipated, and the distribution of energetic electrons) are sensitive to the location of the spectrum in momentum space. Relativistic effects play an important role, especially for wide spectra. The dependence on the ionic charge number Z/sub i/ is also investigated. Particular attention is paid to the perpendicular temperature inside the resonant region and beyond, as well as to the angular energetic particle-temperature distribution, T/sub μ/, a function of the pitch angle parameter μ. The dependence of the perpendicular temperature on the location of the spectrum is also investigated analytically with a model based on the method of moments and the results compared with those found numerically

  7. Exact statistical analysis of nonlinear dynamic power reactor models by the Fokker--Planck method. Part II. Reactor with on-off control

    International Nuclear Information System (INIS)

    Debosscher, A.F.; Dutre, W.L.

    1979-01-01

    The paper deals with the exact stochastic analysis of the low-frequency neutron density fluctuations in an on-off controlled nuclear power reactor without delayed neutrons and perturbed by Gaussian white reactivity noise. The stochastic process, being Markovian, is completely characterized by its first-order probability density function (pdf) and the transition pdf. The first-order pdf is the normalized solution to the time-independent Fokker--Planck equation (FPE). Using this pdf, a general expression for the moments is obtained. The conditions for stochastic stability in probability, in the mean, and in the mean-square are derived. The time-dependent FPE is solved using the Laplace transform technique, which results in four distinct expressions for the transition pdf, according to the relative magnitude of initial and final reactor power with respect to the regulator level. After Laplace inversion, a physical interpretation of the controller's effect on the stochastic process becomes possible. Finally, making use of the obtained pdf's, the spectral density of the reactor power fluctuations is calculated

  8. Loading, absorption, and Fokker-Planck calculations for upcoming ICRF experiments on ATF

    International Nuclear Information System (INIS)

    Shepard, T.D.; Carter, M.D.; Goulding, R.H.; Kwon, M.

    1989-01-01

    ICRF experiments on ATF at the 100-kW level are planned for the current 1989 operating period. These plans include the 2ω/sub cH/ regime at f/sub RF/ = 28.88 MHz, D(H) at 14.44 MHz, and 4 He( 3 He) and D( 3 He) at 9.63 MHz. ECH target plasmas have n/sub eO/ /approxreverse arrowlt/ 0.15 /times/ 10 20 m/sup /minus/3/ and B = 0.95 T. The density and temperature profiles obtained are broader than those from 1988, owing to recent field error corrections. The values used for target-plasma parameters in the calculations were taken from initial 1989 ATF data. Loading and absorption calculations have been performed using the 3D RF heating code ORION with a helically symmetric equilibrium, and Fokker-Planck calculations were performed using the steady-state code RFTRANS with two velocity dimensions and one spatial dimension. 6 refs., 3 figs

  9. About positive, energy conservative and equilibrium state preserving schemes for the isotropic Fokker-Planck-Landau equation; Sur les schemas positifs, conservant l'energie et les etats d'equilibre pour l'equation de Fokker-Planck-Landau isotrope

    Energy Technology Data Exchange (ETDEWEB)

    Buet, Ch. [CEA Bruyeres-le-Chatel, Dept. des Sciences de la Simulation et de l' Information, 91 (France); Le Thanh, K.C. [CEA Bruyeres-le-Chatel, Dept. de Physique Theorique et Appliquee, 91 (France)

    2006-07-01

    The aim of this paper is to describe the discretization of the Fokker-Planck-Landau (FPL) collision term in the isotropic case which models the self collision for the electrons when they are totally isotropized by heavy particles background such as ions. The discussion focus on schemes which could preserve positivity, mass, energy and Maxwellian equilibrium. First, we analyze in detail the popular Chang and Cooper method for this non-linear collision term: derivation, conservation and positivity properties. We show that some variants of this method, based on the drift-diffusion form of the FPL operator, could not be positive or could not conserve the energy. We present a new variant of the Chang and Cooper method derived from the Landau form that is both positive and conservative. We also propose two new alternatives and simpler schemes for the FPL operator which show that the Chang and Cooper method is not the only way to construct positive, energy conservative and equilibrium state preserving schemes for this operator. For all these schemes, we explain clearly the properties of conservation of the density and the energy, the positivity of the solution and the conservation of the equilibrium states, or their lack. The case of Maxwellian and Coulombian potentials are emphasized. (authors)

  10. SU-E-T-22: A Deterministic Solver of the Boltzmann-Fokker-Planck Equation for Dose Calculation

    Energy Technology Data Exchange (ETDEWEB)

    Hong, X; Gao, H [Shanghai Jiao Tong University, Shanghai, Shanghai (China); Paganetti, H [Massachusetts General Hospital, Boston, MA (United States)

    2015-06-15

    Purpose: The Boltzmann-Fokker-Planck equation (BFPE) accurately models the migration of photons/charged particles in tissues. While the Monte Carlo (MC) method is popular for solving BFPE in a statistical manner, we aim to develop a deterministic BFPE solver based on various state-of-art numerical acceleration techniques for rapid and accurate dose calculation. Methods: Our BFPE solver is based on the structured grid that is maximally parallelizable, with the discretization in energy, angle and space, and its cross section coefficients are derived or directly imported from the Geant4 database. The physical processes that are taken into account are Compton scattering, photoelectric effect, pair production for photons, and elastic scattering, ionization and bremsstrahlung for charged particles.While the spatial discretization is based on the diamond scheme, the angular discretization synergizes finite element method (FEM) and spherical harmonics (SH). Thus, SH is used to globally expand the scattering kernel and FFM is used to locally discretize the angular sphere. As a Result, this hybrid method (FEM-SH) is both accurate in dealing with forward-peaking scattering via FEM, and efficient for multi-energy-group computation via SH. In addition, FEM-SH enables the analytical integration in energy variable of delta scattering kernel for elastic scattering with reduced truncation error from the numerical integration based on the classic SH-based multi-energy-group method. Results: The accuracy of the proposed BFPE solver was benchmarked against Geant4 for photon dose calculation. In particular, FEM-SH had improved accuracy compared to FEM, while both were within 2% of the results obtained with Geant4. Conclusion: A deterministic solver of the Boltzmann-Fokker-Planck equation is developed for dose calculation, and benchmarked against Geant4. Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang

  11. Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field

    Science.gov (United States)

    Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

    2017-10-01

    In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

  12. Nonparametric estimates of drift and diffusion profiles via Fokker-Planck algebra.

    Science.gov (United States)

    Lund, Steven P; Hubbard, Joseph B; Halter, Michael

    2014-11-06

    Diffusion processes superimposed upon deterministic motion play a key role in understanding and controlling the transport of matter, energy, momentum, and even information in physics, chemistry, material science, biology, and communications technology. Given functions defining these random and deterministic components, the Fokker-Planck (FP) equation is often used to model these diffusive systems. Many methods exist for estimating the drift and diffusion profiles from one or more identifiable diffusive trajectories; however, when many identical entities diffuse simultaneously, it may not be possible to identify individual trajectories. Here we present a method capable of simultaneously providing nonparametric estimates for both drift and diffusion profiles from evolving density profiles, requiring only the validity of Langevin/FP dynamics. This algebraic FP manipulation provides a flexible and robust framework for estimating stationary drift and diffusion coefficient profiles, is not based on fluctuation theory or solved diffusion equations, and may facilitate predictions for many experimental systems. We illustrate this approach on experimental data obtained from a model lipid bilayer system exhibiting free diffusion and electric field induced drift. The wide range over which this approach provides accurate estimates for drift and diffusion profiles is demonstrated through simulation.

  13. A Fokker-Planck treatment of stochastic particle motion within the framework of a fully coupled 6-dimensional formalism for electron-positron storage rings including classical spin motion in linear approximation

    International Nuclear Information System (INIS)

    Barber, D.P.; Heinemann, K.; Mais, H.; Ripken, G.

    1991-12-01

    In the following report we investigate stochastic particle motion in electron-positron storage ring in the framework of a Fokker-Planck treatment. The motion is described by using the canonical variables χ, p χ , z, p z , σ = s - cxt, p σ = ΔE/E 0 of the fully six-dimensional formalism. Thus synchrotron- and betatron-oscillations are treated simultaneously taking into account all kinds of coupling (synchro-betatron coupling and the coupling of the betatron oscillations by skew quadrupoles and solenoids). In order to set up the Fokker-Planck equation, action-angle variables of the linear coupled motion are introduced. The averaged dimensions of the bunch, resulting from radiation damping of the synchro-betatron oscillations and from an excitation of these oscillations by quantum fluctuations, are calculated by solving the Fokker-Planck equation. The surfaces of constant density in the six-dimensional phase space, given by six-dimensional ellipsoids, are determined. It is shown that the motion of such an ellipsoid under the influence of external fields can be described by six generating orbit vectors which may be combined into a six-dimenional matrix B(s). This 'bunch-shape matrix', B(s), contains complete information about the configuration of the bunch. Classical spin diffusion in linear approximation has also been included so that the dependence of the polarization vector on the orbital phase space coordinates can be studied and another derivation of the linearized depolarization time obtained. (orig.)

  14. Fokker-Planck description of the scattering of radio frequency waves at the plasma edge

    International Nuclear Information System (INIS)

    Hizanidis, Kyriakos; Kominis, Yannis; Tsironis, Christos; Ram, Abhay K.

    2010-01-01

    In magnetic fusion devices, radio frequency (rf) waves in the electron cyclotron (EC) and lower hybrid (LH) range of frequencies are being commonly used to modify the plasma current profile. In ITER, EC waves are expected to stabilize the neoclassical tearing mode (NTM) by providing current in the island region [R. Aymar et al., Nucl. Fusion 41, 1301 (2001)]. The appearance of NTMs severely limits the plasma pressure and leads to the degradation of plasma confinement. LH waves could be used in ITER to modify the current profile closer to the edge of the plasma. These rf waves propagate from the excitation structures to the core of the plasma through an edge region, which is characterized by turbulence--in particular, density fluctuations. These fluctuations, in the form of blobs, can modify the propagation properties of the waves by refraction. In this paper, the effect on rf due to randomly distributed blobs in the edge region is studied. The waves are represented as geometric optics rays and the refractive scattering from a distribution of blobs is formulated as a Fokker-Planck equation. The scattering can have two diffusive effects--one in real space and the other in wave vector space. The scattering can modify the trajectory of rays into the plasma and it can affect the wave vector spectrum. The refraction of EC waves, for example, could make them miss the intended target region where the NTMs occur. The broadening of the wave vector spectrum could broaden the wave generated current profile. The Fokker-Planck formalism for diffusion in real space and wave vector space is used to study the effect of density blobs on EC and LH waves in an ITER type of plasma environment. For EC waves the refractive effects become important since the distance of propagation from the edge to the core in ITER is of the order of a meter. The diffusion in wave vector space is small. For LH waves the refractive effects are insignificant but the diffusion in wave vector space is

  15. Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

    Science.gov (United States)

    Guarnieri, F.; Moon, W.; Wettlaufer, J. S.

    2017-09-01

    Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with a negative constant drift, described by a Fokker-Planck equation with a potential V (x ) =-[b ln(x ) +a x ] , for b >0 and a finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schrödinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a constant negative drift. We conclude with a comparison to other analytical methods and with numerical solutions.

  16. Stationary solution of the Fokker-Planck equation for linearly coupled motion in an electron storage ring

    International Nuclear Information System (INIS)

    Chao, A.W.; Lee, M.J.

    1975-09-01

    Effects upon longitudinal bunch shape in a storage ring due to linear and nonlinear potential can be calculated by finding the stationary solution to the Fokker-Planck equation for the particle distribution. Effects upon transverse bunch shape of a stored electron beam due to photon emissions and damping can be calculated by this method. It has been found that this method can also be used for a case in which the transverse modes of oscillation are coupled to the energy deviation δ. Examples of lattice elements which produce linear coupling between these oscillations are skew quadrupole magnets and solenoid magnets. For the linearly coupled case the stationary solution has been found to be given by exp (ΣΣA/sub ij/ x/sub i/x/sub j/) with x/sub i/ the canonical variables (x,p/sub x/, y, p/sub y/, δ, p/sub δ/) and A /sub ij/ some constants. The solution for the values of A /sub ij/'s will be described in this report. It will be shown that this solution can be expressed in a compact form. For simple cases, this form of solution leads directly to analytic expressions for the values of A /sub ij/'s and the bunch shape can be calculated by integrating the distribution function over some of the coordinates; for the more complex cases, it can be conveniently adapted as an algorithm for numerical evaluation. 16 refs

  17. Nonlinear drift-diffusion model of gating in K and nACh ion channels

    Energy Technology Data Exchange (ETDEWEB)

    Vaccaro, S.R. [Department of Physics, University of Adelaide, Adelaide, South Australia 5005 (Australia)], E-mail: svaccaro@physics.adelaide.edu.au

    2007-09-03

    The configuration of a sensor regulates the transition between the closed and open states of both voltage and ligand gated channels. The closed state dwell-time distribution f{sub c}(t) derived from a Fokker-Planck equation with a nonlinear diffusion coefficient is in good agreement with experimental data and can account for the power law approximation to f{sub c}(t) for a delayed rectifier K channel and a nicotinic acetylcholine (nACh) ion channel. The solution of a master equation which approximates the Fokker-Planck equation provides a better description of the small time behaviour of the dwell-time distribution and can account for the empirical rate-amplitude correlation for these ion channels.

  18. Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes

    International Nuclear Information System (INIS)

    Wehner, M.F.

    1983-01-01

    A path-integral solution is derived for processes described by nonlinear Fokker-Plank equations together with externally imposed boundary conditions. This path-integral solution is written in the form of a path sum for small time steps and contains, in addition to the conventional volume integral, a surface integral which incorporates the boundary conditions. A previously developed numerical method, based on a histogram representation of the probability distribution, is extended to a trapezoidal representation. This improved numerical approach is combined with the present path-integral formalism for restricted processes and is show t give accurate results. 35 refs., 5 figs

  19. Fokker-Planck equation of the reduced Wigner function associated to an Ohmic quantum Langevin dynamics

    Science.gov (United States)

    Colmenares, Pedro J.

    2018-05-01

    This article has to do with the derivation and solution of the Fokker-Planck equation associated to the momentum-integrated Wigner function of a particle subjected to a harmonic external field in contact with an ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung, and Grabert of interpreting the operators as c numbers to derive the quantum master equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the integral functional theory of Grabert, Schramm, and Ingold. By means of a single Wigner transformation, a simpler equation than that mentioned before is found. The Wigner function reproduces the known results of the classical limit. This allowed us to rewrite the underdamped classical Langevin equation as a first-order stochastic differential equation with time-dependent drift and diffusion terms.

  20. Long-Time Dynamic Response and Stochastic Resonance of Subdiffusive Overdamped Bistable Fractional Fokker-Planck Systems

    International Nuclear Information System (INIS)

    Yan-Mei, Kang; Yao-Lin, Jiang

    2008-01-01

    To explore the influence of anomalous diffusion on stochastic resonance (SR) more deeply and effectively, the method of moments is extended to subdiffusive overdamped bistable fractional Fokker-Planck systems for calculating the long-time linear dynamic response. It is found that the method of moments attains high accuracy with the truncation order N = 10, and in normal diffusion such obtained spectral amplification factor (SAF) of the first-order harmonic is also confirmed by stochastic simulation. Observing the SAF of the odd-order harmonics we find some interesting results, i.e. for smaller driving frequency the decrease of sub diffusion exponent inhibits the stochastic resonance (SR), while for larger driving frequency the decrease of sub diffusion exponent enhances the second SR peak, but the first one vanishes and a double SR is induced in the third-order harmonic at the same time. These observations suggest that the anomalous diffusion has important influence on the bistable dynamics

  1. Full-wave and Fokker Planck analysis of ICRF heating experiments in the Alcator C-Mod tokamak

    International Nuclear Information System (INIS)

    Bonoli, P.T.; Golovato, S.; Porkolab, M.; Takase, Y.

    1996-01-01

    The Alcator C-Mod device is a high field, high density, shaped tokamak with parameters a = 0.22 m, R 0 = 0.67 m, B 0 ≤ 9.0 T, κ ≤ 1.8, δ ≤ 0.8, and 1.0 x 10 20 m -3 n e (0) ≤ 1.0 x 10 21 m -3 . Four megawatt of ICRF power is available at 80 MHz. The wide operating range in magnetic field makes several heating schemes possible: (i) Second harmonic heating of hydrogen (f 0 = 2f CH ) at 2.6 T in (D-H); (ii) Fundamental heating of (H) (f 0 = f CH ) at 5.3T in a D-(H) plasma; and (iii) Fundamental heating of ( 3 He) (f 0 = f C 3 He ) at 7.9 T in a D-( 3 He) plasma. The most successful heating regime to date has been (H)-minority heating at 5.3 T. Pellet enhanced performance (PEP) modes have also been achieved in C-Mod in D-(H) at 5.3 T and in D-( 3 He) at 7.9 T, with a combination of intense ICRF heating and Li-pellet injection. A variety of numerical models are used to analyze these heating schemes. A 1-D full-wave code (FELICE) is used to study open-quotes single passclose quotes damping of the ICRF wavefront and damping of mode-converted ion Bernstein waves. A toroidal full-wave code (FISIC) is used to study interference and focussing effects of the ICRF waves as well as damping of the ICRF power upon multiple passes of the ICRF wavefront. A combined bounce averaged Fokker Planck and toroidal full-wave code (FPPRF) is used to study the ion tail formation, orbit losses, and the power partition of the ICRF tail to the background electrons and ions. Full-wave and Fokker Planck analyses confirm the strong single pass absorption of the ICRF power in D-(H) at 5.3 T. Analysis of PEP-mode plasmas in D-( 3 He) indicates improved wave focussing and 3 He-cyclotron absorption of the ICRF waves relative to L-mode. A dramatic increase in the transfer of 3 He tail power to the background deuterium is also found for PEP-mode plasmas

  2. Two-dimensional spectroscopy for harmonic vibrational modes with nonlinear system-bath interactions. II. Gaussian-Markovian case

    NARCIS (Netherlands)

    Tanimura, Y; Steffen, T

    2000-01-01

    The relaxation processes in a quantum system nonlinearly coupled to a harmonic Gaussian-Markovian heat bath are investigated by the quantum Fokker-Planck equation in the hierarchy form. This model describes frequency fluctuations in the quantum system with an arbitrary correlation time and thus

  3. Fractional Brownian motions via random walk in the complex plane and via fractional derivative. Comparison and further results on their Fokker-Planck equations

    International Nuclear Information System (INIS)

    Jumarie, Guy

    2004-01-01

    There are presently two different models of fractional Brownian motions available in the literature: the Riemann-Liouville fractional derivative of white noise on the one hand, and the complex-valued Brownian motion of order n defined by using a random walk in the complex plane, on the other hand. The paper provides a comparison between these two approaches, and in addition, takes this opportunity to contribute some complements. These two models are more or less equivalent on the theoretical standpoint for fractional order between 0 and 1/2, but their practical significances are quite different. Otherwise, for order larger than 1/2, the fractional derivative model has no counterpart in the complex plane. These differences are illustrated by an example drawn from mathematical finance. Taylor expansion of fractional order provides the expression of fractional difference in terms of finite difference, and this allows us to improve the derivation of Fokker-Planck equation and Kramers-Moyal expansion, and to get more insight in their relation with stochastic differential equations of fractional order. In the case of multi-fractal systems, the Fokker-Planck equation can be solved by using path integrals, and the fractional dynamic equations of the state moments of the stochastic system can be easily obtained. By combining fractional derivative and complex white noise of order n, one obtains a family of complex-valued fractional Brownian motions which exhibits long-range dependence. The conclusion outlines suggestions for further research, mainly regarding Lorentz transformation of fractional noises

  4. Time-Dependent Mean-Field Games with Logarithmic Nonlinearities

    KAUST Repository

    Gomes, Diogo A.

    2015-10-06

    In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.

  5. Time-Dependent Mean-Field Games with Logarithmic Nonlinearities

    KAUST Repository

    Gomes, Diogo A.; Pimentel, Edgard

    2015-01-01

    In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.

  6. Two-dimensional spectroscopy for harmonic vibrational modes with nonlinear system-bath interactions. I. Gaussian-white case

    NARCIS (Netherlands)

    Steffen, T; Tanimura, Y

    The quantum Fokker-Planck equation is derived for a system nonlinearly coupled to a harmonic oscillator bath. The system-bath interaction is assumed to be linear in the bath coordinates but quadratic in the system coordinate. The relaxation induced dynamics of a harmonic system are investigated by

  7. Design of foam-buffered high gain target with Fokker-Planck implosion simulation for thermal insulation and imprint mitigation

    International Nuclear Information System (INIS)

    Takeda, T.; Mima, K.; Norimatsu, T.; Nagatomo, H.; Nishiguchi, A.

    2003-01-01

    It is proposed that a thick foam layer on a plastic capsule of fusion pellet is effective not only for reducing the initial imprint, but also for solving the melting problem of cryogenic deuterium-tritium layer, in a reactor chamber. Investigated are the dependences of gain, thermal insulation for preventing the melting, and imprint mitigation of a foam-buffered target on the foam layer thickness. The imprint mitigation, the Rayleigh-Taylor growth factor and the fusion gain of a foam-buffered target are evaluated by the hydrodynamic implosion code HIMICO [A. Nishiguchi et al., Phys. Fluids B 4, 417 (1992)], which includes a Fokker-Planck transport code. As the result, it is found that high gain can be achieved by the foam-buffered target together with thermal insulation and imprint mitigation

  8. 3-D Ray-tracing and 2-D Fokker-Planck Simulations of Radiofrequency Application to Tokamak Plasmas

    International Nuclear Information System (INIS)

    Cardinali, A.; Paoletti, F.; Bernabei, S.

    1999-01-01

    A state of the art numerical tool has been developed to simulate the propagation and the absorption of coexisting different types of waves in a tokamak geometry. The code includes a numerical solution of the three-dimensional (R, Z, Φ) toroidal wave equation for the electric field of the different waves in the WKBJ approximation. At each step of integration, the two-dimensional (v parallel, v perpendicular) Fokker-Planck equation is solved in the presence of quasilinear diffusion coefficients. The electron Landau damping of the waves is modeled taking into account the interaction of the wave electric fields with the quasilinearly modified distribution function. Consistently, the code calculates the radial profiles of non-inductively generated current densities, the transmitted power traces and the total power damping curves. Synergistic effects among the different type of waves (e.g., lower hybrid and ion Bernstein waves) are studied through the separation of the contributions of the single wave from the effects due to their coexistence

  9. Nonlinear electron transport in magnetized laser plasmas

    International Nuclear Information System (INIS)

    Kho, T.H.; Haines, M.G.

    1986-01-01

    Electron transport in a magnetized plasma heated by inverse bremsstrahlung is studied numerically using a nonlinear Fokker--Planck model with self-consistent E and B fields. The numerical scheme is described. Nonlocal transport is found to alter many of the transport coefficients derived from linear transport theory, in particular, the Nernst and Righi--Leduc effects, in addition to the perpendicular heat flux q/sub perpendicular/, are substantially reduced near critical surface. The magnetic field, however, remains strongly coupled to the nonlinear q/sub perpendicular/ and, as has been found in hydrosimulations, convective amplification of the magnetic field occurs in the overdense plasma

  10. Feedback-induced bistability of an optically levitated nanoparticle: A Fokker-Planck treatment

    Science.gov (United States)

    Ge, Wenchao; Rodenburg, Brandon; Bhattacharya, M.

    2016-08-01

    Optically levitated nanoparticles have recently emerged as versatile platforms for investigating macroscopic quantum mechanics and enabling ultrasensitive metrology. In this paper we theoretically consider two damping regimes of an optically levitated nanoparticle cooled by cavityless parametric feedback. Our treatment is based on a generalized Fokker-Planck equation derived from the quantum master equation presented recently and shown to agree very well with experiment [B. Rodenburg, L. P. Neukirch, A. N. Vamivakas, and M. Bhattacharya, Quantum model of cooling and force sensing with an optically trapped nanoparticle, Optica 3, 318 (2016), 10.1364/OPTICA.3.000318]. For low damping, we find that the resulting Wigner function yields the single-peaked oscillator position distribution and recovers the appropriate energy distribution derived earlier using a classical theory and verified experimentally [J. Gieseler, R. Quidant, C. Dellago, and L. Novotny, Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state, Nat. Nano. 9, 358 (2014), 10.1038/nnano.2014.40]. For high damping, in contrast, we predict a double-peaked position distribution, which we trace to an underlying bistability induced by feedback. Unlike in cavity-based optomechanics, stochastic processes play a major role in determining the bistable behavior. To support our conclusions, we present analytical expressions as well as numerical simulations using the truncated Wigner function approach. Our work opens up the prospect of developing bistability-based devices, characterization of phase-space dynamics, and investigation of the quantum-classical transition using levitated nanoparticles.

  11. THE WIGNER–FOKKER–PLANCK EQUATION: STATIONARY STATES AND LARGE TIME BEHAVIOR

    KAUST Repository

    ARNOLD, ANTON

    2012-11-01

    We consider the linear WignerFokkerPlanck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of perturbations we prove that the equation admits a unique stationary solution in a weighted Sobolev space. A key ingredient of the proof is a new result on the existence of spectral gaps for FokkerPlanck type operators in certain weighted L 2-spaces. In addition we show that the steady state corresponds to a positive density matrix operator with unit trace and that the solutions of the time-dependent problem converge towards the steady state with an exponential rate. © 2012 World Scientific Publishing Company.

  12. Fokker-Planck simulation of runaway electron generation in disruptions with the hot-tail effect

    Energy Technology Data Exchange (ETDEWEB)

    Nuga, H., E-mail: nuga@p-grp.nucleng.kyoto-u.ac.jp; Fukuyama, A. [Department of Engineering, Kyoto University, Kyoto 615-8540 (Japan); Yagi, M. [National Institutes for Quantum and Radiological Science and Technology, Aomori 039-3212 (Japan)

    2016-06-15

    To study runaway electron generation in disruptions, we have extended the three-dimensional (two-dimensional in momentum space; one-dimensional in the radial direction) Fokker-Planck code, which describes the evolution of the relativistic momentum distribution function of electrons and the induced toroidal electric field in a self-consistent manner. A particular focus is placed on the hot-tail effect in two-dimensional momentum space. The effect appears if the drop of the background plasma temperature is sufficiently rapid compared with the electron-electron slowing down time for a few times of the pre-quench thermal velocity. It contributes to not only the enhancement of the primary runaway electron generation but also the broadening of the runaway electron distribution in the pitch angle direction. If the thermal energy loss during the major disruption is assumed to be isotropic, there are hot-tail electrons that have sufficiently large perpendicular momentum, and the runaway electron distribution becomes broader in the pitch angle direction. In addition, the pitch angle scattering also yields the broadening. Since the electric field is reduced due to the burst of runaway electron generation, the time required for accelerating electrons to the runaway region becomes longer. The longer acceleration period makes the pitch-angle scattering more effective.

  13. Probability calculus of fractional order and fractional Taylor's series application to Fokker-Planck equation and information of non-random functions

    International Nuclear Information System (INIS)

    Jumarie, Guy

    2009-01-01

    A probability distribution of fractional (or fractal) order is defined by the measure μ{dx} = p(x)(dx) α , 0 α (D x α h α )f(x) provided by the modified Riemann Liouville definition, one can expand a probability calculus parallel to the standard one. A Fourier's transform of fractional order using the Mittag-Leffler function is introduced, together with its inversion formula; and it provides a suitable generalization of the characteristic function of fractal random variables. It appears that the state moments of fractional order are more especially relevant. The main properties of this fractional probability calculus are outlined, it is shown that it provides a sound approach to Fokker-Planck equation which are fractional in both space and time, and it provides new results in the information theory of non-random functions.

  14. Electron acceleration by an obliquely propagating electromagnetic wave in the regime of validity of the Fokker-Planck-Kolmogorov approach

    Science.gov (United States)

    Hizanidis, Kyriakos; Vlahos, L.; Polymilis, C.

    1989-01-01

    The relativistic motion of an ensemble of electrons in an intense monochromatic electromagnetic wave propagating obliquely in a uniform external magnetic field is studied. The problem is formulated from the viewpoint of Hamiltonian theory and the Fokker-Planck-Kolmogorov approach analyzed by Hizanidis (1989), leading to a one-dimensional diffusive acceleration along paths of constant zeroth-order generalized Hamiltonian. For values of the wave amplitude and the propagating angle inside the analytically predicted stochastic region, the numerical results suggest that the diffusion probes proceeds in stages. In the first stage, the electrons are accelerated to relatively high energies by sampling the first few overlapping resonances one by one. During that stage, the ensemble-average square deviation of the variable involved scales quadratically with time. During the second stage, they scale linearly with time. For much longer times, deviation from linear scaling slowly sets in.

  15. A combination between Laplace transformation technique and numerical approximations to the Fokker-Planck equation solutions

    International Nuclear Information System (INIS)

    Monticelli, Cintia O.; Wortmann, Sergio; Segatto, Cynthia F.

    2005-01-01

    In this work is obtained a hybrid solution to the Fokker-Planck equation with energy dependency, very used in ion implantation problems. The main idea relies on the application of Laplace transform in the energy variable, and finite-difference in the spatial variable and in the angular variable. This procedure leads to a symbolic matrix problem for the transformed energy. To solve this system, is needed to do the Laplace inverse of the (sI+A) matrix, where s is a complex parameter, I is the identity matrix and A is a square matrix that was proceeded from the finite-difference in the spatial variable and in the angular variable. The matrix A is not defective, then is taken decomposition of A in a sum of two others matrices, where one is defective. It leads a iterative inversion method, similar the source fixed method combined with the diagonalization method, then is obtained the values to the angular flux. Hereafter we can to determine the energy deposited into the electronic system and in the nuclear system of the target. To comprove the results obtained, the simulation of implantation of B into Si at energies ranging from 1 KeV to 50 MeV was carried out and compared with the results by software SRIM2003. (author)

  16. Neoclassical transport including collisional nonlinearity.

    Science.gov (United States)

    Candy, J; Belli, E A

    2011-06-10

    In the standard δf theory of neoclassical transport, the zeroth-order (Maxwellian) solution is obtained analytically via the solution of a nonlinear equation. The first-order correction δf is subsequently computed as the solution of a linear, inhomogeneous equation that includes the linearized Fokker-Planck collision operator. This equation admits analytic solutions only in extreme asymptotic limits (banana, plateau, Pfirsch-Schlüter), and so must be solved numerically for realistic plasma parameters. Recently, numerical codes have appeared which attempt to compute the total distribution f more accurately than in the standard ordering by retaining some nonlinear terms related to finite-orbit width, while simultaneously reusing some form of the linearized collision operator. In this work we show that higher-order corrections to the distribution function may be unphysical if collisional nonlinearities are ignored.

  17. Addendum: ``The Dynamics of M15: Observations of the Velocity Dispersion Profile and Fokker-Planck Models'' (ApJ, 481, 267 [1997])

    Science.gov (United States)

    Dull, J. D.; Cohn, H. N.; Lugger, P. M.; Murphy, B. W.; Seitzer, P. O.; Callanan, P. J.; Rutten, R. G. M.; Charles, P. A.

    2003-03-01

    It has recently come to our attention that there are axis scale errors in three of the figures presented in Dull et al. (1997, hereafter D97). This paper presented Fokker-Planck models for the collapsed-core globular cluster M15 that include a dense, centrally concentrated population of neutron stars and massive white dwarfs. These models do not include a central black hole. Figure 12 of D97, which presents the predicted mass-to-light profile, is of particular interest, since it was used by Gerssen et al. (2002) as an input to their Jeans equation analysis of the Hubble Space Telescope (HST) STIS velocity measurements reported by van der Marel et al. (2002). On the basis of the original, incorrect version of Figure 12, Gerssen et al. (2002) concluded that the D97 models can fit the new data only with the addition of an intermediate-mass black hole. However, this is counter to our previous finding, shown in Figure 6 of D97, that the Fokker-Planck models predict the sort of moderately rising velocity dispersion profile that Gerssen et al. (2002) infer from the new data. Baumgardt et al. (2003) have independently noted this apparent inconsistency. We appreciate the thoughtful cooperation of Roeland van der Marel in resolving this issue. Using our corrected version of Figure 12 (see below), Gerssen et al. (2003) now find that the velocity dispersion profile that they infer from the D97 mass-to-light ratio profile is entirely consistent with the velocity dispersion profile presented in Figure 6 of D97. Gerssen et al. (2003) further find that there is no statistically significant difference between the fit to the van der Marel et al. (2002) velocity measurements provided by the D97 intermediate-phase model and that provided by their model, which supplements this D97 model with a 1.7+2.7-1.7×103Msolar black hole. Thus, the choice between models with and without black holes will require additional model predictions and observational tests. We present corrected versions of

  18. Quantum Stochastic Trajectories: The Fokker-Planck-Bohm Equation Driven by the Reduced Density Matrix.

    Science.gov (United States)

    Avanzini, Francesco; Moro, Giorgio J

    2018-03-15

    The quantum molecular trajectory is the deterministic trajectory, arising from the Bohm theory, that describes the instantaneous positions of the nuclei of molecules by assuring the agreement with the predictions of quantum mechanics. Therefore, it provides the suitable framework for representing the geometry and the motions of molecules without neglecting their quantum nature. However, the quantum molecular trajectory is extremely demanding from the computational point of view, and this strongly limits its applications. To overcome such a drawback, we derive a stochastic representation of the quantum molecular trajectory, through projection operator techniques, for the degrees of freedom of an open quantum system. The resulting Fokker-Planck operator is parametrically dependent upon the reduced density matrix of the open system. Because of the pilot role played by the reduced density matrix, this stochastic approach is able to represent accurately the main features of the open system motions both at equilibrium and out of equilibrium with the environment. To verify this procedure, the predictions of the stochastic and deterministic representation are compared for a model system of six interacting harmonic oscillators, where one oscillator is taken as the open quantum system of interest. The undeniable advantage of the stochastic approach is that of providing a simplified and self-contained representation of the dynamics of the open system coordinates. Furthermore, it can be employed to study the out of equilibrium dynamics and the relaxation of quantum molecular motions during photoinduced processes, like photoinduced conformational changes and proton transfers.

  19. Supersymmetric quantum mechanics method for the Fokker-Planck equation with applications to protein folding dynamics

    Science.gov (United States)

    Polotto, Franciele; Drigo Filho, Elso; Chahine, Jorge; Oliveira, Ronaldo Junio de

    2018-03-01

    This work developed analytical methods to explore the kinetics of the time-dependent probability distributions over thermodynamic free energy profiles of protein folding and compared the results with simulation. The Fokker-Planck equation is mapped onto a Schrödinger-type equation due to the well-known solutions of the latter. Through a semi-analytical description, the supersymmetric quantum mechanics formalism is invoked and the time-dependent probability distributions are obtained with numerical calculations by using the variational method. A coarse-grained structure-based model of the two-state protein Tm CSP was simulated at a Cα level of resolution and the thermodynamics and kinetics were fully characterized. Analytical solutions from non-equilibrium conditions were obtained with the simulated double-well free energy potential and kinetic folding times were calculated. It was found that analytical folding time as a function of temperature agrees, quantitatively, with simulations and experiments from the literature of Tm CSP having the well-known 'U' shape of the Chevron Plots. The simple analytical model developed in this study has a potential to be used by theoreticians and experimentalists willing to explore, quantitatively, rates and the kinetic behavior of their system by informing the thermally activated barrier. The theory developed describes a stochastic process and, therefore, can be applied to a variety of biological as well as condensed-phase two-state systems.

  20. A closed-form solution for the two-dimensional Fokker-Planck equation for electron transport in the range of Compton Effect

    Energy Technology Data Exchange (ETDEWEB)

    Rodriguez, B.D.A. [Universidade Federal Rio Grande do Sul, Programa de Pos-Graduacao em Engenharia Mecanica, Rua Portuguesa 218/304, 90650-12 Porto Alegre, RS (Brazil)], E-mail: barbara.arodriguez@gmail.com; Vilhena, M.T. [Universidade Federal Rio Grande do Sul, Departamento de Matematica Pura e Aplicada, Porto Alegre, RS (Brazil)], E-mail: vilhena@mat.ufrgs.br; Borges, V. [Universidade Federal Rio Grande do Sul, Programa de Pos-Graduacao em Engenharia Mecanica, Rua Portuguesa 218/304, 90650-12 Porto Alegre, RS (Brazil)], E-mail: borges@ufrgs.br; Hoff, G. [Pontificia Universidade Catolica do Rio Grande do Sul, Faculdade de Fisica, Porto Alegre, RS (Brazil)], E-mail: hoff@pucrs.br

    2008-05-15

    In this paper we solve the Fokker-Planck (FP) equation, an alternative approach for the Boltzmann transport equation for charged particles in a rectangular domain. To construct the solution we begin applying the P{sub N} approximation in the angular variable and the Laplace Transform in the x-variable, thus obtaining a first order linear differential equation in y-variable, which the solution is straightforward. The angular flux of electrons and the parameters of the medium are used for the calculation of the energy deposited by the secondary electrons generated by Compton Effect. The remaining effects will not be taken into account. The results will be presented under absorbed energy form in several points of interested. We present numerical simulations and comparisons with results obtained by using Geant4 (version 8) program which applies the Monte Carlo's technique to low energy libraries for a two-dimensional problem assuming the screened Rutherford differential scattering cross-section.

  1. A closed-form solution for the two-dimensional Fokker-Planck equation for electron transport in the range of Compton Effect

    International Nuclear Information System (INIS)

    Rodriguez, B.D.A.; Vilhena, M.T.; Borges, V.; Hoff, G.

    2008-01-01

    In this paper we solve the Fokker-Planck (FP) equation, an alternative approach for the Boltzmann transport equation for charged particles in a rectangular domain. To construct the solution we begin applying the P N approximation in the angular variable and the Laplace Transform in the x-variable, thus obtaining a first order linear differential equation in y-variable, which the solution is straightforward. The angular flux of electrons and the parameters of the medium are used for the calculation of the energy deposited by the secondary electrons generated by Compton Effect. The remaining effects will not be taken into account. The results will be presented under absorbed energy form in several points of interested. We present numerical simulations and comparisons with results obtained by using Geant4 (version 8) program which applies the Monte Carlo's technique to low energy libraries for a two-dimensional problem assuming the screened Rutherford differential scattering cross-section

  2. Numerical resolution of the Fokker-Planck equation for non-lineal cases

    International Nuclear Information System (INIS)

    Mastropiero, Daniel

    1997-01-01

    The author resolves the Fokker-Plank equation of the statistical thermodynamics of irreversible processes for the flow of particles in a medium, considering two cases: a) The diffusion coefficient of the medium depends on concentration; and b) The medium is unhomogeneous, i.e. the diffusion coefficient varies with the position. Different cases are analyzed and compared

  3. Electron dynamics with radiation and nonlinear wigglers

    International Nuclear Information System (INIS)

    Jowett, J.M.

    1986-06-01

    The physics of electron motion in storage rings is described by supplementing the Hamiltonian equations of motion with fluctuating radiation reaction forces to describe the effects of synchrotron radiation. This leads to a description of radiation damping and quantum diffusion in single-particle phase-space by means of Fokker-Planck equations. For practical purposes, most storage rings remain in the regime of linear damping and diffusion; this is discussed in some detail with examples, concentrating on longitudinal phase space. However special devices such as nonlinear wigglers may permit the new generation of very large rings to go beyond this into regimes of nonlinear damping. It is shown how a special combined-function wiggler can be used to modify the energy distribution and current profile of electron bunches

  4. Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model

    Science.gov (United States)

    Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.

    2009-01-01

    Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.

  5. Directed motion generated by heat bath nonlinearly driven by external noise

    International Nuclear Information System (INIS)

    Chaudhuri, J Ray; Barik, D; Banik, S K

    2007-01-01

    Based on the heat bath system approach where the bath is nonlinearly modulated by an external Gaussian random force, we propose a new microscopic model to study directed motion in the overdamped limit for a nonequilibrium open system. Making use of the coupling between the heat bath and the external modulation as a small perturbation, we construct a Langevin equation with multiplicative noise- and space-dependent dissipation and the corresponding Fokker-Planck-Smoluchowski equation in the overdamped limit. We examine the thermodynamic consistency condition and explore the possibility of observing a phase-induced current as a consequence of state-dependent diffusion and, necessarily, nonlinear driving of the heat bath by the external noise

  6. Directed motion generated by heat bath nonlinearly driven by external noise

    Energy Technology Data Exchange (ETDEWEB)

    Chaudhuri, J Ray [Department of Physics, Katwa College, Katwa, Burdwan 713 130, West Bengal (India); Barik, D [Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032 (India); Banik, S K [Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0435 (United States)

    2007-12-07

    Based on the heat bath system approach where the bath is nonlinearly modulated by an external Gaussian random force, we propose a new microscopic model to study directed motion in the overdamped limit for a nonequilibrium open system. Making use of the coupling between the heat bath and the external modulation as a small perturbation, we construct a Langevin equation with multiplicative noise- and space-dependent dissipation and the corresponding Fokker-Planck-Smoluchowski equation in the overdamped limit. We examine the thermodynamic consistency condition and explore the possibility of observing a phase-induced current as a consequence of state-dependent diffusion and, necessarily, nonlinear driving of the heat bath by the external noise.

  7. THE WIGNER–FOKKER–PLANCK EQUATION: STATIONARY STATES AND LARGE TIME BEHAVIOR

    KAUST Repository

    ARNOLD, ANTON; GAMBA, IRENE M.; GUALDANI, MARIA PIA; MISCHLER, STÉ PHANE; MOUHOT, CLEMENT; SPARBER, CHRISTOF

    2012-01-01

    solution in a weighted Sobolev space. A key ingredient of the proof is a new result on the existence of spectral gaps for FokkerPlanck type operators in certain weighted L 2-spaces. In addition we show that the steady state corresponds to a positive density

  8. A mixed finite element method for nonlinear diffusion equations

    KAUST Repository

    Burger, Martin; Carrillo, José ; Wolfram, Marie-Therese

    2010-01-01

    We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.

  9. A local analytic approach for the fast solution of the Fokker-Planck equation

    International Nuclear Information System (INIS)

    Sajjadi, S.G.; Nicholas, D.J.

    1987-11-01

    In this report we describe a method of obtaining a closed form for the Focker-Planck equation rendering it amenable to solution in time-step with a complete hydrodynamic treatment of a plasma. We present a local expression for the heat flux, by solving the Focker-Planck equation for electrons in one space and two velocity dimensions in the presence of a self consistent electronic field. (author)

  10. Application of the Fokker-Planck molecular mixing model to turbulent scalar mixing using moment methods

    Science.gov (United States)

    Madadi-Kandjani, E.; Fox, R. O.; Passalacqua, A.

    2017-06-01

    An extended quadrature method of moments using the β kernel density function (β -EQMOM) is used to approximate solutions to the evolution equation for univariate and bivariate composition probability distribution functions (PDFs) of a passive scalar for binary and ternary mixing. The key element of interest is the molecular mixing term, which is described using the Fokker-Planck (FP) molecular mixing model. The direct numerical simulations (DNSs) of Eswaran and Pope ["Direct numerical simulations of the turbulent mixing of a passive scalar," Phys. Fluids 31, 506 (1988)] and the amplitude mapping closure (AMC) of Pope ["Mapping closures for turbulent mixing and reaction," Theor. Comput. Fluid Dyn. 2, 255 (1991)] are taken as reference solutions to establish the accuracy of the FP model in the case of binary mixing. The DNSs of Juneja and Pope ["A DNS study of turbulent mixing of two passive scalars," Phys. Fluids 8, 2161 (1996)] are used to validate the results obtained for ternary mixing. Simulations are performed with both the conditional scalar dissipation rate (CSDR) proposed by Fox [Computational Methods for Turbulent Reacting Flows (Cambridge University Press, 2003)] and the CSDR from AMC, with the scalar dissipation rate provided as input and obtained from the DNS. Using scalar moments up to fourth order, the ability of the FP model to capture the evolution of the shape of the PDF, important in turbulent mixing problems, is demonstrated. Compared to the widely used assumed β -PDF model [S. S. Girimaji, "Assumed β-pdf model for turbulent mixing: Validation and extension to multiple scalar mixing," Combust. Sci. Technol. 78, 177 (1991)], the β -EQMOM solution to the FP model more accurately describes the initial mixing process with a relatively small increase in computational cost.

  11. Dynamic least-squares kernel density modeling of Fokker-Planck equations with application to neural population.

    Science.gov (United States)

    Shotorban, Babak

    2010-04-01

    The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.

  12. Computational-physics program of the National MFE Computer Center

    International Nuclear Information System (INIS)

    Mirin, A.A.

    1982-02-01

    The computational physics group is ivolved in several areas of fusion research. One main area is the application of multidimensional Fokker-Planck, transport and combined Fokker-Planck/transport codes to both toroidal and mirror devices. Another major area is the investigation of linear and nonlinear resistive magnetohydrodynamics in two and three dimensions, with applications to all types of fusion devices. The MHD work is often coupled with the task of numerically generating equilibria which model experimental devices. In addition to these computational physics studies, investigations of more efficient numerical algorithms are being carried out

  13. Quantum diffusion

    International Nuclear Information System (INIS)

    Habib, S.

    1994-01-01

    We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the simple case of polynomial noise-couplings this equation reduces to a generalized Fokker-Planck form. With nonlinear noise injection new ''quantum diffusion'' terms rise that have no counterpart in the classical case. Two special examples that are not of a Fokker-Planck form are discussed: the first with a localized noise source and the other with a spatially modulated noise source

  14. A Finite-Orbit-Width Fokker-Planck solver for modeling of energetic particle interactions with waves, with application to Helicons in ITER

    Directory of Open Access Journals (Sweden)

    Petrov Yuri V.

    2017-01-01

    Full Text Available The bounce-average (BA finite-difference Fokker-Planck (FP code CQL3D [1,2] now includes the essential physics to describe the RF heating of Finite-Orbit-Width (FOW ions in tokamaks. The FP equation is reformulated in terms of Constants-Of-Motion coordinates, which we select to be particle speed, pitch angle, and major radius on the equatorial plane thus obtaining the distribution function directly at this location. Full-orbit, low collisionality neoclassical radial transport emerges from averaging the local friction and diffusion coefficients along guiding center orbits. Similarly, the BA of local quasilinear RF diffusion terms gives rise to additional radial transport. The local RF electric field components needed for the BA operator are usually obtained by a ray-tracing code, such as GENRAY, or in conjunction with full-wave codes. As a new, practical application, the CQL3D-FOW version is used for simulation of alpha-particle heating by high-harmonic waves in ITER. Coupling of high harmonic or helicon fast waves power to electrons is a promising current drive (CD scenario for high beta plasmas. However, the efficiency of current drive can be diminished by parasitic channeling of RF power into fast ions, such as alphas, through finite Larmor-radius effects. We investigate possibilities to reduce the fast ion heating in CD scenarios.

  15. On the conditions for the onset of nonlinear chirping structures in NSTX

    Science.gov (United States)

    Duarte, Vinicius; Podesta, Mario; Berk, Herbert; Gorelenkov, Nikolai

    2015-11-01

    The nonlinear dynamics of phase space structures is a topic of interest in tokamak physics in connection with fast ion loss mechanisms. The onset of phase-space holes and clumps has been theoretically shown to be associated with an explosive solution of an integro-differential, nonlocal cubic equation that governs the early mode amplitude evolution in the weakly nonlinear regime. The existence and stability of the solutions of the cubic equation have been theoretically studied as a function of Fokker-Planck coefficients for the idealized case of a single resonant point of a localized mode. From realistic computations of NSTX mode structures and resonant surfaces, we calculate effective pitch angle scattering and slowing-down (drag) collisional coefficients and analyze NSTX discharges for different cases with respect to chirping experimental observation. Those results are confronted to the theory that predicts the parameters region that allow for chirping to take place.

  16. An accurate nonlinear Monte Carlo collision operator

    International Nuclear Information System (INIS)

    Wang, W.X.; Okamoto, M.; Nakajima, N.; Murakami, S.

    1995-03-01

    A three dimensional nonlinear Monte Carlo collision model is developed based on Coulomb binary collisions with the emphasis both on the accuracy and implementation efficiency. The operator of simple form fulfills particle number, momentum and energy conservation laws, and is equivalent to exact Fokker-Planck operator by correctly reproducing the friction coefficient and diffusion tensor, in addition, can effectively assure small-angle collisions with a binary scattering angle distributed in a limited range near zero. Two highly vectorizable algorithms are designed for its fast implementation. Various test simulations regarding relaxation processes, electrical conductivity, etc. are carried out in velocity space. The test results, which is in good agreement with theory, and timing results on vector computers show that it is practically applicable. The operator may be used for accurately simulating collisional transport problems in magnetized and unmagnetized plasmas. (author)

  17. Time domain simulation of the response of geometrically nonlinear panels subjected to random loading

    Science.gov (United States)

    Moyer, E. Thomas, Jr.

    1988-01-01

    The response of composite panels subjected to random pressure loads large enough to cause geometrically nonlinear responses is studied. A time domain simulation is employed to solve the equations of motion. An adaptive time stepping algorithm is employed to minimize intermittent transients. A modified algorithm for the prediction of response spectral density is presented which predicts smooth spectral peaks for discrete time histories. Results are presented for a number of input pressure levels and damping coefficients. Response distributions are calculated and compared with the analytical solution of the Fokker-Planck equations. RMS response is reported as a function of input pressure level and damping coefficient. Spectral densities are calculated for a number of examples.

  18. High-field transport of electrons and radiative effects using coupled force-balance and Fokker-Planck equations beyond the relaxation-time approximation

    International Nuclear Information System (INIS)

    Huang, Danhong; Apostolova, T.; Alsing, P.M.; Cardimona, D.A.

    2004-01-01

    The dynamics of a many-electron system under both dc and infrared fields is separated into a center-of-mass and a relative motion. The first-order force-balance equation is employed for the slow center-of-mass motion of electrons, and the Fokker-Planck equation is used for the ultrafast relative scattering motion of degenerate electrons. This approach allows us to include the anisotropic energy-relaxation process which has been neglected in the energy-balance equation in the past. It also leads us to include the anisotropic coupling to the incident infrared field with different polarizations. Based on this model, the transport of electrons is explored under strong dc and infrared fields by going beyond the relaxation-time approximation. The anisotropic dependence of the electron distribution function on the parallel and perpendicular kinetic energies of electrons is displayed with respect to the dc field direction, and the effect of anisotropic coupling to an incident infrared field with polarizations parallel and perpendicular to the applied dc electric field is shown. The heating of electrons is more accurately described beyond the energy-balance equation with the inclusion of an anisotropic coupling to the infrared field. The drift velocity of electrons is found to increase with the amplitude of the infrared field due to a suppressed momentum-relaxation process (or frictional force) under parallel polarization but decreases with the amplitude due to an enhanced momentum-relaxation process under perpendicular polarization

  19. Fractional Poisson-Nernst-Planck Model for Ion Channels I: Basic Formulations and Algorithms.

    Science.gov (United States)

    Chen, Duan

    2017-11-01

    In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.

  20. Oligarchy as a phase transition: The effect of wealth-attained advantage in a Fokker-Planck description of asset exchange

    Science.gov (United States)

    Boghosian, Bruce M.; Devitt-Lee, Adrian; Johnson, Merek; Li, Jie; Marcq, Jeremy A.; Wang, Hongyan

    2017-06-01

    The ;Yard-Sale Model; of asset exchange is known to result in complete inequality-all of the wealth in the hands of a single agent. It is also known that, when this model is modified by introducing a simple model of redistribution based on the Ornstein-Uhlenbeck process, it admits a steady state exhibiting some features similar to the celebrated Pareto Law of wealth distribution. In the present work, we analyze the form of this steady-state distribution in much greater detail, using a combination of analytic and numerical techniques. We find that, while Pareto's Law is approximately valid for low redistribution, it gives way to something more similar to Gibrat's Law when redistribution is higher. Additionally, we prove in this work that, while this Pareto or Gibrat behavior may persist over many orders of magnitude, it ultimately gives way to gaussian decay at extremely large wealth. Also in this work, we introduce a bias in favor of the wealthier agent-what we call Wealth-Attained Advantage (WAA)-and show that this leads to the phenomenon of ;wealth condensation; when the bias exceeds a certain critical value. In the wealth-condensed state, a finite fraction of the total wealth of the population ;condenses; to the wealthiest agent. We examine this phenomenon in some detail, and derive the corresponding modification to the Fokker-Planck equation. We observe a second-order phase transition to a state of coexistence between an oligarch and a distribution of non-oligarchs. Finally, by studying the asymptotic behavior of the distribution in some detail, we show that the onset of wealth condensation has an abrupt reciprocal effect on the character of the non-oligarchical part of the distribution. Specifically, we show that the above-mentioned gaussian decay at extremely large wealth is valid both above and below criticality, but degenerates to exponential decay precisely at criticality.

  1. Stochastic theory of polarized light in nonlinear birefringent media: An application to optical rotation

    Science.gov (United States)

    Tsuchida, Satoshi; Kuratsuji, Hiroshi

    2018-05-01

    A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker-Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.

  2. Planck-suppressed operators

    International Nuclear Information System (INIS)

    Assassi, Valentin; Baumann, Daniel; Green, Daniel; McAllister, Liam

    2014-01-01

    We show that the recent Planck limits on primordial non-Gaussianity impose strong constraints on light hidden sector fields coupled to the inflaton via operators suppressed by a high mass scale Λ. We study a simple effective field theory in which a hidden sector field is coupled to a shift-symmetric inflaton via arbitrary operators up to dimension five. Self-interactions in the hidden sector lead to non-Gaussianity in the curvature perturbations. To be consistent with the Planck limit on local non-Gaussianity, the coupling to any hidden sector with light fields and natural cubic couplings must be suppressed by a very high scale Λ > 10 5 H. Even if the hidden sector has Gaussian correlations, nonlinearities in the mixing with the inflaton still lead to non-Gaussian curvature perturbations. In this case, the non-Gaussianity is of the equilateral or orthogonal type, and the Planck data requires Λ > 10 2 H

  3. Integral representation of nonlinear heat transport

    International Nuclear Information System (INIS)

    Kishimoto, Y.; Mima, K.; Haines, M.G.

    1985-07-01

    The electron distribution function in a plasma with steep temperature gradient is obtained from a Fokker-Planck equation by Green's function method. The formula describes the nonlocal effects on thermal transport over the range, λ e /L e /L → 0. As an example, the heat wave is analyzed numerically by the integral formula and it is found that the previous simulation results are well reproduced. (author)

  4. Numerical resolution of N-dimensional Fokker-Plank stochastic equations

    International Nuclear Information System (INIS)

    Garcia-Olivares, A.; Muoz, A.

    1992-01-01

    This document describes the use of a library of programs able to solve stochastic Fokker-Planck equations in a N-dimensional space. the input data are essentially: (i) the initial distribution of the stochastic variable, (ii) the drift and fluctuation coefficients as a function of the state (which can be obtained from the transition probabilities between neighboring states) and (iii) some parameters controlling the run. A last version of the library accepts sources and sinks defined in the states space. The output is the temporal evolution of the probability distribution in the space defined by a N-dimensional grid. Some applications and readings in Synergetics, Self-Organization, transport phenomena, Ecology and other fields are suggested. If the probability distribution is interpreted as a distribution of particles then the codes can be used to solve the N-dimensional problem of advection-diffusion. (author) 21 fig. 16 ref

  5. Application of the Fokker-Plank-Kolmogorov equation for affluence forecast to hydropower reservoirs (Betania Case)

    International Nuclear Information System (INIS)

    Dominguez Calle, Efrain Antonio

    2004-01-01

    This paper shows a modeling technique to forecast probability density curves for the flows that represent the monthly affluence to hydropower reservoirs. Briefly, the factors that require affluence forecast in terms of probabilities, the ranges of existing forecast methods as well as the contradiction between those techniques and the real requirements of decision-making procedures are pointed out. The mentioned contradiction is resolved applying the Fokker-Planck-Kolmogorov equation that describes the time evolution of a stochastic process that can be considered as markovian. We show the numerical scheme for this equation, its initial and boundary conditions, and its application results in the case of Betania's reservoir

  6. Using some results about the Lie evolution of differential operators to obtain the Fokker-Planck equation for non-Hamiltonian dynamical systems of interest

    Science.gov (United States)

    Bianucci, Marco

    2018-05-01

    Finding the generalized Fokker-Planck Equation (FPE) for the reduced probability density function of a subpart of a given complex system is a classical issue of statistical mechanics. Zwanzig projection perturbation approach to this issue leads to the trouble of resumming a series of commutators of differential operators that we show to correspond to solving the Lie evolution of first order differential operators along the unperturbed Liouvillian of the dynamical system of interest. In this paper, we develop in a systematic way the procedure to formally solve this problem. In particular, here we show which the basic assumptions are, concerning the dynamical system of interest, necessary for the Lie evolution to be a group on the space of first order differential operators, and we obtain the coefficients of the so-evolved operators. It is thus demonstrated that if the Liouvillian of the system of interest is not a first order differential operator, in general, the FPE structure breaks down and the master equation contains all the power of the partial derivatives, up to infinity. Therefore, this work shed some light on the trouble of the ubiquitous emergence of both thermodynamics from microscopic systems and regular regression laws at macroscopic scales. However these results are very general and can be applied also in other contexts that are non-Hamiltonian as, for example, geophysical fluid dynamics, where important events, like El Niño, can be considered as large time scale phenomena emerging from the observation of few ocean degrees of freedom of a more complex system, including the interaction with the atmosphere.

  7. Estimations hypoelliptiques globales et compacit\\'e de la r\\'esolvante Estimations hypoelliptiques globales et compacit\\'e de la r\\'esolvante pour des op\\'erateurs de Fokker-Planck ou des laplaciens de Witten

    CERN Document Server

    Helffer, B

    2004-01-01

    Ces derni\\`eres ann\\'ees, les estimations hypoelliptiques ont connu une nouvelle jeunesse en liaison avec des questions provenant de la th\\'eorie cin\\'etique des gaz. Dans cette direction de nombreux auteurs ont en effet eu besoin de d\\'emontrer des estimations maximales pour en d\\'eduire la compacit\\'e de l'op\\'erateur de Fokker-Planck et avoir des estimations sur la r\\'esolvante permettant d'aborder la question du retour \\`a l'\\'equilibre. Dans un article tr\\`es r\\'ecent, F.~H\\'erau et F.~Nier (inspir\\'es par des calculs explicites du livre de Risken) ont mis en \\'evidence les liens \\'etroits entre ces questions et des questions analogues pour un laplacien de Witten. L'\\'etude de ces liens est poursuivie et syst\\'ematis\\'ee dans un livre en pr\\'eparation \\'ecrit en collaboration avec F.~Nier dont nous allons pr\\'esenter quelques aspects ici en pr\\'esentant parfois un \\'eclairage diff\\'erent sur un probl\\`eme qui laisse encore beaucoup de conjectures non r\\'esolues.

  8. Computational physics program of the National MFE Computer Center

    International Nuclear Information System (INIS)

    Mirin, A.A.

    1985-12-01

    The development of numerical models for plasma phenomena and magnetic confinement devices is discussed. The multidimensional Fokker-Planck and transport codes are applied to toroidal mirror and compact toroid devices. Linear and nonlinear resistive magnetohydrodynamics in two and three dimensions are used in the investigation of various fusion devices. 362 refs., 4 tabs

  9. Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems

    Science.gov (United States)

    Marston, J. B.; Hastings, M. B.

    2005-03-01

    The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.

  10. Application of the Green's function method to some nonlinear problems of an electron storage ring

    International Nuclear Information System (INIS)

    Kheifets, S.

    1984-01-01

    One of the most important characteristics of an electron storage ring is the size of the beam. However analytical calculations of beam size are beset with problems and the computational methods and programs which are used to overcome these are inadequate for all problems in which stochastic noise is an essential part. Two examples are, for an electron storage ring, beam-size evaluation including beam-beam interactions, and finding the beam size for a nonlinear machine. The method described should overcome some of the problems. It uses the Green's function method applied to the Fokker-Planck equation governing the distribution function in the phase space of particle motion. The new step is to consider the particle motion in two degrees of freedom rather than in one dimension. The technique is described fully and is then applied to a strong-focusing machine. (U.K.)

  11. The Dynamics of M15: Observations of the Velocity Dispersion Profile and Fokker-Planck Models

    Science.gov (United States)

    Dull, J. D.; Cohn, H. N.; Lugger, P. M.; Murphy, B. W.; Seitzer, P. O.; Callanan, P. J.; Rutten, R. G. M.; Charles, P. A.

    1997-05-01

    We report a new measurement of the velocity dispersion profile within 1' (3 pc) of the center of the globular cluster M15 (NGC 7078), using long-slit spectra from the 4.2 m William Herschel Telescope at La Palma Observatory. We obtained spatially resolved spectra for a total of 23 slit positions during two observing runs. During each run, a set of parallel slit positions was used to map out the central region of the cluster; the position angle used during the second run was orthogonal to that used for the first. The spectra are centered in wavelength near the Ca II infrared triplet at 8650 Å, with a spectral range of about 450 Å. We determined radial velocities by cross-correlation techniques for 131 cluster members. A total of 32 stars were observed more than once. Internal and external comparisons indicate a velocity accuracy of about 4 km s-1. The velocity dispersion profile rises from about σ = 7.2 +/- 1.4 km s-1 near 1' from the center of the cluster to σ = 13.9 +/- 1.8 km s-1 at 20". Inside of 20", the dispersion remains approximately constant at about 10.2 +/- 1.4 km s-1 with no evidence for a sharp rise near the center. This last result stands in contrast with that of Peterson, Seitzer, & Cudworth who found a central velocity dispersion of 25 +/- 7 km s-1, based on a line-broadening measurement. Our velocity dispersion profile is in good agreement with those determined in the recent studies of Gebhardt et al. and Dubath & Meylan. We have developed a new set of Fokker-Planck models and have fitted these to the surface brightness and velocity dispersion profiles of M15. We also use the two measured millisecond pulsar accelerations as constraints. The best-fitting model has a mass function slope of x = 0.9 (where 1.35 is the slope of the Salpeter mass function) and a total mass of 4.9 × 105 M⊙. This model contains approximately 104 neutron stars (3% of the total mass), the majority of which lie within 6" (0.2 pc) of the cluster center. Since the

  12. Response of sliding structures to seismic excitation: bibliographical study

    International Nuclear Information System (INIS)

    Sarh, K.; Duval, C.

    1992-11-01

    Calculation of the seismic response of structures on sliding supports involves the dual problem of ''non-linear'' and ''random'' dynamic behaviour. After a review of the non-linearities common in dynamics, slipping is compared with a hysteresis phenomenon. Simple examples are then used to present the Fokker-Planck equation and the equivalent linearization method. Finally, the methods for modification of the excitation spectrum intended for the engineering calculations are recalled. (authors). 21 figs., 23 refs

  13. Quantization of non-Hamiltonian physical systems

    International Nuclear Information System (INIS)

    Bolivar, A.O.

    1998-09-01

    We propose a general method of quantization of non-Hamiltonian physical systems. Applying it, for example, to a dissipative system coupled to a thermal reservoir described by the Fokker-Planck equation, we are able to obtain the Caldeira-Leggett master equation, the non-linear Schroedinger-Langevin equation and Caldirola-Kanai equation (with an additional term), as particular cases. (author)

  14. Currents driven by electron cyclotron waves

    International Nuclear Information System (INIS)

    Karney, C.F.F.; Fisch, N.J.

    1981-07-01

    Certain aspects of the generation of steady-state currents by electron cyclotron waves are explored. A numerical solution of the Fokker-Planck equation is used to verify the theory of Fisch and Boozer and to extend their results into the nonlinear regime. Relativistic effects on the current generated are discussed. Applications to steady-state tokamak reactors are considered

  15. From a stochastic to a macroscopic approach to brownian motion

    International Nuclear Information System (INIS)

    Bocquet, L.

    1998-01-01

    In this lecture, we examine the dynamics of suspensions of mesoscopic (Brownian) particles in a molecular fluid, starting from first principles. We introduce the technique of multiple time-scales to derive the Fokker-Planck equation for a single, or for a set of interacting Brownian particles, starting from the Liouville equation for the full system (Brownian particles and discrete bath). The limitations of the Fokker-Planck equation will then be emphasized. In particular, we shall point out that under ''standard'' experimental conditions, the Fokker-Planck description cannot be correct and that non-Markovian effects are expected. A microscopic description in the true experimental limit confirms this breakdown and leads to a ''generalized'' (non-Markovian and non-local in velocity space) Fokker-Planck equation, which describes the thermalization of the Brownian particle. (author)

  16. Path integral solutions of the master equation. [Lagrangian function, Ehrenfest-type theorem, Cauchy method, inverse functions

    Energy Technology Data Exchange (ETDEWEB)

    Etim, E; Basili, C [Rome Univ. (Italy). Ist. di Matematica

    1978-08-21

    The lagrangian in the path integral solution of the master equation of a stationary Markov process is derived by application of the Ehrenfest-type theorem of quantum mechanics and the Cauchy method of finding inverse functions. Applied to the non-linear Fokker-Planck equation the authors reproduce the result obtained by integrating over Fourier series coefficients and by other methods.

  17. Finite elements for partial differential equations: An introductory survey

    International Nuclear Information System (INIS)

    Succi, S.

    1988-03-01

    After presentation of the basic ideas behind the theory of the Finite Element Method, the application of the method to three equations of particular interest in Physics and Engineering is discussed in some detail, namely, a one-dimensional Sturm-Liouville problem, a two-dimensional linear Fokker-Planck equation and a two-dimensional nonlinear Navier-Stokes equation. 6 refs, 8 figs

  18. Statistical approach to bistable behaviour of a nonlinear system in a stationary field

    International Nuclear Information System (INIS)

    Luks, A.; Perina, J.; Perinova, V.; Bertolotti, M.; Sibilia, C.

    1984-01-01

    The quantum statistical properties of an elastic scattering process are investigated comprising crossed light beams which are in interaction with a particle (electron) beam treated as ''two-step'' system. Using the master equation and the generalized Fokker-Planck equation techniques, the integrated intensities are characterized by their probability distributions and it is demonstrated that single modes exhibit two-peak bistable behaviour. (author)

  19. Pulse-coupled mixed-mode oscillators: Cluster states and extreme noise sensitivity

    Science.gov (United States)

    Karamchandani, Avinash J.; Graham, James N.; Riecke, Hermann

    2018-04-01

    Motivated by rhythms in the olfactory system of the brain, we investigate the synchronization of all-to-all pulse-coupled neuronal oscillators exhibiting various types of mixed-mode oscillations (MMOs) composed of sub-threshold oscillations (STOs) and action potentials ("spikes"). We focus particularly on the impact of the delay in the interaction. In the weak-coupling regime, we reduce the system to a Kuramoto-type equation with non-sinusoidal phase coupling and the associated Fokker-Planck equation. Its linear stability analysis identifies the appearance of various cluster states. Their type depends sensitively on the delay and the width of the pulses. Interestingly, long delays do not imply slow population rhythms, and the number of emerging clusters only loosely depends on the number of STOs. Direct simulations of the oscillator equations reveal that for quantitative agreement of the weak-coupling theory the coupling strength and the noise have to be extremely small. Even moderate noise leads to significant skipping of STO cycles, which can enhance the diffusion coefficient in the Fokker-Planck equation by two orders of magnitude. Introducing an effective diffusion coefficient extends the range of agreement significantly. Numerical simulations of the Fokker-Planck equation reveal bistability and solutions with oscillatory order parameters that result from nonlinear mode interactions. These are confirmed in simulations of the full spiking model.

  20. Pedestrian Flow in the Mean Field Limit

    KAUST Repository

    Haji Ali, Abdul Lateef

    2012-01-01

    -dependent density of two-dimensional pedestrians satisfies a four-dimensional integro-differential Fokker-Planck equation. To approximate the solution of the Fokker-Planck equation we use a time-splitting approach and solve the diffusion part using a Crank

  1. A Simple Stochastic Differential Equation with Discontinuous Drift

    DEFF Research Database (Denmark)

    Simonsen, Maria; Leth, John-Josef; Schiøler, Henrik

    2013-01-01

    In this paper we study solutions to stochastic differential equations (SDEs) with discontinuous drift. We apply two approaches: The Euler-Maruyama method and the Fokker-Planck equation and show that a candidate density function based on the Euler-Maruyama method approximates a candidate density...... function based on the stationary Fokker-Planck equation. Furthermore, we introduce a smooth function which approximates the discontinuous drift and apply the Euler-Maruyama method and the Fokker-Planck equation with this input. The point of departure for this work is a particular SDE with discontinuous...

  2. Delay-controlled primary and stochastic resonances of the SD oscillator with stiffness nonlinearities

    Science.gov (United States)

    Yang, Tao; Cao, Qingjie

    2018-03-01

    This work presents analytical studies of the stiffness nonlinearities SD (smooth and discontinuous) oscillator under displacement and velocity feedback control with a time delay. The SD oscillator can capture the qualitative characteristics of quasi-zero-stiffness and negative-stiffness. We focus mainly on the primary resonance of the quasi-zero-stiffness SD oscillator and the stochastic resonance (SR) of the negative-stiffness SD oscillator. Using the averaging method, we have been analyzed the amplitude response of the quasi-zero-stiffness SD oscillator. In this regard, the optimum time delay for changing the control intensity according to the optimization standard proposed can be obtained. For the optimum time delay, increasing the displacement feedback intensity is advantageous to suppress the vibrations in resonant regime where vibration isolation is needed, however, increasing the velocity feedback intensity is advantageous to strengthen the vibrations. Moreover, the effects of time-delayed feedback on the SR of the negative-stiffness SD oscillator are investigated under harmonic forcing and Gaussian white noise, based on the Langevin and Fokker-Planck approaches. The time-delayed feedback can enhance the SR phenomenon where vibrational energy harvesting is needed. This paper established the relationship between the parameters and vibration properties of a stiffness nonlinearities SD which provides the guidance for optimizing time-delayed control for vibration isolation and vibrational energy harvesting of the nonlinear systems.

  3. Ergodicity of the Stochastic Nosé-Hoover Heat Bath

    Science.gov (United States)

    Wei Chung Lo,; Baowen Li,

    2010-07-01

    We numerically study the ergodicity of the stochastic Nosé-Hoover heat bath whose formalism is based on the Markovian approximation for the Nosé-Hoover equation [J. Phys. Soc. Jpn. 77 (2008) 103001]. The approximation leads to a Langevin-like equation driven by a fluctuating dissipative force and multiplicative Gaussian white noise. The steady state solution of the associated Fokker-Planck equation is the canonical distribution. We investigate the dynamics of this method for the case of (i) free particle, (ii) nonlinear oscillators and (iii) lattice chains. We derive the Fokker-Planck equation for the free particle and present approximate analytical solution for the stationary distribution in the context of the Markovian approximation. Numerical simulation results for nonlinear oscillators show that this method results in a Gaussian distribution for the particles velocity. We also employ the method as heat baths to study nonequilibrium heat flow in one-dimensional Fermi-Pasta-Ulam (FPU-β) and Frenkel-Kontorova (FK) lattices. The establishment of well-defined temperature profiles are observed only when the lattice size is large. Our results provide numerical justification for such Markovian approximation for classical single- and many-body systems.

  4. Effects of electron-electron interactions on the electron distribution function of a plasma in the presence of an external electric field

    International Nuclear Information System (INIS)

    Molinari, V.G.; Pizzio, F.; Spiga, G.

    1979-01-01

    The electron distribution function, the electron temperature and some transport parameters (electrical conductivity and energy flow coefficient) are obtained starting from the nonlinear Boltzmann equation for a plasma under the action of an external electric field. The Fokker-Planck approximation is used for electron-electron and electron-ion interactions. The effects of electron-electron collisions are studied for different values of collision frequencies and electric field. (author)

  5. Mean-field games with logistic population dynamics

    KAUST Repository

    Gomes, Diogo A.; De Lima Ribeiro, Ricardo

    2013-01-01

    In its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.

  6. Mean-field games with logistic population dynamics

    KAUST Repository

    Gomes, Diogo A.

    2013-12-01

    In its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.

  7. Elementary stochastic cooling

    Energy Technology Data Exchange (ETDEWEB)

    Tollestrup, A.V.; Dugan, G

    1983-12-01

    Major headings in this review include: proton sources; antiproton production; antiproton sources and Liouville, the role of the Debuncher; transverse stochastic cooling, time domain; the accumulator; frequency domain; pickups and kickers; Fokker-Planck equation; calculation of constants in the Fokker-Planck equation; and beam feedback. (GHT)

  8. A continuous stochastic model for non-equilibrium dense gases

    Science.gov (United States)

    Sadr, M.; Gorji, M. H.

    2017-12-01

    While accurate simulations of dense gas flows far from the equilibrium can be achieved by direct simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order to cope with that, an efficient yet accurate solution algorithm based on the Fokker-Planck approximation of the Enskog equation is devised in this paper; the approximation is very much associated with the Fokker-Planck model derived from the Boltzmann equation by Jenny et al. ["A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion," J. Comput. Phys. 229, 1077-1098 (2010)] and Gorji et al. ["Fokker-Planck model for computational studies of monatomic rarefied gas flows," J. Fluid Mech. 680, 574-601 (2011)]. The idea behind these Fokker-Planck descriptions is to project the dynamics of discrete collisions implied by the molecular encounters into a set of continuous Markovian processes subject to the drift and diffusion. Thereby, the evolution of particles representing the governing stochastic process becomes independent from each other and thus very efficient numerical schemes can be constructed. By close inspection of the Enskog operator, it is observed that the dense gas effects contribute further to the advection of molecular quantities. That motivates a modelling approach where the dense gas corrections can be cast in the extra advection of particles. Therefore, the corresponding Fokker-Planck approximation is derived such that the evolution in the physical space accounts for the dense effects present in the pressure, stress tensor, and heat fluxes. Hence the consistency between the devised Fokker-Planck approximation and the Enskog operator is shown for the velocity moments up to the heat fluxes. For validation studies, a homogeneous gas inside a box besides Fourier, Couette, and lid-driven cavity flow setups is considered. The results based on the Fokker-Planck model are

  9. Electron-cyclotron-resonant-heated electron distribution functions

    International Nuclear Information System (INIS)

    Matsuda, Y.; Nevins, W.M.; Cohen, R.H.

    1981-01-01

    Recent studies at Lawrence Livermore National Laboratory (LLNL) with a bounce-averaged Fokker-Planck code indicate that the energetic electron tail formed by electron-cyclotron resonant heating (ECRH) at the second harmonic is not Maxwellian. We present the results of our bounce-averaged Fokker-Planck code along with some simple analytic models of hot-electron distribution functions

  10. Doering et al. reply

    International Nuclear Information System (INIS)

    Doering, C.R.; Bagley, R.J.; Hagan, P.S.; Levermore, C.D.

    1988-01-01

    A reply to the comment on bistability driven by weakly colored gaussian noise is presented.The fokker-planck boundary layer and mean first-passage times are evaluated.It is agreed that there is a difference between the two first-passage times, and that alternative may be more appropriate for quantitative comparison with the low lying spectrum of the Fokker-Planck operator

  11. 77 FR 37337 - Airworthiness Directives; Fokker Services B.V. Airplanes

    Science.gov (United States)

    2012-06-21

    ... corrosion pits. The extent of the corrosion indicates that the initial crack existed for a substantial... SBF100-32- 161, dated April 7, 2011; and Fokker Engineering Report, MRB Appendix 1, SE-623, Issue 8... associated thresholds and intervals described in Fokker Engineering Report, MRB Appendix 1, SE-623, Issue 8...

  12. Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

    Science.gov (United States)

    Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

    2017-07-01

    Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

  13. Planck 2013 results. XXIX. Planck catalogue of Sunyaev-Zeldovich sources

    DEFF Research Database (Denmark)

    Ade, P. A. R.; Aghanim, N.; Armitage-Caplan, C.

    2013-01-01

    We describe the all-sky Planck catalogue of clusters and cluster candidates derived from Sunyaev-Zeldovich (SZ) effect detections using the first 15.5 months of Planck satellite observations. The catalogue contains 1227 entries, making it over six times the size of the Planck Early SZ (ESZ) sampl...

  14. Planck 2015 results. VII. HFI TOI and beam processing

    CERN Document Server

    Adam, R.; Aghanim, N.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartolo, N.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bertincourt, B.; Bielewicz, P.; Bock, J.J.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Boulanger, F.; Bucher, M.; Burigana, C.; Calabrese, E.; Cardoso, J.-F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chary, R.-R.; Chiang, H.C.; Christensen, P.R.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Combet, C.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.-M.; Désert, F.-X.; Diego, J.M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T.A.; Eriksen, H.K.; Falgarone, E.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Ghosh, T.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K.M.; Gratton, S.; Gruppuso, A.; Gudmundsson, J.E.; Hansen, F.K.; Hanson, D.; Harrison, D.L.; Henrot-Versillé, S.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Hurier, G.; Jaffe, A.H.; Jaffe, T.R.; Jones, W.C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lamarre, J.-M.; Lasenby, A.; Lattanzi, M.; Lawrence, C.R.; Le Jeune, M.; Leahy, J.P.; Lellouch, E.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Liguori, M.; Lilje, P.B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P.M.; Macías-Pérez, J.F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Maris, M.; Martin, P.G.; Martínez-González, E.; Masi, S.; Matarrese, S.; McGehee, P.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Moreno, R.; Morgante, G.; Mortlock, D.; Moss, A.; Mottet, S.; Munshi, D.; Murphy, J.A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Nørgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Pearson, T.J.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Pratt, G.W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J.P.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rowan-Robinson, M.; Rusholme, B.; Sandri, M.; Santos, D.; Sauvé, A.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J.A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vibert, L.; Vielva, P.; Villa, F.; Wade, L.A.; Wandelt, B.D.; Watson, R.; Wehus, I.K.; Yvon, D.; Zacchei, A.

    2016-01-01

    The Planck High Frequency Instrument (HFI) has observed the full sky at six frequencies (100, 143, 217, 353, 545, and 857 GHz) in intensity and at four frequencies in linear polarization (100, 143, 217, and 353 GHz). In order to obtain sky maps, the time-ordered information (TOI) containing the detector and pointing samples must be processed and the angular response must be assessed. The full mission TOI is included in the Planck 2015 release. This paper describes the HFI TOI and beam processing for the 2015 release. HFI calibration and map-making are described in a companion paper. The main pipeline has been modified since the last release (2013 nominal mission in intensity only), by including a correction for the non-linearity of the warm readout and by improving the model of the bolometer time response. The beam processing is an essential tool that derives the angular response used in all the Planck science papers and we report an improvement in the effective beam window function uncertainty of more than a...

  15. Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

    2013-01-01

    In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

  16. Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

    Science.gov (United States)

    Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

    2017-08-01

    This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

  17. Einstein and Planck

    Science.gov (United States)

    Heilbron, John

    2005-03-01

    As an editor of the Annalen der Physik, Max Planck published Einstein's early papers on thermodynamics and on special relativity, which Planck probably was the first major physicist to appreciate. They respected one another not only as physicists but also, for their inspired creation of world pictures, as artists. Planck helped to establish Einstein in a sinecure at the center of German physics, Berlin. Despite their differences in scientific style, social life, politics, and religion, they became fast friends. Their mutual admiration survived World War I, during which Einstein advocated pacifism and Planck signed the infamous Manifesto of the 93 Intellectuals supporting the German invasion of Belgium. It also survived the Weimar Republic, which Einstein favored and Planck disliked. Physics drew them together, as both opposed the Copenhagen Interpretation; so did common decency, as Planck helped to protect Einstein from anti-semitic attacks. Their friendship did not survive the Nazis. As a standing secretary of the Berlin Academy, Planck had to advise Einstein to resign from it before his colleagues, outraged at his criticism of the new Germany from the safety of California, expelled him. Einstein never forgave his old friend and former fellow artist for not protesting publicly against his expulsion and denigration, and other enormities of National Socialism. .

  18. Prediction of the behavior of structural materials under irradiation through modeling of the microstructure. Progress report, April 1, 1978-August 30, 1979

    International Nuclear Information System (INIS)

    Wolfer, W.G.

    1979-08-01

    The development of the radiation-induced microstructure occurs in several stages: formation of small defect clusters, formation of dislocation loops, nucleation and growth of voids, and regeneration of the dislocation network. With the exception of the latter, these processes can be modeled with rate equations of similar form. However, instead of using one rate equation for each defect cluster of a given size, the discrete formulation is transformed in a continuous one leading to Fokker-Planck equations. It is shown by comparing the steady-state nucleation rates of both formulations that the Fokker-Planck equation derived is the correct continuous description. A path-integral solution for the Fokker-Planck equation was derived to provide the basis for a numerical solution procedure, capable of dealing with the vastly different time scales involved in cluster formation, nucleation, and growth

  19. Green's function-stochastic methods framework for probing nonlinear evolution problems: Burger's equation, the nonlinear Schroedinger's equation, and hydrodynamic organization of near-molecular-scale vorticity

    International Nuclear Information System (INIS)

    Keanini, R.G.

    2011-01-01

    Research highlights: → Systematic approach for physically probing nonlinear and random evolution problems. → Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. → Organization of near-molecular scale vorticity mediated by hydrodynamic modes. → Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the

  20. Time dependent mean-field games

    KAUST Repository

    Gomes, Diogo A.

    2014-01-06

    We consider time dependent mean-field games (MFG) with a local power-like dependence on the measure and Hamiltonians satisfying both sub and superquadratic growth conditions. We establish existence of smooth solutions under a certain set of conditions depending both on the growth of the Hamiltonian as well as on the dimension. In the subquadratic case this is done by combining a Gagliardo-Nirenberg type of argument with a new class of polynomial estimates for solutions of the Fokker-Planck equation in terms of LrLp- norms of DpH. These techniques do not apply to the superquadratic case. In this setting we recur to a delicate argument that combines the non-linear adjoint method with polynomial estimates for solutions of the Fokker-Planck equation in terms of L1L1-norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of Hamilton-Jacobi equations with superquadratic Hamiltonians.

  1. Planck intermediate results: XLVII. Planck constraints on reionization history

    DEFF Research Database (Denmark)

    Adam, R.; Aghanim, N.; Ashdown, M.

    2016-01-01

    obtain a Thomson optical depth τ = 0.058 ± 0.012 for the commonly adopted instantaneous reionization model. This confirms, with data solely from CMB anisotropies, the low value suggested by combining Planck 2015 results with other data sets, and also reduces the uncertainties. We reconstruct the history......We investigate constraints on cosmic reionization extracted from the Planck cosmic microwave background (CMB) data. We combine the Planck CMB anisotropy data in temperature with the low-multipole polarization data to fit ΛCDM models with various parameterizations of the reionization history. We...

  2. Nonlinear Kinetics on Lattices Based on the Kinetic Interaction Principle

    Directory of Open Access Journals (Sweden)

    Giorgio Kaniadakis

    2018-06-01

    Full Text Available Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker–Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker–Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker–Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker–Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker–Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP that governs the particle kinetics of many body systems, introduced in G. Kaniadakis, Physica A 296, 405 (2001, univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker–Planck equation in its most general form.

  3. Errata: Fokker, a clash of culture

    NARCIS (Netherlands)

    Heerkens, Johannes M.G.; Ulijn, Jan

    2000-01-01

    What role do cultural play in the survival of companies that face existential problems? We try to provide some answers by looking at the decline of the Dutch aircraft manufacturer Fokker. In 1996 this company went bankrupt and among the causes of this event cultural factors rank high, at least at

  4. Designing a logistic control system : dealing with changes in Fokker's sheet metal unit

    NARCIS (Netherlands)

    Gomes, Javier

    2008-01-01

    The following report presents the results of the Logistics Design Project carried out at the sheet metal unit of Stork-Fokker AESP, from October 2007 to March 2008. Stork Fokker AESP designs, develops and produces advanced structures and electrical systems for the aerospace and defense industry. The

  5. Kinetic theory and simulation of multi-species plasmas in tokamaks excited with ICRF microwaves

    International Nuclear Information System (INIS)

    Kerbel, G.D.; McCoy, M.G.

    1984-01-01

    This paper presents a description of a bounce-averaged Fokker-Planck quasilinear model for the kinetic description of tokamak plasmas. The non-linear collision and quasilinear resonant diffusion operators are represented in a form conducive to numerical solution with specific attention to the treatment of the boundary layer separating trapped and passing orbit regions of velocity space. The numerical techniques employed are detailed in so far as they constitute significant departure from those used in the conventional uniform magnetic field case. Examples are given to illustrate the combined effects of collisional and resonant diffusion

  6. Time dependent mean-field games

    KAUST Repository

    Gomes, Diogo A.; Pimentel, Edgard; Sá nchez-Morgado, Hé ctor

    2014-01-01

    In this setting we recur to a delicate argument that combines the non-linear adjoint method with polynomial estimates for solutions of the Fokker-Planck equation in terms of L1L1-norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of Hamilton-Jacobi equations with superquadratic Hamiltonians.

  7. Planck 2013 results. XXVIII. The Planck Catalogue of Compact Sources

    DEFF Research Database (Denmark)

    Planck Collaboration,; Ade, P. A. R.; Aghanim, N.

    2013-01-01

    The Planck Catalogue of Compact Sources (PCCS) is the catalogue of sources detected in the Planck nominal mission data. It consists of nine single-frequency catalogues of compact sources containing reliable sources, both Galactic and extragalactic, detected over the entire sky. The PCCS covers th...

  8. Pedestrian Flow in the Mean Field Limit

    KAUST Repository

    Haji Ali, Abdul Lateef

    2012-11-01

    We study the mean-field limit of a particle-based system modeling the behavior of many indistinguishable pedestrians as their number increases. The base model is a modified version of Helbing\\'s social force model. In the mean-field limit, the time-dependent density of two-dimensional pedestrians satisfies a four-dimensional integro-differential Fokker-Planck equation. To approximate the solution of the Fokker-Planck equation we use a time-splitting approach and solve the diffusion part using a Crank-Nicholson method. The advection part is solved using a Lax-Wendroff-Leveque method or an upwind Backward Euler method depending on the advection speed. Moreover, we use multilevel Monte Carlo to estimate observables from the particle-based system. We discuss these numerical methods, and present numerical results showing the convergence of observables that were calculated using the particle-based model as the number of pedestrians increases to those calculated using the probability density function satisfying the Fokker-Planck equation.

  9. Nernst-Planck modeling of multicomponent ion transport in a Nafion membrane at high current density

    NARCIS (Netherlands)

    Moshtari Khah, S.; Oppers, N.A.W.; de Groot, M.T.; Keurentjes, J.T.F.; Schouten, J.C.; van der Schaaf, J.

    A mathematical model of multicomponent ion transport through a cation-exchange membrane is developed based on the Nernst–Planck equation. A correlation for the non-linear potential gradient is derived from current density relation with fluxes. The boundary conditions are determined with the Donnan

  10. Planck 2013 results. XXIX. Planck catalogue of Sunyaev-Zeldovich sources

    CERN Document Server

    Ade, P.A.R.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Aussel, H.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Barrena, R.; Bartelmann, M.; Bartlett, J.G.; Battaner, E.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bikmaev, I.; Bobin, J.; Bock, J.J.; Bohringer, H.; Bonaldi, A.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Bridges, M.; Bucher, M.; Burenin, R.; Burigana, C.; Butler, R.C.; Cardoso, J.F.; Carvalho, P.; Catalano, A.; Challinor, A.; Chamballu, A.; Chary, R.R.; Chen, X.; Chiang, L.Y.; Chiang, H.C.; Chon, G.; Christensen, P.R.; Churazov, E.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Comis, B.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Da Silva, A.; Dahle, H.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.M.; Democles, J.; Desert, F.X.; Dickinson, C.; Diego, J.M.; Dolag, K.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Dupac, X.; Efstathiou, G.; Ensslin, T.A.; Eriksen, H.K.; Feroz, F.; Finelli, F.; Flores-Cacho, I.; Forni, O.; Frailis, M.; Franceschi, E.; Fromenteau, S.; Galeotta, S.; Ganga, K.; Genova-Santos, R.T.; Giard, M.; Giardino, G.; Gilfanov, M.; Giraud-Heraud, Y.; Gonzalez-Nuevo, J.; Gorski, K.M.; Grainge, K.J.B.; Gratton, S.; Gregorio, A.; N, E.Groeneboom; Gruppuso, A.; Hansen, F.K.; Hanson, D.; Harrison, D.; Hempel, A.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Hurier, G.; Hurley-Walker, N.; Jaffe, T.R.; Jaffe, A.H.; Jones, W.C.; Juvela, M.; Keihanen, E.; Keskitalo, R.; Khamitov, I.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Laureijs, R.J.; Lawrence, C.R.; Leahy, J.P.; Leonardi, R.; Leon-Tavares, J.; Lesgourgues, J.; Li, C.; Liddle, A.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lopez-Caniego, M.; Lubin, P.M.; Macias-Perez, J.F.; MacTavish, C.J.; Maffei, B.; Maino, D.; Mandolesi, N.; Maris, M.; Marshall, D.J.; Martin, P.G.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; Matthai, F.; Mazzotta, P.; Mei, S.; Meinhold, P.R.; Melchiorri, A.; Melin, J.B.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschenes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Munshi, D.; Naselsky, P.; Nati, F.; Natoli, P.; Nesvadba, N.P.H.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; O'Dwyer, I.J.; Olamaie, M.; Osborne, S.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Pearson, T.J.; Perdereau, O.; Perotto, L.; Perrott, Y.C.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Reach, W.T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rowan-Robinson, M.; Rubino-Martin, J.A.; Rumsey, C.; Rusholme, B.; Sandri, M.; Santos, D.; Saunders, R.D.E.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Shimwell, T.W.; Spencer, L.D.; Starck, J.L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Turler, M.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vibert, L.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L.A.; Wandelt, B.D.; White, M.; White, S.D.M.; Yvon, D.; Zacchei, A.; Zonca, A.

    2014-01-01

    We describe the all-sky Planck catalogue of clusters and cluster candidates derived from Sunyaev--Zeldovich (SZ) effect detections using the first 15.5 months of Planck satellite observations. The catalogue contains 1227 entries, making it over six times the size of the Planck Early SZ (ESZ) sample and the largest SZ-selected catalogue to date. It contains 861 confirmed clusters, of which 178 have been confirmed as clusters, mostly through follow-up observations, and a further 683 are previously-known clusters. The remaining 366 have the status of cluster candidates, and we divide them into three classes according to the quality of evidence that they are likely to be true clusters. The Planck SZ catalogue is the deepest all-sky cluster catalogue, with redshifts up to about one, and spans the broadest cluster mass range from (0.1 to 1.6) 10^{15}Msun. Confirmation of cluster candidates through comparison with existing surveys or cluster catalogues is extensively described, as is the statistical characterization...

  11. Isostable reduction with applications to time-dependent partial differential equations.

    Science.gov (United States)

    Wilson, Dan; Moehlis, Jeff

    2016-07-01

    Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to 1. We illustrate the utility of this reduction by applying it to two different models with biological relevance. In the first example, isostable reduction of the Fokker-Planck equation provides the necessary framework to design a simple control strategy to desynchronize a population of pathologically synchronized oscillatory neurons, as might be relevant to Parkinson's disease. Another example analyzes a nonlinear reaction-diffusion equation with relevance to action potential propagation in a cardiac system.

  12. The effect of an alternating electric field on a totally ionised plasma; Action d'un champ electrique alternatif sur un plasma totalement ionise

    Energy Technology Data Exchange (ETDEWEB)

    Baglin, H; Brin, A; Ozias, Y; Salmon, J [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires; Delcroix, J L [Ecole Normale Superieure, 75 - Paris (France)

    1960-07-01

    The equation giving the distribution function of the electrons in a steady-state, for a fully ionized plasma in an a.c. field, are provided from the Fokker-Planck equation. The electric conductivity is complex and depends on the frequency. (author) [French] L'equation qui donne la fonction de distribution des electrons dans un etat stationnaire pour un plasma totalement ionise dans un champ electrique alternatif est fournie par l'equation de Fokker-Planck. La conductibilite electrique est complexe et depend de la frequence. (auteur)

  13. A Planck Vacuum Cosmology

    Directory of Open Access Journals (Sweden)

    Daywitt W. C.

    2009-04-01

    Full Text Available Both the big-bang and the quasi-steady-state cosmologies originate in some type of Planck state. This paper presents a new cosmological theory based on the Planck- vacuum negative-energy state, a state consisting of a degenerate collection of negative- energy Planck particles. A heuristic look at the Einstein field equation provides a con- vincing argument that such a vacuum state could provide a theoretical explanation for the visible universe.

  14. Planck 2015 results. XXVIII. The Planck Catalogue of Galactic Cold Clumps

    CERN Document Server

    Ade, P.A.R.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartolo, N.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Boulanger, F.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Catalano, A.; Chamballu, A.; Chiang, H.C.; Christensen, P.R.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Combet, C.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Désert, F.-X.; Dickinson, C.; Diego, J.M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T.A.; Eriksen, H.K.; Falgarone, E.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J.E.; Hansen, F.K.; Hanson, D.; Harrison, D.L.; Helou, G.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Hurier, G.; Jaffe, A.H.; Jaffe, T.R.; Jones, W.C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T.S.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lamarre, J.-M.; Lasenby, A.; Lattanzi, M.; Lawrence, C.R.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Liguori, M.; Lilje, P.B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P.M.; Macías-Pérez, J.F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Marshall, D.J.; Martin, P.G.; Martínez-González, E.; Masi, S.; Matarrese, S.; Mazzotta, P.; McGehee, P.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J.A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Nørgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paladini, R.; Paoletti, D.; Pasian, F.; Patanchon, G.; Pearson, T.J.; Pelkonen, V.-M.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Pratt, G.W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J.P.; Reach, W.T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rubiño-Martín, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Stolyarov, V.; Sudiwala, R.; Sunyaev, R.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J.A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vielva, P.; Villa, F.; Wade, L.A.; Wandelt, B.D.; Wehus, I.K.; Yvon, D.; Zacchei, A.

    2016-01-01

    We present the Planck Catalogue of Galactic Cold Clumps (PGCC), an all-sky catalogue of Galactic cold clump candidates detected by Planck. This catalogue is the full version of the Early Cold Core (ECC) catalogue, which was made available in 2011 with the Early Release Compact Source Catalogue (ERCSC) and contained 915 high S/N sources. It is based on the Planck 48 months mission data that are currently being released to the astronomical community. The PGCC catalogue is an observational catalogue consisting exclusively of Galactic cold sources. The three highest Planck bands (857, 545, 353 GHz) have been combined with IRAS data at 3 THz to perform a multi-frequency detection of sources colder than their local environment. After rejection of possible extragalactic contaminants, the PGCC catalogue contains 13188 Galactic sources spread across the whole sky, i.e., from the Galactic plane to high latitudes, following the spatial distribution of the main molecular cloud complexes. The median temperature of PGCC so...

  15. The development of a Krook model for nonlocal transport in laser produced plasmas. II. Application of the theory and comparisons with other models

    International Nuclear Information System (INIS)

    Colombant, Denis; Manheimer, Wallace

    2008-01-01

    This paper incorporates the Krook model for nonlocal transport into a fluid simulation. It uses these fluid simulations to compare with Fokker-Planck simulations and also with a recent NRL NIKE [S. P. Obenschain et al., Phys. Plasmas 3, 2098 (1996)] experiment. The paper also examines several other models for electron energy transport that have been used in laser fusion research. With regards to the comparison with Fokker-Planck simulation, the Krook model gives better agreement, especially in the time asymptotic limit. With regards to the NRL experiment, all models except one give reasonable agreement

  16. Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation

    Institute of Scientific and Technical Information of China (English)

    Xie Wen-Xian; Xu Wei; Cai Li

    2007-01-01

    This paper shows the Fokker-Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time τ and coloured cross-correlation strength λ.

  17. Max Planck in the Social Context

    International Nuclear Information System (INIS)

    Broda, E.

    1983-01-01

    Planck was the founder of quantum theory, and therefore of modern physics. Moreover, because of the strength of his character and of his towering position in scientific life he had strong public influence. In respect to atomistics Planck went over from the negative position of Mach to the positive position of Boltzmann when he established his radiation law and introduced the quantum of action. Einstein was a supporter of atomistics all his life. From the beginning, Planck furthered the Theory of Relativity and Einstein. In the Weimar Republic he supported Einstein against the socalled 'German Physics'. Planck had the courage to praise Einstein in public even after Hitler came to power. Always interested in philosophy, Planck was initially under the influence of Mach's positivism, but later he turned, like Einstein, to realism. Boltzmann had always been arealist and materialist. Planck produced important ideas also on the problem of Free Will. In politics, Planck was a conventional, conservative, PrussianGerman patriot before the First War. However, under Hitler he became reserved towards the State. As well as he could, but with little success, Planck tried to prevent the worst. Planck was always religious, and he ascribed a strong role to religion also in public life. But he did not accept a personal, and therefore not a Christian, God. An attempt is made to interpret Planck's contradictory position in this respect. Planck's life was full of professional success, but it was tragically darkened by personal blows of fate. A relationship with the path of Germany and of her conservative intellectual leadership is sought. (author) [de

  18. Planck 2013 results. XXVIII. The Planck Catalogue of Compact Sources

    CERN Document Server

    Ade, P.A.R.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartlett, J.G.; Battaner, E.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J.J.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R.C.; Cardoso, J.F.; Carvalho, P.; Catalano, A.; Challinor, A.; Chamballu, A.; Chen, X.; Chiang, L.Y.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clemens, M.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.M.; Desert, F.X.; Dickinson, C.; Diego, J.M.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Dupac, X.; Efstathiou, G.; Ensslin, T.A.; Eriksen, H.K.; Finelli, F.; Forni, O.; Frailis, M.; Franceschi, E.; Galeotta, S.; Ganga, K.; Giard, M.; Giardino, G.; Giraud-Heraud, Y.; Gonzalez-Nuevo, J.; Gorski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Hansen, F.K.; Hanson, D.; Harrison, D.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Jaffe, T.R.; Jaffe, A.H.; Jones, W.C.; Juvela, M.; Keihanen, E.; Keskitalo, R.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Laureijs, R.J.; Lawrence, C.R.; Leahy, J.P.; Leonardi, R.; Leon-Tavares, J.; Leroy, C.; Lesgourgues, J.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lopez-Caniego, M.; Lubin, P.M.; Macias-Perez, J.F.; Maffei, B.; Maino, D.; Mandolesi, N.; Maris, M.; Marshall, D.J.; Martin, P.G.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; Matthai, F.; Mazzotta, P.; McGehee, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschenes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Munshi, D.; Naselsky, P.; Nati, F.; Natoli, P.; Negrello, M.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; O'Dwyer, I.J.; Osborne, S.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paladini, R.; Paoletti, D.; Partridge, B.; Pasian, F.; Patanchon, G.; Pearson, T.J.; Perdereau, O.; Perotto, L.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Reach, W.T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rowan-Robinson, M.; Rubino-Martin, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savini, G.; Schammel, M.P.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Starck, J.L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Turler, M.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Varis, J.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L.A.; Walter, B.; Wandelt, B.D.; Yvon, D.; Zacchei, A.; Zonca, A.

    2014-01-01

    The Planck Catalogue of Compact Sources (PCCS) is the catalogue of sources detected in the first 15 months of Planck operations, the "nominal" mission. It consists of nine single-frequency catalogues of compact sources, both Galactic and extragalactic, detected over the entire sky. The PCCS covers the frequency range 30--857\\,GHz with higher sensitivity (it is 90% complete at 180 mJy in the best channel) and better angular resolution (from ~33' to ~5') than previous all-sky surveys in this frequency band. By construction its reliability is >80% and more than 65% of the sources have been detected at least in two contiguous Planck channels. In this paper we present the construction and validation of the PCCS, its contents and its statistical characterization.

  19. Planck intermediate results XXV. The Andromeda galaxy as seen by Planck

    DEFF Research Database (Denmark)

    Ade, P. A. R.; Aghanim, N.; Arnaud, M.

    2015-01-01

    The Andromeda galaxy (M 31) is one of a few galaxies that has sufficient angular size on the sky to be resolved by the Planck satellite. Planck has detected M 31 in all of its frequency bands, and has mapped out the dust emission with the High Frequency Instrument, clearly resolving multiple spir...

  20. Proceedings of eighth joint workshop on electron cyclotron emission and electron cyclotron resonance heating. Vol. 1

    International Nuclear Information System (INIS)

    1993-03-01

    The theory of electron cyclotron resonance phenomena is highly developed. The main theoretical tools are well established, generally accepted and able to give a satisfactory description of the main results obtained in electron cyclotron emission, absorption and current drive experiments. In this workshop some advanced theoretical and numerical tools have been presented (e.g., 3-D Fokker-Planck codes, treatment of the r.f. beam as a whole, description of non-linear and finite-beam effects) together with the proposal for new scenarios for ECE and ECA measurements (e.g., for diagnosing suprathermal populations and their radial transport). (orig.)

  1. The exact fundamental solution for the Benes tracking problem

    Science.gov (United States)

    Balaji, Bhashyam

    2009-05-01

    The universal continuous-discrete tracking problem requires the solution of a Fokker-Planck-Kolmogorov forward equation (FPKfe) for an arbitrary initial condition. Using results from quantum mechanics, the exact fundamental solution for the FPKfe is derived for the state model of arbitrary dimension with Benes drift that requires only the computation of elementary transcendental functions and standard linear algebra techniques- no ordinary or partial differential equations need to be solved. The measurement process may be an arbitrary, discrete-time nonlinear stochastic process, and the time step size can be arbitrary. Numerical examples are included, demonstrating its utility in practical implementation.

  2. Proceedings of eighth joint workshop on electron cyclotron emission and electron cyclotron resonance heating. Vol. 2

    International Nuclear Information System (INIS)

    1993-03-01

    The theory of electron cyclotron resonance phenomena is highly developed. The main theoretical tools are well established, generally accepted and able to give a satisfactory description of the main results obtained in electron cyclotron emission, absorption and current drive experiments. In this workshop some advanced theoretical and numerical tools have been presented (e.g., 3-D Fokker-Planck codes, treatment of the r.f. beam as a whole, description of non-linear and finite-beam effects) together with the proposal for new scenarios for ECE and ECA measurements (e.g., for diagnosing suprathermal populations and their radial transport). (orig.)

  3. Noise-induced modulation of the relaxation kinetics around a non-equilibrium steady state of non-linear chemical reaction networks.

    Science.gov (United States)

    Ramaswamy, Rajesh; Sbalzarini, Ivo F; González-Segredo, Nélido

    2011-01-28

    Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF) of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM) or fluorescence-correlation spectroscopy (FCS) to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.

  4. Max Planck in the Social Context

    Energy Technology Data Exchange (ETDEWEB)

    Broda, E.

    1983-07-01

    Planck was the founder of quantum theory, and therefore of modern physics. Moreover, because of the strength of his character and of his towering position in scientific life he had strong public influence. In respect to atomistics Planck went over from the negative position of Mach to the positive position of Boltzmann when he established his radiation law and introduced the quantum of action. Einstein was a supporter of atomistics all his life. From the beginning, Planck furthered the Theory of Relativity and Einstein. In the Weimar Republic he supported Einstein against the socalled 'German Physics'. Planck had the courage to praise Einstein in public even after Hitler came to power. Always interested in philosophy, Planck was initially under the influence of Mach's positivism, but later he turned, like Einstein, to realism. Boltzmann had always been arealist and materialist. Planck produced important ideas also on the problem of Free Will. In politics, Planck was a conventional, conservative, PrussianGerman patriot before the First War. However, under Hitler he became reserved towards the State. As well as he could, but with little success, Planck tried to prevent the worst. Planck was always religious, and he ascribed a strong role to religion also in public life. But he did not accept a personal, and therefore not a Christian, God. An attempt is made to interpret Planck's contradictory position in this respect. Planck's life was full of professional success, but it was tragically darkened by personal blows of fate. A relationship with the path of Germany and of her conservative intellectual leadership is sought. (author) [German] Planck war der Begründer der Quantentheorie und daher der modernen Physik. Außerdem hatte er sowohl durch die Kraft seines Charakters als auch durch seine überragenden Funktionen im wissenschaftlichen Leben starken öffentlichen Einfluß. In Bezug auf die Stellung zur Atomistik ging Planck, als er sein Strahlungsgesetz begr

  5. Stochastic dynamics of an inflationary model and initial distribution of universes

    International Nuclear Information System (INIS)

    Nambu, Yasusada.

    1989-01-01

    We investigate the stationary solution of the modified Fokker-Planck equation which governs the global dynamics of the inflation. Contrary to the original FP equation which is for a Hubble horizon size region, we found that the normalizable stationary solution can exist for modified Fokker-Planck equation which is for many Hubble horizon size regions. For a chaotic inflationary model with the potential λψ 2n , we get initial distribution of classical universes using this solution, and discussed the physical meaning of it. Especially for n = 2, this distribution obeys power-law and classical universes which created from the Planck energy region make the fractal structure. Other cases n ≠ 2, creation of large classical universes are strongly suppressed. (author)

  6. Analyzing Planck and low redshift data sets with advanced statistical methods

    Science.gov (United States)

    Eifler, Tim

    The recent ESA/NASA Planck mission has provided a key data set to constrain cosmology that is most sensitive to physics of the early Universe, such as inflation and primordial NonGaussianity (Planck 2015 results XIII). In combination with cosmological probes of the LargeScale Structure (LSS), the Planck data set is a powerful source of information to investigate late time phenomena (Planck 2015 results XIV), e.g. the accelerated expansion of the Universe, the impact of baryonic physics on the growth of structure, and the alignment of galaxies in their dark matter halos. It is the main objective of this proposal to re-analyze the archival Planck data, 1) with different, more recently developed statistical methods for cosmological parameter inference, and 2) to combine Planck and ground-based observations in an innovative way. We will make the corresponding analysis framework publicly available and believe that it will set a new standard for future CMB-LSS analyses. Advanced statistical methods, such as the Gibbs sampler (Jewell et al 2004, Wandelt et al 2004) have been critical in the analysis of Planck data. More recently, Approximate Bayesian Computation (ABC, see Weyant et al 2012, Akeret et al 2015, Ishida et al 2015, for cosmological applications) has matured to an interesting tool in cosmological likelihood analyses. It circumvents several assumptions that enter the standard Planck (and most LSS) likelihood analyses, most importantly, the assumption that the functional form of the likelihood of the CMB observables is a multivariate Gaussian. Beyond applying new statistical methods to Planck data in order to cross-check and validate existing constraints, we plan to combine Planck and DES data in a new and innovative way and run multi-probe likelihood analyses of CMB and LSS observables. The complexity of multiprobe likelihood analyses scale (non-linearly) with the level of correlations amongst the individual probes that are included. For the multi

  7. A comparison of non-local electron transport models relevant to inertial confinement fusion

    Science.gov (United States)

    Sherlock, Mark; Brodrick, Jonathan; Ridgers, Christopher

    2017-10-01

    We compare the reduced non-local electron transport model developed by Schurtz et al. to Vlasov-Fokker-Planck simulations. Two new test cases are considered: the propagation of a heat wave through a high density region into a lower density gas, and a 1-dimensional hohlraum ablation problem. We find the reduced model reproduces the peak heat flux well in the ablation region but significantly over-predicts the coronal preheat. The suitability of the reduced model for computing non-local transport effects other than thermal conductivity is considered by comparing the computed distribution function to the Vlasov-Fokker-Planck distribution function. It is shown that even when the reduced model reproduces the correct heat flux, the distribution function is significantly different to the Vlasov-Fokker-Planck prediction. Two simple modifications are considered which improve agreement between models in the coronal region. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  8. Planck 2013 results. XXXI. Consistency of the Planck data

    CERN Document Server

    Ade, P A R; Ashdown, M; Aumont, J; Baccigalupi, C; Banday, A.J; Barreiro, R.B; Battaner, E; Benabed, K; Benoit-Levy, A; Bernard, J.P; Bersanelli, M; Bielewicz, P; Bond, J.R; Borrill, J; Bouchet, F.R; Burigana, C; Cardoso, J.F; Catalano, A; Challinor, A; Chamballu, A; Chiang, H.C; Christensen, P.R; Clements, D.L; Colombi, S; Colombo, L.P.L; Couchot, F; Coulais, A; Crill, B.P; Curto, A; Cuttaia, F; Danese, L; Davies, R.D; Davis, R.J; de Bernardis, P; de Rosa, A; de Zotti, G; Delabrouille, J; Desert, F.X; Dickinson, C; Diego, J.M; Dole, H; Donzelli, S; Dore, O; Douspis, M; Dupac, X; Ensslin, T.A; Eriksen, H.K; Finelli, F; Forni, O; Frailis, M; Fraisse, A A; Franceschi, E; Galeotta, S; Ganga, K; Giard, M; Gonzalez-Nuevo, J; Gorski, K.M.; Gratton, S.; Gregorio, A; Gruppuso, A; Gudmundsson, J E; Hansen, F.K; Hanson, D; Harrison, D; Henrot-Versille, S; Herranz, D; Hildebrandt, S.R; Hivon, E; Hobson, M; Holmes, W.A.; Hornstrup, A; Hovest, W.; Huffenberger, K.M; Jaffe, T.R; Jaffe, A.H; Jones, W.C; Keihanen, E; Keskitalo, R; Knoche, J; Kunz, M; Kurki-Suonio, H; Lagache, G; Lahteenmaki, A; Lamarre, J.M; Lasenby, A; Lawrence, C.R; Leonardi, R; Leon-Tavares, J; Lesgourgues, J; Liguori, M; Lilje, P.B; Linden-Vornle, M; Lopez-Caniego, M; Lubin, P.M; Macias-Perez, J.F; Maino, D; Mandolesi, N; Maris, M; Martin, P.G; Martinez-Gonzalez, E; Masi, S; Matarrese, S; Mazzotta, P; Meinhold, P.R; Melchiorri, A; Mendes, L; Mennella, A; Migliaccio, M; Mitra, S; Miville-Deschenes, M.A; Moneti, A; Montier, L; Morgante, G; Mortlock, D; Moss, A; Munshi, D; Murphy, J A; Naselsky, P; Nati, F; Natoli, P; Norgaard-Nielsen, H.U; Noviello, F; Novikov, D; Novikov, I; Oxborrow, C.A; Pagano, L; Pajot, F; Paoletti, D; Partridge, B; Pasian, F; Patanchon, G; Pearson, D; Pearson, T.J; Perdereau, O; Perrotta, F; Piacentini, F; Piat, M; Pierpaoli, E; Pietrobon, D; Plaszczynski, S; Pointecouteau, E; Polenta, G; Ponthieu, N; Popa, L; Pratt, G.W; Prunet, S; Puget, J.L; Rachen, J.P; Reinecke, M; Remazeilles, M; Renault, C; Ricciardi, S.; Ristorcelli, I; Rocha, G.; Roudier, G; Rubino-Martin, J.A; Rusholme, B; Sandri, M; Scott, D; Stolyarov, V; Sudiwala, R; Sutton, D; Suur-Uski, A.S; Sygnet, J.F; Tauber, J.A; Terenzi, L; Toffolatti, L; Tomasi, M; Tristram, M; Tucci, M; Valenziano, L; Valiviita, J; Van Tent, B; Vielva, P; Villa, F; Wade, L.A; Wandelt, B.D; Wehus, I K; White, S D M; Yvon, D; Zacchei, A; Zonca, A

    2014-01-01

    The Planck design and scanning strategy provide many levels of redundancy that can be exploited to provide tests of internal consistency. One of the most important is the comparison of the 70 GHz (amplifier) and 100 GHz (bolometer) channels. Based on different instrument technologies, with feeds located differently in the focal plane, analysed independently by different teams using different software, and near the minimum of diffuse foreground emission, these channels are in effect two different experiments. The 143 GHz channel has the lowest noise level on Planck, and is near the minimum of unresolved foreground emission. In this paper, we analyse the level of consistency achieved in the 2013 Planck data. We concentrate on comparisons between the 70, 100, and 143 GHz channel maps and power spectra, particularly over the angular scales of the first and second acoustic peaks, on maps masked for diffuse Galactic emission and for strong unresolved sources. Difference maps covering angular scales from 8°...

  9. Planck 2013 results. XXXII. The updated Planck catalogue of Sunyaev-Zeldovich sources

    DEFF Research Database (Denmark)

    Ade, P. A. R.; Aghanim, N.; Armitage-Caplan, C.

    2015-01-01

    We update the all-sky Planck catalogue of 1227 clusters and cluster candidates (PSZ1) published in March 2013, derived from detections of the Sunyaev-Zeldovich (SZ) effect using the first 15.5 months of Planck satellite observations. As an addendum, we deliver an updated version of the PSZ1 catal...

  10. Strong plasma shock structures based on the Navier--Stokes equations

    International Nuclear Information System (INIS)

    Abe, K.

    1975-01-01

    The structure of a plasma collisional shock wave is examined on the basis of the Navier--Stokes equations and simultaneously on the basis of the Fokker--Planck equation. The resultant structures are compared to check the validity of the Navier--Stokes equations applied to the structures of strong shock waves. The Navier--Stokes equations give quite correct structures for weak shock waves. For the strong shock waves, the detailed structures obtained from the Navier--Stokes equations differ from the results of the Fokker--Planck equation, but the shock thicknesses of the two shock waves are in relatively close agreement

  11. External non-white noise and nonequilibrium phase transitions

    International Nuclear Information System (INIS)

    Sancho, J.M.; San Miguel, M.

    1980-01-01

    Langevin equations with external non-white noise are considered. A Fokker Planck equation valid in general in first order of the correlation time tau of the noise is derived. In some cases its validity can be extended to any value of tau. The effect of a finite tau in the nonequilibrium phase transitions induced by the noise is analyzed, by means of such Fokker Planck equation, in general, for the Verhulst equation under two different kind of fluctuations, and for a genetic model. It is shown that new transitions can appear and that the threshold value of the parameter can be changed. (orig.)

  12. Planck 2013 results. XXXII. The updated Planck catalogue of Sunyaev-Zeldovich sources

    Science.gov (United States)

    Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Aussel, H.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Barrena, R.; Bartelmann, M.; Bartlett, J. G.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bikmaev, I.; Bobin, J.; Bock, J. J.; Böhringer, H.; Bonaldi, A.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Bridges, M.; Bucher, M.; Burenin, R.; Burigana, C.; Butler, R. C.; Cardoso, J.-F.; Carvalho, P.; Catalano, A.; Challinor, A.; Chamballu, A.; Chary, R.-R.; Chen, X.; Chiang, H. C.; Chiang, L.-Y.; Chon, G.; Christensen, P. R.; Churazov, E.; Church, S.; Clements, D. L.; Colombi, S.; Colombo, L. P. L.; Comis, B.; Couchot, F.; Coulais, A.; Crill, B. P.; Curto, A.; Cuttaia, F.; Da Silva, A.; Dahle, H.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.-M.; Démoclès, J.; Désert, F.-X.; Dickinson, C.; Diego, J. M.; Dolag, K.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Dupac, X.; Efstathiou, G.; Enßlin, T. A.; Eriksen, H. K.; Feroz, F.; Ferragamo, A.; Finelli, F.; Flores-Cacho, I.; Forni, O.; Frailis, M.; Franceschi, E.; Fromenteau, S.; Galeotta, S.; Ganga, K.; Génova-Santos, R. T.; Giard, M.; Giardino, G.; Gilfanov, M.; Giraud-Héraud, Y.; González-Nuevo, J.; Górski, K. M.; Grainge, K. J. B.; Gratton, S.; Gregorio, A.; Groeneboom, N., E.; Gruppuso, A.; Hansen, F. K.; Hanson, D.; Harrison, D.; Hempel, A.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huffenberger, K. M.; Hurier, G.; Hurley-Walker, N.; Jaffe, A. H.; Jaffe, T. R.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Khamitov, I.; Kisner, T. S.; Kneissl, R.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Laureijs, R. J.; Lawrence, C. R.; Leahy, J. P.; Leonardi, R.; León-Tavares, J.; Lesgourgues, J.; Li, C.; Liddle, A.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P. M.; Macías-Pérez, J. F.; MacTavish, C. J.; Maffei, B.; Maino, D.; Mandolesi, N.; Maris, M.; Marshall, D. J.; Martin, P. G.; Martínez-González, E.; Masi, S.; Massardi, M.; Matarrese, S.; Matthai, F.; Mazzotta, P.; Mei, S.; Meinhold, P. R.; Melchiorri, A.; Melin, J.-B.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mikkelsen, K.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Nastasi, A.; Nati, F.; Natoli, P.; Nesvadba, N. P. H.; Netterfield, C. B.; Nørgaard-Nielsen, H. U.; Noviello, F.; Novikov, D.; Novikov, I.; O'Dwyer, I. J.; Olamaie, M.; Osborne, S.; Oxborrow, C. A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Pearson, T. J.; Perdereau, O.; Perotto, L.; Perrott, Y. C.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G. W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J. P.; Reach, W. T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rowan-Robinson, M.; Rubiño-Martín, J. A.; Rumsey, C.; Rusholme, B.; Sandri, M.; Santos, D.; Saunders, R. D. E.; Savini, G.; Schammel, M. P.; Scott, D.; Seiffert, M. D.; Shellard, E. P. S.; Shimwell, T. W.; Spencer, L. D.; Starck, J.-L.; Stolyarov, V.; Stompor, R.; Streblyanska, A.; Sudiwala, R.; Sunyaev, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tramonte, D.; Tristram, M.; Tucci, M.; Tuovinen, J.; Türler, M.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vibert, L.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L. A.; Wandelt, B. D.; White, M.; White, S. D. M.; Yvon, D.; Zacchei, A.; Zonca, A.

    2015-09-01

    We update the all-sky Planck catalogue of 1227 clusters and cluster candidates (PSZ1) published in March 2013, derived from detections of the Sunyaev-Zeldovich (SZ) effect using the first 15.5 months of Planck satellite observations. As an addendum, we deliver an updated version of the PSZ1 catalogue, reporting the further confirmation of 86 Planck-discovered clusters. In total, the PSZ1 now contains 947 confirmed clusters, of which 214 were confirmed as newly discovered clusters through follow-up observations undertaken by the Planck Collaboration. The updated PSZ1 contains redshifts for 913 systems, of which 736 (~ 80.6%) are spectroscopic, and associated mass estimates derived from the Yz mass proxy. We also provide a new SZ quality flag for the remaining 280 candidates. This flag was derived from a novel artificial neural-network classification of the SZ signal. Based on this assessment, the purity of the updated PSZ1 catalogue is estimated to be 94%. In this release, we provide the full updated catalogue and an additional readme file with further information on the Planck SZ detections. The catalogue is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/581/A14

  13. Localizability and the planck mass

    International Nuclear Information System (INIS)

    Ne'eman, Y.; Univ. of Texas, Austin, TX

    1993-06-01

    The author combines the assumption of environmental decoherence, as the mechanism generating the classical (i.e. no quantum interferences) nature of spacetime, with the limit on its other classical feature, point-like continuity, namely Planck length. As a result, quantum extended objects with masses larger than Planck mass have to derive their quantum behavior from long-range correlations; objects with masses smaller than Planck mass cannot display classical behavior

  14. Planck 2013 Cosmology Results: a Review

    Directory of Open Access Journals (Sweden)

    José Alberto Rubino-Martín

    2014-12-01

    Full Text Available This talk presents an overview of the cosmological results derived from the first 15.5 months of observations of the ESA’s Planck mission. These cosmological results are mainly based on the Planck measurements of the cosmic microwave background (CMB temperature and lensing-potential power spectra, although we also briefly discuss other aspects of the Planck data, as the statistical characterization of the reconstructed CMB maps, or the constraints on cosmological parameters using the number counts of galaxy clusters detected by means of the Sunyaev-Zeldovich effect in the Planck maps. All these results are described in detail in a series of papers released by ESA and the Planck collaboration in March 2013.

  15. Planck 2015 results: XXVI. The Second Planck Catalogue of Compact Sources

    DEFF Research Database (Denmark)

    Ade, P. A R; Aghanim, N.; Arguëso, F.

    2016-01-01

    The Second Planck Catalogue of Compact Sources is a list of discrete objects detected in single-frequency maps from the full duration of the Planck mission and supersedes previous versions. It consists of compact sources, both Galactic and extragalactic, detected over the entire sky. Compact sour...

  16. Development of a Generalized Version of the Poisson-Nernst-Planck Equations Using the Hybrid Mixture Theory: Presentation of 2D Numerical Examples

    DEFF Research Database (Denmark)

    Johannesson, Björn

    2010-01-01

    A numerical scheme for the transient solution of generalized version of the Poisson-Nernst-Planck equations is presented. The finite element method is used to establish the coupled non-linear matrix system of equations capable of solving the present problem iteratively. The Poisson......-scale and that it includes the volume fractions of phases in its structure. The background to the Poisson-Nernst-Planck equations can by the HMT approach be described by using the postulates of mass conservation of constituents together with the Gauss’ law used together with consistent constitutive laws. The HMT theory......-Nernst-Planck equations represent a set of diffusion equations for charged species, i.e. dissolved ions. These equations are coupled to the ‘internally’ induced electrical field and to the velocity field of the fluid. The Nernst-Planck equations describing the diffusion of the ionic species and the Gauss’ law in used are...

  17. The Planck Legacy Archive

    Science.gov (United States)

    Dupac, X.; Arviset, C.; Fernandez Barreiro, M.; Lopez-Caniego, M.; Tauber, J.

    2015-12-01

    The Planck Collaboration has released in 2015 their second major dataset through the Planck Legacy Archive (PLA). It includes cosmological, Extragalactic and Galactic science data in temperature (intensity) and polarization. Full-sky maps are provided with unprecedented angular resolution and sensitivity, together with a large number of ancillary maps, catalogues (generic, SZ clusters and Galactic cold clumps), time-ordered data and other information. The extensive cosmological likelihood package allows cosmologists to fully explore the plausible parameters of the Universe. A new web-based PLA user interface is made public since Dec. 2014, allowing easier and faster access to all Planck data, and replacing the previous Java-based software. Numerous additional improvements to the PLA are also being developed through the so-called PLA Added-Value Interface, making use of an external contract with the Planetek Hellas and Expert Analytics software companies. This will allow users to process time-ordered data into sky maps, separate astrophysical components in existing maps, simulate the microwave and infrared sky through the Planck Sky Model, and use a number of other functionalities.

  18. Noise-induced modulation of the relaxation kinetics around a non-equilibrium steady state of non-linear chemical reaction networks.

    Directory of Open Access Journals (Sweden)

    Rajesh Ramaswamy

    2011-01-01

    Full Text Available Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM or fluorescence-correlation spectroscopy (FCS to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.

  19. Stochastic substitute for coupled rate equations in the modeling of highly ionized transient plasmas

    International Nuclear Information System (INIS)

    Eliezer, S.; Falquina, R.; Minguez, E.

    1994-01-01

    Plasmas produced by intense laser pulses incident on solid targets often do not satisfy the conditions for local thermodynamic equilibrium, and so cannot be modeled by transport equations relying on equations of state. A proper description involves an excessively large number of coupled rate equations connecting many quantum states of numerous species having different degrees of ionization. Here we pursue a recent suggestion to model the plasma by a few dominant states perturbed by a stochastic driving force. The driving force is taken to be a Poisson impulse process, giving a Langevin equation which is equivalent to a Fokker-Planck equation for the probability density governing the distribution of electron density. An approximate solution to the Langevin equation permits calculation of the characteristic relaxation rate. An exact stationary solution to the Fokker-Planck equation is given as a function of the strength of the stochastic driving force. This stationary solution is used, along with a Laplace transform, to convert the Fokker-Planck equation to one of Schroedinger type. We consider using the classical Hamiltonian formalism and the WKB method to obtain the time-dependent solution

  20. The Markov process admits a consistent steady-state thermodynamic formalism

    Science.gov (United States)

    Peng, Liangrong; Zhu, Yi; Hong, Liu

    2018-01-01

    The search for a unified formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for the master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that (1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; (2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; (3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that general Markov processes admit a unified and self-consistent non-equilibrium steady-state thermodynamic formalism, regardless of underlying detailed models.

  1. Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model

    KAUST Repository

    Erban, Radek

    2009-01-01

    A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example, in the modeling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) are studied. Our approach is based on the chemical Fokker-Planck equation. To gain some insight into the advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, and then the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size. © 2009 Society for Industrial and Applied Mathematics.

  2. Nonlinear optics an analytical approach

    CERN Document Server

    Mandel, Paul

    2010-01-01

    Based on the author's extensive teaching experience and lecture notes, this textbook provides a substantially analytical rather than descriptive presentation of nonlinear optics. Divided into five parts, with most chapters corresponding to a two-hour lecture, the book begins with a unique account of the historical development from Kirchhoff's law for the black-body radiation to Planck's quantum hypothesis and Einstein's discovery of spontaneous emission - providing all the explicit proofs. The subsequent sections deal with matter quantization, ultrashort pulse propagation in 2-level media, cavity nonlinear optics, chi(2) and chi(3) media. For graduate and PhD students in nonlinear optics or photonics, while also representing a valuable reference for researchers in these fields.

  3. BRS symmetry in stochastic quantization of the gravitational field

    International Nuclear Information System (INIS)

    Nakazawa, Naohito.

    1989-12-01

    We study stochastic quantization of gravity in terms of a BRS invariant canonical operator formalism. By introducing artificially canonical momentum variables for the original field variables, a canonical formulation of stochastic quantization is proposed in a sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. Then we show that there exists a nilpotent BRS symmetry in an enlarged phase space for gravity (in general, for the first-class constrained systems). The stochastic action of gravity includes explicitly an unique De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models. (author)

  4. Steady State Analysis of Stochastic Systems with Multiple Time Delays

    Science.gov (United States)

    Xu, W.; Sun, C. Y.; Zhang, H. Q.

    In this paper, attention is focused on the steady state analysis of a class of nonlinear dynamic systems with multi-delayed feedbacks driven by multiplicative correlated Gaussian white noises. The Fokker-Planck equations for delayed variables are at first derived by Novikov's theorem. Then, under small delay assumption, the approximate stationary solutions are obtained by the probability density approach. As a special case, the effects of multidelay feedbacks and the correlated additive and multiplicative Gaussian white noises on the response of a bistable system are considered. It is shown that the obtained analytical results are in good agreement with experimental results in Monte Carlo simulations.

  5. CAS CERN Accelerator School: Advanced accelerator physics. Proceedings. Vol. 2

    International Nuclear Information System (INIS)

    Turner, S.

    1987-01-01

    This advanced course on general accelerator physics is the second of the biennial series given by the CERN Accelerator School and follows on from the first basic course given at Gif-sur-Yvette, Paris, in 1984. Stress is placed on the mathematical tools of Hamiltonian mechanics and the Vlasov and Fokker-Planck equations, which are widely used in accelerator theory. The main topics treated in this present work include: nonlinear resonances, chromaticity, motion in longitudinal phase space, growth and control of longitudinal and transverse beam emittance, space-charge effects and polarization. The seminar programme treats some specific accelerator techniques, devices, projects and future possibilities. (orig.)

  6. Planck early results. XVI. The Planck view of nearby galaxies

    DEFF Research Database (Denmark)

    Lähteenmäki, A.; Poutanen, T.; Natoli, P.

    2011-01-01

    they have been observed. We here present the first results on the properties of nearby galaxies using these data. We match the ERCSC catalogue to IRAS-detected galaxies in the Imperial IRAS Faint Source Redshift Catalogue (IIFSCz), so that we can measure the spectral energy distributions (SEDs......) of these objects from 60 to 850μm. This produces a list of 1717 galaxies with reliable associations between Planck and IRAS, from which we select a subset of 468 for SED studies, namely those with strong detections in the three highest frequency Planck bands and no evidence of cirrus contamination. The SEDs...

  7. Planck intermediate results XXXIX. The Planck list of high-redshift source candidates

    DEFF Research Database (Denmark)

    Ade, P. A. R.; Aghanim, N.; Arnaud, M.

    2016-01-01

    on a component-separation procedure using a combination of Planck and IRAS data, has been validated and characterized on numerous simulations, and applied to select the most luminous cold submillimetre sources with spectral energy distributions peaking between 353 and 857 GHz at 5' resolution. A total of 2151......The Planck mission, thanks to its large frequency range and all-sky coverage, has a unique potential for systematically detecting the brightest, and rarest, submillimetre sources on the sky, including distant objects in the high-redshift Universe traced by their dust emission. A novel method, based...... Planck high-z source candidates (the PHZ) have been detected in the cleanest 26% of the sky, with flux density at 545 GHz above 500 mJy. Embedded in the cosmic infrared background close to the confusion limit, these high-z candidates exhibit colder colours than their surroundings, consistent...

  8. Planck 2013 results. XVI. Cosmological parameters

    CERN Document Server

    Ade, P.A.R.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartlett, J.G.; Battaner, E.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J.J.; Bonaldi, A.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cappellini, B.; Cardoso, J.F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chary, R.R.; Chen, X.; Chiang, L.Y.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.M.; Desert, F.X.; Dickinson, C.; Diego, J.M.; Dolag, K.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Dunkley, J.; Dupac, X.; Efstathiou, G.; Elsner, F.; Ensslin, T.A.; Eriksen, H.K.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschi, E.; Gaier, T.C.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giardino, G.; Giraud-Heraud, Y.; Gjerlow, E.; Gonzalez-Nuevo, J.; Gorski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J.E.; Haissinski, J.; Hamann, J.; Hansen, F.K.; Hanson, D.; Harrison, D.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hou, Z.; Hovest, W.; Huffenberger, K.M.; Jaffe, T.R.; Jaffe, A.H.; Jewell, J.; Jones, W.C.; Juvela, M.; Keihanen, E.; Keskitalo, R.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Lattanzi, M.; Laureijs, R.J.; Lawrence, C.R.; Leach, S.; Leahy, J.P.; Leonardi, R.; Leon-Tavares, J.; Lesgourgues, J.; Lewis, A.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lopez-Caniego, M.; Lubin, P.M.; Macias-Perez, J.F.; Maffei, B.; Maino, D.; Mandolesi, N.; Maris, M.; Marshall, D.J.; Martin, P.G.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; Matthai, F.; Mazzotta, P.; Meinhold, P.R.; Melchiorri, A.; Melin, J.B.; Mendes, L.; Menegoni, E.; Mennella, A.; Migliaccio, M.; Millea, M.; Mitra, S.; Miville-Deschenes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; O'Dwyer, I.J.; Osborne, S.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Partridge, B.; Pasian, F.; Patanchon, G.; Pearson, D.; Pearson, T.J.; Peiris, H.V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Platania, P.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Reach, W.T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rowan-Robinson, M.; Rubino-Martin, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Starck, J.L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Turler, M.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L.A.; Wandelt, B.D.; Wehus, I.K.; White, M.; White, S.D.M.; Wilkinson, A.; Yvon, D.; Zacchei, A.; Zonca, A.

    2014-10-29

    We present the first results based on Planck measurements of the CMB temperature and lensing-potential power spectra. The Planck spectra at high multipoles are extremely well described by the standard spatially-flat six-parameter LCDM cosmology. In this model Planck data determine the cosmological parameters to high precision. We find a low value of the Hubble constant, H0=67.3+/-1.2 km/s/Mpc and a high value of the matter density parameter, Omega_m=0.315+/-0.017 (+/-1 sigma errors) in excellent agreement with constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent-level precision using Planck CMB data alone. We present results from an analysis of extensions to the standard cosmology, using astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured significantly over standard LCDM. The deviation of the scalar spectral index from unity is insensitive to the additi...

  9. Planck intermediate results: IV. the XMM-Newton validation programme for new Planck galaxy clusters

    DEFF Research Database (Denmark)

    Bartlett, J.G.; Delabrouille, J.; Ganga, K.

    2013-01-01

    We present the final results from the XMM-Newton validation follow-up of new Planck galaxy cluster candidates. We observed 15 new candidates, detected with signal-to-noise ratios between 4.0 and 6.1 in the 15.5-month nominal Planck survey. The candidates were selected using ancillary data flags d...

  10. 77 FR 48473 - Airworthiness Directives; Fokker Services B.V. Airplanes

    Science.gov (United States)

    2012-08-14

    ... the corrective actions in accordance with the approved maintenance documentation. If no compliance... the instructions for continued airworthiness for certain airplanes, and the FAA-approved maintenance... Services B.V. issuing a Fokker 70/100 maintenance review board (MRB) document with revised limitations...

  11. Transient finite element analysis of electric double layer using Nernst-Planck-Poisson equations with a modified Stern layer.

    Science.gov (United States)

    Lim, Jongil; Whitcomb, John; Boyd, James; Varghese, Julian

    2007-01-01

    A finite element implementation of the transient nonlinear Nernst-Planck-Poisson (NPP) and Nernst-Planck-Poisson-modified Stern (NPPMS) models is presented. The NPPMS model uses multipoint constraints to account for finite ion size, resulting in realistic ion concentrations even at high surface potential. The Poisson-Boltzmann equation is used to provide a limited check of the transient models for low surface potential and dilute bulk solutions. The effects of the surface potential and bulk molarity on the electric potential and ion concentrations as functions of space and time are studied. The ability of the models to predict realistic energy storage capacity is investigated. The predicted energy is much more sensitive to surface potential than to bulk solution molarity.

  12. Inherent noise can facilitate coherence in collective swarm motion

    KAUST Repository

    Yates, C. A.; Erban, R.; Escudero, C.; Couzin, I. D.; Buhl, J.; Kevrekidis, I. G.; Maini, P. K.; Sumpter, D. J. T.

    2009-01-01

    Among the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directional switching is an intrinsic property of their motion. Similar direction switches are seen in self-propelled particle and other models of group motion. Comprehending the factors that determine such switches is key to understanding the movement of these groups. Here, we adopt a coarse-grained approach to the study of directional switching in a self-propelled particle model assuming an underlying one-dimensional Fokker-Planck equation for the mean velocity of the particles. We continue with this assumption in analyzing experimental data on locusts and use a similar systematic Fokker-Planck equation coefficient estimation approach to extract the relevant information for the assumed Fokker-Planck equation underlying that experimental data. In the experiment itself the motion of groups of 5 to 100 locust nymphs was investigated in a homogeneous laboratory environment, helping us to establish the intrinsic dynamics of locust marching bands. We determine the mean time between direction switches as a function of group density for the experimental data and the self-propelled particle model. This systematic approach allows us to identify key differences between the experimental data and the model, revealing that individual locusts appear to increase the randomness of their movements in response to a loss of alignment by the group. We give a quantitative description of how locusts use noise to maintain swarm alignment. We discuss further how properties of individual animal behavior, inferred by using the Fokker-Planck equation coefficient estimation approach, can be implemented in the self-propelled particle model to replicate qualitatively the group level dynamics seen in the experimental data.

  13. Inherent noise can facilitate coherence in collective swarm motion

    KAUST Repository

    Yates, C. A.

    2009-03-31

    Among the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directional switching is an intrinsic property of their motion. Similar direction switches are seen in self-propelled particle and other models of group motion. Comprehending the factors that determine such switches is key to understanding the movement of these groups. Here, we adopt a coarse-grained approach to the study of directional switching in a self-propelled particle model assuming an underlying one-dimensional Fokker-Planck equation for the mean velocity of the particles. We continue with this assumption in analyzing experimental data on locusts and use a similar systematic Fokker-Planck equation coefficient estimation approach to extract the relevant information for the assumed Fokker-Planck equation underlying that experimental data. In the experiment itself the motion of groups of 5 to 100 locust nymphs was investigated in a homogeneous laboratory environment, helping us to establish the intrinsic dynamics of locust marching bands. We determine the mean time between direction switches as a function of group density for the experimental data and the self-propelled particle model. This systematic approach allows us to identify key differences between the experimental data and the model, revealing that individual locusts appear to increase the randomness of their movements in response to a loss of alignment by the group. We give a quantitative description of how locusts use noise to maintain swarm alignment. We discuss further how properties of individual animal behavior, inferred by using the Fokker-Planck equation coefficient estimation approach, can be implemented in the self-propelled particle model to replicate qualitatively the group level dynamics seen in the experimental data.

  14. Multi-Level iterative methods in computational plasma physics

    International Nuclear Information System (INIS)

    Knoll, D.A.; Barnes, D.C.; Brackbill, J.U.; Chacon, L.; Lapenta, G.

    1999-01-01

    Plasma physics phenomena occur on a wide range of spatial scales and on a wide range of time scales. When attempting to model plasma physics problems numerically the authors are inevitably faced with the need for both fine spatial resolution (fine grids) and implicit time integration methods. Fine grids can tax the efficiency of iterative methods and large time steps can challenge the robustness of iterative methods. To meet these challenges they are developing a hybrid approach where multigrid methods are used as preconditioners to Krylov subspace based iterative methods such as conjugate gradients or GMRES. For nonlinear problems they apply multigrid preconditioning to a matrix-few Newton-GMRES method. Results are presented for application of these multilevel iterative methods to the field solves in implicit moment method PIC, multidimensional nonlinear Fokker-Planck problems, and their initial efforts in particle MHD

  15. Coherence of light. 2. ed.

    International Nuclear Information System (INIS)

    Perina, J.

    1985-01-01

    This book puts the theory of coherence of light on a rigorous mathematical footing. It deals with the classical and quantum theories and with their inter-relationships, including many results from the author's own research. Particular attention is paid to the detection of optical fields, using the correlation functions, photocount statistics and coherent state. Radiometry with light fields of arbitrary states of coherence is discussed and the coherent state methods are demonstrated by photon statistics of radiation in random and nonlinear media, using the Heisenberg-Langevin and Fokker-Planck approaches to the interaction of radiation with matter. Many experimental and theoretical results are compared. A full list of references to theoretical and experimental literature is provided. The book is intended for researchers and postgraduate students in the fields of quantum optics, quantum electronics, statistical optics, nonlinear optics, optical communication and optoelectronics. (Auth.)

  16. Planck 2015 results. XIII. Cosmological parameters

    CERN Document Server

    Ade, P.A.R.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartlett, J.G.; Bartolo, N.; Battaner, E.; Battye, R.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Boulanger, F.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cardoso, J.F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chary, R.R.; Chiang, H.C.; Chluba, J.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Combet, C.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Desert, F.X.; Di Valentino, E.; Dickinson, C.; Diego, J.M.; Dolag, K.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Ducout, A.; Dunkley, J.; Dupac, X.; Efstathiou, G.; Elsner, F.; Ensslin, T.A.; Eriksen, H.K.; Farhang, M.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Gauthier, C.; Gerbino, M.; Ghosh, T.; Giard, M.; Giraud-Heraud, Y.; Giusarma, E.; Gjerlow, E.; Gonzalez-Nuevo, J.; Gorski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J.E.; Hamann, J.; Hansen, F.K.; Hanson, D.; Harrison, D.L.; Helou, G.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huang, Z.; Huffenberger, K.M.; Hurier, G.; Jaffe, A.H.; Jaffe, T.R.; Jones, W.C.; Juvela, M.; Keihanen, E.; Keskitalo, R.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Lattanzi, M.; Lawrence, C.R.; Leahy, J.P.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Lewis, A.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lopez-Caniego, M.; Lubin, P.M.; Macias-Perez, J.F.; Maggio, G.; Mandolesi, N.; Mangilli, A.; Marchini, A.; Martin, P.G.; Martinelli, M.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; Mazzotta, P.; McGehee, P.; Meinhold, P.R.; Melchiorri, A.; Melin, J.B.; Mendes, L.; Mennella, A.; Migliaccio, M.; Millea, M.; Mitra, S.; Miville-Deschenes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J.A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paladini, R.; Paoletti, D.; Partridge, B.; Pasian, F.; Patanchon, G.; Pearson, T.J.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Reach, W.T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; d'Orfeuil, B.Rouille; Rowan-Robinson, M.; Rubino-Martin, J.A.; Rusholme, B.; Said, N.; Salvatelli, V.; Salvati, L.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M.D.; Serra, P.; Shellard, E.P.S.; Spencer, L.D.; Spinelli, M.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Trombetti, T.; Tucci, M.; Tuovinen, J.; Turler, M.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vielva, P.; Villa, F.; Wade, L.A.; Wandelt, B.D.; Wehus, I.K.; White, M.; White, S.D.M.; Wilkinson, A.; Yvon, D.; Zacchei, A.; Zonca, A.

    2016-01-01

    We present results based on full-mission Planck observations of temperature and polarization anisotropies of the CMB. These data are consistent with the six-parameter inflationary LCDM cosmology. From the Planck temperature and lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/- 0.9) km/s/Mpc, a matter density parameter Omega_m = 0.308 +/- 0.012 and a scalar spectral index with n_s = 0.968 +/- 0.006. (We quote 68% errors on measured parameters and 95% limits on other parameters.) Combined with Planck temperature and lensing data, Planck LFI polarization measurements lead to a reionization optical depth of tau = 0.066 +/- 0.016. Combining Planck with other astrophysical data we find N_ eff = 3.15 +/- 0.23 for the effective number of relativistic degrees of freedom and the sum of neutrino masses is constrained to < 0.23 eV. Spatial curvature is found to be |Omega_K| < 0.005. For LCDM we find a limit on the tensor-to-scalar ratio of r <0.11 consistent with the B-mode constraints fr...

  17. Planck 2015. XX. Constraints on inflation

    CERN Document Server

    Ade, P.A.R.; Arnaud, M.; Arroja, F.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Ballardini, M.; Banday, A.J.; Barreiro, R.B.; Bartolo, N.; Battaner, E.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Boulanger, F.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cardoso, J.F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chary, R.R.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Combet, C.; Contreras, D.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Desert, F.X.; Diego, J.M.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Ensslin, T.A.; Eriksen, H.K.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschi, E.; Frejsel, A.; Frolov, A.; Galeotta, S.; Galli, S.; Ganga, K.; Gauthier, C.; Giard, M.; Giraud-Heraud, Y.; Gjerlow, E.; Gonzalez-Nuevo, J.; Gorski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J.E.; Hamann, J.; Handley, W.; Hansen, F.K.; Hanson, D.; Harrison, D.L.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huang, Z.; Huffenberger, K.M.; Hurier, G.; Jaffe, A.H.; Jaffe, T.R.; Jones, W.C.; Juvela, M.; Keihanen, E.; Keskitalo, R.; Kim, J.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Lattanzi, M.; Lawrence, C.R.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Lewis, A.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lopez-Caniego, M.; Lubin, P.M.; Ma, Y.Z.; Macias-Perez, J.F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Martin, P.G.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; Mazzotta, P.; McGehee, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschenes, M.A.; Molinari, D.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munchmeyer, M.; Munshi, D.; Murphy, J.A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paladini, R.; Pandolfi, S.; Paoletti, D.; Pasian, F.; Patanchon, G.; Pearson, T.J.; Peiris, H.V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Reach, W.T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rowan-Robinson, M.; Rubino-Martin, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Shiraishi, M.; Spencer, L.D.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Trombetti, T.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vielva, P.; Villa, F.; Wade, L.A.; Wandelt, B.D.; Wehus, I.K.; White, M.; Yvon, D.; Zacchei, A.; Zibin, J.P.; Zonca, A.

    2016-09-20

    We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be $n_\\mathrm{s} = 0.968 \\pm 0.006$ and tightly constrain its scale dependence to $d n_s/d \\ln k =-0.003 \\pm 0.007$ when combined with the Planck lensing likelihood. When the high-$\\ell$ polarization data is included, the results are consistent and uncertainties are reduced. The upper bound on the tensor-to-scalar ratio is $r_{0.002} < 0.11$ (95% CL), consistent with the B-mode polarization constraint $r< 0.12$ (95% CL) obtained from a joint BICEP2/Keck Array and Planck analysis. These results imply that $V(\\phi) \\propto \\phi^2$ and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as $R^2$ ...

  18. Planck 2015 results. XXVI. The Second Planck Catalogue of Compact Sources

    CERN Document Server

    Ade, P.A.R.; Argueso, F.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartolo, N.; Battaner, E.; Beichman, C.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bock, J.J.; Bohringer, H.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Boulanger, F.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cardoso, J.F.; Carvalho, P.; Catalano, A.; Challinor, A.; Chamballu, A.; Chary, R.R.; Chiang, H.C.; Christensen, P.R.; Clemens, M.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Combet, C.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Desert, F.X.; Dickinson, C.; Diego, J.M.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Ensslin, T.A.; Eriksen, H.K.; Falgarone, E.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giraud-Heraud, Y.; Gjerlow, E.; Gonzalez-Nuevo, J.; Gorski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J.E.; Hansen, F.K.; Hanson, D.; Harrison, D.L.; Helou, G.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Hurier, G.; Jaffe, A.H.; Jaffe, T.R.; Jones, W.C.; Juvela, M.; Keihanen, E.; Keskitalo, R.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Lattanzi, M.; Lawrence, C.R.; Leahy, J.P.; Leonardi, R.; Leon-Tavares, J.; Lesgourgues, J.; Levrier, F.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lopez-Caniego, M.; Lubin, P.M.; Macias-Perez, J.F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Maris, M.; Marshall, D.J.; Martin, P.G.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; McGehee, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschenes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J.A.; Naselsky, P.; Nati, F.; Natoli, P.; Negrello, M.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paladini, R.; Paoletti, D.; Partridge, B.; Pasian, F.; Patanchon, G.; Pearson, T.J.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Reach, W.T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rowan-Robinson, M.; Rubino-Martin, J.A.; Rusholme, B.; Sandri, M.; Sanghera, H.S.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Stolyarov, V.; Sudiwala, R.; Sunyaev, R.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tornikoski, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Turler, M.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vielva, P.; Villa, F.; Wade, L.A.; Walter, B.; Wandelt, B.D.; Wehus, I.K.; Yvon, D.; Zacchei, A.; Zonca, A.

    2016-01-01

    The Second Planck Catalogue of Compact Sources is a catalogue of sources detected in single-frequency maps from the full duration of the Planck mission and supersedes previous versions of the Planck compact source catalogues. It consists of compact sources, both Galactic and extragalactic, detected over the entire sky. Compact sources detected in the lower frequency channels are assigned to the PCCS2, while at higher frequencies they are assigned to one of two sub-catalogues, the PCCS2 or PCCS2E, depending on their location on the sky. The first of these catalogues covers most of the sky and allows the user to produce subsamples at higher reliabilities than the target 80% integral reliability of the catalogue. The PCCS2E contains sources detected in sky regions where the diffuse emission makes it difficult to quantify the reliability of the detections. Both the PCCS2 and PCCS2E include polarization measurements, in the form of polarized flux densities, or upper limits, and orientation angles for all seven pol...

  19. Planck 2015 results: XXVIII. The Planck Catalogue of Galactic cold clumps

    DEFF Research Database (Denmark)

    Ade, P. A R; Aghanim, N.; Arnaud, M.

    2016-01-01

    We present the Planck Catalogue of Galactic Cold Clumps (PGCC), an all-sky catalogue of Galactic cold clump candidates detected by Planck. This catalogue is the full version of the Early Cold Core (ECC) catalogue, which was made available in 2011 with the Early Release Compact Source Catalogue (E...

  20. Stochastic theory of molecular collisions. II. Application to atom--vibrotor collisions

    International Nuclear Information System (INIS)

    Augustin, S.D.; Rabitz, H.

    1977-01-01

    In this work stochastic theory is applied to the treatment of atom--vibrotor collisions. This is an extension of a previous paper which described molecular collisions by a Pauli master equation or a Fokker--Planck equation. In this framework an energy conserving classical path model is explored, and methods for solving the equations numerically are discussed. The coefficients of the Fokker--Planck equation are shown to be expressible as simple functions of the interaction potential. Estimates of the computational labor are also discussed. Finally as a followup on the initial work, numerical solutions of the master equation for the collinear vibrational excitation problem of Secrest and Johnson are presented in an Appendix

  1. Test of models for electron transport in laser produced plasmas

    International Nuclear Information System (INIS)

    Colombant, D.G.; Manheimer, W.M.; Busquet, M.

    2005-01-01

    This paper examines five different models of electron thermal transport in laser produced spherical implosions. These are classical, classical with a flux limit f, delocalization, beam deposition model, and Fokker-Planck solutions. In small targets, the results are strongly dependent on f for flux limit models, with small f's generating very steep temperature gradients. Delocalization models are characterized by large preheat in the center of the target. The beam deposition model agrees reasonably well with the Fokker-Planck simulation results. For large, high gain fusion targets, the delocalization model shows the gain substantially reduced by the preheat. However, flux limitation models show gain largely independent of f, with the beam deposition model also showing the same high gain

  2. Planck 2013 results. XIV. Zodiacal emission

    OpenAIRE

    Ade, PAR; Aghanim, N; Armitage-Caplan, C; Arnaud, M; Ashdown, M; Atrio-Barandela, F; Aumont, J; Baccigalupi, C; Banday, AJ; Barreiro, RB; Bartlett, JG; Battaner, E; Benabed, K; Benoît, A; Benoit-Lévy, A

    2014-01-01

    © 2014 ESO. The Planck satellite provides a set of all-sky maps at nine frequencies from 30GHz to 857GHz. Planets, minor bodies, and diffuse interplanetary dust emission (IPD) are all observed. The IPD can be separated from Galactic and other emissions because Planck views a given point on the celestial sphere multiple times, through different columns of IPD. We use the Planck data to investigate the behaviour of zodiacal emission over the whole sky at sub-millimetre and millimetre wavelength...

  3. Planck 2015 results: VII. High Frequency Instrument data processing: Time-ordered information and beams

    International Nuclear Information System (INIS)

    Adam, R.; Ade, P. A. R.; Aghanim, N.; Arnaud, M.; Ashdown, M.

    2016-01-01

    The Planck High Frequency Instrument (HFI) has observed the full sky at six frequencies (100, 143, 217, 353, 545, and 857 GHz) in intensity and at four frequencies in linear polarization (100, 143, 217, and 353 GHz). In order to obtain sky maps, the time-ordered information (TOI) containing the detector and pointing samples must be processed and the angular response must be assessed. The full mission TOI is included in the Planck 2015 release. This study describes the HFI TOI and beam processing for the 2015 release. HFI calibration and map making are described in a companion paper. The main pipeline has been modified since the last release (2013 nominal mission in intensity only), by including a correction for the nonlinearity of the warm readout and by improving the model of the bolometer time response. The beam processing is an essential tool that derives the angular response used in all the Planck science papers and we report an improvement in the effective beam window function uncertainty of more than a factor of 10 relative to the2013 release. Noise correlations introduced by pipeline filtering function are assessed using dedicated simulations. Finally, angular cross-power spectra using data sets that are decorrelated in time are immune to the main systematic effects.

  4. Angular Multigrid Preconditioner for Krylov-Based Solution Techniques Applied to the Sn Equations with Highly Forward-Peaked Scattering

    Science.gov (United States)

    Turcksin, Bruno; Ragusa, Jean C.; Morel, Jim E.

    2012-01-01

    It is well known that the diffusion synthetic acceleration (DSA) methods for the Sn equations become ineffective in the Fokker-Planck forward-peaked scattering limit. In response to this deficiency, Morel and Manteuffel (1991) developed an angular multigrid method for the 1-D Sn equations. This method is very effective, costing roughly twice as much as DSA per source iteration, and yielding a maximum spectral radius of approximately 0.6 in the Fokker-Planck limit. Pautz, Adams, and Morel (PAM) (1999) later generalized the angular multigrid to 2-D, but it was found that the method was unstable with sufficiently forward-peaked mappings between the angular grids. The method was stabilized via a filtering technique based on diffusion operators, but this filtering also degraded the effectiveness of the overall scheme. The spectral radius was not bounded away from unity in the Fokker-Planck limit, although the method remained more effective than DSA. The purpose of this article is to recast the multidimensional PAM angular multigrid method without the filtering as an Sn preconditioner and use it in conjunction with the Generalized Minimal RESidual (GMRES) Krylov method. The approach ensures stability and our computational results demonstrate that it is also significantly more efficient than an analogous DSA-preconditioned Krylov method.

  5. New and precise construction of the local interstellar electron spectrum from the radio background and an application to the solar modulation of cosmic rays showing an incompatability of the electron and nuclei modulation using the spherically symmetric Fokker-Planck equation

    International Nuclear Information System (INIS)

    Rockstroh, J.M.

    1977-01-01

    Cosmic-ray electrons generate the observed radio-frequency background. Previous attempts in the literature to reconcile quantitatively the measured radio-frequency intensity with the intensity deduced from the electron spectrum measured at earth have culminated in the problem that to get the respective emissivities to agree, an unacceptably high interstellar B field must be chosen. In the light of new experimental data on the emissivity as deduced from H II region studies and on the functional dependence of the diffusion coefficient with solar radius and particle rigidity, the assumptions under which the electron emissivity comparison has been made have been reexamined closely. The paradox between predicted and measured emissivity was resolved by ascribing to the magnetic fields of the galaxy a distribution of magnetic field strengths. From modified synchrotron formulas, the interstellar electron spectrum has been constructed from the radio frequency emission data with greatly improved precision. The interstellar electron spectrum has been determined independently of the solar modulation and provides, therefore, an estimate of the absolute depth of the electron modulation. Then the measured electron, proton, and helium-nuclei fluxes were systematically compared to the predictions of the spherically symmetric Fokker-Planck equation using the electron modulation as a base. A previously unnoticed non-tracking of the modulation parameters was observed during the recent recovery that did not occur during the 1965 to 1969 period. Although the argument could be presented just as well by attributing the anomaly to the nuclei, the discussion here arbitrarily tailored it to the electrons, and this new phenomenon was named, the modulation reluctance of the cosmic-ray electrons

  6. On the Nernst-Planck equation.

    Science.gov (United States)

    Maex, Reinoud

    2017-01-01

    This review first discusses Nernst's and Planck's early papers on electro-diffusion, the brief priority conflict that followed, and the role these papers played in shaping the emerging concept of membrane excitability. The second part discusses in greater detail the constraints of the Nernst-Planck theory, and shows more recent examples of its applicability for neuronal modelling.

  7. The intellectual quadrangle: Mach-Boltzmann-Planck-Einstein

    International Nuclear Information System (INIS)

    Broda, E.

    1981-01-01

    These four men were influential in the transition from classical to modern physics. They interacted as scientists, often antagonistically. Thus Boltzmann was the greatest champion of the atom, while Mach remained unconvinced all his life. As a aphysicist, Einstein was greatly influenced by both Mach and Boltzmann, although Mach in the end rejected relativity as well. Because of his work on statistical mechanics, fluctuations, and quantum theory, Einstein has been called the natural successor to Boltzmann. Planck also was influenced by Mach at first. Hence he and Boltzmann were adversaries antil Planck converted to atomistics in 1900 and used the statistical interpretation of entropy to establish his radiation law. Planck accepted relativity early, but in quantum theory he was for a long time partly opposed to Einstein, and vice versa - Einstein considered Planck's derivation of his radiation law as unsound, while Planck could not accept the light quantum. In the case of all four physicists, science was interwoven with philosophy. Boltzmann consistently fought Mach's positivism, while Planck and Einstein moved from positivism to realism. All were also, though in very different ways, actively interested in public affairs. (orig.)

  8. Simulations of Electron Transport in Laser Hot Spots

    International Nuclear Information System (INIS)

    Brunner, S.; Valeo, E.

    2001-01-01

    Simulations of electron transport are carried out by solving the Fokker-Planck equation in the diffusive approximation. The system of a single laser hot spot, with open boundary conditions, is systematically studied by performing a scan over a wide range of the two relevant parameters: (1) Ratio of the stopping length over the width of the hot spot. (2) Relative importance of the heating through inverse Bremsstrahlung compared to the thermalization through self-collisions. As for uniform illumination [J.P. Matte et al., Plasma Phys. Controlled Fusion 30 (1988) 1665], the bulk of the velocity distribution functions (VDFs) present a super-Gaussian dependence. However, as a result of spatial transport, the tails are observed to be well represented by a Maxwellian. A similar dependence of the distributions is also found for multiple hot spot systems. For its relevance with respect to stimulated Raman scattering, the linear Landau damping of the electron plasma wave is estimated for such VD Fs. Finally, the nonlinear Fokker-Planck simulations of the single laser hot spot system are also compared to the results obtained with the linear non-local hydrodynamic approach [A.V. Brantov et al., Phys. Plasmas 5 (1998) 2742], thus providing a quantitative limit to the latter method: The hydrodynamic approach presents more than 10% inaccuracy in the presence of temperature variations of the order delta T/T greater than or equal to 1%, and similar levels of deformation of the Gaussian shape of the Maxwellian background

  9. 77 FR 33332 - Airworthiness Directives; Fokker Services B.V. Airplanes

    Science.gov (United States)

    2012-06-06

    ...., Washington, DC 20590. Hand Delivery: U.S. Department of Transportation, Docket Operations, M-30, West... crossfeed system and a Fuel-Balance Transfer-Valve (FBTV). In 1993, a dormant failure mode was discovered... Fokker SBF100-28-021, containing instructions for activating the FBTS, had inadvertently been left active...

  10. Occupy the Financial Niche: Saturation and Crisis

    Science.gov (United States)

    Purica, Ionut

    The model presented is one theoretical approach within a broader research program that could verify the nonlinear conjectures made, such that to quantify and predict potential discontinuous behaviour. In this case, the crisis behaviour associated with financial funds reallocation among various credit instruments, described as memes with the sense of Dawkins, is shown to be of discontinuous nature stemming from a logistic penetration in the behaviour niche. Actually the logistic penetration is typical in creating cyclic behaviour of economic structures as shown by Marchetti and others from IIASA. A Fokker-Planck equation description results in a stationary solution having a bifurcation like solution with evolution trajectories on a `cusp' type catastrophe that may describe discontinuous decision behaviour.

  11. Occupy the Financial Niche – Saturation and Crisis (discontinuous decisions

    Directory of Open Access Journals (Sweden)

    Ionut PURICA

    2014-09-01

    Full Text Available The model presented is proposing an approach that could verify the nonlinear behaviour during a crisis, such that to quantify and predict potential discontinuous behaviour. In this case, the crisis behaviour associated with financial funds reallocation among various credit instruments, described as memes with the sense of Dawkins, is shown to be of discontinuous nature stemming from a logistic penetration in the financial behaviour niche. Actually the logistic penetration is typical in creating cyclic behaviour of economic structures as shown by Marchetti and others from IIASA. A Fokker-Planck equation description results in a stationary solution having a bifurcation like solution with evolution trajectories on a ‘cusp’ type catastrophe that may describe discontinuous decision behaviour

  12. Planck intermediate results. XXVI. Optical identification and redshifts of Planck clusters with the RTT150 telescope

    DEFF Research Database (Denmark)

    Ade, P. A. R.; Aghanim, N.; Arnaud, M.

    2015-01-01

    We present the results of approximately three years of observations of Planck Sunyaev-Zeldovich (SZ) sources with the Russian-Turkish 1.5m telescope (RTT150), as a part of the optical follow-up programme undertaken by the Planck collaboration. During this time period approximately 20% of all dark...

  13. Planck driven by vision, broken by war

    CERN Document Server

    Brown, Brandon R

    2015-01-01

    Planck's Law, an equation used by physicists to determine the radiation leaking from any object in the universe, was described by Albert Einstein as "the basis of all twentieth-century physics." Max Planck is credited with being the father of quantum theory, and his work laid the foundation for our modern understanding of matter and energetic processes. But Planck's story is not well known, especially in the United States. A German physicist working during the first half of the twentieth century, his library, personal journals, notebooks, and letters were all destroyed with his home in World War II. What remains, other than his contributions to science, are handwritten letters in German shorthand, and tributes from other scientists of the time, including his close friend Albert Einstein. In Planck: Driven by Vision, Broken by War, Brandon R. Brown interweaves the voices and writings of Planck, his family, and his contemporaries-with many passages appearing in English for the first time-to create a portrait of...

  14. Quantum Gravity corrections and entropy at the Planck time

    International Nuclear Information System (INIS)

    Basilakos, Spyros; Vagenas, Elias C.; Das, Saurya

    2010-01-01

    We investigate the effects of Quantum Gravity on the Planck era of the universe. In particular, using different versions of the Generalized Uncertainty Principle and under specific conditions we find that the main Planck quantities such as the Planck time, length, mass and energy become larger by a factor of order 10−10 4 compared to those quantities which result from the Heisenberg Uncertainty Principle. However, we prove that the dimensionless entropy enclosed in the cosmological horizon at the Planck time remains unchanged. These results, though preliminary, indicate that we should anticipate modifications in the set-up of cosmology since changes in the Planck era will be inherited even to the late universe through the framework of Quantum Gravity (or Quantum Field Theory) which utilizes the Planck scale as a fundamental one. More importantly, these corrections will not affect the entropic content of the universe at the Planck time which is a crucial element for one of the basic principles of Quantum Gravity named Holographic Principle

  15. Planck 2010

    CERN Multimedia

    CERN. Geneva; Grojean, Christophe

    2010-01-01

    Planck 2010 From the Planck Scale to the ElectroWeak Scale The conference will be the twelfth one in a series of meetings on physics beyond the Standard Model, organized jointly by several European groups: Bonn, CERN, Ecole Polytechnique, ICTP, Madrid, Oxford, Padua, Pisa, SISSA and Warsaw as part of activities in the framework of the European network UNILHC.Topics to be discussed: Supersymmetry Supergravity & string phenomenology Extra dimensions Electroweak symmetry breaking LHC and Tevatron Physics Collider physics Flavor & neutrinos physics Astroparticle & cosmology Gravity & holography Strongly coupled physics & CFT Registration: registration will be open until May 1st. Registration fees amount to 150 CHF and cover the cost of the coffee breaks and the social dinner. Payment has to be made online. The deadline for registration has been postponed to May 7th. However, after May 3th, we shall not accept any talk reques...

  16. Fokker-type dynamics with three-body correlations

    International Nuclear Information System (INIS)

    Salas, A.; Sanchez-Ron, J.M.

    1981-01-01

    Dynamical systems of N point particles without internal degrees of freedom are studied. Their equations of motion are derived from a Fokker-type variational principle with n-body correlations (n = 2,3,...,N), with special emphasis on the case n = 3. The distinction between n-body correlation and n-body effective force is analyzed in detail, with the help of an example. Maximal sets of independent three-body Poincare-invariant scalars are given. An example of three-body correlation formally similar to the usual two-body long-range scalar correlation is given and discussed. (author)

  17. Planck 2015 results: V. LFI calibration

    DEFF Research Database (Denmark)

    Ade, P. A R; Aghanim, N.; Ashdown, M.

    2016-01-01

    We present a description of the pipeline used to calibrate the Planck Low Frequency Instrument (LFI) timelines into thermodynamic temperatures for the Planck 2015 data release, covering four years of uninterrupted operations. As in the 2013 data release, our calibrator is provided by the spin-syn...

  18. Planck 2013 results. XIV. Zodiacal emission

    CERN Document Server

    Ade, P A R; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartlett, J.G.; Battaner, E.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J.J.; Bonaldi, A.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Boulanger, F.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R.C.; Cardoso, J.F.; Catalano, A.; Chamballu, A.; Chary, R.-R.; Chen, X.; Chiang, L.Y.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colley, J.-M.; Colombi, S.; Colombo, L.P.L.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.M.; Desert, F.X.; Dickinson, C.; Diego, J.M.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Dupac, X.; Efstathiou, G.; Ensslin, T.A.; Eriksen, H.K.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A. A.; Franceschi, E.; Galeotta, S.; Ganga, K.; Giard, M.; Giraud-Heraud, Y.; Gonzalez-Nuevo, J.; Gorski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Hansen, F.K.; Hanson, D.; Harrison, D.; Helou, G.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Jaffe, T.R.; Jaffe, A.H.; Jones, W.C.; Juvela, M.; Keihanen, E.; Keskitalo, R.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Laureijs, R.J.; Lawrence, C.R.; Leonardi, R.; Lesgourgues, J.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lopez-Caniego, M.; Lubin, P.M.; Macias-Perez, J.F.; Maffei, B.; Maino, D.; Mandolesi, N.; Maris, M.; Marshall, D.J.; Martin, P.G.; Martinez-Gonzalez, E.; Masi, S.; Massardi, M.; Matarrese, S.; Matthai, F.; Mazzotta, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschenes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Mottet, S.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Osborne, S.; O'Sullivan, C.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paladini, R.; Paoletti, D.; Pasian, F.; Patanchon, G.; Perdereau, O.; Perotto, L.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polegre, A. M.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Reach, W.T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rowan-Robinson, M.; Rusholme, B.; Sandri, M.; Santos, D.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Smoot, G. F.; Spencer, L.D.; Starck, J.L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L.A.; Wandelt, B.D.; Yvon, D.; Zacchei, A.; Zonca, A.

    2014-01-01

    The Planck satellite provides a set of all-sky maps at nine frequencies from 30 GHz to 857 GHz. Planets, minor bodies, and diffuse interplanetary dust emission (IPD) are all observed. The IPD can be separated from Galactic and other emissions because Planck views a given point on the celestial sphere multiple times, through different columns of IPD. We use the Planck data to investigate the behaviour of zodiacal emission over the whole sky at sub-millimetre and millimetre wavelengths. We fit the Planck data to find the emissivities of the various components of the COBE zodiacal model -- a diffuse cloud, three asteroidal dust bands, a circumsolar ring, and an Earth-trailing feature. The emissivity of the diffuse cloud decreases with increasing wavelength, as expected from earlier analyses. The emissivities of the dust bands, however, decrease less rapidly, indicating that the properties of the grains in the bands are different from those in the diffuse cloud. We fit the small amount of Galactic emission seen t...

  19. 75 FR 70861 - Airworthiness Directives; Fokker Services B.V. Model F.28 Mark 0100, 1000, 2000, 3000, and 4000...

    Science.gov (United States)

    2010-11-19

    ....V. Model F.28 Mark 0100, 1000, 2000, 3000, and 4000 Airplanes AGENCY: Federal Aviation... Fokker Services B.V. Model F28 Mark 1000, 2000, 3000, and 4000 airplanes, all serial numbers, equipped... Instructions of Fokker Service Bulletin SBF28-28-052, dated April 20, 2010 (for Model F28 Mark 1000, 2000, 3000...

  20. PHYSICS OF ELECTRON CYCLOTRON CURRENT DRIVE ON DIII-D

    International Nuclear Information System (INIS)

    PETTY, C.C.; PRATER, R.; LUCE, T.C.; ELLIS, R.A.; HARVEY, R.W.; KINSEY, J.E.; LAO, L.L.; LOHR, J.; MAKOWSKI, M.A.

    2002-01-01

    OAK A271 PHYSICS OF ELECTRON CYCLOTRON CURRENT DRIVE ON DIII-D. Recent experiments on the DIII-D tokamak have focused on determining the effect of trapped particles on the electron cyclotron current drive (ECCD) efficiency. The measured ECCD efficiency increases as the deposition location is moved towards the inboard midplane or towards smaller minor radius for both co and counter injection. The measured ECCD efficiency also increases with increasing electron density and/or temperature. The experimental ECCD is compared to both the linear theory (Toray-GA) as well as a quasilinear Fokker-Planck model (CQL3D). The experimental ECCD is found to be in better agreement with the more complete Fokker-Planck calculation, especially for cases of high rf power density and/or loop voltage

  1. Stochastic diffusion of dust grains by the interplanetary magnetic field

    International Nuclear Information System (INIS)

    Hassan, M.H.A.; Wallis, M.K.

    1983-10-01

    The effects of the sectored Interplanetary Magnetic Field on charged dust grains orbiting around the sun under radiation pressure and Poynting-Robertson drag forces are examined for initially circular and non-inclined orbits. The distribution function of the charged grains satisfies a Fokker-Planck equation in which the sectored field is taken as a source of stochastic impulses. By adopting the integrals of the impulse-free motion as variable parameters, the Fokker-Planck equation can be properly treated as a diffusion equation. Analytic solutions of the resulting diffusion equation show that dust grains injected near the ecliptic plane are scattered strongly to high helio-latitudes. The scattering is more pronounced for small grains injected at large distances from the Sun. (author)

  2. Statistical properties of single-mode emission in free-electron lasers

    International Nuclear Information System (INIS)

    Bertolotti, M.; Luks, A.; Perina, J.; Perinova, V.; Sibilia, C.

    1984-01-01

    The authors of this paper discuss the statistical properties of radiation produced in the free electron laser, in the case of singlemode emission when the system is used as an amplifier, with very small gain. The coherent states technique and the q-c number correspondence is employed, starting from the master-equation and obtaining the generalized Fokker-Planck equation for the anti-normal quasidistribution function. Solutions of Fokker-Planck equation provide the photocounting distribution and its factorial moments. No losses are included. It is shown that, in the short-time approximation, the radiation field exhibits antibunching, and that the photocounting distributions, when some suitable conditions on the field intensities are fulfilled, in the stationary regime shows a two-peak behavior, evidencing the existence of bistable states

  3. German science. Max Planck charts new path.

    Science.gov (United States)

    Koenig, R

    2000-06-09

    Germany's premier basic research organization, the Max Planck Society, released a long-awaited blueprint for change during its annual meeting this week, recommending that the society's nearly 3000 scientists embrace more interdisciplinary and international projects in a range of new research priorities. The report, called Max Planck 2000-Plus, is the product of an 18-month-long internal review. Its recommendations were formulated by some two dozen Max Planck researchers and administrators, who sought input from every institute.

  4. Planck 2013 results. XXXI. Consistency of the Planck data

    DEFF Research Database (Denmark)

    Ade, P. A. R.; Arnaud, M.; Ashdown, M.

    2014-01-01

    The Planck design and scanning strategy provide many levels of redundancy that can be exploited to provide tests of internal consistency. One of the most important is the comparison of the 70 GHz (amplifier) and 100 GHz (bolometer) channels. Based on dierent instrument technologies, with feeds...... in the HFI channels would result in shifts in the posterior distributions of parameters of less than 0.3σ except for As, the amplitude of the primordial curvature perturbations at 0.05 Mpc-1, which changes by about 1.We extend these comparisons to include the sky maps from the complete nine-year mission...... located dierently in the focal plane, analysed independently by dierent teams using dierent software, and near∫ the minimum of diuse foreground emission, these channels are in eect two dierent experiments. The 143 GHz channel has the lowest noise level on Planck, and is near the minimum of unresolved...

  5. Equilibrium state of colliding electron beams

    Directory of Open Access Journals (Sweden)

    R. L. Warnock

    2003-10-01

    Full Text Available We study a nonlinear integral equation that is a necessary condition on the equilibrium phase-space distribution function of stored, colliding electron beams. It is analogous to the Haïssinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. The equation is analyzed for the case of the Chao-Ruth model of the beam-beam interaction in 1 degree of freedom, a so-called strong-strong model with nonlinear beam-beam force. We prove the existence of a unique solution, for sufficiently small beam current, by an application of the implicit function theorem. We have not yet proved that this solution is positive, as would be required to establish existence of an equilibrium. There is, however, numerical evidence of a positive solution. We expect that our analysis can be extended to more realistic models.

  6. Brief review of Planck law

    International Nuclear Information System (INIS)

    Zamora Carranza, M.

    2001-01-01

    This paper presents a brief review of the scientific events which led to the determination of the law of radiation and the quantisation of energy by Max Planck. From the separation of sunlight by Newton to the reasons which led Planck to quantised the energy of an oscillator. I discuss the theoretical and experimental difficulties which scientists overcame to derive the law of heat radiation. (Author) 6 refs

  7. 76 FR 6541 - Airworthiness Directives; Fokker Services B.V. Model F.28 Mark 0100, 1000, 2000, 3000, and 4000...

    Science.gov (United States)

    2011-02-07

    ... Airworthiness Directives; Fokker Services B.V. Model F.28 Mark 0100, 1000, 2000, 3000, and 4000 Airplanes AGENCY.... Applicability (c) This AD applies to Fokker Services B.V. Model F.28 Mark 1000, 2000, 3000, and 4000 airplanes... April 20, 2010 (for Model F.28 Mark 1000, 2000, 3000, and 4000 airplanes); or SBF100-28-063, dated April...

  8. Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions.

    Science.gov (United States)

    Lu, Benzhuo; Holst, Michael J; McCammon, J Andrew; Zhou, Y C

    2010-09-20

    In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.

  9. Parity at the Planck scale

    Science.gov (United States)

    Arzano, Michele; Gubitosi, Giulia; Magueijo, João

    2018-06-01

    We explore the possibility that well known properties of the parity operator, such as its idempotency and unitarity, might break down at the Planck scale. Parity might then do more than just swap right and left polarized states and reverse the sign of spatial momentum k: it might generate superpositions of right and left handed states, as well as mix momenta of different magnitudes. We lay down the general formalism, but also consider the concrete case of the Planck scale kinematics governed by κ-Poincaré symmetries, where some of the general features highlighted appear explicitly. We explore some of the observational implications for cosmological fluctuations. Different power spectra for right handed and left handed tensor modes might actually be a manifestation of deformed parity symmetry at the Planck scale. Moreover, scale-invariance and parity symmetry appear deeply interconnected.

  10. Representation of the Fokker-Planck collision term for Coulomb interaction as series of Legendre polynomials

    International Nuclear Information System (INIS)

    Almeida Ferreira, A.C. de.

    1984-01-01

    For problems with azimuthal symmetry in velocity space, the distribution function depends only on the speed and on the pitch angle. The angular dependence of the distribution function is expanded in Legendre polynomials, and the expansions of the collision integrals describing two-body Coulomb interactions in a plasma are determined through the use of the Rosenbluth potentials. The electron distribution function is written as a Maxwellian plus a deviation, and the representation in Legendre polynomials of the electron-electron collision term is given for both its linear and nonlinear part. To determine the representation of the electron-ion collision term it is assumed that the ion distribution is much narrower in velocity space than the electron distribution, and shifted from the origin by a flow velocity. The equations are presented in a form that is suitable for their use in a computer. (Author) [pt

  11. Channeling experiments at planar diamond and silicon single crystals with electrons from the Mainz Microtron MAMI

    Science.gov (United States)

    Backe, H.; Lauth, W.; Tran Thi, T. N.

    2018-04-01

    Line structures were observed for (110) planar channeling of electrons in a diamond single crystal even at a beam energy of 180 MeV . This observation motivated us to initiate dechanneling length measurements as function of the beam energy since the occupation of quantum states in the channeling potential is expected to enhance the dechanneling length. High energy loss signals, generated as a result of emission of a bremsstrahlung photon with about half the beam energy at channeling of 450 and 855 MeV electrons, were measured as function of the crystal thickness. The analysis required additional assumptions which were extracted from the numerical solution of the Fokker-Planck equation. Preliminary results for diamond are presented. In addition, we reanalyzed dechanneling length measurements at silicon single crystals performed previously at the Mainz Microtron MAMI at beam energies between 195 and 855 MeV from which we conclude that the quality of our experimental data set is not sufficient to derive definite conclusions on the dechanneling length. Our experimental results are below the predictions of the Fokker-Planck equation and somewhat above the results of simulation calculations of A. V. Korol and A. V. Solov'yov et al. on the basis of the MBN Explorer simulation package. We somehow conservatively conclude that the prediction of the asymptotic dechanneling length on the basis of the Fokker-Planck equation represents an upper limit.

  12. Planck-scale sensitivity of CMB polarization data

    Energy Technology Data Exchange (ETDEWEB)

    Gubitosi, Giulia; Pagano, Luca [Physics Department, University of Rome ' La Sapienza' , and Sezione Roma1 INFN P.le Aldo Moro 2, 00185 Rome (Italy)

    2009-10-15

    We show that the Cosmic Microwave Background (CMB) polarization data gathered by the BOOMERanG 2003 flight and WMAP provide an opportunity to investigate in-vacuo birefringence, of a type expected in some quantum pictures of space-time, with a sensitivity that extends even beyond the desired Planck-scale energy. In order to render this constraint more transparent we rely on a well studied phenomenological model of quantum-gravity-induced birefringence, in which one easily establishes that effects introduced at the Planck scale would amount to values of a dimensionless parameter, denoted by xi, with respect to the Planck energy which are roughly of order 1. By combining BOOMERanG and WMAP data we estimate xiapprox =-0.097+-0.075 at the 68% c.l. Moreover, we forecast on the sensitivity to xi achievable by future CMB polarization experiments (PLANCK, Spider, EPIC), which, in the absence of systematics, will be at the 1-sigma confidence of 8.5x10{sup -4} (PLANCK), 6.1x10{sup -3} (Spider), and 1.0x10{sup -5} (EPIC) respectively. The cosmic variance-limited sensitivity from CMB is 6.1x10{sup -6}.

  13. Planck-scale sensitivity of CMB polarization data

    International Nuclear Information System (INIS)

    Gubitosi, Giulia; Pagano, Luca

    2009-01-01

    We show that the Cosmic Microwave Background (CMB) polarization data gathered by the BOOMERanG 2003 flight and WMAP provide an opportunity to investigate in-vacuo birefringence, of a type expected in some quantum pictures of space-time, with a sensitivity that extends even beyond the desired Planck-scale energy. In order to render this constraint more transparent we rely on a well studied phenomenological model of quantum-gravity-induced birefringence, in which one easily establishes that effects introduced at the Planck scale would amount to values of a dimensionless parameter, denoted by ξ, with respect to the Planck energy which are roughly of order 1. By combining BOOMERanG and WMAP data we estimate ξ≅-0.097±0.075 at the 68% c.l. Moreover, we forecast on the sensitivity to ξ achievable by future CMB polarization experiments (PLANCK, Spider, EPIC), which, in the absence of systematics, will be at the 1-σ confidence of 8.5x10 -4 (PLANCK), 6.1x10 -3 (Spider), and 1.0x10 -5 (EPIC) respectively. The cosmic variance-limited sensitivity from CMB is 6.1x10 -6 .

  14. TMX-U [Tandem Mirror Experiment-Upgrade]: Final report, Volume 2

    International Nuclear Information System (INIS)

    Porter, G.D.

    1988-01-01

    This paper discusses the plasma control and the physics accomplishments of the Tandem Mirror Experiment-Upgrade. This particular volume discusses fueling, ion heating, Fokker-Planck modeling, plasma stability and technical development. 270 refs

  15. Planck constraints on monodromy inflation

    International Nuclear Information System (INIS)

    Easther, Richard; Flauger, Raphael

    2014-01-01

    We use data from the nominal Planck mission to constrain modulations in the primordial power spectrum associated with monodromy inflation. The largest improvement in fit relative to the unmodulated model has Δχ 2 ≈ 10 and we find no evidence for a primordial signal, in contrast to a previous analysis of the WMAP9 dataset, for which Δχ 2 ≈ 20. The Planck and WMAP9 results are broadly consistent on angular scales where they are expected to agree as far as best-fit values are concerned. However, even on these scales the significance of the signal is reduced in Planck relative to WMAP, and is consistent with a fit to the ''noise'' associated with cosmic variance. Our results motivate both a detailed comparison between the two experiments and a more careful study of the theoretical predictions of monodromy inflation

  16. Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems

    KAUST Repository

    Cotter, Simon L.; Vejchodský , Tomá š; Erban, Radek

    2013-01-01

    Stochastic models of chemical systems are often analyzed by solving the corresponding Fokker-Planck equation, which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with nonnegligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the stationary probability density. Numerical examples demonstrate that the presented method is competitive with existing a posteriori methods. © 2013 Society for Industrial and Applied Mathematics.

  17. Kinetic-magnetohydrodynamic simulation study of fast ions and toroidal Alfven eigenmodes

    International Nuclear Information System (INIS)

    Todo, Y.; Sato, T.

    2001-01-01

    Particle-magnetohydrodynamic and Fokker-Planck-magnetohydrodynamic simulations of fast ions and toroidicity-induced Alfven eigenmodes (TAE modes) have been carried out. Alpha particle losses induced by TAE mode are investigated with particle-magnetohydrodynamic simulations. Trapped particles near the passing-trapped boundary in the phase space are also lost appreciably in addition to the counter-passing particles. In Fokker-Planck-magnetohydrodynamic simulation source and slowing-down of fast ions are considered. A coherent pulsating behavior of multiple TAE modes, which occurs in neutral beam injection experiments, is observed when the slowing-down time is much longer than the damping time of the TAE modes and the fast-ion pressure is sufficiently high. For a slowing-down time comparable to the damping time, the TAE modes reach steady saturation levels. (author)

  18. Kinetic-magnetohydrodynamic simulation study of fast ions and toroidal Alfven eigenmodes

    International Nuclear Information System (INIS)

    Todo, Y.; Sato, T.

    1999-01-01

    Particle-magnetohydrodynamic and Fokker-Planck-magnetohydrodynamic simulations of fast ions and toroidicity-induced Alfven eigenmodes (TAE modes) have been carried out. Alpha particle losses induced by TAE mode are investigated with particle-magnetohydrodynamic simulations. Trapped particles near the passing-trapped boundary in the phase space are also lost appreciably in addition to the counter-passing particles. In Fokker-Planck-magnetohydrodynamic simulation source and slowing-down of fast ions are considered. A coherent pulsating behavior of multiple TAE modes, which occurs in neutral beam injection experiments, is observed when the slowing-down time is much longer than the damping time of the TAE modes and the fast-ion pressure is sufficiently high. For a slowing-down time comparable to the damping time, the TAE modes reach steady saturation levels. (author)

  19. Master equations in the microscopic theory of nuclear collective dynamics

    International Nuclear Information System (INIS)

    Matsuo, M.; Sakata, F.; Marumori, T.; Zhuo, Y.

    1988-07-01

    In the first half of this paper, the authors describe briefly a recent theoretical approach where the mechanism of the large-amplitude dissipative collective motions can be investigated on the basis of the microscopic theory of nuclear collective dynamics. Namely, we derive the general coupled master equations which can disclose, in the framework of the TDHF theory, not only non-linear dynamics among the collective and the single-particle modes of motion but also microscopic dynamics responsible for the dissipative processes. In the latter half, the authors investigate, without relying on any statistical hypothesis, one possible microscopic origin which leads us to the transport equation of the Fokker-Planck type so that usefullness of the general framework is demonstrated. (author)

  20. Max Planck and modern physics

    International Nuclear Information System (INIS)

    Hoffmann, Dieter

    2010-01-01

    Max Planck (1858-1947) is according to the words of Max von Laue the ''father of quantum physics''. This characteristic has until today continuance, although Planck stood for long time sceptically in front of his quantum hypothesis and so became a revolutionary in spite of his wishes. Eclipted by this pioneer role of the scholar for the foundation of the quantum theory are the numerous further works of the scholer, by which he has in many other fields provided eminent things. Starting with his fundamental contribution to thermodynamics, which make him to an excellent researcher of the field, until the works in the early history of relativity theory and the promotion of the young Einstein, which let him become also to a pioneer of the second central pillar of modern physics. The present collection attempts to show the whole spectrum of the physical works of Max Planck and his role in the formation of modern physics. [de

  1. Diffusion Forecasting Model with Basis Functions from QR-Decomposition

    Science.gov (United States)

    Harlim, John; Yang, Haizhao

    2017-12-01

    The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to Itô diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the Fokker-Planck equation with a discrete representation of the shift (Koopman) operator on a set of basis functions generated via the diffusion maps algorithm. While the choice of these basis functions is provably optimal under appropriate conditions, computing these basis functions is quite expensive since it requires the eigendecomposition of an N× N diffusion matrix, where N denotes the data size and could be very large. For large-scale forecasting problems, only a few leading eigenvectors are computationally achievable. To overcome this computational bottleneck, a new set of basis functions constructed by orthonormalizing selected columns of the diffusion matrix and its leading eigenvectors is proposed. This computation can be carried out efficiently via the unpivoted Householder QR factorization. The efficiency and effectiveness of the proposed algorithm will be shown in both deterministically chaotic and stochastic dynamical systems; in the former case, the superiority of the proposed basis functions over purely eigenvectors is significant, while in the latter case forecasting accuracy is improved relative to using a purely small number of eigenvectors. Supporting arguments will be provided on three- and six-dimensional chaotic ODEs, a three-dimensional SDE that mimics turbulent systems, and also on the two spatial modes associated with the boreal winter Madden-Julian Oscillation obtained from applying the Nonlinear Laplacian Spectral Analysis on the measured Outgoing Longwave Radiation.

  2. Planck 2013 results. XXII. Constraints on inflation

    CERN Document Server

    Ade, P.A.R.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartlett, J.G.; Bartolo, N.; Battaner, E.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J.J.; Bonaldi, A.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cardoso, J.F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, L.Y.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.M.; Desert, F.X.; Dickinson, C.; Diego, J.M.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Dunkley, J.; Dupac, X.; Efstathiou, G.; Ensslin, T.A.; Eriksen, H.K.; Finelli, F.; Forni, O.; Frailis, M.; Franceschi, E.; Galeotta, S.; Ganga, K.; Gauthier, C.; Giard, M.; Giardino, G.; Giraud-Heraud, Y.; Gonzalez-Nuevo, J.; Gorski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Hamann, J.; Hansen, F.K.; Hanson, D.; Harrison, D.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Jaffe, T.R.; Jaffe, A.H.; Jones, W.C.; Juvela, M.; Keihanen, E.; Keskitalo, R.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Laureijs, R.J.; Lawrence, C.R.; Leach, S.; Leahy, J.P.; Leonardi, R.; Lesgourgues, J.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lopez-Caniego, M.; Lubin, P.M.; Macias-Perez, J.F.; Maffei, B.; Maino, D.; Mandolesi, N.; Maris, M.; Marshall, D.J.; Martin, P.G.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; Matthai, F.; Mazzotta, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschenes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; O'Dwyer, I.J.; Osborne, S.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paladini, R.; Pandolfi, S.; Paoletti, D.; Partridge, B.; Pasian, F.; Patanchon, G.; Peiris, H.V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rowan-Robinson, M.; Rubino-Martin, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Starck, J.L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Varis, J.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L.A.; Wandelt, B.D.; White, M.; Wilkinson, A.; Yvon, D.; Zacchei, A.; Zonca, A.

    2014-01-01

    We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to $n_s = 0.9603 \\pm 0.0073$, ruling out exact scale invariance at over 5 $\\sigma$. Planck establishes an upper bound on the tensor-to-scalar ratio of r 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining $d n_s/d ln k = -0.0134 \\pm 0.0090$. Several analyses dropping the slow-roll approximation are carried out, including detailed model comparison and inflationary potential reconstruction. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit $\\chi^2$ by ~ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining pow...

  3. Redefining Planck Mass: Unlocking the Fundamental Quantum of the Universe

    Science.gov (United States)

    Laubenstein, John

    2008-04-01

    The large value of the Planck Mass relative to the quantum scale raises unanswered questions as to the source of mass itself. While we wait for experimental verification of the elusive Higgs boson, it may be worth recognizing that Planck Mass is not the result of rigorous mathematics -- but rather derived from an intuitive manipulation of physical constants. Recent findings reported by IWPD suggest a quantum scale Planck Mass as small as 10 (-73) kg. At this scale, the Planck Mass joins Planck Length and Time as a truly fundamental quantum entity. This presentation will provide evidence supporting the fundamental quantum nature of a dramatically smaller Planck Mass while discussing the impact of this finding on both the quantum and cosmic scale. A quantum scale Planck Mass will require an accelerating expansion of the universe at an age of 14.2 billion years. No initial conditions are imposed at the earliest Planck Time of 10 (-44) s allowing the universe to evolve as a background free field propagating at the speed of light with a local degree of freedom. This model provides the basis for a quantum theory of gravity and provides a conceptual pathway for the unification of GR and QM.

  4. ESO and Fokker Space Sign Contract about VLTI Delay Line

    Science.gov (United States)

    1998-03-01

    The European Southern Observatory is building the world's largest optical telescope, the Very Large Telescope (VLT) , at the ESO Paranal Observatory in Chile. The VLT consists of four 8.2-m unit telescopes and several smaller, moveable Auxiliary Telescopes. When coupled as the giant VLT Interferometer (VLTI) , they will together provide the sharpest images ever obtained by any optical telescope. It will in principle be able to see an astronaut on the surface of the Moon, 400,000 km away. The VLTI Delay Lines Fokker Space (Leiden, The Netherlands) has been awarded a contract for the delivery of the Delay Line of the VLTI. This is a mechanical-optical system that will compensate the optical path differences of the light beams from the individual telescopes. Such a system is necessary to ensure that the light from all telescopes arrive in the same phase at the focal point of the interferometer. Otherwise, the very sharp interferometric images cannot be obtained. ESO PR Photo 08/98 [JPEG, 102k] Schematic representation of the VLTI Delay Line, showing the retro-reflector on its moving base. For more details, please consult the technical explanation below. This highly accurate system will be developed in close co-operation with the Dutch institute TNO-TPD (Netherlands Organization for Applied Scientific Research - Institute of Applied Physics) . The most innovative feature of the Delay Line is the new control strategy, a two-stage control system, based on linear motor technology, combined with high accuracy piezo-electric control elements. This enables the system to position the so-called cat's eye reflector system with an accuracy of only a few nanometers (millionth of a millimetre (nm)) over a stroke length of 60 metres. Within radio astronomy, interferometric techniques have been applied by Dutch astronomers since many years. They will now be able to contribute with their extensive knowledge of such systems to the next generation of astronomical interferometric

  5. Planck 2013 results. XXII. Constraints on inflation

    DEFF Research Database (Denmark)

    Ade, P. A. R.; Aghanim, N.; Armitage-Caplan, C.

    2014-01-01

    We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to be ns = 0.9603 ± 0:0073, ruling out exact scale invariance at over 5 sigma P...

  6. Planck intermediate results XXXVI. Optical identification and redshifts of Planck SZ sources with telescopes at the Canary Islands observatories

    DEFF Research Database (Denmark)

    Ade, P. A. R.; Aghanim, N.; Arnaud, M.

    2016-01-01

    We present the results of approximately three years of observations of Planck Sunyaev-Zeldovich (SZ) sources with telescopes at the Canary Islands observatories as part of the general optical follow-up programme undertaken by the Planck Collaboration. In total, 78 SZ sources are discussed. Deep-i...

  7. Radio-frequency wave enhanced runaway production rate

    International Nuclear Information System (INIS)

    Chan, V.S.; McClain, F.W.

    1983-01-01

    Enhancement of runaway electron production (over that of an Ohmic discharge) can be achieved by the addition of radio-frequency waves. This effect is studied analytically and numerically using a two-dimensional Fokker--Planck quasilinear equation

  8. Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

    Science.gov (United States)

    Arendt, V.; Shalchi, A.

    2018-06-01

    We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker-Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.

  9. Fokker-Planck code for the quasi-linear absorption of electron cyclotron waves in a tokamak plasma

    International Nuclear Information System (INIS)

    Meyer, R.L.; Giruzzi, G.; Krivenski, V.

    1986-01-01

    We present the solution of the kinetic equation describing the quasi-linear evolution of the electron momentum distribution function under the influence of the electron cyclotron wave absorption. Coulomb collisions and the dc electric field in a tokamak plasma. The solution of the quasi-linear equation is obtained numerically using a two-dimensional initial value code following an ADI scheme. Most emphasis is given to the full non-linear and self-consistent problem, namely, the wave amplitude is evaluated at any instant and any point in space according to the actual damping. This is necessary since wave damping is a very sensitive function of the slope of the local momentum distribution function because the resonance condition relates the electron momentum to the location of wave energy deposition. (orig.)

  10. 100 years of Planck's quantum

    CERN Document Server

    Duck, Ian M

    2000-01-01

    This invaluable book takes the reader from Planck's discovery of the quantum in 1900 to the most recent interpretations and applications of nonrelativistic quantum mechanics.The introduction of the quantum idea leads off the prehistory of quantum mechanics, featuring Planck, Einstein, Bohr, Compton, and de Broglie's immortal contributions. Their original discovery papers are featured with explanatory notes and developments in Part 1.The invention of matrix mechanics and quantum mechanics by Heisenberg, Born, Jordan, Dirac, and Schrödinger is presented next, in Part 2.Following that, in Part 3,

  11. Cosmic Microwave Background: cosmology from the Planck perspective

    Science.gov (United States)

    De Zotti, Gianfranco

    2017-08-01

    The Planck mission has measured the angular anisotropies in the temperature of the Cosmic Microwave Background (CMB) with an accuracy set by fundamental limits. These data have allowed the determination of the cosmological parameters with extraordinary precision. These lecture notes present an overview of the mission and of its cosmological results. After a short history of the project, the Planck instruments and their performances are introduced and compared with those of the WMAP satellite. Next the approach to data analysis adopted by the Planck collaboration is described. This includes the techniques for dealing with the contamination of the CMB signal by astrophysical foreground emissions and for determining cosmological parameters from the analysis of the CMB power spectrum. The power spectra measured by Planck were found to be very well described by the standard spatially flat six-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations. This is a remarkable result, considering that the six parameters account for the about 2500 independent power spectrum values measured by Planck (the power was measured for about 2500 multipoles), not to mention the about one trillion science samples produced. A large grid of cosmological models was also explored, using a range of additional astrophysical data sets in addition to Planck and high-resolution CMB data from ground-based experiments. On the whole, the Planck analysis of the CMB power spectrum allowed to vary and determined 16 parameters. Many other interesting parameters were derived from them. Although Planck was not initially designed to carry out high accuracy measurements of the CMB polarization anisotropies, its capabilities in this respect were significantly enhanced during its development. The quality of its polarization measurements have exceeded all original expectations. Planck's polarisation data confirmed and improved the understanding of the details of the cosmological

  12. Composite inflation confronts BICEP2 and PLANCK

    International Nuclear Information System (INIS)

    Karwan, Khamphee; Channuie, Phongpichit

    2014-01-01

    We examine observational constraints on single-field inflation in which the inflaton is a composite field stemming from a four-dimensional strongly interacting field theory. We confront the predictions with the Planck and very recent BICEP2 data. In the large non-minimal coupling regions, we discover for the minimal composite inflationary model that the predictions lie well inside the joint 68% CL for the Planck data, but is in tension with the recent BICEP2 observations. In the case of the glueball inflationary model, the predictions satisfy the Planck results. However, this model can produce a large tensor-to-scalar ratio consistent with the recent BICEP2 observations if the number of e-foldings is slightly smaller than the range commonly used. For a super Yang-Mills paradigm, we discover that the predictions satisfy the Planck data, and surprisingly a large tensor-to-scalar ratio consistent with the BICEP2 results can also be produced for an acceptable range of the number of e-foldings and of the confining scale. In the small non-minimal coupling regions, all of the models can satisfy the BICEP2 results. However, the predictions of the glueball and superglueball inflationary models cannot satisfy the observational bound on the amplitude of the curvature perturbation launched by Planck, and the techni-inflaton self-coupling in the minimal composite inflationary model is constrained to be extremely small

  13. Planck Intermediate Results. IX. Detection of the Galactic haze with Planck

    DEFF Research Database (Denmark)

    Planck Collaboration,; Ade, P. A. R.; Aghanim, N.

    2013-01-01

    Using precise full-sky observations from Planck, and applying several methods of component separation, we identify and characterize the emission from the Galactic "haze" at microwave wavelengths. The haze is a distinct component of diffuse Galactic emission, roughly centered on the Galactic centre...

  14. A Priori Regularity of Parabolic Partial Differential Equations

    KAUST Repository

    Berkemeier, Francisco

    2018-01-01

    In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular

  15. Planck 2015 results. XXI. The integrated Sachs-Wolfe effect

    CERN Document Server

    Ade, P.A.R.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartolo, N.; Basak, S.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bock, J.J.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cardoso, J.-F.; Casaponsa, B.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Combet, C.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Désert, F.-X.; Diego, J.M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T.A.; Eriksen, H.K.; Fergusson, J.; Fernandez-Cobos, R.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Génova-Santos, R.T.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J.E.; Hansen, F.K.; Hanson, D.; Harrison, D.L.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Hurier, G.; Ilić, S.; Jaffe, A.H.; Jaffe, T.R.; Jones, W.C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Langer, M.; Lasenby, A.; Lattanzi, M.; Lawrence, C.R.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Liguori, M.; Lilje, P.B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P.M.; Ma, Y.-Z.; Macías-Pérez, J.F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Marcos-Caballero, A.; Maris, M.; Martin, P.G.; Martínez-González, E.; Masi, S.; Matarrese, S.; McGehee, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J.A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Nørgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G.W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J.P.; Reach, W.T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rubiño-Martín, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Schaefer, B.M.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J.A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, F.; Vielva, P.; Villa, F.; Wade, L.A.; Wandelt, B.D.; Wehus, I.K.; Yvon, D.; Zacchei, A.

    2016-01-01

    This paper presents a study of the ISW effect from the Planck 2015 temperature and polarization data release. The CMB is cross-correlated with different LSS tracers: the NVSS, SDSS and WISE catalogues, and the Planck 2015 convergence lensing map. This cross-correlation yields a detection at $4\\,\\sigma$, where most of the signal-to-noise is due to the Planck lensing and NVSS. In fact, the ISW effect is detected only from the Planck data (through the ISW-lensing bispectrum) at $\\approx 3\\,\\sigma$, which is similar to the detection level achieved by combining the cross-correlation signal coming from all the catalogues. This cross-correlation analysis is performed only with the Planck temperature data, since the polarization scales available in the 2015 release do not permit significant improvement of the CMB-LSS cross-correlation detectability. Nevertheless, polarization data is used to study the anomalously large ISW signal previously reported through the aperture photometry on stacked CMB features at the locat...

  16. Nucleation rate of critical droplets on an elastic string in a φ6 potential

    International Nuclear Information System (INIS)

    Kerr, W.C.; Graham, A.J.

    2004-01-01

    We obtain the nucleation rate of critical droplets for an elastic string moving in a φ 6 local potential and subject to noise and damping forces. The critical droplet is a bound soliton-antisoliton pair that carries a section of the string out of the metastable central minimum into one of the stable side minima. The frequencies of small oscillations about the critical droplet are obtained from a Heun equation. We solve the Fokker-Planck equation for the phase-space probability density by projecting it onto the eigenfunction basis obtained from the Heun equation. We employ Farkas' 'flux-overpopulation' method to obtain boundary conditions for solving the Fokker-Planck equation; these restrict the validity of our solution to the moderate to heavy damping regime. We present results for the rate as a function of temperature, well depth, and damping

  17. Slowing down of test particles in a plasma (1961); Ralentissement de particules test dans un plasma (1961)

    Energy Technology Data Exchange (ETDEWEB)

    Belayche, P; Chavy, P; Dupoux, M; Salmon, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1961-07-01

    Numerical solution of the Fokker-Planck equation applied to the slowing down of tritons in a deuterium plasma. After the equations and the boundary conditions have been written, some attention is paid to the numerical tricks used to run the problem on a high speed electronic computer. The numerical results thus obtained are then analyzed and as far as possible, mathematically explained. (authors) [French] Resolution numerique de l'equation de Fokker-Planck appliquee au ralentissement de tritons dans un plasma de deuterium. Apres avoir rappele les equations, les conditions aux limites, l'accent est mis sur les artifices numeriques utilises pour traiter le probleme sur une calculatrice a grande vitesse. Les resultats numeriques obtenus sont ensuite analyses et si possible expliques mathematiquement. En particulier ils peuvent se rattacher a ceux obtenus par application directe de la formule de Spitzer. (auteurs)

  18. Non deterministic methods for charged particle transport

    International Nuclear Information System (INIS)

    Besnard, D.C.; Buresi, E.; Hermeline, F.; Wagon, F.

    1985-04-01

    The coupling of Monte-Carlo methods for solving Fokker Planck equation with ICF inertial confinement fusion codes requires them to be economical and to preserve gross conservation properties. Besides, the presence in FPE Fokker-Planck equation of diffusion terms due to collisions between test particles and the background plasma challenges standard M.C. (Monte-Carlo) techniques if this phenomenon is dominant. We address these problems through the use of a fixed mesh in phase space which allows us to handle highly variable sources, avoiding any Russian Roulette for lowering the size of the sample. Also on this mesh are solved diffusion equations obtained from a splitting of FPE. Any non linear diffusion terms of FPE can be handled in this manner. Another method, also presented here is to use a direct particle method for solving the full FPE

  19. A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore

    Science.gov (United States)

    Chaudhry, Jehanzeb Hameed; Comer, Jeffrey; Aksimentiev, Aleksei; Olson, Luke N.

    2013-01-01

    The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a novel, robust finite element solver that combines the applications of the Newton's method to the nonlinear Galerkin form of the equations, augmented with stabilization terms to appropriately handle the drift-diffusion processes. To make direct comparison with particle-based simulations possible, our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution domain. We test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates, calculations of the ionic current though a nanopore subject to an external electric field, and modeling the effect of a DNA molecule on the ion concentration and nanopore current. PMID:24363784

  20. Planck satellite to be presented to media

    Science.gov (United States)

    2007-01-01

    Planck will make the most accurate maps yet of the microwave background radiation that fills space. It will be sensitive to temperature variations of a few millionths of a degree and will map the full sky in nine wavelengths. The immediate outcome of the Big Bang and the initial conditions for the evolution in the universe’s structure are the primary target of this important mission. From the results, a great deal more will be learnt not only about the nature and amount of dark matter, the ‘missing mass’ of the universe, but also about the nature of dark energy and the expansion of the universe itself. To address such challenging objectives, Planck will need to operate at very low, stable temperatures. Once in space, its detectors will have to be cooled to temperature levels close to absolute zero (-273.15ºC), ranging from -253ºC to only a few tenths of a degree above absolute zero. The Planck spacecraft thus has to be a marvel of cryotechnology. After integration, Planck will start a series of tests that will continue into early-2008. It will be launched by end-July 2008 in a dual-launch configuration with Herschel, ESA’s mission to study the formation of galaxies, stars and planetary systems in the infrared. Interested media are invited to fill in the reply form below. Note to editors The Planck spacecraft was built by AAS Cannes, the prime contractor, leading a consortium of industrial partners with the AAS industry branch in Turin, Italy, responsible for the satellite’s service module. ESA and the Danish National Space Centre (Copenhagen, Denmark) are responsible for the hardware provision of Planck’s telescope mirrors, manufactured by EADS Astrium (Friedrichshafen, Germany). AAS Cannes is also responsible for the payload module, the platform that hosts the telescope and the two onboard instruments, HFI and LFI. The instruments themselves are being supplied by a consortium of scientists and institutes led by the Institut d'Astrophysique Spatiale

  1. The contrasting roles of Planck's constant in classical and quantum theories

    Science.gov (United States)

    Boyer, Timothy H.

    2018-04-01

    We trace the historical appearance of Planck's constant in physics, and we note that initially the constant did not appear in connection with quanta. Furthermore, we emphasize that Planck's constant can appear in both classical and quantum theories. In both theories, Planck's constant sets the scale of atomic phenomena. However, the roles played in the foundations of the theories are sharply different. In quantum theory, Planck's constant is crucial to the structure of the theory. On the other hand, in classical electrodynamics, Planck's constant is optional, since it appears only as the scale factor for the (homogeneous) source-free contribution to the general solution of Maxwell's equations. Since classical electrodynamics can be solved while taking the homogenous source-free contribution in the solution as zero or non-zero, there are naturally two different theories of classical electrodynamics, one in which Planck's constant is taken as zero and one where it is taken as non-zero. The textbooks of classical electromagnetism present only the version in which Planck's constant is taken to vanish.

  2. Similarity solutions of the Fokker–Planck equation with time-dependent coefficients

    International Nuclear Information System (INIS)

    Lin, W.-T.; Ho, C.-L.

    2012-01-01

    In this work, we consider the solvability of the Fokker–Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker–Planck equation is reduced to an ordinary differential equation. Adopting the natural requirement that the probability current density vanishes at the boundary, the resulting ordinary differential equation turns out to be integrable, and the probability density function can be given in closed form. New examples of exactly solvable Fokker–Planck equations are presented, and their properties analyzed. - Highlights: ► Scaling form of the Fokker–Planck equation with time-dependent drift and diffusion coefficients is derived. ► Exact similarity solution of the Fokker–Planck equation is given in closed forms. ► New examples of Fokker–Planck equations exactly solvable by similarity methods are discussed.

  3. Quantum black holes and Planck's constant

    International Nuclear Information System (INIS)

    Ross, D.K.

    1987-01-01

    It is shown that the Planck-scale black holes of quantum gravity must obey a consistency condition relating Planck's constant to the integral of the mass of the black holes over time, if the usual path integral formulation of quantum mechanics is to make sense on physical spacetime. It is also shown, using time-dependent perturbation theory in ordinary quantum mechanics, that a massless particle will not propagate on physical spacetime with the black holes present unless the same condition is met. (author)

  4. From Brownian Dynamics to Markov Chain: An Ion Channel Example

    KAUST Repository

    Chen, Wan; Erban, Radek; Chapman, S. Jonathan

    2014-01-01

    is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal

  5. Stochastic Stokes' Drift, Homogenized Functional Inequalities, and Large Time Behavior of Brownian Ratchets

    KAUST Repository

    Blanchet, Adrien; Dolbeault, Jean; Kowalczyk, MichaŁ

    2009-01-01

    -similar variables attached to t he center of mass to a stationary solution of a Fokker-Planck equation modulated by a periodic perturbation with fast oscillations, with an explicit rate. We also give an asymptotic expansion of the traveling diffusion front

  6. Poisson-Boltzmann-Nernst-Planck model

    International Nuclear Information System (INIS)

    Zheng Qiong; Wei Guowei

    2011-01-01

    The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external

  7. Study of the interaction operator between two groups of particles in a completely ionised plasma. Development of the distribution functions in a series of orthogonal polynomials (1963); Etude de l'operateur d'interaction entre deux groupes de particules dans un plasma completement ionise. Developpement des fonctions de distribution en series de polynomes orthogonaux (1963)

    Energy Technology Data Exchange (ETDEWEB)

    Fain, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1963-05-15

    A completely ionised medium is considered in which the variations of the distribution functions for each species of particles is governed by the Fokker-Planck equation. The interaction operator is of a form given by Rosenbluth - Macdonald - Judd. The distribution functions are expanded into orthogonal polynomial series in the velocity space. In a first stage these functions are first split up into spherical harmonic series (or, in an equivalent form, into series of scalar products of irreducible cartesian tensors), with coefficients which are a function of the velocity modulus as well as space and time coordinates. In the second stage these coefficients are expanded into series of orthogonal functions of the velocity modulus; the 1 order harmonic is represented by the product of a Maxwell distribution and of a SONINE polynomial series, having an index of 1 + 1 / 2, which have as variable the reduced energy of the particles (in terms of a basic temperature), with coefficients which then only depend on the space and time coordinates. In the first part the relationship is established between the expansion coefficients and the moments of the distribution function, as well as the hydrodynamic values. In the second part the expansion using spherical harmonics is applied to the Fokker-Planck equation. The general expression for the second member is given as well as the particular expressions corresponding to the cases where the operator is linearized. In the third part the complete expansion in orthogonal polynomial series is applied to the Fokker-Planck equation. The expression of the generating functions is given for all the harmonics in the case of the linearized operator, as well as the transport equations for the first four harmonics. (author) [French] On considere un milieu completement ionise ou l'evolution des fonctions de distribution pour chaque espece de particules est regie par l'equation de FOKKER-PLANCK. L'operateur d'interaction se met sous la forme

  8. Gyrokinetic neoclassical study of the bootstrap current in the tokamak edge pedestal with fully non-linear Coulomb collisions

    Energy Technology Data Exchange (ETDEWEB)

    Hager, Robert, E-mail: rhager@pppl.gov; Chang, C. S., E-mail: cschang@pppl.gov [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543 (United States)

    2016-04-15

    As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steep edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. A new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.

  9. Max Planck et les quanta

    CERN Document Server

    Boudenot, Jean-Claude

    2016-01-01

    « Les atomes, dit Jean Perrin en 1913, ne sont pas ces éléments éternels et insécables dont l'irréductible simplicité donnait au possible une borne, et, dans leur inimaginable petitesse, nous commençons à pressentir un fourmillement prodigieux de mondes nouveaux ». C'est bien dans un monde totalement nouveau, le monde quantique, que nous a fait pénétrer la découverte des quanta par Max Planck. Son article de 1900 est le déclencheur de l'une des plus grandes révolutions scientifiques de tous les temps. Les trente années qui suivent sont les plus riches de la physique ; Planck, Einstein, Bohr, Sommerfeld, de Broglie, Schrödinger, Heisenberg, Dirac, Born, Pauli… reconstruisent la physique sur de nouvelles bases sur fond de conflit des générations. Le monde est par ailleurs secoué par la guerre, Max Planck est tourmenté et vit des épreuves personnelles dramatiques. C'est l'homme, aussi bien que l'oeuvre, que les auteurs ont tenté de dépeindre dans cet ouvrage. Ils ont également souhait�...

  10. Approximating distributions from moments

    Science.gov (United States)

    Pawula, R. F.

    1987-11-01

    A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.

  11. Treatment of constraints in the stochastic quantization method and covariantized Langevin equation

    International Nuclear Information System (INIS)

    Ikegami, Kenji; Kimura, Tadahiko; Mochizuki, Riuji

    1993-01-01

    We study the treatment of the constraints in the stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking into account the Ito calculus. Then we obtain an improved Langevin equation and the Fokker-Planck equation which naturally leads to the correct path integral quantization of the constrained system as the stochastic equilibrium state. This treatment is applied to an O(N) non-linear σ model and it is shown that singular terms appearing in the improved Langevin equation cancel out the δ n (0) divergences in one loop order. We also ascertain that the above Langevin equation, rewritten in terms of independent variables, is actually equivalent to the one in the general-coordinate transformation covariant and vielbein-rotation invariant formalism. (orig.)

  12. Cosmological constraints on neutrinos with Planck data

    International Nuclear Information System (INIS)

    Spinelli, M.

    2015-01-01

    Neutrinos take part in the dance of the evolving Universe influencing its history from leptogenesis, to Big Bang nucleosynthesis, until late time structure formation. This makes cosmology, and in particular one of its primary observables the Cosmic Microwave Background (CMB), an unusual but valuable tool for testing Neutrino Physics. The best measurement to date of full-sky CMB anisotropies comes from the Planck satellite launched in 2009 by the European Space Agency (ESA) and successful follower of COBE and WMAP. Testing Planck data against precise theoretical predictions allow us to shed light on various interesting open questions such as the value of the absolute scale of neutrino masses or their energy density. We revise here the results concerning neutrinos obtained by the Planck Collaboration in the 2013 data release

  13. Cosmological constraints on neutrinos with Planck data

    Energy Technology Data Exchange (ETDEWEB)

    Spinelli, M. [Laboratoire de l’Accélérateur Linéaire, Bat.200, 91400 Orsay (France)

    2015-07-15

    Neutrinos take part in the dance of the evolving Universe influencing its history from leptogenesis, to Big Bang nucleosynthesis, until late time structure formation. This makes cosmology, and in particular one of its primary observables the Cosmic Microwave Background (CMB), an unusual but valuable tool for testing Neutrino Physics. The best measurement to date of full-sky CMB anisotropies comes from the Planck satellite launched in 2009 by the European Space Agency (ESA) and successful follower of COBE and WMAP. Testing Planck data against precise theoretical predictions allow us to shed light on various interesting open questions such as the value of the absolute scale of neutrino masses or their energy density. We revise here the results concerning neutrinos obtained by the Planck Collaboration in the 2013 data release.

  14. Cosmological constraints on neutrinos with Planck data

    Science.gov (United States)

    Spinelli, M.

    2015-07-01

    Neutrinos take part in the dance of the evolving Universe influencing its history from leptogenesis, to Big Bang nucleosynthesis, until late time structure formation. This makes cosmology, and in particular one of its primary observables the Cosmic Microwave Background (CMB), an unusual but valuable tool for testing Neutrino Physics. The best measurement to date of full-sky CMB anisotropies comes from the Planck satellite launched in 2009 by the European Space Agency (ESA) and successful follower of COBE and WMAP. Testing Planck data against precise theoretical predictions allow us to shed light on various interesting open questions such as the value of the absolute scale of neutrino masses or their energy density. We revise here the results concerning neutrinos obtained by the Planck Collaboration in the 2013 data release.

  15. The physicist. Max Planck and the decay of the world; Der Physiker. Max Planck und das Zerfallen der Welt

    Energy Technology Data Exchange (ETDEWEB)

    Fischer, Ernst Peter

    2010-06-15

    The live of the physicist Max Planck was as exciting, conflicting, and rich on catastrophes as the epoch, in which he lived. Ernst Peter Fischer draws in this fascinatingly told biography the eventful history of the Nobel-price bearer and illustrates simultaneously the unique attainment of Planck, the quantum theory of whom not only revolted the science but also changed fundamentally our picture of the world.

  16. Higher order statistics of curvature perturbations in IFF model and its Planck constraints

    International Nuclear Information System (INIS)

    Fujita, Tomohiro; Yokoyama, Shuichiro

    2013-01-01

    We compute the power spectrum P ζ and non-linear parameters f NL and τ NL of the curvature perturbation induced during inflation by the electromagnetic fields in the kinetic coupling model (IFF model). By using the observational result of P ζ ,f NL and τ NL reported by the Planck collaboration, we study the constraint on the model comprehensively. Interestingly, if the single slow-rolling inflaton is responsible for the observed P ζ , the constraint from τ NL is most stringent. We also find a general relationship between f NL and τ NL generated in this model. Even if f NL ∼ O(1), a detectable τ NL can be produced

  17. Calibrating the Planck cluster mass scale with CLASH

    Science.gov (United States)

    Penna-Lima, M.; Bartlett, J. G.; Rozo, E.; Melin, J.-B.; Merten, J.; Evrard, A. E.; Postman, M.; Rykoff, E.

    2017-08-01

    We determine the mass scale of Planck galaxy clusters using gravitational lensing mass measurements from the Cluster Lensing And Supernova survey with Hubble (CLASH). We have compared the lensing masses to the Planck Sunyaev-Zeldovich (SZ) mass proxy for 21 clusters in common, employing a Bayesian analysis to simultaneously fit an idealized CLASH selection function and the distribution between the measured observables and true cluster mass. We used a tiered analysis strategy to explicitly demonstrate the importance of priors on weak lensing mass accuracy. In the case of an assumed constant bias, bSZ, between true cluster mass, M500, and the Planck mass proxy, MPL, our analysis constrains 1-bSZ = 0.73 ± 0.10 when moderate priors on weak lensing accuracy are used, including a zero-mean Gaussian with standard deviation of 8% to account for possible bias in lensing mass estimations. Our analysis explicitly accounts for possible selection bias effects in this calibration sourced by the CLASH selection function. Our constraint on the cluster mass scale is consistent with recent results from the Weighing the Giants program and the Canadian Cluster Comparison Project. It is also consistent, at 1.34σ, with the value needed to reconcile the Planck SZ cluster counts with Planck's base ΛCDM model fit to the primary cosmic microwave background anisotropies.

  18. Planck-scale-modified dispersion relations in FRW spacetime

    Science.gov (United States)

    Rosati, Giacomo; Amelino-Camelia, Giovanni; Marcianò, Antonino; Matassa, Marco

    2015-12-01

    In recent years, Planck-scale modifications of the dispersion relation have been attracting increasing interest also from the viewpoint of possible applications in astrophysics and cosmology, where spacetime curvature cannot be neglected. Nonetheless, the interplay between Planck-scale effects and spacetime curvature is still poorly understood, particularly in cases where curvature is not constant. These challenges have been so far postponed by relying on an ansatz, first introduced by Jacob and Piran. We propose here a general strategy of analysis of the effects of modifications of the dispersion relation in Friedmann-Robertson-Walker spacetimes, applicable both to cases where the relativistic equivalence of frames is spoiled ("preferred-frame scenarios") and to the alternative possibility of "DSR-relativistic theories," theories that are fully relativistic but with relativistic laws deformed so that the modified dispersion relation is observer independent. We show that the Jacob-Piran ansatz implicitly assumes that spacetime translations are not affected by the Planck scale, while under rather general conditions, the same Planck-scale quantum-spacetime structures producing modifications of the dispersion relation also affect translations. Through the explicit analysis of one of the effects produced by modifications of the dispersion relation, an effect amounting to Planck-scale corrections to travel times, we show that our concerns are not merely conceptual but rather can have significant quantitative implications.

  19. Sensitivity analysis in molecular dynamics and chemical kinetics and a theory of intramolecular energy transfer in the presence of intense radiation fields

    International Nuclear Information System (INIS)

    Eslava, L.A.

    1983-01-01

    This thesis is an investigation of two topics in the area of molecular and chemical dynamics phenomena. The first topic, Sensitivity Analysis in Molecular Dynamics and Chemical Kinetics, explores the response of the numerical solutions to variation in the input information. After a brief consideration of elementary sensitivity coefficients (i.e. partial derivatives of observables with respect to model parameters), attention is focused on an entire new family of derived coefficients capable of exhibiting important aspects of the underlying dynamics. Each derived sensitivity coefficient has a unique physical interpretation in terms of an experiment or modeling calculation. Also, a fitting model for rotationally inelastic cross sections that accurately predicts cross sections away from the region of parameter space used in the fitting is presented. The global behavior of cross sections in parameter space is examined, and a nonlinear interpolation formula is suggested which utilizes sensitivity information. The second topic, A Theory of Intramolecular Energy Transfer in the Presence of Intense Radiation Fields, represents a theoretical formulation of energy redistribution based on stochastic considerations. The fundamental assumption is that a random phase approximation is valid at specific time intervals. This results in the replacement of the Schrodinger equation by a master-type equation, which is further approximated by a Fokker-Planck diffusion like equation. Energy transfer is described as a flow of probability among the quantum states, and the dissociation of dynamics are embodied in the boundary conditions. By virtue of the continuous character of the Fokker-Planck equation, the computational difficulty of its numerical solution depends only on the number of degrees of freedom and not on the number of states

  20. Stochastic quantum inflation for a canonical scalar field with linear self-interaction potential

    Energy Technology Data Exchange (ETDEWEB)

    Panotopoulos, Grigoris [CENTRA, Instituto Superior Tecnico, Universidade de Lisboa, Lisboa (Portugal)

    2017-10-15

    We apply Starobinsky's formalism of stochastic inflation to the case of a massless minimally coupled scalar field with linear self-interaction potential. We solve the corresponding Fokker-Planck equation exactly, and we obtain analytical expressions for the stochastic expectation values. (orig.)

  1. On the Hughes model and numerical aspects

    KAUST Repository

    Gomes, Diogo A.; Machado Velho, Roberto

    2017-01-01

    We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori

  2. Some Numerical Aspects on Crowd Motion - The Hughes Model

    KAUST Repository

    Gomes, Diogo A.; Machado Velho, Roberto

    2016-01-01

    Here, we study a crowd model proposed by R. Hughes in [5] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. First, we establish a priori

  3. The effect of an alternating electric field on a totally ionised plasma

    International Nuclear Information System (INIS)

    Baglin, H.; Brin, A.; Ozias, Y.; Salmon, J.

    1960-01-01

    The equation giving the distribution function of the electrons in a steady-state, for a fully ionized plasma in an a.c. field, are provided from the Fokker-Planck equation. The electric conductivity is complex and depends on the frequency. (author) [fr

  4. Planck 2013 results. XIV. Zodiacal emission

    DEFF Research Database (Denmark)

    Ade, P. A. R.; Aghanim, N.; Armitage-Caplan, C.

    2013-01-01

    , three asteroidal dust bands, a circumsolar ring, and an Earth-trailing feature. The emissivity of the diuse cloud decreases with increasing wavelength, as expected from earlier analyses. The emissivities of the dust bands, however, decrease less rapidly, indicating that the properties of the grains......The Planck satellite provides a set of all-sky maps at nine frequencies from 30 GHz to 857 GHz. Planets, minor bodies, and diuse interplanetary dust emission (IPD) are all observed. The IPD can be separated from Galactic and other emissions because Planck views a given point on the celestial sphere...

  5. A Priori Regularity of Parabolic Partial Differential Equations

    KAUST Repository

    Berkemeier, Francisco

    2018-05-13

    In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular initial data. These estimates are obtained by understanding the time decay of norms of solutions. First, we derive regularity results for the heat equation by estimating the decay of Lebesgue norms. Then, we apply similar methods to the Fokker-Planck equation with suitable assumptions on the advection and diffusion. Finally, we conclude by extending our techniques to the porous media equation. The sharpness of our results is confirmed by examining known solutions of these equations. The main contribution of this thesis is the use of functional inequalities to express decay of norms as differential inequalities. These are then combined with ODE methods to deduce estimates for the norms of solutions and their derivatives.

  6. Mobility and volatility: What is behind the rising income inequality in the United States

    Science.gov (United States)

    Wu, Huixuan; Li, Yao

    2018-02-01

    Inequality of family incomes in the United States has increased significantly in the past four decades. This is largely interpreted as a result of unequal mobility, e.g., the rich can get richer at a faster pace than the rest of the population. However, using nationally representative data and the Fokker-Planck equation, our study shows that income mobility in the United States has remained stable. Instead, we find another factor - income volatility, which measures the instability of incomes - has increased considerably and caused the surge of income inequality. In addition, the rising volatility is associated with the plummeting of income-growth opportunity, creating the feeling that the American Dream is in decline. Volatility has often been overlooked in previous studies on inequality, partially because mobility and volatility are usually studied separately. By contrast, the Fokker-Planck equation takes both mobility and volatility into consideration, making it a more comprehensive model.

  7. Non-equilibrium effects upon the non-Markovian Caldeira-Leggett quantum master equation

    International Nuclear Information System (INIS)

    Bolivar, A.O.

    2011-01-01

    Highlights: → Classical Brownian motion described by a non-Markovian Fokker-Planck equation. → Quantization process. → Quantum Brownian motion described by a non-Markovian Caldeira-Leggett equation. → A non-equilibrium quantum thermal force is predicted. - Abstract: We obtain a non-Markovian quantum master equation directly from the quantization of a non-Markovian Fokker-Planck equation describing the Brownian motion of a particle immersed in a generic environment (e.g. a non-thermal fluid). As far as the especial case of a heat bath comprising of quantum harmonic oscillators is concerned, we derive a non-Markovian Caldeira-Leggett master equation on the basis of which we work out the concept of non-equilibrium quantum thermal force exerted by the harmonic heat bath upon the Brownian motion of a free particle. The classical limit (or dequantization process) of this sort of non-equilibrium quantum effect is scrutinized, as well.

  8. Excess B‐modes extracted from the Planck polarization maps

    DEFF Research Database (Denmark)

    Nørgaard-Nielsen, Hans Ulrik

    2016-01-01

    on both temperature and polarization data obtained by the WMAP satellite. The main goal of this paper is to demonstrate the feasibility of neural networks for extracting the CMB signal from the Planck polarization data with high precision. Both auto‐correlation and cross‐correlation power spectra within...... a mask covering about 63 % of the sky have been used together with a “high pass filter” in order to minimize the influence of the remaining systematic errors in the Planck Q and U maps. Using the Planck 2015 released polarization maps, a BB power spectrum have been extracted by Multilayer Perceptron...... tensor to scalar ratios). The feasibility of the neural network to remove the residual systematics from the available Planck polarization data to a high level has been demonstrated. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)...

  9. Poisson–Boltzmann–Nernst–Planck model

    Science.gov (United States)

    Zheng, Qiong; Wei, Guo-Wei

    2011-01-01

    The Poisson–Nernst–Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst–Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst–Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst–Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson–Boltzmann and Nernst–Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations

  10. Poisson-Boltzmann-Nernst-Planck model.

    Science.gov (United States)

    Zheng, Qiong; Wei, Guo-Wei

    2011-05-21

    The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external

  11. Planck 2015 results. V. LFI calibration

    CERN Document Server

    Ade, P.A.R.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartolo, N.; Battaglia, P.; Battaner, E.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bock, J.J.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cardoso, J.F.; Catalano, A.; Chamballu, A.; Christensen, P.R.; Colombi, S.; Colombo, L.P.L.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Dickinson, C.; Diego, J.M.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Ensslin, T.A.; Eriksen, H.K.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giraud-Heraud, Y.; Gjerlow, E.; Gonzalez-Nuevo, J.; Gorski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Hansen, F.K.; Hanson, D.; Harrison, D.L.; Henrot-Versille, S.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Hurier, G.; Jaffe, A.H.; Jaffe, T.R.; Juvela, M.; Keihanen, E.; Keskitalo, R.; Kisner, T.S.; Knoche, J.; Krachmalnicoff, N.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Lattanzi, M.; Lawrence, C.R.; Leahy, J.P.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lopez-Caniego, M.; Lubin, P.M.; Macias-Perez, J.F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Maris, M.; Martin, P.G.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; McGehee, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J.A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Novikov, D.; Novikov, I.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Partridge, B.; Pasian, F.; Patanchon, G.; Pearson, T.J.; Peel, M.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Pierpaoli, E.; Pietrobon, D.; Pointecouteau, E.; Polenta, G.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renzi, A.; Rocha, G.; Romelli, E.; Rosset, C.; Rossetti, M.; Roudier, G.; Rubino-Martin, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Stolyarov, V.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Turler, M.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vassallo, T.; Vielva, P.; Villa, F.; Wade, L.A.; Wandelt, B.D.; Watson, R.; Wehus, I.K.; Wilkinson, A.; Yvon, D.; Zacchei, A.; Zonca, A.

    2016-01-01

    We present a description of the pipeline used to calibrate the Planck Low Frequency Instrument (LFI) timelines into thermodynamic temperatures for the Planck 2015 data release, covering 4 years of uninterrupted operations. As in the 2013 data release, our calibrator is provided by the spin-synchronous modulation of the CMB dipole, exploiting both the orbital and solar components. Our 2015 LFI analysis provides an independent Solar dipole estimate in excellent agreement with that of HFI and within $1\\sigma$ (0.3 % in amplitude) of the WMAP value. This 0.3 % shift in the peak-to-peak dipole temperature from WMAP and a global overhaul of the iterative calibration code increases the overall level of the LFI maps by 0.45 % (30 GHz), 0.64 % (44 GHz), and 0.82 % (70 GHz) in temperature with respect to the 2013 Planck data release, thus reducing the discrepancy with the power spectrum measured by WMAP. We estimate that the LFI calibration uncertainty is at the level of 0.20 % for the 70 GHz map, 0.26 % for the 44 GHz...

  12. De Max-Planck medaille

    NARCIS (Netherlands)

    Heijmans, H.G.; van Woerkom, P.Th.L.M.; Ankersmit, W.; Hagman, R.; Heijmans, H.G.; Olsder, G.J.; van de Schootbrugge, G.

    2017-01-01

    De Max-Planck-Medaille is een onderscheiding die sinds 1929 jaarlijks wordt uitgereikt door de toentertijd grootste vereniging van natuurkundigen ter wereld: de Deutsche Physikalische Gesellschaft. Het is als het ware de Nobelprijs voor de theoretische natuurkunde, volgens de natuurkundigen zelf. In

  13. Planck 2015 results: XXVII. The second Planck catalogue of Sunyaev-Zeldovich sources

    DEFF Research Database (Denmark)

    Ade, P. A R; Aghanim, N.; Arnaud, M.

    2016-01-01

    We present the all-sky Planck catalogue of Sunyaev-Zeldovich (SZ) sources detected from the 29 month full-mission data. The catalogue (PSZ2) is the largest SZ-selected sample of galaxy clusters yet produced and the deepest systematic all-sky surveyof galaxy clusters. It contains 1653 detections, ...

  14. Monte Carlo particle simulation and finite-element techniques for tandem mirror transport

    International Nuclear Information System (INIS)

    Rognlien, T.D.; Cohen, B.I.; Matsuda, Y.; Stewart, J.J. Jr.

    1987-01-01

    A description is given of numerical methods used in the study of axial transport in tandem mirrors owing to Coulomb collisions and rf diffusion. The methods are Monte Carlo particle simulations and direct solution to the Fokker-Planck equations by finite-element expansion. (author)

  15. Non-equipotential magnetic surfaces and mode-transition in tokamaks

    International Nuclear Information System (INIS)

    Li Xingzhong

    1988-01-01

    The solution of the Fokker-Planck equation is used to describe a phase transition in velocity space. This transition is related to the mode-transition in tokamaks. After the transition the electrostatic potential on a magnetic surface cannot be considered as a constant. (orig.)

  16. Impact of radial transport on the quasilinear plateau formation due to electron cyclotron wave absorption

    NARCIS (Netherlands)

    Peeters, A.G.; Westerhof, E.

    1996-01-01

    Numerical simulations using a three-dimensional Fokker-Planck code show that for small tokamaks the transport of electrons across the magnetic surfaces at a level consistent with anomalous transport has a large influence on the formation of the quasilinear plateau during electron cyclotron resonant

  17. Monte Carlo particle simulation and finite-element techniques for tandem mirror transport

    International Nuclear Information System (INIS)

    Rognlien, T.D.; Cohen, B.I.; Matsuda, Y.; Stewart, J.J. Jr.

    1985-12-01

    A description is given of numerical methods used in the study of axial transport in tandem mirrors owing to Coulomb collisions and rf diffusion. The methods are Monte Carlo particle simulations and direct solution to the Fokker-Planck equations by finite-element expansion. 11 refs

  18. Derivation of stochastic differential equations for scrape-off layer plasma fluctuations from experimentally measured statistics

    Energy Technology Data Exchange (ETDEWEB)

    Mekkaoui, Abdessamad [IEK-4 Forschungszentrum Juelich 52428 (Germany)

    2013-07-01

    A method to derive stochastic differential equations for intermittent plasma density dynamics in magnetic fusion edge plasma is presented. It uses a measured first four moments (mean, variance, Skewness and Kurtosis) and the correlation time of turbulence to write a Pearson equation for the probability distribution function of fluctuations. The Fokker-Planck equation is then used to derive a Langevin equation for the plasma density fluctuations. A theoretical expectations are used as a constraints to fix the nonlinearity structure of the stochastic differential equation. In particular when the quadratically nonlinear dynamics is assumed, then it is shown that the plasma density is driven by a multiplicative Wiener process and evolves on the turbulence correlation time scale, while the linear growth is quadratically damped by the fluctuation level. Strong criteria for statistical discrimination of experimental time series are proposed as an alternative to the Kurtosis-Skewness scaling. This scaling is broadly used in contemporary literature to characterize edge turbulence, but it is inappropriate because a large family of distributions could share this scaling. Strong criteria allow us to focus on the relevant candidate distribution and approach a nonlinear structure of edge turbulence model.

  19. Planck 2015 results: XIII. Cosmological parameters

    DEFF Research Database (Denmark)

    Ade, P. A R; Aghanim, N.; Arnaud, M.

    2016-01-01

    is constrained to w =-1.006 ± 0.045, consistent with the expected value for a cosmological constant. The standard big bang nucleosynthesis predictions for the helium and deuterium abundances for the best-fit Planck base ΛCDM cosmology are in excellent agreement with observations. We also constraints...... of the theory; for example, combining Planck observations with other astrophysical data we find Neff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value Neff = 3.046 of the Standard Model of particle physics. The sum of neutrino masses is constrained to â'mν

  20. Microscopic model for the non-linear fluctuating hydrodynamic of 4 He superfluid helium deduced by maximum entropy method

    International Nuclear Information System (INIS)

    Alvarez R, J.T.

    1998-01-01

    This thesis presents a microscopic model for the non-linear fluctuating hydrodynamic of superfluid helium ( 4 He), model developed by means of the Maximum Entropy Method (Maxent). In the chapter 1, it is demonstrated the necessity to developing a microscopic model for the fluctuating hydrodynamic of the superfluid helium, starting from to show a brief overview of the theories and experiments developed in order to explain the behavior of the superfluid helium. On the other hand, it is presented the Morozov heuristic method for the construction of the non-linear hydrodynamic fluctuating of simple fluid. Method that will be generalized for the construction of the non-linear fluctuating hydrodynamic of the superfluid helium. Besides, it is presented a brief summary of the content of the thesis. In the chapter 2, it is reproduced the construction of a Generalized Fokker-Planck equation, (GFP), for a distribution function associated with the coarse grained variables. Function defined with aid of a nonequilibrium statistical operator ρhut FP that is evaluated as Wigneris function through ρ CG obtained by Maxent. Later this equation of GFP is reduced to a non-linear local FP equation from considering a slow and Markov process in the coarse grained variables. In this equation appears a matrix D mn defined with a nonequilibrium coarse grained statistical operator ρhut CG , matrix elements are used in the construction of the non-linear fluctuating hydrodynamics equations of the superfluid helium. In the chapter 3, the Lagrange multipliers are evaluated for to determine ρhut CG by means of the local equilibrium statistical operator ρhut l -tilde with the hypothesis that the system presents small fluctuations. Also are determined the currents associated with the coarse grained variables and furthermore are evaluated the matrix elements D mn but with aid of a quasi equilibrium statistical operator ρhut qe instead of the local equilibrium operator ρhut l -tilde. Matrix

  1. Planck intermediate results - LII. Planet flux densities

    DEFF Research Database (Denmark)

    Akrami, Y.; Ashdown, M.; Aumont, J.

    2017-01-01

    Measurements of flux density are described for five planets, Mars, Jupiter, Saturn, Uranus, and Neptune, across the six Planck High Frequency Instrument frequency bands (100–857 GHz) and these are then compared with models and existing data. In our analysis, we have also included estimates...... of the brightness of Jupiter and Saturn at the three frequencies of the Planck Low Frequency Instrument (30, 44, and 70 GHz). The results provide constraints on the intrinsic brightness and the brightness time-variability of these planets. The majority of the planet flux density estimates are limited by systematic...... errors, but still yield better than 1% measurements in many cases. Applying data from Planck HFI, the Wilkinson Microwave Anisotropy Probe (WMAP), and the Atacama Cosmology Telescope (ACT) to a model that incorporates contributions from Saturn’s rings to the planet’s total flux density suggests a best...

  2. Planck 2013 results. XII. Diffuse component separation

    CERN Document Server

    Ade, P A R; Armitage-Caplan, C; Arnaud, M; Ashdown, M; Atrio-Barandela, F; Aumont, J; Baccigalupi, C; Banday, A J; Barreiro, R B; Bartlett, J G; Battaner, E; Benabed, K; Benoît, A; Benoit-Lévy, A; Bernard, J -P; Bersanelli, M; Bielewicz, P; Bobin, J; Bock, J J; Bonaldi, A; Bonavera, L; Bond, J R; Borrill, J; Bouchet, F R; Boulanger, F; Bridges, M; Bucher, M; Burigana, C; Butler, R C; Cardoso, J -F; Catalano, A; Challinor, A; Chamballu, A; Chary, R -R; Chen, X; Chiang, L -Y; Chiang, H C; Christensen, P R; Church, S; Clements, D L; Colombi, S; Colombo, L P L; Couchot, F; Coulais, A; Crill, B P; Cruz, M; Curto, A; Cuttaia, F; Danese, L; Davies, R D; Davis, R J; de Bernardis, P; de Rosa, A; de Zotti, G; Delabrouille, J; Delouis, J -M; Désert, F -X; Dickinson, C; Diego, J M; Dole, H; Donzelli, S; Doré, O; Douspis, M; Dunkley, J; Dupac, X; Efstathiou, G; Enßlin, T A; Eriksen, H K; Falgarone, E; Finelli, F; Forni, O; Frailis, M; Fraisse, A A; Franceschi, E; Galeotta, S; Ganga, K; Giard, M; Giardino, G; Giraud-Héraud, Y; González-Nuevo, J; Górski, K M; Gratton, S; Gregorio, A; Gruppuso, A; Hansen, F K; Hanson, D; Harrison, D; Helou, G; Henrot-Versillé, S; Hernández-Monteagudo, C; Herranz, D; Hildebrandt, S R; Hivon, E; Hobson, M; Holmes, W A; Hornstrup, A; Hovest, W; Huey, G; Huffenberger, K M; Jaffe, T R; Jaffe, A H; Jewell, J; Jones, W C; Juvela, M; Keihänen, E; Keskitalo, R; Kisner, T S; Kneissl, R; Knoche, J; Knox, L; Kunz, M; Kurki-Suonio, H; Lagache, G; Lähteenmäki, A; Lamarre, J -M; Lasenby, A; Laureijs, R J; Lawrence, C R; Jeune, M Le; Leach, S; Leahy, J P; Leonardi, R; Lesgourgues, J; Liguori, M; Lilje, P B; Linden-Vørnle, M; López-Caniego, M; Lubin, P M; Macías-Pérez, J F; Maffei, B; Maino, D; Mandolesi, N; Marcos-Caballero, A; Maris, M; Marshall, D J; Martin, P G; Martínez-González, E; Masi, S; Matarrese, S; Matthai, F; Mazzotta, P; Meinhold, P R; Melchiorri, A; Mendes, L; Mennella, A; Migliaccio, M; Mikkelsen, K; Mitra, S; Miville-Deschênes, M -A; Moneti, A; Montier, L; Morgante, G; Mortlock, D; Moss, A; Munshi, D; Naselsky, P; Nati, F; Natoli, P; Netterfield, C B; Nørgaard-Nielsen, H U; Noviello, F; Novikov, D; Novikov, I; O'Dwyer, I J; Osborne, S; Oxborrow, C A; Paci, F; Pagano, L; Pajot, F; Paladini, R; Paoletti, D; Partridge, B; Pasian, F; Patanchon, G; Pearson, T J; Perdereau, O; Perotto, L; Perrotta, F; Pettorino, V; Piacentini, F; Piat, M; Pierpaoli, E; Pietrobon, D; Plaszczynski, S; Platania, P; Pointecouteau, E; Polenta, G; Ponthieu, N; Popa, L; Poutanen, T; Pratt, G W; Prézeau, G; Prunet, S; Puget, J -L; Rachen, J P; Reach, W T; Rebolo, R; Reinecke, M; Remazeilles, M; Renault, C; Renzi, A; Ricciardi, S; Riller, T; Ristorcelli, I; Rocha, G; Rosset, C; Roudier, G; Rowan-Robinson, M; Rubiño-Martín, J A; Rusholme, B; Salerno, E; Sandri, M; Santos, D; Savini, G; Schiavon, F; Scott, D; Seiffert, M D; Shellard, E P S; Spencer, L D; Starck, J -L; Stompor, R; Sudiwala, R; Sunyaev, R; Sureau, F; Sutton, D; Suur-Uski, A -S; Sygnet, J -F; Tauber, J A; Tavagnacco, D; Terenzi, L; Toffolatti, L; Tomasi, M; Tristram, M; Tucci, M; Tuovinen, J; Türler, M; Umana, G; Valenziano, L; Valiviita, J; Van Tent, B; Varis, J; Viel, M; Vielva, P; Villa, F; Vittorio, N; Wade, L A; Wandelt, B D; Wehus, I K; Wilkinson, A; Xia, J -Q; Yvon, D; Zacchei, A; Zonca, A

    2014-01-01

    Planck has produced detailed all-sky observations over nine frequency bands between 30 and 857 GHz. These observations allow robust reconstruction of the primordial cosmic microwave background (CMB) temperature fluctuations over nearly the full sky, as well as new constraints on Galactic foregrounds. This paper describes the component separation framework adopted by Planck. We test four foreground-cleaned CMB maps derived using qualitatively different component separation algorithms. The quality of our reconstructions is evaluated through detailed simulations and internal comparisons, and shown through various tests to be internally consistent and robust for CMB power spectrum and cosmological parameter estimation up to l = 2000. The parameter constraints on LambdaCDM cosmologies derived from these maps are consistent with those presented in the cross-spectrum based Planck likelihood analysis. We choose two of the CMB maps for specific scientific goals. We also present maps and frequency spectra of the Galact...

  3. The Atacama Cosmology Telescope: cross correlation with Planck maps

    Energy Technology Data Exchange (ETDEWEB)

    Louis, Thibaut; Calabrese, Erminia; Dunkley, Joanna; Næss, Sigurd [Department of Astrophysics, Oxford University, Oxford OX1 3RH (United Kingdom); Addison, Graeme E.; Hincks, Adam D. [Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z4 (Canada); Hasselfield, Matthew; Hlozek, Renée [Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544 (United States); Bond, J. Richard; Hajian, Amir [Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8 (Canada); Das, Sudeep [Argonne National Laboratory, 9700 S. Cass Ave., Lemont, IL 60439 (United States); Devlin, Mark J. [Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104, U.S.A (United States); Dünner, Rolando; Infante, Leopoldo [Departamento de Astronomía y Astrofísica, Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22 (Chile); Gralla, Megan; Marriage, Tobias A. [Dept. of Physics and Astronomy, The Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218-2686 (United States); Huffenberger, Kevin [Department of Physics, Florida State University, Keen Physics Building, 77 Chieftan Way, Tallahassee, Florida (United States); Kosowsky, Arthur [Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, 15260 (United States); Moodley, Kavilan [Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, Durban, 4041 (South Africa); Niemack, Michael D., E-mail: Thibaut.Louis@astro.ox.ac.uk [Joseph Henry Laboratories of Physics, Jadwin Hall, Princeton University, Princeton, NJ 08544 (United States); and others

    2014-07-01

    We present the temperature power spectrum of the Cosmic Microwave Background obtained by cross-correlating maps from the Atacama Cosmology Telescope (ACT) at 148 and 218 GHz with maps from the Planck satellite at 143 and 217 GHz, in two overlapping regions covering 592 square degrees. We find excellent agreement between the two datasets at both frequencies, quantified using the variance of the residuals between the ACT power spectra and the ACT × Planck cross-spectra. We use these cross-correlations to measure the calibration of the ACT data at 148 and 218 GHz relative to Planck, to 0.7% and 2% precision respectively. We find no evidence for anisotropy in the calibration parameter. We compare the Planck 353 GHz power spectrum with the measured amplitudes of dust and cosmic infrared background (CIB) of ACT data at 148 and 218 GHz. We also compare planet and point source measurements from the two experiments.

  4. Planck 2013 results. XV. CMB power spectra and likelihood

    CERN Document Server

    Ade, P.A.R.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartlett, J.G.; Battaner, E.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J.J.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Boulanger, F.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cardoso, J.F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, L.Y.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Combet, C.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.M.; Desert, F.X.; Dickinson, C.; Diego, J.M.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Dunkley, J.; Dupac, X.; Efstathiou, G.; Elsner, F.; Ensslin, T.A.; Eriksen, H.K.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschi, E.; Gaier, T.C.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giardino, G.; Giraud-Heraud, Y.; Gjerlow, E.; Gonzalez-Nuevo, J.; Gorski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J.E.; Hansen, F.K.; Hanson, D.; Harrison, D.; Helou, G.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Hurier, G.; Jaffe, T.R.; Jaffe, A.H.; Jewell, J.; Jones, W.C.; Juvela, M.; Keihanen, E.; Keskitalo, R.; Kiiveri, K.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Lattanzi, M.; Laureijs, R.J.; Lawrence, C.R.; Le Jeune, M.; Leach, S.; Leahy, J.P.; Leonardi, R.; Leon-Tavares, J.; Lesgourgues, J.; Liguori, M.; Lilje, P.B.; Lindholm, V.; Linden-Vornle, M.; Lopez-Caniego, M.; Lubin, P.M.; Macias-Perez, J.F.; Maffei, B.; Maino, D.; Mandolesi, N.; Marinucci, D.; Maris, M.; Marshall, D.J.; Martin, P.G.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; Matthai, F.; Mazzotta, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Menegoni, E.; Mennella, A.; Migliaccio, M.; Millea, M.; Mitra, S.; Miville-Deschenes, M.A.; Molinari, D.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; O'Dwyer, I.J.; Orieux, F.; Osborne, S.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paladini, R.; Paoletti, D.; Partridge, B.; Pasian, F.; Patanchon, G.; Paykari, P.; Perdereau, O.; Perotto, L.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Rahlin, A.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Ricciardi, S.; Riller, T.; Ringeval, C.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rowan-Robinson, M.; Rubino-Martin, J.A.; Rusholme, B.; Sandri, M.; Sanselme, L.; Santos, D.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Starck, J.L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Turler, M.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Varis, J.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L.A.; Wandelt, B.D.; Wehus, I.K.; White, M.; White, S.D.M.; Yvon, D.; Zacchei, A.; Zonca, A.

    2014-01-01

    We present the Planck likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations. We use this likelihood to derive the Planck CMB power spectrum over three decades in l, covering 2 = 50, we employ a correlated Gaussian likelihood approximation based on angular cross-spectra derived from the 100, 143 and 217 GHz channels. We validate our likelihood through an extensive suite of consistency tests, and assess the impact of residual foreground and instrumental uncertainties on cosmological parameters. We find good internal agreement among the high-l cross-spectra with residuals of a few uK^2 at l <= 1000. We compare our results with foreground-cleaned CMB maps, and with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. The best-fit LCDM cosmology is in excellent agreement with preliminary Planck polarisation spectra. The standard LCDM cosmology is well constrained b...

  5. Does the planck mass run on the cosmological-horizon scale?

    Science.gov (United States)

    Robbers, Georg; Afshordi, Niayesh; Doran, Michael

    2008-03-21

    Einstein's theory of general relativity contains a universal value of the Planck mass. However, one may envisage that in alternative theories of gravity the effective value of the Planck mass (or Newton's constant), which quantifies the coupling of matter to metric perturbations, can run on the cosmological-horizon scale. In this Letter, we study the consequences of a glitch in the Planck mass from subhorizon to superhorizon scales. We show that current cosmological observations severely constrain this glitch to less than 1.2%.

  6. Planck 2015 results: XX. Constraints on inflation

    DEFF Research Database (Denmark)

    Ade, P. A R; Aghanim, N.; Arnaud, M.

    2016-01-01

    data are consistent with adiabatic primordial perturbations, and the estimated values for the parameters of the base Λ cold dark matter (ΛCDM) model are not significantly altered when more general initial conditions are admitted. In correlated mixed adiabatic and isocurvature models, the 95% CL upper...... are consistent with the Planck 2013 analysis based on the nominal mission data and further constrain slow-roll single-field inflationary models, as expected from the increased precision of Planck data using the full set of observations....

  7. Large-scale alignments from WMAP and Planck

    CERN Document Server

    Copi, Craig J.; Schwarz, Dominik J.; Starkman, Glenn D.

    2015-01-01

    We revisit the alignments of the largest structures observed in the cosmic microwave background (CMB) using the seven and nine-year WMAP and first-year Planck data releases. The observed alignments -- the quadrupole with the octopole and their joint alignment with the direction of our motion with respect to the CMB (the dipole direction) and the geometry of the Solar System (defined by the Ecliptic plane) -- are generally in good agreement with results from the previous WMAP data releases. However, a closer look at full-sky data on the largest scales reveals discrepancies between the earlier WMAP data releases (three to seven-year) and the final nine-year release. There are also discrepancies between all the WMAP data releases and the first-year Planck release. Nevertheless, both the WMAP and Planck data confirm the alignments of the largest observable CMB modes in the Universe. In particular, the p-values for the mutual alignment between the quadrupole and octopole, and the alignment of the plane defined by ...

  8. Planck 2013 results. IX. HFI spectral response

    CERN Document Server

    Ade, P A R; Armitage-Caplan, C; Arnaud, M; Ashdown, M; Atrio-Barandela, F; Aumont, J; Baccigalupi, C; Banday, A J; Barreiro, R B; Battaner, E; Benabed, K; Benoît, A; Benoit-Lévy, A; Bernard, J -P; Bersanelli, M; Bielewicz, P; Bobin, J; Bock, J J; Bond, J R; Borrill, J; Bouchet, F R; Boulanger, F; Bridges, M; Bucher, M; Burigana, C; Cardoso, J -F; Catalano, A; Challinor, A; Chamballu, A; Chary, R -R; Chen, X; Chiang, L -Y; Chiang, H C; Christensen, P R; Church, S; Clements, D L; Colombi, S; Colombo, L P L; Combet, C; Comis, B; Couchot, F; Coulais, A; Crill, B P; Curto, A; Cuttaia, F; Danese, L; Davies, R D; de Bernardis, P; de Rosa, A; de Zotti, G; Delabrouille, J; Delouis, J -M; Désert, F -X; Dickinson, C; Diego, J M; Dole, H; Donzelli, S; Doré, O; Douspis, M; Dupac, X; Efstathiou, G; Enßlin, T A; Eriksen, H K; Falgarone, E; Finelli, F; Forni, O; Frailis, M; Franceschi, E; Galeotta, S; Ganga, K; Giard, M; Giraud-Héraud, Y; González-Nuevo, J; Górski, K M; Gratton, S; Gregorio, A; Gruppuso, A; Hansen, F K; Hanson, D; Harrison, D; Henrot-Versillé, S; Hernández-Monteagudo, C; Herranz, D; Hildebrandt, S R; Hivon, E; Hobson, M; Holmes, W A; Hornstrup, A; Hovest, W; Huffenberger, K M; Hurier, G; Jaffe, T R; Jaffe, A H; Jones, W C; Juvela, M; Keihänen, E; Keskitalo, R; Kisner, T S; Kneissl, R; Knoche, J; Knox, L; Kunz, M; Kurki-Suonio, H; Lagache, G; Lamarre, J -M; Lasenby, A; Laureijs, R J; Lawrence, C R; Leahy, J P; Leonardi, R; Leroy, C; Lesgourgues, J; Liguori, M; Lilje, P B; Linden-Vørnle, M; López-Caniego, M; Lubin, P M; Macías-Pérez, J F; Maffei, B; Mandolesi, N; Maris, M; Marshall, D J; Martin, P G; Martínez-González, E; Masi, S; Matarrese, S; Matthai, F; Mazzotta, P; McGehee, P; Melchiorri, A; Mendes, L; Mennella, A; Migliaccio, M; Mitra, S; Miville-Deschênes, M -A; Moneti, A; Montier, L; Morgante, G; Mortlock, D; Munshi, D; Murphy, J A; Naselsky, P; Nati, F; Natoli, P; Netterfield, C B; Nørgaard-Nielsen, H U; North, C; Noviello, F; Novikov, D; Novikov, I; Osborne, S; Oxborrow, C A; Paci, F; Pagano, L; Pajot, F; Paoletti, D; Pasian, F; Patanchon, G; Perdereau, O; Perotto, L; Perrotta, F; Piacentini, F; Piat, M; Pierpaoli, E; Pietrobon, D; Plaszczynski, S; Pointecouteau, E; Polenta, G; Ponthieu, N; Popa, L; Poutanen, T; Pratt, G W; Prézeau, G; Prunet, S; Puget, J -L; Rachen, J P; Reinecke, M; Remazeilles, M; Renault, C; Ricciardi, S; Riller, T; Ristorcelli, I; Rocha, G; Rosset, C; Roudier, G; Rusholme, B; Santos, D; Savini, G; Shellard, E P S; Spencer, L D; Starck, J -L; Stolyarov, V; Stompor, R; Sudiwala, R; Sureau, F; Sutton, D; Suur-Uski, A -S; Sygnet, J -F; Tauber, J A; Tavagnacco, D; Terenzi, L; Tomasi, M; Tristram, M; Tucci, M; Umana, G; Valenziano, L; Valiviita, J; Van Tent, B; Vielva, P; Villa, F; Vittorio, N; Wade, L A; Wandelt, B D; Yvon, D; Zacchei, A; Zonca, A

    2014-01-01

    The Planck High Frequency Instrument (HFI) spectral response was determined through a series of ground based tests conducted with the HFI focal plane in a cryogenic environment prior to launch. The main goal of the spectral transmission tests was to measure the relative spectral response (including out-of-band signal rejection) of all HFI detectors. This was determined by measuring the output of a continuously scanned Fourier transform spectrometer coupled with all HFI detectors. As there is no on-board spectrometer within HFI, the ground-based spectral response experiments provide the definitive data set for the relative spectral calibration of the HFI. The spectral response of the HFI is used in Planck data analysis and component separation, this includes extraction of CO emission observed within Planck bands, dust emission, Sunyaev-Zeldovich sources, and intensity to polarization leakage. The HFI spectral response data have also been used to provide unit conversion and colour correction analysis tools. Ver...

  9. Max Karl Ernst Ludwig Planck (1858-1947

    Directory of Open Access Journals (Sweden)

    Robitaille P.-M.

    2007-10-01

    Full Text Available October 4th, 2007 marks the 60th anniversary of Planck’s death. Planck was not only the father of Quantum Theory. He was also a man of profound moral and ethical values, with far reaching philosophical views. Though he lived a life of public acclaim for his discovery of the Blackbody radiation formula which bares his name, his personal life was beset with tragedy. Yet, Planck never lost his deep faith and belief in a personal God. He was admired by Einstein, not so much for his contributions to physics, but rather, for the ideals which he embodied as a person. In this work, a brief synopsis is provided on Planck, his life, and his philosophical writings. It is hoped that this will serve as an invitation to revisit the philosophical works of the man who, more than any other, helped set the course of early 20th century physics.

  10. A stochastic Friedman Universe with dissipation

    International Nuclear Information System (INIS)

    Gruszczak, J.

    1985-01-01

    A probabilistic measure is constructed for the radiation-filled Friedman Universe with bulk viscosity and the equation of state perturbed by a ''white noise''. The corresponding Fokker-Planck equation is solved. In the stochastic evolution singularities turn out to be irrelevant. 3 refs., 1 fig. (author)

  11. Quasi-steady State Reduction of Molecular Motor-Based Models of Directed Intermittent Search

    KAUST Repository

    Newby, Jay M.; Bressloff, Paul C.

    2010-01-01

    at the other end of the track. Such a scenario is exemplified by the motor-driven transport of vesicular cargo to synaptic targets located on the axon or dendrites of a neuron. The reduced model is described by a scalar Fokker-Planck (FP) equation, which has

  12. Dark radiation sterile neutrino candidates after Planck data

    Energy Technology Data Exchange (ETDEWEB)

    Valentino, Eleonora Di; Melchiorri, Alessandro [Physics Department and INFN, Università di Roma ' ' La Sapienza' ' , Ple Aldo Moro 2, 00185, Rome (Italy); Mena, Olga, E-mail: eleonora.divalentino@roma1.infn.it, E-mail: alessandro.melchiorri@roma1.infn.it, E-mail: omena@ific.uv.es [IFIC, Universidad de Valencia-CSIC, 46071, Valencia (Spain)

    2013-11-01

    Recent Cosmic Microwave Background (CMB) results from the Planck satellite, combined with previous CMB data and Hubble constant measurements from the Hubble Space Telescope, provide a constraint on the effective number of relativistic degrees of freedom 3.62{sup +0.50}{sub −0.48} at 95% CL. New Planck data provide a unique opportunity to place limits on models containing relativistic species at the decoupling epoch. We present here the bounds on sterile neutrino models combining Planck data with galaxy clustering information. Assuming N{sub eff} active plus sterile massive neutrino species, in the case of a Planck+WP+HighL+HST analysis we find m{sub ν,} {sub sterile}{sup eff} < 0.36 eV and 3.14 < N{sub eff} < 4.15 at 95% CL, while using Planck+WP+HighL data in combination with the full shape of the galaxy power spectrum from the Baryon Oscillation Spectroscopic Survey BOSS Data Relase 9 measurements, we find that 3.30 < N{sub eff} < 4.43 and m{sub ν,} {sub sterile}{sup eff} < 0.33 eV both at 95% CL with the three active neutrinos having the minimum mass allowed in the normal hierarchy scheme, i.e. ∑m{sub ν} ∼ 0.06 eV. These values compromise the viability of the (3+2) massive sterile neutrino models for the parameter region indicated by global fits of neutrino oscillation data. Within the (3+1) massive sterile neutrino scenario, we find m{sub ν,} {sub sterile}{sup eff} < 0.34 eV at 95% CL. While the existence of one extra sterile massive neutrino state is compatible with current oscillation data, the values for the sterile neutrino mass preferred by oscillation analyses are significantly higher than the current cosmological bound. We review as well the bounds on extended dark sectors with additional light species based on the latest Planck CMB observations.

  13. Planck 2015 results: XXI. The integrated Sachs-Wolfe effect

    International Nuclear Information System (INIS)

    Ade, P. A. R.; Aghanim, N.; Arnaud, M.; Ashdown, M.; Aumont, J.

    2016-01-01

    Here, this paper presents a study of the integrated Sachs-Wolfe (ISW) effect from the Planck 2015 temperature and polarization data release. This secondary cosmic microwave background (CMB) anisotropy caused by the large-scale time-evolving gravitational potential is probed from different perspectives. The CMB is cross-correlated with different large-scale structure (LSS) tracers: radio sources from the NVSS catalogue; galaxies from the optical SDSS and the infrared WISE surveys; and the Planck 2015 convergence lensing map. The joint cross-correlation of the CMB with the tracers yields a detection at 4σ where most of the signal-to-noise is due to the Planck lensing and the NVSS radio catalogue. In fact, the ISW effect is detected from the Planck data only at ≈3σ (through the ISW-lensing bispectrum), which is similar to the detection level achieved by combining the cross-correlation signal coming from all the galaxy catalogues mentioned above. We study the ability of the ISW effect to place constraints on the dark-energy parameters; in particular, we show that Ω Λ is detected at more than 3σ. This cross-correlation analysis is performed only with the Planck temperature data, since the polarization scales available in the 2015 release do not permit significant improvement of the CMB-LSS cross-correlation detectability. Nevertheless, the Planck polarization data are used to study the anomalously large ISW signal previously reported through the aperture photometry on stacked CMB features at the locations of known superclusters and supervoids, which is in conflict with ΛCDM expectations. We find that the current Planck polarization data do not exclude that this signal could be caused by the ISW effect. In addition, the stacking of the Planck lensing map on the locations of superstructures exhibits a positive cross-correlation with these large-scale structures. Finally, we have improved our previous reconstruction of the ISW temperature fluctuations by combining

  14. Effects of Drift-Shell Splitting by Chorus Waves on Radiation Belt Electrons

    Science.gov (United States)

    Chan, A. A.; Zheng, L.; O'Brien, T. P., III; Tu, W.; Cunningham, G.; Elkington, S. R.; Albert, J.

    2015-12-01

    Drift shell splitting in the radiation belts breaks all three adiabatic invariants of charged particle motion via pitch angle scattering, and produces new diffusion terms that fully populate the diffusion tensor in the Fokker-Planck equation. Based on the stochastic differential equation method, the Radbelt Electron Model (REM) simulation code allows us to solve such a fully three-dimensional Fokker-Planck equation, and to elucidate the sources and transport mechanisms behind the phase space density variations. REM has been used to perform simulations with an empirical initial phase space density followed by a seed electron injection, with a Tsyganenko 1989 magnetic field model, and with chorus wave and ULF wave diffusion models. Our simulation results show that adding drift shell splitting changes the phase space location of the source to smaller L shells, which typically reduces local electron energization (compared to neglecting drift-shell splitting effects). Simulation results with and without drift-shell splitting effects are compared with Van Allen Probe measurements.

  15. Study of the relaxation of electron velocity distributions in gases

    Energy Technology Data Exchange (ETDEWEB)

    Braglia, G L [Parma Univ. (Italy). Ist. di Fisica; Caraffini, G L; Diligenti, M [Parma Univ. (Italy). Ist. di Matematica

    1981-03-11

    The Fokker-Planck equation governing the relaxation of the electron speed (energy) distribution in gases is solved in a number of cases of special interest. The solution is given in terms of eigenfunctions of the Fokker-Planck operator, satisfying an orthonormalization condition in which the steady-state distribution is the weight function. The real cross-sections of the noble gases He, Ne, Ar, Kr and Xe, together with model collision frequencies of the form ..nu..(v) = ..cap alpha..vsup(n) with n = 0.5, 1, 1.5, 3 and 3.5, are used to calculate eigenvalues and eigenfunctions. The first fifteen eigenvalues are obtained in each case both in the absence and in the presence of a d.c. electric field and, in the latter case, both with atoms at rest and atoms in motion. Calculations of relaxation times and examples of evolutions towards their steady-state forms of given initial distributions are reported in several particular cases.

  16. Matter power spectrum in hidden neutrino interacting dark matter models: a closer look at the collision term

    Energy Technology Data Exchange (ETDEWEB)

    Binder, Tobias; Covi, Laura [Institute for Theoretical Physics, Georg-August University Göttingen,Friedrich-Hund-Platz 1, Göttingen, D-37077 (Germany); Kamada, Ayuki [Department of Physics and Astronomy, University of California,Riverside, California 92521 (United States); Murayama, Hitoshi [Kavli Institute for the Physics and Mathematics of the Universe (WPI),University of Tokyo Institutes for Advanced Study, University of Tokyo,Kashiwa 277-8583 (Japan); Department of Physics, University of California, Berkeley,Berkeley, California 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory,Berkeley, California 94720 (United States); Takahashi, Tomo [Department of Physics, Saga University,Saga 840-8502 (Japan); Yoshida, Naoki [Kavli Institute for the Physics and Mathematics of the Universe (WPI),University of Tokyo Institutes for Advanced Study, University of Tokyo,Kashiwa 277-8583 (Japan); Department of Physics, University of Tokyo,Tokyo 113-0033 (Japan); CREST, Japan Science and Technology Agency,4-1-8 Honcho, Kawaguchi, Saitama, 332-0012 (Japan)

    2016-11-21

    Dark Matter (DM) models providing possible alternative solutions to the small-scale crisis of the standard cosmology are nowadays of growing interest. We consider DM interacting with light hidden fermions via well-motivated fundamental operators showing the resultant matter power spectrum is suppressed on subgalactic scales within a plausible parameter region. Our basic description of the evolution of cosmological perturbations relies on a fully consistent first principles derivation of a perturbed Fokker-Planck type equation, generalizing existing literature. The cosmological perturbation of the Fokker-Planck equation is presented for the first time in two different gauges, where the results transform into each other according to the rules of gauge transformation. Furthermore, our focus lies on a derivation of a broadly applicable and easily computable collision term showing important phenomenological differences to other existing approximations. As one of the main results and concerning the small-scale crisis, we show the equal importance of vector and scalar boson mediated interactions between the DM and the light fermions.

  17. Hypocoercivity for linear kinetic equations conserving mass

    KAUST Repository

    Dolbeault, Jean; Mouhot, Clé ment; Schmeiser, Christian

    2015-01-01

    We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

  18. Two-dimensional and relativistic effects in lower-hybrid current drive

    International Nuclear Information System (INIS)

    Hewett, D.; Hizanidis, K.; Krapchev, V.; Bers, A.

    1983-06-01

    We present new numerical and analytic solutions of the two-dimensional Fokker-Planck equation supplemented by a parallel quasilinear diffusion term. The results show a large enhancement of the perpendicular temperature of both the electrons resonant with the applied RF fields and the more energetic electrons in the tail. Both the RF-generated current and power dissipated are substantially increased by the perpendicular energy broadening in the resonant region. In the presence of a small DC electric field the RF current generated is very much enhanced, much more than in a simple additive fashion. In addition, we present a relativistic formulation of the two-dimensional Fokker-Planck quasilinear equation. From conservation equations, based upon this formulation, we derive the characteristics of RF current drive with energetic electrons. These show how the RF-driven current and its figure of merit (I/P/sub d/) increase with the energy of the current-carrying electrons, and that their perpendicular, random momentum must also increase

  19. Ion distribution in the hot spot of an inertial confinement fusion plasma

    Science.gov (United States)

    Tang, Xianzhu; Guo, Zehua; Berk, Herb

    2012-10-01

    Maximizing the fusion gain of inertial confinement fusion (ICF) for inertial fusion energy (IFE) applications leads to the standard scenario of central hot spot ignition followed by propagating burn wave through the cold/dense assembled fuel. The fact that the hot spot is surrounded by cold but dense fuel layer introduces subtle plasma physics which requires a kinetic description. Here we perform Fokker-Planck calculations and kinetic PIC simulations for an ICF plasma initially in pressure balance but having large temperature gradient over a narrow transition layer. The loss of the fast ion tail from the hot spot, which is important for fusion reactivity, is quantified by Fokker-Planck models. The role of electron energy transport and the ambipolar electric field is investigated via kinetic simulations and the fluid moment models. The net effect on both hot spot ion temperature and the ion tail distribution, and hence the fusion reactivity, is elucidated.

  20. Hypocoercivity for linear kinetic equations conserving mass

    KAUST Repository

    Dolbeault, Jean

    2015-02-03

    We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

  1. Effect of Ponderomotive Terms on Heat Flux in Laser-Produced Plasmas

    Science.gov (United States)

    Li, G.

    2005-10-01

    A laser electromagnetic field introduces ponderomotive termsootnotetextV. N. Goncharov and G. Li, Phys. Plasmas 11, 5680 (2004). in the heat flux in a plasma. To account for the nonlocal effects in the ponderomotive terms, first, the kinetic equation coupled with the Maxwell equations is numerically solved for the isotropic part of the electron distribution function. Such an equation includes self-consistent electromagnetic fields and laser absorption through the inverse bremsstrahlung. Then, the anisotropic part is found by solving a simplified Fokker--Planck equation. Using the distribution function, the electric current and heat flux are obtained and substituted into the hydrocode LILAC to simulate ICF implosions. The simulation results are compared against the existing nonlocal electron conduction modelsootnotetextG. P. Schurtz, P. D. Nicola"i, and M. Busquet, Phys. Plasmas 9, 4238 (2000). and Fokker--Planck simulations. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52-92SF19460.

  2. Calibrating the Planck Cluster Mass Scale with Cluster Velocity Dispersions

    Science.gov (United States)

    Amodeo, Stefania; Mei, Simona; Stanford, Spencer A.; Bartlett, James G.; Melin, Jean-Baptiste; Lawrence, Charles R.; Chary, Ranga-Ram; Shim, Hyunjin; Marleau, Francine; Stern, Daniel

    2017-08-01

    We measure the Planck cluster mass bias using dynamical mass measurements based on velocity dispersions of a subsample of 17 Planck-detected clusters. The velocity dispersions were calculated using redshifts determined from spectra that were obtained at the Gemini observatory with the GMOS multi-object spectrograph. We correct our estimates for effects due to finite aperture, Eddington bias, and correlated scatter between velocity dispersion and the Planck mass proxy. The result for the mass bias parameter, (1-b), depends on the value of the galaxy velocity bias, {b}{{v}}, adopted from simulations: (1-b)=(0.51+/- 0.09){b}{{v}}3. Using a velocity bias of {b}{{v}}=1.08 from Munari et al., we obtain (1-b)=0.64+/- 0.11, I.e., an error of 17% on the mass bias measurement with 17 clusters. This mass bias value is consistent with most previous weak-lensing determinations. It lies within 1σ of the value that is needed to reconcile the Planck cluster counts with the Planck primary cosmic microwave background constraints. We emphasize that uncertainty in the velocity bias severely hampers the precision of the measurements of the mass bias using velocity dispersions. On the other hand, when we fix the Planck mass bias using the constraints from Penna-Lima et al., based on weak-lensing measurements, we obtain a positive velocity bias of {b}{{v}}≳ 0.9 at 3σ .

  3. Stochastic inflation lattice simulations: Ultra-large scale structure of the universe

    International Nuclear Information System (INIS)

    Salopek, D.S.

    1990-11-01

    Non-Gaussian fluctuations for structure formation may arise in inflation from the nonlinear interaction of long wavelength gravitational and scalar fields. Long wavelength fields have spatial gradients α -1 triangledown small compared to the Hubble radius, and they are described in terms of classical random fields that are fed by short wavelength quantum noise. Lattice Langevin calculations are given for a ''toy model'' with a scalar field interacting with an exponential potential where one can obtain exact analytic solutions of the Fokker-Planck equation. For single scalar field models that are consistent with current microwave background fluctuations, the fluctuations are Gaussian. However, for scales much larger than our observable Universe, one expects large metric fluctuations that are non-Guassian. This example illuminates non-Gaussian models involving multiple scalar fields which are consistent with current microwave background limits. 21 refs., 3 figs

  4. Critical power for lower hybrid current drive

    International Nuclear Information System (INIS)

    Assis, A.S. de; Sakanaka, P.H.; Azevedo, C.A. de; Busnardo-Neto, J.

    1995-11-01

    We have solved numerically the quasilinear Fokker-Planck equation which models the critical power for lower hybrid wave current drive. An exact value for the critical power necessary for current saturation, for tokamak current drive experiments, has been obtained. The nonlinear treatment presented here leads to a final profile for the parallel distribution function which is a plateau only in a part of the resonance region. This form of the distribution function is intermediate between two well known results: a plateau throughout the resonance region for the linear strong-source regime, D wave >> D coll and no plateau at all in the resonance region the linear weak-source regimen, D wave coll . The strength of the external power source and the value of the dc electric field are treated as given parameters in the integration scheme. (author). 24 refs, 6 figs

  5. Planck Visualization Project: Seeing and Hearing the Cosmic Microwave Background

    Science.gov (United States)

    van der Veen, J.

    2010-08-01

    The Planck Mission, launched May 14, 2009, will measure the sky over nine frequency channels, with temperature sensitivity of a few microKelvin, and angular resolution of up to 5 arc minutes. Planck is expected to provide the data needed to set tight constraints on cosmological parameters, study the ionization history of the Universe, probe the dynamics of the inflationary era, and test fundamental physics. The Planck Education and Public Outreach collaborators at NASA's Jet Propulsion Laboratory, the University of California, Santa Barbara and Purdue University are preparing a variety of materials to present the science goals of the Planck Mission to the public. Two products currently under development are an interactive simulation of the mission which can be run in a virtual reality environment, and an interactive presentation on interpreting the power spectrum of the Cosmic Microwave Background with music. In this paper we present a brief overview of CMB research and the Planck Mission, and discuss how to explain, to non-technical audiences, the theory of how we derive information about the early universe from the power spectrum of the CMB by using the physics of music.

  6. Consistency of the Planck CMB data and ΛCDM cosmology

    Energy Technology Data Exchange (ETDEWEB)

    Shafieloo, Arman [Korea Astronomy and Space Science Institute, Daejeon, 34055 (Korea, Republic of); Hazra, Dhiraj Kumar, E-mail: shafieloo@kasi.re.kr, E-mail: dhiraj.kumar.hazra@apc.univ-paris7.fr [AstroParticule et Cosmologie (APC)/Paris Centre for Cosmological Physics, Université Paris Diderot, CNRS/IN2P3, CEA/lrfu, Observatoire de Paris, Sorbonne Paris Cité, 10, rue Alice Domon et Leonie Duquet, Paris Cedex 13, 75205 France (France)

    2017-04-01

    We test the consistency between Planck temperature and polarization power spectra and the concordance model of Λ Cold Dark Matter cosmology (ΛCDM) within the framework of Crossing statistics. We find that Planck TT best fit ΛCDM power spectrum is completely consistent with EE power spectrum data while EE best fit ΛCDM power spectrum is not consistent with TT data. However, this does not point to any systematic or model-data discrepancy since in the Planck EE data, uncertainties are much larger compared to the TT data. We also investigate the possibility of any deviation from ΛCDM model analyzing the Planck 2015 data. Results from TT, TE and EE data analysis indicate that no deviation is required beyond the flexibility of the concordance ΛCDM model. Our analysis thus rules out any strong evidence for beyond the concordance model in the Planck spectra data. We also report a mild amplitude difference comparing temperature and polarization data, where temperature data seems to have slightly lower amplitude than expected (consistently at all multiples), as we assume both temperature and polarization data are realizations of the same underlying cosmology.

  7. Planck intermediate results XXXI. Microwave survey of Galactic supernova remnants

    DEFF Research Database (Denmark)

    Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.

    2016-01-01

    The all-sky Planck survey in 9 frequency bands was used to search for emission from all 274 known Galactic supernova remnants. Of these, 16 were detected in at least two Planck frequencies. The radio-through-microwave spectral energy distributions were compiled to determine the mechanism for micr......The all-sky Planck survey in 9 frequency bands was used to search for emission from all 274 known Galactic supernova remnants. Of these, 16 were detected in at least two Planck frequencies. The radio-through-microwave spectral energy distributions were compiled to determine the mechanism...... for microwave emission. In only one case, IC 443, is there high-frequency emission clearly from dust associated with the supernova remnant. In all cases, the low-frequency emission is from synchrotron radiation. As predicted for a population of relativistic particles with energy distribution that extends...

  8. Environment-based selection effects of Planck clusters

    Energy Technology Data Exchange (ETDEWEB)

    Kosyra, R.; Gruen, D.; Seitz, S.; Mana, A.; Rozo, E.; Rykoff, E.; Sanchez, A.; Bender, R.

    2015-07-24

    We investigate whether the large-scale structure environment of galaxy clusters imprints a selection bias on Sunyaev–Zel'dovich (SZ) catalogues. Such a selection effect might be caused by line of sight (LoS) structures that add to the SZ signal or contain point sources that disturb the signal extraction in the SZ survey. We use the Planck PSZ1 union catalogue in the Sloan Digital Sky Survey (SDSS) region as our sample of SZ-selected clusters. We calculate the angular two-point correlation function (2pcf) for physically correlated, foreground and background structure in the RedMaPPer SDSS DR8 catalogue with respect to each cluster. We compare our results with an optically selected comparison cluster sample and with theoretical predictions. In contrast to the hypothesis of no environment-based selection, we find a mean 2pcf for background structures of -0.049 on scales of ≲40 arcmin, significantly non-zero at ~4σ, which means that Planck clusters are more likely to be detected in regions of low background density. We hypothesize this effect arises either from background estimation in the SZ survey or from radio sources in the background. We estimate the defect in SZ signal caused by this effect to be negligibly small, of the order of ~10-4 of the signal of a typical Planck detection. Analogously, there are no implications on X-ray mass measurements. However, the environmental dependence has important consequences for weak lensing follow up of Planck galaxy clusters: we predict that projection effects account for half of the mass contained within a 15 arcmin radius of Planck galaxy clusters. We did not detect a background underdensity of CMASS LRGs, which also leaves a spatially varying redshift dependence of the Planck SZ selection function as a possible cause for our findings.

  9. Herschel-ATLAS : Planck sources in the phase 1 fields

    NARCIS (Netherlands)

    Herranz, D.; González-Nuevo, J.; Clements, D.; De, Zotti G.; Lopez-Caniego, M.; Lapi, A.; Rodighiero, G.; Danese, L.; Fu, H.; Cooray, A.; Baes, M.; Bendo, G.; Bonavera, L.; Carrera, F.; Dole, H.; Eales, S.; Ivison, R.; Jarvis, M.; Lagache, G.; Massardi, M.; Michalowski, M.; Negrello, M.; Rigby, E.E.; Scott, D.; Valiante, E.; Valtchanov, I.; Werf, van der P.P.; Auld, R.; Buttiglione, S.; Dariush, A.; Dunne, L.; Hopwood, R.; Hoyos, C.; Ibar, E.; Maddox, S.

    2013-01-01

    We present the results of a cross-correlation of the Planck Early Release Compact Source catalogue (ERCSC) with the catalogue of Herschel-ATLAS sources detected in the phase 1 fields, covering 134.55{deg}$^{2}$. There are 28 ERCSC sources detected by Planck at 857 GHz in this area. As many as 16 of

  10. Planck pre-launch status: The optical system

    DEFF Research Database (Denmark)

    Tauber, J. A.; Nørgaard-Nielsen, Hans Ulrik; Ade, P. A. R.

    2010-01-01

    Planck is a scientific satellite that represents the next milestone in space-based research related to the cosmic microwave background, and in many other astrophysical fields. Planck was launched on 14 May of 2009 and is now operational. The uncertainty in the optical response of its detectors......, based on the knowledge available at the time of launch. We also briefly describe the impact of the major systematic effects of optical origin, and the concept of in-flight optical calibration. Detailed discussions of related areas are provided in accompanying papers....

  11. Planck 2013 results. XV. CMB power spectra and likelihood

    Science.gov (United States)

    Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartlett, J. G.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J. J.; Bonaldi, A.; Bonavera, L.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Boulanger, F.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R. C.; Calabrese, E.; Cardoso, J.-F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H. C.; Chiang, L.-Y.; Christensen, P. R.; Church, S.; Clements, D. L.; Colombi, S.; Colombo, L. P. L.; Combet, C.; Couchot, F.; Coulais, A.; Crill, B. P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.-M.; Désert, F.-X.; Dickinson, C.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Dunkley, J.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T. A.; Eriksen, H. K.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A. A.; Franceschi, E.; Gaier, T. C.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giardino, G.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K. M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J. E.; Hansen, F. K.; Hanson, D.; Harrison, D.; Helou, G.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huffenberger, K. M.; Hurier, G.; Jaffe, A. H.; Jaffe, T. R.; Jewell, J.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kiiveri, K.; Kisner, T. S.; Kneissl, R.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Lattanzi, M.; Laureijs, R. J.; Lawrence, C. R.; Le Jeune, M.; Leach, S.; Leahy, J. P.; Leonardi, R.; León-Tavares, J.; Lesgourgues, J.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; Lindholm, V.; López-Caniego, M.; Lubin, P. M.; Macías-Pérez, J. F.; Maffei, B.; Maino, D.; Mandolesi, N.; Marinucci, D.; Maris, M.; Marshall, D. J.; Martin, P. G.; Martínez-González, E.; Masi, S.; Massardi, M.; Matarrese, S.; Matthai, F.; Mazzotta, P.; Meinhold, P. R.; Melchiorri, A.; Mendes, L.; Menegoni, E.; Mennella, A.; Migliaccio, M.; Millea, M.; Mitra, S.; Miville-Deschênes, M.-A.; Molinari, D.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C. B.; Nørgaard-Nielsen, H. U.; Noviello, F.; Novikov, D.; Novikov, I.; O'Dwyer, I. J.; Orieux, F.; Osborne, S.; Oxborrow, C. A.; Paci, F.; Pagano, L.; Pajot, F.; Paladini, R.; Paoletti, D.; Partridge, B.; Pasian, F.; Patanchon, G.; Paykari, P.; Perdereau, O.; Perotto, L.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G. W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J. P.; Rahlin, A.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Ricciardi, S.; Riller, T.; Ringeval, C.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rowan-Robinson, M.; Rubiño-Martín, J. A.; Rusholme, B.; Sandri, M.; Sanselme, L.; Santos, D.; Savini, G.; Scott, D.; Seiffert, M. D.; Shellard, E. P. S.; Spencer, L. D.; Starck, J.-L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Türler, M.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Varis, J.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L. A.; Wandelt, B. D.; Wehus, I. K.; White, M.; White, S. D. M.; Yvon, D.; Zacchei, A.; Zonca, A.

    2014-11-01

    This paper presents the Planck 2013 likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations that accounts for all known relevant uncertainties, both instrumental and astrophysical in nature. We use this likelihood to derive our best estimate of the CMB angular power spectrum from Planck over three decades in multipole moment, ℓ, covering 2 ≤ ℓ ≤ 2500. The main source of uncertainty at ℓ ≲ 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher ℓs. For ℓ impact of residual foreground and instrumental uncertainties on the final cosmological parameters. We find good internal agreement among the high-ℓ cross-spectra with residuals below a few μK2 at ℓ ≲ 1000, in agreement with estimated calibration uncertainties. We compare our results with foreground-cleaned CMB maps derived from all Planck frequencies, as well as with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. We further show that the best-fit ΛCDM cosmology is in excellent agreement with preliminary PlanckEE and TE polarisation spectra. We find that the standard ΛCDM cosmology is well constrained by Planck from the measurements at ℓ ≲ 1500. One specific example is the spectral index of scalar perturbations, for which we report a 5.4σ deviation from scale invariance, ns = 1. Increasing the multipole range beyond ℓ ≃ 1500 does not increase our accuracy for the ΛCDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the ΛCDM framework. Finally, we report a tension between the Planck best-fit ΛCDM model and the low-ℓ spectrum in the form of a power deficit of 5-10% at ℓ ≲ 40, with a statistical significance of 2.5-3σ. Without a theoretically motivated model for

  12. Analysis of unexpected exits using the Fokker - Planck equation

    NARCIS (Netherlands)

    Herwaarden, van O.A.

    1996-01-01


    In this thesis exit problems are considered for stochastic dynamical systems with small random fluctuations. We study exit from a domain in the state space through a boundary, or a specified part of the boundary, that is unattainable in the underlying deterministic system. We analyze

  13. Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems

    Directory of Open Access Journals (Sweden)

    Hailiang Li

    2003-09-01

    Full Text Available This paper concerns the well-posedness and semiclassical limit of nonlinear Schrodinger-Poisson systems. We show the local well-posedness and the existence of semiclassical limit of the two models for initial data with Sobolev regularity, before shocks appear in the limit system. We establish the existence of a global solution and show the time-asymptotic behavior of a classical solutions of Schrodinger-Poisson system for a fixed re-scaled Planck constant.

  14. The Planck Telescope reflectors

    Science.gov (United States)

    Stute, Thomas

    2004-09-01

    The mechanical division of EADS-Astrium GmbH, Friedrichshafen is currently engaged with the development, manufacturing and testing of the advanced dimensionally stable composite reflectors for the ESA satellite borne telescope Planck. The objective of the ESA mission Planck is to analyse the first light that filled the universe, the cosmic microwave background radiation. Under contract of the Danish Space Research Institute and ESA EADS-Astrium GmbH is developing the all CFRP primary and secondary reflectors for the 1.5-metre telescope which is the main instrument of the Planck satellite. The operational frequency ranges from to 25 GHz to 1000 GHz. The demanding high contour accuracy and surface roughness requirements are met. The design provides the extreme dimensional stability required by the cryogenic operational environment at around 40 K. The elliptical off-axis reflectors display a classical lightweight sandwich design with CFRP core and facesheets. Isostatic mounts provide the interfaces to the telescope structure. Protected VDA provides the reflecting surface. The manufacturing is performed at the Friedrichshafen premises of EADS-Space Transportation GmbH, the former Dornier composite workshops. Advanced manufacturing technologies like true angle lay-up by CNC fibre placement and filament winding are utilized. The protected coating is applied at the CAHA facilities at the Calar Alto Observatory, Spain. The exhaustive environmental testing is performed at the facilities of IABG, Munich (mechanical testing) and for the cryo-optical tests at CSL Liege. The project is in advanced state with both Qualification Models being under environmental testing. The flight models will be delivered in 2004. The paper gives an overview over the requirements and the main structural features how these requirements are met. Special production aspects and available test results are reported.

  15. Cusps enable line attractors for neural computation

    International Nuclear Information System (INIS)

    Xiao, Zhuocheng; Zhang, Jiwei; Sornborger, Andrew T.; Tao, Louis

    2017-01-01

    Here, line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse gating in feed-forward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, nonlinear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, and then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling, and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and, thus, dynamically control the processing of graded information.

  16. Cusps enable line attractors for neural computation

    Science.gov (United States)

    Xiao, Zhuocheng; Zhang, Jiwei; Sornborger, Andrew T.; Tao, Louis

    2017-11-01

    Line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse gating in feed-forward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, nonlinear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, and then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling, and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and, thus, dynamically control the processing of graded information.

  17. Fokker-action principle for a system of particles interacting through a linear potential

    International Nuclear Information System (INIS)

    Rivacoba, A.

    1984-01-01

    A Fokker-action principle for a system of scalar particles interacting through their time-symmetric relativistic generalization of linear potential is obtained. From this action, motion equations and conservation laws for the total energy and angular momentum of the system, in which field contributions are included, are derived. These equations are exactly applied to the problem suggested by Schild of two particles moving in circular concentric orbits

  18. Isotropy analyses of the Planck convergence map

    Science.gov (United States)

    Marques, G. A.; Novaes, C. P.; Bernui, A.; Ferreira, I. S.

    2018-01-01

    The presence of matter in the path of relic photons causes distortions in the angular pattern of the cosmic microwave background (CMB) temperature fluctuations, modifying their properties in a slight but measurable way. Recently, the Planck Collaboration released the estimated convergence map, an integrated measure of the large-scale matter distribution that produced the weak gravitational lensing (WL) phenomenon observed in Planck CMB data. We perform exhaustive analyses of this convergence map calculating the variance in small and large regions of the sky, but excluding the area masked due to Galactic contaminations, and compare them with the features expected in the set of simulated convergence maps, also released by the Planck Collaboration. Our goal is to search for sky directions or regions where the WL imprints anomalous signatures to the variance estimator revealed through a χ2 analyses at a statistically significant level. In the local analysis of the Planck convergence map, we identified eight patches of the sky in disagreement, in more than 2σ, with what is observed in the average of the simulations. In contrast, in the large regions analysis we found no statistically significant discrepancies, but, interestingly, the regions with the highest χ2 values are surrounding the ecliptic poles. Thus, our results show a good agreement with the features expected by the Λ cold dark matter concordance model, as given by the simulations. Yet, the outliers regions found here could suggest that the data still contain residual contamination, like noise, due to over- or underestimation of systematic effects in the simulation data set.

  19. Brans-Dicke inflation in light of the Planck 2015 data

    International Nuclear Information System (INIS)

    Tahmasebzadeh, B.; Rezazadeh, K.; Karami, K.

    2016-01-01

    We study inflation in the Brans-Dicke gravity as a special model of the scalar-tensor gravity. We obtain the inflationary observables containing the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index and the equilateral non-Gaussianity parameter in terms of the general form of the potential in the Jordan frame. Then, we compare the results for various inflationary potentials in light of the Planck 2015 data. Our study shows that in the Brans-Dicke gravity, the power-law, inverse power-law and exponential potentials are ruled out by the Planck 2015 data. But, the hilltop, Higgs, Coleman-Weinberg and natural potentials can be compatible with Planck 2015 TT,TE,EE+lowP data at 95% CL. Moreover, the D-brane, SB SUSY and displaced quadratic potentials can be in well agreement with the observational data since their results can lie inside the 68% CL region of Planck 2015 TT,TE,EE+lowP data.

  20. Brans-Dicke inflation in light of the Planck 2015 data

    Energy Technology Data Exchange (ETDEWEB)

    Tahmasebzadeh, B. [Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), P.O. Box 45195-1159, Zanjan (Iran, Islamic Republic of); Rezazadeh, K.; Karami, K., E-mail: b.tahmasebzadeh@iasbs.ac.ir, E-mail: rezazadeh86@gmail.com, E-mail: kkarami@uok.ac.ir [Department of Physics, University of Kurdistan, Pasdaran St., P.O. Box 66177-15175, Sanandaj (Iran, Islamic Republic of)

    2016-07-01

    We study inflation in the Brans-Dicke gravity as a special model of the scalar-tensor gravity. We obtain the inflationary observables containing the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index and the equilateral non-Gaussianity parameter in terms of the general form of the potential in the Jordan frame. Then, we compare the results for various inflationary potentials in light of the Planck 2015 data. Our study shows that in the Brans-Dicke gravity, the power-law, inverse power-law and exponential potentials are ruled out by the Planck 2015 data. But, the hilltop, Higgs, Coleman-Weinberg and natural potentials can be compatible with Planck 2015 TT,TE,EE+lowP data at 95% CL. Moreover, the D-brane, SB SUSY and displaced quadratic potentials can be in well agreement with the observational data since their results can lie inside the 68% CL region of Planck 2015 TT,TE,EE+lowP data.

  1. Planck 2013 results. I. Overview of products and scientific results

    CERN Document Server

    Ade, P.A.R.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartelmann, M.; Bartlett, J.G.; Battaner, E.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J.J.; Bonaldi, A.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Boulanger, F.; Bowyer, J.W.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R.C.; Cappellini, B.; Cardoso, J.F.; Carr, R.; Casale, M.; Catalano, A.; Challinor, A.; Chamballu, A.; Chary, R.R.; Chen, X.; Chiang, L.Y.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.M.; Desert, F.X.; Dickinson, C.; Diego, J.M.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Dunkley, J.; Dupac, X.; Efstathiou, G.; Ensslin, T.A.; Eriksen, H.K.; Falgarone, E.; Finelli, F.; Foley, S.; Forni, O.; Frailis, M.; Franceschi, E.; Freschi, M.; Fromenteau, S.; Gaier, T.C.; Galeotta, S.; Gallegos, J.; Gandolfo, B.; Ganga, K.; Giard, M.; Giardino, G.; Giraud-Heraud, Y.; Gonzalez-Nuevo, J.; Gorski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Haissinski, J.; Hansen, F.K.; Hanson, D.; Harrison, D.; Helou, G.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Jaffe, T.R.; Jaffe, A.H.; Jewell, J.; Jones, W.C.; Juvela, M.; Kangaslahti, P.; Keihanen, E.; Keskitalo, R.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Laureijs, R.J.; Lawrence, C.R.; Le Jeune, M.; Leach, S.; Leahy, J.P.; Leonardi, R.; Leon-Tavares, J.; Leroy, C.; Lesgourgues, J.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lopez-Caniego, M.; Lowe, S.; Lubin, P.M.; Macias-Perez, J.F.; Maffei, B.; Maino, D.; Mandolesi, N.; Maris, M.; Marshall, D.J.; Martin, P.G.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; Matthai, F.; Mazzotta, P.; McDonald, A.; McGehee, P.; Meinhold, P.R.; Melchiorri, A.; Melin, J.B.; Mendes, L.; Mennella, A.; Migliaccio, M.; Miniscalco, R.; Mitra, S.; Miville-Deschenes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J.A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; North, C.; Noviello, F.; Novikov, D.; Novikov, I.; O'Dwyer, I.J.; Osborne, S.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paladini, R.; Paoletti, D.; Partridge, B.; Pasian, F.; Patanchon, G.; Pearson, D.; Pearson, T.J.; Perdereau, O.; Perotto, L.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Platania, P.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Reach, W.T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Ricciardi, S.; Riller, T.; Ringeval, C.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rowan-Robinson, M.; Rubino-Martin, J.A.; Rusholme, B.; Salerno, E.; Sandri, M.; Santos, D.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Smoot, G.F.; Spencer, L.D.; Starck, J.L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Tavagnacco, D.; Taylor, D.; Terenzi, L.; Texier, D.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Turler, M.; Tuttlebee, M.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Varis, J.; Vibert, L.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L.A.; Wandelt, B.D.; Watson, R.; Watson, C.; White, M.; White, S.D.M.; Wilkinson, A.; Yvon, D.; Zacchei, A.; Zonca, A.

    2014-01-01

    The ESA's Planck satellite, dedicated to studying the early universe, was launched on May 2009 and has been surveying the microwave and submillimetre sky since August 2009. In March 2013, ESA and the Planck Collaboration publicly released the initial cosmology products based on the first 15.5 months of Planck operations, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper describes the mission and its performance, and gives an overview of the processing and analysis of the data, the characteristics of the data, the main scientific results, and the science data products and papers in the release. Scientific results include robust support for the standard, six parameter LCDM model of cosmology and improved measurements for the parameters that define this model, including a highly significant deviation from scale invariance of the primordial power spectrum. The Planck values for some of these parameters and others derived from them are significantly different fr...

  2. Stochastic evolutions and hadronization of highly excited hadronic matter

    International Nuclear Information System (INIS)

    Carruthers, P.

    1984-01-01

    Stochastic ingredients of high energy hadronic collisions are analyzed, with emphasis on multiplicity distributions. The conceptual simplicity of the k-cell negative binomial distribution is related to the evolution of probability distributions via the Fokker-Planck and related equations. The connection to underlying field theory ideas is sketched. 17 references

  3. Passing to the limit in a Wasserstein gradient flow : from diffusion to reaction

    NARCIS (Netherlands)

    Arnrich, S.; Mielke, A.; Peletier, M.A.; Savaré, G.; Veneroni, M.

    2012-01-01

    We study a singular-limit problem arising in the modelling of chemical reactions. At finite e > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1 / e and in the limit e --> 0, the solution concentrates

  4. Inflationary paradigm after Planck 2013

    Energy Technology Data Exchange (ETDEWEB)

    Guth, Alan H., E-mail: guth@ctp.mit.edu [Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Kaiser, David I., E-mail: dikaiser@mit.edu [Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Nomura, Yasunori, E-mail: ynomura@berkeley.edu [Berkeley Center for Theoretical Physics, Department of Physics, and Theoretical Physics Group, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720 (United States)

    2014-06-02

    Models of cosmic inflation posit an early phase of accelerated expansion of the universe, driven by the dynamics of one or more scalar fields in curved spacetime. Though detailed assumptions about fields and couplings vary across models, inflation makes specific, quantitative predictions for several observable quantities, such as the flatness parameter (Ω{sub k}=1−Ω) and the spectral tilt of primordial curvature perturbations (n{sub s}−1=dlnP{sub R}/dlnk), among others—predictions that match the latest observations from the Planck satellite to very good precision. In the light of data from Planck as well as recent theoretical developments in the study of eternal inflation and the multiverse, we address recent criticisms of inflation by Ijjas, Steinhardt, and Loeb. We argue that their conclusions rest on several problematic assumptions, and we conclude that cosmic inflation is on a stronger footing than ever before.

  5. Inflationary paradigm after Planck 2013

    International Nuclear Information System (INIS)

    Guth, Alan H.; Kaiser, David I.; Nomura, Yasunori

    2014-01-01

    Models of cosmic inflation posit an early phase of accelerated expansion of the universe, driven by the dynamics of one or more scalar fields in curved spacetime. Though detailed assumptions about fields and couplings vary across models, inflation makes specific, quantitative predictions for several observable quantities, such as the flatness parameter (Ω k =1−Ω) and the spectral tilt of primordial curvature perturbations (n s −1=dlnP R /dlnk), among others—predictions that match the latest observations from the Planck satellite to very good precision. In the light of data from Planck as well as recent theoretical developments in the study of eternal inflation and the multiverse, we address recent criticisms of inflation by Ijjas, Steinhardt, and Loeb. We argue that their conclusions rest on several problematic assumptions, and we conclude that cosmic inflation is on a stronger footing than ever before.

  6. Planck early results. XIV. ERCSC validation and extreme radio sources

    DEFF Research Database (Denmark)

    Lähteenmäki, A.; Lavonen, N.; León-Tavares, J.

    2011-01-01

    Planck's all-sky surveys at 30-857 GHz provide an unprecedented opportunity to follow the radio spectra of a large sample of extragalactic sources to frequencies 2-20 times higher than allowed by past, large-area, ground-based surveys. We combine the results of the Planck Early Release Compact So...

  7. Planck 2015 results: XXIV. Cosmology from Sunyaev-Zeldovich cluster counts

    DEFF Research Database (Denmark)

    Ade, P. A R; Aghanim, N.; Arnaud, M.

    2016-01-01

    We present cluster counts and corresponding cosmological constraints from the Planck full mission data set. Our catalogue consists of 439 clusters detected via their Sunyaev-Zeldovich (SZ) signal down to a signal-to-noise ratio of 6, and is more than a factor of 2 larger than the 2013 Planck clus...

  8. An atomistic interpretation of Planck's 1900 derivation of his radiation law

    International Nuclear Information System (INIS)

    Irons, F.E.

    2000-01-01

    In deriving his radiation law in 1900, Max Planck employed a simple harmonic oscillator to model the exchange of energy between radiation and matter. Traditionally the harmonic oscillator has been viewed as modelling an entity which is itself oscillating, although a suitable oscillating entity has not been forthcoming. (Opinion is divided between a material oscillator, an imaginary oscillator and a need to revise Planck's derivation to apply to cavity modes of oscillation). We offer a novel, atomistic interpretation of Planck's derivation wherein the harmonic oscillator models a transition between the internal quantum states of an atom|not a normal electronic atom characterised by possible energies 0 and hν, but an atom populated by subatomic bosons (such as pions) and characterised by multiple occupancy of quantum states and possible energies nhν (n = 0;1;2; ...). We show how Planck's derivation can be varied to accommodate electronic atoms. A corollary to the atomistic interpretation is that Planck's derivation can no longer be construed as support for the postulate that material oscillating entities can have only those energies that are multiples of hν. Copyright (2000) CSIRO Australia

  9. Planck Early Results: The thermal performance of Planck

    DEFF Research Database (Denmark)

    Ade, P. A. R.; Aghanim, N.; Arnaud, M.

    2011-01-01

    The performance of the Planck instruments in space is enabled by their low operating temperatures, 20K for LFI and 0.1K for HFI, achieved through a combination of passive radiative cooling and three active mechanical coolers. Active coolers were chosen to minimize straylight on the detectors...... and to maximize lifetime. The scientific requirement for very broad frequency led to two detector technologies with widely dierent temperature and cooling needs. This made use of a helium cryostat, as used by previous cryogenic space missions (IRAS, COBE, ISO, SPITZER, AKARI), infeasible. Radiative cooling...... is provided by three V-groove radiators and a large telescope bae. The active coolers are a hydrogen sorption cooler (cooled in space to operating conditions...

  10. Diffusion-controlled reactions modeling in Geant4-DNA

    Czech Academy of Sciences Publication Activity Database

    Karamitros, M.; Luan, S.; Bernal, M. A.; Allison, J.; Baldacchino, G.; Davídková, Marie; Francis, Z.; Friedland, W.; Ivanchenko, A.; Ivanchenko, V.; Mantero, A.; Nieminen, P.; Santin, G.; Tran, H. N.; Stepan, V.; Incerti, S.

    2014-01-01

    Roč. 274, OCT (2014), s. 841-882 ISSN 0021-9991 Institutional support: RVO:61389005 Keywords : chemical kinetics simulation * radiation chemistry * Fokker-Planck equation * Smoluchowski diffusion equation * Brownian bridge * dynamical time steps * k-d tree * radiolysis * radiobiology * Geant4-DNA * Brownian dynamics Subject RIV: BO - Biophysics Impact factor: 2.434, year: 2014

  11. Transport theory of deep-inelastic collisions between heavy nuclei

    International Nuclear Information System (INIS)

    Ayik, S.; Noerenberg, W.; Schuermann, B.

    1975-01-01

    In collisions between heavy nuclei, the major part of the total cross-section is due to deep-inelastic processes. These processes have been studied within a quantum-statistical approach leading to transport equations of the Fokker-Planck type (generalized diffusion equation). Transport coefficients have been studied within a model. (orig./WL) [de

  12. Kramers-Moyal expansion for stochastic differential equations with single and multiple delays: Applications to financial physics and neurophysics

    International Nuclear Information System (INIS)

    Frank, T.D.

    2007-01-01

    We present a generalized Kramers-Moyal expansion for stochastic differential equations with single and multiple delays. In particular, we show that the delay Fokker-Planck equation derived earlier in the literature is a special case of the proposed Kramers-Moyal expansion. Applications for bond pricing and a self-inhibitory neuron model are discussed

  13. Fast wave heating of two-ion plasmas in the Princeton large torus through minority cyclotron resonance damping

    International Nuclear Information System (INIS)

    Hosea, J.; Bernabei, S.; Colestock, P.

    1979-07-01

    Strong minority proton heating is produced in PLT through ion cyclotron resonance damping of fast waves at moderate rf power levels. In addition to demonstrating good proton confinement, the proton energy distribution is consistent with Fokker--Planck theory which provides the prescription for extrapolation of this heating regime to higher rf power levels

  14. Axisymmetric MHD stable sloshing ion distributions

    International Nuclear Information System (INIS)

    Berk, H.L.; Dominguez, N.; Roslyakov, G.V.

    1986-07-01

    The MHD stability of a sloshing ion distribution is investigated in a symmetric mirror cell. Fokker-Planck calculations show that stable configurations are possible for ion injection energies that are at least 150 times greater than the electron temperture. Special axial magnetic field profiles are suggested to optimize the favorable MHD properties

  15. Problems of phenomenological simulation of the Dst variation

    International Nuclear Information System (INIS)

    Gul'el'mi, A.V.

    1988-01-01

    Stochastic generalization of RBM model, describing the D st -variation is suggested. The corresponding Fokker-Planck equation contains a new phenomenological parameter enabling to obtain the interval estimation of D st forecast. The structure of sources and sinks forming the D st -variation is considered from the viewpoint of critical phenomenon theory

  16. Time-dependent solutions for stochastic systems with delays: Perturbation theory and applications to financial physics

    International Nuclear Information System (INIS)

    Frank, T.D.

    2006-01-01

    First-order approximations of time-dependent solutions are determined for stochastic systems perturbed by time-delayed feedback forces. To this end, the theory of delay Fokker-Planck equations is applied in combination with Bayes' theorem. Applications to a time-delayed Ornstein-Uhlenbeck process and the geometric Brownian walk of financial physics are discussed

  17. Fast-ion dynamics in the TEXTOR tokamak measured by collective Thomson scattering

    DEFF Research Database (Denmark)

    Bindslev, Henrik; Nielsen, Stefan Kragh; Porte, L.

    2007-01-01

    ) and the slowdown after switch off of NBI are measured. The turn on phase of the NBI has, furthermore, been measured in plasmas with a range of electron densities and temperatures. All of these measurements are shown to be in good agreement with simple Fokker-Planck modelling. Bulk ion rotation velocity is also...

  18. Ion energy spectrum just after the application of current pulse for turbulent heating in the TRIAM-1 tokamak

    Energy Technology Data Exchange (ETDEWEB)

    Nakamura, K; Nakamura, Y; Hiraki, N; Itoh, S [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics

    1981-07-01

    Temporal evolution and spatial profile of ion energy spectrum just after the application of current pulse for turbulent heating are investigated experimentally in TRIAM-1 and numerically with a Fokker-Planck equation. Two-component ion energy spectrum formed by turbulent heating relaxes to single one within tau sub(i) (ion collision time).

  19. Ion energy spectrum just after the application of current pulse for turbulent heating in the TRIAM-1 tokamak

    International Nuclear Information System (INIS)

    Nakamura, Kazuo; Nakamura, Yukio; Hiraki, Naoji; Itoh, Satoshi

    1981-01-01

    Temporal evolution and spatial profile of ion energy spectrum just after the application of current pulse for turbulent heating are investigated experimentally in TRIAM-1 and numerically with a Fokker-Planck equation. Two-component ion energy spectrum formed by turbulent heating relaxes to single one within tau sub(i) (ion collision time). (author)

  20. Cosmology with the Planck Satellite

    CERN Multimedia

    CERN. Geneva

    2015-01-01

    Sketched out in 1992, selected by ESA in 1996, and launched in 2009, the Planck satellite was shut off in 2013, after a measuring mission that exceeded all expectations. The Planck collaboration delivered a first set of cosmological data and results in March 21st 2013, and the full set in February 2015. Part of the data delivery is a "definitive" map of the anisotropies of the Cosmic Microwave Background (CMB), its angular power spectrum together with their full statistical characterisation. The 2015 delivery also includes pioneering polarisation data. The temperature anisotropy map displays minuscule variations as a function of the observing direction, of rms ~100microK, of the fossil radiation around its mean temperature of 2.725K. Other maps reveal the CMB polarisation. The anisotropies are the imprint of the primordial fluctuations which initiated the growth of the large scale structures of the Universe, as transformed by their evolution, in particular during the first 370 000 years, as well as finer e...

  1. Planck's Constant as a Natural Unit of Measurement

    Science.gov (United States)

    Quincey, Paul

    2013-01-01

    The proposed revision of SI units would embed Planck's constant into the definition of the kilogram, as a fixed constant of nature. Traditionally, Planck's constant is not readily interpreted as the size of something physical, and it is generally only encountered by students in the mathematics of quantum physics. Richard Feynman's…

  2. The current-voltage relation of a pore and its asymptotic behavior in a Nernst-Planck model

    Directory of Open Access Journals (Sweden)

    Marius Birlea

    2012-08-01

    Full Text Available A model for current-voltage nonlinearity and asymmetry is a good starting point for explaining the electrical behavior of the nanopores in synthetic or biological membranes. Using a Nernst-Planck model, we found three behaviors for the current density in a membrane's pore as a function of voltage: a quasi-ohmic, slow rising linear current at low voltages, a nonlinear current at intermediate voltages, and a non-ohmic, fast rising linear current at large voltages. The slope of the quasi-ohmic current depends mainly on the height of energy barrier inside the pore, w, through an exponential term, ew. The magnitude of the non-ohmic linear current is controlled by the potential energy gradient at the pore entrance, w/r. The current-voltage relation is asymmetric if the ion's potential energy inside the pore has an asymmetric triangular profile. The model has only two assumed parameters, the energy barrier height, w, and the relative size of the entrance region of the pore, r, which is a useful feature for fitting and interpreting experimental data.

  3. Complexity for survival of livings

    Energy Technology Data Exchange (ETDEWEB)

    Zak, Michail [Jet Propulsion Laboratory, California Institute of Technology, Advance Computing Algorithms and IVHM Group, Pasadena, CA 91109 (United States)]. E-mail: Michail.Zak@jpl.nasa.gov

    2007-05-15

    A connection between survivability of livings and complexity of their behavior is established. New physical paradigms-exchange of information via reflections, and chain of abstractions-explaining and describing progressive evolution of complexity in living (active) systems are introduced. A biological origin of these paradigms is associated with a recently discovered mirror neuron that is able to learn by imitation. As a result, an active element possesses the self-nonself images and interacts with them creating the world of mental dynamics. Three fundamental types of complexity of mental dynamics that contribute to survivability are identified. Mathematical model of the corresponding active systems is described by coupled motor-mental dynamics represented by Langevin and Fokker-Planck equations, respectively, while the progressive evolution of complexity is provided by nonlinear evolution of probability density. Application of the proposed formalism to modeling common-sense-based decision-making process is discussed.

  4. From individual to collective behaviour of coupled velocity jump processes: A locust example

    KAUST Repository

    Erban, Radek; Haskovec, Jan

    2012-01-01

    A class of stochastic individual-based models, written in terms of coupled velocity jump processes, is presented and analysed. This modelling approach incorporates recent experimental findings on the behaviour of locusts. It exhibits nontrivial dynamics with a pitchfork bifurcation and recovers the observed group directional switching. Estimates of the expected switching times, in terms of the number of individuals and values of the model coefi-cients, are obtained using the corresponding Fokker-Planck equation. In the limit of large populations, a system of two kinetic equations (with nonlocal and nonlinear right hand side) is derived and analyzed. The existence of its solutions is proven and the system's long-time behaviour is investigated. Finally, a first step towards the mean field limit of topological interactions is made by studying the efiect of shrinking the interaction radius in the individual-based model. © American Institute of Mathematical Sciences.

  5. From individual to collective behaviour of coupled velocity jump processes: A locust example

    KAUST Repository

    Erban, Radek

    2012-11-01

    A class of stochastic individual-based models, written in terms of coupled velocity jump processes, is presented and analysed. This modelling approach incorporates recent experimental findings on the behaviour of locusts. It exhibits nontrivial dynamics with a pitchfork bifurcation and recovers the observed group directional switching. Estimates of the expected switching times, in terms of the number of individuals and values of the model coefi-cients, are obtained using the corresponding Fokker-Planck equation. In the limit of large populations, a system of two kinetic equations (with nonlocal and nonlinear right hand side) is derived and analyzed. The existence of its solutions is proven and the system\\'s long-time behaviour is investigated. Finally, a first step towards the mean field limit of topological interactions is made by studying the efiect of shrinking the interaction radius in the individual-based model. © American Institute of Mathematical Sciences.

  6. Complexity for survival of livings

    International Nuclear Information System (INIS)

    Zak, Michail

    2007-01-01

    A connection between survivability of livings and complexity of their behavior is established. New physical paradigms-exchange of information via reflections, and chain of abstractions-explaining and describing progressive evolution of complexity in living (active) systems are introduced. A biological origin of these paradigms is associated with a recently discovered mirror neuron that is able to learn by imitation. As a result, an active element possesses the self-nonself images and interacts with them creating the world of mental dynamics. Three fundamental types of complexity of mental dynamics that contribute to survivability are identified. Mathematical model of the corresponding active systems is described by coupled motor-mental dynamics represented by Langevin and Fokker-Planck equations, respectively, while the progressive evolution of complexity is provided by nonlinear evolution of probability density. Application of the proposed formalism to modeling common-sense-based decision-making process is discussed

  7. Planck intermediate results: XLV. Radio spectra of northern extragalactic radio sources

    DEFF Research Database (Denmark)

    Ade, P. A R; Aghanim, N.; Aller, H. D.

    2016-01-01

    Continuum spectra covering centimetre to submillimetre wavelengths are presented for a northern sample of 104 extragalactic radio sources, mainly active galactic nuclei, based on four-epoch Planck data. The nine Planck frequencies, from 30 to 857 GHz, are complemented by a set of simultaneous gro...

  8. Planck-scale Lorentz violation constrained by ultra-high-energy cosmic rays

    Energy Technology Data Exchange (ETDEWEB)

    Maccione, L. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Univ. Hamburg, II. Inst. fuer Theoretische Physik (Germany); Taylor, A.M. [Max-Planck-Inst. fuer Kernphysik, Heidelberg (Germany); Mattingly, D.M.; Liberati, S. [Scuola Internazionale Superiore di Studi Avanzati SISSA, Trieste (Italy); Istituto Nazionale di Fisica Nucleare INFN, Sezione di Trieste (Italy)

    2009-09-15

    We investigate the consequences of higher dimension Lorentz violating, CPT even kinetic operators that couple standard model fields to a non-zero vector field in an Effective Field Theory framework. Comparing the ultra-high energy cosmic ray spectrum reconstructed in the presence of such terms with data from the Pierre Auger observatory allows us to establish two sided bounds on the coefficients of the mass dimension five and six operators for the proton and pion. Our bounds imply that for both protons and pions, the energy scale of Lorentz symmetry breaking must be well above the Planck scale. In particular, the dimension five operators are constrained at the level of 10{sup -3}M{sup -1}{sub Planck}. The magnitude of the dimension six proton coefficient is bounded at the level of 10{sup -6}M{sup -2}{sub Planck} except in a narrow range where the pion and proton coefficients are both negative and nearly equal. In this small area, the magnitude of the dimension six proton coefficient must only be below 10{sup -3}M{sup -2}{sub Planck}. Constraints on the dimension six pion coefficient are found to be much weaker, but still below M{sup -2}{sub Planck}. (orig.)

  9. Amplitude growth due to random, correlated kicks

    International Nuclear Information System (INIS)

    Michelotti, L.; Mills, F.

    1989-03-01

    Historically, stochastic processes, such as gas scattering or stochastic cooling, have been treated by the Fokker-Planck equation. In this approach, usually considered for one dimension only, the equation can be considered as a continuity equation for a variable which would be a constant of the motion in the absence of the stochastic process, for example, the action variable, I = ε/2π for betatron oscillations, where ε is the area of the Courant-Snyder ellipse, or energy in the case of unbunched beams, or the action variable for phase oscillations in case the beam is bunched. A flux, /Phi/, including diffusive terms can be defined, usually to second order. /Phi/ = M 1 F(I) + M 2 ∂F/∂I + /hor ellipsis/. M 1 and M 2 are the expectation values of δI and (δI) 2 due to the individual stochastic kicks over some period of time, long enough that the variance of these quantities is sufficiently small. Then the Fokker-Planck equation is just ∂F/∂I + ∂/Phi//∂I = 0. In many cases those where the beam distribution has already achieved its final shape, it is sufficient to find the rate of increase of by taking simple averages over the Fokker-Planck equation. At the time this work was begun, there was good knowledge of the second moment for general stochastic processes due to stochastic cooling theory, but the form of the first moment was known only for extremely wideband processes. The purposes of this note are to derive an expression relating the expected single particle amplitude growth to the noise autocorrelation function and to obtain, thereby, the form of M 1 for narrow band processes. 4 refs

  10. Duality in an asset exchange model for wealth distribution

    Science.gov (United States)

    Li, Jie; Boghosian, Bruce M.

    2018-05-01

    Asset exchange models are agent-based economic models with binary transactions. Previous investigations have augmented these models with mechanisms for wealth redistribution, quantified by a parameter χ, and for trading bias favoring wealthier agents, quantified by a parameter ζ. By deriving and analyzing a Fokker-Planck equation for a particular asset exchange model thus augmented, it has been shown that it exhibits a second-order phase transition at ζ / χ = 1, between regimes with and without partial wealth condensation. In the "subcritical" regime with ζ / χ 1, a fraction 1 - χ / ζ of the wealth is condensed. Intuitively, one may associate the supercritical, wealth-condensed regime as reflecting the presence of "oligarchy," by which we mean that an infinitesimal fraction of the total agents hold a finite fraction of the total wealth in the continuum limit. In this paper, we further elucidate the phase behavior of this model - and hence of the generalized solutions of the Fokker-Planck equation that describes it - by demonstrating the existence of a remarkable symmetry between its supercritical and subcritical regimes in the steady-state. Noting that the replacement { ζ → χ , χ → ζ } , which clearly has the effect of inverting the order parameter ζ / χ, provides a one-to-one correspondence between the subcritical and supercritical states, we demonstrate that the wealth distribution of the subcritical state is identical to that of the corresponding supercritical state when the oligarchy is removed from the latter. We demonstrate this result analytically, both from the microscopic agent-level model and from its macroscopic Fokker-Planck description, as well as numerically. We argue that this symmetry is a kind of duality, analogous to the famous Kramers-Wannier duality between the subcritical and supercritical states of the Ising model, and to the Maldacena duality that underlies AdS/CFT theory.

  11. Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods

    KAUST Repository

    Machado Velho, Roberto

    2017-09-10

    In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia).

  12. Planck intermediate results XXVII. High-redshift infrared galaxy overdensity candidates and lensed sources discovered by Planck and confirmed by Herschel-SPIRE⋆

    DEFF Research Database (Denmark)

    Aghanim, N.; Altieri, B.; Arnaud, M.

    2015-01-01

    We have used the Planck all-sky submillimetre and millimetre maps to search for rare sources distinguished by extreme brightness, a few hundred millijanskies, and their potential for being situated at high redshift. These "cold" Planck sources, selected using the High Frequency Instrument (HFI) d...

  13. Heavy quarks thermalization in heavy-ion ultrarelativistic collisions: elastic or radiative?

    International Nuclear Information System (INIS)

    Gossiaux, Pol Bernard; Guiho, Vincent; Aichelin, Joerg

    2006-01-01

    We present a dynamical model of heavy quark evolution in the quark-gluon plasma (QGP) based on the Fokker-Planck equation. We then apply this model to the case of ultrarelativistic nucleus-nucleus collisions performed at RHIC in order to investigate which experimental observables might help to discriminate the fundamental process leading to thermalization

  14. Noise-induced multistability in chemical systems: Discrete versus continuum modeling

    Czech Academy of Sciences Publication Activity Database

    Duncan, A.; Liao, S.; Vejchodský, Tomáš; Erban, R.; Grima, R.

    2015-01-01

    Roč. 91, č. 4 (2015), s. 042111 ISSN 1539-3755 EU Projects: European Commission(XE) 328008 - STOCHDETBIOMODEL Institutional support: RVO:67985840 Keywords : chemical master equation * chemical Fokker-Planck equation * multimodality Subject RIV: BA - General Mathematics Impact factor: 2.288, year: 2014 http://journals.aps.org/pre/abstract/10.1103/PhysRevE.91.042111

  15. Consistent dynamical and statistical description of fission and comparison

    Energy Technology Data Exchange (ETDEWEB)

    Shunuan, Wang [Chinese Nuclear Data Center, Beijing, BJ (China)

    1996-06-01

    The research survey of consistent dynamical and statistical description of fission is briefly introduced. The channel theory of fission with diffusive dynamics based on Bohr channel theory of fission and Fokker-Planck equation and Kramers-modified Bohr-Wheeler expression according to Strutinsky method given by P.Frobrich et al. are compared and analyzed. (2 figs.).

  16. Dissipative nucleus-nucleus collisions: study of memory effects

    International Nuclear Information System (INIS)

    Agarwal, K.C.; Yadav, H.L.

    2002-01-01

    Dissipative collisions between two heavy nuclei are described in terms of a macroscopic dynamical model within the framework of a multi-dimensional Fokker-Planck equation. The reaction 86 Kr(8.18 MeV/u) + 166 Er has been used as a prototype to study and demonstrate the memory effects for dissipation and diffusion processes

  17. Noise-induced multistability in chemical systems: Discrete versus continuum modeling

    Czech Academy of Sciences Publication Activity Database

    Duncan, A.; Liao, S.; Vejchodský, Tomáš; Erban, R.; Grima, R.

    2015-01-01

    Roč. 91, č. 4 (2015), s. 042111 ISSN 1539-3755 EU Projects: European Commission(XE) 328008 - STOCHDETBIOMODEL Institutional support: RVO:67985840 Keywords : chemical master equation * chemical Fokker-Planck equation * multimodality Subject RIV: BA - General Mathematics Impact factor: 2.288, year: 2014 http://journals. aps .org/pre/abstract/10.1103/PhysRevE.91.042111

  18. Planck early results. IX. XMM-Newton follow-up for validation of Planck cluster candidates

    DEFF Research Database (Denmark)

    Poutanen, T.; Natoli, P.; Polenta, G.

    2011-01-01

    We present the XMM-Newton follow-up for confirmation of Planck cluster candidates. Twenty-five candidates have been observed to date using snapshot (∼10 ks) exposures, ten as part of a pilot programme to sample a low range of signal-to-noise ratios (4

  19. Constraints on cosmological birefringence from PLANCK and Bicep2/Keck data

    Energy Technology Data Exchange (ETDEWEB)

    Gruppuso, A. [INAF-IASF Bologna, Istituto di Astrofisica Spaziale e Fisica Cosmica di Bologna, Istituto Nazionale di Astrofisica, via Gobetti 101, I-40129 Bologna (Italy); Gerbino, M.; Pagano, L.; Melchiorri, A. [Dipartimento di Fisica and INFN, Università di Roma ' ' La Sapienza' ' , P.le Aldo Moro 2, 00185, Rome (Italy); Natoli, P.; Mandolesi, N.; Molinari, D., E-mail: gruppuso@iasbo.inaf.it, E-mail: martina.gerbino@roma1.infn.it, E-mail: ntlpla@unife.it, E-mail: luca.pagano@roma1.infn.it, E-mail: mandolesi@iasfbo.inaf.it, E-mail: alessandro.melchiorri@roma1.infn.it, E-mail: molinari@iasfbo.inaf.it [Dipartimento di Fisica e Scienze della Terra and INFN, Università degli Studi di Ferrara, Via Saragat 1, I-44100 Ferrara (Italy)

    2016-06-01

    The polarization of cosmic microwave background (CMB) can be used to constrain cosmological birefringence, the rotation of the linear polarization of CMB photons potentially induced by parity violating physics beyond the standard model. This effect produces non-null CMB cross correlations between temperature and B mode-polarization, and between E- and B-mode polarization. Both cross-correlations are otherwise null in the standard cosmological model. We use the recently released 2015 PLANCK likelihood in combination with the Bicep2/Keck/Planck (BKP) likelihood to constrain the birefringence angle α. Our findings, that are compatible with no detection, read α = 0.0° ± 1.3° (stat) ± 1° (sys) for PLANCK data and α = 0.30° ± 0.27° (stat) ± 1° (sys) for BKP data. We finally forecast the expected improvements over present constraints when the PLANCK BB, TB and EB spectra at high ℓ will be included in the analysis.

  20. From Brownian Dynamics to Markov Chain: An Ion Channel Example

    KAUST Repository

    Chen, Wan

    2014-02-27

    A discrete rate theory for multi-ion channels is presented, in which the continuous dynamics of ion diffusion is reduced to transitions between Markovian discrete states. In an open channel, the ion permeation process involves three types of events: an ion entering the channel, an ion escaping from the channel, or an ion hopping between different energy minima in the channel. The continuous dynamics leads to a hierarchy of Fokker-Planck equations, indexed by channel occupancy. From these the mean escape times and splitting probabilities (denoting from which side an ion has escaped) can be calculated. By equating these with the corresponding expressions from the Markov model, one can determine the Markovian transition rates. The theory is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal geometry maximizing ion flux is computed. © 2014 Society for Industrial and Applied Mathematics.

  1. NUMERICAL RESEARCH ON THE THREE-DIMENSIONAL FIBER ORIENTATION DISTRIBUTION IN PLANAR SUSPENSION FLOWS

    Directory of Open Access Journals (Sweden)

    Qihua Zhang

    Full Text Available Abstract To describe flow-induced fiber orientation, the Fokker-Planck equation is widely applied in the processing of composites and fiber suspensions. The analytical solution only exists when the Péclet number is infinite. So developing a numerical method covering a full range of Péclet number is of great significance. To accurately solve the Fokker-Planck equation, a numerical scheme based on the finite volume method is developed. Using spherical symmetry, the boundary is discretized and formulated into a cyclic tridiagonal matrix which is further solved by the CTDMA algorithm. To examine its validity, benchmark tests over a wide range of Péclet number are performed in a simple shear flow. For Pe=∞, the results agree well with the analytical solutions. For the other Pe numbers, the results are compared to results available in the literature. The tests show that this algorithm is accurate, stable, and globally conservative. Furthermore, this algorithm can be extended and used to predict the three-dimensional orientation distribution of complex suspension flows.

  2. ZORNOC: a 1 1/2-D tokamak data analysis code for studying noncircular high beta plasmas

    International Nuclear Information System (INIS)

    Zurro, B.; Wieland, R.M.; Murakami, M.; Swain, D.W.

    1980-03-01

    A new tokamak data analysis code, ZORNOC, was developed to study noncircular, high beta plasmas in the Impurity Study Experiment (ISX-B). These plasmas exhibit significant flux surface shifts and elongation in both ohmically heated and beam-heated discharges. The MHD equilibrium flux surface geometry is determined by solving the Grad-Shafranov equation based on: (1) the shape of the outermost flux surface, deduced from the magnetic loop probes; (2) a pressure profile, deduced by means of Thomson scattering data (electrons), charge exchange data (ions), and a Fokker-Planck model (fast ions); and (3) a safety factor profile, determined from the experimental data using a simple model (Z/sub eff/ = const) that is self-consistently altered while the plasma equilibrium is iterated. For beam-heated discharches the beam deposition profile is determined by means of a Monte Carlo scheme and the slowing down of the fast ions by means of an analytical solution of the Fokker-Planck equation. The code also carries out an electron power balance and calculates various confinement parameters. The code is described and examples of its operation are given

  3. Astrochemical Properties of Planck Cold Clumps

    Energy Technology Data Exchange (ETDEWEB)

    Tatematsu, Ken’ichi; Sanhueza, Patricio; Nguyễn Lu’o’ng, Quang; Hirota, Tomoya [National Astronomical Observatory of Japan, National Institutes of Natural Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588 (Japan); Liu, Tie; Choi, Minho; Kang, Miju; Kim, Kee-Tae [Korea Astronomy and Space Science Institute, Daedeokdaero 776, Yuseong, Daejeon 305-348 (Korea, Republic of); Ohashi, Satoshi [Department of Astronomy, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan); Liu, Sheng-Yuan; Hirano, Naomi [Academia Sinica Institute of Astronomy and Astrophysics, 11F of Astronomy-Mathematics Building, AS/NTU. No.1, Section 4, Roosevelt Rd, Taipei 10617, Taiwan (China); Thompson, Mark A. [Centre for Astrophysics Research, Science and Technology Research Institute, University of Hertfordshire, Hatfield, AL10 9AB (United Kingdom); Fuller, Gary [Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL (United Kingdom); Wu, Yuefang [Department of Astronomy, Peking University, 100871, Beijing (China); Li, Di [National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100012 (China); Francesco, James Di [NRC Herzberg Astronomy and Astrophysics, 5071 West Saanich Road, Victoria, BC V9E 2E7 (Canada); Wang, Ke [European Southern Observatory (Germany); Ristorcelli, Isabelle [IRAP, CNRS (UMR5277), Universite Paul Sabatier, 9 avenue du Colonel Roche, BP 44346, F-31028, Toulouse Cedex 4 (France); Juvela, Mika [Department of physics, University of Helsinki, FI-00014, Helsinki (Finland); Shinnaga, Hiroko, E-mail: k.tatematsu@nao.ac.jp [Department of Physics, Kagoshima University, 1-21-35, Korimoto, Kagoshima, 890-0065 (Japan); Collaboration: JCMT Large Program “SCOPE” collaboration; TRAO Key Science Program “TOP” collaboration; and others

    2017-02-01

    We observed 13 Planck cold clumps with the James Clerk Maxwell Telescope/SCUBA-2 and with the Nobeyama 45 m radio telescope. The N{sub 2}H{sup +} distribution obtained with the Nobeyama telescope is quite similar to SCUBA-2 dust distribution. The 82 GHz HC{sub 3}N, 82 GHz CCS, and 94 GHz CCS emission are often distributed differently with respect to the N{sub 2}H{sup +} emission. The CCS emission, which is known to be abundant in starless molecular cloud cores, is often very clumpy in the observed targets. We made deep single-pointing observations in DNC, HN{sup 13}C, N{sub 2}D{sup +}, and cyclic-C{sub 3}H{sub 2} toward nine clumps. The detection rate of N{sub 2}D{sup +} is 50%. Furthermore, we observed the NH{sub 3} emission toward 15 Planck cold clumps to estimate the kinetic temperature, and confirmed that most targets are cold (≲20 K). In two of the starless clumps we observed, the CCS emission is distributed as it surrounds the N{sub 2}H{sup +} core (chemically evolved gas), which resembles the case of L1544, a prestellar core showing collapse. In addition, we detected both DNC and N{sub 2}D{sup +}. These two clumps are most likely on the verge of star formation. We introduce the chemical evolution factor (CEF) for starless cores to describe the chemical evolutionary stage, and analyze the observed Planck cold clumps.

  4. Planck absolute entropy of a rotating BTZ black hole

    Science.gov (United States)

    Riaz, S. M. Jawwad

    2018-04-01

    In this paper, the Planck absolute entropy and the Bekenstein-Smarr formula of the rotating Banados-Teitelboim-Zanelli (BTZ) black hole are presented via a complex thermodynamical system contributed by its inner and outer horizons. The redefined entropy approaches zero as the temperature of the rotating BTZ black hole tends to absolute zero, satisfying the Nernst formulation of a black hole. Hence, it can be regarded as the Planck absolute entropy of the rotating BTZ black hole.

  5. Planck 2015 results IX. Diffuse component separation: CMB maps

    DEFF Research Database (Denmark)

    Adam, R.; Ade, P. A R; Aghanim, N.

    2016-01-01

    We present foreground-reduced cosmic microwave background (CMB) maps derived from the full Planck data set in both temperature and polarization. Compared to the corresponding Planck 2013 temperature sky maps, the total data volume is larger by a factor of 3.2 for frequencies between 30 and 70 GHz......, and between 4.5 and 6.1μK averaged over pixels. The cosmological parameters derived from the analysis of temperature power spectra are in agreement at the 1σ level with the Planck 2015 likelihood. Unresolved mismatches between the noise properties of the data and simulations prevent a satisfactory description...... of the higher-order statistical properties of the polarization maps. Thus, the primary applications of these polarization maps are those that do not require massive simulations for accurate estimation of uncertainties, for instance estimation of cross-spectra and cross-correlations, or stacking analyses...

  6. Planck 2015 results: XXIII. The thermal Sunyaev-Zeldovich effect-cosmic infrared background correlation

    DEFF Research Database (Denmark)

    Ade, P. A R; Aghanim, N.; Arnaud, M.

    2016-01-01

    We use Planck data to detect the cross-correlation between the thermal Sunyaev-Zeldovich (tSZ) effect and the infrared emission from the galaxies that make up the the cosmic infrared background (CIB). We first perform a stacking analysis towards Planck-confirmed galaxy clusters. We detect infrared...... that infrared galaxies in the outskirts of clusters have higher infrared flux than cluster-core galaxies. We also study the cross-correlation between tSZ and CIB anisotropies, following three alternative approaches based on power spectrum analyses: (i) using a catalogue of confirmed clusters detected in Planck...... data; (ii) using an all-sky tSZ map built from Planck frequency maps; and (iii) using cross-spectra between Planck frequency maps. With the three different methods, we detect the tSZ-CIB cross-power spectrum at significance levels of (i) 6σ; (ii) 3σ; and (iii) 4σ. We model the tSZ-CIB cross-correlation...

  7. Excess B-modes extracted from the Planck polarization maps

    Science.gov (United States)

    Nørgaard-Nielsen, H. U.

    2016-06-01

    One of the main obstacles for extracting the Cosmic Microwave Background (CMB) from mm/submm observations is the pollution from the main Galactic components: synchrotron, free-free and thermal dust emission. The feasibility of using simple neural networks to extract CMB has been demonstrated on both temperature and polarization data obtained by the WMAP satellite. The main goal of this paper is to demonstrate the feasibility of neural networks for extracting the CMB signal from the Planck polarization data with high precision. Both auto-correlation and cross-correlation power spectra within a mask covering about 63 % of the sky have been used together with a ``high pass filter'' in order to minimize the influence of the remaining systematic errors in the Planck Q and U maps. Using the Planck 2015 released polarization maps, a BB power spectrum have been extracted by Multilayer Perceptron neural networks. This spectrum contains a bright feature with signal to noise ratios ≃ 4.5 within 200 ≤ l ≤ 250. The spectrum is significantly brighter than the BICEP2 2015 spectrum, with a spectral behaviour quite different from the ``canonical'' models (weak lensing plus B-modes spectra with different tensor to scalar ratios). The feasibility of the neural network to remove the residual systematics from the available Planck polarization data to a high level has been demonstrated.

  8. Max Planck Institute for Human Development and Education: Annual Report 1990.

    Science.gov (United States)

    Max-Planck-Institut fuer Bildungsforschung, Berlin (West Germany).

    The Max Planck Institute for Human Development and Education in Germany consists of four research centers dealing with the following topics: sociology and the study of the life course; development and socialization; psychology and human development; and school systems and instruction. This English-language annual report of the Planck Institute,…

  9. A constraint on Planck-scale modifications to electrodynamics with CMB polarization data

    International Nuclear Information System (INIS)

    Gubitosi, Giulia; Pagano, Luca; Amelino-Camelia, Giovanni; Melchiorri, Alessandro; Cooray, Asantha

    2009-01-01

    We show that the Cosmic Microwave Background (CMB) polarization data gathered by the BOOMERanG 2003 flight and WMAP provide an opportunity to investigate in-vacuo birefringence, of a type expected in some quantum pictures of space-time, with a sensitivity that extends even beyond the desired Planck-scale energy. In order to render this constraint more transparent we rely on a well studied phenomenological model of quantum-gravity-induced birefringence, in which one easily establishes that effects introduced at the Planck scale would amount to values of a dimensionless parameter, denoted by ξ, with respect to the Planck energy which are roughly of order 1. By combining BOOMERanG and WMAP data we estimate ξ ≅ −0.110±0.075 at the 68% c.l. Moreover, we forecast on the sensitivity to ξ achievable by future CMB polarization experiments (PLANCK, Spider, EPIC), which, in the absence of systematics, will be at the 1-σ confidence of 8.5 × 10 −4 (PLANCK), 6.1 × 10 −3 (Spider), and 1.0 × 10 −5 (EPIC) respectively. The cosmic variance-limited sensitivity from CMB is 6.1 × 10 −6

  10. Isocurvature perturbations and tensor mode in light of Planck and BICEP2

    Energy Technology Data Exchange (ETDEWEB)

    Kawasaki, Masahiro; Yokoyama, Shuichiro [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582 (Japan); Sekiguchi, Toyokazu [Helsinki Institute of Physics, University of Helsinki, PO Box 64, FIN-00014 (Finland); Takahashi, Tomo, E-mail: kawasaki@icrr.u-tokyo.ac.jp, E-mail: toyokazu.sekiguchi@helsinki.fi, E-mail: tomot@cc.saga-u.ac.jp, E-mail: shu@icrr.u-tokyo.ac.jp [Department of Physics, Saga University, Saga 840-8502 (Japan)

    2014-08-01

    We investigate the degeneracy of the isocurvature perturbations and the primordial gravitational waves, by using recent observations of the cosmic microwave background (CMB) reported by Planck and BICEP2 collaborations. We show that the tension in the bound on the tensor-to-scalar ratio r between Planck and BICEP2 can be resolved by introducing the anti-correlated isocurvature perturbations. Quantitatively, we find that with the anti-correlated isocurvature perturbations the constraints on r from Planck alone and BICEP2 results can be consistent at 68 % C.L.

  11. Time evolution of the fission-decay width under the influence of dissipation

    International Nuclear Information System (INIS)

    Jurado, B.; Schmidt, K.H.; Benlliure, J.

    2002-12-01

    Different analytical approximations to the time-dependent fission-decay width used to extract the influence of dissipation on the fission process are critically examined. Calculations with a new, highly realistic analytical approximation to the exact solution of the Fokker-Planck equation sheds doubts on previous conclusions on the dissipation strength made on the basis of less realistic approximations. (orig.)

  12. Acceleration of beam ions during major radius compression in TFTR

    International Nuclear Information System (INIS)

    Wong, K.L.; Bitter, M.; Hammett, G.W.

    1985-09-01

    Tangentially co-injected deuterium beam ions were accelerated from 82 keV up to 150 keV during a major radius compression experiment in TFTR. The ion energy spectra and the variation in fusion yield were in good agreement with Fokker-Planck code simulations. In addition, the plasma rotation velocity was observed to rise during compression

  13. FOM-Rijnhuizen contributions to the 23. European Physical Society conference on controlled fusion and plasma physics

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1996-07-01

    Electron Cyclotron Current Drive (ECCD) experiments on the Rijnhuizen tokamak RTP have been performed utilizing 60 GHz waves launched from the high field side of the torus. The ECCD efficiency as a function of the position of the cold resonance layer has been measured and compared with Fokker-Planck simulations. The experimental results are consistent with these simulations. (orig.).

  14. Modeling Populations of Thermostatic Loads with Switching Rate Actuation

    DEFF Research Database (Denmark)

    Totu, Luminita Cristiana; Wisniewski, Rafal; Leth, John-Josef

    2015-01-01

    We model thermostatic devices using a stochastic hybrid description, and introduce an external actuation mechanism that creates random switch events in the discrete dynamics. We then conjecture the form of the Fokker-Planck equation and successfully verify it numerically using Monte Carlo...... simulations. The actuation mechanism and subsequent modeling result are relevant for power system operation....

  15. FOM-Rijnhuizen contributions to the 23. European Physical Society conference on controlled fusion and plasma physics

    International Nuclear Information System (INIS)

    1996-07-01

    Electron Cyclotron Current Drive (ECCD) experiments on the Rijnhuizen tokamak RTP have been performed utilizing 60 GHz waves launched from the high field side of the torus. The ECCD efficiency as a function of the position of the cold resonance layer has been measured and compared with Fokker-Planck simulations. The experimental results are consistent with these simulations. (orig.)

  16. Computational Physics Program of the National MFE Computer Center

    International Nuclear Information System (INIS)

    Mirin, A.A.

    1984-12-01

    The principal objective of the computational physics group is to develop advanced numerical models for the investigation of plasma phenomena and the simulation of present and future magnetic confinement devices. A summary of the groups activities is presented, including computational studies in MHD equilibria and stability, plasma transport, Fokker-Planck, and efficient numerical and programming algorithms. References are included

  17. Statistical measures of Planck scale signal correlations in interferometers

    Energy Technology Data Exchange (ETDEWEB)

    Hogan, Craig J. [Univ. of Chicago, Chicago, IL (United States); Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Kwon, Ohkyung [Univ. of Chicago, Chicago, IL (United States)

    2015-06-22

    A model-independent statistical framework is presented to interpret data from systems where the mean time derivative of positional cross correlation between world lines, a measure of spreading in a quantum geometrical wave function, is measured with a precision smaller than the Planck time. The framework provides a general way to constrain possible departures from perfect independence of classical world lines, associated with Planck scale bounds on positional information. A parametrized candidate set of possible correlation functions is shown to be consistent with the known causal structure of the classical geometry measured by an apparatus, and the holographic scaling of information suggested by gravity. Frequency-domain power spectra are derived that can be compared with interferometer data. As a result, simple projections of sensitivity for specific experimental set-ups suggests that measurements will directly yield constraints on a universal time derivative of the correlation function, and thereby confirm or rule out a class of Planck scale departures from classical geometry.

  18. Inflation after False Vacuum Decay observational Prospects after Planck

    CERN Document Server

    Bousso, Raphael; Senatore, Leonardo

    2015-01-01

    We assess potential signals of the formation of our universe by the decay of a false vacuum. Negative spatial curvature is one possibility, but the window for its detection is now small. However, another possible signal is a suppression of the CMB power spectrum at large angles. This arises from the steepening of the effective potential as it interpolates between a flat inflationary plateau and the high barrier separating us from our parent vacuum. We demonstrate that these two effects can be parametrically separated in angular scale. Observationally, the steepening effect appears to be excluded at large l; but it remains consistent with the slight lack of power below l about 30 found by the WMAP and Planck collaborations. We give two simple models which improve the fit to the Planck data; one with observable curvature and one without. Despite cosmic variance, we argue that future CMB polarization and most importantly large-scale structure observations should be able to corroborate the Planck anomaly if it is...

  19. Beyond the Planck Scale

    International Nuclear Information System (INIS)

    Giddings, Steven B.

    2009-01-01

    I outline motivations for believing that important quantum gravity effects lie beyond the Planck scale at both higher energies and longer distances and times. These motivations arise in part from the study of ultra-high energy scattering, and also from considerations in cosmology. I briefly summarize some inferences about such ultra-planckian physics, and clues we might pursue towards the principles of a more fundamental theory addressing the known puzzles and paradoxes of quantum gravity.

  20. Planck 2013 results. XII. Component separation

    DEFF Research Database (Denmark)

    Planck Collaboration,; Ade, P. A. R.; Aghanim, N.

    2013-01-01

    Planck has produced detailed all-sky observations over nine frequency bands between 30 and 857 GHz. These observations allow robust reconstruction of the primordial cosmic microwave background (CMB) temperature fluctuations over nearly the full sky, as well as new constraints on Galactic foregrou...

  1. Planck 2015 results: XVI. Isotropy and statistics of the CMB

    DEFF Research Database (Denmark)

    Ade, P. A R; Aghanim, N.; Akrami, Y.

    2016-01-01

    We test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also include some polarization measurements. In particular, we consi...

  2. Baryon asymmetry from Planck-scale physics

    International Nuclear Information System (INIS)

    Gelmini, G.; Holman, R.; Carnegie-Mellon Univ., Pittsburgh, PA

    1992-06-01

    It has been noted recently that Planck scale physics may induce the explicit breaking of global symmetries. We point out that in Majoron models, these explicit breakings, combined with sphaleron induced violation of B + L can give rise to the baryon asymmetry of the Universe

  3. A constraint on Planck-scale modifications to electrodynamics with CMB polarization data

    Energy Technology Data Exchange (ETDEWEB)

    Gubitosi, Giulia; Pagano, Luca; Amelino-Camelia, Giovanni; Melchiorri, Alessandro [Physics Department, University of Rome ' ' La Sapienza' ' and Sezione Roma1 INFN, P.le Aldo Moro 2, 00185 Rome (Italy); Cooray, Asantha, E-mail: giulia.gubitosi@roma1.infn.it, E-mail: luca.pagano@roma1.infn.it, E-mail: giovanni.amelino-camelia@roma1.infn.it, E-mail: alessandro.melchiorri@roma1.infn.it, E-mail: acooray@uci.edu [Center for Cosmology, Dept. of Physics and Astronomy, University of California Irvine, Irvine, CA 92697 (United States)

    2009-08-01

    We show that the Cosmic Microwave Background (CMB) polarization data gathered by the BOOMERanG 2003 flight and WMAP provide an opportunity to investigate in-vacuo birefringence, of a type expected in some quantum pictures of space-time, with a sensitivity that extends even beyond the desired Planck-scale energy. In order to render this constraint more transparent we rely on a well studied phenomenological model of quantum-gravity-induced birefringence, in which one easily establishes that effects introduced at the Planck scale would amount to values of a dimensionless parameter, denoted by ξ, with respect to the Planck energy which are roughly of order 1. By combining BOOMERanG and WMAP data we estimate ξ ≅ −0.110±0.075 at the 68% c.l. Moreover, we forecast on the sensitivity to ξ achievable by future CMB polarization experiments (PLANCK, Spider, EPIC), which, in the absence of systematics, will be at the 1-σ confidence of 8.5 × 10{sup −4} (PLANCK), 6.1 × 10{sup −3} (Spider), and 1.0 × 10{sup −5} (EPIC) respectively. The cosmic variance-limited sensitivity from CMB is 6.1 × 10{sup −6}.

  4. Planck 2013 results. I. Overview of products and scientific results

    DEFF Research Database (Denmark)

    Planck Collaboration,; Ade, P. A. R.; Aghanim, N.

    2013-01-01

    , and the science data products and papers in the release. Scientific results include robust support for the standard, six parameter LCDM model of cosmology and improved measurements for the parameters that define this model, including a highly significant deviation from scale invariance of the primordial power......The ESA's Planck satellite, dedicated to studying the early universe, was launched on May 2009 and has been surveying the microwave and submillimetre sky since August 2009. In March 2013, ESA and the Planck Collaboration publicly released the initial cosmology products based on the first 15.......5 months of Planck operations, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper describes the mission and its performance, and gives an overview of the processing and analysis of the data, the characteristics of the data, the main scientific results...

  5. Planck 2015 results: XIX. Constraints on primordial magnetic fields

    DEFF Research Database (Denmark)

    Ade, P. A R; Aghanim, N.; Arnaud, M.

    2016-01-01

    of the CMB angular power spectra, using the Planck likelihood, are B1 Mpc 4.4 nG (where B1 Mpc is the comoving field amplitude at a scale of 1 Mpc) at 95% confidence level, assuming zero helicity. By considering the Planck likelihood, based only on parity-even angular power spectra, we obtain B1 Mpc ... to three applied methods, all below 5 nG. The constraint from the magnetically-induced passive-tensor bispectrum is B1 Mpc Mpc 4.5 nG, whereas the compensated-scalar bispectrum gives B1 Mpc

  6. Planck 2015 results. XV. Gravitational lensing

    CERN Document Server

    Ade, P.A.R.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartlett, J.G.; Bartolo, N.; Basak, S.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bock, J.J.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Boulanger, F.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cardoso, J.-F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Combet, C.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Désert, F.-X.; Diego, J.M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dunkley, J.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T.A.; Eriksen, H.K.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J.E.; Hansen, F.K.; Hanson, D.; Harrison, D.L.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Hurier, G.; Jaffe, A.H.; Jaffe, T.R.; Jones, W.C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Lattanzi, M.; Lawrence, C.R.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Lewis, A.; Liguori, M.; Lilje, P.B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P.M.; Macías-Pérez, J.F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Maris, M.; Martin, P.G.; Martínez-González, E.; Masi, S.; Matarrese, S.; McGehee, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J.A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Nørgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G.W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J.P.; Reach, W.T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rowan-Robinson, M.; Rubiño-Martín, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J.A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vielva, P.; Villa, F.; Wade, L.A.; Wandelt, B.D.; Wehus, I.K.; White, M.; Yvon, D.; Zacchei, A.

    2016-01-01

    We present the most significant measurement of the cosmic microwave background (CMB) lensing potential to date (at a level of 40 sigma), using temperature and polarization data from the Planck 2015 full-mission release. Using a polarization-only estimator we detect lensing at a significance of 5 sigma. We cross-check the accuracy of our measurement using the wide frequency coverage and complementarity of the temperature and polarization measurements. Public products based on this measurement include an estimate of the lensing potential over approximately 70% of the sky, an estimate of the lensing potential power spectrum in bandpowers for the multipole range 40Planck temperature and polarization power spectra. Using the lensing likelihood alone we obtain a percent-level measurement of ...

  7. 75 FR 10696 - Airworthiness Directives; Fokker Services B.V. Model F.28 Mark 0070 and 0100 Airplanes

    Science.gov (United States)

    2010-03-09

    ... revealed that, due to their position on the aircraft, ice may form on actuators P/N 9409122 installed on... replacing the valve actuator with a serviceable part is in the Fokker 70/100 Aircraft Maintenance Manual... airplane, fuel fire shut-off valve actuators P/N [part number] 9409122 are susceptible to freezing, which...

  8. Stationary response of multi-degree-of-freedom vibro-impact systems to Poisson white noises

    International Nuclear Information System (INIS)

    Wu, Y.; Zhu, W.Q.

    2008-01-01

    The stationary response of multi-degree-of-freedom (MDOF) vibro-impact (VI) systems to random pulse trains is studied. The system is formulated as a stochastically excited and dissipated Hamiltonian system. The constraints are modeled as non-linear springs according to the Hertz contact law. The random pulse trains are modeled as Poisson white noises. The approximate stationary probability density function (PDF) for the response of MDOF dissipated Hamiltonian systems to Poisson white noises is obtained by solving the fourth-order generalized Fokker-Planck-Kolmogorov (FPK) equation using perturbation approach. As examples, two-degree-of-freedom (2DOF) VI systems under external and parametric Poisson white noise excitations, respectively, are investigated. The validity of the proposed approach is confirmed by using the results obtained from Monte Carlo simulation. It is shown that the non-Gaussian behaviour depends on the product of the mean arrival rate of the impulses and the relaxation time of the oscillator

  9. BRS invariant stochastic quantization of Einstein gravity

    International Nuclear Information System (INIS)

    Nakazawa, Naohito.

    1989-11-01

    We study stochastic quantization of gravity in terms of a BRS invariant canonical operator formalism. By introducing artificially canonical momentum variables for the original field variables, a canonical formulation of stochastic quantization is proposed in the sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. Then we show that there exists a nilpotent BRS symmetry in an enlarged phase space of the first-class constrained systems. The phase space is spanned by the dynamical variables, their canonical conjugate momentum variables, Faddeev-Popov ghost and anti-ghost. We apply the general BRS invariant formulation to stochastic quantization of gravity which is described as a second-class constrained system in terms of a pair of Langevin equations coupled with white noises. It is shown that the stochastic action of gravity includes explicitly the De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models. (author)

  10. Planck 2015 results: XV. Gravitational lensing

    DEFF Research Database (Denmark)

    Ade, P. A R; Aghanim, N.; Arnaud, M.

    2016-01-01

    We present the most significant measurement of the cosmic microwave background (CMB) lensing potential to date (at a level of 40σ), using temperature and polarization data from the Planck 2015 full-mission release. Using a polarization-only estimator, we detect lensing at a significance of 5σ. We...

  11. Planck 2015 results. I. Overview of products and scientific results

    CERN Document Server

    Adam, R.; Aghanim, N.; Akrami, Y.; Alves, M.I.R.; Arnaud, M.; Arroja, F.; Aumont, J.; Baccigalupi, C.; Ballardini, M.; Banday, A.J.; Barreiro, R.B.; Bartlett, J.G.; Bartolo, N.; Basak, S.; Battaglia, P.; Battaner, E.; Battye, R.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bertincourt, B.; Bielewicz, P.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Boulanger, F.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cardoso, J.F.; Carvalho, P.; Casaponsa, B.; Castex, G.; Catalano, A.; Challinor, A.; Chamballu, A.; Chary, R.R.; Chiang, H.C.; Chluba, J.; Christensen, P.R.; Church, S.; Clemens, M.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Combet, C.; Comis, B.; Contreras, D.; Couchot, F.; Coulais, A.; Crill, B.P.; Cruz, M.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.M.; Desert, F.X.; Di Valentino, E.; Dickinson, C.; Diego, J.M.; Dolag, K.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Ducout, A.; Dunkley, J.; Dupac, X.; Efstathiou, G.; Eisenhardt, P.R.M.; Elsner, F.; Ensslin, T.A.; Eriksen, H.K.; Falgarone, E.; Fantaye, Y.; Farhang, M.; Feeney, S.; Fergusson, J.; Fernandez-Cobos, R.; Feroz, F.; Finelli, F.; Florido, E.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschet, C.; Franceschi, E.; Frejsel, A.; Frolov, A.; Galeotta, S.; Galli, S.; Ganga, K.; Gauthier, C.; Genova-Santos, R.T.; Gerbino, M.; Ghosh, T.; Giard, M.; Giraud-Heraud, Y.; Giusarma, E.; Gjerlow, E.; Gonzalez-Nuevo, J.; Gorski, K.M.; Grainge, K.J.B.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J.E.; Hamann, J.; Handley, W.; Hansen, F.K.; Hanson, D.; Harrison, D.L.; Heavens, A.; Helou, G.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huang, Z.; Huffenberger, K.M.; Hurier, G.; Ilic, S.; Jaffe, A.H.; Jaffe, T.R.; Jin, T.; Jones, W.C.; Juvela, M.; Karakci, A.; Keihanen, E.; Keskitalo, R.; Kiiveri, K.; Kim, J.; Kisner, T.S.; Kneissl, R.; Knoche, J.; Krachmalnicoff, N.; Kunz, M.; Kurki-Suonio, H.; Lacasa, F.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Langer, M.; Lasenby, A.; Lattanzi, M.; Lawrence, C.R.; Le Jeune, M.; Leahy, J.P.; Lellouch, E.; Leonardi, R.; Leon-Tavares, J.; Lesgourgues, J.; Levrier, F.; Lewis, A.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lindholm, V.; Liu, H.; Lopez-Caniego, M.; Lubin, P.M.; Ma, Y.Z.; Macias-Perez, J.F.; Maggio, G.; Mak, D.S.Y.; Mandolesi, N.; Mangilli, A.; Marchini, A.; Marcos-Caballero, A.; Marinucci, D.; Marshall, D.J.; Martin, P.G.; Martinelli, M.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; Mazzotta, P.; McEwen, J.D.; McGehee, P.; Mei, S.; Meinhold, P.R.; Melchiorri, A.; Melin, J.B.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mikkelsen, K.; Mitra, S.; Miville-Deschenes, M.A.; Molinari, D.; Moneti, A.; Montier, L.; Moreno, R.; Morgante, G.; Mortlock, D.; Moss, A.; Mottet, S.; Muenchmeyer, M.; Munshi, D.; Murphy, J.A.; Narimani, A.; Naselsky, P.; Nastasi, A.; Nati, F.; Natoli, P.; Negrello, M.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Olamaie, M.; Oppermann, N.; Orlando, E.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paladini, R.; Pandolfi, S.; Paoletti, D.; Partridge, B.; Pasian, F.; Patanchon, G.; Pearson, T.J.; Peel, M.; Peiris, H.V.; Pelkonen, V.M.; Perdereau, O.; Perotto, L.; Perrott, Y.C.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pogosyan, D.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Racine, B.; Reach, W.T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Roman, M.; Romelli, E.; Rosset, C.; Rossetti, M.; Rotti, A.; Roudier, G.; d'Orfeuil, B.Rouille; Rowan-Robinson, M.; Rubino-Martin, J.A.; Ruiz-Granados, B.; Rumsey, C.; Rusholme, B.; Said, N.; Salvatelli, V.; Salvati, L.; Sandri, M.; Sanghera, H.S.; Santos, D.; Saunders, R.D.E.; Sauve, A.; Savelainen, M.; Savini, G.; Schaefer, B.M.; Schammel, M.P.; Scott, D.; Seiffert, M.D.; Serra, P.; Shellard, E.P.S.; Shimwell, T.W.; Shiraishi, M.; Smith, K.; Souradeep, T.; Spencer, L.D.; Spinelli, M.; Stanford, S.A.; Stern, D.; Stolyarov, V.; Stompor, R.; Strong, A.W.; Sudiwala, R.; Sunyaev, R.; Sutter, P.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Tavagnacco, D.; Terenzi, L.; Texier, D.; Toffolatti, L.; Tomasi, M.; Tornikoski, M.; Tristram, M.; Troja, A.; Trombetti, T.; Tucci, M.; Tuovinen, J.; Turler, M.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vassallo, T.; Vidal, M.; Viel, M.; Vielva, P.; Villa, F.; Wade, L.A.; Walter, B.; Wandelt, B.D.; Watson, R.; Wehus, I.K.; Welikala, N.; Weller, J.; White, M.; White, S.D.M.; Wilkinson, A.; Yvon, D.; Zacchei, A.; Zibin, J.P.; Zonca, A.

    2016-01-01

    The European Space Agency's Planck satellite, dedicated to studying the early Universe and its subsequent evolution, was launched 14~May 2009 and scanned the microwave and submillimetre sky continuously between 12~August 2009 and 23~October 2013. In February~2015, ESA and the Planck Collaboration released the second set of cosmology products based on data from the entire Planck mission, including both temperature and polarization, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the main characteristics of the data and the data products in the release, as well as the associated cosmological and astrophysical science results and papers. The science products include maps of the cosmic microwave background (CMB), the thermal Sunyaev-Zeldovich effect, and diffuse foregrounds in temperature and polarization, catalogues of compact Galactic and extragalactic sources (including separate catalogues of Sunyaev-Zeldovich clusters and Galactic col...

  12. Planck early results. XXIII. The first all-sky survey of Galactic cold clumps

    DEFF Research Database (Denmark)

    Poutanen, T.; Natoli, P.; Polenta, G.

    2011-01-01

    We present the statistical properties of the Cold Clump Catalogue of Planck Objects (C3PO), the first all-sky catalogue of cold objects, in terms of their spatial distribution, dust temperature, distance, mass, and morphology. We have combined Planck and IRAS data to extract 10342 cold sources...... dark clouds where the latter have been catalogued. These cold clumps are not isolated but clustered in groups. Dust temperature and emissivity spectral index values are derived from their spectral energy distributions using both Planck and IRAS data. The temperatures range from 7K to 19K...

  13. Gyrokinetic simulations of neoclassical transport using a minimal collision operator

    International Nuclear Information System (INIS)

    Dif-Pradalier, G.; Grandgirard, V.; Sarazin, Y.; Garbet, X.; Ghendrih, Ph.; Angelino, P.

    2008-01-01

    Conventional neoclassical predictions are successfully recovered within a gyrokinetic framework using a minimal Fokker-Planck collision operator. This operator is shown to accurately describe some essential features of neoclassical theory, namely the neoclassical transport, the poloidal rotation and the linear damping of axisymmetric flows while interestingly preserving a high numerical efficiency. Its form makes it especially adapted to Eulerian or Semi-Lagrangian schemes.

  14. Projection operator techniques in nonequilibrium statistical mechanics

    International Nuclear Information System (INIS)

    Grabert, H.

    1982-01-01

    This book is an introduction to the application of the projection operator technique to the statistical mechanics of irreversible processes. After a general introduction to the projection operator technique and statistical thermodynamics the Fokker-Planck and the master equation approach are described together with the response theory. Then, as applications the damped harmonic oscillator, simple fluids, and the spin relaxation are considered. (HSI)

  15. Charmonia enhancement in quark-gluon plasma with improved description of c-quarks phase distribution

    International Nuclear Information System (INIS)

    Gossiaux, Pol Bernard; Guiho, Vincent; Aichelin, Joerg

    2005-01-01

    We present a dynamical model of heavy quark evolution in the quark-gluon plasma (QGP) based on the Fokker-Planck equation. We then apply this model to the case of central ultra-relativistic nucleus-nucleus collisions performed at RHIC and estimate the component of J/ψ production (integrated and differential) stemming from c-c-bar pairs that are initially uncorrelated

  16. Path integrals for inertialess classical particles under-going rapid stochastic trembling. I

    International Nuclear Information System (INIS)

    Bezak, V.

    1978-01-01

    Feynman path integrals are studied in reference to the Fokker-Planck (Smoluchowski) equation. Examples are presented including the motion of an inertialess classical charged particle between electrodes in plate and cylindrical capacitors with charges fluctuating rapidly as Gaussian white-noise stochastic processes. Another example concerns magnetodiffusion of a charged particle in an non-polarized electromagnetic beam characterized by a white-noise spectrum. (author)

  17. Expectation-based intelligent control

    International Nuclear Information System (INIS)

    Zak, Michail

    2006-01-01

    New dynamics paradigms-negative diffusion and terminal attractors-are introduced to control noise and chaos. The applied control forces are composed of expectations governed by the associated Fokker-Planck and Liouville equations. The approach is expanded to a general concept of intelligent control via expectations. Relevance to control in livings is emphasized and illustrated by neural nets with mirror neurons

  18. Non-thermal electron populations in microwave heated plasmas investigated with X-ray detectors

    Energy Technology Data Exchange (ETDEWEB)

    Belapure, Jaydeep Sanjay

    2013-04-15

    An investigation of the generation and dynamics of superthermal electrons in fusion plasma is carried out. A SDD+CsI(Tl) based X-ray diagnostic is constructed, characterized and installed at ASDEX Upgrade. In various plasma heating power and densities, the fraction and the energy distribution of the superthermal electrons is obtained by a bi-Maxwellian model and compared with Fokker-Planck simulations.

  19. Relaxation of ion energy spectrum just after turbulent heating pulse in TRIAM-1 tokamak

    International Nuclear Information System (INIS)

    Nakamura, Kazuo; Hiraki, Naoji; Nakamura, Yukio; Itoh, Satoshi

    1982-01-01

    The temporal evolution and spatial profile of the ion energy spectrum just after the application of a toroidal current pulse for turbulent heating are investigated experimentally in the TRIAM-1 tokamak and also numerically using the Fokker-Planck equation. The two-component ion energy spectrum formed by turbulent heating relaxes to a single one within tausub(i) (the ion collision time). (author)

  20. Relaxation of ion energy spectrum just after turbulent heating pulse in TRIAM-1 tokamak

    Energy Technology Data Exchange (ETDEWEB)

    Nakamura, Kazuo; Hiraki, Naoji; Nakamura, Yukio; Itoh, Satoshi [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics

    1982-07-01

    The temporal evolution and spatial profile of the ion energy spectrum just after the application of a toroidal current pulse for turbulent heating are investigated experimentally in the TRIAM-1 tokamak and also numerically using the Fokker-Planck equation. The two-component ion energy spectrum formed by turbulent heating relaxes to a single one within tausub(i) (the ion collision time).