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
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.
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)
Computing generalized Langevin equations and generalized Fokker-Planck equations.
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.
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
Cusping, transport and variance of solutions to generalized Fokker-Planck equations
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.
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
Nonlinear Fokker-Planck Equations Fundamentals and Applications
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...
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
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
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.
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.
Maximum Path Information and Fokker Planck Equation
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.
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
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
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.
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)
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
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.
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)
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
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.)
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)
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)
Simulating transient dynamics of the time-dependent time fractional Fokker-Planck systems
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.
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)
The Fokker-Planck equation for coupled Brown-Néel-rotation
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.
The Fokker-Planck equation for coupled Brown-Néel-rotation.
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.
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.
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
Feedback-induced bistability of an optically levitated nanoparticle: A Fokker-Planck treatment
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.
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
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
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
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
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)
Applicability of the Fokker-Planck equation to the description of diffusion effects on nucleation
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.
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
A New Fokker-Planck Approach for the Relaxation-driven Evolution of Galactic Nuclei
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.
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
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.)
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.
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
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
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.
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)
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)
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.
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)
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
On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks
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
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.
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.
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
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
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.)
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
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
Automatic mesh refinement and parallel load balancing for Fokker-Planck-DSMC algorithm
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.
Nonparametric estimates of drift and diffusion profiles via Fokker-Planck algebra.
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.
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.
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.
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)
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.
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.
On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks
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.
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.
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
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.
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
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...
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
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
The Fokker-Planck equation for ray dispersion in gyrotropic stratified media
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
Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field
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.
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
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
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.
An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations
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.
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.
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
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
An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations
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.
Fermi-Dirac-Fokker-Planck equation : well-posedness & long-time asymptotics
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...
Fermi-Dirac-Fokker-Planck equation: well-posedness and long-time asymptotics
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...
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
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)
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)
Remarks on the chemical Fokker-Planck and Langevin equations: Nonphysical currents at equilibrium.
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.
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.
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)
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
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
Diffusion coefficients of Fokker-Planck equation for rotating dust grains in a fusion plasma
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.
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
One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift
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.
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.
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
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
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.
Fokker-Planck description for the queue dynamics of large tick stocks
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.
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
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.
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.
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
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.
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].
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.
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
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)
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.)
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
Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum
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.
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.
A Fokker-Planck based kinetic model for diatomic rarefied gas flows
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.
Efficient statistically accurate algorithms for the Fokker-Planck equation in large dimensions
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
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)
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
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.
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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
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
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.)
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.
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
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)
The theory of hybrid stochastic algorithms
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Duane, S.; Kogut, J.B.
1986-01-01
The theory of hybrid stochastic algorithms is developed. A generalized Fokker-Planck equation is derived and is used to prove that the correct equilibrium distribution is generated by the algorithm. Systematic errors following from the discrete time-step used in the numerical implementation of the scheme are computed. Hybrid algorithms which simulate lattice gauge theory with dynamical fermions are presented. They are optimized in computer simulations and their systematic errors and efficiencies are studied. (orig.)
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.
A transformed path integral approach for solution of the Fokker-Planck equation
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.
When is quasi-linear theory exact. [particle acceleration
Jones, F. C.; Birmingham, T. J.
1975-01-01
We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.
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
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.
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
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
The Dynamics of M15: Observations of the Velocity Dispersion Profile and Fokker-Planck Models
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
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
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
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
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
A Generalized Boltzmann Fokker-Planck Method for Coupled Charged Particle Transport
Energy Technology Data Exchange (ETDEWEB)
Prinja, Anil K
2012-01-09
The goal of this project was to develop and investigate the performance of reduced-physics formulations of high energy charged particle (electrons, protons and heavier ions) transport that are computationally more efficient than not only analog Monte Carlo methods but also the established condensed history Monte Carlo technique. Charged particles interact with matter by Coulomb collisions with target nuclei and electrons, by bremsstrahlung radiation loss and by nuclear reactions such as spallation and fission. Of these, inelastic electronic collisions and elastic nuclear collisions are the dominant cause of energy-loss straggling and angular deflection or range straggling of a primary particle. These collisions are characterized by extremely short mean free paths (sub-microns) and highly peaked, near-singular differential cross sections about forward directions and zero energy loss, with the situation for protons and heavier ions more extreme than for electrons. For this reason, analog or truephysics single-event Monte Carlo simulation, while possible in principle, is computationally prohibitive for routine calculation of charged particle interaction phenomena.
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.
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.
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
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.
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
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
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.
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.
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.
Stochastic processes and applications diffusion processes, the Fokker-Planck and Langevin equations
Pavliotis, Grigorios A
2014-01-01
This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to eq...
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.
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)
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.
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
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
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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)
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
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.)
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.
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.
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
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.
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)
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)
International Nuclear Information System (INIS)
Harvey, R.W.
2009-01-01
This DOE grant supported fusion energy research, a potential long-term solution to the world's energy needs. Magnetic fusion, exemplified by confinement of very hot ionized gases, i.e., plasmas, in donut-shaped tokamak vessels is a leading approach for this energy source. Thus far, a mixture of hydrogen isotopes has produced 10's of megawatts of fusion power for seconds in a tokamak reactor at Princeton Plasma Physics Laboratory in New Jersey. The research grant under consideration, ER54684, uses computer models to aid in understanding and projecting efficacy of heating and current drive sources in the National Spherical Torus Experiment, a tokamak variant, at PPPL. The NSTX experiment explores the physics of very tight aspect ratio, almost spherical tokamaks, aiming at producing steady-state fusion plasmas. The current drive is an integral part of the steady-state concept, maintaining the magnetic geometry in the steady-state tokamak. CompX further developed and applied models for radiofrequency (rf) heating and current drive for applications to NSTX. These models build on a 30 year development of rf ray tracing (the all-frequencies GENRAY code) and higher dimensional Fokker-Planck rf-collisional modeling (the 3D collisional-quasilinear CQL3D code) at CompX. Two mainline current-drive rf modes are proposed for injection into NSTX: (1) electron Bernstein wave (EBW), and (2) high harmonic fast wave (HHFW) modes. Both these current drive systems provide a means for the rf to access the especially high density plasma--termed high beta plasma--compared to the strength of the required magnetic fields. The CompX studies entailed detailed modeling of the EBW to calculate the efficiency of the current drive system, and to determine its range of flexibility for driving current at spatial locations in the plasma cross-section. The ray tracing showed penetration into NSTX bulk plasma, relatively efficient current drive, but a limited ability to produce current over the whole
A kinetic theory of diffusion in general relativity with cosmological scalar field
International Nuclear Information System (INIS)
Calogero, Simone
2011-01-01
A new model to describe the dynamics of particles undergoing diffusion in general relativity is proposed. The evolution of the particle system is described by a Fokker-Planck equation without friction on the tangent bundle of spacetime. It is shown that the energy-momentum tensor for this matter model is not divergence-free, which makes it inconsistent to couple the Fokker-Planck equation to the Einstein equations. This problem can be solved by postulating the existence of additional matter fields in spacetime or by modifying the Einstein equations. The case of a cosmological scalar field term added to the left hand side of the Einstein equations is studied in some details. For the simplest cosmological model, namely the flat Robertson-Walker spacetime, it is shown that, depending on the initial value of the cosmological scalar field, which can be identified with the present observed value of the cosmological constant, either unlimited expansion or the formation of a singularity in finite time will occur in the future. Future collapse into a singularity also takes place for a suitable small but positive present value of the cosmological constant, in contrast to the standard diffusion-free scenario
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
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
International Nuclear Information System (INIS)
Noerenberg, W.
1976-01-01
Relaxation phenomena in deeply inelastic collisions are qualitatively discussed and compared with precompound reactions. Different approaches for describing these processes are reviewed, in particular the microscopic transport theories, which can be understood from a generalized master equation for macroscopic variables. The Markoff approximation and the classical limit for the relative motion lead to two coupled equations, the classical equation of relative motion with friction and a Pauli master equation for the internal degrees of freedom. The master equation approximated by the corresponding Fokker-Planck equation for mass transfer and energy dissipation is discussed in detail. Simple analytic expressions are derived for the transport coefficients as functions of excitation energy, total mass, mass fragmentation and relative angular momentum. Calculated transport coefficients are compared with experimental values. Problems and future developments in microscopic transport theories are outlined. (orig.) [de
Problems of a Statistical Ensemble Theory for Systems Far from Equilibrium
Ebeling, Werner
The development of a general statistical physics of nonequilibrium systems was one of the main unfinished tasks of statistical physics of the 20th century. The aim of this work is the study of a special class of nonequilibrium systems where the formulation of an ensemble theory of some generality is possible. These are the so-called canonical-dissipative systems, where the driving terms are determined by invariants of motion. We construct canonical-dissipative systems which are ergodic on certain surfaces on the phase plane. These systems may be described by a non-equilibrium microcanocical ensemble, corresponding to an equal distribution on the target surface. Next we construct and solve Fokker-Planck equations; this leads to a kind of canonical-dissipative ensemble. In the last part we discuss the thoretical problem how to define bifurcations in the framework of nonequilibrium statistics and several possible applications.
Transport theory of dissipative heavy-ion collisions
International Nuclear Information System (INIS)
Norenberg, W.
1979-01-01
The lectures present the formulation of a transport theory, the derivation of a practicable transport equation (Fokker-Planck equation) and the evaluation of transport coefficients for dissipative (or deeply inelastic) heavy-ion collisions. The applicability of the theoretical concept is tested with remarkable success in the analyses of various experimental information (mass transfer, angular-momentum dissipation and energy loss). Some critical remarks on the present situation of transport theories are added. Future developments are outlined. (author)
Transport theory of dissipative heavy-ion collisions
International Nuclear Information System (INIS)
Noerenberg, W.
1979-03-01
The lectures present the formulation of a transport theory, the derivation of a practicable transport equation (Fokker-Planck equation) and the evaluation of transport coefficients for dissipative (or deeply inelastic) heavyion collisions. The applicability of the theoretical concept is tested with remarkable success in the analyses of various experimental informations (mass transfer, angular-momentum dissipation and energy loss). Some critical remarks on the present situation of transport theories are added. Future developments are outlined. (orig.) [de
Stochastic quantization and topological theories
International Nuclear Information System (INIS)
Fainberg, V.Y.; Subbotin, A.V.; Kuznetsov, A.N.
1992-01-01
In the last two years topological quantum field theories (TQFT) have attached much attention. This paper reports that from the very beginning it was realized that due to a peculiar BRST-like symmetry these models admitted so-called Nicolai mapping: the Nicolai variables, in terms of which actions of the theories become gaussian, are nothing but (anti-) selfduality conditions or their generalizations. This fact became a starting point in the quest of possible stochastic interpretation to topological field theories. The reasons behind were quite simple and included, in particular, the well-known relations between stochastic processes and supersymmetry. The main goal would have been achieved, if it were possible to construct stochastic processes governed by Langevin or Fokker-Planck equations in a real Euclidean time leading to TQFT's path integrals (equivalently: to reformulate TQFTs as non-equilibrium phase dynamics of stochastic processes). Further on, if it would appear that these processes correspond to the stochastic quantization of theories of some definite kind, one could expect (d + 1)-dimensional TQFTs to share some common properties with d-dimensional ones
Pimpinelli, Alberto; Einstein, T. L.; González, Diego Luis; Sathiyanarayanan, Rajesh; Hamouda, Ajmi Bh.
2011-03-01
Earlier we showed [PRL 99, 226102 (2007)] that the CZD in growth could be well described by P (s) = asβ exp (-bs2) , where s is the CZ area divided by its average value. Painstaking simulations by Amar's [PRE 79, 011602 (2009)] and Evans's [PRL 104, 149601 (2010)] groups showed inadequacies in our mean field Fokker-Planck argument relating β to the critical nucleus size. We refine our derivation to retrieve their β ~ i + 2 [PRL 104, 149602 (2010)]. We discuss applications of this formula and methodology to experiments on Ge/Si(001) and on various organics on Si O2 , as well as to kinetic Monte Carlo studies homoepitaxial growth on Cu(100) with codeposited impurities of different sorts. In contrast to theory, there can be significant changes to β with coverage. Some experiments also show temperature dependence. Supported by NSF-MRSEC at UMD, Grant DMR 05-20471.
Generally covariant gauge theories
International Nuclear Information System (INIS)
Capovilla, R.
1992-01-01
A new class of generally covariant gauge theories in four space-time dimensions is investigated. The field variables are taken to be a Lie algebra valued connection 1-form and a scalar density. Modulo an important degeneracy, complex [euclidean] vacuum general relativity corresponds to a special case in this class. A canonical analysis of the generally covariant gauge theories with the same gauge group as general relativity shows that they describe two degrees of freedom per space point, qualifying therefore as a new set of neighbors of general relativity. The modification of the algebra of the constraints with respect to the general relativity case is computed; this is used in addressing the question of how general relativity stands out from its neighbors. (orig.)
Generalized etale cohomology theories
Jardine, John F
1997-01-01
A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the way an ordinary spectrum represents a cohomology theory for spaces. Examples include etale cohomology and etale K-theory. This book gives new and complete proofs of both Thomason's descent theorem for Bott periodic K-theory and the Nisnevich descent theorem. In doing so, it exposes most of the major ideas of the homotopy theory of presheaves of spectra, and generalized etale homology theories in particular. The treatment includes, for the purpose of adequately dealing with cup product structures, a development of stable homotopy theory for n-fold spectra, which is then promoted to the level of presheaves of n-fold spectra. This book should be of interest to all researchers working in fields related to algebraic K-theory. The techniques presented here are essentially combinatorial, and hence algebraic. An extensive background in traditional stable hom...
Generalized chiral perturbation theory
International Nuclear Information System (INIS)
Knecht, M.; Stern, J.
1994-01-01
The Generalized Chiral Perturbation Theory enlarges the framework of the standard χPT (Chiral Perturbation Theory), relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low energy expansion. In this way, experimental tests of the foundations of the standard χPT become possible. Emphasis is put on physical aspects rather than on formal developments of GχPT. (author). 31 refs
International Nuclear Information System (INIS)
Schulze-Halberg, Axel
2010-01-01
We study Green's functions of the generalized Sturm-Liouville problems that are related to each other by Darboux -equivalently, supersymmetrical - transformations. We establish an explicit relation between the corresponding Green's functions and derive a simple formula for their trace. The class of equations considered here includes the conventional Schroedinger equation and generalizations, such as for position-dependent mass and with linearly energy-dependent potential, as well as the stationary Fokker-Planck equation.
International Nuclear Information System (INIS)
Sladkowski, J.
1991-01-01
Various attempts to formulate the fundamental physical interactions in the framework of unified geometric theories have recently gained considerable success (Kaluza, 1921; Klein, 1926; Trautmann, 1970; Cho, 1975). Symmetries of the spacetime and so-called internal spaces seem to play a key role in investigating both the fundamental interactions and the abundance of elementary particles. The author presents a category-theoretic description of a generalization of the G-theory concept and its application to geometric compactification and dimensional reduction. The main reasons for using categories and functors as tools are the clearness and the level of generalization one can obtain
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
Wu, Wei; Wang, Jin
2013-09-28
We established a potential and flux field landscape theory to quantify the global stability and dynamics of general spatially dependent non-equilibrium deterministic and stochastic systems. We extended our potential and flux landscape theory for spatially independent non-equilibrium stochastic systems described by Fokker-Planck equations to spatially dependent stochastic systems governed by general functional Fokker-Planck equations as well as functional Kramers-Moyal equations derived from master equations. Our general theory is applied to reaction-diffusion systems. For equilibrium spatially dependent systems with detailed balance, the potential field landscape alone, defined in terms of the steady state probability distribution functional, determines the global stability and dynamics of the system. The global stability of the system is closely related to the topography of the potential field landscape in terms of the basins of attraction and barrier heights in the field configuration state space. The effective driving force of the system is generated by the functional gradient of the potential field alone. For non-equilibrium spatially dependent systems, the curl probability flux field is indispensable in breaking detailed balance and creating non-equilibrium condition for the system. A complete characterization of the non-equilibrium dynamics of the spatially dependent system requires both the potential field and the curl probability flux field. While the non-equilibrium potential field landscape attracts the system down along the functional gradient similar to an electron moving in an electric field, the non-equilibrium flux field drives the system in a curly way similar to an electron moving in a magnetic field. In the small fluctuation limit, the intrinsic potential field as the small fluctuation limit of the potential field for spatially dependent non-equilibrium systems, which is closely related to the steady state probability distribution functional, is
THE LARGE ASPECT RATIO LIMIT OF NEOCLASSICAL TRANSPORT THEORY
Energy Technology Data Exchange (ETDEWEB)
WONG,SK; CHAN,VS
2002-11-01
OAK B202 THE LARGE ASPECT RATIO LIMIT OF NEOCLASSICAL TRANSPORT THEORY. This article presents a comprehensive description of neoclassical transport theory in the banana regime for large aspect ratio flux surfaces of arbitrary shapes. The method of matched asymptotic expansions is used to obtain analytical solutions for plasma distribution functions and to compute transport coefficients. The method provides justification for retaining only the part of the Fokker-Planck operator that involves the second derivative with respect to the cosine of the pitch angle for the trapped and barely circulating particles. It leads to a simple equation for the freely circulating particles with boundary conditions that embody a discontinuity separating particles moving in opposite directions. Corrections to the transport coefficients are obtained by generalizing an existing boundary layer analysis. The system of moment and field equations is consistently taken in the cylinder limit, which facilitates discussion of the treatment of dynamical constraints. it is shown that the nonlocal nature of Ohm's law in neoclassical theory renders the mathematical problem of plasma transport with changing flux surfaces nonstandard.
THE LARGE ASPECT RATIO LIMIT OF NEOCLASSICAL TRANSPORT THEORY
International Nuclear Information System (INIS)
WONG, S.K.; CHAN, V.S.
2002-01-01
OAK B202 THE LARGE ASPECT RATIO LIMIT OF NEOCLASSICAL TRANSPORT THEORY. This article presents a comprehensive description of neoclassical transport theory in the banana regime for large aspect ratio flux surfaces of arbitrary shapes. The method of matched asymptotic expansions is used to obtain analytical solutions for plasma distribution functions and to compute transport coefficients. The method provides justification for retaining only the part of the Fokker-Planck operator that involves the second derivative with respect to the cosine of the pitch angle for the trapped and barely circulating particles. It leads to a simple equation for the freely circulating particles with boundary conditions that embody a discontinuity separating particles moving in opposite directions. Corrections to the transport coefficients are obtained by generalizing an existing boundary layer analysis. The system of moment and field equations is consistently taken in the cylinder limit, which facilitates discussion of the treatment of dynamical constraints. it is shown that the nonlocal nature of Ohm's law in neoclassical theory renders the mathematical problem of plasma transport with changing flux surfaces nonstandard
Mirror theory applied to toroidal systems
International Nuclear Information System (INIS)
Cohen, R.H.
1987-01-01
Central features of a mirror plasma are strong departures from Maxwellian distribution functions, ambipolar potentials and densities which vary along a field line, and losses, and the mirror field itself. To examine these features, mirror theorists have developed analytical and numerical techniques to solve the Fokker-Planck equation, evaluate the potentials consistent with the resulting distribution functions, and assess the microstability of these distributions. Various combinations of mirror-plasma fetures are present and important in toroidal plasmas as well, particularly in the edge region and in plasmas with strong r.f. heating. In this paper we survey problems in toroidal plasmas where mirror theory and computational techniques are applicable, and discuss in more detail three specific examples: calculation of the toroidal generalization of the Spitzer-Haerm distribution function (from which trapped-particle effects on current drive can be calculated), evaluation of the nonuniform potential and density set up by pulsed electron-cyclotron heating, and calculation of steady-state distribution functions in the presence of strong r.f. heating and collisions. 37 refs., 3 figs
Mirror theory applied to toroidal systems
International Nuclear Information System (INIS)
Cohen, R.H.
1987-01-01
Central features of a mirror plasma are strong departures from Maxwellian distribution functions, ambipolar potentials and densities which vary along a field line, end losses, and the mirror field itself. To examine these features, mirror theorists have developed analytical and numerical techniques to solve the Fokker-Planck equation, evaluate the potentials consistent with the resulting distribution functions, and assess the microstability of these distributions. Various combinations of mirror-plasma features are present and important in toroidal plasmas as well, particularly in the edge region and in plasmas with strong rf heating. In this paper we survey problems in toroidal plasmas where mirror theory and computational techniques are applicable, and discuss in more detail three specific examples: calculation of the toroidal generalization of the Spitzer-Haerm distribution function (from which trapped-particle effects on current drive can be calculated), evaluation of the nonuniform potential and density set up by pulsed electron-cyclotron heating, and calculation of steady-state distribution functions in the presence of strong rf heating and collisions. 37 refs
Theory of relativistic Brownian motion in the presence of electromagnetic field in (1+1) dimension
Mukhopadhyay, Annesh; Bandyopadhyay, M.; Bhamidipati, C.
2018-04-01
In this work, we consider the relativistic generalization of the theory of Brownian motion for the (1+1) dimensional case, which is again consistent with Einstein's special theory of relativity and reduces to standard Brownian motion in the Newtonian limit. All the generalizations are made considering Special theory of relativity into account. The particle under consideration has a velocity close to the speed of light and is a free Brownian particle suspended in a heat bath. With this generalization the velocity probability density functions are also obtained using Ito, Stratonovich and Hanggi-Klimontovich approach of pre-point, mid-point and post-point discretization rule. Subsequently, in our work, we have obtained the relativistic Langevin equations in the presence of an electromagnetic field. Finally, taking a special case of a constant vector potential and a constant electric field into account the Langevin equations are solved for the momentum and subsequently the velocity of the particle. Using a similar approach to the Fokker-planck equations of motion, the velocity distributions are also obtained in the presence of a constant vector potential and are plotted, which shows essential deviations from the one obtained without a potential. Our constant potential model can be realized in an optical potential.
Stochastic cooling of bunched beams from fluctuation and kinetic theory
International Nuclear Information System (INIS)
Chattopadhyay, S.
1982-09-01
A theoretical formalism for stochastic phase-space cooling of bunched beams in storage rings is developed on the dual basis of classical fluctuation theory and kinetic theory of many-body systems in phase-space. The physics is that of a collection of three-dimensional oscillators coupled via retarded nonconservative interactions determined by an electronic feedback loop. At the heart of the formulation is the existence of several disparate time-scales characterizing the cooling process. Both theoretical approaches describe the cooling process in the form of a Fokker-Planck transport equation in phase-space valid up to second order in the strength and first order in the auto-correlation of the cooling signal. With neglect of the collective correlations induced by the feedback loop, identical expressions are obtained in both cases for the coherent damping and Schottky noise diffusion coefficients. These are expressed in terms of Fourier coefficients in a harmonic decomposition in angle of the generalized nonconservative cooling force written in canonical action-angle variables of the particles in six-dimensional phase-space. Comparison of analytic results to a numerical simulation study with 90 pseudo-particles in a model cooling system is presented
Large-aspect-ratio limit of neoclassical transport theory
International Nuclear Information System (INIS)
Wong, S K.; Chan, V.S.
2003-01-01
This paper presents a comprehensive description of neoclassical transport theory in the banana regime for large-aspect-ratio flux surfaces of arbitrary shapes. The method of matched-asymptotic expansions is used to obtain analytical solutions for plasma distribution functions and to compute transport coefficients. The method provides justification for retaining only the part of the Fokker-Planck operator that involves the second derivative with respect to the cosine of the pitch angle for the trapped and barely circulating particles. It leads to a simple equation for the freely circulating particles with boundary conditions that embody a discontinuity separating particles moving in opposite directions. Corrections to the transport coefficients are obtained by generalizing an existing boundary layer analysis. The system of moment and field equations is consistently taken in the cylinder limit, which facilitates the discussion of the treatment of dynamical constraints. It is shown that the nonlocal nature of Ohm's law in neoclassical theory renders the mathematical problem of plasma transport with changing flux surfaces nonstandard
Large-aspect-ratio limit of neoclassical transport theory.
Wong, S K; Chan, V S
2003-06-01
This paper presents a comprehensive description of neoclassical transport theory in the banana regime for large-aspect-ratio flux surfaces of arbitrary shapes. The method of matched-asymptotic expansions is used to obtain analytical solutions for plasma distribution functions and to compute transport coefficients. The method provides justification for retaining only the part of the Fokker-Planck operator that involves the second derivative with respect to the cosine of the pitch angle for the trapped and barely circulating particles. It leads to a simple equation for the freely circulating particles with boundary conditions that embody a discontinuity separating particles moving in opposite directions. Corrections to the transport coefficients are obtained by generalizing an existing boundary layer analysis. The system of moment and field equations is consistently taken in the cylinder limit, which facilitates the discussion of the treatment of dynamical constraints. It is shown that the nonlocal nature of Ohm's law in neoclassical theory renders the mathematical problem of plasma transport with changing flux surfaces nonstandard.
Gravity, general relativity theory and alternative theories
International Nuclear Information System (INIS)
Zel'dovich, Ya.B.; Grishchuk, L.P.; Moskovskij Gosudarstvennyj Univ.
1986-01-01
The main steps in plotting the current gravitation theory and some prospects of its subsequent development are reviewed. The attention is concentrated on a comparison of the relativistic gravitational field with other physical fields. Two equivalent formulations of the general relativity (GR) - geometrical and field-theoretical - are considered in detail. It is shown that some theories of gravity constructed as the field theories at a flat background space-time are in fact just different formulations of GR and not alternative theories
The velocity correlation function in cosmic-ray diffusion theory
International Nuclear Information System (INIS)
Forman, M.A.
1977-01-01
The concept of velocity correlation functions is introduced and applied to the calculation of cosmic ray spatial diffusion coefficients. It is assumed that the pitch angle scattering coefficient is already known from some other theory, and is reasonably well-behaved. Previous results for the coefficient for diffusion parallel to the mean field are recovered when the velocity-changing mechanism is artificially restricted to pitch angle scattering. The velocity correlation method is then applied to the more general case where there are fluctuations in the local mean field. It is found that the parallel diffusion coefficient is reduced in proportion to the amplitude of the field fluctuations, and that the ratio of the perpendicular to parallel diffusion coefficients cannot be greater than 2 >/B 0 2 . It is shown in the appendix that the Liouville form of the scattering equation implies that the Fokker-Planck coefficients (Δμ 2 )/Δt=2Dsub(μμ) and (Δμ)/Δt=deltaDsub(μμ)/deltaμ, and that all higher-order coefficients are identically zero. (Auth.)
Current-drive theory II: the lower-hybrid wave
International Nuclear Information System (INIS)
Fisch, N.J.
1986-01-01
The theory of current-drive seeks to predict the efficiency with which an external power source can produce current in a plasma torus. The theory, which is now well supported by experimental data, becomes especially simple in the important limit of lower-hybrid or electron-cyclotron waves interacting with superthermal electrons. The solution of an equation adjoint to the linearized Fokker-Planck equation gives both the steady-state and ramp-up current-drive efficiencies. Other phenomena, such as rf-induced runaway rates, rf-induced radiation, etc., may be calculated by this method, and analytical solutions have been obtained in several limiting cases. 12 refs
Dissipative motion perturbation theory and exact solutions
International Nuclear Information System (INIS)
Lodder, J.J.
1976-06-01
Dissipative motion of classical and quantum systems is described. In particular, attention is paid to systems coupled to the radiation field. A dissipative equation of motion for a particle in an arbitrary potential coupled to the radiation field is derived by means of perturbation theory. The usual divrgencies associated with the radiation field are eliminated by the application of a theory of generalized functions. This theory is developed as a subject in its own right and is presented independently. The introduction of classical zero-point energy makes the classical equa tion of motion for the phase density formally the same as its quantum counterpart. In particular, it is shown that the classical zero-point energy prevents the collapse of a classical H-atom and gives rise to a classical ground state. For systems with a quadratic Hamiltoian, the equation of motion can be solved exactly, even in the continuum limit for the radiation field, by means of the new generalized functions. Classically, the Fokker-Planck equation is found without any approximations, and quantum mechanically, the only approximation is the neglect of the change in the ground state caused by the interaction. The derivation is valid even for strong damping and arbitrarily short times. There is no transient time. For harmonic oscillators complete equivalence is shown to exist between quantum mechanics and classical mechanics with zero-point energy. A discussion of the derivation of the Pauli equation is given and perturbation theory is compared with the exact derivation. The exactly solvable models are used to calculate the Langevin force of the radiation field. The result is that the classical Langevin force is exactly delta-correlated, while the quantum Langevin force is not delta-correlated at all. The fluctuation-dissipation theorem is shown to be an exact consequence of the solution to the equations of motion
Generalized field theory of gravitation
International Nuclear Information System (INIS)
Yilmaz, H.
1976-01-01
It is shown that if, on empirical grounds, one rules out the existence of cosmic fields of Dicke-Brans (scalar) and Will Nordvedt (vector, tensor) type, then the most general experimentally viable and theoretically reasonable theory of gravitation seems to be a LAMBDA-dependent generalization of Einstein and Yilmez theories, which reduces to the former for LAMBDA=0 and to the latter for LAMBDA=1
Relativistic theory of particles in a scattering flow III: photon transport.
Achterberg, A.; Norman, C. A.
2018-06-01
We use the theory developed in Achterberg & Norman (2018a) and Achterberg & Norman (2018b) to calculate the stress due to photons that are scattered elastically by a relativistic flow. We show that the energy-momentum tensor of the radiation takes the form proposed by Eckart (1940). In particular we show that no terms associated with a bulk viscosity appear if one makes the diffusion approximation for radiation transport and treats the radiation as a separate fluid. We find only shear (dynamic) viscosity terms and heat flow terms in our expression for the energy-momentum tensor. This conclusion holds quite generally for different forms of scattering: Krook-type integral scattering, diffusive (Fokker-Planck) scattering and Thomson scattering. We also derive the transport equation in the diffusion approximation that shows the effects of the flow on the photon gas in the form of a combination of adiabatic heating and an irreversible heating term. We find no diffusive changes to the comoving number density and energy density of the scattered photons, in contrast with some published results in Radiation Hydrodynamics. It is demonstrated that these diffusive corrections to the number- and energy density of the photons are in fact higher-order terms that can (and should) be neglected in the diffusion approximation. Our approach eliminates these terms at the root of the expansion that yields the anisotropic terms in the phase-space density of particles and photons, the terms responsible for the photon viscosity.
International Nuclear Information System (INIS)
Wu, Wei; Wang, Jin
2014-01-01
We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic and thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series
International Nuclear Information System (INIS)
Edenstrasser, J.W.
1995-01-01
A multiple time-scale derivative expansion scheme is applied to the dimensionless Fokker--Planck equation and to Maxwell's equations, where the parameter range of a typical fusion plasma was assumed. Within kinetic theory, the four time scales considered are those of Larmor gyration, particle transit, collisions, and classical transport. The corresponding magnetohydrodynamic (MHD) time scales are those of ion Larmor gyration, Alfven, MHD collision, and resistive diffusion. The solution of the zeroth-order equations results in the force-free equilibria and ideal Ohm's law. The solution of the first-order equations leads under the assumption of a weak collisional plasma to the ideal MHD equations. On the MHD-collision time scale, not only the full set of the MHD transport equations is obtained, but also turbulent terms, where the related transport quantities are one order in the expansion parameter larger than those of classical transport. Finally, at the resistive diffusion time scale the known transport equations are arrived at including, however, also turbulent contributions. copyright 1995 American Institute of Physics
Essays in general equilibrium theory
Konovalov, A.
2001-01-01
The thesis focuses on various issues of general equilibrium theory and can approximately be divided into three parts. The first part of the thesis studies generalized equilibria in the Arrow-Debreu model in the situation where the strong survival assumption is not satisfied. Chapter four deals with
ELECTRON CYCLOTRON CURRENT DRIVE IN DIII-D: EXPERIMENT AND THEORY
International Nuclear Information System (INIS)
PRATER, R; PETTY, CC; LUCE, TC; HARVEY, RW; CHOI, M; LAHAYE, RJ; LIN-LIU, Y-R; LOHR, J; MURAKAMI, M; WADE, MR; WONG, K-L
2003-01-01
A271 ELECTRON CYCLOTRON CURRENT DRIVE IN DIII-D: EXPERIMENT AND THEORY. Experiments on the DIII-D tokamak in which the measured off-axis electron cyclotron current drive has been compared systematically to theory over a broad range of parameters have shown that the Fokker-Planck code CQL3D provides an excellent model of the relevant current drive physics. This physics understanding has been critical in optimizing the application of ECCD to high performance discharges, supporting such applications as suppression of neoclassical tearing modes and control and sustainment of the current profile
General covariance and quantum theory
International Nuclear Information System (INIS)
Mashhoon, B.
1986-01-01
The extension of the principle of relativity to general coordinate systems is based on the hypothesis that an accelerated observer is locally equivalent to a hypothetical inertial observer with the same velocity as the noninertial observer. This hypothesis of locality is expected to be valid for classical particle phenomena as well as for classical wave phenomena but only in the short-wavelength approximation. The generally covariant theory is therefore expected to be in conflict with the quantum theory which is based on wave-particle duality. This is explicitly demonstrated for the frequency of electromagnetic radiation measured by a uniformly rotating observer. The standard Doppler formula is shown to be valid only in the geometric optics approximation. A new definition for the frequency is proposed, and the resulting formula for the frequency measured by the rotating observer is shown to be consistent with expectations based on the classical theory of electrons. A tentative quantum theory is developed on the basis of the generalization of the Bohr frequency condition to include accelerated observers. The description of the causal sequence of events is assumed to be independent of the motion of the observer. Furthermore, the quantum hypothesis is supposed to be valid for all observers. The implications of this theory are critically examined. The new formula for frequency, which is still based on the hypothesis of locality, leads to the observation of negative energy quanta by the rotating observer and is therefore in conflict with the quantum theory
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
Generalized Lorenz-Mie Theories
Gouesbet, Gérard
2011-01-01
The Lorenz-Mie theory, describing the interaction between a homogeneous sphere and an electromagnetic plane wave, is likely to be one of the most famous theories in light scattering. But, with the advent of lasers and their increasing development in various fields, it has become too old-fashioned to meet most of the modern requisites. The book deals with generalized Lorenz-Mie theories when the illuminating beam is an electromagnetic arbitrary shaped beam, relying on the method of separation of variables. A particular emphasis is stressed on the case of the homogeneous sphere but other regular particles are considered too. An extensive discussion of the methods available to the evaluation of beam shape coefficients describing the illuminating beam is provided, and several methods are discussed. Applications concern many fields such as optical particle sizing and, more generally, optical particle characterization, morphology-dependent resonances, or mechanical effects of light for optical trapping, optical twe...
To the theory of the first-type phase transformations for many variables
International Nuclear Information System (INIS)
Fateev, M.P.
2002-01-01
The multidimensional theory on the first-type phase transitions near the one-dimensional saddle point is considered. The transformations of the variables, describing the new phase nucleation, making it possible to achieve their complex separation in the Fokker-Planck equation, and thus to reduce the problem to the one-dimensional one, are proposed. The distribution function and nucleation velocity are determined both for the stationary and nonstationary nucleation stages. The problem on volatile liquid boiling is considered as an example for the case when there are two parameters, characterizing the new phase nucleation [ru
Generalized structural theory of freezing
International Nuclear Information System (INIS)
Yussouff, M.
1980-10-01
The first-principles order parameter theory of freezing, proposed in an earlier work, has been successful in yielding quantitative agreement with known freezing parameters for monoatomic liquids forming solids with one atom per unit cell. A generalization of this theory is presented here to include the effects of a basis set of many atoms per unit cell. The basic equations get modified by the 'density structure factors' fsub(i) which arise from the density variations within the unit cell. Calculations are presented for the important case of monoatomic liquids freezing into hexagonal close packed solids. It is concluded that all freezing transitions can be described by using structural correlations in the liquid instead of the pair potential; and that the three body correlations are important in deciding the type of solid formed after freezing. (author)
Isar, Aurelian
1995-01-01
The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.
Gestalt Therapy and General System Theory.
Whitner, Phillip A.
While General Systems Theory (GST) concepts appear to be applicable in explaining some of the phenomena that occur in a Gestalt Therapy group, research is needed to support this assumption. General Systems Theory may not be a group theory per se. Instead, GST may be a theory about groups. A meta-theory exists where its value and usefulness is…
Theory of generalized Bessel functions
International Nuclear Information System (INIS)
Dattoli, G.; Giannessi, L.; Mezi, L.; Torre, A.
1990-01-01
In this paper it is discussed the theory of generalized Bessel functions which are of noticeable importance in the analysis of scattering processes for which the dipole approximation cannot be used. These functions have been introduced in their standard form and their modified version. The relevant generating functions and Graf-type addition theorems have been stated. The usefulness of the results to construct a fast algorithm for their quantitative computation is also devised. It is commented on the possibility of getting two-index generalized Bessel functions in e.g. the study of sum rules of the type Σ n=-∞ ∞ t n J n 3 (x), where J n is the cylindrical Bessel function of the first kind. The usefulness of the results for problems of practical interest is finally commented on. It is shown that a modified Anger function can be advantageously introduced to get an almost straightforward computation of the Bernstein sum rule in the theory of ion waves
Analysis of unexpected exits using the Fokker - Planck equation
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
Generalized inverses theory and computations
Wang, Guorong; Qiao, Sanzheng
2018-01-01
This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics. It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.
Generalized string theory mapping relations between gravity and gauge theory
International Nuclear Information System (INIS)
Bjerrum-Bohr, N.E.J.
2003-01-01
A previous study of the Kawai, Lewellen and Tye (KLT) relations between gravity and gauge theories, imposed by the relationship of closed and open strings, are here extended in the light of general relativity and Yang-Mills theory as effective field theories. We discuss the possibility of generalizing the traditional KLT mapping in this effective setting. A generalized mapping between the effective Lagrangians of gravity and Yang-Mills theory is presented, and the corresponding operator relations between gauge and gravity theories at the tree level are further explored. From this generalized mapping remarkable diagrammatic relations are found, linking diagrams in gravity and Yang-Mills theory, as well as diagrams in pure effective Yang-Mills theory. Also the possibility of a gravitational coupling to an antisymmetric field in the gravity scattering amplitude is considered, and shown to allow for mixed open-closed string solutions, i.e., closed heterotic strings
Effective potential kinetic theory for strongly coupled plasmas
Baalrud, Scott D.; Daligault, Jérôme
2016-11-01
The effective potential theory (EPT) is a recently proposed method for extending traditional plasma kinetic and transport theory into the strongly coupled regime. Validation from experiments and molecular dynamics simulations have shown it to be accurate up to the onset of liquid-like correlation parameters (corresponding to Γ ≃ 10-50 for the one-component plasma, depending on the process of interest). Here, this theory is briefly reviewed along with comparisons between the theory and molecular dynamics simulations for self-diffusivity and viscosity of the one-component plasma. A number of new results are also provided, including calculations of friction coefficients, energy exchange rates, stopping power, and mobility. The theory is also cast in the Landau and Fokker-Planck kinetic forms, which may prove useful for enabling efficient kinetic computations.
Moment equation approach to neoclassical transport theory
International Nuclear Information System (INIS)
Hirshman, S.P.
1978-01-01
The neoclassical cross-field fluxes for a toroidally confined, axisymmetric plasma are calculated in terms of the thermodynamic forces from the fluid continuity and momentum balance equations. This macroscopic formulation of neoclassical transport theory unifies the numerous complex expressions for the transport coefficients, previously obtained by solving the Fokker--Planck equation, and elucidates their physical basis. In the large aspect ratio limit, the continuous transition in the scaling of the diffusion coefficient throughout various collisionality regimes is shown to depend on the ratio of parallel viscosity coefficients of the plasma species. Comparison of the present results with the kinetic theory expressions for the neoclassical fluxes determines the parallel viscosity coefficients for a multispecies plasma in the long-mean-free-path regime
General Systems Theory and Instructional Design.
Salisbury, David F.
The use of general systems theory in the field of instructional systems design (ISD) is explored in this paper. Drawing on work by Young, the writings of 12 representative ISD writers and researchers were surveyed to determine the use of 60 general systems theory concepts by the individual authors. The average number of concepts used by these…
Generalized Field Theory and Kasner universe
International Nuclear Information System (INIS)
Klotz, A.H.
1986-01-01
It is shown that the only Kasner-like solution of the Generalized Field Theory field equations with a nonzero electromagnetic field corresponds to an empty field geometry of the space-time. In this case, the electromagnetic field tensors of the theory coincide as could be expected from general considerations. 6 refs. (author)
A theory of generalized Bloch oscillations
DEFF Research Database (Denmark)
Duggen, Lars; Lew Yan Voon, L. C.; Lassen, Benny
2016-01-01
Bloch oscillations of electrons are shown to occur for cases when the energy spectrum does not consist of the traditional evenly-spaced ladders and the potential gradient does not result from an external electric field. A theory of such generalized Bloch oscillations is presented and an exact...... oscillations. We stipulate that the presented theory of generalized Bloch oscillations can be extended to other systems such as acoustics and photonics....
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)
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
Toward a generalized probability theory: conditional probabilities
International Nuclear Information System (INIS)
Cassinelli, G.
1979-01-01
The main mathematical object of interest in the quantum logic approach to the foundations of quantum mechanics is the orthomodular lattice and a set of probability measures, or states, defined by the lattice. This mathematical structure is studied per se, independently from the intuitive or physical motivation of its definition, as a generalized probability theory. It is thought that the building-up of such a probability theory could eventually throw light on the mathematical structure of Hilbert-space quantum mechanics as a particular concrete model of the generalized theory. (Auth.)
A General Model for Estimating Macroevolutionary Landscapes.
Boucher, Florian C; Démery, Vincent; Conti, Elena; Harmon, Luke J; Uyeda, Josef
2018-03-01
The evolution of quantitative characters over long timescales is often studied using stochastic diffusion models. The current toolbox available to students of macroevolution is however limited to two main models: Brownian motion and the Ornstein-Uhlenbeck process, plus some of their extensions. Here, we present a very general model for inferring the dynamics of quantitative characters evolving under both random diffusion and deterministic forces of any possible shape and strength, which can accommodate interesting evolutionary scenarios like directional trends, disruptive selection, or macroevolutionary landscapes with multiple peaks. This model is based on a general partial differential equation widely used in statistical mechanics: the Fokker-Planck equation, also known in population genetics as the Kolmogorov forward equation. We thus call the model FPK, for Fokker-Planck-Kolmogorov. We first explain how this model can be used to describe macroevolutionary landscapes over which quantitative traits evolve and, more importantly, we detail how it can be fitted to empirical data. Using simulations, we show that the model has good behavior both in terms of discrimination from alternative models and in terms of parameter inference. We provide R code to fit the model to empirical data using either maximum-likelihood or Bayesian estimation, and illustrate the use of this code with two empirical examples of body mass evolution in mammals. FPK should greatly expand the set of macroevolutionary scenarios that can be studied since it opens the way to estimating macroevolutionary landscapes of any conceivable shape. [Adaptation; bounds; diffusion; FPK model; macroevolution; maximum-likelihood estimation; MCMC methods; phylogenetic comparative data; selection.].
Regularity theory for mean-field game systems
Gomes, Diogo A; Voskanyan, Vardan
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.
2016-09-14
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.; Pimentel, Edgard A.; Voskanyan, Vardan K.
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Intra-beam Scattering Theory and RHIC Experiments
International Nuclear Information System (INIS)
Wei, J.; Fedotov, A.; Fischer, W.; Malitsky, N.; Parzen, G.; Qiang, J.
2005-01-01
Intra-beam scattering is the leading mechanism limiting the luminosity in heavy-ion storage rings like the Relativistic Heavy Ion Collider (RHIC). The multiple Coulomb scattering among the charged particles causes transverse emittance growth and longitudinal beam de-bunching and beam loss, compromising machine performance during collision. Theoretically, the original theories developed by Piwinski, Bjorken, and Mtingwa only describe the rms beam size growth of an unbounded Gaussian distribution. Equations based on the Fokker-Planck approach are developed to further describe the beam density profile evolution and beam loss. During the 2004 RHIC heavy-ion operation, dedicated IBS experiments were performed to bench-mark the rms beam size growth, beam loss, and profile evolution both for a Gaussian-like and a longitudinal hollow beam. This paper summarizes the IBS theory and discusses the experimental bench-marking results
A nonlinear theory of generalized functions
1990-01-01
This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applicati...
Generalized extended Navier-Stokes theory
DEFF Research Database (Denmark)
Hansen, J. S.; Daivis, Peter J.; Dyre, Jeppe C.
2013-01-01
in molecular fluids. To discuss these phenomena in detail, molecular dynamics simulations of molecular chlorine are performed for three different state points. In general, the theory captures the behavior for small wavevector and frequencies as expected. For example, in the hydrodynamic regime......The extended Navier-Stokes theory accounts for the coupling between the translational and rotational molecular degrees of freedom. In this paper, we generalize this theory to non-zero frequencies and wavevectors, which enables a new study of spatio-temporal correlation phenomena present...... and for molecular fluids with small moment of inertia like chlorine, the theory predicts that the longitudinal and transverse intrinsic angular velocity correlation functions are almost identical, which is also seen in the molecular dynamics simulations. However, the theory fails at large wavevector and frequencies...
Canonical formulation of general-relativistic theories
International Nuclear Information System (INIS)
Bergmann, P.G.
1987-01-01
With the birth of quantum field theory in the late twenties physicists decided that nature could not be half classical and half quantum, and that the gravitational field ought to be quanticized, just as the electromagnetic field had been. One could accept the group of differomorphisms as a fundamental characteristic of general relativity (and indeed of all general-relativistic theories), and proceed to construct a quantum field-theory that was adapted to that group. Quantization would be attempted by way of a Hamiltonian formulation of the (classical) theory, and quantum commutation relations be patterned after the Poisson brackets arising in that formulation. This program is usually called the canonical quantization program, whereas the weak-field approach is known as covariant quantization. The first steps, conceived entirely within the framework of the classical theory, turned out to be beset with technical and conceptual difficulties, which today are essentially resolved. In this paper the author traces out these initial steps
Simple recursion relations for general field theories
International Nuclear Information System (INIS)
Cheung, Clifford; Shen, Chia-Hsien; Trnka, Jaroslav
2015-01-01
On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-line constructibility of all gauge theories with fermions and complex scalars in arbitrary representations, all supersymmetric theories, and the standard model. Moreover, all amplitudes in non-renormalizable theories without derivative interactions are constructible; with derivative interactions, a subset of amplitudes is constructible. We illustrate our results with examples from both renormalizable and non-renormalizable theories. Our study demonstrates both the power and limitations of recursion relations as a self-contained formulation of quantum field theory.
General relativity invariance and string field theory
International Nuclear Information System (INIS)
Aref'eva, I.Ya.; Volovich, I.V.
1987-04-01
The general covariance principle in the string field theory is considered. The algebraic properties of the string Lie derivative are discussed. The string vielbein and spin connection are introduced and an action invariant under general co-ordinate transformation is proposed. (author). 18 refs
Victories and defeats in general relativity theory
International Nuclear Information System (INIS)
Moeller, C.
1977-01-01
Only within the last 20 years has it been possible to conduct far-reaching experimental tests of the validity of Einstein's General Relativity Theory. Experimental confirmation in some fields is embarrassed by considerable difficulties in applying the theory to cosmic systems, which indicate that such major systems lie at the limit of the theory's applicability. The lecture here reproduced discusses both the successes and the limitations of the theory, starting with its replacement of the absolute space-time theory of Newton and its historical replacement by the relativistic gravitational postulates of Einstein which, in spite of its more complicated postulates, nevertheless introduced a great simplicity and comprehensiveness into the overall conception of nature. This theoretical 'beauty', however, can only be trusted if vindicated experimentally, which has to a considerable extent proved to be the case. For weak fields Newtonian and Einsteinian concepts coincide, while for stronger fields, and velocities not far from that of light, Einstein's theory is superior, giving,for example, an excellent correspondence with the precession of the perehelion of Mercury. On a larger scale, however, the theory appears to lead to conclusions which would invalidate the very concepts of space and time, even within a finite time-interval. A more generalized theory seems to be required. (A.D.N.)
Canonical perturbation theory in linearized general relativity theory
International Nuclear Information System (INIS)
Gonzales, R.; Pavlenko, Yu.G.
1986-01-01
Canonical perturbation theory in linearized general relativity theory is developed. It is shown that the evolution of arbitrary dynamic value, conditioned by the interaction of particles, gravitation and electromagnetic fields, can be presented in the form of a series, each member of it corresponding to the contribution of certain spontaneous or induced process. The main concepts of the approach are presented in the approximation of a weak gravitational field
General Theory of Absorption in Porous Materials: Restricted Multilayer Theory.
Aduenko, Alexander A; Murray, Andy; Mendoza-Cortes, Jose L
2018-04-18
In this article, we present an approach for the generalization of adsorption of light gases in porous materials. This new theory goes beyond Langmuir and Brunauer-Emmett-Teller theories, which are the standard approaches that have a limited application to crystalline porous materials by their unphysical assumptions on the amount of possible adsorption layers. The derivation of a more general equation for any crystalline porous framework is presented, restricted multilayer theory. Our approach allows the determination of gas uptake considering only geometrical constraints of the porous framework and the interaction energy of the guest molecule with the framework. On the basis of this theory, we calculated optimal values for the adsorption enthalpy at different temperatures and pressures. We also present the use of this theory to determine the optimal linker length for a topologically equivalent framework series. We validate this theoretical approach by applying it to metal-organic frameworks (MOFs) and show that it reproduces the experimental results for seven different reported materials. We obtained the universal equation for the optimal linker length, given the topology of a porous framework. This work applied the general equation to MOFs and H 2 to create energy-storage materials; however, this theory can be applied to other crystalline porous materials and light gases, which opens the possibility of designing the next generations of energy-storage materials by first considering only the geometrical constraints of the porous materials.
Transition operators in electromagnetic-wave diffraction theory - General theory
Hahne, G. E.
1992-01-01
A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.
Between general relativity and quantum theory
International Nuclear Information System (INIS)
Rayski, J.
1982-01-01
Some possibilities of reconciling general relativity with quantum theory are discussed. The procedure of quantization is certainly not unique, but depends upon the choice of the coordinate conditions. Most versions of quantization predict the existence of gravitons, but it is also possible to formulate a quantum theory with a classical gravity whereby the expectation values of Tsub(μν) constitute the sources of the classical metric field. (author)
Generalized continued fractions and ergodic theory
International Nuclear Information System (INIS)
Pustyl'nikov, L D
2003-01-01
In this paper a new theory of generalized continued fractions is constructed and applied to numbers, multidimensional vectors belonging to a real space, and infinite-dimensional vectors with integral coordinates. The theory is based on a concept generalizing the procedure for constructing the classical continued fractions and substantially using ergodic theory. One of the versions of the theory is related to differential equations. In the finite-dimensional case the constructions thus introduced are used to solve problems posed by Weyl in analysis and number theory concerning estimates of trigonometric sums and of the remainder in the distribution law for the fractional parts of the values of a polynomial, and also the problem of characterizing algebraic and transcendental numbers with the use of generalized continued fractions. Infinite-dimensional generalized continued fractions are applied to estimate sums of Legendre symbols and to obtain new results in the classical problem of the distribution of quadratic residues and non-residues modulo a prime. In the course of constructing these continued fractions, an investigation is carried out of the ergodic properties of a class of infinite-dimensional dynamical systems which are also of independent interest
A theory of generalized Bloch oscillations
International Nuclear Information System (INIS)
Duggen, Lars; Lassen, Benny; Lew Yan Voon, L C; Willatzen, Morten
2016-01-01
Bloch oscillations of electrons are shown to occur for cases when the energy spectrum does not consist of the traditional evenly-spaced ladders and the potential gradient does not result from an external electric field. A theory of such generalized Bloch oscillations is presented and an exact calculation is given to confirm this phenomenon. Our results allow for a greater freedom of design for experimentally observing Bloch oscillations. For strongly coupled oscillator systems displaying Bloch oscillations, it is further demonstrated that reordering of oscillators leads to destruction of Bloch oscillations. We stipulate that the presented theory of generalized Bloch oscillations can be extended to other systems such as acoustics and photonics. (paper)
Algebraic K-theory of generalized schemes
DEFF Research Database (Denmark)
Anevski, Stella Victoria Desiree
and geometry over the field with one element. It also permits the construction of important Arakelov theoretical objects, such as the completion \\Spec Z of Spec Z. In this thesis, we prove a projective bundle theorem for the eld with one element and compute the Chow rings of the generalized schemes Sp\\ec ZN......Nikolai Durov has developed a generalization of conventional scheme theory in which commutative algebraic monads replace commutative unital rings as the basic algebraic objects. The resulting geometry is expressive enough to encompass conventional scheme theory, tropical algebraic geometry......, appearing in the construction of \\Spec Z....
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.
The generalized second law of thermodynamics in generalized gravity theories
International Nuclear Information System (INIS)
Wu Shaofeng; Yang Guohong; Wang Bin; Zhang Pengming
2008-01-01
We investigate the generalized second law of thermodynamics (GSL) in generalized theories of gravity. We examine the total entropy evolution with time including the horizon entropy, the non-equilibrium entropy production, and the entropy of all matter, field and energy components. We derive a universal condition to protect the generalized second law and study its validity in different gravity theories. In Einstein gravity (even in the phantom-dominated universe with a Schwarzschild black hole), Lovelock gravity and braneworld gravity, we show that the condition to keep the GSL can always be satisfied. In f(R) gravity and scalar-tensor gravity, the condition to protect the GSL can also hold because the temperature should be positive, gravity is always attractive and the effective Newton constant should be an approximate constant satisfying the experimental bounds
Generalized semilocal theories and higher Hopf maps
International Nuclear Information System (INIS)
Hindmarsh, M.; Holman, R.; Kephart, T.W.; Vachaspati, T.
1993-01-01
In semilocal theories, the vacuum manifold is fibered in a non-trivial way by the action of the gauge group. Here we generalize the original semilocal theory (which was based on the Hopf bundle S 3 → S1 S 2 ) to realize the next Hopf bundle S 7 →S 3 S 4 , and its extensions S 2n+1 → S3 HP n . The semilocal defects in this class of theories are classified by π 3 (S 3 ), and are interpreted as constrained instantons or generalized sphaleron configurations. We fail to find a field theoretic realization of the final Hopf bundle S 15 →S 7 S 8 , but are able to construct other semilocal spaces realizing Stiefel bundles over grassmannian spaces. (orig.)
Generalized locally Toeplitz sequences theory and applications
Garoni, Carlo
2017-01-01
Based on their research experience, the authors propose a reference textbook in two volumes on the theory of generalized locally Toeplitz sequences and their applications. This first volume focuses on the univariate version of the theory and the related applications in the unidimensional setting, while the second volume, which addresses the multivariate case, is mainly devoted to concrete PDE applications. This book systematically develops the theory of generalized locally Toeplitz (GLT) sequences and presents some of its main applications, with a particular focus on the numerical discretization of differential equations (DEs). It is the first book to address the relatively new field of GLT sequences, which occur in numerous scientific applications and are especially dominant in the context of DE discretizations. Written for applied mathematicians, engineers, physicists, and scientists who (perhaps unknowingly) encounter GLT sequences in their research, it is also of interest to those working in the fields of...
Development of Einstein's general theory of relativity
International Nuclear Information System (INIS)
Datta, B.K.
1980-01-01
Starting from Poincare's Lorentz-invariant theory of gravity formulated in 1906, development of Einstein's general theory of relativity during 1906-1916 is discussed. Three stages in this development are recognised. In the first stage during 1907-1914, Einstein tried to extend the relativity principle of uniform motion to the frames in non-uniform motion. For this purpose, he introduced the principle of equivalence which made it possible to calculate the effect of homogeneous gravitational field on arbitrary physical processes. During the second stage comprising years 1912-1914 overlapping the first stage, Einstein and Grossmann were struggling to translate physical postulates into the language of the absolute differential calculus. In the period 1915-1916, Einstein formulated the field equations of general relativity. While discussing these developmental stages, theories of gravitation formulated by Abraham, Nordstroem and Mie are also discussed. (M.G.B.)
General Systems Theory and Counterplan Competition.
Madsen, Arnie
1989-01-01
Discusses the trend in academic debate on policy questions toward a wide acceptance of counterplans, encouraging combinations of proposals which appear at face value able to coexist but upon deeper analysis are incompatible. Argues in opposition to this trend by applying concepts from general systems theory to competition. (KEH)
Educational Interpretations of General Systems Theory.
Hug, William E.; King, James E.
This chapter discusses General Systems Theory as it applies to education, classrooms, innovations, and instructional design. The principles of equifinality, open and closed systems, the individual as the key system, hierarchical structures, optimization, stability, cooperation, and competition are discussed, and their relationship to instructional…
General Systems Theory and Instructional Systems Design.
Salisbury, David F.
1990-01-01
Describes basic concepts in the field of general systems theory (GST) and identifies commonalities that exist between GST and instructional systems design (ISD). Models and diagrams that depict system elements in ISD are presented, and two matrices that show how GST has been used in ISD literature are included. (11 references) (LRW)
Schumpeter's general theory of social evolution
DEFF Research Database (Denmark)
Andersen, Esben Sloth
The recent neo-Schumpeterian and evolutionary economics appears to cover a much smaller range of topics than Joseph Schumpeter confronted. Thus, it has hardly been recognised that Schumpeter wanted to develop a general theory that served the analysis of evolution in any sector of social life...
The Faraday effect revisited: General theory
DEFF Research Database (Denmark)
Cornean, Horia Decebal; Nenciu, Gheorghe; Pedersen, Thomas Garm
2006-01-01
This paper is the first in a series revisiting the Faraday effect, or more generally, the theory of electronic quantum transport/optical response in bulk media in the presence of a constant magnetic field. The independent electron approximation is assumed. At zero temperature and zero frequency...
The Faraday effect revisited: General theory
DEFF Research Database (Denmark)
Cornean, Horia Decebal; Nenciu, Gheorghe; Pedersen, Thomas Garm
This paper is the first in a series revisiting the Faraday effect, or more generally, the theory of electronic quantum transport/optical response in bulk media in the presence of a constant magnetic field. The independent electron approximation is assumed. For free electrons, the transverse...
Performativity: The Special and the General Theory
Directory of Open Access Journals (Sweden)
Sonia Reverter-Bañón
2017-07-01
Full Text Available If in Gender Trouble (1990 Butler presented a proposal of the theory of performativity of speech acts applied to the construction of gender, in her last book, Notes towards a Performative Theory of Assembly (2015, she articulates a theory of performativity applied to collective and concerted action of minorities or populations that are estimated to be “disposable”. The interest of the proposal that we present in this paper is to analyze how the theory of performativity of gender is now extended to the forms of democratic action; going from being a structure that explains the possibilities of gender to explain the possibilities for a livable life. It is what we call here the extension of performativity, from the special case of gender to the general case of a livable life.
Generalized IIB supergravity from exceptional field theory
Energy Technology Data Exchange (ETDEWEB)
Baguet, Arnaud; Magro, Marc; Samtleben, Henning [Laboratoire de Physique, Université Claude Bernard Lyon 1, Ens de Lyon, CNRS,F-69342 Lyon (France)
2017-03-20
The background underlying the η-deformed AdS{sub 5}×S{sup 5} sigma-model is known to satisfy a generalization of the IIB supergravity equations. Their solutions are related by T-duality to solutions of type IIA supergravity with non-isometric linear dilaton. We show how the generalized IIB supergravity equations can be naturally obtained from exceptional field theory. Within this manifestly duality covariant formulation of maximal supergravity, the generalized IIB supergravity equations emerge upon imposing on the fields a simple Scherk-Schwarz ansatz which respects the section constraint.
REQUIREMENTS FOR A GENERAL INTERPRETATION THEORY
Directory of Open Access Journals (Sweden)
Anda Laura Lungu Petruescu
2013-06-01
Full Text Available Time has proved that Economic Analysis is not enough as to ensure all the needs of the economic field. The present study wishes to propose a new approach method of the economic phenomena and processes based on the researches made outside the economic space- a new general interpretation theory- which is centered on the human being as the basic actor of economy. A general interpretation theory must assure the interpretation of the causalities among the economic phenomena and processes- causal interpretation; the interpretation of the correlations and dependencies among indicators- normative interpretation; the interpretation of social and communicational processes in economic organizations- social and communicational interpretation; the interpretation of the community status of companies- transsocial interpretation; the interpretation of the purposes of human activities and their coherency – teleological interpretation; the interpretation of equilibrium/ disequilibrium from inside the economic systems- optimality interpretation. In order to respond to such demands, rigor, pragmatism, praxiology and contextual connectors are required. In order to progress, the economic science must improve its language, both its syntax and its semantics. The clarity of exposure requires a language clarity and the scientific theory progress asks for the need of hypotheses in the building of the theories. The switch from the common language to the symbolic one means the switch from ambiguity to rigor and rationality, that is order in thinking. But order implies structure, which implies formalization. Our paper should be a plea for these requirements, requirements which should be fulfilled by a modern interpretation theory.
Relativity the special and the general theory
Einstein, Albert
2015-01-01
After completing the final version of his general theory of relativity in November 1915, Albert Einstein wrote a book about relativity for a popular audience. His intention was "to give an exact insight into the theory of relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics." The book remains one of the most lucid explanations of the special and general theories ever written. In the early 1920s alone, it was translated into ten languages, and fifteen editions in the original German appeared over the course of Einstein's lifetime. This new edition of Einstein's celebrated book features an authoritative English translation of the text along with an introduction and a reading companion by Hanoch Gutfreund and Jürgen Renn that examines the evolution of Einstein's thinking and casts his ideas in a broader present-day context. A special chapter explores the history...
A general theory for the Uranian satellites
Laskar, J.
1986-01-01
A general analytical theory of the five main satellites of Uranus, including the secular and short period terms hereafter denoted by GUST, is presented. A comparison is made with an internal numerical integration with nominal masses of Veillet (1983). The precision of the theory goes from about 10 km for Miranda to 100 km for Oberon. The short period terms in the motions of Titania and Oberon are larger than 500 km. They should make possible the determination of the masses of the outer satellites through the optical data of Voyager encounter.
Toward a general evolutionary theory of oncogenesis.
Ewald, Paul W; Swain Ewald, Holly A
2013-01-01
We propose an evolutionary framework, the barrier theory of cancer, which is based on the distinction between barriers to oncogenesis and restraints. Barriers are defined as mechanisms that prevent oncogenesis. Restraints, which are more numerous, inhibit but do not prevent oncogenesis. Processes that compromise barriers are essential causes of cancer; those that interfere with restraints are exacerbating causes. The barrier theory is built upon the three evolutionary processes involved in oncogenesis: natural selection acting on multicellular organisms to mold barriers and restraints, natural selection acting on infectious organisms to abrogate these protective mechanisms, and oncogenic selection which is responsible for the evolution of normal cells into cancerous cells. The barrier theory is presented as a first step toward the development of a general evolutionary theory of cancer. Its attributes and implications for intervention are compared with those of other major conceptual frameworks for understanding cancer: the clonal diversification model, the stem cell theory and the hallmarks of cancer. The barrier theory emphasizes the practical value of distinguishing between essential and exacerbating causes. It also stresses the importance of determining the scope of infectious causation of cancer, because individual pathogens can be responsible for multiple essential causes in infected cells.
Lagrangians for generalized Argyres-Douglas theories
Benvenuti, Sergio; Giacomelli, Simone
2017-10-01
We continue the study of Lagrangian descriptions of N=2 Argyres-Douglas theories. We use our recent interpretation in terms of sequential confinement to guess the Lagrangians of all the Argyres-Douglas models with Abelian three dimensional mirror. We find classes of four dimensional N=1 quivers that flow in the infrared to generalized Argyres-Douglas theories, such as the ( A k , A kN + N -1) models. We study in detail how the N=1 chiral rings map to the Coulomb and Higgs Branches of the N=2 CFT's. The three dimensional mirror RG flows are shown to land on the N=4 complete graph quivers. We also compactify to three dimensions the gauge theory dual to ( A 1, D 4), and find the expected Abelianization duality with N=4 SQED with 3 flavors.
Towards a general theory of implementation
2013-01-01
Understanding and evaluating the implementation of complex interventions in practice is an important problem for healthcare managers and policy makers, and for patients and others who must operationalize them beyond formal clinical settings. It has been argued that this work should be founded on theory that provides a foundation for understanding, designing, predicting, and evaluating dynamic implementation processes. This paper sets out core constituents of a general theory of implementation, building on Normalization Process Theory and linking it to key constructs from recent work in sociology and psychology. These are informed by ideas about agency and its expression within social systems and fields, social and cognitive mechanisms, and collective action. This approach unites a number of contending perspectives in a way that makes possible a more comprehensive explanation of the implementation and embedding of new ways of thinking, enacting and organizing practice. PMID:23406398
On the general theory of quantized fields
International Nuclear Information System (INIS)
Fredenhagen, K.
1991-10-01
In my lecture I describe the present stage of the general theory of quantized fields on the example of 5 subjects. They are ordered in the direction from large to small distances. The first one is the by now classical problem of the structure of superselection sectors. It involves the behavior of the theory at spacelike infinity and is directly connected with particle statistics and internal symmetries. It has become popular in recent years by the discovery of a lot of nontrivial models in 2d conformal-field theory, by connections to integrable models and critical behavior in statistical mechanics and by the relations to the Jones' theory of subfactors in von Neumann algebras and to the corresponding geometrical objects (braids, knots, 3d manifolds, ...). At large timelike distances the by far most important feature of quantum field theory is the particle structure. This will be the second subject of my lecture. It follows the technically most involved part which is concerned with the behavior at finite distances. Two aspets, nuclearity which emphasizes the finite density of states in phase space, and the modular structure which relies on the infinite number of degrees of freedom present even locally, and their mutual relations will be treated. The next point, involving the structure at infinitesimal distances, is the connection between the Haag-Kastler framework of algebras of local and the framework of Wightman fields. Finally, problems in approaches to quantum gravity will be discussed, as far as they are accessible by the methods of the general theory of quantized fields. (orig.)
The Faraday effect revisited General theory
Cornean, H D; Pedersen, T G
2005-01-01
This paper is the first in a series revisiting the Faraday effect, or more generally, the theory of electronic quantum transport/optical response in bulk media in the presence of a constant magnetic field. The independent electron approximation is assumed. For free electrons, the transverse conductivity can be explicitly computed and coincides with the classical result. In the general case, using magnetic perturbation theory, the conductivity tensor is expanded in powers of the strength of the magnetic field $B$. Then the linear term in $B$ of this expansion is written down in terms of the zero magnetic field Green function and the zero field current operator. In the periodic case, the linear term in $B$ of the conductivity tensor is expressed in terms of zero magnetic field Bloch functions and energies. No derivatives with respect to the quasimomentum appear and thereby all ambiguities are removed, in contrast to earlier work.
Cosmology in general massive gravity theories
International Nuclear Information System (INIS)
Comelli, D.; Nesti, F.; Pilo, L.
2014-01-01
We study the cosmological FRW flat solutions generated in general massive gravity theories. Such a model are obtained adding to the Einstein General Relativity action a peculiar non derivative potentials, function of the metric components, that induce the propagation of five gravitational degrees of freedom. This large class of theories includes both the case with a residual Lorentz invariance as well as the case with rotational invariance only. It turns out that the Lorentz-breaking case is selected as the only possibility. Moreover it turns out that that perturbations around strict Minkowski or dS space are strongly coupled. The upshot is that even though dark energy can be simply accounted by massive gravity modifications, its equation of state w eff has to deviate from -1. Indeed, there is an explicit relation between the strong coupling scale of perturbations and the deviation of w eff from -1. Taking into account current limits on w eff and submillimiter tests of the Newton's law as a limit on the possible strong coupling scale, we find that it is still possible to have a weakly coupled theory in a quasi dS background. Future experimental improvements on short distance tests of the Newton's law may be used to tighten the deviation of w eff form -1 in a weakly coupled massive gravity theory
Sturmians and generalized sturmians in quantum theory
DEFF Research Database (Denmark)
Avery, John Scales; Avery, James Emil
2012-01-01
The theory of Sturmians and generalized Sturmians is reviewed. It is shown that when generalized Sturmians are used as basis functions, calculations on the spectra and physical properties of few-electron atoms can be performed with great ease and good accuracy. The use of many-center Coulomb Stur...... Sturmians as basis functions in calculations on N-electron molecules is also discussed. Basis sets of this type are shown to have many advantages over other types of ETO’s, especially the property of automatic scaling....
Advances in heuristically based generalized perturbation theory
International Nuclear Information System (INIS)
Gandini, A.
1994-01-01
A distinctive feature of heuristically based generalized perturbation theory methodology consists in the systematic use of importance conservation concepts. As well known, this use leads to fundamental reciprocity relationship. Instead, the alternative variational and differential one approaches make a consistent use of the properties and adjoint functions. The equivalence between the importance and the adjoint functions have been demonstrated in important cases. There are some instances, however, in which the commonly known operator governing the adjoint function are not adequate. In this paper ways proposed to generalize this rules, as adopted with the heuristic generalized perturbation theory methodology, are illustrated. When applied to the neutron/nuclide field characterizing the core evolution in a power reactor system, in which also an intensive control variable (ρ) is defined, these rules leas to an orthogonality relationship connected to this same control variable. A set of ρ-mode eigenfunctions may be correspondingly defined and an extended concept of reactivity (generalizing that commonly associated with the multiplication factor) proposed as more directly indicative of the controllability of a critical reactor system. (author). 25 refs
A thermodynamically general theory for convective vortices
Renno, Nilton O.
2008-08-01
Convective vortices are common features of atmospheres that absorb lower-entropy-energy at higher temperatures than they reject higher-entropy-energy to space. These vortices range from small to large-scale and play an important role in the vertical transport of heat, momentum, and tracer species. Thus, the development of theoretical models for convective vortices is important to our understanding of some of the basic features of planetary atmospheres. The heat engine framework is a useful tool for studying convective vortices. However, current theories assume that convective vortices are reversible heat engines. Since there are questions about how reversible real atmospheric heat engines are, their usefulness for studying real atmospheric vortices is somewhat controversial. In order to reduce this problem, a theory for convective vortices that includes irreversible processes is proposed. The paper's main result is that the proposed theory provides an expression for the pressure drop along streamlines that includes the effects of irreversible processes. It is shown that a simplified version of this expression is a generalization of Bernoulli's equation to convective circulations. It is speculated that the proposed theory not only explains the intensity, but also sheds light on other basic features of convective vortices such as their physical appearance.
A generalized Yang-Mills Theory I: general aspects of the classical theory
International Nuclear Information System (INIS)
Galvao, C.A.P.
1987-01-01
A generalized Yang-Mills theory which is the non-Abelian version of the generalized eletrodinamics proposed by Podolsky is analysed both in the Lagrangian an Hamiltonian formulation. A simple class of solutions to the Euler-Lagrange equations is presented and the structure of the Hamiltonian constraints is studied in details. (Author) [pt
Weak lensing in generalized gravity theories
International Nuclear Information System (INIS)
Acquaviva, Viviana; Baccigalupi, Carlo; Perrotta, Francesca
2004-01-01
We extend the theory of weak gravitational lensing to cosmologies with generalized gravity, described in the Lagrangian by a generic function depending on the Ricci scalar and a nonminimal coupled scalar field. We work out the generalized Poisson equations relating the dynamics of the fluctuating components to the two gauge-invariant scalar gravitational potentials, fixing the contributions from the modified background expansion and fluctuations. We show how the lensing equation gets modified by the cosmic expansion as well as by the presence of anisotropic stress, which is non-null at the linear level both in scalar-tensor gravity and in theories where the gravitational Lagrangian term features a nonminimal dependence on the Ricci scalar. Starting from the geodesic deviation, we derive the generalized expressions for the shear tensor and projected lensing potential, encoding the spacetime variation of the effective gravitational constant and isolating the contribution of the anisotropic stress, which introduces a correction due to the spatial correlation between the gravitational potentials. Finally, we work out the expressions of the lensing convergence power spectrum as well as the correlation between the lensing potential and the integrated Sachs-Wolfe effect affecting cosmic microwave background total intensity and polarization anisotropies. To illustrate phenomenologically the effects, we work out approximate expressions for the quantities above in extended quintessence scenarios where the scalar field coupled to gravity plays the role of the dark energy
Module theory, extending modules and generalizations
Tercan, Adnan
2016-01-01
The main focus of this monograph is to offer a comprehensive presentation of known and new results on various generalizations of CS-modules and CS-rings. Extending (or CS) modules are generalizations of injective (and also semisimple or uniform) modules. While the theory of CS-modules is well documented in monographs and textbooks, results on generalized forms of the CS property as well as dual notions are far less present in the literature. With their work the authors provide a solid background to module theory, accessible to anyone familiar with basic abstract algebra. The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules. In particular, matrix CS-rings are studied and clear proofs of fundamental decomposition results on CS-modules over commutative domains are given, thus complementing existing monographs in this area. Open problems round out the work and establish the...
Kinematic matrix theory and universalities in self-propellers and active swimmers.
Nourhani, Amir; Lammert, Paul E; Borhan, Ali; Crespi, Vincent H
2014-06-01
We describe an efficient and parsimonious matrix-based theory for studying the ensemble behavior of self-propellers and active swimmers, such as nanomotors or motile bacteria, that are typically studied by differential-equation-based Langevin or Fokker-Planck formalisms. The kinematic effects for elementary processes of motion are incorporated into a matrix, called the "kinematrix," from which we immediately obtain correlators and the mean and variance of angular and position variables (and thus effective diffusivity) by simple matrix algebra. The kinematrix formalism enables us recast the behaviors of a diverse range of self-propellers into a unified form, revealing universalities in their ensemble behavior in terms of new emergent time scales. Active fluctuations and hydrodynamic interactions can be expressed as an additive composition of separate self-propellers.
The general physics theory for 21 century
International Nuclear Information System (INIS)
Gassym, T. M.
2006-01-01
By solving the coupled system of kinetic equations for interacting system of electrons positrons (holes) and photons (phonons) at high external electric, arbitrary magnetic and at the propagation of strong electromagnetic waves non-equilibrium and non-stationary distribution function of photons (phonons) and charge carriers by taking into account of arbitrary heating and mutual drag of carriers and photons (phonons) was found. Author was sure that received him in 1976 distribution function of photons (phonons) must lay on the basis of Theoretical Physics of 21 Century, as the equilibrium Planck's distribution function of black-body radiation received in 1900 lied on the basis of Quantum Physics of 20 Century. Authors many years mental work (from 1976 till today) confirmed the rightness of searched him way and leads to the conclusion that Kinetic Theory is more general and fundamental theory of nature, which unificated Non-stationary Dynamics (the left-hand side) with Non-stationary Statistical Mechanics (the right-hand side) of Kinetic Equation. It is shown that other sections of Theoretical Physics such as Newtonian, Hamiltonian and Relativistic Classical Mechanics, Quantum Physics, Optics, Statistical Mechanics and Thermodynamics, Particle Physics may be received from Kinetic Theory under the special conditions and are the special parts of this theory. The problems such as the irreversibility and instability, the paradox of time, quantum paradox and others are solved. This new General Theory explains all the problems and troubles contents with the foundations and interpretation of quantum mechanics and relativity. It was found the mechanism of quantization and transition from one energetic level to another,the squeezed effect, the transition of particles wave-packets through the energetic barriers. It is shown the possibility of superluminal motion of light pulses and wave-packets through the medium and photonic barriers. It is well known that the experiments
A general theory of quantum relativity
International Nuclear Information System (INIS)
Minic, Djordje; Tze, C.-H.
2004-01-01
The geometric form of standard quantum mechanics is compatible with the two postulates: (1) the laws of physics are invariant under the choice of experimental setup and (2) every quantum observation or event is intrinsically statistical. These postulates remain compatible within a background independent extension of quantum theory with a local intrinsic time implying the relativity of the concept of a quantum event. In this extension the space of quantum events becomes dynamical and only individual quantum events make sense observationally. At the core of such a general theory of quantum relativity is the three-way interplay between the symplectic form, the dynamical metric and non-integrable almost complex structure of the space of quantum events. Such a formulation provides a missing conceptual ingredient in the search for a background independent quantum theory of gravity and matter. The crucial new technical element in our scheme derives from a set of recent mathematical results on certain infinite-dimensional almost Kahler manifolds which replace the complex projective spaces of standard quantum mechanics
Toward a holographic theory for general spacetimes
Nomura, Yasunori; Salzetta, Nico; Sanches, Fabio; Weinberg, Sean J.
2017-04-01
We study a holographic theory of general spacetimes that does not rely on the existence of asymptotic regions. This theory is to be formulated in a holographic space. When a semiclassical description is applicable, the holographic space is assumed to be a holographic screen: a codimension-1 surface that is capable of encoding states of the gravitational spacetime. Our analysis is guided by conjectured relationships between gravitational spacetime and quantum entanglement in the holographic description. To understand basic features of this picture, we catalog predictions for the holographic entanglement structure of cosmological spacetimes. We find that qualitative features of holographic entanglement entropies for such spacetimes differ from those in AdS/CFT but that the former reduce to the latter in the appropriate limit. The Hilbert space of the theory is analyzed, and two plausible structures are found: a direct-sum and "spacetime-equals-entanglement" structure. The former preserves a naive relationship between linear operators and observable quantities, while the latter respects a more direct connection between holographic entanglement and spacetime. We also discuss the issue of selecting a state in quantum gravity, in particular how the state of the multiverse may be selected in the landscape.
General theory of the plasmoid instability
International Nuclear Information System (INIS)
Comisso, L.; Lingam, M.; Huang, Y.-M.; Bhattacharjee, A.
2016-01-01
In a general theory of the onset and development of the plasmoid instability is formulated by means of a principle of least time. We derive and show the scaling relations for the final aspect ratio, transition time to rapid onset, growth rate, and number of plasmoids that depend on the initial perturbation amplitude (ŵ_0), the characteristic rate of current sheet evolution (1/τ), and the Lundquist number (S). They are not simple power laws, and are proportional to S"ατ"β[ln f(S,τ,ŵ_0)]"σ. Finally, the detailed dynamics of the instability is also elucidated, and shown to comprise of a period of quiescence followed by sudden growth over a short time scale.
A general theory of sexual differentiation.
Arnold, Arthur P
2017-01-02
A general theory of mammalian sexual differentiation is proposed. All biological sex differences are the result of the inequality in effects of the sex chromosomes, which are the only factors that differ in XX vs. XY zygotes. This inequality leads to male-specific effects of the Y chromosome, including expression of the testis-determining gene Sry that causes differentiation of testes. Thus, Sry sets up lifelong sex differences in effects of gonadal hormones. Y genes also act outside of the gonads to cause male-specific effects. Differences in the number of X chromosomes between XX and XY cells cause sex differences in expression (1) of Xist, (2) of X genes that escape inactivation, and (3) of parentally imprinted X genes. Sex differences in phenotype are ultimately the result of multiple, independent sex-biasing factors, hormonal and sex chromosomal. These factors act in parallel and in combination to induce sex differences. They also can offset each other to reduce sex differences. Other mechanisms, operating at the level of populations, cause groups of males to differ on average from groups of females. The theory frames questions for further study, and directs attention to inherent sex-biasing factors that operate in many tissues to cause sex differences, and to cause sex-biased protection from disease. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Generalized interferometry - I: theory for interstation correlations
Fichtner, Andreas; Stehly, Laurent; Ermert, Laura; Boehm, Christian
2017-02-01
We develop a general theory for interferometry by correlation that (i) properly accounts for heterogeneously distributed sources of continuous or transient nature, (ii) fully incorporates any type of linear and nonlinear processing, such as one-bit normalization, spectral whitening and phase-weighted stacking, (iii) operates for any type of medium, including 3-D elastic, heterogeneous and attenuating media, (iv) enables the exploitation of complete correlation waveforms, including seemingly unphysical arrivals, and (v) unifies the earthquake-based two-station method and ambient noise correlations. Our central theme is not to equate interferometry with Green function retrieval, and to extract information directly from processed interstation correlations, regardless of their relation to the Green function. We demonstrate that processing transforms the actual wavefield sources and actual wave propagation physics into effective sources and effective wave propagation. This transformation is uniquely determined by the processing applied to the observed data, and can be easily computed. The effective forward model, that links effective sources and propagation to synthetic interstation correlations, may not be perfect. A forward modelling error, induced by processing, describes the extent to which processed correlations can actually be interpreted as proper correlations, that is, as resulting from some effective source and some effective wave propagation. The magnitude of the forward modelling error is controlled by the processing scheme and the temporal variability of the sources. Applying adjoint techniques to the effective forward model, we derive finite-frequency Fréchet kernels for the sources of the wavefield and Earth structure, that should be inverted jointly. The structure kernels depend on the sources of the wavefield and the processing scheme applied to the raw data. Therefore, both must be taken into account correctly in order to make accurate inferences on
Generalized quantum theory of recollapsing homogeneous cosmologies
International Nuclear Information System (INIS)
Craig, David; Hartle, James B.
2004-01-01
A sum-over-histories generalized quantum theory is developed for homogeneous minisuperspace type A Bianchi cosmological models, focusing on the particular example of the classically recollapsing Bianchi type-IX universe. The decoherence functional for such universes is exhibited. We show how the probabilities of decoherent sets of alternative, coarse-grained histories of these model universes can be calculated. We consider in particular the probabilities for classical evolution defined by a suitable coarse graining. For a restricted class of initial conditions and coarse grainings we exhibit the approximate decoherence of alternative histories in which the universe behaves classically and those in which it does not. For these situations we show that the probability is near unity for the universe to recontract classically if it expands classically. We also determine the relative probabilities of quasiclassical trajectories for initial states of WKB form, recovering for such states a precise form of the familiar heuristic 'J·dΣ' rule of quantum cosmology, as well as a generalization of this rule to generic initial states
Hamiltonian theory of the ion cyclotron minority heating dynamics in tokamak plasmas
International Nuclear Information System (INIS)
Becoulet, A.; Gambier, D.J.; Samain, A.
1990-03-01
The question of heating a tokamak plasma by means of electromagnetic waves in the Ion Cyclotron Range of Frequency (ICRF) is considered in the perspective of large RF powers and in the low collisionality regime. In such case the Quasi Linear Theory (QLT) is validated by the Hamiltonian dynamics of the wave particle interaction which exceeds the threshold of the intrinsic stochasticity. The Hamiltonian dynamics is represented by the evolution of a set of three canonical action angle variables well adapted to the tokamak magnetic configuration. This approach allows to derive the RF diffusion coefficient with very few assumptions. The distribution function of the resonant ions is written as a Fokker Planck equation but the emphasis is put on the QL diffusion instead of on the usual diffusion induced by collisions. Then the Fokker Planck equation is given a variational from which a solution is derived in the form of a semi analytical trial function of three parameters: the percentage of resonant particle contained in the tail; an isotropic width ΔT and an anisotropic one ΔP. This solution is successfully tested against real experimental observations. Practically it is shown that in the case of JET the distribution function is influenced by adiabatic barriers which in turn limit the Hamiltonian stochasticity domain within energy values typically in the MeV range. Consequently and for a given ICRF power, the tail energy excursion is lower and its concentration higher than that of a bounce averaged prediction. This may actually be an advantage for machines like JET considering the energy range required to simulate the α-particle behaviour in a relevant fusion reactor
International Nuclear Information System (INIS)
Behringer, K.
1991-02-01
In a recent paper by Behringer et al. (1990), the Wiener-Hermite Functional (WHF) method has been applied to point reactor kinetics excited by Gaussian random reactivity noise under stationary conditions, in order to calculate the neutron steady-state value and the neutron power spectral density (PSD) in a second-order (WHF-2) approximation. For simplicity, delayed neutrons and any feedback effects have been disregarded. The present study is a straightforward continuation of the previous one, treating the problem more generally by including any number of delayed neutron groups. For the case of white reactivity noise, the accuracy of the approach is determined by comparison with the exact solution available from the Fokker-Planck method. In the numerical comparisons, the first-oder (WHF-1) approximation of the PSD is also considered. (author) 4 figs., 10 refs
Ghost properties of generalized theories of gravitation
International Nuclear Information System (INIS)
Mann, R.B.; Moffat, J.W.
1982-01-01
We investigate theories of gravitation, in which spacetime is non-Riemannian and the metric g/sub munu/ is nonsymmetric, for ghosts and tachyons, using a spin-projection operator formalism. Ghosts are removed not by gauge invariance but by a Lagrange multiplier W/sub μ/, which occurs due to the breaking of projective invariance in the theory. Unified theories based on a Lagrangian containing a term lambdag/sup munu/g/sub / are proved to contain ghosts or tachyons
Recent developments in the kinetic theory of nucleation.
Ruckenstein, E; Djikaev, Y S
2005-12-30
A review of recent progress in the kinetics of nucleation is presented. In the conventional approach to the kinetic theory of nucleation, it is necessary to know the free energy of formation of a new-phase particle as a function of its independent variables at least for near-critical particles. Thus the conventional kinetic theory of nucleation is based on the thermodynamics of the process. The thermodynamics of nucleation can be examined by using various approaches, such as the capillarity approximation, density functional theory, and molecular simulation, each of which has its own advantages and drawbacks. Relatively recently a new approach to the kinetics of nucleation was proposed [Ruckenstein E, Nowakowski B. J Colloid Interface Sci 1990;137:583; Nowakowski B, Ruckenstein E. J Chem Phys 1991;94:8487], which is based on molecular interactions and does not employ the traditional thermodynamics, thus avoiding such a controversial notion as the surface tension of tiny clusters involved in nucleation. In the new kinetic theory the rate of emission of molecules by a new-phase particle is determined with the help of a mean first passage time analysis. This time is calculated by solving the single-molecule master equation for the probability distribution function of a surface layer molecule moving in a potential field created by the rest of the cluster. The new theory was developed for both liquid-to-solid and vapor-to-liquid phase transitions. In the former case the single-molecule master equation is the Fokker-Planck equation in the phase space which can be reduced to the Smoluchowski equation owing to the hierarchy of characteristic time scales. In the latter case, the starting master equation is a Fokker-Planck equation for the probability distribution function of a surface layer molecule with respect to both its energy and phase coordinates. Unlike the case of liquid-to-solid nucleation, this Fokker-Planck equation cannot be reduced to the Smoluchowski equation
Generalizing Prototype Theory: A Formal Quantum Framework
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper. PMID:27065436
Generalizing Prototype Theory: A Formal Quantum Framework
Directory of Open Access Journals (Sweden)
Diederik eAerts
2016-03-01
Full Text Available Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.
Can one tell Einstein's unimodular theory from Einstein's general relativity?
Alvarez, Enrique
2005-01-01
The so called unimodular theory of gravitation is compared with general relativity in the quadratic (Fierz-Pauli) regime, using a quite broad framework, and it is argued that quantum effects allow in principle to discriminate between both theories.
The role of Einstein's general relativity theory in today's physics
International Nuclear Information System (INIS)
Bicak, J.
The relationships are discussed of the general relativity theory to other fields of today's physics. Recent results are reported of studies into gravitational radiation, relativistic astrophysics, cosmology and the quantum theory. (Z.M.)
70 years of the general theory of relativity
International Nuclear Information System (INIS)
Castro Diaz-Balart, F.; Cabezas Solorzano, R.
1986-06-01
In view of the 70th anniversary of the discovery of the General Theory of Relativity, an analysis was made of the special and general theories. The basic postulates, their consequences in the formulation of the theories, the main results, some aspects related to the experimental verification and its applications are presented, as are some elements of the mathematical formalism of the theories, to facilitate the logical interrelationships between its results and consequences. (author)
Random walk of the baryon number
International Nuclear Information System (INIS)
Kazaryan, A.M.; Khlebnikov, S.Y.; Shaposhnikov, M.E.
1989-01-01
A new approach is suggested for the anomalous nonconservation of baryon number in the electroweak theory at high temperatures. Arguments are presented in support of the idea that the baryon-number changing reactions may be viewed as random Markov processes. Making use of the general theory of Markov processes, the Fokker--Planck equation for the baryon-number distribution density is obtained and kinetic coefficients are calculated
N =1 Lagrangians for generalized Argyres-Douglas theories
Agarwal, Prarit; Sciarappa, Antonio; Song, Jaewon
2017-10-01
We find N = 1 Lagrangian gauge theories that flow to generalized ArgyresDouglas theories with N = 2 supersymmetry. We find that certain SU quiver gauge theories flow to generalized Argyres-Douglas theories of type ( A k-1 , A mk-1) and ( I m,km , S). We also find quiver gauge theories of SO/Sp gauge groups flowing to the ( A 2 m-1 , D 2 mk+1), ( A 2 m , D 2 m( k-1)+ k ) and D m(2 k + 2) m(2 k + 2) [ m] theories.
Towards a General Theory of Immunity?
Eberl, Gérard; Pradeu, Thomas
2018-04-01
Theories are indispensable to organize immunological data into coherent, explanatory, and predictive frameworks. We propose to combine different models to develop a unifying theory of immunity which situates immunology in the wider context of physiology. We believe that the immune system will be increasingly understood as a central component of a network of partner physiological systems that interconnect to maintain homeostasis. Copyright © 2017 Elsevier Ltd. All rights reserved.
Generalized detailed balance theory of solar cells
Energy Technology Data Exchange (ETDEWEB)
Kirchartz, Thomas
2009-12-12
compatible with the Shockley-Queisser limit and the classical diode theory. For organic solar cells, exciton binding energies are sufficiently high, so that purely bipolar models are no longer applicable. Instead, excitonic transport has to be included. Thus, the inclusion of exciton transport into the bipolar detailed balance model leads to a generalized detailed balance model that simulates solar cells with predominantly bipolar transport, with predominantly excitonic transport and with every combination of both. Due to low exciton diffusion lengths, organic solar cells are usually combined with a specific device geometry, the bulk heterojunction. In a bulk heterojunction device, the whole bulk of the absorber is made up of distributed heterojunctions, where the exciton is transferred to a bound pair at the interface, which is then split into free electron and hole. The assumption that exciton transport is only relevant towards the next heterointerface allows to develop also a version of the detailed balance model that is applicable to bulk heterojunction cells. The last variation of the detailed balance model includes the process of impact ionisation as a means to generate more than one exciton from a single high energy photon. The model for multiple exciton generating absorbers identifies possible bottlenecks as well as maximum efficiencies of future solar cells that use this concept. Another direct consequence of the principle of detailed balance is a reciprocity theorem between electroluminescence and solar cell quantum efficiency. The theoretical part of this thesis discusses the validity range of this reciprocity and checks for each version of the model, whether the relation between electroluminescence and quantum efficiency is still applicable. The main result shows that voltage dependent carrier collection as encountered in low mobility pin-junction devices leads to deviations from the reciprocity, while it still holds for most pn-junction solar cells. The
On the Generalized Geometry Origin of Noncommutative Gauge Theory
Jurco, Branislav; Vysoky, Jan
2013-01-01
We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of D-branes.
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
MACCIA, ELIZABETH S.; AND OTHERS
AN ANNOTATED BIBLIOGRAPHY OF 20 ITEMS AND A DISCUSSION OF ITS SIGNIFICANCE WAS PRESENTED TO DESCRIBE CURRENT UTILIZATION OF SUBJECT THEORIES IN THE CONSTRUCTION OF AN EDUCATIONAL THEORY. ALSO, A THEORY MODEL WAS USED TO DEMONSTRATE CONSTRUCTION OF A SCIENTIFIC EDUCATIONAL THEORY. THE THEORY MODEL INCORPORATED SET THEORY (S), INFORMATION THEORY…
Kinetic theory of tearing instabilities
International Nuclear Information System (INIS)
Drake, J.F.; Lee, Y.C.
1977-01-01
The transition of the tearing instability from the collisional to the collisionless regime is investigated kinetically using a Fokker--Planck collision operator to represent electron-ion collisions. As a function of the collisionality of the plasma, the tearing instability falls into three regions, which are referred to as collisionless, semi-collisional, and collisional. The width Δ of the singular layer around kxB 0 =0 is limited by electron thermal motion along B 0 in the collisional and semi-collisional regimes and is typically smaller than rho/sub i/, the ion Larmor radius. Previously accepted theories, which are based on the assumption Δvery-much-greater-thanrho/sub i/, are found to be valid only in the collisional regime. The effects of density and temperature gradients on the instabilities are also studied. The tearing instability is only driven by the temperature gradient in the collisional and semi-collisional regimes. Numerical calculations indicate that the semi-collisional tearing instability is particularly relevant to present day high temperature tokamak discharges
The general theory of convolutional codes
Mceliece, R. J.; Stanley, R. P.
1993-01-01
This article presents a self-contained introduction to the algebraic theory of convolutional codes. This introduction is partly a tutorial, but at the same time contains a number of new results which will prove useful for designers of advanced telecommunication systems. Among the new concepts introduced here are the Hilbert series for a convolutional code and the class of compact codes.
Client-Controlled Case Information: A General System Theory Perspective
Fitch, Dale
2004-01-01
The author proposes a model for client control of case information via the World Wide Web built on principles of general system theory. It incorporates the client into the design, resulting in an information structure that differs from traditional human services information-sharing practices. Referencing general system theory, the concepts of…
A QCD Model Using Generalized Yang-Mills Theory
International Nuclear Information System (INIS)
Wang Dianfu; Song Heshan; Kou Lina
2007-01-01
Generalized Yang-Mills theory has a covariant derivative, which contains both vector and scalar gauge bosons. Based on this theory, we construct a strong interaction model by using the group U(4). By using this U(4) generalized Yang-Mills model, we also obtain a gauge potential solution, which can be used to explain the asymptotic behavior and color confinement.
A general theory of comic entertainment
DEFF Research Database (Denmark)
Grodal, Torben Kragh
2014-01-01
The article claims that comic entertainment consists of five elements 1. priming of the comic events to come 2. some comic entertainment inputs that creates arousal 3. Entertainment-internal signals of the playful nature of the comic input 4. Appraisal processes in audience members that evaluate...... the input as 'not real but playful', 5. this leads to a change in hedonic tone, and arousal is combined with the release of endorphins (a morphine-based neurotransmitter) that makes the arousal pleasant. The theory of comic entertainment accords with the PECMA flow theory proposed in Grodal: Embodied...... Visions, because the evaluation: playful, not real, influences the muscular directness towards the world that drops. Comic entertainment is further linked to human bonding....
Quantum theory and Einstein's general relativity
International Nuclear Information System (INIS)
Borzeszkowski, H.H.v.; Treder, H.J.
1984-01-01
The paper concerns Einstein's general relativity, wave mechanics and the quantization of Einstein's gravitation equations. The principle of equivalence and its association with both wave mechanics and quantum gravity, is discussed. (U.K.)
General Theory versus ENA Theory: Comparing Their Predictive Accuracy and Scope.
Ellis, Lee; Hoskin, Anthony; Hartley, Richard; Walsh, Anthony; Widmayer, Alan; Ratnasingam, Malini
2015-12-01
General theory attributes criminal behavior primarily to low self-control, whereas evolutionary neuroandrogenic (ENA) theory envisions criminality as being a crude form of status-striving promoted by high brain exposure to androgens. General theory predicts that self-control will be negatively correlated with risk-taking, while ENA theory implies that these two variables should actually be positively correlated. According to ENA theory, traits such as pain tolerance and muscularity will be positively associated with risk-taking and criminality while general theory makes no predictions concerning these relationships. Data from Malaysia and the United States are used to test 10 hypotheses derived from one or both of these theories. As predicted by both theories, risk-taking was positively correlated with criminality in both countries. However, contrary to general theory and consistent with ENA theory, the correlation between self-control and risk-taking was positive in both countries. General theory's prediction of an inverse correlation between low self-control and criminality was largely supported by the U.S. data but only weakly supported by the Malaysian data. ENA theory's predictions of positive correlations between pain tolerance, muscularity, and offending were largely confirmed. For the 10 hypotheses tested, ENA theory surpassed general theory in predictive scope and accuracy. © The Author(s) 2014.
General Open Systems Theory and the Substrata-Factor Theory of Reading.
Kling, Martin
This study was designed to extend the generality of the Substrata-Factor Theory by two methods of investigation: (1) theoretically, to est"blish the validity of the hypothesis that an isomorphic relationship exists between the Substrata-Factor Theory and the General Open Systems Theory, and (2) experimentally, to disc"ver through a…
Generalized Jacobi identities in gauge theories
International Nuclear Information System (INIS)
Chaves, F.M.P.
1990-01-01
A spatial generalized Jacobi identity obeyed by the polarization-dependent factors of the vertices in a q q-bar - Wγ process is studied. The amplitude of a scattering gluon-gluon with five particles is worked out. By reorganizing this amplitude in analogy with an interaction process photon-pion, the non existence of the spatial generalized Jacobi identity, but instead many spatial partial identities that compose themselves, in the case of a four particle process, in one single identity is shown. A process with four particles, three of them scalar fields, but in the one loop approximation is studied. In this case also, the non existence of the spatial generalized Jacobi identity is demonstrated. (author)
International Nuclear Information System (INIS)
Zhitnikov, V.V.; Ponomarev, V.N.
1986-01-01
An attempt is made to compare the solution of field equations, corresponding to quadratic equations for the fields (g μν , Γ μν α ) in gauge gravitation theory (GGT) with general relativity theory solutions. Without restrictions for a concrete type of metrics only solutions of equations, for which torsion turns to zero, are considered. Equivalence of vacuum equations of gauge quadratic theory of gravity and general relativity theory is proved using the Newman-Penrose formalism
Quantum Networks: General theory and applications
International Nuclear Information System (INIS)
Bisio, A.; D'Ariano, G. M.; Perinotti, P.; Chiribella, G.
2011-01-01
In this work we present a general mathematical framework to deal with Quantum Networks, i.e. networks resulting from the interconnection of elementary quantum circuits. The cornerstone of our approach is a generalization of the Choi isomorphism that allows one to efficiently represent any given Quantum Network in terms of a single positive operator. Our formalism allows one to face and solve many quantum information processing problems that would be hardly manageable otherwise, the most relevant of which are reviewed in this work: quantum process tomography, quantum cloning and learning of transformations, inversion of a unitary gate, information-disturbance tradeoff in estimating a unitary transformation, cloning and learning of a measurement device (Authors)
The general theory of quantized fields in the 1950s
International Nuclear Information System (INIS)
Wightman, A.S.
1989-01-01
This review describes developments in theoretical particle physics in the 1950s which were important in the race to develop a putative general theory of quantized fields, especially ideas that offered a mathematically rigorous theory. Basic theoretical concepts then available included the Hamiltonian formulation of quantum dynamics, canonical quantization, perturbative renormalization theory and the theory of distributions. Following a description of various important theoretical contributions of this era, the review ends with a summary of the most important contributions of axiomatic field theory to concrete physics applications. (UK)
Client-controlled case information: a general system theory perspective.
Fitch, Dale
2004-07-01
The author proposes a model for client control of case information via the World Wide Web built on principles of general system theory. It incorporates the client into the design, resulting in an information structure that differs from traditional human services information-sharing practices. Referencing general system theory, the concepts of controller and controlled system, as well as entropy and negentropy, are applied to the information flow and autopoietic behavior as they relate to the boundary-maintaining functions of today's organizations. The author's conclusions synthesize general system theory and human services values to lay the foundation for an information-sharing framework for human services in the 21st century.
Generalized Einstein-Aether theories and the Solar System
International Nuclear Information System (INIS)
Bonvin, Camille; Durrer, Ruth; Ferreira, Pedro G.; Zlosnik, Tom G.; Starkman, Glenn
2008-01-01
It has been shown that generalized Einstein-Aether theories may lead to significant modifications to the nonrelativistic limit of the Einstein equations. In this paper we study the effect of a general class of such theories on the Solar System. We consider corrections to the gravitational potential in negative and positive powers of distance from the source. Using measurements of the perihelion shift of Mercury and time delay of radar signals to Cassini, we place constraints on these corrections. We find that a subclass of generalized Einstein-Aether theories is compatible with these constraints
A general sensitivity theory for simulations of nonlinear systems
International Nuclear Information System (INIS)
Kenton, M.A.
1981-01-01
A general sensitivity theory is developed for nonlinear lumped-parameter system simulations. The point-of-departure is general perturbation theory, which has long been used for linear systems in nuclear engineering and reactor physics. The theory allows the sensitivity of particular figures-of-merit of the system behavior to be calculated with respect to any parameter.An explicit procedure is derived for applying the theory to physical systems undergoing sudden events (e.g., reactor scrams, tank ruptures). A related problem, treating figures-of-merit defined as functions of extremal values of system variables occurring at sudden events, is handled by the same procedure. The general calculational scheme for applying the theory to numerical codes is discussed. It is shown that codes which use pre-packaged implicit integration subroutines can be augmented to include sensitivity theory: a companion set of subroutines to solve the sensitivity problem is listed. This combined system analysis code is applied to a simple model for loss of post-accident heat removal in a liquid metal-cooled fast breeder reactor. The uses of the theory for answering more general sensitivity questions are discussed. One application of the theory is to systematically determine whether specific physical processes in a model contribute significantly to the figures-of-merit. Another application of the theory is for selecting parameter values which enable a model to match experimentally observed behavior
Quantum theory and Einstein's general relativity
International Nuclear Information System (INIS)
Borzeszkowski, H. von; Treder, H.
1982-01-01
We dicusss the meaning and prove the accordance of general relativity, wave mechanics, and the quantization of Einstein's gravitation equations themselves. Firstly, we have the problem of the influence of gravitational fields on the de Broglie waves, which influence is in accordance with Einstein's weak principle of equivalence and the limitation of measurements given by Heisenberg's uncertainty relations. Secondly, the quantization of the gravitational fields is a ''quantization of geometry.'' However, classical and quantum gravitation have the same physical meaning according to limitations of measurements given by Einstein's strong principle of equivalence and the Heisenberg uncertainties for the mechanics of test bodies
Theory of generalized Bessel functions: Pt. 2
International Nuclear Information System (INIS)
Dattoli, G.; Torre, A.; Chiccoli, C.
1991-01-01
In this paper the systematic study of the generalized Bessel functions (GBF), recently introduced and often encountered in problems of scattering for which the dipole approximation is inadequate, is continuated. The relations among different GBF are analysed and their importance for the solution of differential finite-difference equation of the Raman-Nath type is discussed. Numerical results for the first-kind cylinder GBF in the preasymptotic region and also a preliminary analysis of the asymptotic properties of the modified GBF are presented
The mathematical theory of general relativity
Katkar, L N
2014-01-01
This book is prepared for M. Sc. Students of Mathematics and Physics. The aim of writing this book is to give the reader a feeling for the necessity and beauty of the laws of general relativity. The contents of the book will attract both mathematicians and physicists which provides motivation and applications of many ideas and powerful mathematical methods of modern analysis and differential geometry. An attempt has been made to make the presentation comprehensive, rigorous and yet simple. Most calculations and transformations have been carried out in great detail. KEY FEATURE: Numerous solved examples using the well known mathematical techniques viz., the tensors and the differential forms in each chapter.
Lederman, Linda Costigan; Rogers, Don
The two papers in this document focus on general systems theory. In her paper, Linda Lederman discusses the emergence and evolution of general systems theory, defines its central concepts, and draws some conclusions regarding the nature of the theory and its value as an epistemology. Don Rogers, in his paper, relates some of the important features…
General algebraic theory of identical particle scattering
International Nuclear Information System (INIS)
Bencze, G.; Redish, E.F.
1978-01-01
We consider the nonrelativistic N-body scattering problem for a system of particles in which some subsets of the particles are identical. We demonstrate how the particle identity can be included in a general class of linear integral equations for scattering operators or components of scattering operators. The Yakubovskii, Yakubovskii--Narodestkii, Rosenberg, and Bencze--Redish--Sloan equations are included in this class. Algebraic methods are used which rely on the properties of the symmetry group of the system. Operators depending only on physically distinguishable labels are introduced and linear integral equations for them are derived. This procedure maximally reduces the number of coupled equations while retaining the connectivity properties of the original equations
Singularities in the general theory of relativity
International Nuclear Information System (INIS)
Treder, H.J.
1980-01-01
'Regular solutions of Einstein's equations' mean very different things. In the case of the empty-space equations, Rsub(ik) = o, such solutions must be metrics gsub(ik)(xsup(l)) without additionaly singular 'field sources' (Einstein's 'Particle problem'). However the 'phenomenological matter' is defined by the Einstein equations Rsub(ik) - 1/2gsub(ik)R = -kappaTsub(ik) itselves. Therefore if 10 regular functions gsub(ik)(xsup(l)) are given (which the inequalities of Lorentz-signature fulfil) then these gsub(ik) define 10 functions Tsub(ik)(xsup(l)) without singularities. But, the matter-tensor Tsub(ik) must fulfil the two inequalities T >= o, T 0 0 >= 1/2 T only and therefore the Einstein-equations with 'phenomenological matter' mean the two inequalities R >= o, R 0 0 <= o which are incompatible with a permanently regular metric with Lorentz-signature, generally. (author)
A theory of strong interactions ''from'' general relativity
International Nuclear Information System (INIS)
Caldirola, P.; Recami, E.
1979-01-01
In this paper a previous letter (where, among other things, a classical ''quark confinement'' was derived from general relativity plus dilatation-covariance), is completed by showing that the theory is compatible also with quarks ''asymptotic freedom''. Then -within a bi-scale theory of gravitational and strong interactions- a classical field theory is proposed for the (strong) interactions between hadrons. Various consequences are briefly analysed
Gauge theories under incorporation of a generalized uncertainty principle
International Nuclear Information System (INIS)
Kober, Martin
2010-01-01
There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of matter field equations like the Dirac equation. If there is postulated invariance of such a generalized field equation under local gauge transformations, the usual covariant derivative containing the gauge potential has to be replaced by a generalized covariant derivative. This leads to a generalized interaction between the matter field and the gauge field as well as to an additional self-interaction of the gauge field. Since the existence of a minimal length scale seems to be a necessary assumption of any consistent quantum theory of gravity, the gauge principle is a constitutive ingredient of the standard model, and even gravity can be described as gauge theory of local translations or Lorentz transformations, the presented extension of gauge theories appears as a very important consideration.
DSR Theories, Conformal Group and Generalized Commutation Relation
International Nuclear Information System (INIS)
Leiva, Carlos
2006-01-01
In this paper the relationship of DSR theories and Conformal Group is reviewed. On the other hand, the relation between DSR Magueijo Smolin generators and generalized commutation relations is also shown
JIT supply chain; an investigation through general system theory
Directory of Open Access Journals (Sweden)
O P Mishra
2013-03-01
Full Text Available This paper explains theoretical approach of the four theories of General system Theory (GST developed by Yourdon (1989 [Yourdon, E. (1989. Modern Structured Analysis. Yourdon Press, Prentice-Hall International, Englewood Cliffs, New Jersey. Senge] while applying it in information technology and subsequently used by caddy (2007 [Caddy I.N., & Helou, M.M. (2007. Supply chains and their management: Application of general systems theory. Journal of Retailing and Consumer Services, 14, 319–327.] in field of supply chain and management. JIT philosophy in core activities of supply chain i.e. procurement, production processes, and logistics are discussed through general system theory. The growing structure of the supply chain poses the implication restrictions and requires a heavy support system, many times a compromise is done while implementing JIT. The study would be useful to understand the general trends generated naturally regarding the adoption of the JIT philosophy in the supply chain.
A generalized theory of chromatography and multistep liquid extraction
Chizhkov, V. P.; Boitsov, V. N.
2017-03-01
A generalized theory of chromatography and multistep liquid extraction is developed. The principles of highly efficient processes for fine preparative separation of binary mixture components on a fixed sorbent layer are discussed.
Test theories of special relativity: a general critique
International Nuclear Information System (INIS)
Maciel, A.K.A.; Tiomno, J.
1988-01-01
Absolute Spacetime Theories conceived for the purpose of testing Special Relativity (SR) are reviewed. It is found that most theories proposed were in fact SR in different coordinate systems, since in general no specific SR violations were introduced. Models based on possible SR violating mechanisms are considered. Misconceptions in recently published papers are examined. (author) [pt
General Systems Theory Approaches to Organizations: Some Problems in Application
Peery, Newman S., Jr.
1975-01-01
Considers the limitations of General Systems Theory (GST) as a major paradigm within administrative theory and concludes that most systems formulations overemphasize growth and show little appreciation for intraorganizational conflict, diversity of values, and political action within organizations. Suggests that these limitations are mainly due to…
Get with the System: General Systems Theory for Business Officials.
Graczyk, Sandra L.
1993-01-01
An introduction to general systems theory and an overview of vocabulary and concepts are presented to introduce school business officials to systems thinking and to foster its use as an analytical tool. The theory is then used to analyze a sample problem: planning changes to a district's administrative computer system. (eight references) (MLF)
A simplified approach to general scalar-tensor theories
International Nuclear Information System (INIS)
Bloomfield, Jolyon
2013-01-01
The most general covariant action describing gravity coupled to a scalar field with only second order equations of motion, Horndeski's theory (also known as ''Generalized Galileons''), provides an all-encompassing model in which single scalar dark energy models may be constrained. However, the generality of the model makes it cumbersome to manipulate. In this paper, we demonstrate that when considering linear perturbations about a Friedmann-Robertson-Walker background, the theory is completely specified by only six functions of time, two of which are constrained by the background evolution. We utilise the ideas of the Effective Field Theory of Inflation/Dark Energy to explicitly construct these six functions of time in terms of the free functions appearing in Horndeski's theory. These results are used to investigate the behavior of the theory in the quasistatic approximation. We find that only four functions of time are required to completely specify the linear behavior of the theory in this limit, which can further be reduced if the background evolution is fixed. This presents a significantly reduced parameter space from the original presentation of Horndeski's theory, giving hope to the possibility of constraining the parameter space. This work provides a cross-check for previous work on linear perturbations in this theory, and also generalizes it to include spatial curvature
Generalized algebra-valued models of set theory
Löwe, B.; Tarafder, S.
2015-01-01
We generalize the construction of lattice-valued models of set theory due to Takeuti, Titani, Kozawa and Ozawa to a wider class of algebras and show that this yields a model of a paraconsistent logic that validates all axioms of the negation-free fragment of Zermelo-Fraenkel set theory.
General Strain Theory, Peer Rejection, and Delinquency/Crime
Higgins, George E.; Piquero, Nicole L.; Piquero, Alex R.
2011-01-01
The development of general strain theory (GST) has led to a renewed focus on the influence of negative life experiences on antisocial behavior. Although a number of studies have generated an impressive array of support for the theory, several avenues remain open for research. In this article, we examine how a specific noxious stimuli, peer…
A generalized theory of preferential linking
Hu, Haibo; Guo, Jinli; Liu, Xuan; Wang, Xiaofan
2014-12-01
There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How do various preferential linking mechanisms produce networks with different features? In this paper we first empirically study preferential linking phenomena in an evolving online social network, find and validate the linear preference. We propose an analyzable model which captures the real growth process of the network and reveals the underlying mechanism dominating its evolution. Furthermore based on preferential linking we propose a generalized model reproducing the evolution of online social networks, and present unified analytical results describing network characteristics for 27 preference scenarios. We study the mathematical structure of degree distributions and find that within the framework of preferential linking analytical degree distributions can only be the combinations of finite kinds of functions which are related to rational, logarithmic and inverse tangent functions, and extremely complex network structure will emerge even for very simple sublinear preferential linking. This work not only provides a verifiable origin for the emergence of various network characteristics in social networks, but bridges the micro individuals' behaviors and the global organization of social networks.
A general theory for gauge-free lifting
International Nuclear Information System (INIS)
Morrison, P. J.
2013-01-01
A theory for lifting equations of motion for charged particle dynamics, subject to given electromagnetic like forces, up to a gauge-free system of coupled Hamiltonian Vlasov-Maxwell like equations is given. The theory provides very general expressions for the polarization and magnetization vector fields in terms of the particle dynamics description of matter. Thus, as is common in plasma physics, the particle dynamics replaces conventional constitutive relations for matter. Several examples are considered including the usual Vlasov-Maxwell theory, a guiding center kinetic theory, Vlasov-Maxwell theory with the inclusion of spin, and a Vlasov-Maxwell theory with the inclusion of Dirac's magnetic monopoles. All are shown to be Hamiltonian field theories and the Jacobi identity is proven directly.
A generalization of the Newton-Cartan theory of gravitation
International Nuclear Information System (INIS)
Nitsure, Nitin
1980-01-01
It is shown that even in the absence of the equivalence principle, the Newtonian theory of gravitation can be given a geometric form in a five-dimensional manifold. The fifth dimension is taken as the ratio of gravitational and inertial mass, which is allowed to be different for different particles. The resulting pondoromotive and field equations in this 5-dimensional space (which are generalizations of Cartan's formulation of Newtonian gravitation) are formulated and their consequences are discussed. It is argued that as general relativity is a 'metric' theory, a similar generalization of general relativity is not possible. (author)
On the mathematical theory of classical fields and general relativity
Klainerman, S
1993-01-01
From the perspective of an analyst, like myself, the General Theory of Relativity provides an extrordinary rich and vastly virgin territory. It is the aim of my lecture to provide, ﬁrst, an account of those aspects of the theory which attract me most and second a perspective of what has been accomplished so far in that respect. In trying to state our main objectives it helps to view General Relativity in the broader context of Classical Field Theory. EinsteiniVacuum equations, or shortly E—V, is already sufﬁciently complicated. I will thus restrict my attention to them.
Implementation of static generalized perturbation theory for LWR design applications
International Nuclear Information System (INIS)
Byron, R.F.; White, J.R.
1987-01-01
A generalized perturbation theory (GPT) formulation is developed for application to light water reactor (LWR) design. The extensions made to standard generalized perturbation theory are the treatment of thermal-hydraulic and fission product poisoning feedbacks, and criticality reset. This formulation has been implemented into a standard LWR design code. The method is verified by comparing direct calculations with GPT calculations. Data are presented showing that feedback effects need to be considered when using GPT for LWR problems. Some specific potential applications of this theory to the field of LWR design are discussed
Do People Use Their Implicit Theories of Creativity as General Theories?
Lee, Hong; Kim, Jungsik; Ryu, Yeonjae; Song, Seokjong
2015-01-01
This study examines whether people use the general implicit theories of creativity or not when applying them to themselves and others. On the basis of the actor-observer asymmetry theory, the authors propose that conception of creativity would be differently constructed depending on the targets of attention: general, self, and other. Three studies…
Sequential approach to Colombeau's theory of generalized functions
International Nuclear Information System (INIS)
Todorov, T.D.
1987-07-01
J.F. Colombeau's generalized functions are constructed as equivalence classes of the elements of a specially chosen ultrapower of the class of the C ∞ -functions. The elements of this ultrapower are considered as sequences of C ∞ -functions, so in a sense, the sequential construction presented here refers to the original Colombeau theory just as, for example, the Mikusinski sequential approach to the distribution theory refers to the original Schwartz theory of distributions. The paper could be used as an elementary introduction to the Colombeau theory in which recently a solution was found to the problem of multiplication of Schwartz distributions. (author). Refs
Sp(2) covariant quantisation of general gauge theories
Energy Technology Data Exchange (ETDEWEB)
Vazquez-Bello, J L
1994-11-01
The Sp(2) covariant quantization of gauge theories is studied. The geometrical interpretation of gauge theories in terms of quasi principal fibre bundles Q(M{sub s}, G{sub s}) is reviewed. It is then described the Sp(2) algebra of ordinary Yang-Mills theory. A consistent formulation of covariant Lagrangian quantisation for general gauge theories based on Sp(2) BRST symmetry is established. The original N = 1, ten dimensional superparticle is considered as an example of infinitely reducible gauge algebras, and given explicitly its Sp(2) BRST invariant action. (author). 18 refs.
Sp(2) covariant quantisation of general gauge theories
International Nuclear Information System (INIS)
Vazquez-Bello, J.L.
1994-11-01
The Sp(2) covariant quantization of gauge theories is studied. The geometrical interpretation of gauge theories in terms of quasi principal fibre bundles Q(M s , G s ) is reviewed. It is then described the Sp(2) algebra of ordinary Yang-Mills theory. A consistent formulation of covariant Lagrangian quantisation for general gauge theories based on Sp(2) BRST symmetry is established. The original N = 1, ten dimensional superparticle is considered as an example of infinitely reducible gauge algebras, and given explicitly its Sp(2) BRST invariant action. (author). 18 refs
Generalization of the test theory of relativity to noninertial frames
International Nuclear Information System (INIS)
Abolghasem, G.H.; Khajehpour, M.R.H.; Mansouri, R.
1988-08-01
We present a generalized test theory of special relativity, using a noninertial frame. Within the framework of the special theory of relativity the transport- and Einstein-synchronizations are equivalent on a rigidly rotating disk. But in any theory with a preferred frame such an equivalence does not hold. The time difference resulting from the two synchronization procedures is a measurable quantity within the reach of existing clock systems on the earth. The final result contains a term which depends on the angular velocity of the rotating system, and hence measures an absolute effect. This term is of crucial importance in our test theory of the special relativity. (author). 13 refs
Equivalence of the theories of reciprocity and general relativity
International Nuclear Information System (INIS)
Qadir, A.
1976-01-01
Khan's theory (Nuovo Cimento; 57B:321 (1968) and Int. J. Theor. Phys.; 6:383 (1972)) of reciprocity has been shown to be equivalent to the theory of general relativity (in a conformally flat space-time) in that the same predictions are made physically. It is is proved that, since 'centrifugal forces' are used by Khan, gravitational phenomena are being considered equal in status to electromagnetic phenomena, and hence the difference claimed to exist between Milne's theory and Khan's theory disappears. (author)
Grima, R
2010-07-21
Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the
Evolution of curvature perturbation in generalized gravity theories
International Nuclear Information System (INIS)
Matsuda, Tomohiro
2009-01-01
Using the cosmological perturbation theory in terms of the δN formalism, we find the simple formulation of the evolution of the curvature perturbation in generalized gravity theories. Compared with the standard gravity theory, a crucial difference appears in the end-boundary of the inflationary stage, which is due to the non-ideal form of the energy-momentum tensor that depends explicitly on the curvature scalar. Recent study shows that ultraviolet-complete quantum theory of gravity (Horava-Lifshitz gravity) can be approximated by using a generalized gravity action. Our paper may give an important step in understanding the evolution of the curvature perturbation during inflation, where the energy-momentum tensor may not be given by the ideal form due to the corrections from the fundamental theory.
Whiteheadian approach to quantum theory and the generalized bell's theorem
International Nuclear Information System (INIS)
Stapp, H.P.
1979-01-01
The model of the world proposed by Whitehead provides a natural theoretical framework in which to imbed quantum theory. This model accords with the ontological ideas of Heisenberg, and also with Einstein's view that physical theories should refer nominally to the objective physical situation, rather than our knowledge of that system. Whitehead imposed on his model the relativistic requirement that what happens in any given spacetime region be determined only by what has happened in its absolute past, i.e., in the backward light-cone drawn from that region. This requirement must be modified, for it is inconsistent with the implications of quantum theory expressed by a generalized version of Bell's theorem. Revamping the causal spacetime structure of the Whitehead-Heisenberg ontology to bring it into accord with the generalized Bell's theorem creates the possibility of a nonlocal causal covariant theory that accords with the statistical prediction of quantum theory
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
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
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)
A comparative study of the tail ion distribution with reduced Fokker-Planck models
McDevitt, C. J.; Tang, Xian-Zhu; Guo, Zehua; Berk, H. L.
2014-03-01
A series of reduced models are used to study the fast ion tail in the vicinity of a transition layer between plasmas at disparate temperatures and densities, which is typical of the gas and pusher interface in inertial confinement fusion targets. Emphasis is placed on utilizing progressively more comprehensive models in order to identify the essential physics for computing the fast ion tail at energies comparable to the Gamow peak. The resulting fast ion tail distribution is subsequently used to compute the fusion reactivity as a function of collisionality and temperature. While a significant reduction of the fusion reactivity in the hot spot compared to the nominal Maxwellian case is present, this reduction is found to be partially recovered by an increase of the fusion reactivity in the neighboring cold region.
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
Multigroup Boltzmann-Fokker-Planck approach for ion transport in amorphous media
Energy Technology Data Exchange (ETDEWEB)
Keen, N.D.; Prinja, A.K.; Dunham, G.D. [New Mexico Univ., Albuquerque, NM (United States). Chemical and Nuclear Engineering Dept.
2001-07-01
We present a MGMC approach for the transport of arbitrary mass ions having energies up to a few MeV. Specifically, we consider interactions with target atoms through Coulomb mediated elastic nuclear and inelastic electronic collisions and restrict considerations to ion implantation and energy deposition of primary ions in amorphous media. (orig.)
Fokker-Planck simulations of interactions of femtosecond laser pulses with dense plasmas
International Nuclear Information System (INIS)
Drska, L.; Limpouch, J.; Liska, R.
1993-01-01
The interaction of femtosecond laser pulses with fully ionized solid-state density plasmas in the regime of the normal skin effect was investigated by means of numerical simulation. For short wavelength lasers and 120 fs FWHM laser pulses the regime of normal skin effect is shown to hold for peak intensities up to 10 17 W/cm 2 . Basic characteristics of the interaction are revealed and certain departures of the electron distribution function, of the plasma dielectric constant and of laser absorption from simplistic models are pointed out. (author) 1 tab., 4 figs., 14 refs
Generalized force in classical field theory. [Euler-Lagrange equations
Energy Technology Data Exchange (ETDEWEB)
Krause, J [Universidad Central de Venezuela, Caracas
1976-02-01
The source strengths of the Euler-Lagrange equations, for a system of interacting fields, are heuristically interpreted as generalized forces. The canonical form of the energy-momentum tensor thus consistently appears, without recourse to space-time symmetry arguments. A concept of 'conservative' generalized force in classical field theory is also briefly discussed.
Theory of mind: A foundational component of human general intelligence.
Estes, David; Bartsch, Karen
2017-01-01
To understand the evolution of general intelligence, Burkart et al. endorse a "cultural intelligence approach," which emphasizes the critical importance of social interaction. We argue that theory of mind provides an essential foundation and shared perspective for the efficient ontogenetic transmission of crucial knowledge and skills during human development and, together with language, can account for superior human general intelligence.
Iz ''general relativity'' necessary for the Einstein gravitation theory gravitation theory
International Nuclear Information System (INIS)
Bondi, G.
1982-01-01
Main principles of relativity and gravitation theories are deeply analyzed. Problems of boundaries of applicability for these theories and possible ways of their change and generalization are discussed. It is shown that the notion of general relativity does not introduce any post-newton physics - it only deals with coordinate transformations. It is supposed that ''general relativity'' is a physically senseless phrase which can be considered only as a historical remainder of an interesting philosophic discourse. The paper reveals that there exists appropriate physical substantiation of the Einstein gravitation theory not including a physically senseless concept of general relativity and promoting its fundamental relations with the experiment
Derivation of Einstein-Cartan theory from general relativity
Petti, Richard
2015-04-01
General relativity cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum. Einstein-Cartan theory fixes this problem in the least invasive way. In the late 20th century, the consensus view was that Einstein-Cartan theory requires inclusion of torsion without adequate justification, it has no empirical support (though it doesn't conflict with any known evidence), it solves no important problem, and it complicates gravitational theory with no compensating benefit. In 1986 the author published a derivation of Einstein-Cartan theory from general relativity, with no additional assumptions or parameters. Starting without torsion, Poincaré symmetry, classical or quantum spin, or spinors, it derives torsion and its relation to spin from a continuum limit of general relativistic solutions. The present work makes the case that this computation, combined with supporting arguments, constitutes a derivation of Einstein-Cartan theory from general relativity, not just a plausibility argument. This paper adds more and simpler explanations, more computational details, correction of a factor of 2, discussion of limitations of the derivation, and discussion of some areas of gravitational research where Einstein-Cartan theory is relevant.
On the relation of the theoretical foundations of quantum theory and general relativity theory
International Nuclear Information System (INIS)
Kober, Martin
2010-01-01
The specific content of the present thesis is presented in the following way. First the most important contents of quantum theory and general relativity theory are presented. In connection with the general relativity theory the mathematical property of the diffeomorphism invariance plays the deciding role, while concerning the quantum theory starting from the Copenhagen interpretation first the measurement problem is treated, before basing on the analysis of concrete phenomena and the mathematical apparatus of quantum theory the nonlocality is brought into focus as an important property. This means that both theories suggest a relationalistic view of the nature of the space. This analysis of the theoretical foundations of quantum theory and general relativity theory in relation to the nature of the space obtains only under inclusion of Kant's philosophy and his analysis of the terms space and time as fundamental forms of perception its full persuasive power. Then von Weizsaeckers quantum theory of the ur-alternatives is presented. Finally attempts are made to apply the obtained knowledge to the question of the quantum-theoretical formulation of general relativity theory.
Analysis of General Power Counting Rules in Effective Field Theory
Gavela, B M; Manohar, A V; Merlo, L
2016-01-01
We derive the general counting rules for a quantum effective field theory (EFT) in $\\mathsf{d}$ dimensions. The rules are valid for strongly and weakly coupled theories, and predict that all kinetic energy terms are canonically normalized. They determine the energy dependence of scattering cross sections in the range of validity of the EFT expansion. The size of cross sections is controlled by the $\\Lambda$ power counting of EFT, not by chiral counting, even for chiral perturbation theory ($\\chi$PT). The relation between $\\Lambda$ and $f$ is generalized to $\\mathsf{d}$ dimensions. We show that the naive dimensional analysis $4\\pi$ counting is related to $\\hbar$ counting. The EFT counting rules are applied to $\\chi$PT, to Standard Model EFT and to the non-trivial case of Higgs EFT, which combines the $\\Lambda$ and chiral counting rules within a single theory.
General theory of light propagation and imaging through the atmosphere
McKechnie, T Stewart
2016-01-01
This book lays out a new, general theory of light propagation and imaging through Earth’s turbulent atmosphere. Current theory is based on the – now widely doubted – assumption of Kolmogorov turbulence. The new theory is based on a generalized atmosphere, the turbulence characteristics of which can be established, as needed, from readily measurable properties of point-object, or star, images. The pessimistic resolution predictions of Kolmogorov theory led to lax optical tolerance prescriptions for large ground-based astronomical telescopes which were widely adhered to in the 1970s and 1980s. Around 1990, however, it became clear that much better resolution was actually possible, and Kolmogorov tolerance prescriptions were promptly abandoned. Most large telescopes built before 1990 have had their optics upgraded (e.g., the UKIRT instrument) and now achieve, without adaptive optics (AO), almost an order of magnitude better resolution than before. As well as providing a more comprehensive and precise under...
A Thermodynamically General Theory for Convective Circulations and Vortices
Renno, N. O.
2007-12-01
Convective circulations and vortices are common features of atmospheres that absorb low-entropy-energy at higher temperatures than they reject high-entropy-energy to space. These circulations range from small to planetary-scale and play an important role in the vertical transport of heat, momentum, and tracer species. Thus, the development of theoretical models for convective phenomena is important to our understanding of many basic features of planetary atmospheres. A thermodynamically general theory for convective circulations and vortices is proposed. The theory includes irreversible processes and quantifies the pressure drop between the environment and any point in a convective updraft. The article's main result is that the proposed theory provides an expression for the pressure drop along streamlines or streamtubes that is a generalization of Bernoulli's equation to convective circulations. We speculate that the proposed theory not only explains the intensity, but also shed light on other basic features of convective circulations and vortices.
Chiral perturbation theory for nucleon generalized parton distributions
Energy Technology Data Exchange (ETDEWEB)
Diehl, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Manashov, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik]|[Sankt-Petersburg State Univ. (Russian Federation). Dept. of Theoretical Physics; Schaefer, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik
2006-08-15
We analyze the moments of the isosinglet generalized parton distributions H, E, H, E of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. We discuss in detail the construction of the operators in the effective theory that are required to obtain all corrections to a given order in the chiral power counting. The results will serve to improve the extrapolation of lattice results to the chiral limit. (orig.)
Classical Belief Conditioning and its Generalization to DSm Theory
Czech Academy of Sciences Publication Activity Database
Daniel, Milan
2008-01-01
Roč. 2, č. 4 (2008), s. 267-279 ISSN 1752-8917 R&D Projects: GA AV ČR 1ET100300419 Institutional research plan: CEZ:AV0Z10300504 Keywords : belief functions * Dempster-Shafer theory * belief conditioning * DSm theory * overlapping elements * hyper-power set * DSm model Subject RIV: BA - General Mathematics http://www.worldacademicunion.com/journal/jus/jusVol02No4paper04.pdf
General coupled mode theory in non-Hermitian waveguides.
Xu, Jing; Chen, Yuntian
2015-08-24
In the presence of loss and gain, the coupled mode equation on describing the mode hybridization of various waveguides or cavities, or cavities coupled to waveguides becomes intrinsically non-Hermitian. In such non-Hermitian waveguides, the standard coupled mode theory fails. We generalize the coupled mode theory with a properly defined inner product based on reaction conservation. We apply our theory to the non-Hermitian parity-time symmetric waveguides, and obtain excellent agreement with results obtained by finite element fullwave simulations. The theory presented here is typically formulated in space to study coupling between waveguides, which can be transformed into time domain by proper reformulation to study coupling between non-Hermitian resonators. Our theory has the strength of studying non-Hermitian optical systems with inclusion of the full vector fields, thus is useful to study and design non-Hermitian devices that support asymmetric and even nonreciprocal light propagations.
Indefinite-metric quantum field theory of general relativity
International Nuclear Information System (INIS)
Nakanishi, Noboru
1978-01-01
Quantum field theory of Einstein's general relativity is formulated in the indefinitemetric Hilbert space in such a way that asymptotic fields are manifestly Lorentz covariant and the physical S-matrix is unitary. The general coordinate transformation is transcribed into a q-number transformation, called the BRS transformation. Its abstract definition is presented on the basis of the BRS transformation for the Yang-Mills theory. The BRS transformation for general relativity is then explicitly constructed. The gauge-fixing Lagrangian density and the Faddeev-Popov one are introduced in such a way that their sum behaves like a scalar density under the BRS transformation. One can then proceed in the same way as in the Kugo-Ojima formalism of the Yang-Mills theory to establish the unitarity of the physical S-matrix. (author)
Some remarks on general covariance of quantum theory
International Nuclear Information System (INIS)
Schmutzer, E.
1977-01-01
If one accepts Einstein's general principle of relativity (covariance principle) also for the sphere of microphysics (quantum, mechanics, quantum field theory, theory of elemtary particles), one has to ask how far the fundamental laws of traditional quantum physics fulfil this principle. Attention is here drawn to a series of papers that have appeared during the last years, in which the author criticized the usual scheme of quantum theory (Heisenberg picture, Schroedinger picture etc.) and presented a new foundation of the basic laws of quantum physics, obeying the 'principle of fundamental covariance' (Einstein's covariance principle in space-time and covariance principle in Hilbert space of quantum operators and states). (author)
General quadratic gauge theory: constraint structure, symmetries and physical functions
Energy Technology Data Exchange (ETDEWEB)
Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V [Lebedev Physics Institute, Moscow (Russian Federation)
2005-06-17
How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation to specific features of the theory in the Lagrangian formulation, especially relate the constraint structure to the gauge transformation structure of the Lagrangian action? How can we construct the general expression for the gauge charge if the constraint structure in the Hamiltonian formulation is known? Whether we can identify the physical functions defined as commuting with first-class constraints in the Hamiltonian formulation and the physical functions defined as gauge invariant functions in the Lagrangian formulation? The aim of the present paper is to consider the general quadratic gauge theory and to answer the above questions for such a theory in terms of strict assertions. To fulfil such a programme, we demonstrate the existence of the so-called superspecial phase-space variables in terms of which the quadratic Hamiltonian action takes a simple canonical form. On the basis of such a representation, we analyse a functional arbitrariness in the solutions of the equations of motion of the quadratic gauge theory and derive the general structure of symmetries by analysing a symmetry equation. We then use these results to identify the two definitions of physical functions and thus prove the Dirac conjecture.
String theory compactifications with fluxes, and generalized geometry
International Nuclear Information System (INIS)
Cassani, D.
2009-06-01
The topic of this thesis is compactifications in string theory and supergravity. We study dimensional reductions of type II theories on backgrounds with fluxes, using the techniques of Hitchin's generalized geometry. We start with an introduction of the needed mathematical tools, focusing on SU(3)xSU(3) structures on the generalized tangent bundle T+T * , and analyzing their deformations. Next we study the four dimensional N equals 2 gauged supergravity which can be defined reducing type II theories on SU(3)*SU(3) structure backgrounds with general NSNS and RR fluxes: we establish the complete bosonic action, and we show how its data are related to the generalized geometry formalism on T+T * . In particular, we derive a geometric expression for the full N = 2 scalar potential. Then we focus on the relations between the 10d and 4d descriptions of supersymmetric flux backgrounds: we spell out the N = 1 vacuum conditions within the 4d N = 2 theory, as well as from its N = 1 truncation, and we establish a precise matching with the equations characterizing the N = 1 backgrounds at the ten dimensional level. We conclude by presenting some concrete examples, based on coset spaces with SU(3) structure. We establish for these spaces the consistency of the truncation based on left-invariance, and we explore the landscape of vacua of the corresponding theory, taking string loop corrections into account. (author)
The theory of stochastic cosmological lensing
Energy Technology Data Exchange (ETDEWEB)
Fleury, Pierre; Uzan, Jean-Philippe [Institut d' Astrophysique de Paris, UMR 7095 du CNRS, 98 bis Bd Arago, 75014 Paris (France); Larena, Julien, E-mail: fleury@iap.fr, E-mail: j.larena@ru.ac.za, E-mail: uzan@iap.fr [Department of Mathematics, Rhodes University, Grahamstown 6140 (South Africa)
2015-11-01
On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show an explicit example of the involved calculations; (2) check the validity of the method against both ray-tracing simulations and direct numerical integration of the Langevin equation. As a byproduct, we obtain a post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal distortions on the angular distance, in excellent agreement with numerical results. Besides, the dispersion of the angular distance is correctly reproduced in some regimes.
Unification of General Relativity with Quantum Field Theory
International Nuclear Information System (INIS)
Ni Jun
2011-01-01
In the frame of quantum field theory, instead of using the action principle, we deduce the Einstein equation from purely the general covariant principle and the homogeneity of spacetime. The Einstein equation is shown to be the gauge equation to guarantee the local symmetry of spacetime translation. Gravity is an apparent force due to the curvature of spacetime resulted from the conservation of energy-momentum. In the action of quantum field theory, only electroweak-strong interactions should be considered with the curved spacetime metric determined by the Einstein equation. (general)
General Relativistic Mean Field Theory for rotating nuclei
Energy Technology Data Exchange (ETDEWEB)
Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki
1998-03-01
The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)
General relativity and gauge gravity theories of higher order
International Nuclear Information System (INIS)
Konopleva, N.P.
1998-01-01
It is a short review of today's gauge gravity theories and their relations with Einstein General Relativity. The conceptions of construction of the gauge gravity theories with higher derivatives are analyzed. GR is regarded as the gauge gravity theory corresponding to the choice of G ∞4 as the local gauge symmetry group and the symmetrical tensor of rank two g μν as the field variable. Using the mathematical technique, single for all fundamental interactions (namely variational formalism for infinite Lie groups), we can obtain Einstein's theory as the gauge theory without any changes. All other gauge approaches lead to non-Einstein theories of gravity. But above-mentioned mathematical technique permits us to construct the gauge gravity theory of higher order (for instance SO (3,1)-gravity) so that all vacuum solutions of Einstein equations are the solutions of the SO (3,1)-gravity theory. The structure of equations of SO(3,1)-gravity becomes analogous to Weeler-Misner geometrodynamics one
Keynes's theories of money and banking in the Treatise and The General Theory
John Smithin
2013-01-01
This paper identifies what seem to have been the five main issues in contention in monetary theory, both historically and in the current era, and discusses the view that J.M. Keynes took on each of them in the Treatise on Money and The General Theory. The key issues in monetary theory are the ontology of money, endogenous versus exogenous money, interest-rate determination, the choice of the monetary policy instrument, and the neutrality versus non-neutrality of money.
On generally covariant quantum field theory and generalized causal and dynamical structures
International Nuclear Information System (INIS)
Bannier, U.
1988-01-01
We give an example of a generally covariant quasilocal algebra associated with the massive free field. Maximal, two-sided ideals of this algebra are algebraic representatives of external metric fields. In some sense, this algebra may be regarded as a concrete realization of Ekstein's ideas of presymmetry in quantum field theory. Using ideas from our example and from usual algebraic quantum field theory, we discuss a generalized scheme, in which maximal ideals are viewed as algebraic representatives of dynamical equations or Lagrangians. The considered frame is no quantum gravity, but may lead to further insight into the relation between quantum theory and space-time geometry. (orig.)
General time-dependent formulation of quantum scattering theory
International Nuclear Information System (INIS)
Althorpe, Stuart C.
2004-01-01
We derive and explain the key ideas behind a time-dependent formulation of quantum scattering theory, applicable generally to systems with a finite-range scattering potential. The scattering is initiated and probed by plane wave packets, which are localized just outside the range of the potential. The asymptotic limits of conventional scattering theory (initiation in the remote past; detection in the remote future) are not taken. Instead, the differential cross section (DCS) is obtained by projecting the scattered wave packet onto the probe plane wave packets. The projection also yields a time-dependent version of the DCS. Cuts through the wave packet, just as it exits the scattering potential, yield time-dependent and time-independent angular distributions that give a close-up picture of the scattering which complements the DCS. We have previously applied the theory to interpret experimental cross sections of chemical reactions [e.g., S. C. Althorpe, F. Fernandez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. This paper gives the derivation of the theory, and explains its relation to conventional scattering theory. For clarity, the derivation is restricted to spherical-particle scattering, though it may readily be extended to general multichannel systems. We illustrate the theory using a simple application to hard-sphere scattering
Generalized perturbation theory (GPT) methods. A heuristic approach
International Nuclear Information System (INIS)
Gandini, A.
1987-01-01
Wigner first proposed a perturbation theory as early as 1945 to study fundamental quantities such as the reactivity worths of different materials. The first formulation, CPT, for conventional perturbation theory is based on universal quantum mechanics concepts. Since that early conception, significant contributions have been made to CPT, in particular, Soodak, who rendered a heuristic interpretation of the adjoint function, (referred to as the GPT method for generalized perturbation theory). The author illustrates the GPT methodology in a variety of linear and nonlinear domains encountered in nuclear reactor analysis. The author begins with the familiar linear neutron field and then generalizes the methodology to other linear and nonlinear fields, using heuristic arguments. The author believes that the inherent simplicity and elegance of the heuristic derivation, although intended here for reactor physics problems might be usefully adopted in collateral fields and includes such examples
Generalized ensemble theory with non-extensive statistics
Shen, Ke-Ming; Zhang, Ben-Wei; Wang, En-Ke
2017-12-01
The non-extensive canonical ensemble theory is reconsidered with the method of Lagrange multipliers by maximizing Tsallis entropy, with the constraint that the normalized term of Tsallis' q -average of physical quantities, the sum ∑ pjq, is independent of the probability pi for Tsallis parameter q. The self-referential problem in the deduced probability and thermal quantities in non-extensive statistics is thus avoided, and thermodynamical relationships are obtained in a consistent and natural way. We also extend the study to the non-extensive grand canonical ensemble theory and obtain the q-deformed Bose-Einstein distribution as well as the q-deformed Fermi-Dirac distribution. The theory is further applied to the generalized Planck law to demonstrate the distinct behaviors of the various generalized q-distribution functions discussed in literature.
Anisotropic cosmological models and generalized scalar tensor theory
Indian Academy of Sciences (India)
Abstract. In this paper generalized scalar tensor theory has been considered in the background of anisotropic cosmological models, namely, axially symmetric Bianchi-I, Bianchi-III and Kortowski–. Sachs space-time. For bulk viscous fluid, both exponential and power-law solutions have been stud- ied and some assumptions ...
Anisotropic cosmological models and generalized scalar tensor theory
Indian Academy of Sciences (India)
In this paper generalized scalar tensor theory has been considered in the background of anisotropic cosmological models, namely, axially symmetric Bianchi-I, Bianchi-III and Kortowski–Sachs space-time. For bulk viscous ﬂuid, both exponential and power-law solutions have been studied and some assumptions among the ...
Variational analysis and generalized differentiation I basic theory
Mordukhovich, Boris S
2006-01-01
Contains a study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces. This title presents many applications to problems in optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, and more.
An experiment designed to verify the general theory of relativity
International Nuclear Information System (INIS)
Surdin, Maurice
1960-01-01
The project for an experiment which uses the effect of gravitation on Maser-type clocks placed on the ground at two different heights and which is designed to verify the general theory of relativity. Reprint of a paper published in Comptes rendus des seances de l'Academie des Sciences, t. 250, p. 299-301, sitting of 11 January 1960 [fr
Anmeldelse: Whitney Davis A General Theory of Visual Culture
DEFF Research Database (Denmark)
Michelsen, Anders Ib
2012-01-01
Whitney Davis bog A General Theory of Visual Culture vil utvivlsomt blive opfattet som en provokation af mange deltagere i forskningsdebatterne om visuel kultur. At basere en »generel« teori om visuel kultur – dvs. en teori, som benytter sig af termer som »visualitet« – på et kerneargument de facto...
Application of generalized perturbation theory to flux disadvantage factor calculations
International Nuclear Information System (INIS)
Sallam, O.H.; Akimov, I.S.; Naguib, K.; Hamouda, I.
1979-01-01
The possibility of using the generalized perturbation theory to calculate the perturbation of the flux disadvantage factors of reactor cell, resulting from the variation of the cell parameters, is studied. For simplicity the one-group diffusion approximation is considered. All necessary equations are derived for variations both of the cell dimensions. Numerical results are presented in the paper
Gender, General Strain Theory, Negative Emotions, and Disordered Eating
Piquero, Nicole Leeper; Fox, Kristan; Piquero, Alex R.; Capowich, George; Mazerolle, Paul
2010-01-01
Much of the prior work on General Strain Theory (GST) has focused on how strain and negative emotions interrelate to produce criminal--especially violent--activity. Very little research has extended GST to examine other types of non-criminal, negative behavior, such as self-harming behaviors associated with disordered eating, a traditionally…
On the general theory of thermo-elastic friction
Alblas, J.B.
1961-01-01
A theory of the thermo-elastic dissipation in vibrating bodies is developed, starting from the three-dimensional thermo-elastic equations. After a discussion of the basic thermodynamical foundations, some general considerations on the problem of the conversion of mechanical energy into heat are
An Application of General System Theory (GST) to Group Therapy.
Matthews, Charles O.
1992-01-01
Demonstrates the compatibility of General System Theory (GST) with the traditional counseling literature in explicating a therapy group's progression through Tuckman's (1965, 1977) developmental stages (forming, storming, norming, performing, and adjourning). Description uses both traditional group literature and GST concepts. (Author/NB)
What Should Instructional Designers Know about General Systems Theory?
Salisbury, David F.
1989-01-01
Describes basic concepts in the field of general systems theory (GST) and explains the relationship between instructional systems design (ISD) and GST. Benefits of integrating GST into the curriculum of ISD graduate programs are discussed, and a short bibliography on GST is included. (LRW)
Indefinite-metric quantum field theory of general relativity, 2
International Nuclear Information System (INIS)
Nakanishi, Noboru
1978-01-01
The canonical commutation relations are analyzed in detail in the manifestly covariant quantum field theory of general relativity proposed previously. It is explicitly proved that the BRS charge is indeed the generator of the BRS transformation both in the Landau gauge and in the non-Landau one. The equivalence between the field equations and the Heisenberg equations is confirmed. (author)
Membrane models and generalized Z2 gauge theories
International Nuclear Information System (INIS)
Lowe, M.J.; Wallace, D.J.
1980-01-01
We consider models of (d-n)-dimensional membranes fluctuating in a d-dimensional space under the action of surface tension. We investigate the renormalization properties of these models perturbatively and in 1/n expansion. The potential relationships of these models to generalized Z 2 gauge theories are indicated. (orig.)
A general mixture theory. I. Mixtures of spherical molecules
Hamad, Esam Z.
1996-08-01
We present a new general theory for obtaining mixture properties from the pure species equations of state. The theory addresses the composition and the unlike interactions dependence of mixture equation of state. The density expansion of the mixture equation gives the exact composition dependence of all virial coefficients. The theory introduces multiple-index parameters that can be calculated from binary unlike interaction parameters. In this first part of the work, details are presented for the first and second levels of approximations for spherical molecules. The second order model is simple and very accurate. It predicts the compressibility factor of additive hard spheres within simulation uncertainty (equimolar with size ratio of three). For nonadditive hard spheres, comparison with compressibility factor simulation data over a wide range of density, composition, and nonadditivity parameter, gave an average error of 2%. For mixtures of Lennard-Jones molecules, the model predictions are better than the Weeks-Chandler-Anderson perturbation theory.
General theory of spontaneous emission near exceptional points.
Pick, Adi; Zhen, Bo; Miller, Owen D; Hsu, Chia W; Hernandez, Felipe; Rodriguez, Alejandro W; Soljačić, Marin; Johnson, Steven G
2017-05-29
We present a general theory of spontaneous emission at exceptional points (EPs)-exotic degeneracies in non-Hermitian systems. Our theory extends beyond spontaneous emission to any light-matter interaction described by the local density of states (e.g., absorption, thermal emission, and nonlinear frequency conversion). Whereas traditional spontaneous-emission theories imply infinite enhancement factors at EPs, we derive finite bounds on the enhancement, proving maximum enhancement of 4 in passive systems with second-order EPs and significantly larger enhancements (exceeding 400×) in gain-aided and higher-order EP systems. In contrast to non-degenerate resonances, which are typically associated with Lorentzian emission curves in systems with low losses, EPs are associated with non-Lorentzian lineshapes, leading to enhancements that scale nonlinearly with the resonance quality factor. Our theory can be applied to dispersive media, with proper normalization of the resonant modes.
Eu, Byung Chan
2016-01-01
This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on relativistic theories, it provides a comprehensive picture of the kinetic theory formulated from the viewpoint of nonequilibrium ensembles in both nonrelativistic and, in Vol. 2, relativistic contexts. Theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids) on the basis of irreversible kinetic equations satisfying the H theorem. They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respe...
On the generalization of the Kaluza-Klein theory
International Nuclear Information System (INIS)
Rosu, Ion
2003-01-01
The goal of this paper is to present the Kaluza-Klein theory. In the first part we will discuss the theory elaborated by Kaluza and Klein, in a Riemann space with five dimensions, which unifies the gravitation with electromagnetism. The second part debates the generalization of this theory in a space with 4+n dimensions. This is a mathematical product between the Riemann 4-dimension variety and the G/H n-dimensional homogenous space. In the last part we will propose a theory Kaluza-Klein like in the fiber bundle space with 4+n dimensions. Every part is structured as follows: the metric tensor G will be identified for the gravitation and the potentials Yang-Mills; then the equations of geodesics and the equations of the field will be deduced. (author)
Generalized information theory: aims, results, and open problems
International Nuclear Information System (INIS)
Klir, George J.
2004-01-01
The principal purpose of this paper is to present a comprehensive overview of generalized information theory (GIT): a research program whose objective is to develop a broad treatment of uncertainty-based information, not restricted to classical notions of uncertainty. After a brief overview of classical information theories, a broad framework for formalizing uncertainty and the associated uncertainty-based information of a great spectrum of conceivable types is sketched. The various theories of imprecise probabilities that have already been developed within this framework are then surveyed, focusing primarily on some important unifying principles applying to all these theories. This is followed by introducing two higher levels of the theories of imprecise probabilities: (i) the level of measuring the amount of relevant uncertainty (predictive, retrodictive, prescriptive, diagnostic, etc.) in any situation formalizable in each given theory, and (ii) the level of some methodological principles of uncertainty, which are contingent upon the capability to measure uncertainty and the associated uncertainty-based information. Various issues regarding both the measurement of uncertainty and the uncertainty principles are discussed. Again, the focus is on unifying principles applicable to all the theories. Finally, the current status of GIT is assessed and future research in the area is discussed
Generalized metric formulation of double field theory on group manifolds
International Nuclear Information System (INIS)
Blumenhagen, Ralph; Bosque, Pascal du; Hassler, Falk; Lüst, Dieter
2015-01-01
We rewrite the recently derived cubic action of Double Field Theory on group manifolds http://dx.doi.org/10.1007/JHEP02(2015)001 in terms of a generalized metric and extrapolate it to all orders in the fields. For the resulting action, we derive the field equations and state them in terms of a generalized curvature scalar and a generalized Ricci tensor. Compared to the generalized metric formulation of DFT derived from tori, all these quantities receive additional contributions related to the non-trivial background. It is shown that the action is invariant under its generalized diffeomorphisms and 2D-diffeomorphisms. Imposing additional constraints relating the background and fluctuations around it, the precise relation between the proposed generalized metric formulation of DFT WZW and of original DFT from tori is clarified. Furthermore, we show how to relate DFT WZW of the WZW background with the flux formulation of original DFT.
Generalized metric formulation of double field theory on group manifolds
Energy Technology Data Exchange (ETDEWEB)
Blumenhagen, Ralph [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Bosque, Pascal du [Arnold-Sommerfeld-Center für Theoretische Physik,Department für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); Hassler, Falk [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Lüst, Dieter [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Arnold-Sommerfeld-Center für Theoretische Physik,Department für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); CERN, PH-TH,1211 Geneva 23 (Switzerland)
2015-08-13
We rewrite the recently derived cubic action of Double Field Theory on group manifolds http://dx.doi.org/10.1007/JHEP02(2015)001 in terms of a generalized metric and extrapolate it to all orders in the fields. For the resulting action, we derive the field equations and state them in terms of a generalized curvature scalar and a generalized Ricci tensor. Compared to the generalized metric formulation of DFT derived from tori, all these quantities receive additional contributions related to the non-trivial background. It is shown that the action is invariant under its generalized diffeomorphisms and 2D-diffeomorphisms. Imposing additional constraints relating the background and fluctuations around it, the precise relation between the proposed generalized metric formulation of DFT{sub WZW} and of original DFT from tori is clarified. Furthermore, we show how to relate DFT{sub WZW} of the WZW background with the flux formulation of original DFT.
Generalized perturbation theory using two-dimensional, discrete ordinates transport theory
International Nuclear Information System (INIS)
Childs, R.L.
1979-01-01
Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using two-dimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions Λ and Λ*. Demonstration calculations were performed for changes in a reaction-rate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions
The general class of the vacuum spherically symmetric equations of the general relativity theory
International Nuclear Information System (INIS)
Karbanovski, V. V.; Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N.; Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R.
2012-01-01
The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g 00 and g 22 is obtained. The properties of the found solutions are analyzed.
Scalar-tensor theory of gravitation: generalizations and experimental limitations
International Nuclear Information System (INIS)
Duruisseau, J.P.
1983-01-01
Several theories with scalar field can be derived from different variational principles. Here a very general variational principle is considered and it is proved that, in the exterior case without electromagnetic field, the solution for a particular case generates the set of solutions for the general case. This is applied to the exterior solution in the static case with spherical symmetry without electromagnetic field. The predictions are investigated for the classic effects and the event horizons and some limitations for the variational principles which generalize the usual limitations are obtained. In all these cases the Schwarzschild solution with his horizon appears as a very particular case. (author)
Generalized diffusion theory for calculating the neutron transport scalar flux
International Nuclear Information System (INIS)
Alcouffe, R.E.
1975-01-01
A generalization of the neutron diffusion equation is introduced, the solution of which is an accurate approximation to the transport scalar flux. In this generalization the auxiliary transport calculations of the system of interest are utilized to compute an accurate, pointwise diffusion coefficient. A procedure is specified to generate and improve this auxiliary information in a systematic way, leading to improvement in the calculated diffusion scalar flux. This improvement is shown to be contingent upon satisfying the condition of positive calculated-diffusion coefficients, and an algorithm that ensures this positivity is presented. The generalized diffusion theory is also shown to be compatible with conventional diffusion theory in the sense that the same methods and codes can be used to calculate a solution for both. The accuracy of the method compared to reference S/sub N/ transport calculations is demonstrated for a wide variety of examples. (U.S.)
On a Geometric Theory of Generalized Chiral Elasticity with Discontinuities
Directory of Open Access Journals (Sweden)
Suhendro I.
2008-01-01
Full Text Available In this work we develop, in a somewhat extensive manner, a geometric theory of chiral elasticity which in general is endowed with geometric discontinuities (sometimes referred to as defects. By itself, the present theory generalizes both Cosserat and void elasticity theories to a certain extent via geometrization as well as by taking intoaccount the action of the electromagnetic field, i.e., the incorporation of the electromagnetic field into the description of the so-called microspin (chirality also forms the underlying structure of this work. As we know, the description of the electromagnetic field as a unified phenomenon requires four-dimensional space-time rather than three-dimensional space as its background. For this reason we embed the three-dimensional material space in four-dimensional space-time. This way, the electromagnetic spin is coupled to the non-electromagnetic microspin, both being parts of the completemicrospin to be added to the macrospin in the full description of vorticity. In short, our objective is to generalize the existing continuum theories by especially describing microspin phenomena in a fully geometric way.
On a Geometric Theory of Generalized Chiral Elasticity with Discontinuities
Directory of Open Access Journals (Sweden)
Suhendro I.
2008-01-01
Full Text Available In this work we develop, in a somewhat extensive manner, a geometric theory of chiral elasticity which in general is endowed with geometric discontinuities (sometimes re- ferred to as defects . By itself, the present theory generalizes both Cosserat and void elasticity theories to a certain extent via geometrization as well as by taking into ac- count the action of the electromagnetic field, i.e., the incorporation of the electromag- netic field into the description of the so-called microspin ( chirality also forms the un- derlying structure of this work. As we know, the description of the electromagnetic field as a unified phenomenon requires four-dimensional space-time rather than three- dimensional space as its background. For this reason we embed the three-dimensional material space in four-dimensional space-time. This way, the electromagnetic spin is coupled to the non-electromagnetic microspin, both being parts of the complete mi- crospin to be added to the macrospin in the full description of vorticity. In short, our objective is to generalize the existing continuum theories by especially describing mi- crospin phenomena in a fully geometric way.
A few comments on general theory of quantized fields
International Nuclear Information System (INIS)
Yamaguchi, Yoshio
2005-01-01
Several important comments on General Theory of Quantized Fields shall be supplemented here. Our theory is based on (Riemannian) momentum spaces with finite volumes. Our theory is formulated in the specific inertial frame, i.e., the rest frame of the cosmic back-ground radiation (RF-CBR). To go to other reference frame, we reply on general co-ordinate (in our case, energy and momentum variables, p-representation) transformations and the principle of general relativity. We find the degeneracy on energy levels of all elementary particles (same values of all particle energies appear twice) (as compared to the conventional field theories). This doubling of energy levels might be important at the beginning (very early stage) of our evolutional universe. However, we may not wish to have such a doubling at the present epoch. We can avoid the doubling by introducing appropriate (natural and rational, of course) Yukawa interactions among fermions and bosons. Then it is easy to realize the situation in which elementary particles populated in the half of the energy levels (called 'our particles' having normal spin multiplicity) shall not 'interact' with particles populated in the other half of energy levels except gravity. The particles in the latter group may be called 'dark matter particles', which give the most natural candidates of dark matter. We have already emphasized that other candidates of dark matter are zero-point vibration energy of all elementary particles and the energy of the vacuum due to interaction Hamiltonians. (author)
Entropy and information causality in general probabilistic theories
International Nuclear Information System (INIS)
Barnum, Howard; Leifer, Matthew; Spekkens, Robert; Barrett, Jonathan; Clark, Lisa Orloff; Stepanik, Nicholas; Wilce, Alex; Wilke, Robin
2010-01-01
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality (IC) recently proposed by Pawlowski et al (2009 arXiv:0905.2292). We consider two entropic quantities, which we term measurement and mixing entropy. In the context of classical and quantum theory, these coincide, being given by the Shannon and von Neumann entropies, respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state space is a non-simplicial polytope. Thus, the condition that measurement and mixing entropies coincide is a strong constraint on possible theories. We call theories with this property monoentropic. Measurement entropy is subadditive, but not in general strongly subadditive. Equivalently, if we define the mutual information between two systems A and B by the usual formula I(A: B)=H(A)+H(B)-H(AB), where H denotes the measurement entropy and AB is a non-signaling composite of A and B, then it can happen that I(A:BC)< I(A:B). This is relevant to IC in the sense of Pawlowski et al: we show that any monoentropic non-signaling theory in which measurement entropy is strongly subadditive, and also satisfies a version of the Holevo bound, is informationally causal, and on the other hand we observe that Popescu-Rohrlich boxes, which violate IC, also violate strong subadditivity. We also explore the interplay between measurement and mixing entropy and various natural conditions on theories that arise in quantum axiomatics.
Master equations and the theory of stochastic path integrals
Weber, Markus F.; Frey, Erwin
2017-04-01
them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.
Master equations and the theory of stochastic path integrals.
Weber, Markus F; Frey, Erwin
2017-04-01
expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.
Generalized absorber theory and the Einstein-Podolsky-Rosen paradox
International Nuclear Information System (INIS)
Cramer, J.G.
1980-01-01
A generalized form of Wheeler-Feynman absorber theory is used to explain the quantum-mechanical paradox proposed by Einstein, Podolsky, and Rosen (EPR). The advanced solutions of the electromagnetic wave equation and of relativistic quantum-mechanical wave equations are shown to play the role of ''verifier'' in quantum-mechanical ''transactions,'' providing microscopic communication paths between detectors across spacelike intervals in violation of the EPR locality postulate. The principle of causality is discussed in the context of this approach, and possibilities for experimental tests of the theory are examined
On complicated continuum models in general relativity theory
International Nuclear Information System (INIS)
Tsypkin, A.G.
1987-01-01
A set of Euler's equations is obtained in the framework of the general relativity theory from the variational equation in the supposition that lagrangian of the material depends on additional (in comparison with classical theories) thermodynamic parameters and taking into account possible irreversible processes. Momentum equations for continuous medium of a thermodynamic closed set are shown to be the consequence of field equations. The problem about the type of energy-momentum material tensor in the presence of derivatives from additional thermodynamic parameters in the number of lagrangian arguments is considered
General scalar-tensor theories for induced gravity inflation
International Nuclear Information System (INIS)
Boutaleb J, H.; Marrakchi, A.L.
1992-07-01
Some cosmological implications of a general scalar-tensor theory for induced gravity are discussed. The model exhibits a slow-rolling phase provided that the coupling function ε(φ) varies slowly enough such that φ dlnε(φ)/dφ much less than 2 during almost the inflationary epoch. It is then shown that, as in the ordinary induced gravity inflation, the chaotic scenario is more natural than the new scenario which proves to be even not self-consistent. The results are applied, for illustration, to a scalar-tensor theory of the Barker type. (author). 25 refs
Indefinite-metric quantum field theory of general relativity, 5
International Nuclear Information System (INIS)
Nakanishi, Noboru
1979-01-01
The indefinite-metric quantum field theory of general relativity is extended to the coupled system of the gravitational field and a Dirac field on the basis of the vierbein formalism. The six extra degrees of freedom involved in vierbein are made unobservable by introducing an extra subsidiary condition Q sub(s) + phys> = 0, where Q sub(s) denotes a new BRS charge corresponding to the local Lorentz invariance. It is shown that a manifestly covariant, unitary, canonical theory can be constructed consistently on the basis of the vierbein formalism. (author)
Generalized canonical formalism and the S-matrix of theories with constraints of the general type
International Nuclear Information System (INIS)
Fradkina, T.Ye.
1987-01-01
A canonical quantization method is given for systems with first and second class constraints of arbitrary rank. The effectiveness of the method is demonstrated using sample Yang-Mills and gravitational fields. A correct expression is derived for the S-matrix of theories that are momentum-quadratic within the scope of canonical gauges, including ghost fields. Generalized quantization is performed and the S-matrix is derived in configurational space for theories of relativistic membranes representing a generalization of theories of strings to the case of an extended spatial implementation. It is demonstrated that the theory of membranes in n+l-dimensional space is a system with rank-n constraints
A General Framework for Portfolio Theory. Part I: theory and various models
Maier-Paape, Stanislaus; Zhu, Qiji Jim
2017-01-01
Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two dimensional space of utility and risk. This is a rather general pattern. The modern portfolio theory of Markowitz [H. Markowitz, Portfolio Selection, 1959] and its natural generalization, the capital market pricing model, [W. F. Sharpe, Mutual fund performance , 1966] are spe...
Generalized second law of thermodynamic in modified teleparallel theory
Energy Technology Data Exchange (ETDEWEB)
Zubair, M. [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); Bahamonde, Sebastian [University College London, Department of Mathematics, London (United Kingdom); Jamil, Mubasher [National University of Sciences and Technology (NUST), Department of Mathematics, School of Natural Sciences (SNS), Islamabad (Pakistan)
2017-07-15
This study is conducted to examine the validity of the generalized second law of thermodynamics (GSLT) in flat FRW for modified teleparallel gravity involving coupling between a scalar field with the torsion scalar T and the boundary term B = 2∇{sub μ}T{sup μ}. This theory is very useful, since it can reproduce other important well-known scalar field theories in suitable limits. The validity of the first and second law of thermodynamics at the apparent horizon is discussed for any coupling. As examples, we have also explored the validity of those thermodynamics laws in some new cosmological solutions under the theory. Additionally, we have also considered the logarithmic entropy corrected relation and discuss the GSLT at the apparent horizon. (orig.)
Generalized second law of thermodynamic in modified teleparallel theory
International Nuclear Information System (INIS)
Zubair, M.; Bahamonde, Sebastian; Jamil, Mubasher
2017-01-01
This study is conducted to examine the validity of the generalized second law of thermodynamics (GSLT) in flat FRW for modified teleparallel gravity involving coupling between a scalar field with the torsion scalar T and the boundary term B = 2∇ μ T μ . This theory is very useful, since it can reproduce other important well-known scalar field theories in suitable limits. The validity of the first and second law of thermodynamics at the apparent horizon is discussed for any coupling. As examples, we have also explored the validity of those thermodynamics laws in some new cosmological solutions under the theory. Additionally, we have also considered the logarithmic entropy corrected relation and discuss the GSLT at the apparent horizon. (orig.)
Theory and interpretation in qualitative studies from general practice
DEFF Research Database (Denmark)
Malterud, Kirsti
2016-01-01
Objective: In this article, I want to promote theoretical awareness and commitment among qualitative researchers in general practice and suggest adequate and feasible theoretical approaches. Approach: I discuss different theoretical aspects of qualitative research and present the basic foundations...... theory is a consistent and soundly based set of assumptions about a specific aspect of the world, predicting or explaining a phenomenon. Qualitative research is situated in an interpretative paradigm where notions about particular human experiences in context are recognized from different subject...... in qualitative analysis are presented, emphasizing substantive theories to sharpen the interpretative focus. Such approaches are clearly within reach for a general practice researcher contributing to clinical practice by doing more than summarizing what the participants talked about, without trying to become...
Beyond heat baths II: framework for generalized thermodynamic resource theories
Yunger Halpern, Nicole
2018-03-01
Thermodynamics, which describes vast systems, has been reconciled with small scales, relevant to single-molecule experiments, in resource theories. Resource theories have been used to model exchanges of energy and information. Recently, particle exchanges were modeled; and an umbrella family of thermodynamic resource theories was proposed to model diverse baths, interactions, and free energies. This paper motivates and details the family’s structure and prospective applications. How to model electrochemical, gravitational, magnetic, and other thermodynamic systems is explained. Szilárd’s engine and Landauer’s Principle are generalized, as resourcefulness is shown to be convertible not only between information and gravitational energy, but also among diverse degrees of freedom. Extensive variables are associated with quantum operators that might fail to commute, introducing extra nonclassicality into thermodynamic resource theories. An early version of this paper partially motivated the later development of noncommutative thermalization. This generalization expands the theories’ potential for modeling realistic systems with which small-scale statistical mechanics might be tested experimentally.
Laser Theory for Optomechanics: Limit Cycles in the Quantum Regime
Directory of Open Access Journals (Sweden)
Niels Lörch
2014-01-01
Full Text Available Optomechanical systems can exhibit self-sustained limit cycles where the quantum state of the mechanical resonator possesses nonclassical characteristics such as a strongly negative Wigner density, as was shown recently in a numerical study by Qian et al. [Phys. Rev. Lett. 109, 253601 (2012]. Here, we derive a Fokker-Planck equation describing mechanical limit cycles in the quantum regime that correctly reproduces the numerically observed nonclassical features. The derivation starts from the standard optomechanical master equation and is based on techniques borrowed from the laser theory due to Haake and Lewenstein. We compare our analytical model with numerical solutions of the master equation based on Monte Carlo simulations and find very good agreement over a wide and so far unexplored regime of system parameters. As one main conclusion, we predict negative Wigner functions to be observable even for surprisingly classical parameters, i.e., outside the single-photon strong-coupling regime, for strong cavity drive and rather large limit-cycle amplitudes. The approach taken here provides a natural starting point for further studies of quantum effects in optomechanics.
Smalley, L. L.
1983-01-01
The proper framework for testing Rastall's theory and its generalizations is in the case of non-negligible (i.e. discernible) gravitational effects such as gravity gradients. These theories have conserved integral four-momentum and angular momentum. The Nordtvedt effect then provides limits on the parameters which arise as the result of the non-zero divergence of the energy-momentum tensor.
Fuel management optimization based on generalized perturbation theory
International Nuclear Information System (INIS)
White, J.R.; Chapman, D.M.; Biswas, D.
1986-01-01
A general methodology for optimization of assembly shuffling and burnable poison (BP) loadings for LWR reload design has been developed. The uniqueness of this approach lies in the coupling of Generalized Perturbation Theory (GPT) methods and standard Integer Programming (IP) techniques. An IP algorithm can simulate the discrete nature of the fuel shuffling and BP loading problems, and the use of GPT sensitivity data provides an efficient means for modeling the behavior of the important core performance parameters. The method is extremely flexible since the choice of objective function and the number and mix of constraints depend only on the ability of GPT to determine the appropriate sensitivity functions
Generalized Poisson processes in quantum mechanics and field theory
International Nuclear Information System (INIS)
Combe, P.; Rodriguez, R.; Centre National de la Recherche Scientifique, 13 - Marseille; Hoegh-Krohn, R.; Centre National de la Recherche Scientifique, 13 - Marseille; Sirugue, M.; Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille
1981-01-01
In section 2 we describe more carefully the generalized Poisson processes, giving a realization of the underlying probability space, and we characterize these processes by their characteristic functionals. Section 3 is devoted to the proof of the previous formula for quantum mechanical systems, with possibly velocity dependent potentials and in section 4 we give an application of the previous theory to some relativistic Bose field models. (orig.)
Renormalization in general theories with inter-generation mixing
International Nuclear Information System (INIS)
Kniehl, Bernd A.; Sirlin, Alberto
2011-11-01
We derive general and explicit expressions for the unrenormalized and renormalized dressed propagators of fermions in parity-nonconserving theories with inter-generation mixing. The mass eigenvalues, the corresponding mass counterterms, and the effect of inter-generation mixing on their determination are discussed. Invoking the Aoki-Hioki-Kawabe-Konuma-Muta renormalization conditions and employing a number of very useful relations from Matrix Algebra, we show explicitly that the renormalized dressed propagators satisfy important physical properties. (orig.)
Magnetotail equilibrium theory - The general three-dimensional solution
Birn, J.
1987-01-01
The general magnetostatic equilibrium problem for the geomagnetic tail is reduced to the solution of ordinary differential equations and ordinary integrals. The theory allows the integration of the self-consistent magnetotail equilibrium field from the knowledge of four functions of two space variables: the neutral sheet location, the total pressure, the magnetic field strength, and the z component of the magnetic field at the neutral sheet.
Stringy horizons and generalized FZZ duality in perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Giribet, Gaston [Martin Fisher School of Physics, Brandeis University,Waltham, Massachusetts 02453 (United States); Departamento de Física, Universidad de Buenos Aires FCEN-UBA and IFIBA-CONICET,Ciudad Universitaria, Pabellón I, 1428, Buenos Aires (Argentina)
2017-02-14
We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation functions of sine-Liouville theory in terms of a special set of correlators in the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality. In particular, we prove that n-point correlation functions in sine-Liouville theory involving n−2 winding modes actually coincide with the correlation functions in the SL(2,ℝ)/U(1) gauged WZW model that include n−2 oscillator operators of the type described by Giveon, Itzhaki and Kutasov in reference https://www.doi.org/10.1007/JHEP10(2016)157. This proves the GFZZ duality for the case of tree level maximally winding violating n-point amplitudes with arbitrary n. We also comment on the connection between GFZZ and other marginal deformations previously considered in the literature.
Communication: On the diffusion tensor in macroscopic theory of cavitation
Shneidman, Vitaly A.
2017-08-01
The classical description of nucleation of cavities in a stretched fluid relies on a one-dimensional Fokker-Planck equation (FPE) in the space of their sizes r, with the diffusion coefficient D(r) constructed for all r from macroscopic hydrodynamics and thermodynamics, as shown by Zeldovich. When additional variables (e.g., vapor pressure) are required to describe the state of a bubble, a similar approach to construct a diffusion tensor D ^ generally works only in the direct vicinity of the thermodynamic saddle point corresponding to the critical nucleus. It is shown, nevertheless, that "proper" kinetic variables to describe a cavity can be selected, allowing to introduce D ^ in the entire domain of parameters. In this way, for the first time, complete FPE's are constructed for viscous volatile and inertial fluids. In the former case, the FPE with symmetric D ^ is solved numerically. Alternatively, in the case of an inertial fluid, an equivalent Langevin equation is considered; results are compared with analytics. The suggested approach is quite general and can be applied beyond the cavitation problem.
Theory of Nonlocal Point Transformations in General Relativity
Directory of Open Access Journals (Sweden)
Massimo Tessarotto
2016-01-01
Full Text Available A discussion of the functional setting customarily adopted in General Relativity (GR is proposed. This is based on the introduction of the notion of nonlocal point transformations (NLPTs. While allowing the extension of the traditional concept of GR-reference frame, NLPTs are important because they permit the explicit determination of the map between intrinsically different and generally curved space-times expressed in arbitrary coordinate systems. For this purpose in the paper the mathematical foundations of NLPT-theory are laid down and basic physical implications are considered. In particular, explicit applications of the theory are proposed, which concern (1 a solution to the so-called Einstein teleparallel problem in the framework of NLPT-theory; (2 the determination of the tensor transformation laws holding for the acceleration 4-tensor with respect to the group of NLPTs and the identification of NLPT-acceleration effects, namely, the relationship established via general NLPT between particle 4-acceleration tensors existing in different curved space-times; (3 the construction of the nonlocal transformation law connecting different diagonal metric tensors solution to the Einstein field equations; and (4 the diagonalization of nondiagonal metric tensors.
Moon, Byongook; Hwang, Hye-Won; McCluskey, John D.
2011-01-01
A growing number of studies indicate the ubiquity of school bullying: It is a global concern, regardless of cultural differences. Little previous research has examined whether leading criminological theories can explain bullying, despite the commonality between bullying and delinquency. The current investigation uses longitudinal data on 655…
Relativistic theory of gravitation and nonuniqueness of the predictions of general relativity theory
International Nuclear Information System (INIS)
Logunov, A.A.; Loskutov, Yu.M.
1986-01-01
It is shown that while the predictions of relativistic theory of gravitation (RTG) for the gravitational effects are unique and consistent with the experimental data available, the relevant predictions of general relativity theory are not unique. Therewith the above nonuniqueness manifests itself in some effects in the first order in the gravitational interaction constant in others in the second one. The absence in GRT of the energy-momentum and angular momentum conservation laws for the matter and gravitational field taken together and its inapplicability to give uniquely determined predictions for the gravitational phenomena compel to reject GRT as a physical theory
Cook, Desmond L.
This document, one of a series of reports examining the possible contribution of other disciplines to evaluation methodology, describes the major elements of general systems theory (GST), cybernetics theory (CT) and management control theory (MCT). The author suggests that MCT encapsulates major concerns of evaluation since it reveals that…
Generalized perturbation theory in DRAGON: application to CANDU cell calculations
International Nuclear Information System (INIS)
Courau, T.; Marleau, G.
2001-01-01
Generalized perturbation theory (GPT) in neutron transport is a means to evaluate eigenvalue and reaction rate variations due to small changes in the reactor properties (macroscopic cross sections). These variations can be decomposed in two terms: a direct term corresponding to the changes in the cross section themselves and an indirect term that takes into account the perturbations in the neutron flux. As we will show, taking into account the indirect term using a GPT method is generally straight forward since this term is the scalar product of the unperturbed generalized adjoint with the product of the variation of the transport operator and the unperturbed flux. In the case where the collision probability (CP) method is used to solve the transport equation, evaluating the perturbed transport operator involves calculating the variations in the CP matrix for each change in the reactor properties. Because most of the computational effort is dedicated to the CP matrix calculation the gains expected form the GPT method would therefore be annihilated. Here we will present a technique to approximate the variations in the CP matrices thereby replacing the variations in the transport operator with source term variations. We will show that this approximation yields errors fully compatible with the standard generalized perturbation theory errors. Results for 2D CANDU cell calculations will be presented. (author)
Magnetized plasma kinetic theory
International Nuclear Information System (INIS)
Hassan, M.H.A.; Watson, C.J.H.
1977-01-01
The magnetized Balescu-Lenard Collision integral for a multi-species plasma in the form derived by Hassan and Watson (1976) is approximated by ignoring wave effects. The resulting collision integral is put in Fokker-Planck form and most of the integrals occurring in the coefficients are performed analytically. The remaining integral is evaluated approximately in various limits for ion-electron, electron-electron and electron-ion interactions. (author)
Theory and experiments in general relativity and other metric theories of gravity
International Nuclear Information System (INIS)
Ciufolini, I.
1984-01-01
In Chapter I, after an introduction to theories of gravity alternative to general relativity, metric theories, and the post-Newtonian parameterized (PNN) formalism, a new class of metric theories of gravity is defined. As a result the post-Newtonian approximation of the new theories is not described by the PPN formalism. In fact under the weak field and slow motion hypothesis, the post-Newtonian expression of the metric tensor contains an infinite set of new terms and correspondingly an infinite set of new PPN parameters. Chapter II, III, and IV are devoted to new experiments to test general relativity and other metric theories of gravity. In particular, in chapter IV, it is shown that two general relativistics effects, the Lense-Thirring and De Sitter-Fokker precessions of the nodal lines of an Earth artificial satellite are today detectable using high altitude laser ranged artificial satellites such as Lageos. The orbit of this satellite is known with unprecedented accuracy. The author then describes a method of measuring these relativistic precessions using Lageos together with another high altitude laser ranged similar satellite with appropriately chosen orbital parameters
A multistep general theory of transition to addiction.
Piazza, Pier Vincenzo; Deroche-Gamonet, Véronique
2013-10-01
Several theories propose alternative explanations for drug addiction. We propose a general theory of transition to addiction that synthesizes knowledge generated in the field of addiction into a unitary explanatory frame. Transition to addiction results from a sequential three-step interaction between: (1) individual vulnerability; (2) degree/amount of drug exposure. The first step, sporadic recreational drug use is a learning process mediated by overactivation of neurobiological substrates of natural rewards that allows most individuals to perceive drugs as highly rewarding stimuli. The second, intensified, sustained, escalated drug use occurs in some vulnerable individuals who have a hyperactive dopaminergic system and impaired prefrontal cortex function. Sustained and prolonged drug use induces incentive sensitization and an allostatic state that makes drugs strongly wanted and needed. Habit formation can also contribute to stabilizing sustained drug use. The last step, loss of control of drug intake and full addiction, is due to a second vulnerable phenotype. This loss-of-control-prone phenotype is triggered by long-term drug exposure and characterized by long-lasting loss of synaptic plasticity in reward areas in the brain that induce a form of behavioral crystallization resulting in loss of control of drug intake. Because of behavioral crystallization, drugs are now not only wanted and needed but also pathologically mourned when absent. This general theory demonstrates that drug addiction is a true psychiatric disease caused by a three-step interaction between vulnerable individuals and amount/duration of drug exposure.
Potential Performance Theory (PPT): A General Theory of Task Performance Applied to Morality
Trafimow, David; Rice, Stephen
2008-01-01
People can use a variety of different strategies to perform tasks and these strategies all have two characteristics in common. First, they can be evaluated in comparison with either an absolute or a relative standard. Second, they can be used at varying levels of consistency. In the present article, the authors develop a general theory of task…
Towards a General Theory of Bilingual Legal Lexicography
DEFF Research Database (Denmark)
Nielsen, Sandro
2003-01-01
As the need for intercultural communication in the field of law has increased, the foundation of a general theory of bilingual legal lexicography must be given priority. This paper introduces, describes and explains the elements necessary for compiling the optimal bilingual law dictionary....... The theory deals with much more than the traditional question of equivalence, and shows which considerations are necessary to fully exploit the potential of printed dictionaries for the benefit of the users. Most users need linguistic and factual information that must be organised and presented...... in a structured way. This includes user research, organisation of dictionary chapters, and the presentation and structure of the linguistic and factual information in the articles and elsewhere in the dictionary....
Generalized Effective Medium Theory for Particulate Nanocomposite Materials
Directory of Open Access Journals (Sweden)
Muhammad Usama Siddiqui
2016-08-01
Full Text Available The thermal conductivity of particulate nanocomposites is strongly dependent on the size, shape, orientation and dispersion uniformity of the inclusions. To correctly estimate the effective thermal conductivity of the nanocomposite, all these factors should be included in the prediction model. In this paper, the formulation of a generalized effective medium theory for the determination of the effective thermal conductivity of particulate nanocomposites with multiple inclusions is presented. The formulated methodology takes into account all the factors mentioned above and can be used to model nanocomposites with multiple inclusions that are randomly oriented or aligned in a particular direction. The effect of inclusion dispersion non-uniformity is modeled using a two-scale approach. The applications of the formulated effective medium theory are demonstrated using previously published experimental and numerical results for several particulate nanocomposites.
On special and general relativity theory. 24. ed.
International Nuclear Information System (INIS)
Einstein, Albert
2009-01-01
The present booklet shall mediate to such an as possible exact view in relativity theory, who are especially interested for the theory from a generally scientific, philosophical, point of view, without mastering the mathematical apparatus. The lecture presupposes some maturity knowledge and - in spite of the shortness of the booklet - quite much perseverance and strength of mind. The author has token very much efforts in order to present the main thoughts as distinctly and simply as possible, in the whole in such a sequence and in such connection, as it has really been arose. With the aim of distinctiveness it seemed to me unavoidable to repeat myself frequently without paying the smallest regard to the elegance of the presentation; I maintained conscientiously the prescription of the ingenious theoretician L. Boltzmann, elegance should by the object of the taylors ans shoemakers [de
A general theory for ball lightning structure and light output
Morrow, R.
2018-03-01
A general theory for free-floating ball lightning is presented which unifies the phantom plasma ball theory involving the production of very little light, with theories for ball lightning involving light output produced by burning particles from the soil. The mechanism for the formation of plasma balls is shown to be quite general, producing very similar plasma balls independent of initial ion densities over four orders of magnitude. All that is required is an excess of positive ions in the initial ball of ions. The central plasma density after 1 s is shown to be the reciprocal of the ion neutralization coefficient for all cases, both analytically and computationally. Further, the plasma region has zero electric field in all cases. Surrounding the plasma ball is a sphere of positive ions moving away from the centre via their own space-charge field; this space-charge field, which is the same in all cases near the plasma ball, drives negative ions and negative particles towards the plasma centre. The connection with burning particle theories is the proposition that the burning particles are highly-charged which is very likely after a lightning strike. Burning negatively charged particles would be driven into the plasma ball region and trapped while any positively charged particles would be driven away. The plasma ball structure is shown to last more than 10 s and the ‘burnout time’ for a typical coal particle (as an example) has been measured at 5-10 s this is comparable with the lifetimes observed for ball lightning. The light output from a few hundred particles is estimated to be ~1 W, a typical output for ball lightning. Finally, suggestions are made for the generation of ball lightning in the laboratory.
General Strain Theory and Substance Use among American Indian Adolescents.
Eitle, Tamela McNulty; Eitle, David; Johnson-Jennings, Michelle
2013-01-01
Despite the well-established finding that American Indian adolescents are at a greater risk of illicit substance use and abuse than the general population, few generalist explanations of deviance have been extended to American Indian substance use. Using a popular generalist explanation of deviance, General Strain Theory, we explore the predictive utility of this model with a subsample of American Indian adolescents from waves one and two of the National Longitudinal Study of Adolescent Health (Add-Health). Overall, we find mixed support for the utility of General Strain Theory to account for American Indian adolescent substance use. While exposure to recent life events, a common measure of stress exposure, was found to be a robust indicator of substance use, we found mixed support for the thesis that negative affect plays a key role in mediating the link between strain and substance use. However, we did find evidence that personal and social resources serve to condition the link between stress exposure and substance use, with parental control, self-restraint, religiosity, and exposure to substance using peers each serving to moderate the association between strain and substance use, albeit in more complex ways than expected.
Generalized probabilistic theories and conic extensions of polytopes
Fiorini, Samuel; Massar, Serge; Patra, Manas K.; Tiwary, Hans Raj
2015-01-01
Generalized probabilistic theories (GPT) provide a general framework that includes classical and quantum theories. It is described by a cone C and its dual C*. We show that whether some one-way communication complexity problems can be solved within a GPT is equivalent to the recently introduced cone factorization of the corresponding communication matrix M. We also prove an analogue of Holevo's theorem: when the cone C is contained in {{{R}}n}, the classical capacity of the channel realized by sending GPT states and measuring them is bounded by log n. Polytopes and optimising functions over polytopes arise in many areas of discrete mathematics. A conic extension of a polytope is the intersection of a cone C with an affine subspace whose projection onto the original space yields the desired polytope. Extensions of polytopes can sometimes be much simpler geometric objects than the polytope itself. The existence of a conic extension of a polytope is equivalent to that of a cone factorization of the slack matrix of the polytope, on the same cone. We show that all 0/1 polytopes whose vertices can be recognized by a polynomial size circuit, which includes as a special case the travelling salesman polytope and many other polytopes from combinatorial optimization, have small conic extension complexity when the cone is the completely positive cone. Using recent exponential lower bounds on the linear extension complexity of polytopes, this provides an exponential gap between the communication complexity of GPT based on the completely positive cone and classical communication complexity, and a conjectured exponential gap with quantum communication complexity. Our work thus relates the communication complexity of generalizations of quantum theory to questions of mainstream interest in the area of combinatorial optimization.
Generalized probabilistic theories and conic extensions of polytopes
International Nuclear Information System (INIS)
Fiorini, Samuel; Massar, Serge; Patra, Manas K; Tiwary, Hans Raj
2015-01-01
Generalized probabilistic theories (GPT) provide a general framework that includes classical and quantum theories. It is described by a cone C and its dual C*. We show that whether some one-way communication complexity problems can be solved within a GPT is equivalent to the recently introduced cone factorization of the corresponding communication matrix M. We also prove an analogue of Holevo's theorem: when the cone C is contained in R n , the classical capacity of the channel realized by sending GPT states and measuring them is bounded by logn. Polytopes and optimising functions over polytopes arise in many areas of discrete mathematics. A conic extension of a polytope is the intersection of a cone C with an affine subspace whose projection onto the original space yields the desired polytope. Extensions of polytopes can sometimes be much simpler geometric objects than the polytope itself. The existence of a conic extension of a polytope is equivalent to that of a cone factorization of the slack matrix of the polytope, on the same cone. We show that all 0/1 polytopes whose vertices can be recognized by a polynomial size circuit, which includes as a special case the travelling salesman polytope and many other polytopes from combinatorial optimization, have small conic extension complexity when the cone is the completely positive cone. Using recent exponential lower bounds on the linear extension complexity of polytopes, this provides an exponential gap between the communication complexity of GPT based on the completely positive cone and classical communication complexity, and a conjectured exponential gap with quantum communication complexity. Our work thus relates the communication complexity of generalizations of quantum theory to questions of mainstream interest in the area of combinatorial optimization. (paper)
Nonextensive kinetic theory and H-theorem in general relativity
Santos, A. P.; Silva, R.; Alcaniz, J. S.; Lima, J. A. S.
2017-11-01
The nonextensive kinetic theory for degenerate quantum gases is discussed in the general relativistic framework. By incorporating nonadditive modifications in the collisional term of the relativistic Boltzmann equation and entropy current, it is shown that Tsallis entropic framework satisfies a H-theorem in the presence of gravitational fields. Consistency with the 2nd law of thermodynamics is obtained only whether the entropic q-parameter lies in the interval q ∈ [ 0 , 2 ] . As occurs in the absence of gravitational fields, it is also proved that the local collisional equilibrium is described by the extended Bose-Einstein (Fermi-Dirac) q-distributions.
Cosmology and a general scalar-tensor theory of gravity
International Nuclear Information System (INIS)
Bishop, N.T.
1976-01-01
The cosmological models resulting from a general scalar-tensor theory of gravity are discussed. Those models for which the scalar field varies as a power of the cosmological expansion factor (i.e. phi varies as Rsup(n)) are considered in detail, leading to a set of such models compatible with observation. This set includes models in which the scalar coupling parameter ω is negative. The models described here are similar to those of Newtonian cosmology obtained from an impotence principle. (author)
The two-loop renormalization of general quantum field theories
International Nuclear Information System (INIS)
Damme, R.M.J. van.
1984-01-01
This thesis provides a general method to compute all first order corrections to the renormalization group equations. This requires the computation of the first perturbative corrections to the renormalization group β-functions. These corrections are described by Feynman diagrams with two loops. The two-loop renormalization is treated for an arbitrary renormalization field theory. Two cases are considered: 1. the Yukawa sector; 2. the gauge coupling and the scalar potential. In a final section, the breakdown of unitarity in the dimensional reduction scheme is discussed. (Auth.)
General theory of intensity correlation on light scattering
International Nuclear Information System (INIS)
Villaeys, A.A.
1978-01-01
A general theory for spatio-temporal intensity correlations measurements for a scattered beam is developed. A completely quantum mechanical description for both excitation and detection set up is used. This description is essentially valid for weak incident light beams and single photon absorption processes. From a unified point of view both, stationary as well as, time resolved experiments are described. The interest for such experiments in the study of processes like resonance raman scattering and resonance fluorescence is emphasized. Also an observable coherent contribution associated to different final levels of the target-atoms or molecules is obtained a result which cannot be reached by intensity measurements
Application of Neutrosophic Set Theory in Generalized Assignment Problem
Directory of Open Access Journals (Sweden)
Supriya Kar
2015-09-01
Full Text Available This paper presents the application of Neutrosophic Set Theory (NST in solving Generalized Assignment Problem (GAP. GAP has been solved earlier under fuzzy environment. NST is a generalization of the concept of classical set, fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set. Elements of Neutrosophic set are characterized by a truth-membership function, falsity and also indeterminacy which is a more realistic way of expressing the parameters in real life problem. Here the elements of the cost matrix for the GAP are considered as neutrosophic elements which have not been considered earlier by any other author. The problem has been solved by evaluating score function matrix and then solving it by Extremum Difference Method (EDM [1] to get the optimal assignment. The method has been demonstrated by a suitable numerical example.
General Theory of Relativity: Will It Survive the Next Decade?
Bertolami, Orfeu; Paramos, Jorge; Turyshev, Slava G.
2006-01-01
The nature of gravity is fundamental to our understanding of our own solar system, the galaxy and the structure and evolution of the Universe. Einstein's general theory of relativity is the standard model that is used for almost ninety years to describe gravitational phenomena on these various scales. We review the foundations of general relativity, discuss the recent progress in the tests of relativistic gravity, and present motivations for high-accuracy gravitational experiments in space. We also summarize the science objectives and technology needs for the laboratory experiments in space with laboratory being the entire solar system. We discuss the advances in our understanding of fundamental physics anticipated in the near future and evaluate discovery potential for the recently proposed gravitational experiments.
A Theory of the Perturbed Consumer with General Budgets
DEFF Research Database (Denmark)
McFadden, Daniel L; Fosgerau, Mogens
We consider demand systems for utility-maximizing consumers facing general budget constraints whose utilities are perturbed by additive linear shifts in marginal utilities. Budgets are required to be compact but are not required to be convex. We define demand generating functions (DGF) whose...... subgradients with respect to these perturbations are convex hulls of the utility-maximizing demands. We give necessary as well as sufficient conditions for DGF to be consistent with utility maximization, and establish under quite general conditions that utility-maximizing demands are almost everywhere single......-valued and smooth in their arguments. We also give sufficient conditions for integrability of perturbed demand. Our analysis provides a foundation for applications of consumer theory to problems with nonlinear budget constraints....
Conformal field theories near a boundary in general dimensions
International Nuclear Information System (INIS)
McAvity, D.M.
1995-01-01
The implications of restricted conformal invariance under conformal transformations preserving a plane boundary are discussed for general dimensions d. Calculations of the universal function of a conformal invariant ξ which appears in the two-point function of scalar operators in conformally invariant theories with a plane boundary are undertaken to first order in the ε=4-d expansion for the operator φ 2 in φ 4 theory. The form for the associated functions of ξ for the two-point functions for the basic field φ α and the auxiliary field λ in the N→∞ limit of the O(N) non-linear sigma model for any d in the range 2 α φ β and λλ. Using this method the form of the two-point function for the energy-momentum tensor in the conformal O(N) model with a plane boundary is also found. General results for the sum of the contributions of all derivative operators appearing in the operator product expansion, and also in a corresponding boundary operator expansion, to the two-point functions are also derived making essential use of conformal invariance. (orig.)
An almost general theory of mean size perception.
Allik, Jüri; Toom, Mai; Raidvee, Aire; Averin, Kristiina; Kreegipuu, Kairi
2013-05-03
A general explanation for the observer's ability to judge the mean size of simple geometrical figures, such as circles, was advanced. Results indicated that, contrary to what would be predicted by statistical averaging, the precision of mean size perception decreases with the number of judged elements. Since mean size discrimination was insensitive to how total size differences were distributed among individual elements, this suggests that the observer has a limited cognitive access to the size of individual elements pooled together in a compulsory manner before size information reaches awareness. Confirming the associative law of addition means, observers are indeed sensitive to the mean, not the sizes of individual elements. All existing data can be explained by an almost general theory, namely, the Noise and Selection (N&S) Theory, formulated in exact quantitative terms, implementing two familiar psychophysical principles: the size of an element cannot be measured with absolute accuracy and only a limited number of elements can be taken into account in the computation of the average size. It was concluded that the computation of ensemble characteristics is not necessarily a tool for surpassing the capacity limitations of perceptual processing. Copyright © 2013 Elsevier Ltd. All rights reserved.
Efficient molecular density functional theory using generalized spherical harmonics expansions.
Ding, Lu; Levesque, Maximilien; Borgis, Daniel; Belloni, Luc
2017-09-07
We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r≡(x,y,z) and of the three Euler angles Ω≡(θ,ϕ,ψ) describing the solvent orientation. The standard density functional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r,Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water.
Lattice gauge theory on a parallel computer
International Nuclear Information System (INIS)
Flower, J.W.
1987-01-01
The results of several numerical simulations of QCD by Monte Carlo lattice gauge theory are presented. Studying the mesonic potential on a 20 4 lattice, we conclude that asymptotic scaling does not hold over the range 6.1 ≤ β ≤ 6.7, although we are not able to quantify the discrepancies. The effect of discrete rotational symmetry on physical parameters is examined and seems to modify the string tension by 15% at β = 6.1, while at β = 6.3 the change was less than 1%. The potential between three charges is studied and yields a string tension of .18 GeV 2 , consistent with mesonic calculations and relativized potential models. Contributions to the potential from low-energy string vibrations appear small in the range x ≤ .5 fm. We perform energy density measurements in the color fields surrounding both mesons and baryons, which provide strong evidence in favor of the dual superconductor picture of confinement. It is also suggested that the confining strings in the baryon meet at a central point rather than joining the quarks pairwise. Several algorithms are explored in an attempt to develop simulation methods which are able to directly account for the currents generated by color sources. The extension of the Langevin equation to complex degrees of freedom is derived leading to a Fokker-Planck equation for a complex 'Probability distribution'. Using this technique we are then able to calculate energy densities in U(1) gauge theory at large charge separations. The extension of the method to non-Abelian theories comes up against an unresolved problem in segregation for certain types of observable. 145 refs., 36 figs
Dynamic statistical information theory
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation of respective dynamic systems, i.e. Fokker-Planck equation and Liouville diffusion equation can be regarded as their information symbol evolution equation, we derived the nonlinear evolution equations of Shannon dynamic entropy density and dynamic information density and the nonlinear evolution equations of Boltzmann dynamic entropy density and dynamic information density, that describe respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes; and that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes. Entropy and information have been combined with the state and its law of motion of the systems. Furthermore we presented the formulas of two kinds of entropy production rates and information dissipation rates, the expressions of two kinds of drift information flows and diffusion information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information) were equal to their corresponding entropy production rates (or the increase rates of the total entropy) in the same dynamic system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel
Aerodynamic coefficients in generalized unsteady thin airfoil theory
Williams, M. H.
1980-01-01
Two cases are considered: (1) rigid body motion of an airfoil-flap combination consisting of vertical translation of given amplitude, rotation of given amplitude about a specified axis, and rotation of given amplitude of the control surface alone about its hinge; the upwash for this problem is defined mathematically; and (2) sinusoidal gust of given amplitude and wave number, for which the upwash is defined mathematically. Simple universal formulas are presented for the most important aerodynamic coefficients in unsteady thin airfoil theory. The lift and moment induced by a generalized gust are evaluated explicitly in terms of the gust wavelength. Similarly, in the control surface problem, the lift, moment, and hinge moments are given as explicit algebraic functions of hinge location. These results can be used together with any of the standard numerical inversion routines for the elementary loads (pitch and heave).
Generalized on-shell ward identities in string theory
International Nuclear Information System (INIS)
Lee, Jen-Chi
1994-01-01
It is demonstrated that an infinite set of string-tree level on-shell Ward identities, which are valid to all σ-model loop orders, can be systematically constructed without referring to the string field theory. As examples, bosonic massive scattering amplitudes are calculated explicitly up to the second massive excited states. Ward identities satisfied by these amplitudes are derived by using zero-norm states in the spectrum. In particular, the inter-particle Ward identity generated by the D 2 xD 2' zero-norm state at the second massive level is demonstrated. The four physical propagating states of this mass level are then shown to form a large gauge multiplet. This result justifies our previous consideration on higher inter-spin symmetry from the generalized worldsheet σ-model point of view. (author)
Riemannian geometry of Hamiltonian chaos: hints for a general theory.
Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco
2008-10-01
We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.
General theory for environmental effects on (vertical) electronic excitation energies.
Schwabe, Tobias
2016-10-21
Almost 70 years ago, the first theoretical model for environmental effects on electronic excitation energies has been derived. Since then, several different interpretations and refined models have been proposed for the perichromic shift of a chromophore due to its surrounding medium. Some of these models are contradictory. Here, the contributing terms are derived within the framework of long-range perturbation theory with the least approximations so far. The derivation is based on a state-specific interpretation of the interaction energies and all terms can be identified with individual properties of either the chromophore or the surroundings, respectively. Further, the much debated contribution due to transition moments coupled to the environment can be verified in the form of a non-resonant excitonic coupling to the dynamic polarizabilities in the environment. These general insights should clarify discussions and interpretations of environmental effects on electronic excitations and should foster the development of new models for the computation of these effects.
A general field-covariant formulation of quantum field theory
International Nuclear Information System (INIS)
Anselmi, Damiano
2013-01-01
In all nontrivial cases renormalization, as it is usually formulated, is not a change of integration variables in the functional integral, plus parameter redefinitions, but a set of replacements, of actions and/or field variables and parameters. Because of this, we cannot write simple identities relating bare and renormalized generating functionals, or generating functionals before and after nonlinear changes of field variables. In this paper we investigate this issue and work out a general field-covariant approach to quantum field theory, which allows us to treat all perturbative changes of field variables, including the relation between bare and renormalized fields, as true changes of variables in the functional integral, under which the functionals Z and W=lnZ behave as scalars. We investigate the relation between composite fields and changes of field variables, and we show that, if J are the sources coupled to the elementary fields, all changes of field variables can be expressed as J-dependent redefinitions of the sources L coupled to the composite fields. We also work out the relation between the renormalization of variable-changes and the renormalization of composite fields. Using our transformation rules it is possible to derive the renormalization of a theory in a new variable frame from the renormalization in the old variable frame, without having to calculate it anew. We define several approaches, useful for different purposes, in particular a linear approach where all variable changes are described as linear source redefinitions. We include a number of explicit examples. (orig.)
General Systems Theory: Application To The Design Of Speech Communication Courses
Tucker, Raymond K.
1971-01-01
General systems theory can be applied to problems in the teaching of speech communication courses. The author describes general systems theory as it is applied to the designing, conducting and evaluation of speech communication courses. (Author/MS)
2010-12-02
will face in an uncertain future. Complexity Theory , History, Practice, Military Theory , Leadership 14. SUBJECT TERMS 70 15. NUMBER OF PAGES...complexity theory : scale, adaptive leadership , and bottom up feedback from the agents (the soldiers in the field). These are all key sub components of...Approved for Public Release; Distribution is Unlimited COMPARING THEORY AND PRACTICE: AN APPLICATION OF COMPLEXITY THEORY TO GENERAL RIDGWAY’S
Huang, Yun-An; Jastorff, Jan; Van den Stock, Jan; Van de Vliet, Laura; Dupont, Patrick; Vandenbulcke, Mathieu
2018-05-15
Psychological construction models of emotion state that emotions are variable concepts constructed by fundamental psychological processes, whereas according to basic emotion theory, emotions cannot be divided into more fundamental units and each basic emotion is represented by a unique and innate neural circuitry. In a previous study, we found evidence for the psychological construction account by showing that several brain regions were commonly activated when perceiving different emotions (i.e. a general emotion network). Moreover, this set of brain regions included areas associated with core affect, conceptualization and executive control, as predicted by psychological construction models. Here we investigate directed functional brain connectivity in the same dataset to address two questions: 1) is there a common pathway within the general emotion network for the perception of different emotions and 2) if so, does this common pathway contain information to distinguish between different emotions? We used generalized psychophysiological interactions and information flow indices to examine the connectivity within the general emotion network. The results revealed a general emotion pathway that connects neural nodes involved in core affect, conceptualization, language and executive control. Perception of different emotions could not be accurately classified based on the connectivity patterns from the nodes of the general emotion pathway. Successful classification was achieved when connections outside the general emotion pathway were included. We propose that the general emotion pathway functions as a common pathway within the general emotion network and is involved in shared basic psychological processes across emotions. However, additional connections within the general emotion network are required to classify different emotions, consistent with a constructionist account. Copyright © 2018 Elsevier Inc. All rights reserved.
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.
On the de Sitter and Nariai spacetimes in a generalized theory of gravitation
International Nuclear Information System (INIS)
Nariai, Hidekazu.
1985-07-01
A possibility of obtaining the de Sitter and Nariai spacetimes in a generalized theory of gravitation (which was in succession proposed by Utiyama-DeWitt, Parker-Fulling-Hu and Gurovich-Starobinski) is examined. It is shown that the generalized theory with a suitable fixation of three parameters admit both spacetimes, just like the general theory of relativity. (author)
Essay on a general theory of nervous system functions
Energy Technology Data Exchange (ETDEWEB)
Schweizer, H J
1985-01-01
The axiomatic theory unites the aspects of neurophysiology, psychology and system-theory. The formulation of the structural-nucleus of the theory relies on basic insights from biology, neurophysiology and system-theory. The structural-nucleus allows the reconstruction of the essential properties of nervous system functions, organisation and development. The theory also contributes to the discussion of stochastic automata and artificial intelligence.
A general theory for radioactive processes in rare earth compounds
International Nuclear Information System (INIS)
Acevedo, R.; Meruane, T.
1998-01-01
The formal theory of radiative processes in centrosymmetric coordination compounds of the Ln X 3+ is a trivalent lanthanide ion and X -1 =Cl -1 , Br -1 ) is put forward based on a symmetry vibronic crystal field-ligand polarisation model. This research considers a truncated basis set for the intermediate states of the central metal ion and have derived general master equations to account for both the overall observed spectral intensities and the measured relative vibronic intensity distributions for parity forbidden but vibronically allowed electronic transitions. In addition, a procedure which includes the closure approximation over the intermediate electronic states is included in order to estimate quantitative crystal field contribution to the total transition dipole moments of various and selected electronic transitions. This formalism is both general and flexible and it may be employed in any electronic excitations involving f N type configurations for the rare earths in centrosymmetric co-ordination compounds in cubic environments and also in doped host crystals belonging to the space group Fm 3m. (author)
Generalized rate-code model for neuron ensembles with finite populations
International Nuclear Information System (INIS)
Hasegawa, Hideo
2007-01-01
We have proposed a generalized Langevin-type rate-code model subjected to multiplicative noise, in order to study stationary and dynamical properties of an ensemble containing a finite number N of neurons. Calculations using the Fokker-Planck equation have shown that, owing to the multiplicative noise, our rate model yields various kinds of stationary non-Gaussian distributions such as Γ, inverse-Gaussian-like, and log-normal-like distributions, which have been experimentally observed. The dynamical properties of the rate model have been studied with the use of the augmented moment method (AMM), which was previously proposed by the author from a macroscopic point of view for finite-unit stochastic systems. In the AMM, the original N-dimensional stochastic differential equations (DEs) are transformed into three-dimensional deterministic DEs for the means and fluctuations of local and global variables. The dynamical responses of the neuron ensemble to pulse and sinusoidal inputs calculated by the AMM are in good agreement with those obtained by direct simulation. The synchronization in the neuronal ensemble is discussed. The variabilities of the firing rate and of the interspike interval are shown to increase with increasing magnitude of multiplicative noise, which may be a conceivable origin of the observed large variability in cortical neurons
A general theory of multimetric indices and their properties
Schoolmaster, Donald R.; Grace, James B.; Schweiger, E. William
2012-01-01
1. Stewardship of biological and ecological resources requires the ability to make integrative assessments of ecological integrity. One of the emerging methods for making such integrative assessments is multimetric indices (MMIs). These indices synthesize data, often from multiple levels of biological organization, with the goal of deriving a single index that reflects the overall effects of human disturbance. Despite the widespread use of MMIs, there is uncertainty about why this approach can be effective. An understanding of MMIs requires a quantitative theory that illustrates how the properties of candidate metrics relates to MMIs generated from those metrics. 2. We present the initial basis for such a theory by deriving the general mathematical characteristics of MMIs assembled from metrics. We then use the theory to derive quantitative answers to the following questions: Is there an optimal number of metrics to comprise an index? How does covariance among metrics affect the performance of the index derived from those metrics? And what are the criteria to decide whether a given metric will improve the performance of an index? 3. We find that the optimal number of metrics to be included in an index depends on the theoretical distribution of signal of the disturbance gradient contained in each metric. For example, if the rank-ordered parameters of a metric-disturbance regression can be described by a monotonically decreasing function, then an optimum number of metrics exists and can often be derived analytically. We derive the conditions by which adding a given metric can be expected to improve an index. 4. We find that the criterion defining such conditions depends nonlinearly of the signal of the disturbance gradient, the noise (error) of the metric and the correlation of the metric errors. Importantly, we find that correlation among metric errors increases the signal required for the metric to improve the index. 5. The theoretical framework presented in this
Collins, William
1989-01-01
The magnetohydrodynamic wave emission from several localized, periodic, kinematically specified fluid velocity fields are calculated using Lighthill's method for finding the far-field wave forms. The waves propagate through an isothermal and uniform plasma with a constant B field. General properties of the energy flux are illustrated with models of pulsating flux tubes and convective rolls. Interference theory from geometrical optics is used to find the direction of minimum fast-wave emission from multipole sources and slow-wave emission from discontinuous sources. The distribution of total flux in fast and slow waves varies with the ratios of the source dimensions l to the acoustic and Alfven wavelengths.
On the general theory of the origins of retroviruses
Directory of Open Access Journals (Sweden)
Wayengera Misaki
2010-02-01
Full Text Available Abstract Background The order retroviridae comprises viruses based on ribonucleic acids (RNA. Some, such as HIV and HTLV, are human pathogens. Newly emerged human retroviruses have zoonotic origins. As far as has been established, both repeated infections (themselves possibly responsible for the evolution of viral mutations (Vm and host adaptability (Ha; along with interplay between inhibitors and promoters of cell tropism, are needed to effect retroviral cross-species transmissions. However, the exact modus operadi of intertwine between these factors at molecular level remains to be established. Knowledge of such intertwine could lead to a better understanding of retrovirology and possibly other infectious processes. This study was conducted to derive the mathematical equation of a general theory of the origins of retroviruses. Methods and results On the basis of an arbitrarily non-Euclidian geometrical "thought experiment" involving the cross-species transmission of simian foamy virus (sfv from a non-primate species Xy to Homo sapiens (Hs, initially excluding all social factors, the following was derived. At the port of exit from Xy (where the species barrier, SB, is defined by the Index of Origin, IO, sfv shedding is (1 enhanced by two transmitting tensors (Tt, (i virus-specific immunity (VSI and (ii evolutionary defenses such as APOBEC, RNA interference pathways, and (when present expedited therapeutics (denoted e2D; and (2 opposed by the five accepting scalars (At: (a genomic integration hot spots, gIHS, (b nuclear envelope transit (NMt vectors, (c virus-specific cellular biochemistry, VSCB, (d virus-specific cellular receptor repertoire, VSCR, and (e pH-mediated cell membrane transit, (↓pH CMat. Assuming As and Tt to be independent variables, IO = Tt/As. The same forces acting in an opposing manner determine SB at the port of sfv entry (defined here by the Index of Entry, IE = As/Tt. Overall, If sfv encounters no unforeseen effects on
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)
Weak circulation theorems as a way of distinguishing between generalized gravitation theories
International Nuclear Information System (INIS)
Enosh, M.
1980-01-01
It was proved in a previous paper that a generalized circulation theorem characterizes Einstein's theory of gravitation as a special case of a more general theory of gravitation, which is also based on the principle of equivalence. Here the question of whether it is possible to weaken this circulation theorem in such ways that it would imply more general theories than Einstein's is posed. This problem is solved. Principally, there are two possibilities. One of them is essentially Weyl's theory. (author)
Cross section recondensation method via generalized energy condensation theory
International Nuclear Information System (INIS)
Douglass, Steven; Rahnema, Farzad
2011-01-01
Highlights: → A new method is presented which corrects for core environment error from specular boundaries at the lattice cell level. → Solution obtained with generalized energy condensation provides improved approximation to the core level fine-group flux. → Iterative recondensation of the cross sections and unfolding of the flux provides on-the-fly updating of the core cross sections. → Precomputation of energy integrals and fine-group cross sections allows for easy implementation and efficient solution. → Method has been implemented in 1D and shown to correct the environment error, particularly in strongly heterogeneous cores. - Abstract: The standard multigroup method used in whole-core reactor analysis relies on energy condensed (coarse-group) cross sections generated from single lattice cell calculations, typically with specular reflective boundary conditions. Because these boundary conditions are an approximation and not representative of the core environment for that lattice, an error is introduced in the core solution (both eigenvalue and flux). As current and next generation reactors trend toward increasing assembly and core heterogeneity, this error becomes more significant. The method presented here corrects for this error by generating updated coarse-group cross sections on-the-fly within whole-core reactor calculations without resorting to additional cell calculations. In this paper, the fine-group core flux is unfolded by making use of the recently published Generalized Condensation Theory and the cross sections are recondensed at the whole-core level. By iteratively performing this recondensation, an improved core solution is found in which the core-environment has been fully taken into account. This recondensation method is both easy to implement and computationally very efficient because it requires precomputation and storage of only the energy integrals and fine-group cross sections. In this work, the theoretical basis and development
International Nuclear Information System (INIS)
Tamaki, Takashi; Torii, Takashi; Maeda, Kei-ichi
2003-01-01
We perform a linear perturbation analysis for black hole solutions with a 'massive' Yang-Mills field (the Proca field) in Brans-Dicke theory and find that the results are quite consistent with those via catastrophe theory where thermodynamic variables play an intrinsic role. Based on this observation, we show the general relation between these two methods in generalized theories of gravity which are conformally related to the Einstein-Hilbert action
Does general relativity theory possess the classical newtonian limit
International Nuclear Information System (INIS)
Denisov, V.I.; Logunov, A.A.
1980-01-01
A detailed comparison of newtonian approximation of the Einstein theory and the Newton theory of gravity is made. A difference of principle between these two theories is clarified at the stage of obtaining integrals of motion. Exact eqautions of motion and Einstein equations shows the existence only zero integrals of motion as well as in the newtonian approximation. A conclusion is that GRT has no classical newtonian limit, since the integrals of motion in the Newton theory of gravity and in the newtonian approximation of the Einstein theory do not coincide [ru
Raising Keynes: A General Theory for the 21st century
Directory of Open Access Journals (Sweden)
Stephen A. Marglin
2018-01-01
Full Text Available Keynes’s General Theory argues there is no self-regulating mechanism that guarantees full employment. Keynes’s vision has been distorted by mainstream Keynesians to mean that it is the warts on the body of capitalism, not capitalism itself, that are the problem: frictions and imperfections and rigidities may interfere with the mechanism for self-regulation that inheres in the perfectly competitive model. This distortion has two supposed corollaries, first, that the more the economy resembles the textbook model of perfect competition, the less likely are lapses from full employment; second, that since imperfections are limited to the short run, so are lapses from full employment.Keynes was unable to convince the economics profession that the problem is capitalism; that the warts, real though they are, obscure a more fundamental problem. The reason is that Keynes lacked the mathematical tools to substantiate his vision. This paper deploys tools that were unavailable to Keynes, in order to lay the foundations of a Keynesian macroeconomics for the 21st century. Keywords: Keynes, Dynamic vs static models, Flexprice adjustment, Fixprice adjustment, JEL codes: B22, B41, E12
On the role of general system theory for functional neuroimaging.
Stephan, Klaas Enno
2004-12-01
One of the most important goals of neuroscience is to establish precise structure-function relationships in the brain. Since the 19th century, a major scientific endeavour has been to associate structurally distinct cortical regions with specific cognitive functions. This was traditionally accomplished by correlating microstructurally defined areas with lesion sites found in patients with specific neuropsychological symptoms. Modern neuroimaging techniques with high spatial resolution have promised an alternative approach, enabling non-invasive measurements of regionally specific changes of brain activity that are correlated with certain components of a cognitive process. Reviewing classic approaches towards brain structure-function relationships that are based on correlational approaches, this article argues that these approaches are not sufficient to provide an understanding of the operational principles of a dynamic system such as the brain but must be complemented by models based on general system theory. These models reflect the connectional structure of the system under investigation and emphasize context-dependent couplings between the system elements in terms of effective connectivity. The usefulness of system models whose parameters are fitted to measured functional imaging data for testing hypotheses about structure-function relationships in the brain and their potential for clinical applications is demonstrated by several empirical examples.
Cognitive performance modeling based on general systems performance theory.
Kondraske, George V
2010-01-01
General Systems Performance Theory (GSPT) was initially motivated by problems associated with quantifying different aspects of human performance. It has proved to be invaluable for measurement development and understanding quantitative relationships between human subsystem capacities and performance in complex tasks. It is now desired to bring focus to the application of GSPT to modeling of cognitive system performance. Previous studies involving two complex tasks (i.e., driving and performing laparoscopic surgery) and incorporating measures that are clearly related to cognitive performance (information processing speed and short-term memory capacity) were revisited. A GSPT-derived method of task analysis and performance prediction termed Nonlinear Causal Resource Analysis (NCRA) was employed to determine the demand on basic cognitive performance resources required to support different levels of complex task performance. This approach is presented as a means to determine a cognitive workload profile and the subsequent computation of a single number measure of cognitive workload (CW). Computation of CW may be a viable alternative to measuring it. Various possible "more basic" performance resources that contribute to cognitive system performance are discussed. It is concluded from this preliminary exploration that a GSPT-based approach can contribute to defining cognitive performance models that are useful for both individual subjects and specific groups (e.g., military pilots).
Generalized polarizabilities of the nucleon in baryon chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Lensky, Vadim [Johannes Gutenberg Universitaet Mainz, Institut fuer Kernphysik, Cluster of Excellence PRISMA, Mainz (Germany); Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation); Pascalutsa, Vladimir; Vanderhaeghen, Marc [Johannes Gutenberg Universitaet Mainz, Institut fuer Kernphysik, Cluster of Excellence PRISMA, Mainz (Germany)
2017-02-15
The nucleon generalized polarizabilities (GPs), probed in virtual Compton scattering (VCS), describe the spatial distribution of the polarization density in a nucleon. They are accessed experimentally via the process of electron-proton bremsstrahlung (ep → epγ) at electron-beam facilities, such as MIT-Bates, CEBAF (Jefferson Lab), and MAMI (Mainz). We present the calculation of the nucleon GPs and VCS observables at next-to-leading order in baryon chiral perturbation theory (BχPT), and confront the results with the empirical information. At this order our results are predictions, in the sense that all the parameters are well known from elsewhere. Within the relatively large uncertainties of our calculation we find good agreement with the experimental observations of VCS and the empirical extractions of the GPs. We find large discrepancies with previous chiral calculations - all done in heavy-baryon χPT (HBχPT) - and discuss the differences between BχPT and HBχPT responsible for these discrepancies. (orig.)
Theory of mind and hypomanic traits in general population.
Terrien, Sarah; Stefaniak, Nicolas; Blondel, Marine; Mouras, Harold; Morvan, Yannick; Besche-Richard, Chrystel
2014-03-30
Theory of Mind (ToM) is the ability to assign a set of mental states to yourself and others. In bipolar disorders, alteration of social relationship can be explained by the impairment of the functioning of ToM. Deficit in ToM could be a trait marker of bipolar disorder and people in the general population with high hypomanic personality scores would be more likely to develop bipolar disorders. This study examined 298 participants. Measures of hypomanic personality were evaluated using the Hypomanic Personality Scale. ToM was explored using the Yoni task. Participants also completed the BDI-II. Forward multiple regressions were performed to examine the effect of components of the HPS on the total score in the ToM task. In the women's group, no subscales of the HPS were included in the model. Conversely, the analyses performed on men revealed that the mood vitality and excitement subscale was a significant predictor of ToM abilities. Our study is the first to show the impact of certain dimensions of hypomanic personality on performance in ToM in a male sample. This result supports the idea that deficits in ToM can be a trait marker of bipolar disorder in a healthy male population. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
Does the General Strain Theory Explain Gambling and Substance Use?
Greco, Romy; Curci, Antonietta
2017-09-01
General Strain Theory (GST: Agnew Criminology 30:47-87, 1992) posits that deviant behaviour results from adaptation to strain and the consequent negative emotions. Empirical research on GST has mainly focused on aggressive behaviours, while only few research studies have considered alternative manifestations of deviance, like substance use and gambling. The aim of the present study is to test the ability of GST to explain gambling behaviours and substance use. Also, the role of family in promoting the adoption of gambling and substance use as coping strategies was verified. Data from 266 families with in mean 8 observations for each group were collected. The multilevel nature of the data was verified before appropriate model construction. The clustered nature of gambling data was analysed by a two-level Hierarchical Linear Model while substance use was analysed by Multivariate Linear Model. Results confirmed the effect of strain on gambling and substance use while the positive effect of depressive emotions on these behaviours was not supported. Also, the impact of family on the individual tendency to engage in addictive behaviours was confirmed only for gambling.
Supergravity and Yang-Mills theories as generalized topological fields with constraints
International Nuclear Information System (INIS)
Ling Yi; Tung Rohsuan; Guo Hanying
2004-01-01
We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF formulations of general relativity and Yang-Mills theories, but also the N=1,2 chiral supergravities can be reformulated as these constrained generalized topological field theories once the free parameters in the Lagrangian are specially chosen. We also show that the Chern-Simons action on the boundary may naturally be induced from the generalized topological action in the bulk, rather than introduced by hand
Toward a General Research Process for Using Dubin's Theory Building Model
Holton, Elwood F.; Lowe, Janis S.
2007-01-01
Dubin developed a widely used methodology for theory building, which describes the components of the theory building process. Unfortunately, he does not define a research process for implementing his theory building model. This article proposes a seven-step general research process for implementing Dubin's theory building model. An example of a…
International Nuclear Information System (INIS)
Warnock, R.L.
2000-01-01
The authors propose and illustrate a general numerical method to follow the probability distribution in phase space as a function of time. It applies to any multiparticle system governed by Liouville, Vlasov or Vlasov-Fokker-Planck dynamics. The technique, based on discretization of the local Perron-Frobenius operator, is simple in concept, easy to implement, and numerically stable in examples studied to date. The authors illustrate by treating longitudinal dynamics in electron storage rings with realistic wake field. Applied to the SLC damping rings, the method gives the observed current threshold for bunch lengthening, and several aspects of observed behavior above threshold, including the presence of a bursting or sawtooth mode. In contrast to previous particle-in-cell simulations, the authors have very low numerical noise and the ability to follow the motion over several damping times. The method has also been applied to the coherent beam-beam interaction. It appears likely that this approach will be of interest for some of the central problems of this workshop, for instance matching of space-charge dominated beams to a focusing channel, and coherent synchrotron radiation with self-consistent charge/current density
A general action for topological quantum field theories
International Nuclear Information System (INIS)
Dayi, O.F.
1989-03-01
Topological field theories can be formulated by beginning from a higher dimensional action. The additional dimension is an unphysical time parameter and the action is the derivative of a functional W with respect to this variable. In the d = 4 case, it produces actions which are shown to give topological quantum field theory after gauge fixing. In d = 3 this action leads to the Hamiltonian, which yields the Floer groups if the additional parameter is treated as physical when W is the pure Chern-Simons action. This W can be used to define a topological quantum field theory in d = 3 by treating the additional parameter as unphysical. The BFV-BRST operator quantization of this theory yields to an enlarged system which has only first class constraints. This is not identical to the previously introduced d = 3 topological quantum field theory, even if it is shown that the latter theory also gives the theory which we began with, after a partial gauge fixing. (author). 18 refs
International Nuclear Information System (INIS)
Buchbinder, I.L.; Lyakhovich, S.L.; Pershin, V.D.; Fradkin, E.S.
1991-01-01
At present, superstring theory is the only candidate to be a unified theory of all fundamental interactions. For this reason, the various aspects of the string theory have been attracting great attention. String theory has a nontrivial gauge symmetry and therefore is an interesting object from the viewpoint of application of general quantization methods. This paper discusses the bosonic string theory. The purpose of this paper is a consistent operator quantization of the theory with the action. The natural basis for it is provided by the method of the generalized canonical quantization
Exact marginality in open string field theory. A general framework
International Nuclear Information System (INIS)
Kiermaier, M.
2007-07-01
We construct analytic solutions of open bosonic string field theory for any exactly marginal deformation in any boundary conformal field theory when properly renormalized operator products of the marginal operator are given. We explicitly provide such renormalized operator products for a class of marginal deformations which include the deformations of flat D-branes in flat backgrounds by constant massless modes of the gauge field and of the scalar fields on the D-branes, the cosine potential for a space-like coordinate, and the hyperbolic cosine potential for the time-like coordinate. In our construction we use integrated vertex operators, which are closely related to finite deformations in boundary conformal field theory, while previous analytic solutions were based on unintegrated vertex operators. We also introduce a modified star product to formulate string field theory around the deformed background. (orig.)
Florentina Xhelili Krasniqi; Rahmie Topxhiu; Donat Rexha
2016-01-01
Nobel Laureates with their contributions to the development of the theory of general equilibrium have enabled this theory to be one of the most important for theoretical and practical analysis of the overall economy and the efficient use of economic resources. Results of the research showing that contributions of Nobel Laureates in the economy belong to two main frameworks of development of the general equilibrium theory: one was the mathematical model of general equilibrium developed by J...
General fluid theories, variational principles and self-organization
International Nuclear Information System (INIS)
Mahajan, S.M.
2002-01-01
This paper reports two distinct but related advances: (1) The development and application of fluid theories that transcend conventional magnetohydrodynamics (MHD), in particular, theories that are valid in the long-mean-free-path limit and in which pressure anisotropy, heat flow, and arbitrarily strong sheared flows are treated consistently. (2) The discovery of new pressure-confining plasma configurations that are self-organized relaxed states. (author)
Topics in the Foundations of General Relativity and Newtonian Gravitation Theory
Malament, David B
2012-01-01
In Topics in the Foundations of General Relativity and Newtonian Gravitation Theory, David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativity and its relation to Newtonian gravitation theory. These special topics include the geometrized formulation of Newtonian theory (also known as Newton-Cartan theory), the concept of rotation in general relativity, and Gödel spacetime. One of the highlights of the book is a no-go theorem that can be understood to show that there is
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.)
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.)
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.)
Generalized uncertainty principle as a consequence of the effective field theory
Energy Technology Data Exchange (ETDEWEB)
Faizal, Mir, E-mail: mirfaizalmir@gmail.com [Irving K. Barber School of Arts and Sciences, University of British Columbia – Okanagan, Kelowna, British Columbia V1V 1V7 (Canada); Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta T1K 3M4 (Canada); Ali, Ahmed Farag, E-mail: ahmed.ali@fsc.bu.edu.eg [Department of Physics, Faculty of Science, Benha University, Benha, 13518 (Egypt); Netherlands Institute for Advanced Study, Korte Spinhuissteeg 3, 1012 CG Amsterdam (Netherlands); Nassar, Ali, E-mail: anassar@zewailcity.edu.eg [Department of Physics, Zewail City of Science and Technology, 12588, Giza (Egypt)
2017-02-10
We will demonstrate that the generalized uncertainty principle exists because of the derivative expansion in the effective field theories. This is because in the framework of the effective field theories, the minimum measurable length scale has to be integrated away to obtain the low energy effective action. We will analyze the deformation of a massive free scalar field theory by the generalized uncertainty principle, and demonstrate that the minimum measurable length scale corresponds to a second more massive scale in the theory, which has been integrated away. We will also analyze CFT operators dual to this deformed scalar field theory, and observe that scaling of the new CFT operators indicates that they are dual to this more massive scale in the theory. We will use holographic renormalization to explicitly calculate the renormalized boundary action with counter terms for this scalar field theory deformed by generalized uncertainty principle, and show that the generalized uncertainty principle contributes to the matter conformal anomaly.
Generalized uncertainty principle as a consequence of the effective field theory
Directory of Open Access Journals (Sweden)
Mir Faizal
2017-02-01
Full Text Available We will demonstrate that the generalized uncertainty principle exists because of the derivative expansion in the effective field theories. This is because in the framework of the effective field theories, the minimum measurable length scale has to be integrated away to obtain the low energy effective action. We will analyze the deformation of a massive free scalar field theory by the generalized uncertainty principle, and demonstrate that the minimum measurable length scale corresponds to a second more massive scale in the theory, which has been integrated away. We will also analyze CFT operators dual to this deformed scalar field theory, and observe that scaling of the new CFT operators indicates that they are dual to this more massive scale in the theory. We will use holographic renormalization to explicitly calculate the renormalized boundary action with counter terms for this scalar field theory deformed by generalized uncertainty principle, and show that the generalized uncertainty principle contributes to the matter conformal anomaly.
Directory of Open Access Journals (Sweden)
Stefan Hollands
2009-09-01
Full Text Available In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.
A general theory of macrofinance: Towards a new paradigm
Directory of Open Access Journals (Sweden)
Chen Yulu
2017-01-01
Full Text Available The 2008 international financial crisis triggered retrospection on both theory and policy, reaching a macroeconomic consensus that the financial system plays an important role in the macro economy and macroeconomic theory must be restructured to incorporate endogenous financial factors. Reflecting on the inherent flaws of traditional mainstream economics, this paper puts forward a “macrofinance” proposition as a new paradigm for macro financial analysis. As a scientific methodology based on systematic logic, the major feature of the macrofinance framework is that we must analyze the financial system as a core part of a complete and endogenous analytical framework, instead of only focusing on the money or credit. The goal of “macrofinance” is to return to scientific economic methodologies by analyzing the inherent laws of modern financial systems to set up a comprehensive theoretical framework that unifies the financial sector with the real economy and combines theory and policy practice.
Nonequilibrium statistical mechanics in the general theory of relativity. I. A general formalism
International Nuclear Information System (INIS)
Israel, W.; Kandrup, H.E.
1984-01-01
This is the first in a series of papers, the overall objective of which is the formulation of a new covariant approach to nonequilibrium statistical mechanics in classical general relativity. The objecct here is the development of a tractable theory for self-gravitating systems. It is argued that the ''state'' of an N-particle system may be characterized by an N-particle distribution function, defined in an 8N-dimensional phase space, which satisfies a collection of N conservation equations. By mapping the true physics onto a fictitious ''background'' spacetime, which may be chosen to satisfy some ''average'' field equations, one then obtains a useful covariant notion of ''evolution'' in response to a fluctuating ''gravitational force.'' For many cases of practical interest, one may suppose (i) that these fluctuating forces satisfy linear field equations and (ii) that they may be modeled by a direct interaction. In this case, one can use a relativistic projection operator formalism to derive exact closed equations for the evolution of such objects as an appropriately defined reduced one-particle distribution function. By capturing, in a natural way, the notion of a dilute gas, or impulse, approximation, one is then led to a comparatively simple equation for the one-particle distribution. If, furthermore, one treats the effects of the fluctuating forces as ''localized'' in space and time, one obtains a tractable kinetic equation which reduces, in the Newtonian limit, to the stardard Landau equation
Directory of Open Access Journals (Sweden)
Yongbin Chang
2011-09-01
Full Text Available By introducing a cutoff on the cumulative measure of a force, a unified kinetic theory is developed for both rigid-sphere and inverse-square force laws. The difference between the two kinds of interactions is characterized by a parameter, γ, which is 1 for rigid-sphere interactions and -3 for inverse-square force law interactions. The quantities governed by γ include the specific reaction rates, kernels, collision frequencies, arbitrarily high orders of transition moments, arbitrarily high orders of Fokker-Planck expansion (also called Kramers-Moyal expansion coefficients, and arbitrarily high orders of energy exchange rates. The cutoff constants are shown to be incomplete gamma functions of different orders. The widely used cutoff constant in plasma physics (usually known as Coulomb logarithm is found to be exactly the zeroth order of the incomplete gamma function. The well known Arrhenius reaction rate formula comes from the first order of the incomplete gamma functions, while the negative first order can be used for fitting the fusion reaction rate between deuterium and tritium.
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
A General Theory of Markovian Time Inconsistent Stochastic Control Problems
DEFF Research Database (Denmark)
Björk, Tomas; Murgochi, Agatha
We develop a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for Nash subgame perfect equilibrium points...... examples of time inconsistency in the literature are easily seen to be special cases of the present theory. We also prove that for every time inconsistent problem, there exists an associated time consistent problem such that the optimal control and the optimal value function for the consistent problem...
International Nuclear Information System (INIS)
Cohendet, O.
1989-01-01
We consider a quantum system with a finite number N of states and we show that a Markov process evolving in an 'extended' discrete phase can be associated with the discrete Wigner function of the system. This Wigner function is built using the Weyl quantization procedure on the group Z N xZ N . Moreover we can use this process to compute the quantum mean values as probabilistic expectations of functions of this process. This probabilistic formulation can be seen as a stochastic mechanics in phase space. (orig.)
International Nuclear Information System (INIS)
Catto, P.J.; Myra, J.R.; Russell, D.A.
1994-01-01
The off-axis quasilinear fast wave minority heating description of Catto and Myra [Phys. Fluids B 4, 187 (1992)] has been improved and implemented in a code which solves the combined quasilinear and collision operator equation for the minority distribution function. Geometrical complications of a minority resonance nearly tangent to a flux surface in the presence of trapped as well as passing particles are retained. The tangency interactions alter the moments and the fusion reaction rate parameter in a model which explores heating on a single flux surface. The strong tangency interactions enhance the more familiar interactions due to trapped particles turning in the vicinity of the minority resonance. An asymmetry in off-axis heating effects occurs because heating on the low field side of the magnetic axis heats more trapped particles than high field side heating. This asymmetry is responsible for the better performance of the low field side case relative to the high and on-axis cases and provides some control over the power absorbed by and the energy stored in the trapped particles
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.)
International Nuclear Information System (INIS)
Prinja, A.K.
1995-08-01
We have developed and successfully implemented a two-dimensional bilinear discontinuous in space and time, used in conjunction with the S N angular approximation, to numerically solve the time dependent, one-dimensional, one-speed, slab geometry, (ion) transport equation. Numerical results and comparison with analytical solutions have shown that the bilinear-discontinuous (BLD) scheme is third-order accurate in the space ad time dimensions independently. Comparison of the BLD results with diamond-difference methods indicate that the BLD method is both quantitavely and qualitatively superior to the DD scheme. We note that the form of the transport operator is such that these conclusions carry over to energy dependent problems that include the constant-slowing-down-approximation term, and to multiple space dimensions or combinations thereof. An optimized marching or inversion scheme or a parallel algorithm should be investigated to determine if the increased accuracy can compensate for the extra overhead required for a BLD solution, and then could be compared to other discretization methods such as nodal or characteristic schemes
DEFF Research Database (Denmark)
Visser, Andre
2008-01-01
The movement of plankton, either by turbulent mixing or their own inherent motility, can be simulated in a Lagrangian framework as a random walk. Validation of random walk simulations is essential. There is a continuum of mathematically valid stochastic integration schemes upon which random walk...
General practice and the new science emerging from the theories of 'chaos' and complexity.
Griffiths, F; Byrne, D
1998-01-01
This paper outlines the general practice world view and introduces the main features of the theories of 'chaos' and complexity. From this, analogies are drawn between general practice and the theories, which suggest a different way of understanding general practice and point to future developments in general practice research. A conceptual and practical link between qualitative and quantitative methods of research is suggested. Methods of combining data about social context with data about in...
Generalized KKR-theory for non-muffin-tin potentials
Molenaar, J.
1989-01-01
The author shows that the secular equation in KKR (Korringa, Kohn and Rostoker) theory retains its separable structure also in the case of non-muffin-tin potentials. This generalisation has been extensively discussed recently. During this discussion, in which the possible necessity of so-called near
Indefinite-metric quantum field theory of general relativity, 6
International Nuclear Information System (INIS)
Nakanishi, Noboru
1979-01-01
The canonical commutation relations are analyzed in detail in the indefinite-metric quantum field theory of gravity based on the vierbein formalism. It is explicitly verified that the BRS charge, the local-Lorentz-BRS charge and the Poincare generators satisfy the expected commutation relations. (author)
Cyberbullying among Adolescents: A General Strain Theory Perspective
Paez, Gabriel R.
2018-01-01
Cyber bullying has become more pervasive as a result of advances in communication technology such as email, text messaging, chat rooms, and social media sites. Despite the growth in research on correlates associated with engagement in cyber bullying, few studies test the applicability of criminological theories to explain engagement in cyber…
Principles of general relativity theory in terms of the present day physics
International Nuclear Information System (INIS)
Pervushin, V.N.
1986-01-01
A hystory of gradual unification of general relativity theory and quantum field theory on the basis of unified geometrical principles is detected. The gauge invariance principles became universal for construction of all physical theories. Quantum mechanics, electrodynamics and Einstein gravitation theory were used to form geometrical principles. Identity of inertial and gravitational masses is an experimental basis of the general relativity theory (GRT). It is shown that correct understanding of GRT bases is a developing process related to the development of the present physics and stimulating this development
Generalized perturbation theory based on the method of cyclic characteristics
Energy Technology Data Exchange (ETDEWEB)
Assawaroongruengchot, M.; Marleau, G. [Institut de Genie Nucleaire, Departement de Genie Physique, Ecole Polytechnique de Montreal, 2900 Boul. Edouard-Montpetit, Montreal, Que. H3T 1J4 (Canada)
2006-07-01
A GPT algorithm for estimation of eigenvalues and reaction-rate ratios is developed for the neutron transport problems in 2D fuel assemblies with isotropic scattering. In our study the GPT formulation is based on the integral transport equations. The mathematical relationship between the generalized flux importance and generalized source importance functions is applied to transform the generalized flux importance transport equations into the integro-differential forms. The resulting adjoint and generalized adjoint transport equations are then solved using the method of cyclic characteristics (MOCC). Because of the presence of negative adjoint sources, a biasing/decontamination scheme is applied to make the generalized adjoint functions positive in such a way that it can be used for the multigroup re-balance technique. To demonstrate the efficiency of the algorithms, perturbative calculations are performed on a 17 x 17 PWR lattice. (authors)
Generalized perturbation theory based on the method of cyclic characteristics
International Nuclear Information System (INIS)
Assawaroongruengchot, M.; Marleau, G.
2006-01-01
A GPT algorithm for estimation of eigenvalues and reaction-rate ratios is developed for the neutron transport problems in 2D fuel assemblies with isotropic scattering. In our study the GPT formulation is based on the integral transport equations. The mathematical relationship between the generalized flux importance and generalized source importance functions is applied to transform the generalized flux importance transport equations into the integro-differential forms. The resulting adjoint and generalized adjoint transport equations are then solved using the method of cyclic characteristics (MOCC). Because of the presence of negative adjoint sources, a biasing/decontamination scheme is applied to make the generalized adjoint functions positive in such a way that it can be used for the multigroup re-balance technique. To demonstrate the efficiency of the algorithms, perturbative calculations are performed on a 17 x 17 PWR lattice. (authors)
Calculus of variations in rate of reactions tax using the general pertubation theory
International Nuclear Information System (INIS)
Silva, F.C. da.
1981-02-01
A perturbation expression to calculate the variations in the rates of integral parameters (such as reaction rates) of a reactor using a Time-Independent Generalized Perturbation Theory, was developed. This theory makes use of the concepts of neutron generation and neutron importance with respect to a given process occurring in a system. The application of Time-Dependent Generalized Perturbation Theory to the calculation of Burnup, by using the expressions derived by A. Gandini, along with the perturbation expression derived in the Time Independent Generalized Perturbation Theory, is done. (Author) [pt
A generalized non-local optical response theory for plasmonic nanostructures
DEFF Research Database (Denmark)
Mortensen, N. Asger; Raza, Søren; Wubs, Martijn
2014-01-01
for their description. Here instead we present a comparatively simple semiclassical generalized non-local optical response theory that unifies quantum pressure convection effects and induced charge diffusion kinetics, with a concomitant complex-valued generalized non-local optical response parameter. Our theory...