Design and optimization of a Holweck pump via linear kinetic theory

International Nuclear Information System (INIS)

Naris, Steryios; Koutandou, Eirini; Valougeorgis, Dimitris

2012-01-01

The Holweck pump is widely used in the vacuum pumping industry. It can be a self standing apparatus or it can be part of a more advanced pumping system. It is composed by an inner rotating cylinder (rotor) and an outer stationary cylinder (stator). One of them, has spiral guided grooves resulting to a gas motion from the high towards the low vacuum port. Vacuum pumps may be simulated by the DSMC method but due to the involved high computational cost in many cases manufactures commonly resort to empirical formulas and experimental data. Recently a computationally efficient simulation of the Holweck pump via linear kinetic theory has been proposed by Sharipov et al [1]. Neglecting curvature and end effects the gas flow configuration through the helicoidal channels is decomposed into four basic flows. They correspond to pressure and boundary driven flows through a grooved channel and through a long channel with a T shape cross section. Although the formulation and the methodology are explained in detail, results are very limited and more important they are presented in a normalized way which does not provide the needed information about the pump performance in terms of the involved geometrical and flow parameters. In the present work the four basic flows are solved numerically based on the linearized BGK model equation subjected to diffuse boundary conditions. The results obtained are combined in order to create a database of the flow characteristics for a large spectrum of the rarefaction parameter and various geometrical configurations. Based on this database the performance characteristics which are critical in the design of the Holweck pump are computed and the design parameters such as the angle of the pump and the rotational speed, are optimized. This modeling may be extended to other vacuum pumps.

Quantum Kinetic Theory and Applications Electrons, Photons, Phonons

CERN Document Server

Vasko, Fedir T

2006-01-01

This lecture-style monograph is addressed to several categories of readers. First, it will be useful for graduate students studying theory. Second, the topics covered should be interesting for postgraduate students of various specializations. Third, the researchers who want to understand the background of modern theoretical issues in more detail can find a number of useful results here. The phenomena covered involve kinetics of electron, phonon, and photon systems in solids. The dynamical properties and interactions of electrons, phonons, and photons are briefly described in Chapter 1. Further, in Chapters 2-8, the authors present the main theoretical methods: linear response theory, various kinetic equations for the quasiparticles under consideration, and diagram technique. The presentation of the key approaches is always accompanied by solutions of concrete problems to illustrate ways to apply the theory. The remaining chapters are devoted to various manifestations of quantum transport in solids. The choice...

Relaxation and kinetics in scalar field theories

International Nuclear Information System (INIS)

Boyanovsky, D.; Lawrie, I.D.; Lee, D.

1996-01-01

A new approach to the dynamics of relaxation and kinetics of thermalization in a scalar field theory is presented that incorporates the relevant time scales through the resummation of hard thermal loops. An alternative derivation of the kinetic equations for the open-quote open-quote quasiparticle close-quote close-quote distribution functions is obtained that allows a clear understanding of the different open-quote open-quote coarse-graining close-quote close-quote approximations usually involved in a kinetic description. This method leads to a systematic perturbative expansion to obtain the kinetic equations including hard thermal loop resummation and to an improvement including renormalization, off-shell effects, and contributions that change chemical equilibrium on short time scales. As a by-product of these methods we establish the equivalence between the relaxation time scale in the linearized equation of motion of the quasiparticles and the thermalization time scale of the quasiparticle distribution function in the open-quote open-quote relaxation time approximation close-quote close-quote including hard thermal loop effects. Hard thermal loop resummation dramatically modifies the scattering rate for long wavelength modes as compared to the usual (semi)classical estimate. Relaxation and kinetics are studied both in the unbroken and broken symmetry phases of the theory. The broken symmetry phase also provides the setting to obtain the contribution to the kinetic equations from processes that involve decay of a heavy scalar into light scalar particles in the medium. copyright 1996 The American Physical Society

Gyrocenter-gauge kinetic theory

International Nuclear Information System (INIS)

Qin, H.; Tang, W.M.; Lee, W.W.

2000-01-01

Gyrocenter-gauge kinetic theory is developed as an extension of the existing gyrokinetic theories. In essence, the formalism introduced here is a kinetic description of magnetized plasmas in the gyrocenter coordinates which is fully equivalent to the Vlasov-Maxwell system in the particle coordinates. In particular, provided the gyroradius is smaller than the scale-length of the magnetic field, it can treat high frequency range as well as the usual low frequency range normally associated with gyrokinetic approaches. A significant advantage of this formalism is that it enables the direct particle-in-cell simulations of compressional Alfven waves for MHD applications and of RF waves relevant to plasma heating in space and laboratory plasmas. The gyrocenter-gauge kinetic susceptibility for arbitrary wavelength and arbitrary frequency electromagnetic perturbations in a homogeneous magnetized plasma is shown to recover exactly the classical result obtained by integrating the Vlasov-Maxwell system in the particle coordinates. This demonstrates that all the waves supported by the Vlasov-Maxwell system can be studied using the gyrocenter-gauge kinetic model in the gyrocenter coordinates. This theoretical approach is so named to distinguish it from the existing gyrokinetic theory, which has been successfully developed and applied to many important low-frequency and long parallel wavelength problems, where the conventional meaning of gyrokinetic has been standardized. Besides the usual gyrokinetic distribution function, the gyrocenter-gauge kinetic theory emphasizes as well the gyrocenter-gauge distribution function, which sometimes contains all the physics of the problems being studied, and whose importance has not been realized previously. The gyrocenter-gauge distribution function enters Maxwell's equations through the pull-back transformation of the gyrocenter transformation, which depends on the perturbed fields. The efficacy of the gyrocenter-gauge kinetic approach is

The Pade approximate method for solving problems in plasma kinetic theory

International Nuclear Information System (INIS)

Jasperse, J.R.; Basu, B.

1992-01-01

The method of Pade Approximates has been a powerful tool in solving for the time dependent propagator (Green function) in model quantum field theories. We have developed a modified Pade method which we feel has promise for solving linearized collisional and weakly nonlinear problems in plasma kinetic theory. In order to illustrate the general applicability of the method, in this paper we discuss Pade solutions for the linearized collisional propagator and the collisional dielectric function for a model collisional problem. (author) 3 refs., 2 tabs

Relativistic Chiral Kinetic Theory

International Nuclear Information System (INIS)

Stephanov, Mikhail

2016-01-01

This very brief review of the recent progress in chiral kinetic theory is based on the results of Refs. [J.-Y. Chen, D. T. Son, M. A. Stephanov, H.-U. Yee, Y. Yin, Lorentz Invariance in Chiral Kinetic Theory, Phys. Rev. Lett. 113 (18) (2014) 182302. doi: (10.1103/PhysRevLett.113.182302); J.-Y. Chen, D. T. Son, M. A. Stephanov, Collisions in Chiral Kinetic Theory, Phys. Rev. Lett. 115 (2) (2015) 021601. doi: (10.1103/PhysRevLett.115.021601); M. A. Stephanov, H.-U. Yee, The no-drag frame for anomalous chiral fluid, Phys. Rev. Lett. 116 (12) (2016) 122302. doi: (10.1103/PhysRevLett.116.122302)].

Relativistic Chiral Kinetic Theory

Energy Technology Data Exchange (ETDEWEB)

Stephanov, Mikhail

2016-12-15

This very brief review of the recent progress in chiral kinetic theory is based on the results of Refs. [J.-Y. Chen, D. T. Son, M. A. Stephanov, H.-U. Yee, Y. Yin, Lorentz Invariance in Chiral Kinetic Theory, Phys. Rev. Lett. 113 (18) (2014) 182302. doi: (10.1103/PhysRevLett.113.182302); J.-Y. Chen, D. T. Son, M. A. Stephanov, Collisions in Chiral Kinetic Theory, Phys. Rev. Lett. 115 (2) (2015) 021601. doi: (10.1103/PhysRevLett.115.021601); M. A. Stephanov, H.-U. Yee, The no-drag frame for anomalous chiral fluid, Phys. Rev. Lett. 116 (12) (2016) 122302. doi: (10.1103/PhysRevLett.116.122302)].

Quantum kinetic theory

CERN Document Server

Bonitz, Michael

2016-01-01

This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat nonequilibrium dynamics in quantum many-body systems. Of particular interest are ultrafast processes in plasmas, condensed matter and trapped atoms that are stimulated by rapidly developing experiments with short pulse lasers and free electron lasers. To describe these experiments theoretically, the most powerful approach is given by non-Markovian quantum kinetic equations that are discussed in detail, including computational aspects.

Kinetic theory of nonequilibrium ensembles, irreversible thermodynamics, and generalized hydrodynamics

CERN Document Server

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...

Kinetic theory of nonideal gases and nonideal plasmas

CERN Document Server

Klimontovich, Yu L

2013-01-01

Kinetic Theory of Nonideal Gases and Nonideal Plasmas presents the fundamental aspects of the kinetic theory of gases and plasmas. The book consists of three parts, which attempts to present some of the ideas, methods and applications in the study of the kinetic processes in nonideal gases and plasmas. The first part focuses on the classical kinetic theory of nonideal gases. The second part discusses the classical kinetic theory of fully ionized plasmas. The last part is devoted to the quantum kinetic theory of nonideal gases and plasmas. A concluding chapter is included, which presents a shor

Asymptotic kinetic theory of magnetized plasmas: quasi-particle concept

International Nuclear Information System (INIS)

Sosenko, P.P.; Zagorodny, A.H.

2004-01-01

The asymptotic kinetic theory of magnetized plasmas is elaborated within the context of general statistical approach and asymptotic methods, developed by M. Krylov and M. Bohol'ubov, for linear and non-linear dynamic systems with a rapidly rotating phase. The quasi-particles are introduced already on the microscopic level. Asymptotic expansions enable to close the description for slow processes, and to relate consistently particles and guiding centres to quasi-particles. The kinetic equation for quasi-particles is derived. It makes a basis for the reduced description of slow collective phenomena in the medium. The kinetic equation for quasi-particles takes into account self-consistent interaction fields, quasi-particle collisions and collective-fluctuation-induced relaxation of quasi-particle distribution function. The relationships between the distribution functions for particles, guiding centres and quasi-particles are derived taking into account fluctuations, which can be especially important in turbulent states. In this way macroscopic (statistical) particle properties can be obtained from those of quasi-particles in the general case of non-equilibrium. (authors)

The Einstein-Vlasov System/Kinetic Theory.

Science.gov (United States)

Andréasson, Håkan

2011-01-01

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.

Classical Michaelis-Menten and system theory approach to modeling metabolite formation kinetics.

Science.gov (United States)

Popović, Jovan

2004-01-01

When single doses of drug are administered and kinetics are linear, techniques, which are based on the compartment approach and the linear system theory approach, in modeling the formation of the metabolite from the parent drug are proposed. Unlike the purpose-specific compartment approach, the methodical, conceptual and computational uniformity in modeling various linear biomedical systems is the dominant characteristic of the linear system approach technology. Saturation of the metabolic reaction results in nonlinear kinetics according to the Michaelis-Menten equation. The two compartment open model with Michaelis-Menten elimination kinetics is theorethicaly basic when single doses of drug are administered. To simulate data or to fit real data using this model, one must resort to numerical integration. A biomathematical model for multiple dosage regimen calculations of nonlinear metabolic systems in steady-state and a working example with phenytoin are presented. High correlation between phenytoin steady-state serum levels calculated from individual Km and Vmax values in the 15 adult epileptic outpatients and the observed levels at the third adjustment of phenytoin daily dose (r=0.961, p<0.01) were found.

Rethinking wave-kinetic theory applied to zonal flows

Science.gov (United States)

Parker, Jeffrey

2017-10-01

Over the past two decades, a number of studies have employed a wave-kinetic theory to describe fluctuations interacting with zonal flows. Recent work has uncovered a defect in this wave-kinetic formulation: the system is dominated by the growth of (arbitrarily) small-scale zonal structures. Theoretical calculations of linear growth rates suggest, and nonlinear simulations confirm, that this system leads to the concentration of zonal flow energy in the smallest resolved scales, irrespective of the numerical resolution. This behavior results from the assumption that zonal flows are extremely long wavelength, leading to the neglect of key terms responsible for conservation of enstrophy. A corrected theory, CE2-GO, is presented; it is free of these errors yet preserves the intuitive phase-space mathematical structure. CE2-GO properly conserves enstrophy as well as energy, and yields accurate growth rates of zonal flow. Numerical simulations are shown to be well-behaved and not dependent on box size. The steady-state limit simplifies into an exact wave-kinetic form which offers the promise of deeper insight into the behavior of wavepackets. The CE2-GO theory takes its place in a hierarchy of models as the geometrical-optics reduction of the more complete cumulant-expansion statistical theory CE2. The new theory represents the minimal statistical description, enabling an intuitive phase-space formulation and an accurate description of turbulence-zonal flow dynamics. This work was supported by an NSF Graduate Research Fellowship, a US DOE Fusion Energy Sciences Fellowship, and US DOE Contract Nos. DE-AC52-07NA27344 and DE-AC02-09CH11466.

Second-order kinetic model for the sorption of cadmium onto tree fern: a comparison of linear and non-linear methods.

Science.gov (United States)

Ho, Yuh-Shan

2006-01-01

A comparison was made of the linear least-squares method and a trial-and-error non-linear method of the widely used pseudo-second-order kinetic model for the sorption of cadmium onto ground-up tree fern. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. A type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a better way to obtain the desired parameters.

The Einstein-Vlasov System/Kinetic Theory

Directory of Open Access Journals (Sweden)

Håkan Andréasson

2002-12-01

Full Text Available The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically, and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (i.e., fluid models. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to good comprehension of kinetic theory in general relativity.

Unified kinetic theory in toroidal systems

International Nuclear Information System (INIS)

Hitchcock, D.A.; Hazeltine, R.D.

1980-12-01

The kinetic theory of toroidal systems has been characterized by two approaches: neoclassical theory which ignores instabilities and quasilinear theory which ignores collisions. In this paper we construct a kinetic theory for toroidal systems which includes both effects. This yields a pair of evolution equations; one for the spectrum and one for the distribution function. In addition, this theory yields a toroidal generalization of the usual collision operator which is shown to have many similar properties - conservation laws, H theorem - to the usual collision operator

Kinetic theory and transport phenomena

CERN Document Server

Soto, Rodrigo

2016-01-01

This textbook presents kinetic theory, which is a systematic approach to describing nonequilibrium systems. The text is balanced between the fundamental concepts of kinetic theory (irreversibility, transport processes, separation of time scales, conservations, coarse graining, distribution functions, etc.) and the results and predictions of the theory, where the relevant properties of different systems are computed. The book is organised in thematic chapters where different paradigmatic systems are studied. The specific features of these systems are described, building and analysing the appropriate kinetic equations. Specifically, the book considers the classical transport of charges, the dynamics of classical gases, Brownian motion, plasmas, and self-gravitating systems, quantum gases, the electronic transport in solids and, finally, semiconductors. Besides these systems that are studied in detail, concepts are applied to some modern examples including the quark–gluon plasma, the motion of bacterial suspen...

Stochastic theory of interfacial enzyme kinetics: A kinetic Monte Carlo study

International Nuclear Information System (INIS)

Das, Biswajit; Gangopadhyay, Gautam

2012-01-01

Graphical abstract: Stochastic theory of interfacial enzyme kinetics is formulated. Numerical results of macroscopic phenomenon of lag-burst kinetics is obtained by using a kinetic Monte Carlo approach to single enzyme activity. Highlights: ► An enzyme is attached with the fluid state phospholipid molecules on the Langmuir monolayer. ► Through the diffusion, the enzyme molecule reaches the gel–fluid interface. ► After hydrolysing a phospholipid molecule it predominantly leaves the surface in the lag phase. ► The enzyme is strictly attached to the surface with scooting mode of motion and the burst phase appears. - Abstract: In the spirit of Gillespie’s stochastic approach we have formulated a theory to explore the advancement of the interfacial enzyme kinetics at the single enzyme level which is ultimately utilized to obtain the ensemble average macroscopic feature, lag-burst kinetics. We have provided a theory of the transition from the lag phase to the burst phase kinetics by considering the gradual development of electrostatic interaction among the positively charged enzyme and negatively charged product molecules deposited on the phospholipid surface. It is shown that the different diffusion time scales of the enzyme over the fluid and product regions are responsible for the memory effect in the correlation of successive turnover events of the hopping mode in the single trajectory analysis which again is reflected on the non-Gaussian distribution of turnover times on the macroscopic kinetics in the lag phase unlike the burst phase kinetics.

Non-topological solitons in field theories with kinetic self-coupling

International Nuclear Information System (INIS)

Diaz-Alonso, Joaquin; Rubiera-Garcia, Diego

2007-01-01

We investigate some fundamental features of a class of non-linear relativistic Lagrangian field theories with kinetic self-coupling. We focus our attention upon theories admitting static, spherically symmetric solutions in three space dimensions which are finite-energy and stable. We determine general conditions for the existence and stability of these non-topological soliton solutions. In particular, we perform a linear stability analysis that goes beyond the usual Derrick-like criteria. On the basis of these considerations we obtain a complete characterization of the soliton-supporting members of the aforementioned class of non-linear field theories. We then classify the family of soliton-supporting theories according to the central and asymptotic behaviors of the soliton field, and provide illustrative explicit examples of models belonging to each of the corresponding sub-families. In the present work we restrict most of our considerations to one and many-components scalar models. We show that in these cases the finite-energy static spherically symmetric solutions are stable against charge-preserving perturbations, provided that the vacuum energy of the model vanishes and the energy density is positive definite. We also discuss briefly the extension of the present approach to models involving other types of fields, but a detailed study of this more general scenario will be addressed in a separate publication

Hypocoercivity for linear kinetic equations conserving mass

KAUST Repository

Dolbeault, Jean; Mouhot, Clé ment; Schmeiser, Christian

2015-01-01

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

Hypocoercivity for linear kinetic equations conserving mass

KAUST Repository

Dolbeault, Jean

2015-02-03

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

The Theory of Linear Prediction

CERN Document Server

Vaidyanathan, PP

2007-01-01

Linear prediction theory has had a profound impact in the field of digital signal processing. Although the theory dates back to the early 1940s, its influence can still be seen in applications today. The theory is based on very elegant mathematics and leads to many beautiful insights into statistical signal processing. Although prediction is only a part of the more general topics of linear estimation, filtering, and smoothing, this book focuses on linear prediction. This has enabled detailed discussion of a number of issues that are normally not found in texts. For example, the theory of vecto

On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models

International Nuclear Information System (INIS)

Mieussens, Luc

2013-01-01

The unified gas kinetic scheme (UGKS) of K. Xu et al. (2010) [37], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of radiative transfer theory. While such problems exhibit purely diffusive behavior in the optically thick (or small Knudsen) regime, we prove that UGKS is still asymptotic preserving (AP) in this regime, but for the free transport regime as well. Moreover, this scheme is modified to include a time implicit discretization of the limit diffusion equation, and to correctly capture the solution in case of boundary layers. Contrary to many AP schemes, this method is based on a standard finite volume approach, it does neither use any decomposition of the solution, nor staggered grids. Several numerical tests demonstrate the properties of the scheme

Omega-mode perturbation theory and reactor kinetics for analyzing accelerator-driven subcritical systems

International Nuclear Information System (INIS)

Ren-Tai, Chiang

2003-01-01

An ω-mode first-order perturbation theory is developed for analyzing the time- and space-dependent neutron behavior in Accelerator-Driven Subcritical Systems (ADSS). The generalized point-kinetics equations are systematically derived using the ω-mode first-order perturbation theory and Fredholm Alternative Theorem. Seven sets of the ω-mode eigenvalues exist with using six groups of delayed neutrons and all ω eigenvalues are negative in ADSS. Seven ω-mode adjoint and forward eigenfunctions are employed to form the point-kinetic parameters. The neutron flux is expressed as a linear combination of the products of seven ω-eigenvalue-mode shape functions and their corresponding time functions up to the first order terms, and the lowest negative ω-eigenvalue mode is the dominant mode. (author)

Linear contextual modal type theory

DEFF Research Database (Denmark)

Schack-Nielsen, Anders; Schürmann, Carsten

Abstract. When one implements a logical framework based on linear type theory, for example the Celf system [?], one is immediately con- fronted with questions about their equational theory and how to deal with logic variables. In this paper, we propose linear contextual modal type theory that gives...... a mathematical account of the nature of logic variables. Our type theory is conservative over intuitionistic contextual modal type theory proposed by Nanevski, Pfenning, and Pientka. Our main contributions include a mechanically checked proof of soundness and a working implementation....

Thermal physics kinetic theory and thermodynamics

CERN Document Server

Singh, Devraj; Yadav, Raja Ram

2016-01-01

THERMAL PHYSICS: Kinetic Theory and Thermodynamics is designed for undergraduate course in Thermal Physics and Thermodynamics. The book provides thorough understanding of the fundamental principles of the concepts in Thermal Physics. The book begins with kinetic theory, then moves on liquefaction, transport phenomena, the zeroth, first, second and third laws, thermodynamics relations and thermal conduction. The book concluded with radiation phenomenon. KEY FEATURES: * Include exercises * Short Answer Type Questions * Long Answer Type Questions * Numerical Problems * Multiple Choice Questions

Linear and nonlinear kinetic-stability studies in tokamaks

International Nuclear Information System (INIS)

Tang, W.M.; Chance, M.S.; Chen, L.; Krommes, J.A.; Lee, W.W.; Rewoldt, G.

1982-09-01

This paper presents results of theoretical investigations on important linear kinetic properties of low frequency instabilities in toroidal systems and on nonlinear processes which could significantly influence their impact on anomalous transport. Analytical and numerical methods and also particle simulations have been employed to carry out these studies. In particular, the following subjects are considered: (1) linear stability analysis of kinetic instabilities for realistic tokamak equilibria and the application of such calculations to the PDX and PLT tokamak experiments including the influence of a hot beam-ion component; (2) determination of nonlinearly saturated, statistically steady states of three interacting drift modes; and (3) gyrokinetic particle simulation of drift instabilities

Employing Theories Far beyond Their Limits - Linear Dichroism Theory.

Science.gov (United States)

Mayerhöfer, Thomas G

2018-05-15

Using linear polarized light, it is possible in case of ordered structures, such as stretched polymers or single crystals, to determine the orientation of the transition moments of electronic and vibrational transitions. This not only helps to resolve overlapping bands, but also assigning the symmetry species of the transitions and to elucidate the structure. To perform spectral evaluation quantitatively, a sometimes "Linear Dichroism Theory" called approach is very often used. This approach links the relative orientation of the transition moment and polarization direction to the quantity absorbance. This linkage is highly questionable for several reasons. First of all, absorbance is a quantity that is by its definition not compatible with Maxwell's equations. Furthermore, absorbance seems not to be the quantity which is generally compatible with linear dichroism theory. In addition, linear dichroism theory disregards that it is not only the angle between transition moment and polarization direction, but also the angle between sample surface and transition moment, that influences band shape and intensity. Accordingly, the often invoked "magic angle" has never existed and the orientation distribution influences spectra to a much higher degree than if linear dichroism theory would hold strictly. A last point that is completely ignored by linear dichroism theory is the fact that partially oriented or randomly-oriented samples usually consist of ordered domains. It is their size relative to the wavelength of light that can also greatly influence a spectrum. All these findings can help to elucidate orientation to a much higher degree by optical methods than currently thought possible by the users of linear dichroism theory. Hence, it is the goal of this contribution to point out these shortcomings of linear dichroism theory to its users to stimulate efforts to overcome the long-lasting stagnation of this important field. © 2018 Wiley-VCH Verlag GmbH & Co. KGa

Kinetic theory for electron dynamics near a positive ion

International Nuclear Information System (INIS)

Wrighton, Jeffrey M; Dufty, James W

2008-01-01

A theoretical description of time correlation functions for electron properties in the presence of a positive ion of charge number Z is given. The simplest case of an electron gas distorted by a single ion is considered. A semi-classical representation with a regularized electron–ion potential is used to obtain a linear kinetic theory that is asymptotically exact at short times. This Markovian approximation includes all initial (equilibrium) electron–electron and electron–ion correlations through renormalized pair potentials. The kinetic theory is solved in terms of single-particle trajectories of the electron–ion potential and a dielectric function for the inhomogeneous electron gas. The results are illustrated by a calculation of the autocorrelation function for the electron field at the ion. The dependence on charge number Z is shown to be dominated by the bound states of the effective electron–ion potential. On this basis, a very simple practical representation of the trajectories is proposed and shown to be accurate over a wide range including strong electron–ion coupling. This simple representation is then used for a brief analysis of the dielectric function for the inhomogeneous electron gas

Kinetic Theory of the Inner Magnetospheric Plasma

CERN Document Server

Khazanov, George V

2011-01-01

This book provides a broad introduction to the kinetic theory of space plasma physics with the major focus on the inner magnetospheric plasma. It is designed to provide a comprehensive description of the different kinds of transport equations for both plasma particles and waves with an emphasis on the applicability and limitations of each set of equations. The major topics are: Kinetic Theory of Superthermal Electrons, Kinetic Foundation of the Hydrodynamic Description of Space Plasmas (including wave-particle interaction processes), and Kinetic Theory of the Terrestrial Ring Current. Distinguishable features of this book are the analytical solutions of simplified transport equations. Approximate analytic solutions of transport phenomena are very useful because they help us gain physical insight into how the system responds to varying sources of mass, momentum and energy and also to various external boundary conditions. They also provide us a convenient method to test the validity of complicated numerical mod...

Effective potential kinetic theory for strongly coupled plasmas

Science.gov (United States)

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.

Relativistic thermodynamics and kinetic theory, with applications to cosmology

International Nuclear Information System (INIS)

Stewart, J.M.

1973-01-01

The discussion of relativistic thermodynamics and kinetic theory with applications to cosmology also covers the fundamentals and nonequilibrium relativistic kinetic theory and applications to cosmology and astrophysics. (U.S.)

Modeling in applied sciences a kinetic theory approach

CERN Document Server

Pulvirenti, Mario

2000-01-01

Modeling complex biological, chemical, and physical systems, in the context of spatially heterogeneous mediums, is a challenging task for scientists and engineers using traditional methods of analysis Modeling in Applied Sciences is a comprehensive survey of modeling large systems using kinetic equations, and in particular the Boltzmann equation and its generalizations An interdisciplinary group of leading authorities carefully develop the foundations of kinetic models and discuss the connections and interactions between model theories, qualitative and computational analysis and real-world applications This book provides a thoroughly accessible and lucid overview of the different aspects, models, computations, and methodology for the kinetic-theory modeling process Topics and Features * Integrated modeling perspective utilized in all chapters * Fluid dynamics of reacting gases * Self-contained introduction to kinetic models * Becker–Doring equations * Nonlinear kinetic models with chemical reactions * Kinet...

Modern quantum kinetic theory and spectral line shapes

International Nuclear Information System (INIS)

Monchick, L.

1991-01-01

The modern quantum kinetic theory of spectral line shapes is outlined and a typical calculation of a Raman scattered line shape described. The distinguishing feature of this calculation is that it was completely ab initio and therefore constituted a test of modern quantum kinetic theory, the state of the art in computing molecular-scattering cross sections, and novel methods of solving kinetic equations. The computation employed a large assortment of tools: group theory, finite-element methods, classic methods of solving coupled sets of ordinary differential equations, graph methods of combining angular momenta, and matrix methods of solving integral equations. Agreement with experimental results was excellent. 13 refs

Kinetic theory of fermions in curved spacetime

Energy Technology Data Exchange (ETDEWEB)

Fidler, Christian [Catholic University of Louvain, Center for Cosmology, Particle Physics and Phenomenology (CP3), 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve (Belgium); Pitrou, Cyril, E-mail: christian.fidler@uclouvain.be, E-mail: pitrou@iap.fr [Institut d' Astrophysique de Paris, CNRS-UMR 7095, UPMC—Paris VI, Sorbonne Universités, 98 bis Bd Arago, 75014 Paris (France)

2017-06-01

We build a statistical description of fermions, taking into account the spin degree of freedom in addition to the momentum of particles, and we detail its use in the context of the kinetic theory of gases of fermions particles. We show that the one-particle distribution function needed to write a Liouville equation is a spinor valued operator. The degrees of freedom of this function are covariantly described by an intensity function and by a polarisation vector which are parallel transported by free streaming. Collisions are described on the microscopic level and lead to a Boltzmann equation for this operator. We apply our formalism to the case of weak interactions, which at low energies can be considered as a contact interaction between fermions, allowing us to discuss the structure of the collision term for a few typical weak-interaction mediated reactions. In particular we find for massive particles that a dipolar distribution of velocities in the interacting species is necessary to generate linear polarisation, as opposed to the case of photons for which linear polarisation is generated from the quadrupolar distribution of velocities.

Semi-continuous and multigroup models in extended kinetic theory

International Nuclear Information System (INIS)

Koller, W.

2000-01-01

The aim of this thesis is to study energy discretization of the Boltzmann equation in the framework of extended kinetic theory. In case that external fields can be neglected, the semi- continuous Boltzmann equation yields a sound basis for various generalizations. Semi-continuous kinetic equations describing a three component gas mixture interacting with monochromatic photons as well as a four component gas mixture undergoing chemical reactions are established and investigated. These equations reflect all major aspects (conservation laws, equilibria, H-theorem) of the full continuous kinetic description. For the treatment of the spatial dependence, an expansion of the distribution function in terms of Legendre polynomials is carried out. An implicit finite differencing scheme is combined with the operator splitting method. The obtained numerical schemes are applied to the space homogeneous study of binary chemical reactions and to spatially one-dimensional laser-induced acoustic waves. In the presence of external fields, the developed overlapping multigroup approach (with the spline-interpolation as its extension) is well suited for numerical studies. Furthermore, two formulations of consistent multigroup approaches to the non-linear Boltzmann equation are presented. (author)

Kinetic mean field theories: Results of energy constraint in maximizing entropy

NARCIS (Netherlands)

Stell, G.; Karkheck, J.; Beijeren, H. van

1983-01-01

Structure of liquids and solids; crystallography Classical, semiclassical, and quantum theories of liquid structure Statistical theories of liquid structure - Kinetic and transport theory of fluids; physical properties of gases Kinetic and transport theory

Linear system theory

Science.gov (United States)

Callier, Frank M.; Desoer, Charles A.

1991-01-01

The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.

Kinetic theory of radiation effects

International Nuclear Information System (INIS)

Mansur, L.K.

1987-01-01

To help achieve the quantitative and mechanistic understanding of these processes, the kinetic theory of radiation effects has been developed in the DOE basic energy sciences radiation effects and fusion reactor materials programs, as well as in corresponding efforts in other countries. This discipline grapples with a very wide range of phenomena and draws on numerous sub-fields of theory such as defect physics, diffusion, elasticity, chemical reaction rates, phase transformations and thermodynamics. The theory is cast in a mathematical framework of continuum dynamics. Issues particularly relevant to the present inquiry can be viewed from the standpoints of applications of the theory and areas requiring further progress

Linear network theory

CERN Document Server

Sander, K F

1964-01-01

Linear Network Theory covers the significant algebraic aspect of network theory, with minimal reference to practical circuits. The book begins the presentation of network analysis with the exposition of networks containing resistances only, and follows it up with a discussion of networks involving inductance and capacity by way of the differential equations. Classification and description of certain networks, equivalent networks, filter circuits, and network functions are also covered. Electrical engineers, technicians, electronics engineers, electricians, and students learning the intricacies

The kinetic theory of open systems

International Nuclear Information System (INIS)

Klimontovich, Yu.L.

2001-01-01

This paper begins with a survey of recently obtained results in the statistical theory of open systems, including quantum open systems. Then the definition of the thermal flux in the kinetic theory is considered, further the collision nature of the Landau damping. Finally the Lamb shift and Bethe's formula are analyzed. (orig.)

Stochastic chemical kinetics theory and (mostly) systems biological applications

CERN Document Server

Érdi, Péter; Lente, Gabor

2014-01-01

This volume reviews the theory and simulation methods of stochastic kinetics by integrating historical and recent perspectives, presents applications, mostly in the context of systems biology and also in combustion theory. In recent years, due to the development in experimental techniques, such as optical imaging, single cell analysis, and fluorescence spectroscopy, biochemical kinetic data inside single living cells have increasingly been available. The emergence of systems biology brought renaissance in the application of stochastic kinetic methods.

Linear spaces: history and theory

OpenAIRE

Albrecht Beutelspracher

1990-01-01

Linear spaces belong to the most fundamental geometric and combinatorial structures. In this paper I would like to give an onerview about the theory of embedding finite linear spaces in finite projective planes.

Relativistic kinetic theory with applications in astrophysics and cosmology

CERN Document Server

Vereshchagin, Gregory V

2017-01-01

Relativistic kinetic theory has widespread application in astrophysics and cosmology. The interest has grown in recent years as experimentalists are now able to make reliable measurements on physical systems where relativistic effects are no longer negligible. This ambitious monograph is divided into three parts. It presents the basic ideas and concepts of this theory, equations and methods, including derivation of kinetic equations from the relativistic BBGKY hierarchy and discussion of the relation between kinetic and hydrodynamic levels of description. The second part introduces elements of computational physics with special emphasis on numerical integration of Boltzmann equations and related approaches, as well as multi-component hydrodynamics. The third part presents an overview of applications ranging from covariant theory of plasma response, thermalization of relativistic plasma, comptonization in static and moving media to kinetics of self-gravitating systems, cosmological structure formation and neut...

Transport in simple liquids and dense gases: kinetic mean-field theory and the KAC limit

International Nuclear Information System (INIS)

Karkheck, J.; Stell, G.; Martina, E.

1982-01-01

Maximization of entropy is used in conjunction with the BBGKY hierarchy to obtain a closed one-particle kinetic equation. For an interparticle potential of hard-sphere core plus smooth attractive tail, this equation contains a hard-core collision integral, identical to that of the revised Enskog theory, plus a mean-field term which is linear in the tail strength. The thermodynamics contained therein leads directly to the now-standard statistical-mechanical methods to construct a state-dependent effective hard-core potential in relation to a more realistic potential. These methods induce an extension of the transport coefficients to the Lennard-Jones potential. Predictions of the resulting transport theory compare very favorably with thermal conductivity and shear viscosity experimental results for real simple liquids and dense gases, and also with molecular dynamics simulation results. Poor agreement between theory and experiment is found for moderately dense and dilute gases. The kinetic theory also contains an entropy functional and an H-theorem is proven. Extension to mixtures is straightforward and the Kac-limit is discussed in detail

Theory of linear operations

CERN Document Server

Banach, S

1987-01-01

This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series.A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'''') complements this important monograph.

Lifetime estimation of zirconia ceramics by linear ageing kinetics

International Nuclear Information System (INIS)

Zhang, Fei; Inokoshi, Masanao; Vanmeensel, Kim; Van Meerbeek, Bart; Naert, Ignace; Vleugels, Jef

2015-01-01

Up to now, the ageing kinetics of zirconia ceramics were mainly derived from the sigmoidal evolution of the surface phase transformation as a function of time, as quantified by means of X-ray diffraction (XRD). However, the transformation propagation into the material should be better to monitor the ageing kinetics. In this work, μ-Raman spectroscopy was used to quantitatively measure the transformation profiles in depth as a function of ageing time at 160 °C, 140 °C, 134 °C and 110 °C. A linear relationship between the transformed depth and the ageing time was observed for all investigated yttria stabilized tetragonal zirconia polycrystals (3Y-TZP). Furthermore, the μ-Raman investigation of residual stresses in the subsurface of aged 3Y-TZPs showed that the highest tensile stress was located just ahead of the transformation front, indicating the key responsibility of stress accumulation for transformation front propagating into the material. Moreover, the linear kinetics of the transformation propagation were more accurate to calculate the apparent activation energy of the ageing process and allowed a more straightforward estimation of the lifetime of 3Y-TZP at body temperature, as compared to the conventional ageing kinetic parameters obtained from the surface transformation analysis by XRD

Extended symmetries of the kinetic plasma theory models

International Nuclear Information System (INIS)

Taranov, V.B.

2005-01-01

Symmetry extension of the kinetic theory of collisionless plasma containing particles with equal charge to mass ratio is considered. It is shown that this symmetry allows us to reduce the number of equations. Symmetries obtained for the integro-differential equations of the kinetic theory by the indirect algorithm are compared to those obtained by direct methods. The importance of additional conditions - positiveness and integrability of distribution functions, existence of their moments - is underlined

Some remarks concerning relativistic kinetic theory

International Nuclear Information System (INIS)

Schroeter, J.

1990-01-01

The starting point of our investigation is a classical kinetic theory which includes correlational effects as well as the complete electromagnetic interaction. Also classical gravitation can be incorporated. The relativistic version of this theory is written down using some heuristic arguments. Its essential feature is the difference between terms representing gravitational interaction and the metric tensor representing geometrical properties. (author)

Rate kernel theory for pseudo-first-order kinetics of diffusion-influenced reactions and application to fluorescence quenching kinetics.

Science.gov (United States)

Yang, Mino

2007-06-07

Theoretical foundation of rate kernel equation approaches for diffusion-influenced chemical reactions is presented and applied to explain the kinetics of fluorescence quenching reactions. A many-body master equation is constructed by introducing stochastic terms, which characterize the rates of chemical reactions, into the many-body Smoluchowski equation. A Langevin-type of memory equation for the density fields of reactants evolving under the influence of time-independent perturbation is derived. This equation should be useful in predicting the time evolution of reactant concentrations approaching the steady state attained by the perturbation as well as the steady-state concentrations. The dynamics of fluctuation occurring in equilibrium state can be predicted by the memory equation by turning the perturbation off and consequently may be useful in obtaining the linear response to a time-dependent perturbation. It is found that unimolecular decay processes including the time-independent perturbation can be incorporated into bimolecular reaction kinetics as a Laplace transform variable. As a result, a theory for bimolecular reactions along with the unimolecular process turned off is sufficient to predict overall reaction kinetics including the effects of unimolecular reactions and perturbation. As the present formulation is applied to steady-state kinetics of fluorescence quenching reactions, the exact relation between fluorophore concentrations and the intensity of excitation light is derived.

On the kinetic theory of quantum systems

International Nuclear Information System (INIS)

Calkoen, C.J.

1986-01-01

The contents of this thesis which deals with transport phenomena of specific gases, plasmas and fluids, can be separated into two distinct parts. In the first part a statistical way is suggested to estimate the neutrino mass. Herefore use is made of the fact that massive neutrinos possess a non-zero volume viscosity in contrast with massless neutrinos. The second part deals with kinetic theory of strongly condensed quantum systems of which examples in nature are: liquid Helium, heavy nuclei, electrons in a metal and the interior of stars. In degenerate systems fermions in general interact strongly so that ordinary kinetic theory is not directly applicable. For such cases Landau-Fermi-liquid theory, in which the strongly interacting particles are replaced by much weaker interacting quasiparticles, proved to be very useful. A method is developed in this theory to calculate transport coefficients. Applications of this method on liquid 3 Helium yield surprisingly good agreement with experimental results for thermal conductivities. (Auth.)

Low-frequency linear waves and instabilities in uniform and stratified plasmas: the role of kinetic effects

Directory of Open Access Journals (Sweden)

K. M. Ferrière

2004-01-01

Full Text Available We review the basic approximations underlying magnetohydrodynamic (MHD theory, with special emphasis on the closure approximations, i.e. the approximations used in any fluid approach to close the hierarchy of moment equations. We then present the main closure models that have been constructed for collisionless plasmas in the large-scale regime, and we describe our own mixed MHD-kinetic model, which is designed to study low-frequency linear waves and instabilities in collisionless plasmas. We write down the full dispersion relation in a new, general form, which gathers all the specific features of our MHD-kinetic model into four polytropic indices, and which can be applied to standard adiabatic MHD and to double-adiabatic MHD through a simple change in the expressions of the polytropic indices. We study the mode solutions and the stability properties of the full dispersion relation in each of these three theories, first in the case of a uniform plasma, and then in the case of a stratified plasma. In both cases, we show how the results are affected by the collisionless nature of the plasma.

Numerical linear algebra theory and applications

CERN Document Server

Beilina, Larisa; Karchevskii, Mikhail

2017-01-01

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

Kinetic theory of free electron lasers

Energy Technology Data Exchange (ETDEWEB)

Hafizi, B. [Naval Research Lab., Washington, DC (United States); Roberson, C.W. [Office of Naval Research, Arlington, VA (United States)

1995-12-31

We have developed a relativistic kinetic theory of free electron lasers (FELs). The growth rate, efficiency, filling factor and radius of curvature of the radiation wave fronts are determined. We have used the theory to examine the effects of beam compression on growth rate. The theory has been extended to include self field effects on FEL operation. These effects are particularly important in compact, low voltage FELs. The surprising result is that the self field contribution to the beam quality is opposite to the emittance contribution. Hence self fields can improve beam quality, particularly in compact, low voltage FELs.

Kinetic theory of two-temperature polyatomic plasmas

Science.gov (United States)

Orlac'h, Jean-Maxime; Giovangigli, Vincent; Novikova, Tatiana; Roca i Cabarrocas, Pere

2018-03-01

We investigate the kinetic theory of two-temperature plasmas for reactive polyatomic gas mixtures. The Knudsen number is taken proportional to the square root of the mass ratio between electrons and heavy-species, and thermal non-equilibrium between electrons and heavy species is allowed. The kinetic non-equilibrium framework also requires a weak coupling between electrons and internal energy modes of heavy species. The zeroth-order and first-order fluid equations are derived by using a generalized Chapman-Enskog method. Expressions for transport fluxes are obtained in terms of macroscopic variable gradients and the corresponding transport coefficients are expressed as bracket products of species perturbed distribution functions. The theory derived in this paper provides a consistent fluid model for non-thermal multicomponent plasmas.

Association of footprint measurements with plantar kinetics: a linear regression model.

Science.gov (United States)

Fascione, Jeanna M; Crews, Ryan T; Wrobel, James S

2014-03-01

The use of foot measurements to classify morphology and interpret foot function remains one of the focal concepts of lower-extremity biomechanics. However, only 27% to 55% of midfoot variance in foot pressures has been determined in the most comprehensive models. We investigated whether dynamic walking footprint measurements are associated with inter-individual foot loading variability. Thirty individuals (15 men and 15 women; mean ± SD age, 27.17 ± 2.21 years) walked at a self-selected speed over an electronic pedography platform using the midgait technique. Kinetic variables (contact time, peak pressure, pressure-time integral, and force-time integral) were collected for six masked regions. Footprints were digitized for area and linear boundaries using digital photo planimetry software. Six footprint measurements were determined: contact area, footprint index, arch index, truncated arch index, Chippaux-Smirak index, and Staheli index. Linear regression analysis with a Bonferroni adjustment was performed to determine the association between the footprint measurements and each of the kinetic variables. The findings demonstrate that a relationship exists between increased midfoot contact and increased kinetic values in respective locations. Many of these variables produced large effect sizes while describing 38% to 71% of the common variance of select plantar kinetic variables in the medial midfoot region. In addition, larger footprints were associated with larger kinetic values at the medial heel region and both masked forefoot regions. Dynamic footprint measurements are associated with dynamic plantar loading kinetics, with emphasis on the midfoot region.

Elements of plasma kinetic theory

International Nuclear Information System (INIS)

Guasp, J.

1976-01-01

The physical foundations of plasma kinetic equations are exposed inside a series of seminars on plasma and fusion physics. The Vlasov and collisional equations with its application range have been discussed. The momenta equations for the macroscopic magnitudes and the more usual approximations have been obtained: two fluid equations for cold and warm plasmas, magnetohydrodynamic equations and the double-adiabatic theory. (author)

Algebraic Theory of Linear Viscoelastic Nematodynamics

International Nuclear Information System (INIS)

Leonov, Arkady I.

2008-01-01

This paper consists of two parts. The first one develops algebraic theory of linear anisotropic nematic 'N-operators' build up on the additive group of traceless second rank 3D tensors. These operators have been implicitly used in continual theories of nematic liquid crystals and weakly elastic nematic elastomers. It is shown that there exists a non-commutative, multiplicative group N 6 of N-operators build up on a manifold in 6D space of parameters. Positive N-operators, which in physical applications hold thermodynamic stability constraints, do not generally form a subgroup of group N 6 . A three-parametric, commutative transversal-isotropic subgroup S 3 subset of N 6 of positive symmetric nematic operators is also briefly discussed. The special case of singular, non-negative symmetric N-operators reveals the algebraic structure of nematic soft deformation modes. The second part of the paper develops a theory of linear viscoelastic nematodynamics applicable to liquid crystalline polymer. The viscous and elastic nematic components in theory are described by using the Leslie-Ericksen-Parodi (LEP) approach for viscous nematics and de Gennes free energy for weakly elastic nematic elastomers. The case of applied external magnetic field exemplifies the occurrence of non-symmetric stresses. In spite of multi-(10) parametric character of the theory, the use of nematic operators presents it in a transparent form. When the magnetic field is absent, the theory is simplified for symmetric case with six parameters, and takes an extremely simple, two-parametric form for viscoelastic nematodynamics with possible soft deformation modes. It is shown that the linear nematodynamics is always reducible to the LEP-like equations where the coefficients are changed for linear memory functionals whose parameters are calculated from original viscosities and moduli

Analyzing Students’ Level of Understanding on Kinetic Theory of Gases

Science.gov (United States)

Nurhuda, T.; Rusdiana, D.; Setiawan, W.

2017-02-01

The purpose of this research is to analysis students’ level of understanding on gas kinetic theory. The method used is descriptive analytic with 32 students at the 11th grade of one high school in Bandung city as a sample. The sample was taken using random sampling technique. Data collection tool used is an essay test with 23 questions. The instrument was used to identify students’ level of understanding and was judged by four expert judges before it was employed, from 27 questions become to 23 questions, for data collection. Questions used are the conceptual understanding including the competence to explain, extrapolate, translate and interpret. Kinetic theory of gases section that was tested includes ideal gas law, kinetic molecular theory and equipartition of energy. The result shows from 0-4 level of understanding, 19% of the students have partial understanding on the 3th level and 81% of them have partial understanding with a specific misconception on 2th level. For the future research, it is suggested to overcome these conceptual understanding with an Interactive Lecture Demonstrations teaching model and coupled with some teaching materials based on multi-visualization because kinetic theory of gases is a microscopic concept.

Kinetic theory for strongly coupled Coulomb systems

Science.gov (United States)

Dufty, James; Wrighton, Jeffrey

2018-01-01

The calculation of dynamical properties for matter under extreme conditions is a challenging task. The popular Kubo-Greenwood model exploits elements from equilibrium density-functional theory (DFT) that allow a detailed treatment of electron correlations, but its origin is largely phenomenological; traditional kinetic theories have a more secure foundation but are limited to weak ion-electron interactions. The objective here is to show how a combination of the two evolves naturally from the short-time limit for the generator of the effective single-electron dynamics governing time correlation functions without such limitations. This provides a theoretical context for the current DFT-related approach, the Kubo-Greenwood model, while showing the nature of its corrections. The method is to calculate the short-time dynamics in the single-electron subspace for a given configuration of the ions. This differs from the usual kinetic theory approach in which an average over the ions is performed as well. In this way the effective ion-electron interaction includes strong Coulomb coupling and is shown to be determined from DFT. The correlation functions have the form of the random-phase approximation for an inhomogeneous system but with renormalized ion-electron and electron-electron potentials. The dynamic structure function, density response function, and electrical conductivity are calculated as examples. The static local field corrections in the dielectric function are identified in this way. The current analysis is limited to semiclassical electrons (quantum statistical potentials), so important quantum conditions are excluded. However, a quantization of the kinetic theory is identified for broader application while awaiting its detailed derivation.

Kinetic theory for dilute cohesive granular gases with a square well potential.

Science.gov (United States)

Takada, Satoshi; Saitoh, Kuniyasu; Hayakawa, Hisao

2016-07-01

We develop the kinetic theory of dilute cohesive granular gases in which the attractive part is described by a square well potential. We derive the hydrodynamic equations from the kinetic theory with the microscopic expressions for the dissipation rate and the transport coefficients. We check the validity of our theory by performing the direct simulation Monte Carlo.

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

The Students’ misconceptions profile on chapter gas kinetic theory

Science.gov (United States)

Jauhariyah, M. N. R.; Suprapto, N.; Suliyanah; Admoko, S.; Setyarsih, W.; Harizah, Z.; Zulfa, I.

2018-03-01

Students have conception and misconceptions in the learning process. Misconceptions are caused by the teacher, students, and learning source. In the previous study, the researcher developed a misconception diagnosis instrument using three-tier on chapter gas kinetic theory. There are 14 items including 5 sub-chapters on gas kinetic theory. The profile of students’ misconceptions shows that students have misconceptions in each sub-chapter. The cause of misconceptions came from preconceptions, associative thinking, reasoning, intuition, and false negative. The highest cause of misconception in this chapter is student’s humanistic thinking.

Linear theory of the tearing instability in axisymmetric toroidal devices

International Nuclear Information System (INIS)

Rogister, A.; Singh, R.

1988-08-01

We derive a very general kinetic equation describing the linear evolution of low m/l modes in axisymmetric toroidal plasmas with arbitrary cross sections. Included are: Ion sound, inertia, diamagnetic drifts, finite poloidal beta, and finite ion Larmor radius effects. Assuming the magnetic surfaces to form a set of nested tori with circular cross sections of shifted centers, and introducing adequate simplifications justified by our knowledge of experimental tokamak plasmas, we then obtain explicitely the sets of equations describing the coupling of the quasimodes 0/1, 1/1, 2/1, and, for m≥2, m/1, (m+1)/1. By keeping finite aspect ratio effects into account when calculating the jump of the derivative of the eigenfunction, it is shown that the theory can explain the rapid evolution, within one sawtooth period, of the growth rate of the sawteeth precursors from resistive values to magnetohydrodynamic ones. The characteristics thus theoretically required from current profiles in sawtoothing discharges have clearly been observed. Other aspects of the full theory could be relevant to the phenomenon of major disruptions. (orig.)

Linear programming mathematics, theory and algorithms

CERN Document Server

1996-01-01

Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

Quasi-linear landau kinetic equations for magnetized plasmas: compact propagator formalism, rotation matrices and interaction

International Nuclear Information System (INIS)

Misguich, J.H.

2004-04-01

As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation

Quasi-linear landau kinetic equations for magnetized plasmas: compact propagator formalism, rotation matrices and interaction

Energy Technology Data Exchange (ETDEWEB)

Misguich, J.H

2004-04-01

As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation.

Nonequilibrium transition and pattern formation in a linear reaction-diffusion system with self-regulated kinetics

Science.gov (United States)

Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar

2018-02-01

We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.

Recent developments in the kinetic theory of nucleation.

Science.gov (United States)

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

Linear radial pulsation theory. Lecture 5

International Nuclear Information System (INIS)

Cox, A.N.

1983-01-01

We describe a method for getting an equilibrium stellar envelope model using as input the total mass, the envelope mass, the surface effective temperature, the total surface luminosity, and the composition of the envelope. Then wih the structure of the envelope model known, we present a method for obtaining the raidal pulsation periods and growth rates for low order modes. The large amplitude pulsations observed for the yellow and red giants and supergiants are always these radial models, but for the stars nearer the main sequence, as for all of our stars and for the white dwarfs, there frequently are nonradial modes occuring also. Application of linear theory radial pulsation theory is made to the giant star sigma Scuti variables, while the linear nonradial theory will be used for the B stars in later lectures

Kinetic theory of nonlinear transport phenomena in complex plasmas

International Nuclear Information System (INIS)

Mishra, S. K.; Sodha, M. S.

2013-01-01

In contrast to the prevalent use of the phenomenological theory of transport phenomena, a number of transport properties of complex plasmas have been evaluated by using appropriate expressions, available from the kinetic theory, which are based on Boltzmann's transfer equation; in particular, the energy dependence of the electron collision frequency has been taken into account. Following the recent trend, the number and energy balance of all the constituents of the complex plasma and the charge balance on the particles is accounted for; the Ohmic loss has also been included in the energy balance of the electrons. The charging kinetics for the complex plasma comprising of uniformly dispersed dust particles, characterized by (i) uniform size and (ii) the Mathis, Rumpl, and Nordsieck power law of size distribution has been developed. Using appropriate expressions for the transport parameters based on the kinetic theory, the system of equations has been solved to investigate the parametric dependence of the complex plasma transport properties on the applied electric field and other plasma parameters; the results are graphically illustrated.

Estimating kinetic mechanisms with prior knowledge I: Linear parameter constraints.

Science.gov (United States)

Salari, Autoosa; Navarro, Marco A; Milescu, Mirela; Milescu, Lorin S

2018-02-05

To understand how ion channels and other proteins function at the molecular and cellular levels, one must decrypt their kinetic mechanisms. Sophisticated algorithms have been developed that can be used to extract kinetic parameters from a variety of experimental data types. However, formulating models that not only explain new data, but are also consistent with existing knowledge, remains a challenge. Here, we present a two-part study describing a mathematical and computational formalism that can be used to enforce prior knowledge into the model using constraints. In this first part, we focus on constraints that enforce explicit linear relationships involving rate constants or other model parameters. We develop a simple, linear algebra-based transformation that can be applied to enforce many types of model properties and assumptions, such as microscopic reversibility, allosteric gating, and equality and inequality parameter relationships. This transformation converts the set of linearly interdependent model parameters into a reduced set of independent parameters, which can be passed to an automated search engine for model optimization. In the companion article, we introduce a complementary method that can be used to enforce arbitrary parameter relationships and any constraints that quantify the behavior of the model under certain conditions. The procedures described in this study can, in principle, be coupled to any of the existing methods for solving molecular kinetics for ion channels or other proteins. These concepts can be used not only to enforce existing knowledge but also to formulate and test new hypotheses. © 2018 Salari et al.

Problems of linear electron (polaron) transport theory in semiconductors

CERN Document Server

Klinger, M I

1979-01-01

Problems of Linear Electron (Polaron) Transport Theory in Semiconductors summarizes and discusses the development of areas in electron transport theory in semiconductors, with emphasis on the fundamental aspects of the theory and the essential physical nature of the transport processes. The book is organized into three parts. Part I focuses on some general topics in the theory of transport phenomena: the general dynamical theory of linear transport in dissipative systems (Kubo formulae) and the phenomenological theory. Part II deals with the theory of polaron transport in a crystalline semicon

Two new proofs of the test particle superposition principle of plasma kinetic theory

International Nuclear Information System (INIS)

Krommes, J.A.

1976-01-01

The test particle superposition principle of plasma kinetic theory is discussed in relation to the recent theory of two-time fluctuations in plasma given by Williams and Oberman. Both a new deductive and a new inductive proof of the principle are presented; the deductive approach appears here for the first time in the literature. The fundamental observation is that two-time expectations of one-body operators are determined completely in terms of the (x,v) phase space density autocorrelation, which to lowest order in the discreteness parameter obeys the linearized Vlasov equation with singular initial condition. For the deductive proof, this equation is solved formally using time-ordered operators, and the solution is then re-arranged into the superposition principle. The inductive proof is simpler than Rostoker's although similar in some ways; it differs in that first-order equations for pair correlation functions need not be invoked. It is pointed out that the superposition principle is also applicable to the short-time theory of neutral fluids

Two new proofs of the test particle superposition principle of plasma kinetic theory

International Nuclear Information System (INIS)

Krommes, J.A.

1975-12-01

The test particle superposition principle of plasma kinetic theory is discussed in relation to the recent theory of two-time fluctuations in plasma given by Williams and Oberman. Both a new deductive and a new inductive proof of the principle are presented. The fundamental observation is that two-time expectations of one-body operators are determined completely in terms of the (x,v) phase space density autocorrelation, which to lowest order in the discreteness parameter obeys the linearized Vlasov equation with singular initial condition. For the deductive proof, this equation is solved formally using time-ordered operators, and the solution then rearranged into the superposition principle. The inductive proof is simpler than Rostoker's, although similar in some ways; it differs in that first order equations for pair correlation functions need not be invoked. It is pointed out that the superposition principle is also applicable to the short-time theory of neutral fluids

Kinetic theory for dilute cohesive granular gases with a square well potential

NARCIS (Netherlands)

Takada, Satoshi; Saitoh, K.; Hayakawa, Hisao

2016-01-01

We develop the kinetic theory of dilute cohesive granular gases in which the attractive part is described by a square well potential. We derive the hydrodynamic equations from the kinetic theory with the microscopic expressions for the dissipation rate and the transport coefficients. We check the

Game Theory and its Relationship with Linear Programming Models ...

African Journals Online (AJOL)

Game Theory and its Relationship with Linear Programming Models. ... This paper shows that game theory and linear programming problem are closely related subjects since any computing method devised for ... AJOL African Journals Online.

An enstrophy-based linear and nonlinear receptivity theory

Science.gov (United States)

Sengupta, Aditi; Suman, V. K.; Sengupta, Tapan K.; Bhaumik, Swagata

2018-05-01

In the present research, a new theory of instability based on enstrophy is presented for incompressible flows. Explaining instability through enstrophy is counter-intuitive, as it has been usually associated with dissipation for the Navier-Stokes equation (NSE). This developed theory is valid for both linear and nonlinear stages of disturbance growth. A previously developed nonlinear theory of incompressible flow instability based on total mechanical energy described in the work of Sengupta et al. ["Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003)] is used to compare with the present enstrophy based theory. The developed equations for disturbance enstrophy and disturbance mechanical energy are derived from NSE without any simplifying assumptions, as compared to other classical linear/nonlinear theories. The theory is tested for bypass transition caused by free stream convecting vortex over a zero pressure gradient boundary layer. We explain the creation of smaller scales in the flow by a cascade of enstrophy, which creates rotationality, in general inhomogeneous flows. Linear and nonlinear versions of the theory help explain the vortex-induced instability problem under consideration.

Hydrodynamization and transient modes of expanding plasma in kinetic theory

CERN Document Server

Heller, Michal P.; Spalinski, Michal

2016-01-01

We study the transition to hydrodynamics in a weakly-coupled model of quark-gluon plasma given by kinetic theory in the relaxation time approximation. Our studies uncover qualitative similarities to the results on hydrodynamization in strongly coupled gauge theories. In particular, we demonstrate that the gradient expansion in this model has vanishing radius of convergence. The asymptotic character of the hydrodynamic gradient expansion is crucial for the recently discovered applicability of hydrodynamics at large gradients. Furthermore, the analysis of the resurgent properties of the series provides, quite remarkably, indication for the existence of a novel transient, damped oscillatory mode of expanding plasmas in kinetic theory.

Overview of nonlinear theory of kinetically driven instabilities

International Nuclear Information System (INIS)

Berk, H.L.; Breizman, B.N.

1998-09-01

An overview is presented of the theory for the nonlinear behavior of instabilities driven by the resonant wave particle interaction. The approach should be applicable to a wide variety of kinetic systems in magnetic fusion devices and accelerators. Here the authors emphasize application to Alfven were driven instability, and the principles of the theory are used to interpret experimental data

Detectable states, cycle fluxes, and motility scaling of molecular motor kinesin: An integrative kinetic graph theory analysis

Science.gov (United States)

Ren, Jie

2017-12-01

The process by which a kinesin motor couples its ATPase activity with concerted mechanical hand-over-hand steps is a foremost topic of molecular motor physics. Two major routes toward elucidating kinesin mechanisms are the motility performance characterization of velocity and run length, and single-molecular state detection experiments. However, these two sets of experimental approaches are largely uncoupled to date. Here, we introduce an integrative motility state analysis based on a theorized kinetic graph theory for kinesin, which, on one hand, is validated by a wealth of accumulated motility data, and, on the other hand, allows for rigorous quantification of state occurrences and chemomechanical cycling probabilities. An interesting linear scaling for kinesin motility performance across species is discussed as well. An integrative kinetic graph theory analysis provides a powerful tool to bridge motility and state characterization experiments, so as to forge a unified effort for the elucidation of the working mechanisms of molecular motors.

Scattering theory of the linear Boltzmann operator

International Nuclear Information System (INIS)

Hejtmanek, J.

1975-01-01

In time dependent scattering theory we know three important examples: the wave equation around an obstacle, the Schroedinger and the Dirac equation with a scattering potential. In this paper another example from time dependent linear transport theory is added and considered in full detail. First the linear Boltzmann operator in certain Banach spaces is rigorously defined, and then the existence of the Moeller operators is proved by use of the theorem of Cook-Jauch-Kuroda, that is generalized to the case of a Banach space. (orig.) [de

Laser driven electron-positron pair creation-kinetic theory versus analytical approximations

International Nuclear Information System (INIS)

Smolyansky, S.A.; Prozorkevich, A.V.; Bonitz, M.

2013-01-01

The dynamical Schwinger effect of vacuum pair creation driven by an intense external laser pulse is studied on the basis of quantum kinetic theory. The numerical solutions of these kinetic equations exhibit a complex time dependence which makes an analysis of the physical processes difficult. In particular, the question of secondary effects, such as creation of secondary annihilation photons from the focus spot of the colliding laser beams, remains an important open problem. In the present work we, therefore, develop a perturbation theory which is able to capture the dominant time dependence of the produced electron-positron pair density. The theory shows excellent agreement with the exact kinetic results during the laser pulse, but fails to reproduce the residual pair density remaining in the system after termination of the pulse. (copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Linear response theory for quantum open systems

OpenAIRE

Wei, J. H.; Yan, YiJing

2011-01-01

Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.

Spectral theories for linear differential equations

International Nuclear Information System (INIS)

Sell, G.R.

1976-01-01

The use of spectral analysis in the study of linear differential equations with constant coefficients is not only a fundamental technique but also leads to far-reaching consequences in describing the qualitative behaviour of the solutions. The spectral analysis, via the Jordan canonical form, will not only lead to a representation theorem for a basis of solutions, but will also give a rather precise statement of the (exponential) growth rates of various solutions. Various attempts have been made to extend this analysis to linear differential equations with time-varying coefficients. The most complete such extensions is the Floquet theory for equations with periodic coefficients. For time-varying linear differential equations with aperiodic coefficients several authors have attempted to ''extend'' the Foquet theory. The precise meaning of such an extension is itself a problem, and we present here several attempts in this direction that are related to the general problem of extending the spectral analysis of equations with constant coefficients. The main purpose of this paper is to introduce some problems of current research. The primary problem we shall examine occurs in the context of linear differential equations with almost periodic coefficients. We call it ''the Floquet problem''. (author)

Berry Fermi liquid theory

Energy Technology Data Exchange (ETDEWEB)

Chen, Jing-Yuan, E-mail: chjy@uchicago.edu [Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637 (United States); Stanford Institute for Theoretical Physics, Stanford University, CA 94305 (United States); Son, Dam Thanh, E-mail: dtson@uchicago.edu [Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637 (United States)

2017-02-15

We develop an extension of the Landau Fermi liquid theory to systems of interacting fermions with non-trivial Berry curvature. We propose a kinetic equation and a constitutive relation for the electromagnetic current that together encode the linear response of such systems to external electromagnetic perturbations, to leading and next-to-leading orders in the expansion over the frequency and wave number of the perturbations. We analyze the Feynman diagrams in a large class of interacting quantum field theories and show that, after summing up all orders in perturbation theory, the current–current correlator exactly matches with the result obtained from the kinetic theory. - Highlights: • We extend Landau’s kinetic theory of Fermi liquid to incorporate Berry phase. • Berry phase effects in Fermi liquid take exactly the same form as in Fermi gas. • There is a new “emergent electric dipole” contribution to the anomalous Hall effect. • Our kinetic theory is matched to field theory to all orders in Feynman diagrams.

On the theory of time dilation in chemical kinetics

Science.gov (United States)

Baig, Mirza Wasif

2017-10-01

The rates of chemical reactions are not absolute but their magnitude depends upon the relative speeds of the moving observers. This has been proved by unifying basic theories of chemical kinetics, which are transition state theory, collision theory, RRKM and Marcus theory, with the special theory of relativity. Boltzmann constant and energy spacing between permitted quantum levels of molecules are quantum mechanically proved to be Lorentz variant. The relativistic statistical thermodynamics has been developed to explain quasi-equilibrium existing between reactants and activated complex. The newly formulated Lorentz transformation of the rate constant from Arrhenius equation, of the collision frequency and of the Eyring and Marcus equations renders the rate of reaction to be Lorentz variant. For a moving observer moving at fractions of the speed of light along the reaction coordinate, the transition state possess less kinetic energy to sweep translation over it. This results in the slower transformation of reactants into products and in a stretched time frame for the chemical reaction to complete. Lorentz transformation of the half-life equation explains time dilation of the half-life period of chemical reactions and proves special theory of relativity and presents theory in accord with each other. To demonstrate the effectiveness of the present theory, the enzymatic reaction of methylamine dehydrogenase and radioactive disintegration of Astatine into Bismuth are considered as numerical examples.

Separation-induced boundary layer transition: Modeling with a non-linear eddy-viscosity model coupled with the laminar kinetic energy equation

International Nuclear Information System (INIS)

Vlahostergios, Z.; Yakinthos, K.; Goulas, A.

2009-01-01

We present an effort to model the separation-induced transition on a flat plate with a semi-circular leading edge, using a cubic non-linear eddy-viscosity model combined with the laminar kinetic energy. A non-linear model, compared to a linear one, has the advantage to resolve the anisotropic behavior of the Reynolds-stresses in the near-wall region and it provides a more accurate expression for the generation of turbulence in the transport equation of the turbulence kinetic energy. Although in its original formulation the model is not able to accurately predict the separation-induced transition, the inclusion of the laminar kinetic energy increases its accuracy. The adoption of the laminar kinetic energy by the non-linear model is presented in detail, together with some additional modifications required for the adaption of the laminar kinetic energy into the basic concepts of the non-linear eddy-viscosity model. The computational results using the proposed combined model are shown together with the ones obtained using an isotropic linear eddy-viscosity model, which adopts also the laminar kinetic energy concept and in comparison with the existing experimental data.

Sensitivity theory for general non-linear algebraic equations with constraints

International Nuclear Information System (INIS)

Oblow, E.M.

1977-04-01

Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

Kinetic approach to plasma end loss from linear devices

International Nuclear Information System (INIS)

Dreicer, H.

1976-01-01

A first step in the direction of a kinetic approach to end loss has been presented. This approach brings to light some fundamental processes not uncovered by the magnetohydrodynamic or guiding center approach. Attention was focused on the basically transient phenomenon in a way that describes the quite different behavior of collision dominated and collisionless ions, but ignores the magnetic nozzle effects near the ends of the system. The treatment illuminates some of the roles played by the parameter l/sub ii//L, and suggests the direction for more detailed investigations. End loss from linear systems is a very many faceted problem. Kinetic effects, magnetic effects, heat flow, etc. are all intermixed, and it will require a strong long term experimental and theoretical program to unravel all of its mysteries

Quantum kinetics of a superconducting tunnel junction: Theory and comparison with experiment

International Nuclear Information System (INIS)

Chow, K.S.; Browne, D.A.; Ambegaokar, V.

1988-01-01

We develop a kinetic theory for the real-time response of a quantum particle interacting with a macroscopic reservoir. We discuss the equilibrium and long-time behavior of the solution of the kinetic equation for such a system. In the limit of low damping, the kinetic equation reduces to a master equation. Using the theory to model a Josephson junction loaded with an external impedance, we make contact with the experiments of Clark, Devoret, Esteve, and Martinis. We argue that a stationary solution of the master equation sufficiently describes the experiments, and make detailed comparison with data

Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

DEFF Research Database (Denmark)

Zhang, H.W.; Schäffer, Hemming Andreas

2007-01-01

An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

Non-linear punctual kinetics applied to PWR reactors simulation

International Nuclear Information System (INIS)

Cysne, F.S.

1978-11-01

In order to study some kinds of nuclear reactor accidents, a simulation is made using the punctual kinetics model for the reactor core. The following integration methods are used: Hansen's method in which a linearization is made and CSMP using a variable interval fourth-order Runge Kutta method. The results were good and were compared with those obtained by the code Dinamica I which uses a finite difference integration method of backward kind. (Author) [pt

BOOK REVIEW: Kinetic theory of plasma waves, homogeneous plasmas

Science.gov (United States)

Porkolab, Miklos

1998-11-01

The linear theory of plasma waves in homogeneous plasma is arguably the most mature and best understood branch of plasma physics. Given the recently revised version of Stix's excellent Waves in Plasmas (1992), one might ask whether another book on this subject is necessary only a few years later. The answer lies in the scope of this volume; it is somewhat more detailed in certain topics than, and complementary in many fusion research relevant areas to, Stix's book. (I am restricting these comments to the homogeneous plasma theory only, since the author promises a second volume on wave propagation in inhomogeneous plasmas.) This book is also much more of a theorist's approach to waves in plasmas, with the aim of developing the subject within the logical framework of kinetic theory. This may indeed be pleasing to the expert and to the specialist, but may be too difficult to the graduate student as an `introduction' to the subject (which the author explicitly states in the Preface). On the other hand, it may be entirely appropriate for a second course on plasma waves, after the student has mastered fluid theory and an introductory kinetic treatment of waves in a hot magnetized `Vlasov' plasma. For teaching purposes, my personal preference is to review the cold plasma wave treatment using the unified Stix formalism and notation (which the author wisely adopts in the present book, but only in Chapter 5). Such an approach allows one to deal with CMA diagrams early on, as well as to provide a framework to discuss electromagnetic wave propagation and accessibility in inhomogeneous plasmas (for which the cold plasma wave treatment is perfectly adequate). Such an approach does lack some of the rigour, however, that the author achieves with the present approach. As the author correctly shows, the fluid theory treatment of waves follows logically from kinetic theory in the cold plasma limit. I only question the pedagogical value of this approach. Otherwise, I welcome this

An advanced kinetic theory for morphing continuum with inner structures

Science.gov (United States)

Chen, James

2017-12-01

Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing equations at equilibrium state are derived and compared with Eringen's morphing (micropolar) continuum theory derived under the framework of rational continuum thermomechanics. Although rational continuum thermomechanics has the advantages of mathematical rigor and simplicity, the presented statistical kinetic theory approach provides a clear physical picture for what the governing equations represent.

Methods in half-linear asymptotic theory

Directory of Open Access Journals (Sweden)

Pavel Rehak

2016-10-01

Full Text Available We study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation $$ (r(t|y'|^{\\alpha-1}\\hbox{sgn} y''=p(t|y|^{\\alpha-1}\\hbox{sgn} y, $$ where r(t and p(t are positive continuous functions on $[a,\\infty$, $\\alpha\\in(1,\\infty$. The aim of this article is twofold. On the one hand, we show applications of a wide variety of tools, like the Karamata theory of regular variation, the de Haan theory, the Riccati technique, comparison theorems, the reciprocity principle, a certain transformation of dependent variable, and principal solutions. On the other hand, we solve open problems posed in the literature and generalize existing results. Most of our observations are new also in the linear case.

Linear {GLP}-algebras and their elementary theories

Science.gov (United States)

Pakhomov, F. N.

2016-12-01

The polymodal provability logic {GLP} was introduced by Japaridze in 1986. It is the provability logic of certain chains of provability predicates of increasing strength. Every polymodal logic corresponds to a variety of polymodal algebras. Beklemishev and Visser asked whether the elementary theory of the free {GLP}-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable [1]. For every positive integer n we solve the corresponding question for the logics {GLP}_n that are the fragments of {GLP} with n modalities. We prove that the elementary theory of the free {GLP}_n-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable for all n. We introduce the notion of a linear {GLP}_n-algebra and prove that all free {GLP}_n-algebras generated by the constants \\mathbf{0}, \\mathbf{1} are linear. We also consider the more general case of the logics {GLP}_α whose modalities are indexed by the elements of a linearly ordered set α: we define the notion of a linear algebra and prove the latter result in this case.

WKB approximation and tunneling in theories with noncanonical kinetic terms

Science.gov (United States)

González, Mariana Carrillo; Masoumi, Ali; Solomon, Adam R.; Trodden, Mark

2017-09-01

Tunneling is a fascinating aspect of quantum mechanics that renders the local minima of a potential meta-stable, with important consequences for particle physics, for the early hot stage of the universe, and more speculatively, for the behavior of the putative multiverse. While this phenomenon has been studied extensively for systems which have canonical kinetic terms, many theories of fundamental physics contain fields with noncanonical kinetic structures. It is therefore desirable to have a detailed framework for calculating tunneling rates and initial states after tunneling for these theories. In this work we present such a rigorous formulation and illustrate its use by applying it to a number of examples.

Alternative theories of the non-linear negative mass instability

International Nuclear Information System (INIS)

Channell, P.J.

1974-01-01

A theory non-linear negative mass instability is extended to include resistance. The basic assumption is explained physically and an alternative theory is offered. The two theories are compared computationally. 7 refs., 8 figs

Instabilities and chaos in a kinetic equation for active nematics

International Nuclear Information System (INIS)

Shi, Xia-qing; Ma, Yu-qiang; Chaté, Hugues

2014-01-01

We study dry active nematics at the kinetic equation level, stressing the differences with the well-known Doi theory for non-active rods near thermal equilibrium. By deriving hydrodynamic equations from the kinetic equation, we show analytically that these two description levels share the same qualitative phase diagram, as defined by the linear instability limits of spatially-homogeneous solutions. In particular, we show that the ordered, homogeneous state is unstable in a region bordering the linear onset of nematic order, and is only linearly stable deeper in the ordered phase. Direct simulations of the kinetic equation reveal that its solutions are chaotic in the region of linear instability of the ordered homogeneous state. The local mechanisms for this large-scale chaos are discussed. (paper)

Bayes linear statistics, theory & methods

CERN Document Server

Goldstein, Michael

2007-01-01

Bayesian methods combine information available from data with any prior information available from expert knowledge. The Bayes linear approach follows this path, offering a quantitative structure for expressing beliefs, and systematic methods for adjusting these beliefs, given observational data. The methodology differs from the full Bayesian methodology in that it establishes simpler approaches to belief specification and analysis based around expectation judgements. Bayes Linear Statistics presents an authoritative account of this approach, explaining the foundations, theory, methodology, and practicalities of this important field. The text provides a thorough coverage of Bayes linear analysis, from the development of the basic language to the collection of algebraic results needed for efficient implementation, with detailed practical examples. The book covers:The importance of partial prior specifications for complex problems where it is difficult to supply a meaningful full prior probability specification...

Graph-based linear scaling electronic structure theory

Energy Technology Data Exchange (ETDEWEB)

Niklasson, Anders M. N., E-mail: amn@lanl.gov; Negre, Christian F. A.; Cawkwell, Marc J.; Swart, Pieter J.; Germann, Timothy C.; Bock, Nicolas [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Mniszewski, Susan M.; Mohd-Yusof, Jamal; Wall, Michael E.; Djidjev, Hristo [Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Rubensson, Emanuel H. [Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala (Sweden)

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Linear circuits, systems and signal processing: theory and application

International Nuclear Information System (INIS)

Byrnes, C.I.; Saeks, R.E.; Martin, C.F.

1988-01-01

In part because of its universal role as a first approximation of more complicated behaviour and in part because of the depth and breadth of its principle paradigms, the study of linear systems continues to play a central role in control theory and its applications. Enhancing more traditional applications to aerospace and electronics, application areas such as econometrics, finance, and speech and signal processing have contributed to a renaissance in areas such as realization theory and classical automatic feedback control. Thus, the last few years have witnessed a remarkable research effort expended in understanding both new algorithms and new paradigms for modeling and realization of linear processes and in the analysis and design of robust control strategies. The papers in this volume reflect these trends in both the theory and applications of linear systems and were selected from the invited and contributed papers presented at the 8th International Symposium on the Mathematical Theory of Networks and Systems held in Phoenix on June 15-19, 1987

Electromagnetic response in kinetic energy driven cuprate superconductors: Linear response approach

International Nuclear Information System (INIS)

Krzyzosiak, Mateusz; Huang, Zheyu; Feng, Shiping; Gonczarek, Ryszard

2010-01-01

Within the framework of the kinetic energy driven superconductivity, the electromagnetic response in cuprate superconductors is studied in the linear response approach. The kernel of the response function is evaluated and employed to calculate the local magnetic field profile, the magnetic field penetration depth, and the superfluid density, based on the specular reflection model for a purely transverse vector potential. It is shown that the low temperature magnetic field profile follows an exponential decay at the surface, while the magnetic field penetration depth depends linearly on temperature, except for the strong deviation from the linear characteristics at extremely low temperatures. The superfluid density is found to decrease linearly with decreasing doping concentration in the underdoped regime. The problem of gauge invariance is addressed and an approximation for the dressed current vertex, which does not violate local charge conservation is proposed and discussed.

Global kinetic theory of astrophysical jets

International Nuclear Information System (INIS)

Chang, T.

1989-01-01

We suggest that an astrophysical plasma stream flowing outward from a central object aling an open magnetic field line with decreasing field strength generally will have anisotropic velocity distributions. I particular, the electron distribution function of this type of plasma streams will contain a 'thermally populated' region and a stretche out high energy tail (or 'jet-like') region collimated in the utward direction of the magnetic field line. Our argument is based on a global, collisional, kinetic theory. Because the 'kinetic jets' are always pointed aling the outward direction of the field lines, thy are automatically collimated and will assume whatever the peculiar geometries dictated by the magnetic field. This result should be useful in the understanding of the basic structures of such diverse astrophysical objects as the extragalactic radio jets, stellar winds, the solar wind, planetary polar winds, and galactic jets. (author). 8 refs.; 2 figs

Detection of kinetic change points in piece-wise linear single molecule motion

Science.gov (United States)

Hill, Flynn R.; van Oijen, Antoine M.; Duderstadt, Karl E.

2018-03-01

Single-molecule approaches present a powerful way to obtain detailed kinetic information at the molecular level. However, the identification of small rate changes is often hindered by the considerable noise present in such single-molecule kinetic data. We present a general method to detect such kinetic change points in trajectories of motion of processive single molecules having Gaussian noise, with a minimum number of parameters and without the need of an assumed kinetic model beyond piece-wise linearity of motion. Kinetic change points are detected using a likelihood ratio test in which the probability of no change is compared to the probability of a change occurring, given the experimental noise. A predetermined confidence interval minimizes the occurrence of false detections. Applying the method recursively to all sub-regions of a single molecule trajectory ensures that all kinetic change points are located. The algorithm presented allows rigorous and quantitative determination of kinetic change points in noisy single molecule observations without the need for filtering or binning, which reduce temporal resolution and obscure dynamics. The statistical framework for the approach and implementation details are discussed. The detection power of the algorithm is assessed using simulations with both single kinetic changes and multiple kinetic changes that typically arise in observations of single-molecule DNA-replication reactions. Implementations of the algorithm are provided in ImageJ plugin format written in Java and in the Julia language for numeric computing, with accompanying Jupyter Notebooks to allow reproduction of the analysis presented here.

Kinetic Scale Structure of Low-frequency Waves and Fluctuations

Energy Technology Data Exchange (ETDEWEB)

López, Rodrigo A.; Yoon, Peter H. [Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742 (United States); Viñas, Adolfo F. [NASA Goddard Space Flight Center, Heliophysics Science Division, Geospace Physics Laboratory, Mail Code 673, Greenbelt, MD 20771 (United States); Araneda, Jaime A., E-mail: rlopezh@umd.edu, E-mail: yoonp@umd.edu [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción (Chile)

2017-08-10

The dissipation of solar wind turbulence at kinetic scales is believed to be important for the heating of the corona and for accelerating the wind. The linear Vlasov kinetic theory is a useful tool for identifying various wave modes, including kinetic Alfvén, fast magnetosonic/whistler, and ion-acoustic (or kinetic slow), and their possible roles in the dissipation. However, the kinetic mode structure in the vicinity of ion-cyclotron modes is not clearly understood. The present paper aims to further elucidate the structure of these low-frequency waves by introducing discrete particle effects through hybrid simulations and Klimontovich formalism of spontaneous emission theory. The theory and simulation of spontaneously emitted low-frequency fluctuations are employed to identify and distinguish the detailed mode structures associated with ion-Bernstein modes versus quasi-modes. The spontaneous emission theory and simulation also confirm the findings of the Vlasov theory in that the kinetic Alfvén waves can be defined over a wide range of frequencies, including the proton cyclotron frequency and its harmonics, especially for high-beta plasmas. This implies that these low-frequency modes may play predominant roles even in the fully kinetic description of kinetic scale turbulence and dissipation despite the fact that cyclotron harmonic and Bernstein modes may also play important roles in wave–particle interactions.

Linear algebra and group theory for physicists

CERN Document Server

Rao, K N Srinivasa

2006-01-01

Professor Srinivasa Rao's text on Linear Algebra and Group Theory is directed to undergraduate and graduate students who wish to acquire a solid theoretical foundation in these mathematical topics which find extensive use in physics. Based on courses delivered during Professor Srinivasa Rao's long career at the University of Mysore, this text is remarkable for its clear exposition of the subject. Advanced students will find a range of topics such as the Representation theory of Linear Associative Algebras, a complete analysis of Dirac and Kemmer algebras, Representations of the Symmetric group via Young Tableaux, a systematic derivation of the Crystallographic point groups, a comprehensive and unified discussion of the Rotation and Lorentz groups and their representations, and an introduction to Dynkin diagrams in the classification of Lie groups. In addition, the first few chapters on Elementary Group Theory and Vector Spaces also provide useful instructional material even at an introductory level. An author...

A local homology theory for linearly compact modules

International Nuclear Information System (INIS)

Nguyen Tu Cuong; Tran Tuan Nam

2004-11-01

We introduce a local homology theory for linearly modules which is in some sense dual to the local cohomology theory of A. Grothendieck. Some basic properties of local homology modules are shown such as: the vanishing and non-vanishing, the noetherianness of local homology modules. By using duality, we extend some well-known results in theory of local cohomology of A. Grothendieck. (author)

Kinetic approach to the initial value problem in quantum field theory

International Nuclear Information System (INIS)

Lin Chi Yong; Toledo Piza, A.F.R. de.

1989-06-01

Time-dependente projection techniques developed to derive kinetic equations in the context of the quantum many-body problem are applied to φ 4 field theory. The approach is illustrated by working out the 0+1 dimensional case explicitly, including numerical solutions of the kinetic equations. Extension to higher dimensions is briefly discussed. (author) [pt

Perturbative method for the derivation of quantum kinetic theory based on closed-time-path formalism

International Nuclear Information System (INIS)

Koide, Jun

2002-01-01

Within the closed-time-path formalism, a perturbative method is presented, which reduces the microscopic field theory to the quantum kinetic theory. In order to make this reduction, the expectation value of a physical quantity must be calculated under the condition that the Wigner distribution function is fixed, because it is the independent dynamical variable in the quantum kinetic theory. It is shown that when a nonequilibrium Green function in the form of the generalized Kadanoff-Baym ansatz is utilized, this condition appears as a cancellation of a certain part of contributions in the diagrammatic expression of the expectation value. Together with the quantum kinetic equation, which can be derived in the closed-time-path formalism, this method provides a basis for the kinetic-theoretical description

Coarse-graining free theories with gauge symmetries: the linearized case

International Nuclear Information System (INIS)

Bahr, Benjamin; Dittrich, Bianca; He Song

2011-01-01

Discretizations of continuum theories often do not preserve the gauge symmetry content. This occurs in particular for diffeomorphism symmetry in general relativity, which leads to severe difficulties in both canonical and covariant quantization approaches. We discuss here the method of perfect actions, which attempts to restore gauge symmetries by mirroring exactly continuum physics on a lattice via a coarse graining process. Analytical results can only be obtained via a perturbative approach, for which we consider the first step, namely the coarse graining of the linearized theory. The linearized gauge symmetries are exact also in the discretized theory; hence, we develop a formalism to deal with gauge systems. Finally, we provide a discretization of linearized gravity as well as a coarse graining map and show that with this choice the three-dimensional (3D) linearized gravity action is invariant under coarse graining.

Three caveats for linear stability theory: Rayleigh-Benard convection

International Nuclear Information System (INIS)

Greenside, H.S.

1984-06-01

Recent theories and experiments challenge the applicability of linear stability theory near the onset of buoyancy-driven (Rayleigh-Benard) convection. This stability theory, based on small perturbations of infinite parallel rolls, is found to miss several important features of the convective flow. The reason is that the lateral boundaries have a profound influence on the possible wave numbers and flow patterns even for the largest cells studied. Also, the nonlinear growth of incoherent unstable modes distorts the rolls, leading to a spatially disordered and sometimes temporally nonperiodic flow. Finally, the relation of the skewed varicose instability to the onset of turbulence (nonperiodic time dependence) is examined. Linear stability theory may not suffice to predict the onset of time dependence in large cells close to threshold

Relativistic nuclear fluid dynamics and VUU kinetic theory

International Nuclear Information System (INIS)

Molitoris, J.J.; Hahn, D.; Alonso, C.; Collazo, I.; D'Alessandris, P.; McAbee, T.; Wilson, J.; Zingman, J.

1987-01-01

Relativistic kinetic theory may be used to understand hot dense hadronic matter. We address the questions of collective flow and pion production in a 3 D relativistic fluid dynamic model and in the VUU microscopic theory. The GSI/LBL collective flow and pion data point to a stiff equation of state. The effect of the nuclear equation of state on the thermodynamic parameters is discussed. The properties of dense hot hadronic matter are studied in Au + Au collisions from 0.1 to 10 GeV/nucleon. 22 refs., 5 figs

On the kinetic theory of the one-component plasma

International Nuclear Information System (INIS)

Cohen, J.S.

1984-01-01

In this thesis, kinetic theory is applied to transport phenomena of a one-component plasma. Existing kinetic equations, containing both dynamical screening effects and close binary collisions do not suffer from divergencies. Recently an approximation for the pair correlation function has been proposed that is valid for small values of the plasma collision parameter. Upon insertion of this expression into the general form of the collision integral, one obtains another convergent kinetic equation. This thesis shows that both kinetic equations yield the same coefficient of heat conductivity and viscosity; and that for a hot dilute plasma the arbitrary transport coefficient is rather insensitive to the pair correlation function. In the second part, the author studies the diffusion of a tagged particle in an external magnetic field. It is found that the longitudinal self-diffusion coefficient contra-varies monotonically with the magnetic field strength. (Auth.)

Formulated linear programming problems from game theory and its ...

African Journals Online (AJOL)

Formulated linear programming problems from game theory and its computer implementation using Tora package. ... Game theory, a branch of operations research examines the various concepts of decision ... AJOL African Journals Online.

Active matter beyond mean-field: ring-kinetic theory for self-propelled particles.

Science.gov (United States)

Chou, Yen-Liang; Ihle, Thomas

2015-02-01

Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013)] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not-too-small noises and mean free paths. This shows that there are parameter ranges in Vicsek-like models where the correlated closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with an exponent around -1.8, followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.

Modeling non-linear kinetics of hyperpolarized [1-(13)C] pyruvate in the crystalloid-perfused rat heart

NARCIS (Netherlands)

Mariotti, E.; Orton, M. R.; Eerbeek, O.; Ashruf, J. F.; Zuurbier, C. J.; Southworth, R.; Eykyn, T. R.

2016-01-01

Hyperpolarized (13)C MR measurements have the potential to display non-linear kinetics. We have developed an approach to describe possible non-first-order kinetics of hyperpolarized [1-(13)C] pyruvate employing a system of differential equations that agrees with the principle of conservation of mass

Kinetic theory in maximal-acceleration invariant phase space

International Nuclear Information System (INIS)

Brandt, H.E.

1989-01-01

A vanishing directional derivative of a scalar field along particle trajectories in maximal acceleration invariant phase space is identical in form to the ordinary covariant Vlasov equation in curved spacetime in the presence of both gravitational and nongravitational forces. A natural foundation is thereby provided for a covariant kinetic theory of particles in maximal-acceleration invariant phase space. (orig.)

Analysis of senior high school student understanding on gas kinetic theory material

Science.gov (United States)

Anri, Y.; Maknun, J.; Chandra, D. T.

2018-05-01

The purpose of this research conducted to find out student understanding profile about gas kinetic theory. Particularly, on ideal gas law material, ideal gas equations and kinetic energy of ideal gas. This research was conducted on student of class XII in one of the schools in Bandung. This research is a descriptive research. The data of this research collected by using test instrument which was the essay that has been developed by the researcher based on Bloom’s Taxonomy revised. Based on the analysis result to student answer, this research discovered that whole student has low understanding in the material of gas kinetic theory. This low understanding caused of the misconception of the student, student attitude on physic subjects, and teacher teaching method who are less helpful in obtaining clear pictures in material being taught.

Linear bosonic and fermionic quantum gauge theories on curved spacetimes

International Nuclear Information System (INIS)

Hack, Thomas-Paul; Schenkel, Alexander

2012-05-01

We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearized pure N=1 supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.

Linear bosonic and fermionic quantum gauge theories on curved spacetimes

Energy Technology Data Exchange (ETDEWEB)

Hack, Thomas-Paul [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Schenkel, Alexander [Bergische Univ., Wuppertal (Germany). Fachgruppe Physik

2012-05-15

We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearized pure N=1 supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.

Non-equilibrium reacting gas flows kinetic theory of transport and relaxation processes

CERN Document Server

Nagnibeda, Ekaterina; Nagnibeda, Ekaterina

2009-01-01

This volume develops the kinetic theory of transport phenomena and relaxation processes in the flows of reacting gas mixtures. The theory is applied to the modeling of non-equilibrium flows behind strong shock waves, in the boundary layer, and in nozzles.

Collisionless two-fluid theory of toroidal ηi stability

International Nuclear Information System (INIS)

Mondt, J.; Weiland, J.

1989-01-01

A collisionless two-fluid theory based on a fourteen-moment generalization of the 'double-adiabatic' equations is developed to lowest order in the Larmor radius parameter, and applied to derive the toroidal η i stability boundary for all values of the ratio of the density gradient scale length divided by the field curvature length. The present model is an improvement over existing collisional two-fluid models in view of the collisionless nature of the η i instability, while retaining the advantage over kinetic theory of the practability of mode-coupling simulations. The linear stability boundary, linear growth rate and real frequency agree fairly accurately with draft-kinetic theory

The linearization method in hydrodynamical stability theory

CERN Document Server

Yudovich, V I

1989-01-01

This book presents the theory of the linearization method as applied to the problem of steady-state and periodic motions of continuous media. The author proves infinite-dimensional analogues of Lyapunov's theorems on stability, instability, and conditional stability for a large class of continuous media. In addition, semigroup properties for the linearized Navier-Stokes equations in the case of an incompressible fluid are studied, and coercivity inequalities and completeness of a system of small oscillations are proved.

Kinetic theory of surface waves in plasma jets

International Nuclear Information System (INIS)

Shokri, B.

2002-01-01

The kinetic theory analysis of surface waves propagating along a semi-bounded plasma jet is presented. The frequency spectra and their damping rate are obtained in both the high and low frequency regions. Finally, the penetration of the static field in the plasma jet under the condition that the plasma jet velocity is smaller than the sound velocity is studied

A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

Science.gov (United States)

Martin, C. J.; Lee, Y. M.

1972-01-01

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

Rheokinetics and effect of shear rate on the kinetics of linear polyurethane formation

NARCIS (Netherlands)

Navarchian, AH; Picchioni, F; Janssen, LPBM

In this article, the rheokinetics of polyurethane formation and the influence of shear rate on its kinetics have been studied. Two different linear polyurethane systems with 0% and 100% hard segments are examined in a cone and plate rheometer. The isothermal increase of viscosity during polyurethane

Kinetic theory of spectral line broadening in plasmas

International Nuclear Information System (INIS)

Hussey, T.W.

1974-01-01

A formal kinetic theory is used to cast the line shape function into a form that, while similar to the ''unified'' theories of Smith, Cooper, and Vidal and of Voslamber, does not introduce some of the usual approximations. The resulting line shape function explicitly includes the initial correlations between the atom and perturbers, and also demonstrates the natural separation of plasma mean field and collisional effects. The classical path and no-quenching approximations are discussed and ultimately employed; however, they are not required in the formal development. The weak coupling limit is considered as a systematic approximation to the formal results. It is shown tha different ways of applying this limit lead to different expressions for the memory operator, some of which correspond to existing theories. One approximation is considered which systematically incorporates the effects of electron correlations within the framework of a unified theory. In addition, a practical approximation suitable for a strongly interacting plasma is discussed

Noise-Induced Modulation of the Relaxation Kinetics around a Non-Equilibrium Steady State of Non-Linear Chemical Reaction Networks

OpenAIRE

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

2011-01-01

Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confi...

Linear kinetic enlightenment of a slab of nonuniform plasma

International Nuclear Information System (INIS)

Revenchuk, S.M.

1996-01-01

A phenomenon of linear kinetic regeneration of a harmonic electric-field perturbation beyond the nonuniform opacity barrier due to electrons trapped by a potential well is investigated. Such electrons are reflected by the well walls without loss of phase memory about the external perturbation, which is rehabilitated on the other side of the barrier. The incidence of the electromagnetic wave polarized in the plane of incidence on a plasma slab. Analytic expressions for the regenerated electric field and regeneration coefficient are obtained in the ballistic approximation. The dependence of the regeneration coefficient on shape of the electrostatic potential confining the wave barrier is discussed

Collective learning modeling based on the kinetic theory of active particles

Science.gov (United States)

Burini, D.; De Lillo, S.; Gibelli, L.

2016-03-01

This paper proposes a systems approach to the theory of perception and learning in populations composed of many living entities. Starting from a phenomenological description of these processes, a mathematical structure is derived which is deemed to incorporate their complexity features. The modeling is based on a generalization of kinetic theory methods where interactions are described by theoretical tools of game theory. As an application, the proposed approach is used to model the learning processes that take place in a classroom.

Azerbaijan Technical University’s Experience in Teaching Linear Electrical Circuit Theory

Directory of Open Access Journals (Sweden)

G. A. Mamedov

2006-01-01

Full Text Available An experience in teaching linear electrical circuit theory at the Azerbaijan Technical University is presented in the paper. The paper describes structure of the Linear Electrical Circuit Theory course worked out by the authors that contains a section on electrical calculation of track circuits, information on electro-magnetic compatibility and typical tests for better understanding of the studied subject.

Kinetic theory of flocking: derivation of hydrodynamic equations.

Science.gov (United States)

Ihle, Thomas

2011-03-01

It is shown how to explicitly coarse-grain the microscopic dynamics of the rule-based Vicsek model for self-propelled agents. The hydrodynamic equations are derived by means of an Enskog-type kinetic theory. Expressions for all transport coefficients are given. The transition from a disordered to a flocking state, which at large particle speeds appears to be a fluctuation-induced first-order phase transition, is studied numerically and analytically.

Sequence-dependent theory of oligonucleotide hybridization kinetics

International Nuclear Information System (INIS)

Marimuthu, Karthikeyan; Chakrabarti, Raj

2014-01-01

A theoretical approach to the prediction of the sequence and temperature-dependent rate constants for oligonucleotide hybridization reactions has been developed based on the theory of relaxation kinetics. One-sided and two-sided melting reaction mechanisms for oligonucleotide hybridization reactions have been considered, analyzed, modified, and compared to select a physically consistent as well as robust model for prediction of the relaxation times of DNA hybridization reactions that agrees with the experimental evidence. The temperature- and sequence-dependent parameters of the proposed model have been estimated using available experimental data. The relaxation time model that we developed has been combined with the nearest neighbor model of hybridization thermodynamics to estimate the temperature- and sequence-dependent rate constants of an oligonucleotide hybridization reaction. The model-predicted rate constants are compared to experimentally determined rate constants for the same oligonucleotide hybridization reactions. Finally, we consider a few important applications of kinetically controlled DNA hybridization reactions

A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

Science.gov (United States)

Freed, Alan D.; Leonov, Arkady I.

2002-01-01

The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

Particle linear theory on a self-gravitating perturbed cubic Bravais lattice

International Nuclear Information System (INIS)

Marcos, B.

2008-01-01

Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called ''particle linear theory''(PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits us to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body, and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects--in the linear regime--of N-body simulations for which initial conditions have been set up using these different lattices.

Feasibility of combining linear theory and impact theory methods for the analysis and design of high speed configurations

Science.gov (United States)

Brooke, D.; Vondrasek, D. V.

1978-01-01

The aerodynamic influence coefficients calculated using an existing linear theory program were used to modify the pressures calculated using impact theory. Application of the combined approach to several wing-alone configurations shows that the combined approach gives improved predictions of the local pressure and loadings over either linear theory alone or impact theory alone. The approach not only removes most of the short-comings of the individual methods, as applied in the Mach 4 to 8 range, but also provides the basis for an inverse design procedure applicable to high speed configurations.

Electromagnetic theory of plasma light scattering

International Nuclear Information System (INIS)

Bobin, J.L.

1969-01-01

The theory of light scattering by a plasma is formulated using Klimontovich's microscopic distribution functions and Landau method to solve linear kinetic equations. First, Salpeter's derivation and results are given for the spectrum of light scattered by a collisionless plasma. Then, the influence of collision is investigated through B.G.K. kinetic equation. (author) [fr

Kinetic theory of the sausage instability of a z-pinch

International Nuclear Information System (INIS)

Isichenko, M.B.; Kulyabin, K.L.; Yan'kov, V.V.

1989-01-01

A linear problem of z-pinch sausage development is considered taking into account the influence of kinetic effects for ideal scanning current. Plasma electrons are considered to be cold and ions - collisionless. It is also supposed that the magnetic field inside a pinch doesn't affect the motion of ions, which are reflected like in a mirror from a jump of an electric potential arising on the plasma boundary. In case of long-wave perturbations ka >1 the acount of kinetics leads to considerable decrease of the increment [(ka) 1/2 times] in comparison with the hydrodynamic description, that permits to explain the increased instability of z-pinches observed in experiments

Cross-beam energy transfer: On the accuracy of linear stationary models in the linear kinetic regime

Science.gov (United States)

Debayle, A.; Masson-Laborde, P.-E.; Ruyer, C.; Casanova, M.; Loiseau, P.

2018-05-01

We present an extensive numerical study by means of particle-in-cell simulations of the energy transfer that occurs during the crossing of two laser beams. In the linear regime, when ions are not trapped in the potential well induced by the laser interference pattern, a very good agreement is obtained with a simple linear stationary model, provided the laser intensity is sufficiently smooth. These comparisons include different plasma compositions to cover the strong and weak Landau damping regimes as well as the multispecies case. The correct evaluation of the linear Landau damping at the phase velocity imposed by the laser interference pattern is essential to estimate the energy transfer rate between the laser beams, once the stationary regime is reached. The transient evolution obtained in kinetic simulations is also analysed by means of a full analytical formula that includes 3D beam energy exchange coupled with the ion acoustic wave response. Specific attention is paid to the energy transfer when the laser presents small-scale inhomogeneities. In particular, the energy transfer is reduced when the laser inhomogeneities are comparable with the Landau damping characteristic length of the ion acoustic wave.

Optically Controlled Electron-Transfer Reaction Kinetics and Solvation Dynamics : Effect of Franck-Condon States

NARCIS (Netherlands)

Gupta, Kriti; Patra, Aniket; Dhole, Kajal; Samanta, Alok Kumar; Ghosh, Swapan K.

2017-01-01

Experimental results for optically controlled electron-transfer reaction kinetics (ETRK) and nonequilibrium solvation dynamics (NESD) of Coumarin 480 in DMPC vesicle show their dependence on excitation wavelength λex. However, the celebrated Marcus theory and linear-response-theory-based approaches

When is quasi-linear theory exact. [particle acceleration

Science.gov (United States)

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.

Heat and Kinetic Theory in 19th-Century Physics Textbooks: The Case of Spain.

Science.gov (United States)

Vaquero, Jose M.; Santos, Andres

2001-01-01

Presents an analysis of the contents of 19th century Spanish textbooks. These textbooks are centered on imponderable fluids, the concept of energy, the mechanical theory of heat, and the kinetic theory of gases. (SAH)

Collective learning modeling based on the kinetic theory of active particles.

Science.gov (United States)

Burini, D; De Lillo, S; Gibelli, L

2016-03-01

This paper proposes a systems approach to the theory of perception and learning in populations composed of many living entities. Starting from a phenomenological description of these processes, a mathematical structure is derived which is deemed to incorporate their complexity features. The modeling is based on a generalization of kinetic theory methods where interactions are described by theoretical tools of game theory. As an application, the proposed approach is used to model the learning processes that take place in a classroom. Copyright © 2015 Elsevier B.V. All rights reserved.

Wigner's little group as a gauge generator in linearized gravity theories

International Nuclear Information System (INIS)

Scaria, Tomy; Chakraborty, Biswajit

2002-01-01

We show that the translational subgroup of Wigner's little group for massless particles in 3 + 1 dimensions generates gauge transformation in linearized Einstein gravity. Similarly, a suitable representation of the one-dimensional translational group T(1) is shown to generate gauge transformation in the linearized Einstein-Chern-Simons theory in 2 + 1 dimensions. These representations are derived systematically from appropriate representations of translational groups which generate gauge transformations in gauge theories living in spacetime of one higher dimension by the technique of dimensional descent. The unified picture thus obtained is compared with a similar picture available for vector gauge theories in 3 + 1 and 2 + 1 dimensions. Finally, the polarization tensor of the Einstein-Pauli-Fierz theory in 2 + 1 dimensions is shown to split into the polarization tensors of a pair of Einstein-Chern-Simons theories with opposite helicities suggesting a doublet structure for the Einstein-Pauli-Fierz theory

A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories

Directory of Open Access Journals (Sweden)

V. V. Zozulya

2013-01-01

Full Text Available A high order theory for linear thermoelasticity and heat conductivity of shells has been developed. The proposed theory is based on expansion of the 3-D equations of theory of thermoelasticity and heat conductivity into Fourier series in terms of Legendre polynomials. The first physical quantities that describe thermodynamic state have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity and heat conductivity including generalized Hooke's and Fourier's laws have been transformed to the corresponding equations for coefficients of the polynomial expansion. Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. First approximation theory is considered in more detail. The obtained equations for the first approximation theory are compared with the corresponding equations for Timoshenko's and Kirchhoff-Love's theories. Special case of plates and cylindrical shell is also considered, and corresponding equations in displacements are presented.

Effective-field theory on the kinetic Ising model

International Nuclear Information System (INIS)

Shi Xiaoling; Wei Guozhu; Li Lin

2008-01-01

As an analytical method, the effective-field theory (EFT) is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the square lattice (Z=4) and the simple cubic lattice (Z=6), respectively. The dynamic order parameter, the hysteresis loop area and the dynamic correlation are calculated. In the field amplitude h 0 /ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn, and the dynamical tricritical point has been observed. We also make the compare results of EFT with that given by using the mean field theory (MFT)

Transport phenomena and kinetic theory applications to gases, semiconductors, photons, and biological systems

CERN Document Server

Gabetta, Ester

2007-01-01

The study of kinetic equations related to gases, semiconductors, photons, traffic flow, and other systems has developed rapidly in recent years because of its role as a mathematical tool in many applications in areas such as engineering, meteorology, biology, chemistry, materials science, nanotechnology, and pharmacy. Written by leading specialists in their respective fields, this book presents an overview of recent developments in the field of mathematical kinetic theory with a focus on modeling complex systems, emphasizing both mathematical properties and their physical meaning. The overall presentation covers not only modeling aspects and qualitative analysis of mathematical problems, but also inverse problems, which lead to a detailed assessment of models in connection with their applications, and to computational problems, which lead to an effective link of models to the analysis of real-world systems. "Transport Phenomena and Kinetic Theory" is an excellent self-study reference for graduate students, re...

Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

KAUST Repository

Kabanov, Dmitry I.

2017-12-08

We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

KAUST Repository

Kabanov, Dmitry; Kasimov, Aslan R.

2018-01-01

We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

KAUST Repository

Kabanov, Dmitry

2018-03-20

We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

A thermostatted kinetic theory model for event-driven pedestrian dynamics

Science.gov (United States)

Bianca, Carlo; Mogno, Caterina

2018-06-01

This paper is devoted to the modeling of the pedestrian dynamics by means of the thermostatted kinetic theory. Specifically the microscopic interactions among pedestrians and an external force field are modeled for simulating the evacuation of pedestrians from a metro station. The fundamentals of the stochastic game theory and the thermostatted kinetic theory are coupled for the derivation of a specific mathematical model which depicts the time evolution of the distribution of pedestrians at different exits of a metro station. The perturbation theory is employed in order to establish the stability analysis of the nonequilibrium stationary states in the case of a metro station consisting of two exits. A general sensitivity analysis on the initial conditions, the magnitude of the external force field and the number of exits is presented by means of numerical simulations which, in particular, show how the asymptotic distribution and the convergence time are affected by the presence of an external force field. The results show how, in evacuation conditions, the interaction dynamics among pedestrians can be negligible with respect to the external force. The important role of the thermostat term in allowing the reaching of the nonequilibrium stationary state is stressed out. Research perspectives are underlined at the end of paper, in particular for what concerns the derivation of frameworks that take into account the definition of local external actions and the introduction of the space and velocity dynamics.

Kinetic theory of age-structured stochastic birth-death processes

Science.gov (United States)

Greenman, Chris D.; Chou, Tom

2016-01-01

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control

CERN Document Server

Johnson, Russell; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

2016-01-01

This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hami...

Kinetic theory of a rarefied gas of rough spheres

International Nuclear Information System (INIS)

Kremer, G.M.

1987-01-01

A Kinetic theory for the rarefied gas consisting of rough-spherical molecules is developed, in which a macroscopic state is characterized by the 29 scalar fields of density, velocity, pressure tensor, temperature, translational heat flux, rotational heat flux, spin and spin flux. The relations of Navier-Stokes and Fourier are obtained by the use of an iteration method akin to the Maxwellian procedure. (author) [pt

Linear control theory for gene network modeling.

Science.gov (United States)

Shin, Yong-Jun; Bleris, Leonidas

2010-09-16

Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain) and linear state-space (time domain) can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.

An experimental test of the linear no-threshold theory of radiation carcinogenesis

International Nuclear Information System (INIS)

Cohen, B.L.

1990-01-01

There is a substantial body of quantitative information on radiation-induced cancer at high dose, but there are no data at low dose. The usual method for estimating effects of low-level radiation is to assume a linear no-threshold dependence. if this linear no-threshold assumption were not used, essentially all fears about radiation would disappear. Since these fears are costing tens of billions of dollars, it is most important that the linear no-threshold theory be tested at low dose. An opportunity for possibly testing the linear no-threshold concept is now available at low dose due to radon in homes. The purpose of this paper is to attempt to use this data to test the linear no-threshold theory

KINETIC-J: A computational kernel for solving the linearized Vlasov equation applied to calculations of the kinetic, configuration space plasma current for time harmonic wave electric fields

Science.gov (United States)

Green, David L.; Berry, Lee A.; Simpson, Adam B.; Younkin, Timothy R.

2018-04-01

We present the KINETIC-J code, a computational kernel for evaluating the linearized Vlasov equation with application to calculating the kinetic plasma response (current) to an applied time harmonic wave electric field. This code addresses the need for a configuration space evaluation of the plasma current to enable kinetic full-wave solvers for waves in hot plasmas to move beyond the limitations of the traditional Fourier spectral methods. We benchmark the kernel via comparison with the standard k →-space forms of the hot plasma conductivity tensor.

Kinetic aspects of the embedded clusters: Reaction - Rate Theory

International Nuclear Information System (INIS)

Despa, F.; Apostol, M.

1995-07-01

The main stages of the cluster growth process are reviewed using Reaction - Rate Theory. The precipitation stage is shown as a relaxation of the solute towards a cluster state characterized by a higher stability. The kinetic of the late stage of phase separation, the coarsening process, is analyzed by an off-centre diffusion mechanism. The theoretical results are compared to the experimental ones. (author). 37 refs, 6 figs

Relativistic Kinetic Theory

Science.gov (United States)

Vereshchagin, Gregory V.; Aksenov, Alexey G.

2017-02-01

Preface; Acknowledgements; Acronyms and definitions; Introduction; Part I. Theoretical Foundations: 1. Basic concepts; 2. Kinetic equation; 3. Averaging; 4. Conservation laws and equilibrium; 5. Relativistic BBGKY hierarchy; 6. Basic parameters in gases and plasmas; Part II. Numerical Methods: 7. The basics of computational physics; 8. Direct integration of Boltzmann equations; 9. Multidimensional hydrodynamics; Part III. Applications: 10. Wave dispersion in relativistic plasma; 11. Thermalization in relativistic plasma; 12. Kinetics of particles in strong fields; 13. Compton scattering in astrophysics and cosmology; 14. Self-gravitating systems; 15. Neutrinos, gravitational collapse and supernovae; Appendices; Bibliography; Index.

Diamagnetic boundary layers: a kinetic theory

International Nuclear Information System (INIS)

Lemaire, J.; Burlaga, L.F.

1976-01-01

A kinetic theory for boundary layers associated with MHD tangential 'discontinuities' in a collisionless magnetized plasma such as those observed in the solar wind is presented. The theory consists of finding self-consistent solutions of Vlasov's equation and Maxwell's equation for stationary, one-dimensional boundary layers separating two Maxwellian plasma states. Layers in which the current is carried by electrons are found to have a thickness of the order of a few electron gyroradii, but the drift speed of the current-carrying electrons is found to exceed the Alfven speed, and accordingly such layers are not stable. Several types of layers, in which the current is carried by protons are discussed; in particular, cases in which the magnetic field intensity and/or direction changed across the layer were considered. In every case, the thickness was of the order of a few proton gyroradii and the field changed smoothly , although the characteristics depended somewhat on the boundary conditions. The drift speed was always less than the Alfven speed, consistent with stability of such structures. The results are consistent with the observations of boundary layers in the solar wind near 1 AU. (Auth.)

Clifford Algebras and Spinorial Representation of Linear Canonical Transformations in Quantum Theory

International Nuclear Information System (INIS)

Raoelina Andriambololona; Ranaivoson, R.T.R.; Rakotoson, H.

2017-11-01

This work is a continuation of previous works that we have done concerning linear canonical transformations and a phase space representation of quantum theory. It is mainly focused on the description of an approach which permits to establish spinorial representation of linear canonical transformations. It begins with an introduction section in which the reason and context of the content are discussed. The introduction section is followed by a brief recall about Clifford algebra and spin group. The description of the approach is started with the presentation of an adequate parameterization of linear canonical transformations which permits to represent them with special pseudo-orthogonal transformations in an operators space. The establishment of the spinorial representation is deduced using relation between special pseudo-orthogonal groups and spin groups. The cases of one dimension quantum mechanics and general multidimensional theory are both studied. The case of linear canonical transformation related to Minkowski space is particularly studied and it is shown that Lorentz transformation may be considered as particular case of linear canonical transformation. Some results from the spinorial representation are also exploited to define operators which may be used to establish equations for fields if one considers the possibility of envisaging a field theory which admits as main symmetry group the group constituted by linear canonical transformations.

Linear control theory for gene network modeling.

Directory of Open Access Journals (Sweden)

Yong-Jun Shin

Full Text Available Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain and linear state-space (time domain can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.

Inverse problems in linear transport theory

International Nuclear Information System (INIS)

Dressler, K.

1988-01-01

Inverse problems for a class of linear kinetic equations are investigated. The aim is to identify the scattering kernel of a transport equation (corresponding to the structure of a background medium) by observing the 'albedo' part of the solution operator for the corresponding direct initial boundary value problem. This means to get information on some integral operator in an integrodifferential equation through on overdetermined boundary value problem. We first derive a constructive method for solving direct halfspace problems and prove a new factorization theorem for the solutions. Using this result we investigate stationary inverse problems with respect to well posedness (e.g. reduce them to classical ill-posed problems, such as integral equations of first kind). In the time-dependent case we show that a quite general inverse problem is well posed and solve it constructively. (orig.)

Rate theory of solvent exchange and kinetics of Li(+) - BF4 (-)/PF6 (-) ion pairs in acetonitrile.

Science.gov (United States)

Dang, Liem X; Chang, Tsun-Mei

2016-09-07

In this paper, we describe our efforts to apply rate theories in studies of solvent exchange around Li(+) and the kinetics of ion pairings in lithium-ion batteries (LIBs). We report one of the first computer simulations of the exchange dynamics around solvated Li(+) in acetonitrile (ACN), which is a common solvent used in LIBs. We also provide details of the ion-pairing kinetics of Li(+)-[BF4] and Li(+)-[PF6] in ACN. Using our polarizable force-field models and employing classical rate theories of chemical reactions, we examine the ACN exchange process between the first and second solvation shells around Li(+). We calculate exchange rates using transition state theory and weighted them with the transmission coefficients determined by the reactive flux, Impey, Madden, and McDonald approaches, and Grote-Hynes theory. We found the relaxation times changed from 180 ps to 4600 ps and from 30 ps to 280 ps for Li(+)-[BF4] and Li(+)-[PF6] ion pairs, respectively. These results confirm that the solvent response to the kinetics of ion pairing is significant. Our results also show that, in addition to affecting the free energy of solvation into ACN, the anion type also should significantly influence the kinetics of ion pairing. These results will increase our understanding of the thermodynamic and kinetic properties of LIB systems.

Plane answers to complex questions the theory of linear models

CERN Document Server

Christensen, Ronald

1987-01-01

This book was written to rigorously illustrate the practical application of the projective approach to linear models. To some, this may seem contradictory. I contend that it is possible to be both rigorous and illustrative and that it is possible to use the projective approach in practical applications. Therefore, unlike many other books on linear models, the use of projections and sub­ spaces does not stop after the general theory. They are used wherever I could figure out how to do it. Solving normal equations and using calculus (outside of maximum likelihood theory) are anathema to me. This is because I do not believe that they contribute to the understanding of linear models. I have similar feelings about the use of side conditions. Such topics are mentioned when appropriate and thenceforward avoided like the plague. On the other side of the coin, I just as strenuously reject teaching linear models with a coordinate free approach. Although Joe Eaton assures me that the issues in complicated problems freq...

On the current-voltage relationship in fluid theory

Directory of Open Access Journals (Sweden)

P. Janhunen

1999-01-01

Full Text Available The kinetic theory of precipitating electrons with Maxwellian source plasma yields the well-known current-voltage relationship (CV-relationship; Knight formula, which can in most cases be accurately approximated by a reduced linear formula. Our question is whether it is possible to obtain this CV-relationship from fluid theory, and if so, to what extent it is physically equivalent with the more accurate kinetic counterpart. An answer to this question is necessary before trying to understand how one could combine time-dependent and transient phenomena such as Alfvénic waves with a slowly evolving background described by the CV-relationship. We first compute the fluid quantity profiles (density, pressure etc. along a flux tube based on kinetic theory solution. A parallel potential drop accumulates plasma (and pressure below it, which explains why the current is linearly proportional to the potential drop in the kinetic theory even though the velocity of the accelerated particles is only proportional to the square root of the accelerating voltage. Electron fluid theory reveals that the kinetic theory results can be reproduced, except for different numerical constants, if and only if the polytropic index γ is equal to three, corresponding to one-dimensional motion. The convective derivative term v·∇v provides the equivalent of the "mirror force" and is therefore important to include in a fluid theory trying to describe a CV-relationship. In one-fluid equations the parallel electric field, at least in its functional form, emerges self-consistently. We find that the electron density enhancement below the potential drop disappears because the magnetospheric ions would be unable to neutralize it, and a square root CV-relationship results, in disagreement with kinetic theory and observations. Also, the potential drop concentrates just above the ionosphere, which is at odds with observations as well. To resolve this puzzle, we show that considering

On the current-voltage relationship in fluid theory

Directory of Open Access Journals (Sweden)

P. Janhunen

Full Text Available The kinetic theory of precipitating electrons with Maxwellian source plasma yields the well-known current-voltage relationship (CV-relationship; Knight formula, which can in most cases be accurately approximated by a reduced linear formula. Our question is whether it is possible to obtain this CV-relationship from fluid theory, and if so, to what extent it is physically equivalent with the more accurate kinetic counterpart. An answer to this question is necessary before trying to understand how one could combine time-dependent and transient phenomena such as Alfvénic waves with a slowly evolving background described by the CV-relationship. We first compute the fluid quantity profiles (density, pressure etc. along a flux tube based on kinetic theory solution. A parallel potential drop accumulates plasma (and pressure below it, which explains why the current is linearly proportional to the potential drop in the kinetic theory even though the velocity of the accelerated particles is only proportional to the square root of the accelerating voltage. Electron fluid theory reveals that the kinetic theory results can be reproduced, except for different numerical constants, if and only if the polytropic index γ is equal to three, corresponding to one-dimensional motion. The convective derivative term v·∇v provides the equivalent of the "mirror force" and is therefore important to include in a fluid theory trying to describe a CV-relationship. In one-fluid equations the parallel electric field, at least in its functional form, emerges self-consistently. We find that the electron density enhancement below the potential drop disappears because the magnetospheric ions would be unable to neutralize it, and a square root CV-relationship results, in disagreement with kinetic theory and observations. Also, the potential drop concentrates just above the ionosphere, which is at odds with observations as well. To resolve this puzzle, we show that considering

Gas-Kinetic Theory Based Flux Splitting Method for Ideal Magnetohydrodynamics

Science.gov (United States)

Xu, Kun

1998-01-01

A gas-kinetic solver is developed for the ideal magnetohydrodynamics (MHD) equations. The new scheme is based on the direct splitting of the flux function of the MHD equations with the inclusion of "particle" collisions in the transport process. Consequently, the artificial dissipation in the new scheme is much reduced in comparison with the MHD Flux Vector Splitting Scheme. At the same time, the new scheme is compared with the well-developed Roe-type MHD solver. It is concluded that the kinetic MHD scheme is more robust and efficient than the Roe- type method, and the accuracy is competitive. In this paper the general principle of splitting the macroscopic flux function based on the gas-kinetic theory is presented. The flux construction strategy may shed some light on the possible modification of AUSM- and CUSP-type schemes for the compressible Euler equations, as well as to the development of new schemes for a non-strictly hyperbolic system.

A simple theory of linear mode conversion

International Nuclear Information System (INIS)

Cairns, R.A.; Lashmore-Davies, C.N.; Woods, A.M.

1984-01-01

A summary is given of the basic theory of linear mode conversion involving the construction of differential equations for the mode amplitudes based on the properties of the dispersion relation in the neighbourhood of the mode conversion point. As an example the transmission coefficient for tunneling from the upper hybrid resonance through the evanescent region to the adjacent cut-off is treated. 7 refs, 3 figs

A quantum-mechanical perspective on linear response theory within polarizable embedding

DEFF Research Database (Denmark)

List, Nanna Holmgaard; Norman, Patrick; Kongsted, Jacob

2017-01-01

We present a derivation of linear response theory within polarizable embedding starting from a rigorous quantum-mechanical treatment of a composite system. To this aim, two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are introduced and the pole...

On the interaction of small-scale linear waves with nonlinear solitary waves

Science.gov (United States)

Xu, Chengzhu; Stastna, Marek

2017-04-01

In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow

A Qualitative Linear Utility Theory for Spohn's Theory of Epistemic Beliefs

OpenAIRE

Giang, Phan H.; Shenoy, Prakash P.

2013-01-01

In this paper, we formulate a qualitative "linear" utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision problem in which the uncertainty is expressed qualitatively should behave so as to maximize "qualitative expected utility." Our axiomatization of the qualitative utility is similar to the axiomatization developed by von Neumann and Morgenstern for probabilistic l...

Primer on theory and operation of linear accelerators in radiation therapy

International Nuclear Information System (INIS)

Karzmark, C.J.; Morton, R.J.

1981-12-01

This primer is part of an educational package that also includes a series of 3 videotapes entitled Theory and Operation of Linear Accelerators in Radiation Therapy, Parts I, II, and III. This publication provides an overview of the components of the linear accelerator and how they function and interrelate. The auxiliary systems necessary to maintain the operation of the linear accelerator are also described

Quantum kinetic theory of metal clusters in an intense electromagnetic field

Directory of Open Access Journals (Sweden)

M.Bonitz

2004-01-01

Full Text Available A quantum kinetic theory for weakly inhomogeneous charged particle systems is derived within the framework of nonequilibrium Green's functions. The results are of relevance for valence electrons of metal clusters as well as for confined Coulomb systems, such as electrons in quantum dots or ultracold ions in traps and similar systems. To be specific, here we concentrate on the application to metal clusters, but the results are straightforwardly generalized. Therefore, we first give an introduction to the physics of correlated valence electrons of metal clusters in strong electromagnetic fields. After a brief overview on the jellium model and the standard density functional approach to the ground state properties, we focus on the extension of the theory to nonequilibrium. To this end a general gauge-invariant kinetic theory is developed. The results include the equations of motion of the two-time correlation functions, the equation for the Wigner function and an analysis of the spectral function. Here, the concept of an effective quantum potential is introduced which retains the convenient local form of the propagators. This allows us to derive explicit results for the spectral function of electrons in a combined strong electromagnetic field and a weakly inhomogeneous confinement potential.

Kinetic Typography

DEFF Research Database (Denmark)

van Leeuwen, Theo; Djonov, Emilia

2014-01-01

After discussing broad cultural drivers behind the development of kinetic typography, the chapter outlines an approach to analysing kinetic typography which is based on Halliday's theory of transitivity, as applied by Kress and Van Leeuwen to visual images.......After discussing broad cultural drivers behind the development of kinetic typography, the chapter outlines an approach to analysing kinetic typography which is based on Halliday's theory of transitivity, as applied by Kress and Van Leeuwen to visual images....

Linearized analysis of (2+1)-dimensional Einstein-Maxwell theory

International Nuclear Information System (INIS)

Soda, Jiro.

1989-08-01

On the basis of previous result by Hosoya and Nakao that (2+1)-dimensional gravity reduces the geodesic motion in moduli space, we investigate the effects of matter fields on the geodesic motion using the linearized theory. It is shown that the transverse-traceless parts of energy-momentum tensor make the deviation from the geodesic motion. This result is important for the Einstein-Maxwell theory due to the existence of global modes of Maxwell fields on torus. (author)

A non-linear theory of strong interactions

International Nuclear Information System (INIS)

Skyrme, T.H.R.

1994-01-01

A non-linear theory of mesons, nucleons and hyperons is proposed. The three independent fields of the usual symmetrical pseudo-scalar pion field are replaced by the three directions of a four-component field vector of constant length, conceived in an Euclidean four-dimensional isotopic spin space. This length provides the universal scaling factor, all other constants being dimensionless; the mass of the meson field is generated by a φ 4 term; this destroys the continuous rotation group in the iso-space, leaving a 'cubic' symmetry group. Classification of states by this group introduces quantum numbers corresponding to isotopic spin and to 'strangeness'; one consequences is that, at least in elementary interactions, charge is only conserved module 4. Furthermore, particle states have not a well-defined parity, but parity is effectively conserved for meson-nucleon interactions. A simplified model, using only two dimensions of space and iso-space, is considered further; the non-linear meson field has solutions with particle character, and an indication is given of the way in which the particle field variables might be introduced as collective co-ordinates describing the dynamics of these particular solutions of the meson field equations, suggesting a unified theory based on the meson field alone. (author). 7 refs

Kinetics of oriented crystallization of polymers in the linear stress-orientation range in the series expansion approach

Directory of Open Access Journals (Sweden)

L. Jarecki

2018-04-01

Full Text Available An analytical formula is derived for the oriented crystallization coefficient governing kinetics of oriented crystallization under uniaxial amorphous orientation in the entire temperature range. A series expansion approach is applied to the free energy of crystallization in the Hoffman-Lauritzen kinetic model of crystallization at accounting for the entropy of orientation of the amorphous chains. The series expansion coefficients are calculated for systems of Gaussian chains in linear stress-orientation range. Oriented crystallization rate functions are determined basing on the ‘proportional expansion’ approach proposed by Ziabicki in the steady-state limit. Crystallization kinetics controlled by separate predetermined and sporadic primary nucleation is considered, as well as the kinetics involving both nucleation mechanisms potentially present in oriented systems. The involvement of sporadic nucleation in the transformation kinetics is predicted to increase with increasing amorphous orientation. Example computations illustrate the dependence of the calculated functions on temperature and amorphous orientation, as well as qualitative agreement of the calculations with experimental results.

Comparison of Linear Induction Motor Theories for the LIMRV and TLRV Motors

Science.gov (United States)

1978-01-01

The Oberretl, Yamamura, and Mosebach theories of the linear induction motor are described and also applied to predict performance characteristics of the TLRV & LIMRV linear induction motors. The effect of finite motor width and length on performance ...

Asymptotic solutions and spectral theory of linear wave equations

International Nuclear Information System (INIS)

Adam, J.A.

1982-01-01

This review contains two closely related strands. Firstly the asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation - particularly spectral theory - are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of astrophysical (particularly solar) and geophysical fluid dynamics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interest in problems of linear wave propagation in these areas. (orig./HSI)

A Study on the Kinetics of Propane-Activated Carbon: Theory and Experiments

KAUST Repository

Ismail, Azhar bin

2013-08-01

Experimental kinetics results of propane in Maxsorb III activated carbon is obtained at temperatures of 10°C and 30°C, and pressures up to 800kPa using a magnetic suspension balance. A multi-gradient linear driving force (LDF) approximation is used for adsorbate uptake as a function of time. The LDF mass-transfer-rate coefficients were thus determined. Using this approach, the experimentally derived LDF coefficients based on independently measured kinetic parameters for propane in the activated-carbon bed agree very well with experimental results. The computational efficiency is gained by adopting this extended LDF model. © (2013) Trans Tech Publications, Switzerland.

A Study on the Kinetics of Propane-Activated Carbon: Theory and Experiments

KAUST Repository

Ismail, Azhar bin; Loh, Wai Soong; Thu, Kyaw; Ng, Kim Choon

2013-01-01

Experimental kinetics results of propane in Maxsorb III activated carbon is obtained at temperatures of 10°C and 30°C, and pressures up to 800kPa using a magnetic suspension balance. A multi-gradient linear driving force (LDF) approximation is used for adsorbate uptake as a function of time. The LDF mass-transfer-rate coefficients were thus determined. Using this approach, the experimentally derived LDF coefficients based on independently measured kinetic parameters for propane in the activated-carbon bed agree very well with experimental results. The computational efficiency is gained by adopting this extended LDF model. © (2013) Trans Tech Publications, Switzerland.

Physical kinetics

International Nuclear Information System (INIS)

Lifschitz, E.M.; Pitajewski, L.P.

1983-01-01

The textbook covers the subject under the following headings: kinetic gas theory, diffusion approximation, collisionless plasma, collisions within the plasma, plasma in the magnetic field, theory of instabilities, dielectrics, quantum fluids, metals, diagram technique for nonequilibrium systems, superconductors, and kinetics of phase transformations

PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

Energy Technology Data Exchange (ETDEWEB)

Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com [Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)

2015-07-20

A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic 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

Linear and nonlinear instability theory of a noble gas MHD generator

International Nuclear Information System (INIS)

Mesland, A.J.

1982-01-01

This thesis deals with the stability of the working medium of a seeded noble gas magnetohydrodynamic generator. The aim of the study is to determine the instability mechanism which is most likely to occur in experimental MHD generators and to describe its behaviour with linear and nonlinear theories. In chapter I a general introduction is given. The pertinent macroscopic basic equations are derived in chapter II, viz. the continuity, the momentum and the energy equation for the electrons and the heavy gas particles, consisting of the seed particles and the noble gas atoms. Chapter III deals with the linear plane wave analysis of small disturbances of a homogeneous steady state. The steady state is discussed in chapter IV. The values for the steady state parameters used for the calculations both for the linear analysis as for the nonlinear analysis are made plausible with the experimental values. Based on the results of the linear plane wave theory a nonlinear plane wave model of the electrothermal instability is introduced in chapter V. (Auth.)

Modification of linear response theory for mean-field approximations

NARCIS (Netherlands)

Hütter, M.; Öttinger, H.C.

1996-01-01

In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response theory is studied. A procedure, analogous to one where no mean-field approximation is involved, is used in order to determine the first order response of the

Linear response theory an analytic-algebraic approach

CERN Document Server

De Nittis, Giuseppe

2017-01-01

This book presents a modern and systematic approach to Linear Response Theory (LRT) by combining analytic and algebraic ideas. LRT is a tool to study systems that are driven out of equilibrium by external perturbations. In particular the reader is provided with a new and robust tool to implement LRT for a wide array of systems. The proposed formalism in fact applies to periodic and random systems in the discrete and the continuum. After a short introduction describing the structure of the book, its aim and motivation, the basic elements of the theory are presented in chapter 2. The mathematical framework of the theory is outlined in chapters 3–5: the relevant von Neumann algebras, noncommutative $L^p$- and Sobolev spaces are introduced; their construction is then made explicit for common physical systems; the notion of isopectral perturbations and the associated dynamics are studied. Chapter 6 is dedicated to the main results, proofs of the Kubo and Kubo-Streda formulas. The book closes with a chapter about...

JET VELOCITY OF LINEAR SHAPED CHARGES

Directory of Open Access Journals (Sweden)

Vječislav Bohanek

2012-12-01

Full Text Available Shaped explosive charges with one dimension significantly larger than the other are called linear shaped charges. Linear shaped charges are used in various industries and are applied within specific technologies for metal cutting, such as demolition of steel structures, separating spent rocket fuel tanks, demining, cutting holes in the barriers for fire service, etc. According to existing theories and models efficiency of linear shaped charges depends on the kinetic energy of the jet which is proportional to square of jet velocity. The original method for measuring velocity of linear shaped charge jet is applied in the aforementioned research. Measurements were carried out for two different linear materials, and the results are graphically presented, analysed and compared. Measurement results show a discrepancy in the measured velocity of the jet for different materials with the same ratio between linear and explosive mass (M/C per unit of surface, which is not described by presented models (the paper is published in Croatian.

Spectral theory of linear operators and spectral systems in Banach algebras

CERN Document Server

Müller, Vladimir

2003-01-01

This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach alg...

Determination Of Enzyme Kinetic Parameters on Sago Starch Hydrolysis By Linearized Graphical Methods

International Nuclear Information System (INIS)

Lai, L.W.; Teo, C.L.; Suzana Wahidin; Mohamad Suffian Mohamad Annuar

2014-01-01

Amyloglucosidase (E.C. 3.2.1.3) from Aspergillus niger was used to hydrolyze the sago (Metro xylon sagu) starch into reducing sugars. The experiment was conducted at constant temperature, 55 degree Celsius; pH, 4.5 and enzyme amount, 0.2 U/ ml, respectively. In this investigation, the substrate concentration was varied ranging from 1.0 - 7.0 g/ L. The obtained data were then fixed into linearized plots namely Lineweaver-Burk and Langmuir models to calculate enzyme kinetic parameters, K m and V max . Both of the K m and V max (mM, mol/min) values from each plot were: Lineweaver-Burk (26.53, 3.31) and Langmuir (13.52, 2.35). Among the linearized models, K m and V max values acquired from Langmuir plot was chosen. (author)

Relativistic Boltzmann theory for a plasma

International Nuclear Information System (INIS)

Erkelens, H. van.

1984-01-01

This thesis gives a self-contained treatment of the relativistic Boltzmann theory for a plasma. Here plasma means any mixture containing electrically charged particles. The relativistic Boltzmann equation is linearized for the case of a plasma. The Chapman-Enskog method is elaborated further for transport phenomena. Linear laws for viscous phenomena are derived. Then the collision term in the Boltzmann theory is dealt with. Using the transport equation, a kinetic theory of wave phenomena is developed and the dissipation of hydromagnetic waves in a relativistic plasma is investigated. In the final chapter, it is demonstrated how the relativistic Boltzmann theory can be applied in cosmology. In doing so, expressions are derived for the electric conductivity of the cosmological plasma in the lepton era, the plasma era and the annihilation era. (Auth.)

Theory of linear operators in Hilbert space

CERN Document Server

Akhiezer, N I

1993-01-01

This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.

The onset of fluid-dynamical behavior in relativistic kinetic theory

Science.gov (United States)

Noronha, Jorge; Denicol, Gabriel S.

2017-11-01

In this proceedings we discuss recent findings regarding the large order behavior of the Chapman-Enskog expansion in relativistic kinetic theory. It is shown that this series in powers of the Knudsen number has zero radius of convergence in the case of a Bjorken expanding fluid described by the Boltzmann equation in the relaxation time approximation. This divergence stems from the presence of non-hydrodynamic modes, which give non-perturbative contributions to the Knudsen series.

Kinetic theory of Jeans instability

NARCIS (Netherlands)

Trigger, S.A.; Ershkovic, A.I.; Heijst, van G.J.F.; Schram, P.P.J.M.

2004-01-01

Kinetic treatment of the Jeans gravitational instability, with collisions taken into account, is presented. The initial-value problem for the distribution function which obeys the kinetic equation, with the collision integral conserving the number of particles, is solved. Dispersion relation is

Modern aspects of the kinetic theory of glass transition

International Nuclear Information System (INIS)

Tropin, T V; Aksenov, V L; Schmelzer, J W

2016-01-01

This paper reviews glass transition kinetics models that are developed to describe the formation of structural (for example, covalent and metallic) glasses, as well as to account for the transition of a polymer to a solid glassy state. As the two approaches most frequently used over the last decade to model the glass transition, the Tool–Narayanaswamy–Moynihan model and the Adam–Gibbs theory of glass transition are described together with examples of their applications. Also discussed are entropy-based approaches that rely on irreversible thermodynamics methods originated in the work of De Donder, Mandelstam, and Leontovich. The actual problems that arise in applying these methods and the prospects of their development are discussed. A brief overview of statistical glass transition models is given, including the mode-coupling and energy-landscape theories. (reviews of topical problems)

Exploring the chemical kinetics of partially oxidized intermediates by combining experiments, theory, and kinetic modeling.

Science.gov (United States)

Hoyermann, Karlheinz; Mauß, Fabian; Olzmann, Matthias; Welz, Oliver; Zeuch, Thomas

2017-07-19

Partially oxidized intermediates play a central role in combustion and atmospheric chemistry. In this perspective, we focus on the chemical kinetics of alkoxy radicals, peroxy radicals, and Criegee intermediates, which are key species in both combustion and atmospheric environments. These reactive intermediates feature a broad spectrum of chemical diversity. Their reactivity is central to our understanding of how volatile organic compounds are degraded in the atmosphere and converted into secondary organic aerosol. Moreover, they sensitively determine ignition timing in internal combustion engines. The intention of this perspective article is to provide the reader with information about the general mechanisms of reactions initiated by addition of atomic and molecular oxygen to alkyl radicals and ozone to alkenes. We will focus on critical branching points in the subsequent reaction mechanisms and discuss them from a consistent point of view. As a first example of our integrated approach, we will show how experiment, theory, and kinetic modeling have been successfully combined in the first infrared detection of Criegee intermediates during the gas phase ozonolysis. As a second example, we will examine the ignition timing of n-heptane/air mixtures at low and intermediate temperatures. Here, we present a reduced, fuel size independent kinetic model of the complex chemistry initiated by peroxy radicals that has been successfully applied to simulate standard n-heptane combustion experiments.

On the kinetic theory of a fully ionized gas

International Nuclear Information System (INIS)

Bezerra Junior, A.G.; Rodbard, M.G.; Kremer, G.M.

1993-01-01

An alternative method for kinetic theory recently proposed, that combines the features of the Chapman-Enskog and Grad methods, neither using a solution of the integral equation nor the field equations of the moments, is applied to ionized gases. Like in the Grad method, the deviation from equilibrium of the moments are used. Like in the method of Grad, the deviation from equilibrium of the distribution function is written in terms of the moments of the distribution function, but the constitutive equations follow direct from the Boltzmann equation through the Chapman-Enskog method. (author)

Multiphase Flow and Fluidization Continuum and Kinetic Theory Descriptions

CERN Document Server

Gidaspow, Dimitri

1994-01-01

Useful as a reference for engineers in industry and as an advanced level text for graduate engineering students, Multiphase Flow and Fluidization takes the reader beyond the theoretical to demonstrate how multiphase flow equations can be used to provide applied, practical, predictive solutions to industrial fluidization problems. Written to help advance progress in the emerging science of multiphase flow, this book begins with the development of the conservation laws and moves on through kinetic theory, clarifying many physical concepts (such as particulate viscosity and solids pressure) and i

Kinetic theory of the interdiffusion coefficient in dense plasmas

International Nuclear Information System (INIS)

Boercker, D.B.

1986-08-01

Naive applications of Spitzer's theory to very dense plasmas can lead to negative diffusion coefficients. The interdiffusion coefficients in Binary Ionic Mixtures (two species of point ions in a uniform neutralizing background) have been calculated recently using molecular dynamics techniques. These calculations can provide useful benchmarks for theoretical evaluations of the diffusion coefficient in dense plasma mixtures. This paper gives a brief description of a kinetic theoretic approximation to the diffusion coefficient which generalizes Spitzer to high density and is in excellent agreement with the computer simulations. 15 refs., 1 fig., 2 tabs

Theory and simulation of discrete kinetic beta induced Alfven eigenmode in tokamak plasmas

International Nuclear Information System (INIS)

Wang, X; Zonca, F; Chen, L

2010-01-01

It is shown, both analytically and by numerical simulations, that, in the presence of thermal ion kinetic effects, the beta induced Alfven eigenmode (BAE)-shear Alfven wave continuous spectrum can be discretized into radially trapped eigenstates known as kinetic BAE (KBAE). While thermal ion compressibility gives rise to finite BAE accumulation point frequency, the discretization occurs via the finite Larmor radius and finite orbit width effects. Simulations and analytical theories agree both qualitatively and quantitatively. Simulations also demonstrate that KBAE can be readily excited by the finite radial gradients of energetic particles.

Validity of the Taylor hypothesis for linear kinetic waves in the weakly collisional solar wind

International Nuclear Information System (INIS)

Howes, G. G.; Klein, K. G.; TenBarge, J. M.

2014-01-01

The interpretation of single-point spacecraft measurements of solar wind turbulence is complicated by the fact that the measurements are made in a frame of reference in relative motion with respect to the turbulent plasma. The Taylor hypothesis—that temporal fluctuations measured by a stationary probe in a rapidly flowing fluid are dominated by the advection of spatial structures in the fluid rest frame—is often assumed to simplify the analysis. But measurements of turbulence in upcoming missions, such as Solar Probe Plus, threaten to violate the Taylor hypothesis, either due to slow flow of the plasma with respect to the spacecraft or to the dispersive nature of the plasma fluctuations at small scales. Assuming that the frequency of the turbulent fluctuations is characterized by the frequency of the linear waves supported by the plasma, we evaluate the validity of the Taylor hypothesis for the linear kinetic wave modes in the weakly collisional solar wind. The analysis predicts that a dissipation range of solar wind turbulence supported by whistler waves is likely to violate the Taylor hypothesis, while one supported by kinetic Alfvén waves is not.

Turnpike theory of continuous-time linear optimal control problems

CERN Document Server

Zaslavski, Alexander J

2015-01-01

Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems.  The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control, and in applied functional analysis. Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous nonconvex and nonsmooth integrands.  Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integran...

Kinetic theory of rf current drive and helicity injection

International Nuclear Information System (INIS)

Mett, R.R.

1992-01-01

Current drive and helicity injection by plasma waves are examined with the use of kinetic theory. The Vlasov equation yields a general current drive formula that contains resonant and nonresonant (ponderomotivelike) contributions. Standard quasilinear current drive is described by the former, while helicity current drive may be contained in the latter. Since direct analytical comparison of the sizes of the two terms is, in general, difficult, a new approach is taken. Solution of the drift-kinetic equation shows that the standard Landau damping/transit time magnetic pumping quasilinear diffusion coefficient is the only contribution to steady-state current drive to leading order in ε=ρ L /l, where ρ L is the Larmor radius and l is the inhomogeneity scale length. All nonresonant contributions, including the helicity, appear at higher order, after averages are taken over a flux surface, over azimuth, and over time. Consequently, at wave frequencies well below the electron cyclotron frequency, a wave helicity flux perpendicular to the magnetic field does not influence the parallel motion of electrons to leading order and therefore will not drive a significant current. Any current associated with a wave helicity flux is then either ion current (and thus inefficient) or electron current stemming from effects not included in the drift-kinetic treatment, such as cyclotron, collisional, or nonlinear (i.e., not quasilinear)

KINETIC THEORY OF PLASMA WAVES: Part II: Homogeneous Plasma

NARCIS (Netherlands)

Westerhof, E.

2010-01-01

The theory of electromagnetic waves in a homogeneous plasma is reviewed. The linear response of the plasma to the waves is obtained in the form of the dielectric tensor. Waves ranging from the low frequency Alfven to the high frequency electron cyclotron waves are discussed in the limit of the cold

Kinetic theory of plasma waves: Part II homogeneous plasma

NARCIS (Netherlands)

Westerhof, E.

2000-01-01

The theory of electromagnetic waves in a homogeneous plasma is reviewed. The linear response of the plasma to the waves is obtained in the form of the dielectric tensor. Waves ranging from the low frequency Alfven to the high frequency electron cyclotron waves are discussed in the limit of the cold

Kinetic theory of plasma waves - Part II: Homogeneous plasma

NARCIS (Netherlands)

Westerhof, E.

2008-01-01

The theory of electromagnetic waves in a homogeneous plasma is reviewed. The linear response of the plasma to the waves is obtained in the form of the dielectric tensor. Waves ranging from the low frequency Alfven to the high frequency electron cyclotron waves axe discussed in the limit of the cold

Linear conversion theory on the second harmonic emission from a plasma filament

International Nuclear Information System (INIS)

Tan Weihan; Gu Min

1989-01-01

The linear conversion theory of laser produced plasma filaments is studied. By calculations for the energy flux of the second harmonic emission on the basis of the planar wave-plasma interaction model, it has been found that there exists no 2ω 0 harmonic emission in the direction perpendicular to the incident laser, in contradiction with the experiments. A linear conversion theory is proposed on the second harmonic emission from a plasma filament and discovered the intense 2ω 0 harmonic emission in the direction perpendicular to the incident laser, which is in agreement with the experiments. (author)

Janus field theories from non-linear BF theories for multiple M2-branes

International Nuclear Information System (INIS)

Ryang, Shijong

2009-01-01

We integrate the nonpropagating B μ gauge field for the non-linear BF Lagrangian describing N M2-branes which includes terms with even number of the totally antisymmetric tensor M IJK in arXiv:0808.2473 and for the two-types of non-linear BF Lagrangians which include terms with odd number of M IJK as well in arXiv:0809:0985. For the former Lagrangian we derive directly the DBI-type Lagrangian expressed by the SU(N) dynamical A μ gauge field with a spacetime dependent coupling constant, while for the low-energy expansions of the latter Lagrangians the B μ integration is iteratively performed. The derived Janus field theory Lagrangians are compared.

Quantum Kramers model: Corrections to the linear response theory for continuous bath spectrum

Science.gov (United States)

Rips, Ilya

2017-01-01

Decay of the metastable state is analyzed within the quantum Kramers model in the weak-to-intermediate dissipation regime. The decay kinetics in this regime is determined by energy exchange between the unstable mode and the stable modes of thermal bath. In our previous paper [Phys. Rev. A 42, 4427 (1990), 10.1103/PhysRevA.42.4427], Grabert's perturbative approach to well dynamics in the case of the discrete bath [Phys. Rev. Lett. 61, 1683 (1988), 10.1103/PhysRevLett.61.1683] has been extended to account for the second order terms in the classical equations of motion (EOM) for the stable modes. Account of the secular terms reduces EOM for the stable modes to those of the forced oscillator with the time-dependent frequency (TDF oscillator). Analytic expression for the characteristic function of energy loss of the unstable mode has been derived in terms of the generating function of the transition probabilities for the quantum forced TDF oscillator. In this paper, the approach is further developed and applied to the case of the continuous frequency spectrum of the bath. The spectral density functions of the bath of stable modes are expressed in terms of the dissipative properties (the friction function) of the original bath. They simplify considerably for the one-dimensional systems, when the density of phonon states is constant. Explicit expressions for the fourth order corrections to the linear response theory result for the characteristic function of the energy loss and its cumulants are obtained for the particular case of the cubic potential with Ohmic (Markovian) dissipation. The range of validity of the perturbative approach in this case is determined (γ /ωbrate for the quantum and for the classical Kramers models. Results for the classical escape rate are in very good agreement with the numerical simulations for high barriers. The results can serve as an additional proof of the robustness and accuracy of the linear response theory.

Suppression of Phase Mixing in Drift-Kinetic Plasma Turbulence

Science.gov (United States)

Parker, J. T.; Dellar, P. J.; Schekochihin, A. A.; Highcock, E. G.

2017-12-01

The solar wind and interstellar medium are examples of strongly magnetised, weakly collisional, astrophysical plasmas. Their turbulent fluctuations are strongly anisotropic, with small amplitudes, and frequencies much lower than the Larmor frequency. This regime is described by gyrokinetic theory, a reduced five-dimensional kinetic system describing averages over Larmor orbits. A turbulent plasma may transfer free energy, a measure of fluctuation amplitudes, from injection at large scales, typically by an instability, to dissipation at small physical scales like a turbulent fluid. Alternatively, a turbulent plasma may form fine scale structures in velocity space via phase-mixing, the mechanism that leads to Landau damping in linear plasma theory. Macroscopic plasma properties like heat and momentum transport are affected by both mechanisms. While each is understood in isolation, their interaction is not. We study this interaction using a Hankel-Hermite velocity space representation of gyrokinetic theory. The Hankel transform interacts neatly with the Bessel functions that arise from averaging over Larmor orbits, so the perpendicular velocity space is decoupled for linearized problems. The Hermite transform expresses phase mixing as nearest-neighbor coupling between parallel velocity space scales represented by Hermite mode numbers. We use this representation to study transfer mechanisms in drift-kinetic plasma turbulence, the long wavelength limit of gyrokinetic theory. We show that phase space is divided into two regions, with one transfer mechanism dominating in each. Most energy is contained in the region where the fluid-like nonlinear cascade dominates. Moreover, in that region the nonlinear cascade interferes with phase mixing by exciting an "anti phase mixing" transfer of free energy from small to large velocity space scales. This cancels out the usual phase mixing, and renders the overall behavior fluid-like. These results profoundly change our understanding

Linearized propulsion theory of flapping airfoils revisited

Science.gov (United States)

Fernandez-Feria, Ramon

2016-11-01

A vortical impulse theory is used to compute the thrust of a plunging and pitching airfoil in forward flight within the framework of linear potential flow theory. The result is significantly different from the classical one of Garrick that considered the leading-edge suction and the projection in the flight direction of the pressure force. By taking into account the complete vorticity distribution on the airfoil and the wake the mean thrust coefficient contains a new term that generalizes the leading-edge suction term and depends on Theodorsen function C (k) and on a new complex function C1 (k) of the reduced frequency k. The main qualitative difference with Garrick's theory is that the propulsive efficiency tends to zero as the reduced frequency increases to infinity (as 1 / k), in contrast to Garrick's efficiency that tends to a constant (1 / 2). Consequently, for pure pitching and combined pitching and plunging motions, the maximum of the propulsive efficiency is not reached as k -> ∞ like in Garrick's theory, but at a finite value of the reduced frequency that depends on the remaining non-dimensional parameters. The present analytical results are in good agreement with experimental data and numerical results for small amplitude oscillations. Supported by the Ministerio de Economia y Competitividad of Spain Grant No. DPI2013-40479-P.

Symmetric linear systems - An application of algebraic systems theory

Science.gov (United States)

Hazewinkel, M.; Martin, C.

1983-01-01

Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

Linear response theory of activated surface diffusion with interacting adsorbates

Energy Technology Data Exchange (ETDEWEB)

Marti' nez-Casado, R. [Department of Chemistry, Imperial College London, South Kensington, London SW7 2AZ (United Kingdom); Sanz, A.S.; Vega, J.L. [Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain); Rojas-Lorenzo, G. [Instituto Superior de Tecnologi' as y Ciencias Aplicadas, Ave. Salvador Allende, esq. Luaces, 10400 La Habana (Cuba); Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cienti' ficas, Serrano 123, 28006 Madrid (Spain); Miret-Artes, S., E-mail: s.miret@imaff.cfmac.csic.es [Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cienti' ficas, Serrano 123, 28006 Madrid (Spain)

2010-05-12

Graphical abstract: Activated surface diffusion with interacting adsorbates is analyzed within the Linear Response Theory framework. The so-called interacting single adsorbate model is justified by means of a two-bath model, where one harmonic bath takes into account the interaction with the surface phonons, while the other one describes the surface coverage, this leading to defining a collisional friction. Here, the corresponding theory is applied to simple systems, such as diffusion on flat surfaces and the frustrated translational motion in a harmonic potential. Classical and quantum closed formulas are obtained. Furthermore, a more realistic problem, such as atomic Na diffusion on the corrugated Cu(0 0 1) surface, is presented and discussed within the classical context as well as within the framework of Kramer's theory. Quantum corrections to the classical results are also analyzed and discussed. - Abstract: Activated surface diffusion with interacting adsorbates is analyzed within the Linear Response Theory framework. The so-called interacting single adsorbate model is justified by means of a two-bath model, where one harmonic bath takes into account the interaction with the surface phonons, while the other one describes the surface coverage, this leading to defining a collisional friction. Here, the corresponding theory is applied to simple systems, such as diffusion on flat surfaces and the frustrated translational motion in a harmonic potential. Classical and quantum closed formulas are obtained. Furthermore, a more realistic problem, such as atomic Na diffusion on the corrugated Cu(0 0 1) surface, is presented and discussed within the classical context as well as within the framework of Kramer's theory. Quantum corrections to the classical results are also analyzed and discussed.

Kinetic modeling and fitting software for interconnected reaction schemes: VisKin.

Science.gov (United States)

Zhang, Xuan; Andrews, Jared N; Pedersen, Steen E

2007-02-15

Reaction kinetics for complex, highly interconnected kinetic schemes are modeled using analytical solutions to a system of ordinary differential equations. The algorithm employs standard linear algebra methods that are implemented using MatLab functions in a Visual Basic interface. A graphical user interface for simple entry of reaction schemes facilitates comparison of a variety of reaction schemes. To ensure microscopic balance, graph theory algorithms are used to determine violations of thermodynamic cycle constraints. Analytical solutions based on linear differential equations result in fast comparisons of first order kinetic rates and amplitudes as a function of changing ligand concentrations. For analysis of higher order kinetics, we also implemented a solution using numerical integration. To determine rate constants from experimental data, fitting algorithms that adjust rate constants to fit the model to imported data were implemented using the Levenberg-Marquardt algorithm or using Broyden-Fletcher-Goldfarb-Shanno methods. We have included the ability to carry out global fitting of data sets obtained at varying ligand concentrations. These tools are combined in a single package, which we have dubbed VisKin, to guide and analyze kinetic experiments. The software is available online for use on PCs.

The kinetic theory and stability of a stochastic plasma with respect to low frequency perturbations and magnetospheric convection

International Nuclear Information System (INIS)

Hurricane, O.A.

1994-09-01

In this dissertation, a new linear Vlasov kinetic theory is developed for calculating the plasma response to perturbing electromagnetic fields in cases where the particle dynamics are stochastic; for modes with frequencies less than the typical particle bounce frequency. A variational form is arrived at which allows one to properly perform a stability analysis for a stochastic plasma. In the case of stochastic dynamics, the authors demonstrate that the plasma responds to the flux tube volume average of the perturbing potentials as opposed to the usual case of adiabatic dynamics where plasma responds to the bounce average of the perturbed potentials. They show that for the stochastic plasma, the kinetic variational form maps into the Bernstein energy principle if the perturbation frequency is large compared to all drift frequencies, the perpendicular wavelength is large compared to the Larmor radius, and vanishing of the potentials associated with the parallel electric field are all assumed. By explicit minimization of the energy principle, it is established that the stochastic plasma is always less stable than an adiabatic plasma. Lastly, the effect of strictly enforcing the quasi-neutrality (QN) condition upon a gyro-kinetic type stability analysis is explored. From simple mathematical considerations, it is shown that when the QN condition is imposed convective type modes that are equipotentials along magnetic field lines are created that alter the stability properties of the plasma. The pertinent modifications to the Bernstein energy principle are given

Linear-response theory of Coulomb drag in coupled electron systems

DEFF Research Database (Denmark)

Flensberg, Karsten; Hu, Ben Yu-Kuang; Jauho, Antti-Pekka

1995-01-01

We report a fully microscopic theory for the transconductivity, or, equivalently, the momentum transfer rate, of Coulomb coupled electron systems. We use the Kubo linear-response formalism and our main formal result expresses the transconductivity in terms of two fluctuation diagrams, which...

Kinetics of the chiral phase transition

Energy Technology Data Exchange (ETDEWEB)

Hees, Hendrik van [Johann-Wolfgang-Goethe-Universitaet Frankfurt, Institut fuer Theoretische Physik, Frankfurt (Germany); Frankfurt Institute for Advanced Studies (FIAS), Frankfurt (Germany); Wesp, Christian; Meistrenko, Alex; Greiner, Carsten [Johann-Wolfgang-Goethe-Universitaet Frankfurt, Institut fuer Theoretische Physik, Frankfurt (Germany)

2016-07-01

We simulate the kinetics of the chiral phase transition in hot and dense strongly interacting matter within a novel kinetic-theory approach. Employing an effective linear σ model for quarks, σ mesons, and pions we treat the quarks within a test-particle ansatz for solving the Boltzmann transport equation and the mesons in terms of classical fields. The decay-recombination processes like σ <-> anti q+q are treated using a kind of wave-particle dualism using the exact conservation of energy and momentum. After demonstrating the correct thermodynamic limit for particles and fields in a ''box calculation'' we apply the simulation to the dynamics of an expanding fireball similar to the medium created in ultrarelativistic heavy-ion collisions.

Linear theory of equatorial spread F

International Nuclear Information System (INIS)

Hudson, M.K.; Kennel, C.F.

1975-01-01

A fluid dispersion relation for the drift and interchange (Rayleigh-Taylor) modes in a collisional plasma forms the basis for a linear theory of equatorial spread F. The collisional drift mode growth rate will exceed the growth rate of the Rayleigh-Taylor mode at short perpendicular wavelengths and density gradient scale lengths, and the drift mode can grow on top side as well as on bottom side density gradients. However, below the F peak, where spread F predominates, it is concluded that both the drift and the Rayleigh-Taylor modes contribute to the total spread F spectrum, the Rayleigh-Taylor mode dominating at long and the drift mode at short perpendicular wavelengths above the ion Larmor radius

Stochastic linear programming models, theory, and computation

CERN Document Server

Kall, Peter

2011-01-01

This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...

Rate theory of solvent exchange and kinetics of Li+ − BF4−/PF6− ion pairs in acetonitrile

International Nuclear Information System (INIS)

Dang, Liem X.; Chang, Tsun-Mei

2016-01-01

In this paper, we describe our efforts to apply rate theories in studies of solvent exchange around Li + and the kinetics of ion pairings in lithium-ion batteries (LIBs). We report one of the first computer simulations of the exchange dynamics around solvated Li + in acetonitrile (ACN), which is a common solvent used in LIBs. We also provide details of the ion-pairing kinetics of Li + -[BF 4 ] and Li + -[PF 6 ] in ACN. Using our polarizable force-field models and employing classical rate theories of chemical reactions, we examine the ACN exchange process between the first and second solvation shells around Li + . We calculate exchange rates using transition state theory and weighted them with the transmission coefficients determined by the reactive flux, Impey, Madden, and McDonald approaches, and Grote-Hynes theory. We found the relaxation times changed from 180 ps to 4600 ps and from 30 ps to 280 ps for Li + -[BF 4 ] and Li + -[PF 6 ] ion pairs, respectively. These results confirm that the solvent response to the kinetics of ion pairing is significant. Our results also show that, in addition to affecting the free energy of solvation into ACN, the anion type also should significantly influence the kinetics of ion pairing. These results will increase our understanding of the thermodynamic and kinetic properties of LIB systems.

Linearly Polarized IR Spectroscopy Theory and Applications for Structural Analysis

CERN Document Server

Kolev, Tsonko

2011-01-01

A technique that is useful in the study of pharmaceutical products and biological molecules, polarization IR spectroscopy has undergone continuous development since it first emerged almost 100 years ago. Capturing the state of the science as it exists today, "Linearly Polarized IR Spectroscopy: Theory and Applications for Structural Analysis" demonstrates how the technique can be properly utilized to obtain important information about the structure and spectral properties of oriented compounds. The book starts with the theoretical basis of linear-dichroic infrared (IR-LD) spectroscop

Linear and nonlinear thermodynamics of a kinetic heat engine with fast transformations

Science.gov (United States)

Cerino, Luca; Puglisi, Andrea; Vulpiani, Angelo

2016-04-01

We investigate a kinetic heat engine model composed of particles enclosed in a box where one side acts as a thermostat and the opposite side is a piston exerting a given pressure. Pressure and temperature are varied in a cyclical protocol of period τ : their relative excursions, δ and ɛ , respectively, constitute the thermodynamic forces dragging the system out of equilibrium. The analysis of the entropy production of the system allows us to define the conjugated fluxes, which are proportional to the extracted work and the consumed heat. In the limit of small δ and ɛ the fluxes are linear in the forces through a τ -dependent Onsager matrix whose off-diagonal elements satisfy a reciprocal relation. The dynamics of the piston can be approximated, through a coarse-graining procedure, by a Klein-Kramers equation which—in the linear regime—yields analytic expressions for the Onsager coefficients and the entropy production. A study of the efficiency at maximum power shows that the Curzon-Ahlborn formula is always an upper limit which is approached at increasing values of the thermodynamic forces, i.e., outside of the linear regime. In all our analysis the adiabatic limit τ →∞ and the the small-force limit δ ,ɛ →0 are not directly related.

Reactivity-induced time-dependencies of EBR-II linear and non-linear feedbacks

International Nuclear Information System (INIS)

Grimm, K.N.; Meneghetti, D.

1988-01-01

Time-dependent linear feedback reactivities are calculated for stereotypical subassemblies in the EBR-II reactor. These quantities are calculated from nodal reactivities obtained from a kinetic code analysis of an experiment in which the change in power resulted from the dropping of a control rod. Shown with these linear reactivities are the reactivity associated with the control-rod shaft contraction and also time-dependent non-linear (mainly bowing) component deduced from the inverse kinetics of the experimentally measured fission power and the calculated linear reactivities. (author)

Simulating Chemical Kinetics Without Differential Equations: A Quantitative Theory Based on Chemical Pathways.

Science.gov (United States)

Bai, Shirong; Skodje, Rex T

2017-08-17

A new approach is presented for simulating the time-evolution of chemically reactive systems. This method provides an alternative to conventional modeling of mass-action kinetics that involves solving differential equations for the species concentrations. The method presented here avoids the need to solve the rate equations by switching to a representation based on chemical pathways. In the Sum Over Histories Representation (or SOHR) method, any time-dependent kinetic observable, such as concentration, is written as a linear combination of probabilities for chemical pathways leading to a desired outcome. In this work, an iterative method is introduced that allows the time-dependent pathway probabilities to be generated from a knowledge of the elementary rate coefficients, thus avoiding the pitfalls involved in solving the differential equations of kinetics. The method is successfully applied to the model Lotka-Volterra system and to a realistic H 2 combustion model.

Theory of multiwave mixing within the superconducting kinetic-inductance traveling-wave amplifier

Science.gov (United States)

Erickson, R. P.; Pappas, D. P.

2017-03-01

We present a theory of parametric mixing within the coplanar waveguide (CPW) of a superconducting nonlinear kinetic-inductance traveling-wave (KIT) amplifier engineered with periodic dispersion loadings. This is done by first developing a metamaterial band theory of the dispersion-engineered KIT using a Floquet-Bloch construction and then applying it to the description of mixing of the nonlinear RF traveling waves. Our theory allows us to calculate signal gain versus signal frequency in the presence of a frequency stop gap, based solely on loading design. We present results for both three-wave mixing (3WM), with applied dc bias, and four-wave mixing (4WM), without dc. Our theory predicts an intrinsic and deterministic origin to undulations of 4WM signal gain with signal frequency, apart from extrinsic sources, such as impedance mismatch, and shows that such undulations are absent from 3WM signal gain achievable with dc. Our theory is extensible to amplifiers based on Josephson junctions in a lumped LC-ladder transmission line (TWPA).

Nonextensive kinetic theory and H-theorem in general relativity

Science.gov (United States)

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.

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

Science.gov (United States)

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

2011-01-28

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

Heat and Kinetic Theory in 19th-Century Physics Textbooks: The Case of Spain

OpenAIRE

Vaquero, J. M.; Santos, A.

2000-01-01

Spain was a scientifically backward country in the early 19th-century. The causes were various political events, the War of Independence, and the reign of Fernando VII. The introduction of contemporary physics into textbooks was therefore a slow process. An analysis of the contents of 19th-century Spanish textbooks is here presented, centred on imponderable fluids, the concept of energy, the mechanical theory of heat, and the kinetic theory of gases.

Application of linear programming and perturbation theory in optimization of fuel utilization in a nuclear reactor

International Nuclear Information System (INIS)

Zavaljevski, N.

1985-01-01

Proposed optimization procedure is fast due to application of linear programming. Non-linear constraints which demand iterative application of linear programming are slowing down the calculation. Linearization can be done by different procedures starting from simple empirical rules for fuel in-core management to complicated general perturbation theory with higher order of corrections. A mathematical model was formulated for optimization of improved fuel cycle. A detailed algorithm for determining minimum of fresh fuel at the beginning of each fuel cycle is shown and the problem is linearized by first order perturbation theory and it is optimized by linear programming. Numerical illustration of the proposed method was done for the experimental reactor mostly for saving computer time

A dynamical theory for linearized massive superspin 3/2

International Nuclear Information System (INIS)

Gates, James S. Jr.; Koutrolikos, Konstantinos

2014-01-01

We present a new theory of free massive superspin Y=3/2 irreducible representation of the 4D, N=1 Super-Poincaré group, which has linearized non-minimal supergravity (superhelicity Y=3/2) as it’s massless limit. The new results will illuminate the underlying structure of auxiliary superfields required for the description of higher massive superspin systems

System theory as applied differential geometry. [linear system

Science.gov (United States)

Hermann, R.

1979-01-01

The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.

Non-cooperative stochastic differential game theory of generalized Markov jump linear systems

CERN Document Server

Zhang, Cheng-ke; Zhou, Hai-ying; Bin, Ning

2017-01-01

This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the...

Non-linear electrodynamics in Kaluza-Klein theory

International Nuclear Information System (INIS)

Kerner, R.

1987-01-01

The most general variational principle based on the invariants of the Riemann tensor and leading to the second order differential equations should contain, in dimensions higher than four, the invariants of the Gauss-Bonnet type. In five dimensions the lagrangian should be a linear combination of the scalar curvature and the second-order invariant. The equations of the electromagnetic field are derived in the absence of scalar and gravitational fields of the Kaluza-Klein model. They yield the unique extension of Maxwell's system in the Kaluza-Klein theory. Some properties of eventual solutions are discussed [fr

The (kinetic) theory of active particles applied to learning dynamics. Comment on "Collective learning modeling based on the kinetic theory of active particles" by D. Burini et al.

Science.gov (United States)

Nieto, J.

2016-03-01

The learning phenomena, their complexity, concepts, structure, suitable theories and models, have been extensively treated in the mathematical literature in the last century, and [4] contains a very good introduction to the literature describing the many approaches and lines of research developed about them. Two main schools have to be pointed out [5] in order to understand the two -not exclusive- kinds of existing models: the stimulus sampling models and the stochastic learning models. Also [6] should be mentioned as a survey where two methods of learning are pointed out, the cognitive and the social, and where the knowledge looks like a mathematical unknown. Finally, as the authors do, we refer to the works [9,10], where the concept of population thinking was introduced and which motivate the game theory rules as a tool (both included in [4] to develop their theory) and [7], where the ideas of developing a mathematical kinetic theory of perception and learning were proposed.

Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...

Thermodynamics and relativistic kinetic theory for q-generalized Bose-Einstein and Fermi-Dirac systems

Science.gov (United States)

Mitra, Sukanya

2018-01-01

The thermodynamics and covariant kinetic theory are elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis' entropy formula, the fundamental principles of thermostatistics are established for a grand canonical system having q-generalized BE/FD degrees of freedom. Many particle kinetic theory is set up in terms of the relativistic transport equation with q-generalized Uehling-Uhlenbeck collision term. The conservation laws are realized in terms of appropriate moments of the transport equation. The thermodynamic quantities are obtained in a weak non-extensive environment for a massive pion-nucleon and a massless quark-gluon system with non-zero baryon chemical potential. In order to get an estimate of the impact of non-extensivity on the system dynamics, the q-modified Debye mass and hence the q-modified effective coupling are estimated for a quark-gluon system.

Calculation of the interfacial tension of the methane-water system with the linear gradient theory

DEFF Research Database (Denmark)

Schmidt, Kurt A. G.; Folas, Georgios; Kvamme, Bjørn

2007-01-01

The linear gradient theory (LGT) combined with the Soave-Redlich-Kwong (SRK EoS) and the Peng-Robinson (PR EoS) equations of state has been used to correlate the interfacial tension data of the methane-water system. The pure component influence parameters and the binary interaction coefficient...... for the mixture influence parameter have been obtained for this system. The model was successfully applied to correlate the interfacial tension data set to within 2.3% for the linear gradient theory and the SRK EoS (LGT-SRK) and 2.5% for the linear gradient theory and PE EoS (LGT-PR). A posteriori comparison...... of data not used in the parameterisation were to within 3.2% for the LGT-SRK model and 2.7% for the LGT-PR model. An exhaustive literature review resulted in a large database for the investigation which covers a wide range of temperature and pressures. The results support the success of the linear...

Linear Water Waves

Science.gov (United States)

Kuznetsov, N.; Maz'ya, V.; Vainberg, B.

2002-08-01

This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'

The spin polarized linear response from density functional theory: Theory and application to atoms

Energy Technology Data Exchange (ETDEWEB)

Fias, Stijn, E-mail: sfias@vub.ac.be; Boisdenghien, Zino; De Proft, Frank; Geerlings, Paul [General Chemistry (ALGC), Vrije Universiteit Brussel (Free University Brussels – VUB), Pleinlaan 2, 1050 Brussels (Belgium)

2014-11-14

Within the context of spin polarized conceptual density functional theory, the spin polarized linear response functions are introduced both in the [N, N{sub s}] and [N{sub α}, N{sub β}] representations. The mathematical relations between the spin polarized linear response functions in both representations are examined and an analytical expression for the spin polarized linear response functions in the [N{sub α}, N{sub β}] representation is derived. The spin polarized linear response functions were calculated for all atoms up to and including argon. To simplify the plotting of our results, we integrated χ(r, r′) to a quantity χ(r, r{sup ′}), circumventing the θ and ϕ dependence. This allows us to plot and to investigate the periodicity throughout the first three rows in the periodic table within the two different representations. For the first time, χ{sub αβ}(r, r{sup ′}), χ{sub βα}(r, r{sup ′}), and χ{sub SS}(r, r{sup ′}) plots have been calculated and discussed. By integration of the spin polarized linear response functions, different components to the polarisability, α{sub αα}, α{sub αβ}, α{sub βα}, and α{sub ββ} have been calculated.

Quantum optimal control theory in the linear response formalism

International Nuclear Information System (INIS)

Castro, Alberto; Tokatly, I. V.

2011-01-01

Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice, this normally means optimizing the value of some observable, a so-called merit function. In consequence, a key part of the theory is a set of equations, which provides the gradient of the merit function with respect to parameters that control the shape of the driving field. We show that these equations can be straightforwardly derived using the standard linear response theory, only requiring a minor generalization: the unperturbed Hamiltonian is allowed to be time dependent. As a result, the aforementioned gradients are identified with certain response functions. This identification leads to a natural reformulation of QOCT in terms of the Keldysh contour formalism of the quantum many-body theory. In particular, the gradients of the merit function can be calculated using the diagrammatic technique for nonequilibrium Green's functions, which should be helpful in the application of QOCT to computationally difficult many-electron problems.

Consensus for linear multi-agent system with intermittent information transmissions using the time-scale theory

Science.gov (United States)

Taousser, Fatima; Defoort, Michael; Djemai, Mohamed

2016-01-01

This paper investigates the consensus problem for linear multi-agent system with fixed communication topology in the presence of intermittent communication using the time-scale theory. Since each agent can only obtain relative local information intermittently, the proposed consensus algorithm is based on a discontinuous local interaction rule. The interaction among agents happens at a disjoint set of continuous-time intervals. The closed-loop multi-agent system can be represented using mixed linear continuous-time and linear discrete-time models due to intermittent information transmissions. The time-scale theory provides a powerful tool to combine continuous-time and discrete-time cases and study the consensus protocol under a unified framework. Using this theory, some conditions are derived to achieve exponential consensus under intermittent information transmissions. Simulations are performed to validate the theoretical results.

Generation companies decision-making modeling by linear control theory

International Nuclear Information System (INIS)

Gutierrez-Alcaraz, G.; Sheble, Gerald B.

2010-01-01

This paper proposes four decision-making procedures to be employed by electric generating companies as part of their bidding strategies when competing in an oligopolistic market: naive, forward, adaptive, and moving average expectations. Decision-making is formulated in a dynamic framework by using linear control theory. The results reveal that interactions among all GENCOs affect market dynamics. Several numerical examples are reported, and conclusions are presented. (author)

Corrections to classical kinetic and transport theory for a two-temparature, fully ionized plasma in electromagnetic fields

International Nuclear Information System (INIS)

Oeien, A.H.

1977-06-01

Sets of lower order and higher order kinetic and macroscopic equations are developed for a plasma where collisions are important but electrons and ions are allowed to have different temperatures when transports, due to gradients and fields, set in. Solving the lower order kinetic equations and taking appropriate velocity moments we show that usual classical transports emerge. From the higher order kinetic equations special notice is taken of some new correction terms to the classical transports. These corrections are linear in gradients and fields, some of which are found in a two-temperature state only. (Auth.)

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

Directory of Open Access Journals (Sweden)

Rajesh Ramaswamy

2011-01-01

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

Diffusion-kinetic theories for LET effects on the radiolysis of water

International Nuclear Information System (INIS)

Pimblott, S.M.; LaVerne, J.A.

1994-01-01

Diffusion-kinetic methods are used to investigate the effects of incident particle linear energy transfer (LET) on the radiolysis of water and aqueous solutions. Chemically realistic deterministic diffusion-kinetic calculations examining the scavenging capacity dependences of the scavenged yield of e aq - and of OH demonstrate that the scavenged yields are related to the underlying time-dependent kinetics in the absence of the scavenger by a simple Laplace transform relationship. This relationship is also shown to link the effect of an e eq - scavenger on the formation of H 2 with the time dependence of H 2 production in the absence of the scavenger. The simple Laplace relationship does not work well when applied to H 2 O 2 formation in high-LET particle tracks even though such a relationship is valid with low-LET particles. It is found that while the secondary reaction of H 2 O 2 with e aq - can be neglected in low-LET particle radiolysis, it is of considerable significance in the tracks produced by high-LET particles. The increased importance of this reaction with increasing LET is the major reason for the failure of the Laplace relationship for H 2 O 2 . 55 refs., 9 figs., 2 tabs

Thermodynamics and relativistic kinetic theory for q-generalized Bose-Einstein and Fermi-Dirac systems

Energy Technology Data Exchange (ETDEWEB)

Mitra, Sukanya [Indian Institute of Technology Gandhinagar, Gandhinagar, Gujarat (India)

2018-01-15

The thermodynamics and covariant kinetic theory are elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis' entropy formula, the fundamental principles of thermostatistics are established for a grand canonical system having q-generalized BE/FD degrees of freedom. Many particle kinetic theory is set up in terms of the relativistic transport equation with q-generalized Uehling-Uhlenbeck collision term. The conservation laws are realized in terms of appropriate moments of the transport equation. The thermodynamic quantities are obtained in a weak non-extensive environment for a massive pion-nucleon and a massless quark-gluon system with non-zero baryon chemical potential. In order to get an estimate of the impact of non-extensivity on the system dynamics, the q-modified Debye mass and hence the q-modified effective coupling are estimated for a quark-gluon system. (orig.)

Kinetic Modeling of the Lif:Mg,Ti TL System including Defect Creation: Implications to, and Development of Track Structure Theory Calculations of Heavy Charged Particle Radiation Effects

International Nuclear Information System (INIS)

Eliyahu, Ian

2015-01-01

In this research, various kinetic models were developed for LiF:Mg,Ti crystals, both in the irradiation and recombination stages. The models were later used to improve on track structure theory, which attempts to describe radiation effects of Heavy charged particle. To achieve this goal, the research focused on three main areas of endeavor. 1. In the first experimental measurements of optical absorption on LiF:Mg,Ti following low ionization density radiation (photons) and high ionization density protons and He ions were carried out in order to investigate the degree of applicability of track structure theory to the prediction of heavy charged particle induced effects of radiation. These measurements are described below. a) Photon induced optical absorption (OA) dose response was measured over an extended dose-range from 10 Gy to 105 Gy for the main OA bands in LiF:Mg,Ti, i.e., the 4.0 eV band (trapping center associated with glow peak 5 in the thermoluminescence glow curve), 4.77 eV band , 5.08 eV (F band) and 5.45 eV band. The extended dose-range allowed the unambiguous determination of linear/exponentially saturation behavior for all the OA bands. For the two main OA bands of interest at 4.0 eV and 5.08 eV, the dose filling factor was determined to be 5 ± 0.6.10-4 Gy-1 and 6.1 ± 0.4 × 10-5 Gy-1 respectively. The surprising, previously unexplained, linear/exponentially saturating dose response of the F band even though vacancies/F centers are being created by the radiation was explained in a kinetic analysis also described in the following. b) Heavy charged particle (HCP) optical absorption was carried out for 1.4 MeV protons and 4 MeV He ions at the SARAF, RARAF and BINA accelerators. Fluence response was measured over the extended range from 1010 cm-2 to 2.1014 cm-2. The low fluence region from 1010 cm-2 to 1011 cm-2 in the no-track-overlap regime allows a comparison of the experimental measurements and the track structure theory (TST) evaluations of the

Can a Linear Sigma Model Describe Walking Gauge Theories at Low Energies?

Science.gov (United States)

Gasbarro, Andrew

2018-03-01

In recent years, many investigations of confining Yang Mills gauge theories near the edge of the conformal window have been carried out using lattice techniques. These studies have revealed that the spectrum of hadrons in nearly conformal ("walking") gauge theories differs significantly from the QCD spectrum. In particular, a light singlet scalar appears in the spectrum which is nearly degenerate with the PNGBs at the lightest currently accessible quark masses. This state is a viable candidate for a composite Higgs boson. Presently, an acceptable effective field theory (EFT) description of the light states in walking theories has not been established. Such an EFT would be useful for performing chiral extrapolations of lattice data and for serving as a bridge between lattice calculations and phenomenology. It has been shown that the chiral Lagrangian fails to describe the IR dynamics of a theory near the edge of the conformal window. Here we assess a linear sigma model as an alternate EFT description by performing explicit chiral fits to lattice data. In a combined fit to the Goldstone (pion) mass and decay constant, a tree level linear sigma model has a Χ2/d.o.f. = 0.5 compared to Χ2/d.o.f. = 29.6 from fitting nextto-leading order chiral perturbation theory. When the 0++ (σ) mass is included in the fit, Χ2/d.o.f. = 4.9. We remark on future directions for providing better fits to the σ mass.

Relation between nonlinear or 'not-linear' characteristics in nuclear kinetics and noise analysis of neutron flux

International Nuclear Information System (INIS)

Kataoka, H.

1975-01-01

The 'not-linear' or '2nd-class-nonlinear' characteristics in nuclear reactor kinetics with the feedback effect in the high-power operation and induce the increase in the amplitude of the neutron flux noise, specially in the very low frequency region. The fundamental behaviour of 'not-linear' characteristics and its effect for the reactor noise was investigated. Application of the reactor noise analysis technique to power reactors has not been successful because of unknown large disagreement between the result of the conventional theoretical analysis and the experimental facts. When the cause of this discrepancy is clear, reactor noise analysis techniques can be effectively applied to instrumentation, control, monitoring and diagnosis of power reactors. (author)

Mathematical foundations of transport theory

International Nuclear Information System (INIS)

Ershov, Yu.I.; Shikhov, S.B.

1985-01-01

Foundations of mathematical transport theory are presented. Definitions and theorems of functional analysis are given. Linear kinetic equation of neutron transport in multiplication media is derived. A model of neutron interaction with nuclei of medium determining completely the coefficient properties in transport equation is described. Non-stationary problems regarding and without regard of d=e layed neutrons are analyzed. Results of solving Cauchy problem are discussed

Relativistic theory of nuclear spin-rotation tensor with kinetically balanced rotational London orbitals

Energy Technology Data Exchange (ETDEWEB)

Xiao, Yunlong; Zhang, Yong; Liu, Wenjian, E-mail: liuwjbdf@gmail.com [Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871 (China)

2014-10-28

Both kinetically balanced (KB) and kinetically unbalanced (KU) rotational London orbitals (RLO) are proposed to resolve the slow basis set convergence in relativistic calculations of nuclear spin-rotation (NSR) coupling tensors of molecules containing heavy elements [Y. Xiao and W. Liu, J. Chem. Phys. 138, 134104 (2013)]. While they perform rather similarly, the KB-RLO Ansatz is clearly preferred as it ensures the correct nonrelativistic limit even with a finite basis. Moreover, it gives rise to the same “direct relativistic mapping” between nuclear magnetic resonance shielding and NSR coupling tensors as that without using the London orbitals [Y. Xiao, Y. Zhang, and W. Liu, J. Chem. Theory Comput. 10, 600 (2014)].

A simple theory of motor protein kinetics and energetics. II.

Science.gov (United States)

Qian, H

2000-01-10

A three-state stochastic model of motor protein [Qian, Biophys. Chem. 67 (1997) pp. 263-267] is further developed to illustrate the relationship between the external load on an individual motor protein in aqueous solution with various ATP concentrations and its steady-state velocity. A wide variety of dynamic motor behavior are obtained from this simple model. For the particular case of free-load translocation being the most unfavorable step within the hydrolysis cycle, the load-velocity curve is quasi-linear, V/Vmax = (cF/Fmax-c)/(1-c), in contrast to the hyperbolic relationship proposed by A.V. Hill for macroscopic muscle. Significant deviation from the linearity is expected when the velocity is less than 10% of its maximal (free-load) value--a situation under which the processivity of motor diminishes and experimental observations are less certain. We then investigate the dependence of load-velocity curve on ATP (ADP) concentration. It is shown that the free load Vmax exhibits a Michaelis-Menten like behavior, and the isometric Fmax increases linearly with ln([ATP]/[ADP]). However, the quasi-linear region is independent of the ATP concentration, yielding an apparently ATP-independent maximal force below the true isometric force. Finally, the heat production as a function of ATP concentration and external load are calculated. In simple terms and solved with elementary algebra, the present model provides an integrated picture of biochemical kinetics and mechanical energetics of motor proteins.

Transient response of nonlinear polymer networks: A kinetic theory

Science.gov (United States)

Vernerey, Franck J.

2018-06-01

Dynamic networks are found in a majority of natural materials, but also in engineering materials, such as entangled polymers and physically cross-linked gels. Owing to their transient bond dynamics, these networks display a rich class of behaviors, from elasticity, rheology, self-healing, or growth. Although classical theories in rheology and mechanics have enabled us to characterize these materials, there is still a gap in our understanding on how individuals (i.e., the mechanics of each building blocks and its connection with others) affect the emerging response of the network. In this work, we introduce an alternative way to think about these networks from a statistical point of view. More specifically, a network is seen as a collection of individual polymer chains connected by weak bonds that can associate and dissociate over time. From the knowledge of these individual chains (elasticity, transient attachment, and detachment events), we construct a statistical description of the population and derive an evolution equation of their distribution based on applied deformation and their local interactions. We specifically concentrate on nonlinear elastic response that follows from the strain stiffening response of individual chains of finite size. Upon appropriate averaging operations and using a mean field approximation, we show that the distribution can be replaced by a so-called chain distribution tensor that is used to determine important macroscopic measures such as stress, energy storage and dissipation in the network. Prediction of the kinetic theory are then explored against known experimental measurement of polymer responses under uniaxial loading. It is found that even under the simplest assumptions of force-independent chain kinetics, the model is able to reproduce complex time-dependent behaviors of rubber and self-healing supramolecular polymers.

Sorption of malachite green from aqueous solution by potato peel: Kinetics and equilibrium modeling using non-linear analysis method

Directory of Open Access Journals (Sweden)

El-Khamsa Guechi

2016-09-01

Full Text Available Potato peel (PP was used as a biosorbent to remove malachite green (MG from aqueous solution under various operating conditions. The effect of the experimental parameters such as initial dye concentration, biosorbent dose, initial pH, stirring speed, temperature, ionic strength and biosorbent particle size was investigated through a number of batch sorption experiments. The sorption kinetic uptake for MG by PP at various initial dye concentrations was analyzed by non-linear method using pseudo-first, pseudo-second and pseudo-nth order models. It was found that the pseudo-nth order kinetic model was the best applicable model to describe the sorption kinetic data and the order n of sorption reaction was calculated in the range from 0.71 to 2.71. Three sorption isotherms namely the Langmuir, Freundlich and Redlich–Peterson isotherms in their non-linear forms were applied to the biosorption equilibrium data. Both the Langmuir and Redlich–Peterson models were found to fit the sorption isotherm data well, but the Redlich–Peterson model was better. Thermodynamic parameters show that the sorption process of MG is endothermic and more effective process at high temperatures. The results revealed that PP is very effective for the biosorption of MG from aqueous solutions.

Relativistic mean-field theory for unstable nuclei with non-linear σ and ω terms

International Nuclear Information System (INIS)

Sugahara, Y.; Toki, H.

1994-01-01

We search for a new parameter set for the description of stable as well as unstable nuclei in the wide mass range within the relativistic mean-field theory. We include a non-linear ω self-coupling term in addition to the non-linear σ self-coupling terms, the necessity of which is suggested by the relativistic Brueckner-Hartree-Fock (RBHF) theory of nuclear matter. We find two parameter sets, one of which is for nuclei above Z=20 and the other for nuclei below that. The calculated results agree very well with the existing data for finite nuclei. The parameter set for the heavy nuclei provides the equation of state of nuclear matter similar to the one of the RBHF theory. ((orig.))

Linear spin-wave theory of incommensurably modulated magnets

DEFF Research Database (Denmark)

Ziman, Timothy; Lindgård, Per-Anker

1986-01-01

Calculations of linearized theories of spin dynamics encounter difficulties when applied to incommensurable magnetic phases: lack of translational invariance leads to an infinite coupled system of equations. The authors resolve this for the case of a `single-Q' structure by mapping onto the problem......: at higher frequency there appear bands of response sharply defined in frequency, but broad in momentum transfer; at low frequencies there is a response maximum at the q vector corresponding to the modulation vector. They discuss generalizations necessary for application to rare-earth magnets...

Estimating the kinetic parameters of activated sludge storage using weighted non-linear least-squares and accelerating genetic algorithm.

Science.gov (United States)

Fang, Fang; Ni, Bing-Jie; Yu, Han-Qing

2009-06-01

In this study, weighted non-linear least-squares analysis and accelerating genetic algorithm are integrated to estimate the kinetic parameters of substrate consumption and storage product formation of activated sludge. A storage product formation equation is developed and used to construct the objective function for the determination of its production kinetics. The weighted least-squares analysis is employed to calculate the differences in the storage product concentration between the model predictions and the experimental data as the sum of squared weighted errors. The kinetic parameters for the substrate consumption and the storage product formation are estimated to be the maximum heterotrophic growth rate of 0.121/h, the yield coefficient of 0.44 mg CODX/mg CODS (COD, chemical oxygen demand) and the substrate half saturation constant of 16.9 mg/L, respectively, by minimizing the objective function using a real-coding-based accelerating genetic algorithm. Also, the fraction of substrate electrons diverted to the storage product formation is estimated to be 0.43 mg CODSTO/mg CODS. The validity of our approach is confirmed by the results of independent tests and the kinetic parameter values reported in literature, suggesting that this approach could be useful to evaluate the product formation kinetics of mixed cultures like activated sludge. More importantly, as this integrated approach could estimate the kinetic parameters rapidly and accurately, it could be applied to other biological processes.

Checking the foundation: recent radiobiology and the linear no-threshold theory.

Science.gov (United States)

Ulsh, Brant A

2010-12-01

The linear no-threshold (LNT) theory has been adopted as the foundation of radiation protection standards and risk estimation for several decades. The "microdosimetric argument" has been offered in support of the LNT theory. This argument postulates that energy is deposited in critical cellular targets by radiation in a linear fashion across all doses down to zero, and that this in turn implies a linear relationship between dose and biological effect across all doses. This paper examines whether the microdosimetric argument holds at the lowest levels of biological organization following low dose, low dose-rate exposures to ionizing radiation. The assumptions of the microdosimetric argument are evaluated in light of recent radiobiological studies on radiation damage in biological molecules and cellular and tissue level responses to radiation damage. There is strong evidence that radiation initially deposits energy in biological molecules (e.g., DNA) in a linear fashion, and that this energy deposition results in various forms of prompt DNA damage that may be produced in a pattern that is distinct from endogenous (e.g., oxidative) damage. However, a large and rapidly growing body of radiobiological evidence indicates that cell and tissue level responses to this damage, particularly at low doses and/or dose-rates, are nonlinear and may exhibit thresholds. To the extent that responses observed at lower levels of biological organization in vitro are predictive of carcinogenesis observed in vivo, this evidence directly contradicts the assumptions upon which the microdosimetric argument is based.

Linear canonical transforms theory and applications

CERN Document Server

Kutay, M; Ozaktas, Haldun; Sheridan, John

2016-01-01

This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.

CINESP - computational program of spatial kinetics for nuclear reactors in the one-two dimension multigroup diffusion theory

International Nuclear Information System (INIS)

Santos, R.S. dos

1993-01-01

This paper presents a computational program to solve numerically the reactor kinetics equations in the multigroup diffusion theory. One or two-dimensional problems in cylindrical or Cartesian geometries, with any number of energy and delayed-neutron precursors groups are dealt with. The main input and output of the program are briefly discussed. Various results demonstrate the accuracy and versatility of the program, when compared with other kinetics programs. (author)

Kinetic theory of beam-induced plasmas generalised to sophisticated atomic structures

International Nuclear Information System (INIS)

Peyraud-Cuenca, Nelly

1987-01-01

We present an analytic kinetic model available for all particle-beam-induced atomic plasmas, without any restriction on the distribution of electronic levels. The method is an iteration of the already known solution available only for the distribution of atomic levels as in the rare gases. We recall a universal atomic kinetic model which, independently of its applications to the study of efficient laser systems, might be a first step in the analytic investigation of molecular problems. Then, the iteration is systematically applied to all possible atomic structures whose number is increased by the non-local character of inelastic processes. We deduce a general analytic representation of the 'tail' of the electron distribution function as a ratio between non-local source terms and a combination of inelastic cross sections, from which we exhibit a physical interpretation and essential scaling laws. The theory is applied to sodium which is an important element in the research of efficient laser systems. (author)

Kinetic theory for radiation interacting with sound waves in ultrarelativistic pair plasmas

International Nuclear Information System (INIS)

Marklund, Mattias; Shukla, Padma K.; Stenflo, Lennart

2006-01-01

A kinetic theory for radiation interacting with sound waves in an ultrarelativistic electron-positron plasma is developed. It is shown that the effect of a spatial spectral broadening of the electromagnetic pulse is to introduce a reduction of the growth rates for the decay and modulational instabilities. Such spectral broadening could be due to a finite pulse coherence length, or through the use of random phase filters, and would stabilize the propagation of electromagnetic pulses

Laboratory beam-plasma interactions linear and nonlinear

International Nuclear Information System (INIS)

Christiansen, P.J.; Bond, J.W.; Jain, V.K.

1982-01-01

This chapter attempts to demonstrate that despite unavoidable scaling limitations, laboratory experiments can uncover details of beam plasma interaction processes which could never be revealed through space plasma physics. Topics covered include linear theory, low frequency couplings, indirect effects, nonlinear effects, quasi-linear effects, trapping effects, nonlinear wave-wave interactions, and self modulation and cavitation. Unstable electrostatic waves arising from an exchange of energy with the ''free energy'' beam features are considered as kinetic and as hydrodynamic, or fluid, instabilities. The consequences of such instabilities (e.g. when the waves have grown to a finite level) are examined and some studies are reviewed which have attempted to understand how the free energy originally available in the beam is redistributed to produce a final state of equilibrium turbulence

Background field method in gauge theories and on linear sigma models

International Nuclear Information System (INIS)

van de Ven, A.E.M.

1986-01-01

This dissertation constitutes a study of the ultraviolet behavior of gauge theories and two-dimensional nonlinear sigma-models by means of the background field method. After a general introduction in chapter 1, chapter 2 presents algorithms which generate the divergent terms in the effective action at one-loop for arbitrary quantum field theories in flat spacetime of dimension d ≤ 11. It is demonstrated that global N = 1 supersymmetric Yang-Mills theory in six dimensions in one-loop UV-finite. Chapter 3 presents an algorithm which produces the divergent terms in the effective action at two-loops for renormalizable quantum field theories in a curved four-dimensional background spacetime. Chapter 4 presents a study of the two-loop UV-behavior of two-dimensional bosonic and supersymmetric non-linear sigma-models which include a Wess-Zumino-Witten term. It is found that, to this order, supersymmetric models on quasi-Ricci flat spaces are UV-finite and the β-functions for the bosonic model depend only on torsionful curvatures. Chapter 5 summarizes a superspace calculation of the four-loop β-function for two-dimensional N = 1 and N = 2 supersymmetric non-linear sigma-models. It is found that besides the one-loop contribution which vanishes on Ricci-flat spaces, the β-function receives four-loop contributions which do not vanish in the Ricci-flat case. Implications for superstrings are discussed. Chapters 6 and 7 treat the details of these calculations

Size dependence of adsorption kinetics of nano-MgO: a theoretical and experimental study

International Nuclear Information System (INIS)

Wang, Shuting; Wen, Yanzhen; Cui, Zixiang; Xue, Yongqiang

2016-01-01

Nanoparticles present tremendous differences in adsorption kinetics compared with corresponding bulk particles which have great influences on the applications of nanoparticles. A size-dependent adsorption kinetic theory was proposed, the relations between adsorption kinetic parameters, respectively, and particle size of nano-adsorbent were derived theoretically, and the influence mechanism of particle size on the adsorption kinetic parameters was discussed. In experiment, nanoscale magnesium oxide (nano-MgO) with different diameters between 11.5 and 41.4 nm with narrow size distribution and low agglomeration were prepared, and the kinetic parameters of adsorption of benzene on nano-MgO in aqueous solution were obtained. Then the influence regularities of the particle size on the adsorption kinetic parameters were obtained. The experimental results are consistent with the nano-adsorption kinetic theory. With particle size decreasing, the adsorption rate constant increases; the adsorption activation energy and the adsorption pre-exponential factor decrease. Furthermore, the logarithm of adsorption rate constant, the adsorption activation energy, and the logarithm of adsorption pre-exponential factor are linearly related to the reciprocal of particle diameter, respectively. The mechanism of particle size influence on the kinetic parameters is that the activation energy is influenced by the molar surface enthalpy of nano-adsorbent, the pre-exponential factor by the molar surface entropy, and the rate constant by both the molar surface enthalpy and the molar surface entropy

Evidence for cluster shape effects on the kinetic energy spectrum in thermionic emission.

Science.gov (United States)

Calvo, F; Lépine, F; Baguenard, B; Pagliarulo, F; Concina, B; Bordas, C; Parneix, P

2007-11-28

Experimental kinetic energy release distributions obtained for the thermionic emission from C(n) (-) clusters, 10theory, these different features are analyzed and interpreted as the consequence of contrasting shapes in the daughter clusters; linear and nonlinear isomers have clearly distinct signatures. These results provide a novel indirect structural probe for atomic clusters associated with their thermionic emission spectra.

Modeling the kinetics of essential oil hydrodistillation from juniper berries (Juniperus communis L. using non-linear regression

Directory of Open Access Journals (Sweden)

Radosavljević Dragana B.

2017-01-01

Full Text Available This paper presents kinetics modeling of essential oil hydrodistillation from juniper berries (Juniperus communis L. by using a non-linear regression methodology. The proposed model has the polynomial-logarithmic form. The initial equation of the proposed non-linear model is q = q∞•(a•(logt2 + b•logt + c and by substituting a1=q∞•a, b1 = q∞•b and c1 = q∞•c, the final equation is obtained as q = a1•(logt2 + b1•logt + c1. In this equation q is the quantity of the obtained oil at time t, while a1, b1 and c1 are parameters to be determined for each sample. From the final equation it can be seen that the key parameter q∞, which presents the maximal oil quantity obtained after infinite time, is already included in parameters a1, b1 and c1. In this way, experimental determination of this parameter is avoided. Using the proposed model with parameters obtained by regression, the values of oil hydrodistillation in time are calculated for each sample and compared to the experimental values. In addition, two kinetic models previously proposed in literature were applied to the same experimental results. The developed model provided better agreements with the experimental values than the two, generally accepted kinetic models of this process. The average values of error measures (RSS, RSE, AIC and MRPD obtained for our model (0.005; 0.017; –84.33; 1.65 were generally lower than the corresponding values of the other two models (0.025; 0.041; –53.20; 3.89 and (0.0035; 0.015; –86.83; 1.59. Also, parameter estimation for the proposed model was significantly simpler (maximum 2 iterations per sample using the non-linear regression than that for the existing models (maximum 9 iterations per sample. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. TR-35026

Worked problems in heat, thermodynamics and kinetic theory for physics students

CERN Document Server

Pincherle, L; Green, L L

2013-01-01

Worked Problems in Heat, Thermodynamics and Kinetic Theory for Physics Students is a complementary to textbooks in physics. This book is a collection of exercise problems that have been part of tutorial classes in heat and thermodynamics at the University of London. This collection of exercise problems, with answers that are fully worked out, deals with various topics. This book poses problems covering the definition of temperature such as calculating the assigned value of the temperature of boiling water under specific conditions. This text also gives example of problems dealing with the fir

Kinetic theory of cross-modulation in a weakly ionized plasma

International Nuclear Information System (INIS)

Garrett, A.J.M.

1991-01-01

Cross-modulation in plasma is an electromagnetic wave interaction in which the modulation of one 'disturbing' wave is imposed nonlinearly on the transport properties of the medium, and thence onto a second, 'wanted' wave propagating linearly through it. This analysis is restricted to weakly ionized plasma with allowance for ambient magnetic field, as in the lower ionosphere. A kinetic description is used, based on the Boltzmann equation for the electrons, with electron-molecule collisions described by Boltzmann's collision integral. Because of the small mass ratio this simplifies to a differential form. There is no cross-modulation if the collision frequency is independent of collision speed, when contributions from all parts of velocity space cancel. (author)

Validation of Bayesian analysis of compartmental kinetic models in medical imaging.

Science.gov (United States)

Sitek, Arkadiusz; Li, Quanzheng; El Fakhri, Georges; Alpert, Nathaniel M

2016-10-01

Kinetic compartmental analysis is frequently used to compute physiologically relevant quantitative values from time series of images. In this paper, a new approach based on Bayesian analysis to obtain information about these parameters is presented and validated. The closed-form of the posterior distribution of kinetic parameters is derived with a hierarchical prior to model the standard deviation of normally distributed noise. Markov chain Monte Carlo methods are used for numerical estimation of the posterior distribution. Computer simulations of the kinetics of F18-fluorodeoxyglucose (FDG) are used to demonstrate drawing statistical inferences about kinetic parameters and to validate the theory and implementation. Additionally, point estimates of kinetic parameters and covariance of those estimates are determined using the classical non-linear least squares approach. Posteriors obtained using methods proposed in this work are accurate as no significant deviation from the expected shape of the posterior was found (one-sided P>0.08). It is demonstrated that the results obtained by the standard non-linear least-square methods fail to provide accurate estimation of uncertainty for the same data set (P<0.0001). The results of this work validate new methods for a computer simulations of FDG kinetics. Results show that in situations where the classical approach fails in accurate estimation of uncertainty, Bayesian estimation provides an accurate information about the uncertainties in the parameters. Although a particular example of FDG kinetics was used in the paper, the methods can be extended for different pharmaceuticals and imaging modalities. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

On the Connection between Kinetic Monte Carlo and the Burton-Cabrera-Frank Theory

Science.gov (United States)

Patrone, Paul; Margetis, Dionisios; Einstein, T. L.

2013-03-01

In the many years since it was first proposed, the Burton- Cabrera-Frank (BCF) model of step-flow has been experimentally established as one of the cornerstones of surface physics. However, many questions remain regarding the underlying physical processes and theoretical assumptions that give rise to the BCF theory. In this work, we formally derive the BCF theory from an atomistic, kinetic Monte Carlo model of the surface in 1 +1 dimensions with one step. Our analysis (i) shows how the BCF theory describes a surface with a low density of adsorbed atoms, and (ii) establishes a set of near-equilibrium conditions ensuring that the theory remains valid for all times. Support for PP was provided by the NIST-ARRA Fellowship Award No. 70NANB10H026 through UMD. Support for TLE and PP was also provided by the CMTC at UMD, with ancillary support from the UMD MRSEC. Support for DM was provided by NSF DMS0847587 at UMD.

Non-linear theory of elasticity and optimal design

CERN Document Server

Ratner, LW

2003-01-01

In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it

Linear extended neutron diffusion theory for semi-in finites homogeneous means

International Nuclear Information System (INIS)

Vazquez R, R.; Vazquez R, A.; Espinosa P, G.

2009-10-01

Originally developed for heterogeneous means, the linear extended neutron diffusion theory is applied to the limit case of monoenergetic neutron diffusion in a semi-infinite homogeneous mean with a neutron source, located in the coordinate origin situated in the frontier of dispersive material. The monoenergetic neutron diffusion is studied taking into account the spatial deviations in the neutron flux to the interfacial current caused by the neutron source, as well as the influence of the spatial deviations in the absorption rate. The developed pattern is an unidimensional model for an energy group obtained of application of volumetric average diffusion equation in the moderator. The obtained results are compared against the classic diffusion theory and qualitatively against the neutron transport theory. (Author)

Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations

Science.gov (United States)

Vescovi, D.; Berzi, D.; Richard, P.; Brodu, N.

2014-05-01

We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature.

Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations

International Nuclear Information System (INIS)

Vescovi, D.; Berzi, D.; Richard, P.; Brodu, N.

2014-01-01

We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature

ONETEP: linear-scaling density-functional theory with plane-waves

International Nuclear Information System (INIS)

Haynes, P D; Mostof, A A; Skylaris, C-K; Payne, M C

2006-01-01

This paper provides a general overview of the methodology implemented in onetep (Order-N Electronic Total Energy Package), a parallel density-functional theory code for largescale first-principles quantum-mechanical calculations. The distinctive features of onetep are linear-scaling in both computational effort and resources, obtained by making well-controlled approximations which enable simulations to be performed with plane-wave accuracy. Titanium dioxide clusters of increasing size designed to mimic surfaces are studied to demonstrate the accuracy and scaling of onetep

General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles.

Science.gov (United States)

Navarrete-Benlloch, Carlos; Weiss, Talitha; Walter, Stefan; de Valcárcel, Germán J

2017-09-29

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, being the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. Here, we introduce a linearization scheme adapted to such situations, using the driven Van der Pol oscillator as a test bed for the method, which allows us to compare it with full numerical simulations. On a conceptual level, the scheme relies on the connection between the emergence of limit cycles and the spontaneous breaking of the symmetry under temporal translations. On the practical side, the method keeps the simplicity and linear scaling with the size of the problem (number of modes) characteristic of standard linearization, making it applicable to large (many-body) systems.

Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: a non-linear systems theory

Directory of Open Access Journals (Sweden)

2007-01-01

Full Text Available Hysteresis is a rate-independent non-linearity that is expressed through thresholds, switches, and branches. Exceedance of a threshold, or the occurrence of a turning point in the input, switches the output onto a particular output branch. Rate-independent branching on a very large set of switches with non-local memory is the central concept in the new definition of hysteresis. Hysteretic loops are a special case. A self-consistent mathematical description of hydrological systems with hysteresis demands a new non-linear systems theory of adequate generality. The goal of this paper is to establish this and to show how this may be done. Two results are presented: a conceptual model for the hysteretic soil-moisture characteristic at the pedon scale and a hysteretic linear reservoir at the catchment scale. Both are based on the Preisach model. A result of particular significance is the demonstration that the independent domain model of the soil moisture characteristic due to Childs, Poulavassilis, Mualem and others, is equivalent to the Preisach hysteresis model of non-linear systems theory, a result reminiscent of the reduction of the theory of the unit hydrograph to linear systems theory in the 1950s. A significant reduction in the number of model parameters is also achieved. The new theory implies a change in modelling paradigm.

A test of the linear-no threshold theory of radiation carcinogenesis

International Nuclear Information System (INIS)

Cohen, B.L.

1990-01-01

It has been pointed out that, while an ecological study cannot determine whether radon causes lung cancer, it can test the validity of a linear-no threshold relationship between them. The linear-no threshold theory predicts a substantial positive correlation between the average radon exposure in various counties and their lung cancer mortality rates. Data on living areas of houses in 411 counties from all parts of the United States exhibit, rather, a substantial negative correlation with the slopes of the lines of regression differing from zero by 10 and 7 standard deviations for males and females, respectively, and from the positive slope predicted by the theory by at least 16 and 12 standard deviations. When the data are segmented into 23 groups of states or into 7 regions of the country, the predominantly negative slopes and correlations persist, applying to 18 of the 23 state groups and 6 of the 7 regions. Five state-sponsored studies are analyzed, and four of these give a strong negative slope (the other gives a weak positive slope, in agreement with our data for that state). A strong negative slope is also obtained in our data on basements in 253 counties. A random selection-no charge study of 39 high and low lung cancer counties (+4 low population states) gives a much stronger negative correlation. When nine potential confounding factors are included in a multiple linear regression analysis, the discrepancy with theory is reduced only to 12 and 8.5 standard deviations for males and females, respectively. When the data are segmented into four groups by population, the multiple regression vs radon level gives a strong negative slope for each of the four groups. Other considerations are introduced to reduce the discrepancy, but it remains very substantial

Kinetic Effects on the Stability Properties of Field-reversed Configurations: I. Linear Stability

Energy Technology Data Exchange (ETDEWEB)

Elena V. Belova; Ronald C. Davidson; Hantao Ji; Masaaki Yamada

2003-01-28

New computational results are presented which advance the understanding of the stability properties of the Field-Reversed Configuration (FRC). We present results of hybrid and two-fluid (Hall-MHD) simulations of prolate FRCs. The n = 1 tilt instability mechanism and growth rate reduction mechanisms are investigated in detail including resonant particle effects, finite Larmor radius and Hall stabilization, and profile effects. It is shown that the Hall effect determines the mode rotation and the change in the linear mode structure in the kinetic regime; however, the reduction in the growth rate is mostly due to finite Larmor radius effects. Resonant wave-particle interactions are studied as a function of (a) elongation, (b) the kinetic parameter S*, which is proportional to the ratio of the separatrix radius to the thermal ion Larmor radius, and (c) the separatrix shape. It is demonstrated that, contrary to the usually assumed stochasticity of the ion orbits in the FRC, a large fraction of the orbits are regular in long configurations when S* is small. A stochasticity condition is found, and a scaling with the S* parameter is presented. Resonant particle effects are shown to maintain the instability in the large gyroradius regime regardless of the separatrix shape.

Chiral anomaly, Berry phase, and chiral kinetic theory from worldlines in quantum field theory

Science.gov (United States)

Mueller, Niklas; Venugopalan, Raju

2018-03-01

In previous work, we outlined a worldline framework that can be used for systematic computations of the chiral magnetic effect (CME) in ultrarelativistic heavy-ion collisions. Towards this end, we first expressed the real part of the fermion determinant in the QCD effective action as a supersymmetric worldline action of spinning, colored, Grassmanian point particles in background gauge fields, with equations of motion that are covariant generalizations of the Bargmann-Michel-Telegdi and Wong equations. The chiral anomaly, in contrast, arises from the phase of the fermion determinant. Remarkably, the latter too can be expressed as a point particle worldline path integral, which can be employed to derive the anomalous axial vector current. We will show here how Berry's phase can be obtained in a consistent nonrelativistic adiabatic limit of the real part of the fermion determinant. Our work provides a general first principles demonstration that the topology of Berry's phase is distinct from that of the chiral anomaly confirming prior arguments by Fujikawa in specific contexts. This suggests that chiral kinetic treatments of the CME in heavy-ion collisions that include Berry's phase alone are incomplete. We outline the elements of a worldline covariant relativistic chiral kinetic theory that captures the physics of how the chiral current is modified by many-body scattering and topological fluctuations.

On the non-linear scale of cosmological perturbation theory

Energy Technology Data Exchange (ETDEWEB)

Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2013-04-15

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

On the non-linear scale of cosmological perturbation theory

International Nuclear Information System (INIS)

Blas, Diego; Garny, Mathias; Konstandin, Thomas

2013-04-01

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

On the non-linear scale of cosmological perturbation theory

CERN Document Server

Blas, Diego; Konstandin, Thomas

2013-01-01

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

A simplified density matrix minimization for linear scaling self-consistent field theory

International Nuclear Information System (INIS)

Challacombe, M.

1999-01-01

A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 10891 (1993)] and Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimization is introduced that requires four fewer matrix multiplies per minimization step relative to previous formulations. The simplified method also exhibits superior convergence properties, such that the bulk of the work may be shifted to the quadratically convergent McWeeny purification, which brings the density matrix to idempotency. Both orthogonal and nonorthogonal versions are derived. The AINV algorithm of Benzi, Meyer, and Tuma [SIAM J. Sci. Comp. 17, 1135 (1996)] is introduced to linear scaling electronic structure theory, and found to be essential in transformations between orthogonal and nonorthogonal representations. These methods have been developed with an atom-blocked sparse matrix algebra that achieves sustained megafloating point operations per second rates as high as 50% of theoretical, and implemented in the MondoSCF suite of linear scaling SCF programs. For the first time, linear scaling Hartree - Fock theory is demonstrated with three-dimensional systems, including water clusters and estane polymers. The nonorthogonal minimization is shown to be uncompetitive with minimization in an orthonormal representation. An early onset of linear scaling is found for both minimal and double zeta basis sets, and crossovers with a highly optimized eigensolver are achieved. Calculations with up to 6000 basis functions are reported. The scaling of errors with system size is investigated for various levels of approximation. copyright 1999 American Institute of Physics

Profile of student’s understanding in Kinetic Theory of Gases

Science.gov (United States)

Putri, E. E. R.; Sukarmin; Cari

2018-04-01

Students in eleven grade had a different style for answering the physics problems. They could do anything to solve the problem. The way they thought and revealed it into the answer in many styles could be used as a data to know their conception. One of the sub-chapter in physics was the effective velocity of gases. It included in Kinetic Theory of Gases. It was one of the most difficult scientific theories to accept. This research aimed to identify student’s understanding in effective velocity of gases problem. The research was qualitative research. It was taken place at MAN Yogyakarta I in semester two on grade eleven. The obtained datas were collected by test sheet that contained of essay form. The respondents were all of the students in XI MIA 3. The data was analyzed by quantitative analysis using rubric of scoring in essay test and it contained of two problems. The results were the students had resolved the test and it was divided into three categories which are high 10,42%, medium 29,17%, and low 50,00%.

Stochastic field-line wandering in magnetic turbulence with shear. I. Quasi-linear theory

Energy Technology Data Exchange (ETDEWEB)

Shalchi, A. [Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2 (Canada); Negrea, M.; Petrisor, I. [Department of Physics, University of Craiova, Association Euratom-MEdC, 13A.I.Cuza Str, 200585 Craiova (Romania)

2016-07-15

We investigate the random walk of magnetic field lines in magnetic turbulence with shear. In the first part of the series, we develop a quasi-linear theory in order to compute the diffusion coefficient of magnetic field lines. We derive general formulas for the diffusion coefficients in the different directions of space. We like to emphasize that we expect that quasi-linear theory is only valid if the so-called Kubo number is small. We consider two turbulence models as examples, namely, a noisy slab model as well as a Gaussian decorrelation model. For both models we compute the field line diffusion coefficients and we show how they depend on the aforementioned Kubo number as well as a shear parameter. It is demonstrated that the shear effect reduces all field line diffusion coefficients.

Stochastic field-line wandering in magnetic turbulence with shear. I. Quasi-linear theory

International Nuclear Information System (INIS)

Shalchi, A.; Negrea, M.; Petrisor, I.

2016-01-01

We investigate the random walk of magnetic field lines in magnetic turbulence with shear. In the first part of the series, we develop a quasi-linear theory in order to compute the diffusion coefficient of magnetic field lines. We derive general formulas for the diffusion coefficients in the different directions of space. We like to emphasize that we expect that quasi-linear theory is only valid if the so-called Kubo number is small. We consider two turbulence models as examples, namely, a noisy slab model as well as a Gaussian decorrelation model. For both models we compute the field line diffusion coefficients and we show how they depend on the aforementioned Kubo number as well as a shear parameter. It is demonstrated that the shear effect reduces all field line diffusion coefficients.

Generalized theory of a free-electron laser in a helical wiggler and guide magnetic fields using the kinetic approach

International Nuclear Information System (INIS)

Misra, K.D.; Mishra, P.K.

2002-01-01

A self-consistent theory of a free-electron laser is developed by the kinetic approach, using the method of characteristics in helical wiggler and guide magnetic fields. The detailed relativistic particle trajectories obtained in wiggler and guide magnetic fields are used in linearized Vlasov-Maxwell equations having variations in perpendicular and parallel momenta to obtain the perturbed distribution function in terms of perturbed electric and magnetic fields deviating from the vector potential approach. The perturbed distribution function thus obtained, having variations in perpendicular and parallel momenta for an arbitrary distribution function, is used to obtain current, conductivity and dielectric tensors. The full dispersion relation (FDR) and Compton dispersion relation (CDR) have been obtained. The dispersion diagram has been obtained and the interaction of the negative longitudinal space charge with the electromagnetic wave has been shown. The temporal growth rates obtained from the full dispersion relation and Compton dispersion relation for the tenuous cold relativistic beam in microwave region have been discussed

Flow-Induced New Channels of Energy Exchange in Multi-Scale Plasma Dynamics - Revisiting Perturbative Hybrid Kinetic-MHD Theory.

Science.gov (United States)

Shiraishi, Junya; Miyato, Naoaki; Matsunaga, Go

2016-05-10

It is found that new channels of energy exchange between macro- and microscopic dynamics exist in plasmas. They are induced by macroscopic plasma flow. This finding is based on the kinetic-magnetohydrodynamic (MHD) theory, which analyses interaction between macroscopic (MHD-scale) motion and microscopic (particle-scale) dynamics. The kinetic-MHD theory is extended to include effects of macroscopic plasma flow self-consistently. The extension is realised by generalising an energy exchange term due to wave-particle resonance, denoted by δ WK. The first extension is generalisation of the particle's Lagrangian, and the second one stems from modification to the particle distribution function due to flow. These extensions lead to a generalised expression of δ WK, which affects the MHD stability of plasmas.

Natural excitation orbitals from linear response theories : Time-dependent density functional theory, time-dependent Hartree-Fock, and time-dependent natural orbital functional theory

NARCIS (Netherlands)

Van Meer, R.; Gritsenko, O. V.; Baerends, E. J.

2017-01-01

Straightforward interpretation of excitations is possible if they can be described as simple single orbital-to-orbital (or double, etc.) transitions. In linear response time-dependent density functional theory (LR-TDDFT), the (ground state) Kohn-Sham orbitals prove to be such an orbital basis. In

Two-time temperature Green functions in kinetic theory and molecular hydrodynamics. 3. Account of interactions of hydrodynamic fluctuations

International Nuclear Information System (INIS)

Tserkovnikov, Yu.A.

2001-01-01

The regular method for deriving the equations for the Green functions in the tasks on the molecular hydrodynamics and kinetics, making it possible to account consequently the contribution into the generalized kinetics coefficients, conditioned by interaction of two, three and more hydrodynamic modes. In contrast to the general theory of perturbations by the interaction constant the consequent approximations are accomplished by the degree of accounting for the higher correlations, described by the irreducible functions [ru

Spectral methods in chemistry and physics applications to kinetic theory and quantum mechanics

CERN Document Server

Shizgal, Bernard

2015-01-01

This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficient...

Jeans' criterion and nonextensive velocity distribution function in kinetic theory

International Nuclear Information System (INIS)

Du Jiulin

2004-01-01

The effect of nonextensivity of self-gravitating systems on the Jeans' criterion for gravitational instability is studied in the framework of Tsallis statistics. The nonextensivity is introduced in the Jeans problem by a generalized q-nonextensive velocity distribution function through the equation of state of ideal gas in nonextensive kinetic theory. A new Jeans' criterion is deduced with a factor √(2/(5-3q)) that, however, differs from that one in [Astron. Astrophys. 396 (2002) 309] and new results of gravitational instability are analyzed for the nonextensive parameter q. An understanding of physical meaning of q and a possible seismic observation to find astronomical evidence for a value of q different from unity are also discussed

Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory

DEFF Research Database (Denmark)

Frier, Christian; Sørensen, John Dalsgaard

2003-01-01

A Finite Element Reliability Method (FERM) is introduced to perform reliability analyses on two-dimensional structures in plane stress, modeled by non-linear plasticity theory. FERM is a coupling between the First Order Reliability Method (FORM) and the Finite Element Method (FEM). FERM can be us...

Kinetic theory of tearing instability

International Nuclear Information System (INIS)

Hazeltine, R.D.; Dobrott, D.; Wang, T.S.

1975-01-01

The guiding-center kinetic equation with Fokker-Planck collision term is used to study, in cylindrical geometry, a class of dissipative instabilities of which the classical tearing mode is an archetype. Variational solution of the kinetic equation obviates the use of an approximate Ohm's law or adiabatic assumption, as used in previous studies, and it provides a dispersive relation which is uniformly valid for any ratio of wave frequency to collision frequency. One result of using the rigorous collision operator is the prediction of a new instability. This instability, driven by the electron temperature gradient, is predicted to occur under the long mean-free path conditions of present tokamak experiments, and has significant features in common with the kink-like oscillations observed in such experiments

Nonlinear responses of chiral fluids from kinetic theory

Science.gov (United States)

Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun

2018-01-01

The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.

Influence of magnetic flutter on tearing growth in linear and nonlinear theory

Science.gov (United States)

Kreifels, L.; Hornsby, W. A.; Weikl, A.; Peeters, A. G.

2018-06-01

Recent simulations of tearing modes in turbulent regimes show an unexpected enhancement in the growth rate. In this paper the effect is investigated analytically. The enhancement is linked to the influence of turbulent magnetic flutter, which is modelled by diffusion terms in magnetohydrodynamics (MHD) momentum balance and Ohm’s law. Expressions for the linear growth rate as well as the island width in nonlinear theory for small amplitudes are derived. The results indicate an enhanced linear growth rate and a larger linear layer width compared with resistive MHD. Also the island width in the nonlinear regime grows faster in the diffusive model. These observations correspond well to simulations in which the effect of turbulence on the magnetic island width and tearing mode growth is analyzed.

Linear theory of density perturbations in a neutrino+baryon universe

International Nuclear Information System (INIS)

Wasserman, I.

1981-01-01

Various aspects of the linear theory of density perturbations in a universe containing a significant population of massive neutrinos are calculated. Because linear perturbations in the neutrino density are subject to nonviscous damping on length scales smaller than the effective neutrino Jeans length, the fluctuation spectrum of the neutrino density perturbations just after photon decoupling is expected to peak near the maximum neutrino Jeans mass. The gravitational effects of nonneutrino species are included in calculating the maximum neutrino Jeans mass, which is found to be [M/sub J/(t)]/sub max/approx.10 17 M/sub sun//[m/sub ν/(eV)] 2 , about an order of magnitude smaller than is obtained when nonneutrino species are ignored. An explicit expression for the nonviscous damping of neutrino density perturbations less massive than the maximum neutrino Jeans mass is derived. The linear evolution of density perturbations after photon decoupling is discussed. Of particular interest is the possibility that fluctuations in the neutrino density induce baryon density perturbations after photon decoupling and that the maximum neutrino Jeans determines the characteristic bound mass of galaxy clusters

Classes and Theories of Trees Associated with a Class Of Linear Orders

DEFF Research Database (Denmark)

Goranko, Valentin; Kellerman, Ruaan

2011-01-01

Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between...... these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms of the first-order theory of the generating class C, and indicate the problems obstructing such general...... results for the other classes. These problems arise from the possible existence of nondefinable paths in trees, that need not satisfy the first-order theory of C, so we have started analysing first order definable and undefinable paths in trees....

Linear theory on temporal instability of megahertz faraday waves for monodisperse microdroplet ejection.

Science.gov (United States)

Tsai, Shirley C; Tsai, Chen S

2013-08-01

A linear theory on temporal instability of megahertz Faraday waves for monodisperse microdroplet ejection based on mass conservation and linearized Navier-Stokes equations is presented using the most recently observed micrometer- sized droplet ejection from a millimeter-sized spherical water ball as a specific example. The theory is verified in the experiments utilizing silicon-based multiple-Fourier horn ultrasonic nozzles at megahertz frequency to facilitate temporal instability of the Faraday waves. Specifically, the linear theory not only correctly predicted the Faraday wave frequency and onset threshold of Faraday instability, the effect of viscosity, the dynamics of droplet ejection, but also established the first theoretical formula for the size of the ejected droplets, namely, the droplet diameter equals four-tenths of the Faraday wavelength involved. The high rate of increase in Faraday wave amplitude at megahertz drive frequency subsequent to onset threshold, together with enhanced excitation displacement on the nozzle end face, facilitated by the megahertz multiple Fourier horns in resonance, led to high-rate ejection of micrometer- sized monodisperse droplets (>10(7) droplets/s) at low electrical drive power (<;1 W) with short initiation time (<;0.05 s). This is in stark contrast to the Rayleigh-Plateau instability of a liquid jet, which ejects one droplet at a time. The measured diameters of the droplets ranging from 2.2 to 4.6 μm at 2 to 1 MHz drive frequency fall within the optimum particle size range for pulmonary drug delivery.

Simple kinetic theory model of reactive collisions. IV. Laboratory fixed orientational cross sections

International Nuclear Information System (INIS)

Evans, G.T.

1987-01-01

The differential orientational cross section, obtainable from molecular beam experiments on aligned molecules, is calculated using the line-of-normals model for reactive collisions involving hard convex bodies. By means of kinetic theory methods, the dependence of the cross section on the angle of attack γ 0 is expressed in a Legendre function expansion. Each of the Legendre expansion coefficients is given by an integral over the molecule-fixed cross section and functions of the orientation dependent threshold energy

On the Discrete Kinetic Theory for Active Particles. Modelling the Immune Competition

Directory of Open Access Journals (Sweden)

I. Brazzoli

2006-01-01

Full Text Available This paper deals with the application of the mathematical kinetic theory for active particles, with discrete activity states, to the modelling of the immune competition between immune and cancer cells. The first part of the paper deals with the assessment of the mathematical framework suitable for the derivation of the models. Two specific models are derived in the second part, while some simulations visualize the applicability of the model to the description of biological events characterizing the immune competition. A final critical outlines some research perspectives.

Kinetic theory of runaway air breakdown and the implications for lightning initiation

International Nuclear Information System (INIS)

Roussel-Dupre, R.A.; Gurevich, A.V.; Tunnell, T.; Milikh, G.M.

1993-11-01

The kinetic theory for a new air breakdown mechanism advanced in a previous paper is developed. The relevant form of the Boltzmann equation is derived and the particle orbits in both velocity space and configuration space are computed. A numerical solution of the Boltzmann equation, assuring a spatially uniform electric field, is obtained and the temporal evolution of the electron velocity distribution function is described. The results of our analysis are used to estimate the magnitude of potential x-ray emissions from discharges in thunderstorms and are examined in the context of lightning initiation

Linear response theory for magnetic Schrodinger operators in disordered media

CERN Document Server

Bouclet, J M; Klein, A; Schenker, J

2004-01-01

We justify the linear response theory for an ergodic Schrodinger operator with magnetic field within the non-interacting particle approximation, and derive a Kubo formula for the electric conductivity tensor. To achieve that, we construct suitable normed spaces of measurable covariant operators where the Liouville equation can be solved uniquely. If the Fermi level falls into a region of localization, we recover the well-known Kubo-Streda formula for the quantum Hall conductivity at zero temperature.

A statistical mechanical theory of proton transport kinetics in hydrogen-bonded networks based on population correlation functions with applications to acids and bases.

Science.gov (United States)

Tuckerman, Mark E; Chandra, Amalendu; Marx, Dominik

2010-09-28

Extraction of relaxation times, lifetimes, and rates associated with the transport of topological charge defects in hydrogen-bonded networks from molecular dynamics simulations is a challenge because proton transfer reactions continually change the identity of the defect core. In this paper, we present a statistical mechanical theory that allows these quantities to be computed in an unbiased manner. The theory employs a set of suitably defined indicator or population functions for locating a defect structure and their associated correlation functions. These functions are then used to develop a chemical master equation framework from which the rates and lifetimes can be determined. Furthermore, we develop an integral equation formalism for connecting various types of population correlation functions and derive an iterative solution to the equation, which is given a graphical interpretation. The chemical master equation framework is applied to the problems of both hydronium and hydroxide transport in bulk water. For each case it is shown that the theory establishes direct links between the defect's dominant solvation structures, the kinetics of charge transfer, and the mechanism of structural diffusion. A detailed analysis is presented for aqueous hydroxide, examining both reorientational time scales and relaxation of the rotational anisotropy, which is correlated with recent experimental results for these quantities. Finally, for OH(-)(aq) it is demonstrated that the "dynamical hypercoordination mechanism" is consistent with available experimental data while other mechanistic proposals are shown to fail. As a means of going beyond the linear rate theory valid from short up to intermediate time scales, a fractional kinetic model is introduced in the Appendix in order to describe the nonexponential long-time behavior of time-correlation functions. Within the mathematical framework of fractional calculus the power law decay ∼t(-σ), where σ is a parameter of the

Solar Wind Proton Temperature Anisotropy: Linear Theory and WIND/SWE Observations

Science.gov (United States)

Hellinger, P.; Travnicek, P.; Kasper, J. C.; Lazarus, A. J.

2006-01-01

We present a comparison between WIND/SWE observations (Kasper et al., 2006) of beta parallel to p and T perpendicular to p/T parallel to p (where beta parallel to p is the proton parallel beta and T perpendicular to p and T parallel to p are the perpendicular and parallel proton are the perpendicular and parallel proton temperatures, respectively; here parallel and perpendicular indicate directions with respect to the ambient magnetic field) and predictions of the Vlasov linear theory. In the slow solar wind, the observed proton temperature anisotropy seems to be constrained by oblique instabilities, by the mirror one and the oblique fire hose, contrary to the results of the linear theory which predicts a dominance of the proton cyclotron instability and the parallel fire hose. The fast solar wind core protons exhibit an anticorrelation between beta parallel to c and T perpendicular to c/T parallel to c (where beta parallel to c is the core proton parallel beta and T perpendicular to c and T parallel to c are the perpendicular and parallel core proton temperatures, respectively) similar to that observed in the HELIOS data (Marsch et al., 2004).

Kinetic-energy matrix elements for atomic Hylleraas-CI wave functions

Energy Technology Data Exchange (ETDEWEB)

Harris, Frank E., E-mail: harris@qtp.ufl.edu [Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA and Quantum Theory Project, University of Florida, P.O. Box 118435, Gainesville, Florida 32611 (United States)

2016-05-28

Hylleraas-CI is a superposition-of-configurations method in which each configuration is constructed from a Slater-type orbital (STO) product to which is appended (linearly) at most one interelectron distance r{sub ij}. Computations of the kinetic energy for atoms by this method have been difficult due to the lack of formulas expressing these matrix elements for general angular momentum in terms of overlap and potential-energy integrals. It is shown here that a strategic application of angular-momentum theory, including the use of vector spherical harmonics, enables the reduction of all atomic kinetic-energy integrals to overlap and potential-energy matrix elements. The new formulas are validated by showing that they yield correct results for a large number of integrals published by other investigators.

Analytical solution of point kinetics equations for linear reactivity variation during the start-up of a nuclear reactor

International Nuclear Information System (INIS)

Palma, Daniel A.P.; Martinez, Aquilino S.; Goncalves, Alessandro C.

2009-01-01

The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.

Analytical solution of point kinetics equations for linear reactivity variation during the start-up of a nuclear reactor

Energy Technology Data Exchange (ETDEWEB)

Palma, Daniel A.P. [CEFET QUIMICA de Nilopolis/RJ, 21941-914 Rio de Janeiro (Brazil)], E-mail: agoncalves@con.ufrj.br; Martinez, Aquilino S.; Goncalves, Alessandro C. [COPPE/UFRJ - Programa de Engenharia Nuclear, Rio de Janeiro (Brazil)

2009-09-15

The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.

Theory of linear physical systems theory of physical systems from the viewpoint of classical dynamics, including Fourier methods

CERN Document Server

Guillemin, Ernst A

2013-01-01

An eminent electrical engineer and authority on linear system theory presents this advanced treatise, which approaches the subject from the viewpoint of classical dynamics and covers Fourier methods. This volume will assist upper-level undergraduates and graduate students in moving from introductory courses toward an understanding of advanced network synthesis. 1963 edition.

ANCON, Space-Independent Reactor Kinetics with Linear or Nonlinear Thermal Feedback

International Nuclear Information System (INIS)

Vigil, John C.; Dugan, E.T.

1988-01-01

1 - Description of problem or function: ANCON solves the point-reactor kinetic equations including thermal feedback. Lump-type heat balance equations are used to represent the thermodynamics, and the heat capacity of each lump can vary with temperature. Thermal feedback can be either a linear or a non-linear function of lump temperature, and the impressed reactivity can be either a polynomial or sinusoidal function. 2 - Method of solution: In ANCON the system of coupled first-order differential equations is solved by a method based on continuous analytic continuation (references 2 and 3). The basic procedure consists of expanding all the dependent variables except reactivity in Taylor series, with a truncation error criterion, over successive intervals on the time axis. Variations of the basic procedure are used to increase the efficiency of the method in special situations. Automatic switching from the basic procedure to one of its variations (and vice-versa) may occur during the course of a transient. The method yields an analytic criterion for the magnitude of the time-step at any point in the transient. 3 - Restrictions on the complexity of the problem: The program is currently restricted to a maximum of six delayed neutron groups and a maximum of 56 lumps. Larger problems can be accommodated on a 65 K computer by increasing the dimensions of a few subscripted variables. Also, the code is currently restricted to a constant external transport delays, only the open-loop response of a reactor can be computed with ANCON

Kinetic modelling of hydrocracking catalytic reactions by the single events theory; Modelisation cinetique des reactions catalytiques d`hydrocraquage par la theorie des evenements constitutifs

Energy Technology Data Exchange (ETDEWEB)

Schweitzer, J.M.

1998-11-23

Kinetic modelling of petroleum hydrocracking is particularly difficult given the complexity of the feedstocks. There are two distinct classes of kinetics models: lumped empirical models and detailed molecular models. The productivity of lumped empirical models is generally not very accurate, and the number of kinetic parameters increases rapidly with the number of lumps. A promising new methodology is the use of kinetic modelling based on the single events theory. Due to the molecular approach, a finite and limited number of kinetic parameters can describe the kinetic behaviour of the hydrocracking of heavy feedstock. The parameters are independent of the feedstock. However, the available analytical methods are not able to identify the products on the molecular level. This can be accounted for by means of an posteriori lamping technique, which incorporates the detailed knowledge of the elementary step network. Thus, the lumped kinetic parameters are directly calculated from the fundamental kinetic coefficients and the single event model is reduced to a re-lumped molecular model. Until now, the ability of the method to extrapolate to higher carbon numbers had not been demonstrated. In addition, no study had been published for three phase (gas-liquid-solid) systems and a complex feedstock. The objective of this work is to validate the `single events` method using a paraffinic feedstock. First of all, a series of experiments was conducted on a model compound (hexadecane) in order to estimate the fundamental kinetic parameters for acyclic molecules. To validate the single event approach, these estimated kinetic coefficients were used to simulate hydrocracking of a paraffinic mixture ranging from C11 to C18. The simulation results were then compared to the results obtained from the hydrocracking experiments. The comparison allowed to validate the model for acyclic molecules and to demonstrate that the model is applicable to compounds with higher carbon numbers. (author

Empiricism or self-consistent theory in chemical kinetics?

International Nuclear Information System (INIS)

Gutman, E.M.

2007-01-01

To give theoretical background for mechanochemical kinetics, we need first of all to find a possibility to predict the kinetic parameters for real chemical processes by determining rate constants and reaction orders without developing strictly specialized and, to a great extent, artificial models, i.e. to derive the kinetic law of mass action from 'first principles'. However, the kinetic law of mass action has had only an empirical basis from the first experiments of Gulberg and Waage until now, in contrast to the classical law of mass action for chemical equilibrium rigorously derived in chemical thermodynamics from equilibrium condition. Nevertheless, in this paper, an attempt to derive the kinetic law of mass action from 'first principles' is made in macroscopic formulation. It has turned out to be possible owing to the methods of thermodynamics of irreversible processes that were unknown in Gulberg and Waage's time

Test of the linear-no threshold theory of radiation carcinogenesis

International Nuclear Information System (INIS)

Cohen, B.L.

1994-01-01

We recently completed a compilation of radon measurements from available sources which gives the average radon level, in homes for 1730 counties, well over half of all U.S. counties and comprising about 90% of the total U.S. population. Epidemiologists normally study the relationship between mortality risks to individuals, m, vs their personal exposure, r, whereas an ecological study like ours deals with the relationship between the average risk to groups of individuals (population of counties) and their average exposure. It is well known to epidemiologists that, in general, the average dose does not determine the average risk, and to assume otherwise is called 'the ecological fallacy'. However, it is easy to show that, in testing a linear-no threshold theory, 'the ecological fallacy' does not apply; in that theory, the average dose does determine the average risk. This is widely recognized from the fact that 'person-rem' determines the number of deaths. Dividing person-rem by population gives average dose, and dividing number of deaths by population gives mortality rate. Because of the 'ecological fallacy', epidemiology textbooks often state that an ecological study cannot determine a causal relationship between risk and exposure. That may be true, but it is irrelevant here because the purpose of our study is not to determine a causal relationship; it is rather to test the linear-no threshold dependence of m on r. (author)

A statistical theory of cell killing by radiation of varying linear energy transfer

International Nuclear Information System (INIS)

Hawkins, R.B.

1994-01-01

A theory is presented that provides an explanation for the observed features of the survival of cultured cells after exposure to densely ionizing high-linear energy transfer (LET) radiation. It starts from a phenomenological postulate based on the linear-quadratic form of cell survival observed for low-LET radiation and uses principles of statistics and fluctuation theory to demonstrate that the effect of varying LET on cell survival can be attributed to random variation of dose to small volumes contained within the nucleus. A simple relation is presented for surviving fraction of cells after exposure to radiation of varying LET that depends on the α and β parameters for the same cells in the limit of low-LET radiation. This relation implies that the value of β is independent of LET. Agreement of the theory with selected observations of cell survival from the literature is demonstrated. A relation is presented that gives relative biological effectiveness (RBE) as a function of the α and β parameters for low-LET radiation. Measurements from microdosimetry are used to estimate the size of the subnuclear volume to which the fluctuation pertains. 11 refs., 4 figs., 2 tabs

Nuclear reactor kinetics and control

International Nuclear Information System (INIS)

Lewins, J.

1978-01-01

A consistent, integrated account of modern developments in the study of nuclear reactor kinetics and the problem of their efficient and safe control. It aims to prepare the student for advanced study and research or practical work in the field. Special features include treatments of noise theory, reliability theory and safety related studies. It covers all aspects of the operation and control of nuclear reactors, power and research and is complete in providing physical data methods of calculation and solution including questions of equipment reliability. The work uses illustrations of the main types of reactors in use in the UK, USA and Europe. Each chapter contains problems and worked examples suitable for course work and study. The subject is covered in chapters, entitled: introductory review; neutron and precursor equations; elementary solutions at low power; linear reactor process dynamics with feedback; power reactor control systems; fluctuations and reactor noise; safety and reliability; nonlinear systems (safety and control); analogue computing. (author)

Theory and procedures for finding a correct kinetic model for the bacteriorhodopsin photocycle.

Science.gov (United States)

Hendler, R W; Shrager, R; Bose, S

2001-04-26

In this paper, we present the implementation and results of new methodology based on linear algebra. The theory behind these methods is covered in detail in the Supporting Information, available electronically (Shragerand Hendler). In brief, the methods presented search through all possible forward sequential submodels in order to find candidates that can be used to construct a complete model for the BR-photocycle. The methodology is limited only to forward sequential models. If no such models are compatible with the experimental data,none will be found. The procedures apply objective tests and filters to eliminate possibilities that cannot be correct, thus cutting the total number of candidate sequences to be considered. In the current application,which uses six exponentials, the total sequences were cut from 1950 to 49. The remaining sequences were further screened using known experimental criteria. The approach led to a solution which consists of a pair of sequences, one with 5 exponentials showing BR* f L(f) M(f) N O BR and the other with three exponentials showing BR* L(s) M(s) BR. The deduced complete kinetic model for the BR photocycle is thus either a single photocycle branched at the L intermediate or a pair of two parallel photocycles. Reasons for preferring the parallel photocycles are presented. Synthetic data constructed on the basis of the parallel photocycles were indistinguishable from the experimental data in a number of analytical tests that were applied.

Quantifying the uncertainty of kinetic-theory predictions of clustering. Final Report covering 21 September 2011 - 20 September 2014

Energy Technology Data Exchange (ETDEWEB)

Hrenya, Christine [Univ. of Colorado, Boulder, CO (United States). Chemical and Biological Engineering

2014-09-20

Previous work has indicated that inelastic grains undergoing homogeneous cooling may be unstable, giving rise to the formation of velocity vortices and particle clusters for sufficiently large systems. Such instabilities are observed in industrial coal and biomass gasifiers and are known to influence gas-solid contact area, mixing dynamics, and heat/mass transfer rates. However, the driving mechanisms that lead to vortices and clusters are not well understood. Discrete-particle simulations provide a well-established method for understanding such mechanisms but are not a feasible technique for predicting the behavior of large-scale systems. Kinetic-theory-based continuum models offer an effective means of describing such flows, and instabilities present a stringent test of such models due to the transient, three-dimensional nature of instabilities and the large range of time and length scales over which these mechanisms occur.This work begins with the study, via a combination of continuum models and discrete- particle simulations, of a relatively simple flow and includes additional complexities in a stepwise manner to assess various driving mechanisms. Comparisons with discrete-particle simulations, which offer detailed, well-established (but computationally limited) descriptions of particle flows, indicate the ability of continuum models to accurately incorporate each mechanism. Specifically, the critical length scale for velocity vortices and/or particle clusters are studied via direct numerical simulation, molecular dynamics simulations, linear stability analyses of the continuum model, and transient simulations of the continuum model in a range of flow complexities, including moderate dissipation and particle concentration, frictional particles collisions, high gradients, and gas-solid flows. Strong agreement between kinetic-theory-based continuum models and discrete-particle simulations is found for a range for conditions. Furthermore, discrete

Digital linear control theory applied to automatic stepsize control in electrical circuit simulation

NARCIS (Netherlands)

Verhoeven, A.; Beelen, T.G.J.; Hautus, M.L.J.; Maten, ter E.J.W.; Di Bucchianico, A.; Mattheij, R.M.M.; Peletier, M.A.

2006-01-01

Adaptive stepsize control is used to control the local errors of the numerical solution. For optimization purposes smoother stepsize controllers are wanted, such that the errors and stepsizes also behave smoothly. We consider approaches from digital linear control theory applied to multistep

Digital linear control theory applied to automatic stepsize control in electrical circuit simulation

NARCIS (Netherlands)

Verhoeven, A.; Beelen, T.G.J.; Hautus, M.L.J.; Maten, ter E.J.W.

2005-01-01

Adaptive stepsize control is used to control the local errors of the numerical solution. For optimization purposes smoother stepsize controllers are wanted, such that the errors and stepsizes also behave smoothly. We consider approaches from digital linear control theory applied to multistep

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

Discovering the Gas Laws and Understanding the Kinetic Theory of Gases with an iPad App

Science.gov (United States)

Davies, Gary B.

2017-01-01

Carrying out classroom experiments that demonstrate Boyle's law and Gay-Lussac's law can be challenging. Even if we are able to conduct classroom experiments using pressure gauges and syringes, the results of these experiments do little to illuminate the kinetic theory of gases. However, molecular dynamics simulations that run on computers allow…

Linearized gyro-kinetic equation

International Nuclear Information System (INIS)

Catto, P.J.; Tsang, K.T.

1976-01-01

An ordering of the linearized Fokker-Planck equation is performed in which gyroradius corrections are retained to lowest order and the radial dependence appropriate for sheared magnetic fields is treated without resorting to a WKB technique. This description is shown to be necessary to obtain the proper radial dependence when the product of the poloidal wavenumber and the gyroradius is large (k rho much greater than 1). A like particle collision operator valid for arbitrary k rho also has been derived. In addition, neoclassical, drift, finite β (plasma pressure/magnetic pressure), and unperturbed toroidal electric field modifications are treated

Synthetic Domain Theory and Models of Linear Abadi & Plotkin Logic

DEFF Research Database (Denmark)

Møgelberg, Rasmus Ejlers; Birkedal, Lars; Rosolini, Guiseppe

2008-01-01

Plotkin suggested using a polymorphic dual intuitionistic/linear type theory (PILLY) as a metalanguage for parametric polymorphism and recursion. In recent work the first two authors and R.L. Petersen have defined a notion of parametric LAPL-structure, which are models of PILLY, in which one can...... reason using parametricity and, for example, solve a large class of domain equations, as suggested by Plotkin.In this paper, we show how an interpretation of a strict version of Bierman, Pitts and Russo's language Lily into synthetic domain theory presented by Simpson and Rosolini gives rise...... to a parametric LAPL-structure. This adds to the evidence that the notion of LAPL-structure is a general notion, suitable for treating many different parametric models, and it provides formal proofs of consequences of parametricity expected to hold for the interpretation. Finally, we show how these results...

Linear theory of drift-tearing and interchange modes in a screw pinch

International Nuclear Information System (INIS)

Copenhaver, C.

1978-04-01

A drift dispersion relation, as applied to a resistive incompressible plasma in a screw pinch, is derived. This dispersion relation incorporates both drift-tearing and drift-interchange modes and is valid throughout the collisional regime by including kinetic theory factors. The dispersion relation reduces to the drift-tearing dispersion relation in the zero pressure gradient limit, and to the classical resistive dispersion relation in the zero drift limit. The electron temperature gradient instability is still present. Now, however, the introduction of the interchange-drift instability increases the growth rate further above the tearing-drift case. (orig.) [de

Non-linear wave loads and ship responses by a time-domain strip theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hydroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented as a Timoshenko beam. Numerical calculations are presented for the S175 Containership...

Application of linear and higher perturbation theory in reactor physics

International Nuclear Information System (INIS)

Woerner, D.

1978-01-01

For small perturbations in the material composition of a reactor according to the first approximation of perturbation theory the eigenvalue perturbation is proportional to the perturbation of the system. This assumption is true for the neutron flux not influenced by the perturbance. The two-dimensional code LINESTO developed for such problems in this paper on the basis of diffusion theory determines the relative change of the multiplication constant. For perturbations varying the neutron flux in the space of energy and position the eigenvalue perturbation is also influenced by this changed neutron flux. In such cases linear perturbation theory yields larger errors. Starting from the methods of calculus of variations there is additionally developed in this paper a perturbation method of calculation permitting in a quick and simple manner to assess the influence of flux perturbation on the eigenvalue perturbation. While the source of perturbations is evaluated in isotropic approximation of diffusion theory the associated inhomogeneous equation may be used to determine the flux perturbation by means of diffusion or transport theory. Possibilities of application and limitations of this method are studied in further systematic investigations on local perturbations. It is shown that with the integrated code system developed in this paper a number of local perturbations may be checked requiring little computing time. With it flux perturbations in first approximation and perturbations of the multiplication constant in second approximation can be evaluated. (orig./RW) [de

Linearized modified gravity theories with a cosmological term: advance of perihelion and deflection of light

Science.gov (United States)

Özer, Hatice; Delice, Özgür

2018-03-01

Two different ways of generalizing Einstein’s general theory of relativity with a cosmological constant to Brans–Dicke type scalar–tensor theories are investigated in the linearized field approximation. In the first case a cosmological constant term is coupled to a scalar field linearly whereas in the second case an arbitrary potential plays the role of a variable cosmological term. We see that the former configuration leads to a massless scalar field whereas the latter leads to a massive scalar field. General solutions of these linearized field equations for both cases are obtained corresponding to a static point mass. Geodesics of these solutions are also presented and solar system effects such as the advance of the perihelion, deflection of light rays and gravitational redshift were discussed. In general relativity a cosmological constant has no role in these phenomena. We see that for the Brans–Dicke theory, the cosmological constant also has no effect on these phenomena. This is because solar system observations require very large values of the Brans–Dicke parameter and the correction terms to these phenomena becomes identical to GR for these large values of this parameter. This result is also observed for the theory with arbitrary potential if the mass of the scalar field is very light. For a very heavy scalar field, however, there is no such limit on the value of this parameter and there are ranges of this parameter where these contributions may become relevant in these scales. Galactic and intergalactic dynamics is also discussed for these theories at the latter part of the paper with similar conclusions.

A Linear Gradient Theory Model for Calculating Interfacial Tensions of Mixtures

DEFF Research Database (Denmark)

Zou, You-Xiang; Stenby, Erling Halfdan

1996-01-01

excellent agreement between the predicted and experimental IFTs at high and moderate levels of IFTs, while the agreement is reasonably accurate in the near-critical region as the used equations of state reveal classical scaling behavior. To predict accurately low IFTs (sigma ... with proper scaling behavior at the critical point is at least required.Key words: linear gradient theory; interfacial tension; equation of state; influence parameter; density profile....

Kinetic theory approach to modeling of cellular repair mechanisms under genome stress.

Directory of Open Access Journals (Sweden)

Jinpeng Qi

Full Text Available Under acute perturbations from outer environment, a normal cell can trigger cellular self-defense mechanism in response to genome stress. To investigate the kinetics of cellular self-repair process at single cell level further, a model of DNA damage generating and repair is proposed under acute Ion Radiation (IR by using mathematical framework of kinetic theory of active particles (KTAP. Firstly, we focus on illustrating the profile of Cellular Repair System (CRS instituted by two sub-populations, each of which is made up of the active particles with different discrete states. Then, we implement the mathematical framework of cellular self-repair mechanism, and illustrate the dynamic processes of Double Strand Breaks (DSBs and Repair Protein (RP generating, DSB-protein complexes (DSBCs synthesizing, and toxins accumulating. Finally, we roughly analyze the capability of cellular self-repair mechanism, cellular activity of transferring DNA damage, and genome stability, especially the different fates of a certain cell before and after the time thresholds of IR perturbations that a cell can tolerate maximally under different IR perturbation circumstances.

Kinetic theory approach to modeling of cellular repair mechanisms under genome stress.

Science.gov (United States)

Qi, Jinpeng; Ding, Yongsheng; Zhu, Ying; Wu, Yizhi

2011-01-01

Under acute perturbations from outer environment, a normal cell can trigger cellular self-defense mechanism in response to genome stress. To investigate the kinetics of cellular self-repair process at single cell level further, a model of DNA damage generating and repair is proposed under acute Ion Radiation (IR) by using mathematical framework of kinetic theory of active particles (KTAP). Firstly, we focus on illustrating the profile of Cellular Repair System (CRS) instituted by two sub-populations, each of which is made up of the active particles with different discrete states. Then, we implement the mathematical framework of cellular self-repair mechanism, and illustrate the dynamic processes of Double Strand Breaks (DSBs) and Repair Protein (RP) generating, DSB-protein complexes (DSBCs) synthesizing, and toxins accumulating. Finally, we roughly analyze the capability of cellular self-repair mechanism, cellular activity of transferring DNA damage, and genome stability, especially the different fates of a certain cell before and after the time thresholds of IR perturbations that a cell can tolerate maximally under different IR perturbation circumstances.

Kinetic theory of thermotransport of polar semiconductors: Degenerate limit

Energy Technology Data Exchange (ETDEWEB)

Rangel-Huerta, A. [Facultad de Ciencias de la Computacion Benemerita, Universidad Autonoma de Puebla, 14 Sur y San Claudio C.U., Puebla 72570 (Mexico); Rodriguez-Meza, M.A. [Instituto Nacional de Investigaciones Nucleares, Apdo. Postal 18-1027, Mexico D.F. 11801 (Mexico)

2005-08-01

We develop a kinetic theory approach from the semiclassical Boltzmann transport equation for the thermotransport of electrons in degenerate polar semiconductors. The method of moments applied to the Boltzmann equation gives us a set of hydrodynamical equations which are closed up to thirteen relevant variables, including energy density, the stress tensor and the heat flux in the description. The closure of the balance equations is achieved by evaluating the higher order momenta, as well as the production terms, through a non equilibrium distribution function coming from the maximum entropy principle. We assume that electronoptical polar phonon interaction is the leading scattering process in order to obtain analytical expressions for both, the characteristic relaxation times and the usual thermoelectric coefficients. We also show that in this case the Onsager symmetry relationship is not satisfied. (copyright 2005 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Kinetics of drug release from ointments: Role of transient-boundary layer.

Science.gov (United States)

Xu, Xiaoming; Al-Ghabeish, Manar; Krishnaiah, Yellela S R; Rahman, Ziyaur; Khan, Mansoor A

2015-10-15

In the current work, an in vitro release testing method suitable for ointment formulations was developed using acyclovir as a model drug. Release studies were carried out using enhancer cells on acyclovir ointments prepared with oleaginous, absorption, and water-soluble bases. Kinetics and mechanism of drug release was found to be highly dependent on the type of ointment bases. In oleaginous bases, drug release followed a unique logarithmic-time dependent profile; in both absorption and water-soluble bases, drug release exhibited linearity with respect to square root of time (Higuchi model) albeit differences in the overall release profile. To help understand the underlying cause of logarithmic-time dependency of drug release, a novel transient-boundary hypothesis was proposed, verified, and compared to Higuchi theory. Furthermore, impact of drug solubility (under various pH conditions) and temperature on drug release were assessed. Additionally, conditions under which deviations from logarithmic-time drug release kinetics occur were determined using in situ UV fiber-optics. Overall, the results suggest that for oleaginous ointments containing dispersed drug particles, kinetics and mechanism of drug release is controlled by expansion of transient boundary layer, and drug release increases linearly with respect to logarithmic time. Published by Elsevier B.V.

Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence.

Science.gov (United States)

Ozaktas, Haldun M; Yüksel, Serdar; Kutay, M Alper

2002-08-01

A linear algebraic theory of partial coherence is presented that allows precise mathematical definitions of concepts such as coherence and incoherence. This not only provides new perspectives and insights but also allows us to employ the conceptual and algebraic tools of linear algebra in applications. We define several scalar measures of the degree of partial coherence of an optical field that are zero for full incoherence and unity for full coherence. The mathematical definitions are related to our physical understanding of the corresponding concepts by considering them in the context of Young's experiment.

New Methods for Processing and Quantifying VO2 Kinetics to Steady State: VO2 Onset Kinetics

Directory of Open Access Journals (Sweden)

Craig R. McNulty

2017-09-01

Full Text Available Current methods of oxygen uptake (VO2 kinetics data handling may be too simplistic for the complex physiology involved in the underlying physiological processes. Therefore, the aim of this study was to quantify the VO2 kinetics to steady state across the full range of sub-ventilatory threshold work rates, with a particular focus on the VO2 onset kinetics. Ten healthy, moderately trained males participated in five bouts of cycling. Each bout involved 10 min at a percentage of the subject's ventilation threshold (30, 45, 60, 75, 90% from unloaded cycling. The VO2 kinetics was quantified using the conventional mono-exponential time constant (tau, τ, as well as the new methods for VO2 onset kinetics. Compared to linear modeling, non-linear modeling caused a deterioration of goodness of fit (main effect, p < 0.001 across all exercise intensities. Remainder kinetics were also improved using a modified application of the mono-exponential model (main effect, p < 0.001. Interestingly, the slope from the linear regression of the onset kinetics data is similar across all subjects and absolute exercise intensities, and thereby independent of subject fitness and τ. This could indicate that there are no functional limitations between subjects during this onset phase, with limitations occurring for the latter transition to steady state. Finally, the continuing use of mono-exponential modeling could mask important underlying physiology of more instantaneous VO2 responses to steady state. Consequently, further research should be conducted on this new approach to VO2 onset kinetics.

Alfven wave. [Book on linear and nonlinear properties for fusion applications

Energy Technology Data Exchange (ETDEWEB)

Hasegawa, A.; Uberoi, C.

1978-11-01

Seven chapters are included. Chapters 1 and 2 introduce the Alfven wave and describe its linear properties in a homogeneous medium. Chapters 3 and 4 cover the effects of inhomogeneities on these linear properties. Particular emphasis is placed on the appearance of a continuum spectrum and the associated absorption of the Alfven wave which arise due to the inhomogeneity. The explanation of the physical origin of absorption is given using kinetic theory. Chapter 5 is devoted to the associated plasma instabilities. Nonlinear effects discussed in Chapter 6 include quasilinear diffusion, decay, a solitary wave, and a modulational instability. The principles of Alfven wave heating, a design example and present-day experimental results are described in Chapter 7.

Shear-transformation-zone theory of linear glassy dynamics.

Science.gov (United States)

Bouchbinder, Eran; Langer, J S

2011-06-01

We present a linearized shear-transformation-zone (STZ) theory of glassy dynamics in which the internal STZ transition rates are characterized by a broad distribution of activation barriers. For slowly aging or fully aged systems, the main features of the barrier-height distribution are determined by the effective temperature and other near-equilibrium properties of the configurational degrees of freedom. Our theory accounts for the wide range of relaxation rates observed in both metallic glasses and soft glassy materials such as colloidal suspensions. We find that the frequency-dependent loss modulus is not just a superposition of Maxwell modes. Rather, it exhibits an α peak that rises near the viscous relaxation rate and, for nearly jammed, glassy systems, extends to much higher frequencies in accord with experimental observations. We also use this theory to compute strain recovery following a period of large, persistent deformation and then abrupt unloading. We find that strain recovery is determined in part by the initial barrier-height distribution, but that true structural aging also occurs during this process and determines the system's response to subsequent perturbations. In particular, we find by comparison with experimental data that the initial deformation produces a highly disordered state with a large population of low activation barriers, and that this state relaxes quickly toward one in which the distribution is dominated by the high barriers predicted by the near-equilibrium analysis. The nonequilibrium dynamics of the barrier-height distribution is the most important of the issues raised and left unresolved in this paper.

Using system theory and energy methods to prove existence of non-linear PDE's

NARCIS (Netherlands)

Zwart, H.J.

2015-01-01

In this discussion paper we present an idea of combining techniques known from systems theory with energy estimates to show existence for a class of non-linear partial differential equations (PDE's). At the end of the paper a list of research questions with possible approaches is given.

Basic microscopic theory of the distribution, transfer and uptake kinetics of dissolved radionuclides by suspended particulate matter - Part I; Theory development

International Nuclear Information System (INIS)

Abril, J.M.

1998-01-01

Recently much experimental effort has been focused on determining those factors which affect the kinetics and the final equilibrium conditions for the uptake of radionuclides from the aqueous phase by particulate matter. At present, some of these results appear to be either surprising or contradictory and introduce some uncertainty in which parameter values are most appropriate for environmental modelling. In this paper, we study the ionic exchange between the dissolved phase and suspended particles from a microscopic viewpoint, developing a mathematical description of the kinetic transfer and the k d distribution coefficients. The most relevant contribution is the assumption that the exchange of radionuclides occurs in a specific surface layer on the particles, with a non-zero thickness. A wide range of experimental findings can be explained with this theory. (Copyright (c) 1998 Elsevier Science B.V., Amsterdam. All rights reserved.)

Two-fluid static spherical configurations with linear mass function in the Einstein-Cartan theory

International Nuclear Information System (INIS)

Gallakhmetov, A.M.

2002-01-01

In the framework of the Einstein-Cartan theory, two-fluid static spherical configurations with linear mass function are considered. One of these modelling anisotropic matter distributions within star and the other fluid is a perfect fluid representing a source of torsion. It is shown that the solutions of the Einstein equations for anisotropic relativistic spheres in General Relativity may generate the solutions in the Einstein-Cartan theory. Some exact solutions are obtained

Theory of Kinetics of Registration and Anti-Registration in Lipid Bilayers

Science.gov (United States)

Olmsted, Peter; Williamson, John

Lipid bilayer leaflets are often treated as if they are coupled; i.e., that the two leaflets undergo simultaneous transitions between phases, and that domains involve both leaflets together in a registered fashion. We present theory and simulation showing how interleaflet couplings and hydrophobic mismatch can lead to a complex phase diagram with multiple metastable two-phase and three-phase states. Many of these states can be discerned in the experimental literature, and are expected in the early stages of coarsening when domains are sub-micron (and thus perhaps of significance to lipid rafts). We present different kinetic scenarios for transitions between these state, and show how lipid flip flop can surprisingly lead to non-symmetric anti-registered patterns.

Group-kinetic theory of turbulence

Science.gov (United States)

Tchen, C. M.

1986-01-01

The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.

Simulation studies of plasma waves in the electron foreshock - The transition from reactive to kinetic instability

Science.gov (United States)

Dum, C. T.

1990-01-01

Particle simulation experiments were used to analyze the electron beam-plasma instability. It is shown that there is a transition from the reactive state of the electron beam-plasma instability to the kinetic instability of Langmuir waves. Quantitative tests, which include an evaluation of the dispersion relation for the evolving non-Maxwellian beam distribution, show that a quasi-linear theory describes the onset of this transition and applies again fully to the kinetic stage. This stage is practically identical to the late stage seen in simulations of plasma waves in the electron foreshock described by Dum (1990).

Dielectric lattice gauge theory

International Nuclear Information System (INIS)

Mack, G.

1983-06-01

Dielectric lattice gauge theory models are introduced. They involve variables PHI(b)epsilong that are attached to the links b = (x+esub(μ),x) of the lattice and take their values in the linear space g which consists of real linear combinations of matrices in the gauge group G. The polar decomposition PHI(b)=U(b)osub(μ)(x) specifies an ordinary lattice gauge field U(b) and a kind of dielectric field epsilonsub(ij)proportionalosub(i)osub(j)sup(*)deltasub(ij). A gauge invariant positive semidefinite kinetic term for the PHI-field is found, and it is shown how to incorporate Wilson fermions in a way which preserves Osterwalder Schrader positivity. Theories with G = SU(2) and without matter fields are studied in some detail. It is proved that confinement holds, in the sense that Wilson loop expectation values show an area law decay, if the Euclidean action has certain qualitative features which imply that PHI = 0 (i.e. dielectric field identical 0) is the unique maximum of the action. (orig.)

Dielectric lattice gauge theory

International Nuclear Information System (INIS)

Mack, G.

1984-01-01

Dielectric lattice gauge theory models are introduced. They involve variables PHI(b)element ofG that are attached to the links b = (x+esub(μ), x) of the lattice and take their values in the linear space G which consists of real linear combinations of matrices in the gauge group G. The polar decomposition PHI(b)=U(b)sigmasub(μ)(x) specifies an ordinary lattice gauge field U(b) and a kind of dielectric field epsilonsub(ij)proportional sigmasub(i)sigmasub(j)sup(*)deltasub(ij). A gauge invariant positive semidefinite kinetic term for the PHI-field is found, and it is shown how to incorporate Wilson fermions in a way which preserves Osterwalder-Schrader positivity. Theories with G = SU(2) and without matter fields are studied in some detail. It is proved that confinement holds, in the sense that Wilson-loop expectation values show an area law decay, if the euclidean action has certain qualitative features which imply that PHI=0 (i.e. dielectric field identical 0) is the unique maximum of the action. (orig.)

Microscopic theory of ultrafast spin linear reversal

Energy Technology Data Exchange (ETDEWEB)

Zhang, G P, E-mail: gpzhang@indstate.edu [Department of Physics, Indiana State University, Terre Haute, IN 47809 (United States)

2011-05-25

A recent experiment (Vahaplar et al 2009 Phys. Rev. Lett. 103 117201) showed that a single femtosecond laser can reverse the spin direction without spin precession, or spin linear reversal (SLR), but its microscopic theory has been missing. Here we show that SLR does not occur naturally. Two generic spin models, the Heisenberg and Hubbard models, are employed to describe magnetic insulators and metals, respectively. We find analytically that the spin change is always accompanied by a simultaneous excitation of at least two spin components. The only model that has prospects for SLR is the Stoner single-electron band model. However, under the influence of the laser field, the orbital angular momenta are excited and are coupled to each other. If a circularly polarized light is used, then all three components of the orbital angular momenta are excited, and so are their spins. The generic spin commutation relation further reveals that if SLR exists, it must involve a complicated multiple state excitation.

Non-equilibrium Thermodynamic Dissolution Theory for Multi-Component Solid/Liquid Surfaces Involving Surface Adsorption and Radiolysis Kinetics

International Nuclear Information System (INIS)

Stout, R B

2001-01-01

A theoretical expression is developed for the dissolution rate response for multi-component radioactive materials that have surface adsorption kinetics and radiolysis kinetics when wetted by a multi-component aqueous solution. An application for this type of dissolution response is the performance evaluation of multi-component spent nuclear fuels (SNFs) for long term interim storage and for geological disposition. Typically, SNF compositions depend on initial composition, uranium oxide and metal alloys being most common, and on reactor burnup which results in a wide range of fission product and actinide concentrations that decay by alpha, beta, and gamma radiation. These compositional/burnup ranges of SNFs, whether placed in interim storage or emplaced in a geologic repository, will potentially be wetted by multi-component aqueous solutions, and these solutions may be further altered by radiolytic aqueous species due to three radiation fields. The solid states of the SNFs are not thermodynamically stable when wetted and will dissolve, with or without radiolysis. The following development of a dissolution theory is based on a non-equilibrium thermodynamic analysis of energy reactions and energy transport across a solid-liquid phase change discontinuity that propagates at a quasi-steady, dissolution velocity. The integral form of the energy balance equation is used for this spatial surface discontinuity analysis. The integral formulation contains internal energy functional of classical thermodynamics for both the SNFs' solid state and surface adsorption species, and the adjacent liquid state, which includes radiolytic chemical species. The steady-state concentrations of radiolytic chemical species are expressed by an approximate analysis of the decay radiation transport equation. For purposes of illustration a modified Temkin adsorption isotherm was assumed for the surface adsorption kinetics on an arbitrary, finite area of the solid-liquid dissolution interface. For

Kinetic Ising model in a time-dependent oscillating external magnetic field: effective-field theory

International Nuclear Information System (INIS)

Deviren, Bayram; Canko, Osman; Keskin, Mustafa

2010-01-01

Recently, Shi et al. [2008 Phys. Lett. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tomé and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tomé and de Oliveira; hence the dynamic phase diagrams calculated by Shi et al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (ω) and static external field amplitude (h 0 ) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of ω and h 0 . (general)

Conformal field theory with two kinds of Bosonic fields and two linear dilatons

International Nuclear Information System (INIS)

Kamani, Davoud

2010-01-01

We consider a two-dimensional conformal field theory which contains two kinds of the bosonic degrees of freedom. Two linear dilaton fields enable to study a more general case. Various properties of the model such as OPEs, central charge, conformal properties of the fields and associated algebras will be studied. (author)

Non-linearities in Theory-of-Mind Development.

Science.gov (United States)

Blijd-Hoogewys, Els M A; van Geert, Paul L C

2016-01-01

Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72-78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths.

Linear methods in band theory

DEFF Research Database (Denmark)

Andersen, O. Krogh

1975-01-01

of Korringa-Kohn-Rostoker, linear-combination-of-atomic-orbitals, and cellular methods; the secular matrix is linear in energy, the overlap integrals factorize as potential parameters and structure constants, the latter are canonical in the sense that they neither depend on the energy nor the cell volume...

Gyrokinetic Electron and Fully Kinetic Ion Particle Simulation of Collisionless Plasma Dynamics

Energy Technology Data Exchange (ETDEWEB)

Yu Lin; Xueyi Wang; Liu Chen; Zhihong Lin

2009-08-11

Fully kinetic-particle simulations and hybrid simulations have been utilized for decades to investigate various fundamental plasma processes, such as magnetic reconnection, fast compressional waves, and wave-particle interaction. Nevertheless, due to disparate temporal and spatial scales between electrons and ions, existing fully kinetic-particle codes have to employ either unrealistically high electron-to-ion mass ratio, me/mi, or simulation domain limited to a few or a few ten's of the ion Larmor radii, or/and time much less than the global Alfven time scale in order to accommodate available computing resources. On the other hand, in the hybrid simulation, the ions are treated as fully kinetic particles but the electrons are treated as a massless fluid. The electron kinetic effects, e.g., wave-particle resonances and finite electron Larmor radius effects, are completely missing. Important physics, such as the electron transit time damping of fast compressional waves or the triggering mechanism of magnetic reconnection in collisionless plasmas is absent in the hybrid codes. Motivated by these considerations and noting that dynamics of interest to us has frequencies lower than the electron gyrofrequency, we planned to develop an innovative particle simulation model, gyrokinetic (GK) electrons and fully kinetic (FK) ions. In the GK-electron and FK-ion (GKe/FKi) particle simulation model, the rapid electron cyclotron motion is removed, while keeping finite electron Larmor radii, realistic me/mi ratio, wave-particle interactions, and off-diagonal components of electron pressure tensor. The computation power can thus be significantly improved over that of the full-particle codes. As planned in the project DE-FG02-05ER54826, we have finished the development of the new GK-electron and FK-ion scheme, finished its benchmark for a uniform plasma in 1-D, 2-D, and 3-D systems against linear waves obtained from analytical theories, and carried out a further convergence

Gyrokinetic Electron and Fully Kinetic Ion Particle Simulation of Collisionless Plasma Dynamics

International Nuclear Information System (INIS)

Lin, Yu; Wang, Xueyi; Chen, Liu; Lin, Zhihong

2009-01-01

Fully kinetic-particle simulations and hybrid simulations have been utilized for decades to investigate various fundamental plasma processes, such as magnetic reconnection, fast compressional waves, and wave-particle interaction. Nevertheless, due to disparate temporal and spatial scales between electrons and ions, existing fully kinetic-particle codes have to employ either unrealistically high electron-to-ion mass ratio, me/mi, or simulation domain limited to a few or a few ten's of the ion Larmor radii, or/and time much less than the global Alfven time scale in order to accommodate available computing resources. On the other hand, in the hybrid simulation, the ions are treated as fully kinetic particles but the electrons are treated as a massless fluid. The electron kinetic effects, e.g., wave-particle resonances and finite electron Larmor radius effects, are completely missing. Important physics, such as the electron transit time damping of fast compressional waves or the triggering mechanism of magnetic reconnection in collisionless plasmas is absent in the hybrid codes. Motivated by these considerations and noting that dynamics of interest to us has frequencies lower than the electron gyrofrequency, we planned to develop an innovative particle simulation model, gyrokinetic (GK) electrons and fully kinetic (FK) ions. In the GK-electron and FK-ion (GKe/FKi) particle simulation model, the rapid electron cyclotron motion is removed, while keeping finite electron Larmor radii, realistic me/mi ratio, wave-particle interactions, and off-diagonal components of electron pressure tensor. The computation power can thus be significantly improved over that of the full-particle codes. As planned in the project DE-FG02-05ER54826, we have finished the development of the new GK-electron and FK-ion scheme, finished its benchmark for a uniform plasma in 1-D, 2-D, and 3-D systems against linear waves obtained from analytical theories, and carried out a further convergence test

Boundary value problems of the circular cylinders in the strain-gradient theory of linear elasticity

International Nuclear Information System (INIS)

Kao, B.G.

1979-11-01

Three boundary value problems in the strain-gradient theory of linear elasticity are solved for circular cylinders. They are the twisting of circular cylinder, uniformly pressuring of concentric circular cylinder, and pure-bending of simply connected cylinder. The comparisons of these solutions with the solutions in classical elasticity and in couple-stress theory reveal the differences in the stress fields as well as the apparent stress fields due to the influences of the strain-gradient. These aspects of the strain-gradient theory could be important in modeling the failure behavior of structural materials

A unified theory of resonant excitation of kinetic ballooning modes by energetic ions/alpha particles in tokamaks

International Nuclear Information System (INIS)

Biglari, H.; Chen, L.

1991-10-01

A complete theory of wave-particle interactions is presented whereby both circulating and trapped energetic ions can destabilize kinetic ballooning modes in tokamaks. Four qualitatively different types of resonances, involving wave-precessional drift, wave-transit, wave-bounce, and precessional drift-bounce interactions, are identified, and the destabilization potential of each is assessed. For a characteristic slowing-down distribution function, the dominant interaction is that which taps those resonant ions with the highest energy. Implications of the theory for present and future generation fusion experiments are discussed. 16 refs

Covariant kinetic dispersion theory of linear transverse waves parallel propagating in magnetized plasmas with thermal anisotropy

International Nuclear Information System (INIS)

Lazar, M.; Schlickeiser, R.

2006-01-01

The properties of transverse waves parallel propagating in magnetized plasmas with arbitrary composition and thermally anisotropic, are investigated on the basis of relativistic Vlasov-Maxwell equations. The transverse dispersion relations for plasmas with arbitrary distribution functions are derived. These dispersion relations describe the linear response of the system to the initial perturbations and thus define all existing linear (transverse) plasma modes in the system. By analytic continuation the dispersion relations in the whole complex frequency plane are constructed. Further analysis is restricted to the important case of anisotropic bi-Maxwellian equilibrium plasma distribution functions. Explicit forms of the relativistically correct transverse dispersion relations are derived that hold for any values of the plasma temperatures and the temperature anisotropy. In the limit of nonrelativistic plasma temperatures the dispersion relations are expressed in terms of plasma dispersion function, however, the dependence on frequency and wave numbers is markedly different from the standard noncovariant nonrelativistic analysis. Only in the strictly unphysical formal limit of an infinitely large speed of light, c→∞, does the nonrelativistic dispersion relations reduce to the standard noncovariant dispersion relations

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

International Nuclear Information System (INIS)

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

1984-01-01

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

Obtention of the ponderomotive force in the mark of the kinetic theory in the injection of high power in a plasma

International Nuclear Information System (INIS)

Gutierrez T, C.; Beltran P, M.

2006-01-01

To reach the quasi stationary work regime of a Tokamak, it is necessary to optimize the current generation by non inductive methods with the injection of radio-frequency waves (RF), such as the electron cyclotron waves, cyclotron ion, and in the inferior hybrid one. At the moment, the powers of the radiation sources are very big for what the such no-lineal effects as the ponderomotive force are very important. In the case of the electron cyclotron waves, in the mark of the lineal theory of waves propagation, using extraordinary waves (first and second harmonic), the problem of the singularity always arises in the exact resonance. One of the ways of eliminating this singularity is considering that the group of electrons under resonance conditions is big (quasi lineal theory) or introducing such non lineal effects such as the ponderomotive force. In the obtaining of the ponderomotive force under resonance conditions this indetermination arises also. In this work the kinetic theory to obtain the expression of the ponderomotive force in the cyclotron resonance of the electrons, where the Vlasov kinetic equation expands up to second order with regard to the electric field of the RF wave. The kinetic approach allows to the analysis of the ponderomotive force under resonance conditions considering the Landau integration method. (Author)

Three-dimensional linear peeling-ballooning theory in magnetic fusion devices

Energy Technology Data Exchange (ETDEWEB)

Weyens, T., E-mail: tweyens@fis.uc3m.es; Sánchez, R.; García, L. [Departamento de Física, Universidad Carlos III de Madrid, Madrid 28911 (Spain); Loarte, A.; Huijsmans, G. [ITER Organization, Route de Vinon sur Verdon, 13067 Saint Paul Lez Durance (France)

2014-04-15

Ideal magnetohydrodynamics theory is extended to fully 3D magnetic configurations to investigate the linear stability of intermediate to high n peeling-ballooning modes, with n the toroidal mode number. These are thought to be important for the behavior of edge localized modes and for the limit of the size of the pedestal that governs the high confinement H-mode. The end point of the derivation is a set of coupled second order ordinary differential equations with appropriate boundary conditions that minimize the perturbed energy and that can be solved to find the growth rate of the perturbations. This theory allows of the evaluation of 3D effects on edge plasma stability in tokamaks such as those associated with the toroidal ripple due to the finite number of toroidal field coils, the application of external 3D fields for elm control, local modification of the magnetic field in the vicinity of ferromagnetic components such as the test blanket modules in ITER, etc.

Long-time tails of the heat-conductivity time correlation functions for a magnetized plasma - a kinetic theory approach

NARCIS (Netherlands)

Schoolderman, A.J.; Suttorp, L.G.

1989-01-01

The long-time behaviour of the longitudinal and the transverse heat conductivity time correlation functions for a magnetized one-component plasma is studied by means of kinetic theory. To that end these correlation functions, which are defined as the inverse Laplace transforms of the dynamic heat

Recent development of linear scaling quantum theories in GAMESS

Energy Technology Data Exchange (ETDEWEB)

Choi, Cheol Ho [Kyungpook National Univ., Daegu (Korea, Republic of)

2003-06-01

Linear scaling quantum theories are reviewed especially focusing on the method adopted in GAMESS. The three key translation equations of the fast multipole method (FMM) are deduced from the general polypolar expansions given earlier by Steinborn and Rudenberg. Simplifications are introduced for the rotation-based FMM that lead to a very compact FMM formalism. The OPS (optimum parameter searching) procedure, a stable and efficient way of obtaining the optimum set of FMM parameters, is established with complete control over the tolerable error {epsilon}. In addition, a new parallel FMM algorithm requiring virtually no inter-node communication, is suggested which is suitable for the parallel construction of Fock matrices in electronic structure calculations.

Nuclear reactor kinetics and plant control

CERN Document Server

Oka, Yoshiaki

2013-01-01

Understanding time-dependent behaviors of nuclear reactors and the methods of their control is essential to the operation and safety of nuclear power plants. This book provides graduate students, researchers, and engineers in nuclear engineering comprehensive information on both the fundamental theory of nuclear reactor kinetics and control and the state-of-the-art practice in actual plants, as well as the idea of how to bridge the two. The first part focuses on understanding fundamental nuclear kinetics. It introduces delayed neutrons, fission chain reactions, point kinetics theory, reactivit

Thermodynamic and kinetic properties of hydrogen defect pairs in SrTiO3 from density functional theory

DEFF Research Database (Denmark)

Bork, Nicolai Christian; Bonanos, Nikolaos; Rossmeisl, Jan

2011-01-01

A density functional theory investigation of the thermodynamic and kinetic properties of hydrogen–hydrogen defect interactions in the cubic SrTiO3 perovskite is presented. We find a net attraction between two hydrogen atoms with an optimal separation of ∼2.3 Å. The energy gain is ca. 0.33 eV comp...

Development of the kinetic molecular theory of gases concept inventory: Preliminary results on university students’ misconceptions

Directory of Open Access Journals (Sweden)

Nataša Erceg

2016-11-01

Full Text Available In this study, we investigated students’ understanding of concepts related to the microscopic model of gas. We thoroughly reviewed the relevant literature and conducted think alouds with students by asking them to answer open-ended questions about the kinetic molecular theory of gases. Thereafter, we transformed the open-ended questions into multiple-choice questions, whereby distractors were based on the results of the think alouds. Thus, we obtained a set of 22 questions, which constitutes our current version of the kinetic molecular theory of gases concept inventory. The inventory has been administered to 250 students from different universities in Croatia, and its content validity has been investigated trough physics teacher surveys. The results of our study not only corroborate the existence of some already known student misconceptions, but also reveal new insights about a great spectrum of students’ misconceptions that had not been reported in earlier research (e.g., misconceptions about intermolecular potential energy and molecular velocity distribution. Moreover, we identified similar distribution of students’ responses across the surveyed student groups, despite the fact that they had been enrolled in different curricular environments.

Oxidation kinetics of hazelnut oil treated with ozone

Directory of Open Access Journals (Sweden)

H. Uzun

2018-01-01

Full Text Available The present study investigates the oxidation kinetics of hazelnut oil ozonated in different treatment periods (1, 5, 60 and 180 min. The kinetic rate constant (k was taken as the inverse of oxidation onset time (To observing a linear relationship from the plot of lnTo to isothermal temperatures (373, 383, 393, and 403 K carried out at differential scanning calorimetry. Kinetic parameters, activation energy (Ea, activation enthalpy (ΔH‡ and entropy (ΔS‡ were calculated based on the Arrhenius equation and activated complex theory. k values showed an exponential rise with the increase of ozone treatment time. The increase in k correlated well with the increase in the peroxide and free fatty acid values of all samples. Ea and ∆H‡ of the ozone treated oils showed a reducing trend and reflected an increased oxidation sensitivity after ozone treatment. Consistently, an increase in ∆S‡ indicated a faster oxidation reaction with an increase in ozone exposure time. However, no significant difference was observed in k, Ea, ΔH‡, ΔS‡ (p < 0.05 as a function of storage period, after the hazelnut oil was treated with ozone for 1 min.

Oxidation kinetics of hazelnut oil treated with ozone

International Nuclear Information System (INIS)

Uzun, H.; Ibanoglu, E.

2017-01-01

The present study investigates the oxidation kinetics of hazelnut oil ozonated in different treatment periods (1, 5, 60 and 180 min). The kinetic rate constant (k) was taken as the inverse of oxidation onset time (To) observing a linear relationship from the plot of ln To to isothermal temperatures (373, 383, 393, and 403 K) carried out at differential scanning calorimetry. Kinetic parameters, activation energy (Ea), activation enthalpy (ΔH‡) and entropy (ΔS‡) were calculated based on the Arrhenius equation and activated complex theory. k values showed an exponential rise with the increase of ozone treatment time. The increase in k correlated well with the increase in the peroxide and free fatty acid values of all samples. Ea and ΔH‡ of the ozone treated oils showed a reducing trend and reflected an increased oxidation sensitivity after ozone treatment. Consistently, an increase in ΔS‡ indicated a faster oxidation reaction with an increase in ozone exposure time. However, no significant difference was observed in k, Ea, ΔH‡, ΔS‡ (p < 0.05) as a function of storage period, after the hazelnut oil was treated with ozone for 1 min. [es

Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.

Science.gov (United States)

Scott, M

2012-08-01

The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.

Some Aspects of Extended Kinetic Equation

Directory of Open Access Journals (Sweden)

Dilip Kumar

2015-09-01

Full Text Available Motivated by the pathway model of Mathai introduced in 2005 [Linear Algebra and Its Applications, 396, 317–328] we extend the standard kinetic equations. Connection of the extended kinetic equation with fractional calculus operator is established. The solution of the general form of the fractional kinetic equation is obtained through Laplace transform. The results for the standard kinetic equation are obtained as the limiting case.

Direct integral linear least square regression method for kinetic evaluation of hepatobiliary scintigraphy

International Nuclear Information System (INIS)

Shuke, Noriyuki

1991-01-01

In hepatobiliary scintigraphy, kinetic model analysis, which provides kinetic parameters like hepatic extraction or excretion rate, have been done for quantitative evaluation of liver function. In this analysis, unknown model parameters are usually determined using nonlinear least square regression method (NLS method) where iterative calculation and initial estimate for unknown parameters are required. As a simple alternative to NLS method, direct integral linear least square regression method (DILS method), which can determine model parameters by a simple calculation without initial estimate, is proposed, and tested the applicability to analysis of hepatobiliary scintigraphy. In order to see whether DILS method could determine model parameters as good as NLS method, or to determine appropriate weight for DILS method, simulated theoretical data based on prefixed parameters were fitted to 1 compartment model using both DILS method with various weightings and NLS method. The parameter values obtained were then compared with prefixed values which were used for data generation. The effect of various weights on the error of parameter estimate was examined, and inverse of time was found to be the best weight to make the error minimum. When using this weight, DILS method could give parameter values close to those obtained by NLS method and both parameter values were very close to prefixed values. With appropriate weighting, the DILS method could provide reliable parameter estimate which is relatively insensitive to the data noise. In conclusion, the DILS method could be used as a simple alternative to NLS method, providing reliable parameter estimate. (author)

Weak turbulence theory for beam-plasma interaction

Science.gov (United States)

Yoon, Peter H.

2018-01-01

The kinetic theory of weak plasma turbulence, of which Ronald C. Davidson was an important early pioneer [R. C. Davidson, Methods in Nonlinear Plasma Theory, (Academic Press, New York, 1972)], is a venerable and valid theory that may be applicable to a large number of problems in both laboratory and space plasmas. This paper applies the weak turbulence theory to the problem of gentle beam-plasma interaction and Langmuir turbulence. It is shown that the beam-plasma interaction undergoes various stages of physical processes starting from linear instability, to quasilinear saturation, to mode coupling that takes place after the quasilinear stage, followed by a state of quasi-static "turbulent equilibrium." The long term quasi-equilibrium stage is eventually perturbed by binary collisional effects in order to bring the plasma to a thermodynamic equilibrium with increased entropy.

Classical Noether theory with application to the linearly damped particle

International Nuclear Information System (INIS)

Leone, Raphaël; Gourieux, Thierry

2015-01-01

This paper provides a modern presentation of Noether’s theory in the realm of classical dynamics, with application to the problem of a particle submitted to both a potential and a linear dissipation. After a review of the close relationships between Noether symmetries and first integrals, we investigate the variational point symmetries of the Lagrangian introduced by Bateman, Caldirola and Kanai. This analysis leads to the determination of all the time-independent potentials allowing such symmetries, in the one-dimensional and the radial cases. Then we develop a symmetry-based transformation of Lagrangians into autonomous others, and apply it to our problem. To be complete, we enlarge the study to Lie point symmetries which we associate logically to the Noether ones. Finally, we succinctly address the issue of a ‘weakened’ Noether’s theory, in connection with ‘on-flows’ symmetries and non-local constant of motions, because it has a direct physical interpretation in our specific problem. Since the Lagrangian we use gives rise to simple calculations, we hope that this work will be of didactic interest to graduate students, and give teaching material as well as food for thought for physicists regarding Noether’s theory and the recent developments around the idea of symmetry in classical mechanics. (paper)

Linear theory period ratios for surface helium enhanced double-mode Cepheids

International Nuclear Information System (INIS)

Cox, A.N.; Hodson, S.W.; King, D.S.

1979-01-01

Linear nonadiabatic theory period ratios for models of double-mode Cepheids with their two periods between 1 and 7 days have been computed, assuming differing amounts and depths of surface helium enhancement. Evolution theory masses and luminosities are found to be consistent with the observed periods. All models give Pi 1 /Pi 0 approx. =0.70 as observed for the 11 known variables, contrary to previous theoretical conclusions. The composition structure that best fits the period ratios has the helium mass fraction in the outer 10 -3 of the stellar mass (T< or =250,000 K) as 0.65, similar to a previous model for the triple-mode pulsator AC And. This enrichment can be established by a Cepheid wind and downward inverted μ gradient instability mixing in the lifetime of these low-mass classical Cepheids

Tantalum high-temperature oxidation kinetics

International Nuclear Information System (INIS)

Grigor'ev, Yu.M.; Sarkisyan, A.A.; Merzhanov, A.G.

1981-01-01

Kinetics of heat release and scale growth during tantalum oxidation within 650-1300 deg C temperature range in oxygen-containing media is investigated. Kinetic equations and temperature and pressure dependences of constants are ound Applicability of the kinetic Lorie mechanism for the description of the tantalum oxidation kinetics applicably to rapid-passing processes is shown. It is stated that the process rate (reaction ability) is determined by adsorption desorption factors on the external surface of the ''protective'' oxide for the ''linear'' oxidation stage [ru

A non-linear field theory

International Nuclear Information System (INIS)

Skyrme, T.H.R.

1994-01-01

A unified field theory of mesons and their particle sources is proposed and considered in its classical aspects. The theory has static solutions of a singular nature, but finite energy, characterized by spin directions; the number of such entities is a rigorously conserved constant of motion; they interact with an external meson field through a derivative-type coupling with the spins, akin to the formalism of strong-coupling meson theory. There is a conserved current identifiable with isobaric spin, and another that may be related to hypercharge. The postulates include one constant of the dimensions of length, and another that is conjecture necessarily to have the value (h/2π)c, or perhaps 1/2(h/2π)c, in the quantized theory. (author). 5 refs

Kinetics of microstructure formation of high-pressure induced gel from a whey protein isolate

Science.gov (United States)

He, Jin-Song; Yang, Hongwei; Zhu, Wanpeng; Mu, Tai-Hua

2010-03-01

The kinetic process of pressure-induced gelation of whey protein isolate (WPI) solutions was studied using in situ light scattering. The relationship of the logarithm of scattered light intensity (I) versus time (t) was linear after the induced time and could be described by the Cahn-Hilliard linear theory. With increasing time, the scattered intensity deviated from the exponential relationship, and the time evolution of the scattered light intensity maximum Im and the corresponding wavenumber qm could be described in terms of the power-law relationship as Im~fβ and qm~f-α, respectively. These results indicated that phase separation occurred during the gelation of WPI solutions under high pressure.

Linear algebra and group theory

CERN Document Server

Smirnov, VI

2011-01-01

This accessible text by a Soviet mathematician features material not otherwise available to English-language readers. Its three-part treatment covers determinants and systems of equations, matrix theory, and group theory. 1961 edition.

Shear viscosity of the quark-gluon plasma in a kinetic theory approach

International Nuclear Information System (INIS)

Puglisi, A.; Plumari, S.; Scardina, F.; Greco, V.

2014-01-01

One of the main results of heavy ions collision (HIC) at relativistic energy experiments is the very small shear viscosity to entropy density ratio of the Quark-Gluon Plasma, close to the conjectured lower bound η/s=1/4π for systems in the infinite coupling limit. Transport coefficients like shear viscosity are responsible of non-equilibrium properties of a system: Green-Kubo relations give us an exact expression to compute these coefficients. We compute shear viscosity numerically using Green-Kubo relation in the framework of Kinetic Theory solving the relativistic transport Boltzmann equation in a finite box with periodic boundary conditions. We investigate a system of particles interacting via anisotropic and energy dependent cross-section in the range of temperature of interest for HIC. Green-Kubo results are in agreement with Chapman-Enskog approximation while Relaxation Time approximation can underestimates the viscosity of a factor 2. The correct analytic formula for shear viscosity can be used to develop a transport theory with a fixed η/s and have a comparison with physical observables like elliptic flow

Stochastic lumping analysis for linear kinetics and its application to the fluctuation relations between hierarchical kinetic networks

Energy Technology Data Exchange (ETDEWEB)

Deng, De-Ming; Chang, Cheng-Hung [Institute of Physics, National Chiao Tung University, Hsinchu 300, Taiwan (China)

2015-05-14

Conventional studies of biomolecular behaviors rely largely on the construction of kinetic schemes. Since the selection of these networks is not unique, a concern is raised whether and under which conditions hierarchical schemes can reveal the same experimentally measured fluctuating behaviors and unique fluctuation related physical properties. To clarify these questions, we introduce stochasticity into the traditional lumping analysis, generalize it from rate equations to chemical master equations and stochastic differential equations, and extract the fluctuation relations between kinetically and thermodynamically equivalent networks under intrinsic and extrinsic noises. The results provide a theoretical basis for the legitimate use of low-dimensional models in the studies of macromolecular fluctuations and, more generally, for exploring stochastic features in different levels of contracted networks in chemical and biological kinetic systems.

Stochastic lumping analysis for linear kinetics and its application to the fluctuation relations between hierarchical kinetic networks.

Science.gov (United States)

Deng, De-Ming; Chang, Cheng-Hung

2015-05-14

Conventional studies of biomolecular behaviors rely largely on the construction of kinetic schemes. Since the selection of these networks is not unique, a concern is raised whether and under which conditions hierarchical schemes can reveal the same experimentally measured fluctuating behaviors and unique fluctuation related physical properties. To clarify these questions, we introduce stochasticity into the traditional lumping analysis, generalize it from rate equations to chemical master equations and stochastic differential equations, and extract the fluctuation relations between kinetically and thermodynamically equivalent networks under intrinsic and extrinsic noises. The results provide a theoretical basis for the legitimate use of low-dimensional models in the studies of macromolecular fluctuations and, more generally, for exploring stochastic features in different levels of contracted networks in chemical and biological kinetic systems.

Sequential double excitations from linear-response time-dependent density functional theory

Energy Technology Data Exchange (ETDEWEB)

Mosquera, Martín A.; Ratner, Mark A.; Schatz, George C., E-mail: g-schatz@northwestern.edu [Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208 (United States); Chen, Lin X. [Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208 (United States); Chemical Sciences and Engineering Division, Argonne National Laboratory, 9700 South Cass Ave., Lemont, Illinois 60439 (United States)

2016-05-28

Traditional UV/vis and X-ray spectroscopies focus mainly on the study of excitations starting exclusively from electronic ground states. However there are many experiments where transitions from excited states, both absorption and emission, are probed. In this work we develop a formalism based on linear-response time-dependent density functional theory to investigate spectroscopic properties of excited states. We apply our model to study the excited-state absorption of a diplatinum(II) complex under X-rays, and transient vis/UV absorption of pyrene and azobenzene.

The flow analysis of supercavitating cascade by linear theory

Energy Technology Data Exchange (ETDEWEB)

Park, E.T. [Sung Kyun Kwan Univ., Seoul (Korea, Republic of); Hwang, Y. [Seoul National Univ., Seoul (Korea, Republic of)

1996-06-01

In order to reduce damages due to cavitation effects and to improve performance of fluid machinery, supercavitation around the cascade and the hydraulic characteristics of supercavitating cascade must be analyzed accurately. And the study on the effects of cavitation on fluid machinery and analysis on the performances of supercavitating hydrofoil through various elements governing flow field are critically important. In this study comparison of experiment results with the computed results of linear theory using singularity method was obtainable. Specially singularity points like sources and vortexes on hydrofoil and freestreamline were distributed to analyze two dimensional flow field of supercavitating cascade, and governing equations of flow field were derived and hydraulic characteristics of cascade were calculated by numerical analysis of the governing equations. 7 refs., 6 figs.

A temperature and mass dependence of the linear Boltzmann collision operator from group theory point of view

International Nuclear Information System (INIS)

Saveliev, V.

1996-01-01

The Lie group of the transformations affecting the parameters of the linear Boltzmann collision operator such as temperature of background gas and ratio of masses of colliding particles and molecules is discovered. The group also describes the conservation laws for collisions and main symmetries of the collision operator. New algebraic properties of the collision operator are derived. Transformations acting on the variables and parameters and leaving the linear Boltzmann kinetic equation invariant are found. For the constant collision frequency the integral representation of solutions for nonuniform case in terms of the distribution function of particles drifting in a gas with zero temperature is deduced. The new exact relaxation solutions are obtained too. copyright 1996 American Institute of Physics

Mapping the kinetic barriers of a Large RNA molecule's folding landscape.

Directory of Open Access Journals (Sweden)

Jörg C Schlatterer

Full Text Available The folding of linear polymers into discrete three-dimensional structures is often required for biological function. The formation of long-lived intermediates is a hallmark of the folding of large RNA molecules due to the ruggedness of their energy landscapes. The precise thermodynamic nature of the barriers (whether enthalpic or entropic that leads to intermediate formation is still poorly characterized in large structured RNA molecules. A classic approach to analyzing kinetic barriers are temperature dependent studies analyzed with Eyring's transition state theory. We applied Eyring's theory to time-resolved hydroxyl radical (•OH footprinting kinetics progress curves collected at eight temperature from 21.5 °C to 51 °C to characterize the thermodynamic nature of folding intermediate formation for the Mg(2+-mediated folding of the Tetrahymena thermophila group I ribozyme. A common kinetic model configuration describes this RNA folding reaction over the entire temperature range studied consisting of primary (fast transitions to misfolded intermediates followed by much slower secondary transitions, consistent with previous studies. Eyring analysis reveals that the primary transitions are moderate in magnitude and primarily enthalpic in nature. In contrast, the secondary transitions are daunting in magnitude and entropic in nature. The entropic character of the secondary transitions is consistent with structural rearrangement of the intermediate species to the final folded form. This segregation of kinetic control reveals distinctly different molecular mechanisms during the two stages of RNA folding and documents the importance of entropic barriers to defining rugged RNA folding landscapes.

The results of a non-linear mathematical model for the kinetics of 10B after BPA-F infusion in BNCT

International Nuclear Information System (INIS)

Ryynaenen, P.; Savolainen, S.; Hiismaeki, P.; Kangasmaeki, A.

2001-01-01

The aim of this study was to create a model for the kinetics of 10 B in glioma patients after p-boronophenylalanine fructose complex (BPA-F) infusion in order to predict the 10 B concentration in blood during the neutron irradiations in BNCT. The more specific aim was to create a flexible model that would work with variable infusion duration and variable amounts of infused BRA, by forehand carrying out only 1 to 2 kinetic studies per different trials. Previously used bi-exponential fitting and open compartmental model are capable, but, however, heavy kinetic studies are needed before they are reliable enough. A model probe with a memory effect based on phenomenological findings was created. The model development was based on the data from 10 glioblastoma multiforme patients from the Brookhaven National Laboratory BNCT trials. These patients received i.v. 290 mg BPA/kg body weight as a fructose complex during two hours. Blood samples were collected during and after the infusion. The accuracy of the model was verified with distinctive fitting of 10 new glioma patient data from the Finnish BNCT-trials. The 10 B- concentration in whole blood samples was determined by ICP-AES method. In the study it is concluded that the constructed non-linear model is flexible and capable in describing the kinetics of 10 B concentration in blood after a single infusion of BPA-F. (author)

On the kinetic theory of QPEMIC instabilities in weakly ionized plasmas placed in non-parallel fields

International Nuclear Information System (INIS)

Milic, B.S.; Gajic, D.Z.

1994-01-01

Quasi-perpendicular electromagnetic ion-cyclotron (QPEMIC) modes and instabilities are studied, on the ground of linear theory of perturbations and kinetic equations with BGK collision integrals, in weakly ionized, low-β and moderately non-isothermal plasmas placed in non-parallel electric and magnetic fields. The magnetization is assumed to be sufficiently high to cut off the perpendicular steady-state current. Special attention is given to evaluation of magnitudes of the threshold drifts required for the onset of instabilities. It is found that these drifts are smaller than those for the corresponding quasi-perpendicular electrostatic ion-cyclotron (QPESIC) instabilities studied previously for the same type of plasmas. Both QPEMIC and QPESIC threshold drifts exhibit the same behavioural pattern if the order of harmonic, magnetization, non-isothermality or the angle between the fields are varied. An increase of the angle between the fields lowers the threshold drifts, which means that the presence of u perpendicular to (or E perpendicular to ) facilitates the excitation of both QPEMIC and QPESIC instabilities. The QPEMIC threshold drifts are found to depend on the overall gas pressure, and to decrease as the pressure is lowered, which is a feature not found in the QPESIC case. The discrepancies between the QPEMIC and QPESIC threshold drifts increase if the pressure decreases, or if magnetization, degree of ionization or ion charge number increase. (orig.)

Complex Toda theories and twisted reality conditions

International Nuclear Information System (INIS)

Evans, J.M.

1993-01-01

The Toda equations (based on a finite-dimensional or affine Lie algebra of superalgebra) are discussed as integrable non-linear differential equations for a set of complex scalar fields. We show that such complex Toda fields can either be restricted to take real values in the standard way or else they can be subjected to a 'twisted' reality condition associated to any Z 2 symmetry of the Cartan matrix or Dynkin diagram of the underlying algebra. Different reality conditions give rise to different lagrangian field theories. In the conformal case, however, these theories have the same central charge, while in the affine case they have the same mass spectrum. The construction of N=2 superconformal theories based on the superalgebras A(n, n-1) is clarified, and a new class of conformal field theories with positive kinetic energy based on the superalgebras C(n) is presented. The ideas developed are also relevant to understanding solition solutions in affine Toda theories with imaginary coupling constant. (orig.)

Linear systems formulation of scattering theory for rough surfaces with arbitrary incident and scattering angles.

Science.gov (United States)

Krywonos, Andrey; Harvey, James E; Choi, Narak

2011-06-01

Scattering effects from microtopographic surface roughness are merely nonparaxial diffraction phenomena resulting from random phase variations in the reflected or transmitted wavefront. Rayleigh-Rice, Beckmann-Kirchhoff. or Harvey-Shack surface scatter theories are commonly used to predict surface scatter effects. Smooth-surface and/or paraxial approximations have severely limited the range of applicability of each of the above theoretical treatments. A recent linear systems formulation of nonparaxial scalar diffraction theory applied to surface scatter phenomena resulted first in an empirically modified Beckmann-Kirchhoff surface scatter model, then a generalized Harvey-Shack theory that produces accurate results for rougher surfaces than the Rayleigh-Rice theory and for larger incident and scattered angles than the classical Beckmann-Kirchhoff and the original Harvey-Shack theories. These new developments simplify the analysis and understanding of nonintuitive scattering behavior from rough surfaces illuminated at arbitrary incident angles.

Test of the linear-no threshold theory of radiation carcinogenesis for inhaled radon decay products

International Nuclear Information System (INIS)

Cohen, B.L.

1995-01-01

Data on lung cancer mortality rates vs. average radon concentration in homes for 1,601 U.S. counties are used to test the linear-no threshold theory. The widely recognized problems with ecological studies, as applied to this work, are addressed extensively. With or without corrections for variations in smoking prevalence, there is a strong tendency for lung cancer rates to decrease with increasing radon exposure, in sharp contrast to the increase expected from the theory. The discrepancy in slope is about 20 standard deviations. It is shown that uncertainties in lung cancer rates, radon exposures, and smoking prevalence are not important and that confounding by 54 socioeconomic factors, by geography, and by altitude and climate can explain only a small fraction of the discrepancy. Effects of known radon-smoking prevalence correlations - rural people have higher radon levels and smoke less than urban people, and smokers are exposed to less radon than non-smokers - are calculated and found to be trivial. In spite of extensive efforts, no potential explanation for the discrepancy other than failure of the linear-no threshold theory for carcinogenesis from inhaled radon decay products could be found. (author)

Kinetic Theory of a Confined Quasi-Two-Dimensional Gas of Hard Spheres

Directory of Open Access Journals (Sweden)

J. Javier Brey

2017-02-01

Full Text Available The dynamics of a system of hard spheres enclosed between two parallel plates separated a distance smaller than two particle diameters is described at the level of kinetic theory. The interest focuses on the behavior of the quasi-two-dimensional fluid seen when looking at the system from above or below. In the first part, a collisional model for the effective two-dimensional dynamics is analyzed. Although it is able to describe quite well the homogeneous evolution observed in the experiments, it is shown that it fails to predict the existence of non-equilibrium phase transitions, and in particular, the bimodal regime exhibited by the real system. A critical revision analysis of the model is presented , and as a starting point to get a more accurate description, the Boltzmann equation for the quasi-two-dimensional gas has been derived. In the elastic case, the solutions of the equation verify an H-theorem implying a monotonic tendency to a non-uniform steady state. As an example of application of the kinetic equation, here the evolution equations for the vertical and horizontal temperatures of the system are derived in the homogeneous approximation, and the results compared with molecular dynamics simulation results.

Selected topics in the quantum theory of solids: collective excitations and linear response

International Nuclear Information System (INIS)

Balakrishnan, V.

1977-08-01

This report is based on the lecture notes of a course given at the Department of Physics, Indian Institute of Technology, Madras, during the period January-April 1976 for M.Sc. students. The emphasis is on the concept of elementary excitations in many-body systems, and on the technique of linear response theory. Various topics are covered in 7 sections. The second section following the introductory section is on 'second quantization' and includes discussion on creation and destruction operators, multiparticle states, time-dependent operators etc. Section 3 deals with the 'electron gas' and includes discussion on non-interacting Fermi gas, Coulomb interaction and exchange energy, the two-electron correlation function etc. Section 4 deals with the dielectric response analysis of the electron gas and includes discussion on Coulomb interaction in terms of density fluctuations, self-consistent field dielectric function etc. In section 5 the 'linear response theory' is explained. The Liouville operator, Boltzmann's superposition integral, dispersion relations etc. are explained. Quasiparticles and plasmous are discussed in the Section 6. Section 7 deals with 'lattice dynamics and phonons'. In the last section 8, spin waves are explained. The Heisenberg exchange hamiltonian, Green Function for noninteracting magnons etc. are discussed. (author)

From 6D superconformal field theories to dynamic gauged linear sigma models

Science.gov (United States)

Apruzzi, Fabio; Hassler, Falk; Heckman, Jonathan J.; Melnikov, Ilarion V.

2017-09-01

Compactifications of six-dimensional (6D) superconformal field theories (SCFTs) on four- manifolds generate a large class of novel two-dimensional (2D) quantum field theories. We consider in detail the case of the rank-one simple non-Higgsable cluster 6D SCFTs. On the tensor branch of these theories, the gauge group is simple and there are no matter fields. For compactifications on suitably chosen Kähler surfaces, we present evidence that this provides a method to realize 2D SCFTs with N =(0 ,2 ) supersymmetry. In particular, we find that reduction on the tensor branch of the 6D SCFT yields a description of the same 2D fixed point that is described in the UV by a gauged linear sigma model (GLSM) in which the parameters are promoted to dynamical fields, that is, a "dynamic GLSM" (DGLSM). Consistency of the model requires the DGLSM to be coupled to additional non-Lagrangian sectors obtained from reduction of the antichiral two-form of the 6D theory. These extra sectors include both chiral and antichiral currents, as well as spacetime filling noncritical strings of the 6D theory. For each candidate 2D SCFT, we also extract the left- and right-moving central charges in terms of data of the 6D SCFT and the compactification manifold.

Space-time reactor kinetics for heterogeneous reactor structure

Energy Technology Data Exchange (ETDEWEB)

Raisic, N [Boris Kidric Institute of nuclear sciences Vinca, Belgrade (Yugoslavia)

1969-11-15

An attempt is made to formulate time dependent diffusion equation based on Feinberg-Galanin theory in the from analogue to the classical reactor kinetic equation. Parameters of these equations could be calculated using the existing codes for static reactor calculation based on the heterogeneous reactor theory. The obtained kinetic equation could be analogues in form to the nodal kinetic equation. Space-time distribution of neutron flux in the reactor can be obtained by solving these equations using standard methods.

Hadronic equation of state in the statistical bootstrap model and linear graph theory

International Nuclear Information System (INIS)

Fre, P.; Page, R.

1976-01-01

Taking a statistical mechanical point og view, the statistical bootstrap model is discussed and, from a critical analysis of the bootstrap volume comcept, it is reached a physical ipothesis, which leads immediately to the hadronic equation of state provided by the bootstrap integral equation. In this context also the connection between the statistical bootstrap and the linear graph theory approach to interacting gases is analyzed

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

A KINETIC ALFVEN WAVE AND THE PROTON DISTRIBUTION FUNCTION IN THE FAST SOLAR WIND

International Nuclear Information System (INIS)

Li Xing; Lu Quanming; Chen Yao; Li Bo; Xia Lidong

2010-01-01

Using one-dimensional test particle simulations, the effect of a kinetic Alfven wave on the velocity distribution function (VDF) of protons in the collisionless solar wind is investigated. We first use linear Vlasov theory to numerically obtain the property of a kinetic Alfven wave (the wave propagates in the direction almost perpendicular to the background magnetic field). We then numerically simulate how the wave will shape the proton VDF. It is found that Landau resonance may be able to generate two components in the initially Maxwellian proton VDF: a tenuous beam component along the direction of the background magnetic field and a core component. The streaming speed of the beam relative to the core proton component is about 1.2-1.3 Alfven speed.

A group-kinetic theory of turbulent collective collisions

International Nuclear Information System (INIS)

Tchen, C.M.; Misguich, J.H.

1983-05-01

The main objective is the derivation of the kinetic equation of turbulence which has a memory in the turbulent collision integral. We consider the basic pair-interaction, and the interaction between a fluctuation and the organized cluster of other fluctuations in the collection systems, called the multiple interaction. By a group-scaling procedure, a fluctuation is decomposed into three groups to represent the three coupled transport processes of evolution, transport coefficient, and relaxation. The kinetic equation of the scaled singlet distribution is capable of investigating the spectrum of turbulence without the need of the knowledge of the pair distribution. The exact propagator describes the detailed trajectory in the phase space, and is fundamental to the Lagrangian-Eulerian transformation. We calculate the propagator and its scaled groups by means of a probability of retrograde transition. Thus our derivation of the kinetic equation of the distribution involves a parallel development of the kinetic equations of the propagator and the transition probability. In this way, we can avoid the assumptions of independence and normality. Our result shows that the multiple interaction contributes to a shielding and an enchancement of the collision in weak turbulence and strong turbulence, respectively. The weak turbulence is dominated by the wave resonance, and the strong turbulence is dominated by the diffusion

Li+ solvation and kinetics of Li+-BF4-/PF6- ion pairs in ethylene carbonate. A molecular dynamics study with classical rate theories

Science.gov (United States)

Chang, Tsun-Mei; Dang, Liem X.

2017-10-01

Using our polarizable force-field models and employing classical rate theories of chemical reactions, we examine the ethylene carbonate (EC) exchange process between the first and second solvation shells around Li+ and the dissociation kinetics of ion pairs Li+-[BF4] and Li+-[PF6] in this solvent. We calculate the exchange rates using transition state theory and correct them with transmission coefficients computed by the reactive flux, Impey, Madden, and McDonald approaches, and Grote-Hynes theory. We found that the residence times of EC around Li+ ions varied from 60 to 450 ps, depending on the correction method used. We found that the relaxation times changed significantly from Li+-[BF4] to Li+-[PF6] ion pairs in EC. Our results also show that, in addition to affecting the free energy of dissociation in EC, the anion type also significantly influences the dissociation kinetics of ion pairing.

Chemical kinetics and reaction mechanism

International Nuclear Information System (INIS)

Jung, Ou Sik; Park, Youn Yeol

1996-12-01

This book is about chemical kinetics and reaction mechanism. It consists of eleven chapters, which deal with reaction and reaction speed on reaction mechanism, simple reaction by rate expression, reversible reaction and simultaneous reaction, successive reaction, complicated reaction mechanism, assumption for reaction mechanism, transition state theory, successive reaction and oscillating reaction, reaction by solution, research method high except kinetics on reaction mechanism, high reaction of kinetics like pulsed radiolysis.

Neoclassical kinetic theory near the edge of a diverted tokamak plasma

International Nuclear Information System (INIS)

Solano, E.R.; Hazeltine, R.D.

1993-01-01

In a diverted plasma, the poloidal magnetic field has a strong poloidal variation, approaching zero near the X-point. Typically, neoclassical theory is based on ordering assumptions about the 3 characteristic frequencies present in the problem: streaming, collisions and drift. In a circular geometry, the streaming freuency is constant, while the drift frequency has a sin(θ) variation. In a shaped plasma, the streaming frequency also has a poloidal variation. The ordering is now established by the amplitude of these frequencies. With a model poloidal flux function, the authors solve the drift kinetic equation inside, but near, the separatrix. Both the plateau and collisional regime are considered. Ion rotation rates, and their poloidal variation, are calculated. It is shown that the standard neoclassical rotation predictions still hold, when correctly interpreted. Other neoclassical fluxes are calculated as well

Kinetic theory of magnetic island stability in tokamaks

International Nuclear Information System (INIS)

Zabiego, M.; Garbet, X.

1993-10-01

The non linear behavior of low and large wave number tearing modes is studied. The emphasis is layed on diamagnetic effects. A kinetic equation, including transport processes associated with a background of microturbulence, is used to describe the electron component. Such transport processes are shown to play a significant role in the adjustment of density and temperature profile and also in the calculation of the island rotation frequency. The fluctuating electric potential is calculated self-consistently, using the differential response of electrons and ions. Four regimes are considered, related to island width (smaller or larger than an ion Larmor radius) and transport regime (electron-ion collisions or electro-viscosity dominated). It is shown that diamagnetism does not influence the island stability for small island width in the viscous regime, as long as the constant A constraint is maintained. It turns out that the release of this constraint may strongly modify the previously calculated stability thresholds. Finally, it is found that diamagnetism is destabilizing (stabilizing) for island width smaller (larger) than an ion Larmor radius, in both resistive and viscous regimes. A typical island evolution scenario is studied which shows that even large scale tearing modes with positive Δ ' could saturate to island width of order of a few ion Larmor radii. Illustrative Δ ' threshold and island saturation size are calculated. (authors). 31 refs., 5 figs., 3 tabs

Kinetics of microstructure formation of high-pressure induced gel from a whey protein isolate

International Nuclear Information System (INIS)

He Jinsong; Yang Hongwei; Zhu Wanpeng; Mu Taihua

2010-01-01

The kinetic process of pressure-induced gelation of whey protein isolate (WPI) solutions was studied using in situ light scattering. The relationship of the logarithm of scattered light intensity (I) versus time (t) was linear after the induced time and could be described by the Cahn-Hilliard linear theory. With increasing time, the scattered intensity deviated from the exponential relationship, and the time evolution of the scattered light intensity maximum I m and the corresponding wavenumber q m could be described in terms of the power-law relationship as I m ∼f β and q m ∼f -α , respectively. These results indicated that phase separation occurred during the gelation of WPI solutions under high pressure.

Linear Programming (LP)

International Nuclear Information System (INIS)

Rogner, H.H.

1989-01-01

The submitted sections on linear programming are extracted from 'Theorie und Technik der Planung' (1978) by W. Blaas and P. Henseler and reformulated for presentation at the Workshop. They consider a brief introduction to the theory of linear programming and to some essential aspects of the SIMPLEX solution algorithm for the purposes of economic planning processes. 1 fig

An analogue of Morse theory for planar linear networks and the generalized Steiner problem

International Nuclear Information System (INIS)

Karpunin, G A

2000-01-01

A study is made of the generalized Steiner problem: the problem of finding all the locally minimal networks spanning a given boundary set (terminal set). It is proposed to solve this problem by using an analogue of Morse theory developed here for planar linear networks. The space K of all planar linear networks spanning a given boundary set is constructed. The concept of a critical point and its index is defined for the length function l of a planar linear network. It is shown that locally minimal networks are local minima of l on K and are critical points of index 1. The theorem is proved that the sum of the indices of all the critical points is equal to χ(K)=1. This theorem is used to find estimates for the number of locally minimal networks spanning a given boundary set

Linear optical response of finite systems using multishift linear system solvers

Energy Technology Data Exchange (ETDEWEB)

Hübener, Hannes; Giustino, Feliciano [Department of Materials, University of Oxford, Oxford OX1 3PH (United Kingdom)

2014-07-28

We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.

Airfoil wake and linear theory gust response including sub and superresonant flow conditions

Science.gov (United States)

Henderson, Gregory H.; Fleeter, Sanford

1992-01-01

The unsteady aerodynamic gust response of a high solidity stator vane row is examined in terms of the fundamental gust modeling assumptions with particular attention given to the effects near an acoustic resonance. A series of experiments was performed with gusts generated by rotors comprised of perforated plates and airfoils. It is concluded that, for both the perforated plate and airfoil wake generated gusts, the unsteady pressure responses do not agree with the linear-theory gust predictions near an acoustic resonance. The effects of the acoustic resonance phenomena are clearly evident on the airfoil surface unsteady pressure responses. The transition of the measured lift coefficients across the acoustic resonance from the subresonant regime to the superresonant regime occurs in a simple linear fashion.

Linear and nonlinear stability analysis, associated to experimental fast reactors

International Nuclear Information System (INIS)

Amorim, E.S. do; Moura Neto, C. de; Rosa, M.A.P.

1980-07-01

Phenomena associated to the physics of fast neutrons were analysed by linear and nonlinear Kinetics with arbitrary feedback. The theoretical foundations of linear kinetics and transfer functions aiming at the analysis of fast reactors stability, are established. These stability conditions were analitically proposed and investigated by digital and analogic programs. (E.G.) [pt

Jet energy loss in quark-gluon plasma. Kinetic theory with a Bhatnagar-Gross-Krook collisional kernel

Energy Technology Data Exchange (ETDEWEB)

Han, Cheng; Hou, De-fu; Li, Jia-rong [Central China Normal University, Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Wuhan, Hubei (China); Jiang, Bing-feng [Hubei University for Nationalities, Center for Theoretical Physics and School of Sciences, Enshi, Hubei (China)

2017-10-15

The dielectric functions ε{sub L}, ε{sub T} of the quark-gluon plasma (QGP) are derived within the framework of the kinetic theory with BGK-type collisional kernel. The collision effect manifested by the collision rate is encoded in the dielectric functions. Based on the derived dielectric functions we study the collisional energy loss suffered by a fast parton traveling through the QGP. The numerical results show that the collision rate increases the energy loss. (orig.)

Extension of a Kinetic-Theory Approach for Computing Chemical-Reaction Rates to Reactions with Charged Particles

Science.gov (United States)

Liechty, Derek S.; Lewis, Mark J.

2010-01-01

Recently introduced molecular-level chemistry models that predict equilibrium and nonequilibrium reaction rates using only kinetic theory and fundamental molecular properties (i.e., no macroscopic reaction rate information) are extended to include reactions involving charged particles and electronic energy levels. The proposed extensions include ionization reactions, exothermic associative ionization reactions, endothermic and exothermic charge exchange reactions, and other exchange reactions involving ionized species. The extensions are shown to agree favorably with the measured Arrhenius rates for near-equilibrium conditions.

Evaluation of energy collapsing effect on reactor kinetics parameters by diffusion theory

International Nuclear Information System (INIS)

Unesaki, Hironobu

1989-01-01

Reactor kinetics parameters play an important role as scaling factors between observed and calculated reactivities in the analysis of reactor physics experiments. In this report, energy collapsing errors in two kinetic parameters, the effective delayed neutron fraction and the neutron life time, are investigated by means of the diffusion theory. Coarse group calculations are made for various energy group structures. Cores of various moderator-to-fuel volume ratios are selected to investigate the influence of neutron spectrum changes on the energy collapsing error. The energy collapsing errors in the effective delayed neutron fraction and neutron life time are much larger than those in k eff . This might be because the former two parameters are functions of both the foward and adjoint flux, whereas the latter is a function of the forward flux alone. The use of coarse constants will cause errors in both fluxes, and the resulting errors in the former will be much more emphasized. As the effective delayed neutron fraction is sensitive to the treatment of an energy region in the vicinity of the fission spectrum peak, the coarse group error in it might differ between cores with different enrichment and composition. Inaccurate weighting of group constants leads to neutron spectra which do not conserve the fine group spectra, and those errors will be emphasized in calculated integral parameters. (N.K.)

A theory for the Langmuir waves in the electron foreshock

International Nuclear Information System (INIS)

Cairns, I.H.

1987-01-01

A theory for the Langmuir (L) waves observed in the electron foreshock is suggested. Free energy for the Langmuir wave growth is contained in cutoff distributions of energetic electrons streaming from the bow shock. These cutoff distributions drive Langmuir wave growth primarily by the kinetic version of the beam instability, and wave growth is limited by quasi-linear relaxation. The observed bump-on-tail electron distributions are interpreted as the remnants of cutoff distributions after quasi-linear relaxation has limited the wave growth. Only plausibility arguments for this theory are given since suitable treatments of quasi-linear relaxation are not presently available. However, it is shown that the wave processes L ± S → L' and L ± S → T (where S and T denote ion sound and transverse waves, respectively), refraction in steady-state density structures, diffusion due to interactions with ion sound turbulence, and effects due to wave convection and spatial gradients in the beam velocity, are unable to suppress the beam instability. The theory leads to natural interpretations of the Langmuir electric field waveforms observed and of the decrease in the Langmuir wave electric fields with increasing distance from the foreshock boundary. The theory for the beam instability is reviewed, and previous analytic and numerical treatments of the beam instability are related

Non-linear σ-models and string theories

International Nuclear Information System (INIS)

Sen, A.

1986-10-01

The connection between σ-models and string theories is discussed, as well as how the σ-models can be used as tools to prove various results in string theories. Closed bosonic string theory in the light cone gauge is very briefly introduced. Then, closed bosonic string theory in the presence of massless background fields is discussed. The light cone gauge is used, and it is shown that in order to obtain a Lorentz invariant theory, the string theory in the presence of background fields must be described by a two-dimensional conformally invariant theory. The resulting constraints on the background fields are found to be the equations of motion of the string theory. The analysis is extended to the case of the heterotic string theory and the superstring theory in the presence of the massless background fields. It is then shown how to use these results to obtain nontrivial solutions to the string field equations. Another application of these results is shown, namely to prove that the effective cosmological constant after compactification vanishes as a consequence of the classical equations of motion of the string theory. 34 refs

Derivation of fluid dynamics from kinetic theory with the 14-moment approximation

International Nuclear Information System (INIS)

Denicol, G.S.; Molnar, E.; Niemi, H.; Rischke, D.H.

2012-01-01

We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely many moments of the Boltzmann equation which can serve as equations of motion for the dissipative currents. All resulting equations of motion have the same form, but the transport coefficients are different in each case. (orig.)

Relevance of sampling schemes in light of Ruelle's linear response theory

International Nuclear Information System (INIS)

Lucarini, Valerio; Wouters, Jeroen; Faranda, Davide; Kuna, Tobias

2012-01-01

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We first show that using a general functional decomposition for space–time dependent forcings, we can define elementary susceptibilities that allow us to construct the linear response of the system to general perturbations. Starting from the definition of SRB measure, we then study the consequence of taking different sampling schemes for analysing the response of the system. We show that only a specific choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows us to obtain the formula first presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be fine-tuned to make the definition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analysing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick

Reaction mechanisms and kinetics of the elimination processes of 2-chloroethylsilane and derivatives: A DFT study using CTST, RRKM, and BET theories

Science.gov (United States)

Shiroudi, Abolfazl; Zahedi, Ehsan; Oliaey, Ahmad Reza; Deleuze, Michael S.

2017-03-01

The thermal decomposition kinetics of 2-chloroethylsilane and derivatives in the gas phase has been studied computationally using density functional theory, along with various exchange-correlation functionals (UM06-2x and ωB97XD) and the aug-cc-pVTZ basis set. The calculated energy profile has been supplemented with calculations of kinetic rate constants under atmospheric pressure and in the fall-off regime, using transition state theory (TST) and statistical Rice-Ramsperger-Kassel-Marcus (RRKM) theory. Activation energies and rate constants obtained using the UM06-2x/aug-cc-pVTZ approach are in good agreement with the experimental data. The decomposition of 2-chloroethyltriethylsilane species into the related products [C2H4 + Et3SiCl] is characterized by 6 successive structural stability domains associated to the sequence of catastrophes C8H19SiCl: 6-C†FCC†[FF]-0: C6H15SiCl + C2H4. Breaking of Si-C bonds and formation of Si-Cl bonds occur in the vicinity of the transition state.

Kinetic parameters for source driven systems

International Nuclear Information System (INIS)

Dulla, S.; Ravetto, P.; Carta, M.; D'Angelo, A.

2006-01-01

The definition of the characteristic kinetic parameters of a subcritical source-driven system constitutes an interesting problem in reactor physics with important consequences for practical applications. Consistent and physically meaningful values of the parameters allow to obtain accurate results from kinetic simulation tools and to correctly interpret kinetic experiments. For subcritical systems a preliminary problem arises for the adoption of a suitable weighting function to be used in the projection procedure to derive a point model. The present work illustrates a consistent factorization-projection procedure which leads to the definition of the kinetic parameters in a straightforward manner. The reactivity term is introduced coherently with the generalized perturbation theory applied to the source multiplication factor ks, which is thus given a physical role in the kinetic model. The effective prompt lifetime is introduced on the assumption that a neutron generation can be initiated by both the fission process and the source emission. Results are presented for simplified configurations to fully comprehend the physical features and for a more complicated highly decoupled system treated in transport theory. (authors)

Foundations of linear and generalized linear models

CERN Document Server

Agresti, Alan

2015-01-01

A valuable overview of the most important ideas and results in statistical analysis Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linear statistical models. The book presents a broad, in-depth overview of the most commonly used statistical models by discussing the theory underlying the models, R software applications, and examples with crafted models to elucidate key ideas and promote practical model building. The book begins by illustrating the fundamentals of linear models,

Non-linear gauge transformations in D=10 SYM theory and the BCJ duality

Energy Technology Data Exchange (ETDEWEB)

Lee, Seungjin [Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut,14476 Potsdam (Germany); Mafra, Carlos R. [Institute for Advanced Study, School of Natural Sciences,Einstein Drive, Princeton, NJ 08540 (United States); DAMTP, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Schlotterer, Oliver [Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut,14476 Potsdam (Germany)

2016-03-14

Recent progress on scattering amplitudes in super Yang-Mills and superstring theory benefitted from the use of multiparticle superfields. They universally capture tree-level subdiagrams, and their generating series solve the non-linear equations of ten-dimensional super Yang-Mills. We provide simplified recursions for multiparticle superfields and relate them to earlier representations through non-linear gauge transformations of their generating series. Moreover, we discuss the gauge transformations which enforce their Lie symmetries as suggested by the Bern-Carrasco-Johansson duality between color and kinematics. Another gauge transformation due to Harnad and Shnider is shown to streamline the theta-expansion of multiparticle superfields, bypassing the need to use their recursion relations beyond the lowest components. The findings of this work tremendously simplify the component extraction from kinematic factors in pure spinor superspace.

Selected readings in chemical kinetics

CERN Document Server

Back, Margaret H

2013-01-01

Selected Readings in Chemical Kinetics covers excerpts from 12 papers in the field of general and gas-phase kinetics. The book discusses papers on the laws of connexion between the conditions of a chemical change and its amount; on the reaction velocity of the inversion of the cane sugar by acids; and the calculation in absolute measure of velocity constants and equilibrium constants in gaseous systems. The text then tackles papers on simple gas reactions; on the absolute rate of reactions in condensed phases; on the radiation theory of chemical action; and on the theory of unimolecular reacti

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

Science.gov (United States)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

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

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

International Nuclear Information System (INIS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-01-01

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. (paper)

Theory of First Order Chemical Kinetics at the Critical Point of Solution.

Science.gov (United States)

Baird, James K; Lang, Joshua R

2017-10-26

Liquid mixtures, which have a phase diagram exhibiting a miscibility gap ending in a critical point of solution, have been used as solvents for chemical reactions. The reaction rate in the forward direction has often been observed to slow down as a function of temperature in the critical region. Theories based upon the Gibbs free energy of reaction as the driving force for chemical change have been invoked to explain this behavior. With the assumption that the reaction is proceeding under relaxation conditions, these theories expand the free energy in a Taylor series about the position of equilibrium. Since the free energy is zero at equilibrium, the leading term in the Taylor series is proportional to the first derivative of the free energy with respect to the extent of reaction. To analyze the critical behavior of this derivative, the theories exploit the principle of critical point isomorphism, which is thought to govern all critical phenomena. They find that the derivative goes to zero in the critical region, which accounts for the slowing down observed in the reaction rate. As has been pointed out, however, most experimental rate investigations have been carried out under irreversible conditions as opposed to relaxation conditions [Shen et al. J. Phys. Chem. A 2015, 119, 8784-8791]. Below, we consider a reaction governed by first order kinetics and invoke transition state theory to take into account the irreversible conditions. We express the apparent activation energy in terms of thermodynamic derivatives evaluated under standard conditions as well as the pseudoequilibrium conditions associated with the reactant and the activated complex. We show that these derivatives approach infinity in the critical region. The apparent activation energy follows this behavior, and its divergence accounts for the slowing down of the reaction rate.

Scalar-tensor linear inflation

Energy Technology Data Exchange (ETDEWEB)

Artymowski, Michał [Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków (Poland); Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee [National Institute of Chemical Physics and Biophysics, Rävala 10, 10143 Tallinn (Estonia)

2017-04-01

We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.

Simplified non-linear time-history analysis based on the Theory of Plasticity

DEFF Research Database (Denmark)

Costa, Joao Domingues

2005-01-01

This paper aims at giving a contribution to the problem of developing simplified non-linear time-history (NLTH) analysis of structures which dynamical response is mainly governed by plastic deformations, able to provide designers with sufficiently accurate results. The method to be presented...... is based on the Theory of Plasticity. Firstly, the formulation and the computational procedure to perform time-history analysis of a rigid-plastic single degree of freedom (SDOF) system are presented. The necessary conditions for the method to incorporate pinching as well as strength degradation...

A modification to linearized theory for prediction of pressure loadings on lifting surfaces at high supersonic Mach numbers and large angles of attack

Science.gov (United States)

Carlson, H. W.

1979-01-01

A new linearized-theory pressure-coefficient formulation was studied. The new formulation is intended to provide more accurate estimates of detailed pressure loadings for improved stability analysis and for analysis of critical structural design conditions. The approach is based on the use of oblique-shock and Prandtl-Meyer expansion relationships for accurate representation of the variation of pressures with surface slopes in two-dimensional flow and linearized-theory perturbation velocities for evaluation of local three-dimensional aerodynamic interference effects. The applicability and limitations of the modification to linearized theory are illustrated through comparisons with experimental pressure distributions for delta wings covering a Mach number range from 1.45 to 4.60 and angles of attack from 0 to 25 degrees.

The fully relativistic foundation of linear transfer theory in electron optics based on the Dirac equation

NARCIS (Netherlands)

Ferwerda, H.A.; Hoenders, B.J.; Slump, C.H.

The fully relativistic quantum mechanical treatment of paraxial electron-optical image formation initiated in the previous paper (this issue) is worked out and leads to a rigorous foundation of the linear transfer theory. Moreover, the status of the relativistic scaling laws for mass and wavelength,

A kinetic-theory approach for computing chemical-reaction rates in upper-atmosphere hypersonic flows.