A relativistic correlationless kinetic equation with radiation reaction fully incorporated
Lai, H. M.
1984-06-01
The Landau-Lifshitz expression for the Lorentz-Dirac equation is used to derive a relativistic correlationless kinetic equation for a system of electrons with radiation reaction fully incorporated. Various situations and possible applications are discussed.
The heat flux from a relativistic kinetic equation with a simplified collision kernel
Sandoval-Villalbazo, A; García-Colin, L S
2009-01-01
We show how using a special relativistic kinetic equation with a BGK- like collision operator the ensuing expression for the heat flux can be casted in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so-called "first order in the gradients theories" contend. Here we calculate explicitly the ensuing transport coefficients and compare them with the results obtained by other authors.
PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY
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.
Berry curvature and four-dimensional monopoles in the relativistic chiral kinetic equation.
Chen, Jiunn-Wei; Pu, Shi; Wang, Qun; Wang, Xin-Nian
2013-06-28
We derive a relativistic chiral kinetic equation with manifest Lorentz covariance from Wigner functions of spin-1/2 massless fermions in a constant background electromagnetic field. It contains vorticity terms and a four-dimensional Euclidean Berry monopole which gives an axial anomaly. By integrating out the zeroth component of the 4-momentum p, we reproduce the previous three-dimensional results derived from the Hamiltonian approach, together with the newly derived vorticity terms. The phase space continuity equation has an anomalous source term proportional to the product of electric and magnetic fields (FσρF[over ˜]σρ∼EσBσ). This provides a unified interpretation of the chiral magnetic and vortical effects, chiral anomaly, Berry curvature, and the Berry monopole in the framework of Wigner functions.
Relativistic Guiding Center Equations
White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
Relativistic and non-relativistic geodesic equations
Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
Relativistic Langevin equation for runaway electrons
Mier, J. A.; Martin-Solis, J. R.; Sanchez, R.
2016-10-01
The Langevin approach to the kinetics of a collisional plasma is developed for relativistic electrons such as runaway electrons in tokamak plasmas. In this work, we consider Coulomb collisions between very fast, relativistic electrons and a relatively cool, thermal background plasma. The model is developed using the stochastic equivalence of the Fokker-Planck and Langevin equations. The resulting Langevin model equation for relativistic electrons is an stochastic differential equation, amenable to numerical simulations by means of Monte-Carlo type codes. Results of the simulations will be presented and compared with the non-relativistic Langevin equation for RE electrons used in the past. Supported by MINECO (Spain), Projects ENE2012-31753, ENE2015-66444-R.
Decker, J.; Peysson, Y
2004-12-01
A new original code for solving the 3-D relativistic and bounce-averaged electron drift kinetic equation is presented. It designed for the current drive problem in tokamak with an arbitrary magnetic equilibrium. This tool allows self-consistent calculations of the bootstrap current in presence of other external current sources. RF current drive for arbitrary type of waves may be used. Several moments of the electron distribution function are determined, like the exact and effective fractions of trapped electrons, the plasma current, absorbed RF power, runaway and magnetic ripple loss rates and non-thermal Bremsstrahlung. Advanced numerical techniques have been used to make it the first fully implicit (reverse time) 3-D solver, particularly well designed for implementation in a chain of code for realistic current drive calculations in high {beta}{sub p} plasmas. All the details of the physics background and the numerical scheme are presented, as well a some examples to illustrate main code capabilities. Several important numerical points are addressed concerning code stability and potential numerical and physical limitations. (authors)
Relativistic and Non-relativistic Equations of Motion
Mangiarotti, L
1998-01-01
It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied.
Abada, A; Zhuang, P; Heinz, Ulrich W; Abada, Abdellatif; Birse, Michael C; Zhuang, Pengfei; Heinz, Ulrich
1996-01-01
It is found that the extra quantum constraints to the spinor components of the equal-time Wigner function given in a recent paper by Zhuang and Heinz should vanish identically. We point out here the origin of the error and give an interpretation of the result. However, the principal idea of obtaining a complete equal-time transport theory by energy averaging the covariant theory remains valid. The classical transport equation for the spin density is also found to be incorrect. We give here the correct form of that equation and discuss briefly its structure.
Relativistic Kinetic Theory: An Introduction
Sarbach, Olivier
2013-01-01
We present a brief introduction to the relativistic kinetic theory of gases with emphasis on the underlying geometric and Hamiltonian structure of the theory. Our formalism starts with a discussion on the tangent bundle of a Lorentzian manifold of arbitrary dimension. Next, we introduce the Poincare one-form on this bundle, from which the symplectic form and a volume form are constructed. Then, we define an appropriate Hamiltonian on the bundle which, together with the symplectic form yields the Liouville vector field. The corresponding flow, when projected onto the base manifold, generates geodesic motion. Whenever the flow is restricted to energy surfaces corresponding to a negative value of the Hamiltonian, its projection describes a family of future-directed timelike geodesics. A collisionless gas is described by a distribution function on such an energy surface, satisfying the Liouville equation. Fibre integrals of the distribution function determine the particle current density and the stress-energy ten...
Relativistic kinetic theory with applications in astrophysics and cosmology
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...
Solutions of relativistic radial quasipotential equations
Minh, V.X.; Kadyshevskii, V.G.; Zhidkov, E.P.
1985-11-01
A systematic approach to the investigation of relativistic radial quasipotential equations is developed. The quasipotential equations can be interpreted either as linear equations in finite differences of fourth and second orders, respectively, or as differential equations of infinite order.
Relativistic effects and quasipotential equations
Ramalho, G; Peña, M T
2002-01-01
We compare the scattering amplitude resulting from the several quasipotential equations for scalar particles. We consider the Blankenbecler-Sugar, Spectator, Thompson, Erkelenz-Holinde and Equal-Time equations, which were solved numerically without decomposition into partial waves. We analyze both negative-energy state components of the propagators and retardation effects. We found that the scattering solutions of the Spectator and the Equal-Time equations are very close to the nonrelativistic solution even at high energies. The overall relativistic effect increases with the energy. The width of the band for the relative uncertainty in the real part of the scattering $T$ matrix, due to different dynamical equations, is largest for backward-scattering angles where it can be as large as 40%.
Lattice Boltzmann equation for relativistic quantum mechanics.
Succi, Sauro
2002-03-15
Relativistic versions of the quantum lattice Boltzmann equation are discussed. It is shown that the inclusion of nonlinear interactions requires the standard collision operator to be replaced by a pair of dynamic fields coupling to the relativistic wave function in a way which can be described by a multicomponent complex lattice Boltzmann equation.
Bruce, Adam L
2015-01-01
We show the traditional rocket problem, where the ejecta velocity is assumed constant, can be reduced to an integral quadrature of which the completely non-relativistic equation of Tsiolkovsky, as well as the fully relativistic equation derived by Ackeret, are limiting cases. By expanding this quadrature in series, it is shown explicitly how relativistic corrections to the mass ratio equation as the rocket transitions from the Newtonian to the relativistic regime can be represented as products of exponential functions of the rocket velocity, ejecta velocity, and the speed of light. We find that even low order correction products approximate the traditional relativistic equation to a high accuracy in flight regimes up to $0.5c$ while retaining a clear distinction between the non-relativistic base-case and relativistic corrections. We furthermore use the results developed to consider the case where the rocket is not moving relativistically but the ejecta stream is, and where the ejecta stream is massless.
General relativistic Boltzmann equation, I: Covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
This series of two articles aims at dissipating the rather dense haze existing in the present literature around the General Relativistic Boltzmann equation. In this first article, the general relativistic one-particle distribution function in phase space is defined as an average of delta functions.
Kinetic equations: computation
Pareschi, Lorenzo
2013-01-01
Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity.
Relativistic Kinetic-Balance Condition for Explicitly Correlated Basis Functions
Simmen, Benjamin; Reiher, Markus
2015-01-01
This paper presents the derivation of a kinetic-balance condition for explicitly correlated basis functions employed in semi-classical relativistic calculations. Such a condition is important to ensure variational stability in algorithms based on the first-quantized Dirac theory of 1/2-fermions. We demonstrate that the kinetic-balance condition can be obtained from the row reduction process commonly applied to solve systems of linear equations. The resulting form of kinetic balance establishes a relation for the $4^N$ components of the spinor of an $N$-fermion system to the non-relativistic limit, which is in accordance with recent developments in the field of exact decoupling in relativistic orbital-based many-electron theory.
Relativistic diffusion equation from stochastic quantization
Kazinski, P O
2007-01-01
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck constant). We apply this method to the models of nonrelativistic and relativistic particles interacting with an electromagnetic field. In the first case we establish the equivalence of such a quantization to the Fokker-Planck equation with a special force. The application of the proposed quantization procedure to the model of a relativistic particle results in a relativistic generalization of the Fokker-Planck equation in the coordinate space, which in the absence of the electromagnetic field reduces to the relativistic diffusion (heat) equation. The stationary probability distribution functions for a stochastically quantized particle diffusing under a barrier and a particle in the potential of a harmonic oscillator are derived.
Relativistic wave equations: an operational approach
Dattoli, G.; Sabia, E.; Górska, K.; Horzela, A.; Penson, K. A.
2015-03-01
The use of operator methods of an algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential equations, such as relativistic Schrödinger, Klein-Gordon, and Dirac. We discuss the free-particle hypotheses and those relevant to particles subject to non-trivial potentials. In the latter case we will show how the proposed method leads to easily implementable numerical algorithms.
Kinetic energy equations for the average-passage equation system
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Kinetic energy equations for the average-passage equation system
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
BIRKHOFF'S EQUATIONS AND GEOMETRICAL THEORY OF ROTATIONAL RELATIVISTIC SYSTEM
LUO SHAO-KAI; CHEN XIANG-WEI; FU JING-LI
2001-01-01
The Birkhoffian and Birkhoff's functions of a rotational relativistic system are constructed, the Pfaff action of rotational relativistic system is defined, the Pfaff-Birkhoff principle of a rotational relativistic system is given, and the Pfaff-Birkhoff-D'Alembert principles and Birkhoff's equations of rotational relativistic system are constructed. The geometrical description of a rotational relativistic system is studied, and the exact properties of Birkhoff's equations and their forms onR × T*M for a rotational relativistic system are obtained. The global analysis of Birkhoff's equations for a rotational relativistic system is studied, the global properties of autonomous, semi-autonomous and non-autonomous rotational relativistic Birkhoff's equations, and the geometrical properties of energy change for rotational relativistic Birkhoff's equations are given.
Minimal relativistic three-particle equations
Lindesay, J.
1981-07-01
A minimal self-consistent set of covariant and unitary three-particle equations is presented. Numerical results are obtained for three-particle bound states, elastic scattering and rearrangement of bound pairs with a third particle, and amplitudes for breakup into states of three free particles. The mathematical form of the three-particle bound state equations is explored; constraints are set upon the range of eigenvalues and number of eigenstates of these one parameter equations. The behavior of the number of eigenstates as the two-body binding energy decreases to zero in a covariant context generalizes results previously obtained non-relativistically by V. Efimov.
Arzeliès, Henri
1972-01-01
Relativistic Point Dynamics focuses on the principles of relativistic dynamics. The book first discusses fundamental equations. The impulse postulate and its consequences and the kinetic energy theorem are then explained. The text also touches on the transformation of main quantities and relativistic decomposition of force, and then discusses fields of force derivable from scalar potentials; fields of force derivable from a scalar potential and a vector potential; and equations of motion. Other concerns include equations for fields; transfer of the equations obtained by variational methods int
LOCAL CLASSICAL SOLUTIONS TO THE EQUATIONS OF RELATIVISTIC HYDRODYNAMICS
史一蓬
2001-01-01
In this paper, we prove that the convexity of the negative thermodynamical entropy of the equations of relativistic hydrodynamics for ideal gas keeps its invariance under the Lorentz transformation if and only if the local sound speed is less than the light speed in vacuum. Then a symmetric form for the equations of relativistic hydrodynamics is presented and the local classical solution is obtained. Based on this,we prove that the nonrelativistic limit of the local classical solution to the relativistic hydrodynamics equations for relativistic gas is the local classical solution of the Euler equations for polytropic gas.
Relativistic bound-state equations for fermions with instantaneous interactions
Suttorp, L.G.
1979-01-01
Three types of relativistic bound-state equations for a fermion pair with instantaneous interaction are studied, viz., the instantaneous Bethe-Salpeter equation, the quasi-potential equation, and the two-particle Dirac equation. General forms for the equations describing bound states with arbitrary
On the microscopic nature of dissipative effects in special relativistic kinetic theory
Garcia-Perciante, A L; Garcia-Colin, L S
2010-01-01
A microscopic formulation of the definition of both the heat flux and the viscous stress tensor is proposed in the framework of kinetic theory for relativistic gases emphasizing on the physical nature of such fluxes. A Lorentz transformation is introduced as the link between the laboratory and local comoving frames and thus between molecular and chaotic velocities. With such transformation, the dissipative effects can be identified as the averages of the chaotic kinetic energy and the momentum flux out of equilibrium, respectively. Within this framework, a kinetic foundation of the ensuing transport equations for the relativistic gas is achieved. To our knowledge, this result is completely novel.
Balance equations in semi-relativistic quantum hydrodynamics
Ivanov, A Yu; Kuz'menkov, L S
2014-01-01
Method of the quantum hydrodynamics has been applied in quantum plasmas studies. As the first step in our consideration, derivation of classical semi-relativistic (i. e. described by the Darwin Lagrangian on microscopic level) hydrodynamical equations is given after a brief review of method development. It provides better distinguishing between classic and quantum semi-relativistic effects. Derivation of the classical equations is interesting since it is made by a natural, but not very widespread method. This derivation contains explicit averaging of the microscopic dynamics. Derivation of corresponding quantum hydrodynamic equations is presented further. Equations are obtained in the five-momentum approximation including the continuity equation, Euler and energy balance equations. It is shown that relativistic corrections lead to presence of new quantum terms in expressions for a force field, a work field etc. The semi-relativistic generalization of the quantum Bohm potential is obtained. Quantum part of the...
Time-dependent closure relations for relativistic collisionless fluid equations.
Bendib-Kalache, K; Bendib, A; El Hadj, K Mohammed
2010-11-01
Linear fluid equations for relativistic and collisionless plasmas are derived. Closure relations for the fluid equations are analytically computed from the relativistic Vlasov equation in the Fourier space (ω,k), where ω and k are the conjugate variables of time t and space x variables, respectively. The mathematical method used is based on the projection operator techniques and the continued fraction mathematical tools. The generalized heat flux and stress tensor are calculated for arbitrary parameter ω/kc where c is the speed of light, and for arbitrary relativistic parameter z=mc²/T , where m is the particle rest mass and T, the plasma temperature in energy units.
Relativistic wave equation for hypothetic composite quarks
Krolikowski, W. [Institute of Theoretical Physics, Warsaw University, Warsaw (Poland)
1997-05-01
A two-body wave equation is derived, corresponding to the hypothesis (discussed already in the past) that u and d current quarks are relativistic bound states of a spin-1/2 preon existing in two weak flavors and three colors, and a spin-0 preon with no weak flavor nor color, held together by a new strong but Abelian, vectorlike gauge force. Some non-conventional (though somewhat nostalgic) consequences of this strong Abelian binding within composite quarks are pointed out. Among them are: new tiny magnetic-type moments of quarks (and nucleons) and new isomeric nucleon states possibly excitable at some high energies. The letter may arise through a rearrangement mechanism for quark preons inside nucleons. In the interaction q (anti)q{yields}q (anti)q of preon-composite quarks, beside the color forces, there act additional exchange forces corresponding to diagrams analogical to the so called dual diagrams for the interaction {pi}{pi}{yields}{pi}{pi} of quark-composite pions. (author)
Equations of motion in relativistic gravity
Lämmerzahl, Claus; Schutz, Bernard
2015-01-01
The present volume aims to be a comprehensive survey on the derivation of the equations of motion, both in General Relativity as well as in alternative gravity theories. The topics covered range from the description of test bodies, to self-gravitating (heavy) bodies, to current and future observations. Emphasis is put on the coverage of various approximation methods (e.g., multipolar, post-Newtonian, self-force methods) which are extensively used in the context of the relativistic problem of motion. Applications discussed in this volume range from the motion of binary systems -- and the gravitational waves emitted by such systems -- to observations of the galactic center. In particular the impact of choices at a fundamental theoretical level on the interpretation of experiments is highlighted. This book provides a broad and up-do-date status report, which will not only be of value for the experts working in this field, but also may serve as a guideline for students with background in General Relativity who ...
Equations of motion for a relativistic wave packet
L Kocis
2012-05-01
The time derivative of the position of a relativistic wave packet is evaluated. It is found that it is equal to the mean value of the momentum of the wave packet divided by the mass of the particle. The equation derived represents a relativistic version of the second Ehrenfest theorem.
Kinetic approach to a relativistic Bose-Einstein condensate
Meistrenko, Alex; Zhou, Kai; Greiner, Carsten
2015-01-01
We apply a Boltzmann approach to the kinetic regime of a relativistic Bose-Einstein condensate of scalar bosons by decomposing the one-particle distribution function in a condensate part and a non-zero momentum part of excited modes, leading to a coupled set of evolution equations which are then solved efficiently with an adaptive higher order Runge-Kutta scheme. We compare our results to the partonic cascade Monte-Carlo simulation BAMPS for an underpopulated but far from equilibrium case of massless bosons. Motivated by the color glass condensate initial conditions in QCD with a strongly overpopulated initial glasma state, we also discuss the time evolution starting from an overpopulated initial distribution function of massive scalar bosons.
Non-Relativistic Limit of the Dirac Equation
Ajaib, Muhammad Adeel
2016-01-01
We show that the first order form of the Schrodinger equation proposed in [1] can be obtained from the Dirac equation in the non-relativistic limit. We also show that the Pauli Hamiltonian is obtained from this equation by requiring local gauge invariance. In addition, we study the problem of a spin up particle incident on a finite potential barrier and show that the known quantum mechanical results are obtained. Finally, we consider the symmetric potential well and show that the quantum mechanical expression for the quantized energy levels of a particle is obtained with periodic boundary conditions. Based on these conclusions, we propose that the equation introduced in [1] is the non-relativistic limit of the Dirac equation and more appropriately describes spin 1/2 particles in the non-relativistic limit.
Generalized Relativistic Chapman-Enskog Solution of the Boltzmann Equation
García-Perciante, A L; García-Colin, L S
2007-01-01
The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to the thermodynamic force in its first order solution. Both existence and uniqueness of such a solution are proved based on the standard theory of integral equations. The mathematical implications of the generalization here introduced are briefly explored.
Relativistic Spinning Particle without Grassmann Variables and the Dirac Equation
A. A. Deriglazov
2011-01-01
Full Text Available We present the relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Classical dynamics of the model is in correspondence with the dynamics of mean values of the corresponding operators in the Dirac theory. Classical equations for the spin tensor are the same as those of the Barut-Zanghi model of spinning particle.
Some Aspects of Extended Kinetic Equation
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.
On numerical relativistic hydrodynamics and barotropic equations of state
Ibáñez, José María; Miralles, Juan Antornio
2012-01-01
The characteristic formulation of the relativistic hydrodynamic equations (Donat et al 1998 J. Comput. Phys. 146 58), which has been implemented in many relativistic hydro-codes that make use of Godunov-type methods, has to be slightly modified in the case of evolving barotropic flows. For a barotropic equation of state, a removable singularity appears in one of the eigenvectors. The singularity can be avoided by means of a simple renormalization which makes the system of eigenvectors well defined and complete. An alternative strategy for the particular case of barotropic flows is discussed.
KINETIC BALANCE IN CONTRACTED BASIS-SETS FOR RELATIVISTIC CALCULATIONS
VISSCHER, L; AERTS, PJC; VISSER, O; NIEUWPOORT, WC
1991-01-01
A demonstration of kinetic balance failure in heavily contracted basis sets is given. Other possible methods of constructing small component basis sets for 4-component relativistic calculations are discussed. The position of the additional negative energy levels in extended balance calculations in s
Mass, Momentum and Kinetic Energy of a Relativistic Particle
Zanchini, Enzo
2010-01-01
A rigorous definition of mass in special relativity, proposed in a recent paper, is recalled and employed to obtain simple and rigorous deductions of the expressions of momentum and kinetic energy for a relativistic particle. The whole logical framework appears as the natural extension of the classical one. Only the first, second and third laws of…
General relativistic Boltzmann equation, II: Manifestly covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann equati
Derivation of relativistic wave equation from the Poisson process
Tomoshige Kudo; Ichiro Ohba
2002-08-01
A Poisson process is one of the fundamental descriptions for relativistic particles: both fermions and bosons. A generalized linear photon wave equation in dispersive and homogeneous medium with dissipation is derived using the formulation of the Poisson process. This formulation provides a possible interpretation of the passage time of a photon moving in the medium, which never exceeds the speed of light in vacuum.
General relativistic Boltzmann equation, II: Manifestly covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann
General Relativistic Transfer Equation on a Kerr Black Hole
Zannias, T.
1998-12-01
The general relativistic transfer equation describing the interaction of a massless gas with a hot plasma is analyzed on the background of a Kerr black hole. On physical grounds we single out two natural orthonormal frames relative to which the radiative transfer equation takes its simplest form. First the field of the local rest frame defined by the plasma and secondly the local rest frame associated with Bardeens-ZAMOS observers. Applications of the formalism to accretion problems will also briefly discussed.
Relativistic Brownian motion: from a microscopic binary collision model to the Langevin equation.
Dunkel, Jörn; Hänggi, Peter
2006-11-01
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy pointlike Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, nonrelativistic LE is deduced from this model, by taking into account the nonrelativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still delta correlated (white noise) but no longer corresponds to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.
Estakhr, Ahmad Reza
2016-10-01
DJ̲μ/Dτ =J̲ν ∂νU̲μ + ∂νT̲μν +Γαβμ J̲αU̲β ︷ Steady Component + ∂νRμν +Γαβμ Rαβ ︷ Perturbations EAMG equations are proper time-averaged equations of relativistic motion for fluid flow and used to describe Relativistic Turbulent Flows. The EAMG equations are used to describe Relativistic Jet.
Relativistic five-quark equations and u, d- pentaquark spectroscopy
Gerasyuta, S M
2003-01-01
The relativistic five-quark equations are found in the framework of the dispersion relation technique. The five-quark amplitudes for the low-lying pentaquarks including u, d quarks are calculated. The poles of the five-quark amplitudes determine the masses of the lowest pentaquarks. The calculation of pentaquark amplitudes estimates the contributions of four subamplitudes. The main contributions to the pentaquark amplitude are determined by the subamplitudes, which include the meson states M.
Generalized Bloch-Wangsness-Redfield Kinetic Equations
Fatkullin, Nail
2011-01-01
We present a compact and general derivation of the generalized Bloch-Wangsness-Redfield kinetic equations for systems with the static spin Hamiltonian utilizing the concept of the Liouville space. We show that the assumptions of short correlation times and large heat capacity of the lattice are sufficient to derive the kinetic equations without the use of perturbation theory for the spin-lattice interaction operator. The perturbation theory is only applied for calculation of the kinetic coeff...
Relativistic Lagrangians for the Lorentz–Dirac equation
Deguchi, Shinichi, E-mail: deguchi@phys.cst.nihon-u.ac.jp [Institute of Quantum Science, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan); Nakano, Kunihiko [Institute of Quantum Science, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan); Suzuki, Takafumi [Junior College Funabashi Campus, Nihon University, Narashinodai, Funabashi, Chiba 274-8501 (Japan)
2015-09-15
We present two types of relativistic Lagrangians for the Lorentz–Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends on the world-line parameter. Another Lagrangian includes additional cross-terms consisting of auxiliary dynamical variables and does not depend explicitly on the world-line parameter. We demonstrate that both the Lagrangians actually yield the Lorentz–Dirac equation with a source-like term.
Generalized Relativistic Wave Equations with Intrinsic Maximum Momentum
Ching, Chee Leong
2013-01-01
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential are stronger than vector potential. The energy spectrum of the systems studied are bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.
Generalized relativistic wave equations with intrinsic maximum momentum
Ching, Chee Leong; Ng, Wei Khim
2014-05-01
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.
Relativistic five-quark equations and hybrid baryon spectroscopy
Gerasyuta, S M
2002-01-01
The relativistic five-quark equations are found in the framework of the dispersion relation technique. The Behavior of the low-energy five-particle amplitude is determined by its leading singularities in the pair invariant masses. The solutions of these equations using the method based on the extraction leading singularities of the amplitudes are obtained. The mass spectra of nucleon and delta-isobar hybrid baryons are calculated. The calculations of hybrid baryon amplitudes estimate the contributions of four subamplitudes. The main contributions to the hybrid baryon amplitude are determined by the subamplitudes, which include the excited gluon states.
Relativistic (Dirac equation) effects in microscopic elastic scattering calculations
Hynes, M. V.; Picklesimer, A.; Tandy, P. C.; Thaler, R. M.
1985-04-01
A simple relativistic extension of the first-order multiple scattering mechanism for the optical potential is employed within the context of a Dirac equation description of elastic nucleon-nucleus scattering. A formulation of this problem in terms of a momentum-space integral equation displaying an identifiable nonrelativistic sector is described and applied. Extensive calculations are presented for proton scattering from 40Ca and 16O at energies between 100 and 500 MeV. Effects arising from the relativistic description of the propagation of the projectile are isolated and are shown to be responsible for most of the departures from typical nonrelativistic (Schrödinger) results. Off-shell and nonlocal effects are included and these, together with uncertainties in the nuclear densities, are shown not to compromise the characteristic improvement of forward angle spin observable predictions provided by the relativistic approach. The sensitivity to ambiguities in the Lorentz scalar and vector composition of the optical potential is displayed and discussed.
Relativistic (Dirac equation) effects in microscopic elastic scattering calculations
Hynes, M.V.; Picklesimer, A.; Tandy, P.C.; Thaler, R.M.
1985-04-01
A simple relativistic extension of the first-order multiple scattering mechanism for the optical potential is employed within the context of a Dirac equation description of elastic nucleon-nucleus scattering. A formulation of this problem in terms of a momentum-space integral equation displaying an identifiable nonrelativistic sector is described and applied. Extensive calculations are presented for proton scattering from /sup 40/Ca and /sup 16/O at energies between 100 and 500 MeV. Effects arising from the relativistic description of the propagation of the projectile are isolated and are shown to be responsible for most of the departures from typical nonrelativistic (Schroedinger) results. Off-shell and nonlocal effects are included and these, together with uncertainties in the nuclear densities, are shown not to compromise the characteristic improvement of forward angle spin observable predictions provided by the relativistic approach. The sensitivity to ambiguities in the Lorentz scalar and vector composition of the optical potential is displayed and discussed.
Equation of State in a Generalized Relativistic Density Functional Approach
Typel, Stefan
2015-01-01
The basic concepts of a generalized relativistic density functional approach to the equation of state of dense matter are presented. The model is an extension of relativistic mean-field models with density-dependent couplings. It includes explicit cluster degrees of freedom. The formation and dissolution of nuclei is described with the help of mass shifts. The model can be adapted to the description of finite nuclei in order to study the effect of $\\alpha$-particle correlations at the nuclear surface on the neutron skin thickness of heavy nuclei. Further extensions of the model to include quark degrees of freedom or an energy dependence of the nucleon self-energies are outlined.
Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations.
Muhammad Yousaf
Full Text Available The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD. Such models are more complicated than the non-relativistic ones due to the nonlinear relations between the conserved and state variables. A high-resolution shock-capturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCL-type initial reconstruction and Runge-Kutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and two-dimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic flux-vector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic two-dimensional test problems.
Rębilas, Krzysztof
2014-01-01
Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion $\\vec{F}=d\\vec{p}/dt$, where $\\vec{p}$ is the relativistic momentum. The relativistic momentum is then derived without referring to any additional assumptions concerning elastic collisions of bodies. Lorentz-invariance of the relativistic law is proved without tensor formalism. Some new method of force transformation is also presented.
Classical Equation of State for Dilute Relativistic Plasma
Hussein, N. A.; Eisa, D. A.; Sayed, E. G.
2016-06-01
The aim of this paper is to calculate the analytical form of the equation of state for dilute relativistic plasma. We obtained the excess free energy and pressure in the form of a convergent series expansion in terms of the thermal parameter μ where μ = {{m{c^2}} over {KT}}, m is the mass of charge, c is the speed of light, K is the Boltzmann's constant, and T is the absolute temperature. The results are discussed and compared with previous work of other authors.
Accretion of a relativistic, collisionless kinetic gas into a Schwarzschild black hole
Rioseco, Paola
2016-01-01
We provide a systematic study for the accretion of a collisionless, relativistic kinetic gas into a nonrotating black hole. To this end, we first solve the relativistic Liouville equation on a Schwarzschild background spacetime. The most general solution for the distribution function is given in terms of appropriate symplectic coordinates on the cotangent bundle, and the associated observables, including the particle current density and stress energy-momentum tensor, are determined. Next, we explore the case where the flow is steady-state and spherically symmetric. Assuming that in the asymptotic region the gas is described by an equilibrium distribution function, we determine the relevant parameters of the accretion flow as a function of the particle density and the temperature of the gas at infinity. In particular, we find that in the low temperature limit the tangential pressure at the horizon is about an order of magnitude larger than the radial one, showing explicitly that a collisionless gas, despite ex...
Turbulence kinetic energy equation for dilute suspensions
Abou-Arab, T. W.; Roco, M. C.
1989-01-01
A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.
Spectrum Analysis of Some Kinetic Equations
Yang, Tong; Yu, Hongjun
2016-11-01
We analyze the spectrum structure of some kinetic equations qualitatively by using semigroup theory and linear operator perturbation theory. The models include the classical Boltzmann equation for hard potentials with or without angular cutoff and the Landau equation with {γ≥q-2}. As an application, we show that the solutions to these two fundamental equations are asymptotically equivalent (mod time decay rate {t^{-5/4}}) as {tto∞} to that of the compressible Navier-Stokes equations for initial data around an equilibrium state.
Relativistic simulation of the Vlasov equation for plasma expansion into vacuum
H Abbasi
2012-12-01
Full Text Available In this study, relativistic Vlasov simulation of plasma for expansion of collisionless plasma for into vacuum is presented. The model is based on 1+1 dimensional phase space and electrostatic approximation. For this purpose, the electron dynamics is studied by the relativistic Vlasov equation. Regardless of the ions temperature, fluid equations are used for their dynamics. The initial electrons distribution function is the relativistic Maxwellian. The results show that due to the electrons relativistic temperature, the process of the plasma expansion takes place faster, the resulting electric field is stronger and the ions are accelerated to higher velocities, in comparison to the non-relativistic case.
Kinetic Boltzmann, Vlasov and Related Equations
Sinitsyn, Alexander; Vedenyapin, Victor
2011-01-01
Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in
Relativistic simulation of the Vlasov equation for plasma expansion into vacuum
H ABBASI; R Shokoohi; Moridi, M.
2012-01-01
In this study, relativistic Vlasov simulation of plasma for expansion of collisionless plasma for into vacuum is presented. The model is based on 1+1 dimensional phase space and electrostatic approximation. For this purpose, the electron dynamics is studied by the relativistic Vlasov equation. Regardless of the ions temperature, fluid equations are used for their dynamics. The initial electrons distribution function is the relativistic Maxwellian. The results show that due to the electrons ...
Electric Conductivity from the solution of the Relativistic Boltzmann Equation
Puglisi, A; Greco, V
2014-01-01
We present numerical results of electric conductivity $\\sigma_{el}$ of a fluid obtained solving the Relativistic Transport Boltzmann equation in a box with periodic boundary conditions. We compute $\\sigma_{el}$ using two methods: the definition itself, i.e. applying an external electric field, and the evaluation of the Green-Kubo relation based on the time evolution of the current-current correlator. We find a very good agreement between the two methods. We also compare numerical results with analytic formulas in Relaxation Time Approximation (RTA) where the relaxation time for $\\sigma_{el}$ is determined by the transport cross section $\\sigma_{tr}$, i.e. the differential cross section weighted with the collisional momentum transfer. We investigate the electric conductivity dependence on the microscopic details of the 2-body scatterings: isotropic and anisotropic cross-section, and massless and massive particles. We find that the RTA underestimates considerably $\\sigma_{el}$; for example at screening masses $...
Hot QCD equations of state and relativistic heavy ion collisions
Chandra, Vinod; Kumar, Ravindra; Ravishankar, V.
2007-11-01
We study two recently proposed equations of state obtained from high-temperature QCD and show how they can be adapted to use them for making predictions for relativistic heavy ion collisions. The method involves extracting equilibrium distribution functions for quarks and gluons from the equation of state (EOS), which in turn will allow a determination of the transport and other bulk properties of the quark gluon-plasma. Simultaneously, the method also yields a quasiparticle description of interacting quarks and gluons. The first EOS is perturbative in the QCD coupling constant and has contributions of O(g5). The second EOS is an improvement over the first, with contributions up to O[g6ln(1/g)]; it incorporates the nonperturbative hard thermal contributions. The interaction effects are shown to be captured entirely by the effective chemical potentials for the gluons and the quarks, in both cases. The chemical potential is seen to be highly sensitive to the EOS. As an application, we determine the screening lengths, which are, indeed, the most important diagnostics for QGP. The screening lengths are seen to behave drastically differently depending on the EOS considered and therefore yield a way to distinguish the two equations of state in heavy ion collisions.
Massless and Massive Gauge-Invariant Fields in the Theory of Relativistic Wave Equations
Pletyukhov, V A
2010-01-01
In this work consideration is given to massless and massive gauge-invariant spin 0 and spin 1 fields (particles) within the scope of a theory of the generalized relativistic wave equations with an extended set of the Lorentz group representations. The results obtained may be useful as regards the application of a relativistic wave-equation theory in modern field models.
Hypocoercivity for linear kinetic equations conserving mass
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
Heinz, U; Denicol, G S; Martinez, M; Nopoush, M; Noronha, J; Ryblewski, R; Strickland, M
2015-01-01
Several recent results are reported from work aiming to improve the quantitative precision of relativistic viscous fluid dynamics for relativistic heavy-ion collisions. The dense matter created in such collisions expands in a highly anisotropic manner. Due to viscous effects this also renders the local momentum distribution anisotropic. Optimized hydrodynamic approaches account for these anisotropies already at leading order in a gradient expansion. Recently discovered exact solutions of the relativistic Boltzmann equation in anisotropically expanding systems provide a powerful testbed for such improved hydrodynamic approximations. We present the latest status of our quest for a formulation of relativistic viscous fluid dynamics that is optimized for applications to relativistic heavy-ion collisions.
Ding, Min; Li, Yachun
2017-04-01
We study the 1-D piston problem for the relativistic Euler equations under the assumption that the total variations of both the initial data and the velocity of the piston are sufficiently small. By a modified wave front tracking method, we establish the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength. Meanwhile, we consider the convergence of the entropy solutions to the corresponding entropy solutions of the classical non-relativistic Euler equations as the light speed c→ +∞.
Relativistic Momentum and Kinetic Energy, and E = mc[superscript 2
Hu, Ben Yu-Kuang
2009-01-01
Based on relativistic velocity addition and the conservation of momentum and energy, I present simple derivations of the expressions for the relativistic momentum and kinetic energy of a particle, and for the formula E = mc[superscript 2]. (Contains 5 footnotes and 2 figures.)
Thermodynamics and Kinetic Theory of Relativistic Gases in 2-D Cosmological Models
Kremer, G M
2002-01-01
A kinetic theory of relativistic gases in a two-dimensional space is developed in order to obtain the equilibrium distribution function and the expressions for the fields of energy per particle, pressure, entropy per particle and heat capacities in equilibrium. Furthermore, by using the method of Chapman and Enskog for a kinetic model of the Boltzmann equation the non-equilibrium energy-momentum tensor and the entropy production rate are determined for a universe described by a two-dimensional Robertson-Walker metric. The solutions of the gravitational field equations that consider the non-equilibrium energy-momentum tensor - associated with the coefficient of bulk viscosity - show that opposed to the four-dimensional case, the cosmic scale factor attains a maximum value at a finite time decreasing to a "big crunch" and that there exists a solution of the gravitational field equations corresponding to a "false vacuum". The evolution of the fields of pressure, energy density and entropy production rate with th...
Equation of state of the relativistic free electron gas at arbitrary degeneracy
Faussurier, Gérald
2016-12-01
We study the problem of the relativistic free electron gas at arbitrary degeneracy. The specific heat at constant volume and particle number CV and the specific heat at constant pressure and particle number CP are calculated. The question of equation of state is also studied. Non degenerate and degenerate limits are considered. We generalize the formulas obtained in the non-relativistic and ultra-relativistic regimes.
A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit
Denicol, Gabriel S; Martinez, Mauricio; Noronha, Jorge; Strickland, Michael
2014-01-01
We present an exact solution of the relativistic Boltzmann equation for a system undergoing boost-invariant longitudinal and azimuthally symmetric transverse flow ("Gubser flow"). The resulting exact non-equilibrium dynamics is compared to 1st- and 2nd-order relativistic hydrodynamic approximations for various shear viscosity to entropy density ratios. This novel solution can be used to test the validity and accuracy of different hydrodynamic approximations in conditions similar to those generated in relativistic heavy-ion collisions.
Non relativistic limit of the Landau-Lifshitz equation: A new equation
Ares de Parga, G.; Domínguez-Hernández, S.; Salinas-Hernández, E.
2016-06-01
It is shown that Ford equation is not adequate in general to describe the motion of a charged particle including the reaction force in the non relativistic limit. As in General Relativity where a post-Newtonian method is developed in order to describe the gravitational effects at low velocities and small energies, an extra term inherited from Special Relativity must be added to the Ford equation. This is due to that the new term is greater than the reaction force in many physical situations. The Coulombic case is analyzed showing the necessity of including the new term. Comparison with General Relativity results is analyzed. The Vlasov equation to first order in 1 /c2 is proposed for the constant electric and magnetic fields.
Hot QCD equation of state and relativistic heavy ion collisions
Chandra, Vinod; Ravishankar, V
2007-01-01
We study two recently proposed equations of state (EOS) which are obtained from high temperature QCD, and show how they can be adapted to use them for making predictions for relativistic heavy ion collisions. The method involves extracting equilibrium distribution functions for quarks and gluons from the EOS, which in turn will allow a determination of the transport and other bulk properties of the quark gluon plasma. Simultaneously, the method also yields a quasi particle description of interacting quarks and gluons. The first EOS is perturbative in the QCD coupling constant and has contributions of $O(g^5)$. The second EOS is an improvement over the first, with contributions upto $ O(g^6 ln(\\frac{1}{g}))$; it incorporates the nonperturbative hard thermal contributions. The interaction effects are shown to be captured entirely by the effective chemical potentials for the gluons and the quarks, in both the cases. The chemical potential is seen to be highly sensitive to the EOS. As an application, we determine...
Kinetic equation for strongly interacting dense Fermi systems
Lipavsky, P; Spicka, V
2001-01-01
We review the non-relativistic Green's-function approach to the kinetic equations for Fermi liquids far from equilibrium. The emphasis is on the consistent treatment of the off-shell motion between collisions and on the non-instant and non-local picture of binary collisions. The resulting kinetic equation is of the Boltzmann type, and it represents an interpolation between the theory of transport in metals and the theory of moderately dense gases. The free motion of particles is renormalised by various mean field and mass corrections in the spirit of Landau's quasiparticles in metals. The collisions are non-local in the spirit of Enskog's theory of non-ideal gases. The collisions are moreover non-instant, a feature which is absent in the theory of gases, but which is shown to be important for dense Fermi systems. In spite of its formal complexity, the presented theory has a simple implementation within the Monte-Carlo simulation schemes. Applications in nuclear physics are given for heavy-ion reactions and th...
The impact of kinetic effects on the properties of relativistic electron-positron shocks
Stockem, A; Fonseca, R A; Silva, L O
2012-01-01
We assess the impact of non-thermally shock-accelerated particles on the magnetohydrodynamic (MHD) jump conditions of relativistic shocks. The adiabatic constant is calculated directly from first principle particle-in-cell simulation data, enabling a semi-kinetic approach to improve the standard fluid model and allowing for an identification of the key parameters that define the shock structure. We find that the evolving upstream parameters have a stronger impact than the corrections due to non-thermal particles. We find that the decrease of the upstream bulk speed yields deviations from the standard MHD model up to 10%. Furthermore, we obtain a quantitative definition of the shock transition region from our analysis. For Weibel-mediated shocks the inclusion of a magnetic field in the MHD conservation equations is addressed for the first time.
Genuinely Multidimensional Kinetic Scheme For Euler Equations
Tiwari, Praveer
2015-01-01
A new framework based on Boltzmann equation which is genuinely multidimensional and mesh-less is developed for solving Euler's equations. The idea is to use the method of moment of Boltzmann equation to operate in multidimensions using polar coordinates. The aim is to develop a framework which is genuinely multidimensional and can be implemented with different methodologies, no matter whether it is in finite difference, finite volume or finite element form. There is a considerable improvement in capturing shocks and other discontinuities. Also, since the method is multidimensional, the flow features are captured isotropically. The method is further extended to second order using 'Arc of Approach' concept. The framework is developed as a finite difference method (called as GINEUS) and is tested on the benchmark test cases. The results are compared against Kinetic Flux Vector Splitting Method.
Relativistic n-body wave equations in scalar quantum field theory
Emami-Razavi, Mohsen [Centre for Research in Earth and Space Science, York University, Toronto, Ontario, M3J 1P3 (Canada)]. E-mail: mohsen@yorku.ca
2006-09-21
The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schroedinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields.
Donker, H. C.; Katsnelson, M. I.; De Raedt, H.; Michielsen, K.
2016-09-01
The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space-time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds.
On the spectrum of relativistic Schrödinger equation in finite differences
Berezin, V A; Neronov, Andrii Yu
1999-01-01
We develop a method for constructing asymptotic solutions of finite-difference equations and implement it to a relativistic Schroedinger equation which describes motion of a selfgravitating spherically symmetric dust shell. Exact mass spectrum of black hole formed due to the collapse of the shell is determined from the analysis of asymptotic solutions of the equation.
Equation of State in Relativistic Magnetohydrodynamics: variable versus constant adiabatic index
Mignone, A
2007-01-01
The role of the equation of state for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant $\\Gamma$-law equation of state, commonly adopted in a wide range of astrophysical applications, is compared with a more realistic equation of state that better approximates the single-specie relativistic gas. The paper focus on three different topics. First, the influence of a more realistic equation of state on the propagation of fast magneto-sonic shocks is investigated. This calls into question the validity of the constant $\\Gamma$-law equation of state in problems where the temperature of the gas substantially changes across hydromagnetic waves. Second, we present a new inversion scheme to recover primitive variables (such as rest-mass density and pressure) from conservative ones that allows for a general equation of state and avoids catastrophic numerical cancellations in the non-relativistic and ultrarelativistic limits. Finally, selected numerical tests of ast...
Matrix Continued Fraction Solution to the Relativistic Spin-0 Feshbach-Villars Equations
Brown, N. C.; Papp, Z.; Woodhouse, R.
2016-03-01
The Feshbach-Villars equations, like the Klein-Gordon equation, are relativistic quantum mechanical equations for spin-0 particles.We write the Feshbach-Villars equations into an integral equation form and solve them by applying the Coulomb-Sturmian potential separable expansion method. We consider boundstate problems in a Coulomb plus short range potential. The corresponding Feshbach-Villars CoulombGreen's operator is represented by a matrix continued fraction.
Stahl, A.; Landreman, M.; Embréus, O.; Fülöp, T.
2017-03-01
Energetic electrons are of interest in many types of plasmas, however previous modeling of their properties has been restricted to the use of linear Fokker-Planck collision operators or non-relativistic formulations. Here, we describe a fully non-linear kinetic-equation solver, capable of handling large electric-field strengths (compared to the Dreicer field) and relativistic temperatures. This tool allows modeling of the momentum-space dynamics of the electrons in cases where strong departures from Maxwellian distributions may arise. As an example, we consider electron runaway in magnetic-confinement fusion plasmas and describe a transition to electron slide-away at field strengths significantly lower than previously predicted.
Stahl, A; Embréus, O; Fülöp, T
2016-01-01
Energetic electrons are of interest in many types of plasmas, however previous modelling of their properties have been restricted to the use of linear Fokker-Planck collision operators or non-relativistic formulations. Here, we describe a fully non-linear kinetic-equation solver, capable of handling large electric-field strengths (compared to the Dreicer field) and relativistic temperatures. This tool allows modelling of the momentum-space dynamics of the electrons in cases where strong departures from Maxwellian distributions may arise. As an example, we consider electron runaway in magnetic-confinement fusion plasmas and describe a transition to electron slide-away at field strengths significantly lower than previously predicted.
Dynamics of low dimensional model for weakly relativistic Zakharov equations for plasmas
Sahu, Biswajit [Department of Mathematics, West Bengal State University, Barasat, Kolkata-700126 (India); Pal, Barnali; Poria, Swarup [Department of Applied Mathematics, University of Calcutta, Kolkata-700009 (India); Roychoudhury, Rajkumar [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108 (India)
2013-05-15
In the present paper, the nonlinear interaction between Langmuir waves and ion acoustic waves described by the one-dimensional Zakharov equations (ZEs) for relativistic plasmas are investigated formulating a low dimensional model. Equilibrium points of the model are found and it is shown that the existence and stability conditions of the equilibrium point depend on the relativistic parameter. Computational investigations are carried out to examine the effects of relativistic parameter and other plasma parameters on the dynamics of the model. Power spectrum analysis using fast fourier transform and also construction of first return map confirm that periodic, quasi-periodic, and chaotic type solution exist for both relativistic as well as in non-relativistic case. Existence of supercritical Hopf bifurcation is noted in the system for two critical plasmon numbers.
A remark concerning Chandrasekhar's derivation of the pulsation equation for relativistic stars
Knutsen, Henning; Pedersen, Janne [Stavanger University, 4036 Stavanger (Norway)
2007-01-15
It is shown that Chandrasekhar gives some misleading comments concerning his method to derive the pulsation equation for relativistic stars. Strictly following his procedure and approximations, we find that this equation should contain an extra term which destroys the beauty and simplicity of the pulsation equation. However, using a better approximation, we find that just this extra term cancels, and the nice original version of the pulsation equation is correct after all.
A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations
Carrié, Michael, E-mail: mcarrie2@unl.edu; Shadwick, B. A., E-mail: shadwick@mailaps.org [Department of Physics and Astronomy, University of Nebraska-Lincoln, Lincoln, Nebraska 68588 (United States)
2016-01-15
We present a time-implicit numerical method to solve the relativistic Vlasov–Ampere system of equations on a two dimensional phase space grid. The time-splitting algorithm we use allows the generalization of the work presented here to higher dimensions keeping the linear aspect of the resulting discrete set of equations. The implicit method is benchmarked against linear theory results for the relativistic Landau damping for which analytical expressions using the Maxwell-Jüttner distribution function are derived. We note that, independently from the shape of the distribution function, the relativistic treatment features collective behaviours that do not exist in the nonrelativistic case. The numerical study of the relativistic two-stream instability completes the set of benchmarking tests.
Hafez, M. G.; Talukder, M. R.; Hossain Ali, M.
2017-04-01
The Burgers equation is obtained to study the characteristics of nonlinear propagation of ionacoustic shock, singular kink, and periodic waves in weakly relativistic plasmas containing relativistic thermal ions, nonextensive distributed electrons, Boltzmann distributed positrons, and kinematic viscosity of ions using the well-known reductive perturbation technique. This equation is solved by employing the ( G'/ G)-expansion method taking unperturbed positron-to-electron concentration ratio, electron-to-positron temperature ratio, strength of electrons nonextensivity, ion kinematic viscosity, and weakly relativistic streaming factor. The influences of plasma parameters on nonlinear propagation of ion-acoustic shock, periodic, and singular kink waves are displayed graphically and the relevant physical explanations are described. It is found that these parameters extensively modify the shock structures excitation. The obtained results may be useful in understanding the features of small but finite amplitude localized relativistic ion-acoustic shock waves in an unmagnetized plasma system for some astrophysical compact objects and space plasmas.
Similarities and Differences Between Freundlich Kinetic Equation and Two—Constant Equation
ZHANGZENGQIANG; ZHANGYIPING
1999-01-01
A mathematical expression of Freundlich kinetic equation,lnS=A'+B'lnt,is presented,and the physical meanings of its parameters are indicated.Although the Freundlich kinetic equation and the two-constant equation are the same in the form,the derivation of the Freundlich kinetic equation is precise,while the derivation of the two-constant equation has some contradictions and is unreasonable,And it is suggested that the Freundlich kinetic equation should have prority over the two-constant equation to be used.
A causality analysis of the linearized relativistic Navier-Stokes equations
Sandoval-Villalbazo, A
2010-01-01
It is shown by means of a simple analysis that the linearized system of transport equations for a relativistic, single component ideal gas at rest obeys the \\textit{antecedence principle}, which is often referred to as causality principle. This task is accomplished by examining the roots of the dispersion relation for such a system. This result is important for recent experiments performed in relativistic heavy ion colliders, since it suggests that the Israel-Stewart like formalisms may be unnecessary in order to describe relativistic fluids.
Neutrino quantum kinetic equations: The collision term
Blaschke, Daniel N.; Cirigliano, Vincenzo
2016-08-01
We derive the collision term relevant for neutrino quantum kinetic equations in the early universe and compact astrophysical objects, displaying its full matrix structure in both flavor and spin degrees of freedom. We include in our analysis neutrino-neutrino processes, scattering and annihilation with electrons and positrons, and neutrino scattering off nucleons (the latter in the low-density limit). After presenting the general structure of the collision terms, we take two instructive limiting cases. The one-flavor limit highlights the structure in helicity space and allows for a straightforward interpretation of the off-diagonal entries in terms of the product of scattering amplitudes of the two helicity states. The isotropic limit is relevant for studies of the early universe: in this case the terms involving spin coherence vanish and the collision term can be expressed in terms of two-dimensional integrals, suitable for computational implementation.
Neutrino Quantum Kinetic Equations: The Collision Term
Blaschke, Daniel N
2016-01-01
We derive the collision term relevant for neutrino quantum kinetic equations in the early universe and compact astrophysical objects, displaying its full matrix structure in both flavor and spin degrees of freedom. We include in our analysis neutrino-neutrino processes, scattering and annihilation with electrons and positrons, and neutrino scattering off nucleons (the latter in the low-density limit). After presenting the general structure of the collision terms, we take two instructive limiting cases. The one-flavor limit highlights the structure in helicity space and allows for a straightforward interpretation of the off-diagonal entries in terms of the product of scattering amplitudes of the two helicity states. The isotropic limit is relevant for studies of the early universe: in this case the terms involving spin coherence vanish and the collision term can be expressed in terms of two-dimensional integrals, suitable for computational implementation.
Probability representation of kinetic equation for open quantum system
Man'ko, V I; Shchukin, E V
2003-01-01
The tomographic probability distribution is used to decribe the kinetic equations for open quantum systems. Damped oscillator is studied. Purity parameter evolution for different damping regime is considered.
Asymptotic domination of cold relativistic MHD winds by kinetic energy flux
Begelman, Mitchell C.; Li, Zhi-Yun
1994-01-01
We study the conditions which lead to the conversion of most Poynting flux into kinetic energy flux in cold, relativistic hydromagnetic winds. It is shown that plasma acceleration along a precisely radial flow is extremely inefficient due to the near cancellation of the toroidal magnetic pressure and tension forces. However, if the flux tubes in a flow diverge even slightly faster than radially, the fast magnetosonic point moves inward from infinity to a few times the light cylinder radius. Once the flow becomes supermagnetosonic, further divergence of the flux tubes beyond the fast point can accelerate the flow via the 'magnetic nozzle' effect, thereby further converting Poynting flux to kinetic energy flux. We show that the Grad-Shafranov equation admits a generic family of kinetic energy-dominated asymptotic wind solutions with finite total magnetic flux. The Poynting flux in these solutions vanishes logarithmically with distance. The way in which the flux surfaces are nested within the flow depends only on the ratio of angular velocity to poliodal 4-velocity as a function of magnetic flux. Radial variations in flow structure can be expressed in terms of a pressure boundary condition on the outermost flux surface, provided that no external toriodal field surrounds the flow. For a special case, we show explicitly how the flux surfaces merge gradually to their asymptotes. For flows confined by an external medium of pressure decreasing to zero at infinity we show that, depending on how fast the ambient pressure declines, the final flow state could be either a collimated jet or a wind that fills the entire space. We discuss the astrophysical implications of our results for jets from active galactic nuclei and for free pulsar winds such as that believed to power the Crab Nebula.
Self-consistent retardation in a three-dimensional relativistic equation
Crawford, G.A.; Thaler, R.M.
1988-12-01
A new technique for approximating solutions of the two-body Bethe-Salpeter equation is presented. Coupled equations for the relative energy dependence and the relative three-momentum dependence of the relativistic T matrix are derived. These equations are solved self consistently for the Wick-rotated T matrix in a simple model problem and the numerical results are compared with exact as well as usual three-dimensional reduction results.
Relativistic Dirac equation for particles with arbitrary half-integral spin
Guseinov, I I
2008-01-01
The sets of 2(2s+1)-component matrices through the four-component Dirac matrices are suggested, where s=3/2, 5/2,.... Using these matrices sets the Dirac relativistic equation for a description of arbitrary half-integral spin particles is constructed. The new Dirac equation of motion leads to an equation of continuity with a positive-definite probability density.
Relativistic magnetohydrodynamics in one dimension.
Lyutikov, Maxim; Hadden, Samuel
2012-02-01
We derive a number of solutions for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary one-dimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: A system of highly nonlinear, relativistic, time-dependent equations describing arbitrary (not necessarily self-similar) dynamics of highly magnetized plasma reduces to a single linear differential equation.
The kinetics of the population and spectral gain for a relativistic hydrogenlike ion
Derzhiev, V.I.; Zhidkov, A.G.; Magunov, A.I.; Tkachev, A.N.; Iakovlenko, S.I. (Institut Obshchei Fiziki, Moscow (USSR))
1989-07-01
The kinetics of the population and spectral gain for an H-like Ti-XXII ion is calculated with allowance for fine level splitting. Allowance for the relativistic effects in the kinetics of relaxation and broadening of the spectral lines of an H-like ion leads to a sharp increase in the gain. For a Ti XXII ion, x43 amounted to 100/cm. 11 refs.
Relativistic superfluidity and vorticity from the nonlinear Klein-Gordon equation
Xiong, Chi; Guo, Yulong; Liu, Xiaopei; Huang, Kerson
2014-01-01
We investigate superfluidity, and the mechanism for creation of quantized vortices, in the relativistic regime. The general framework is a nonlinear Klein-Gordon equation in curved spacetime for a complex scalar field, whose phase dynamics gives rise to superfluidity. The mechanisms discussed are local inertial forces (Coriolis and centrifugal), and current-current interaction with an external source. The primary application is to cosmology, but we also discuss the reduction to the non-relativistic nonlinear Schr\\"{o}dinger equation, which is widely used in describing superfluidity and vorticity in liquid helium and cold-trapped atomic gases.
Quarkonium and hydrogen spectra with spin-dependent relativistic wave equation
V H Zaveri
2010-10-01
The non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of hydrogen atom are exactly the same as that of Dirac theory. The theory accounts for the energy due to spin-orbit interaction and for the additional potential energy due to spin and spin-orbit coupling. Spin angular momentum operator is integrated into the equation of motion. This requires modification to classical Laplacian operator. Consequently, the Dirac matrices and the k operator of Dirac’s theory are dispensed with. The theory points out that the curvature of the orbit draws on certain amount of kinetic and potential energies affecting the momentum of electron and the spin-orbit interaction energy constitutes a part of this energy. The theory is developed for spin-1/2 bound state single electron in Coulomb potential and then extended further to quarkonium physics by introducing the linear confining potential. The unique feature of this quarkonium model is that the radial distance can be exactly determined and does not have a statistical interpretation. The established radial distance is then used to determine the wave function. The observed energy levels are used as the input parameters and the radial distance and the string tension are predicted. This ensures 100% conformance to all observed energy levels for the heavy quarkonium.
Numerical solutions of general-relativistic field equations for rapidly rotating neutron stars
吴雪君; 须重明
1997-01-01
Stationary axial symmetric equilibrium configurations rapidly rotating with uniform angular velocity in the framework of genera! relativity are considered. Sequences of models are numerically computed by means of a computer code that solves the full Einstein equations exactly. This code employs Neugebauer’s minimal surface formalism, where the field equations are equivalent to two-dimensional minimal surface equations for 4 metric potentials. The calculations are based upon 10 different equations of state. Results of various structures of neutron stars and the rotational effects on stellar structures and properties are reported. Finally some limits to equations of state of neutron stars and the stability for rapidly rotating relativistic neutron stars are discussed.
Relativistic wave equations with fractional derivatives and pseudo-differential operators
Závada, P
2000-01-01
The class of the free relativistic covariant equations generated by the fractional powers of the D'Alambertian operator $(\\Box ^{1/n})$ is studied. Meanwhile the equations corresponding to n=1 and 2 (Klein-Gordon and Dirac equations) are local in their nature, the multicomponent equations for arbitrary n>2 are non-local. It is shown, how the representation of generalized algebra of Pauli and Dirac matrices looks like and how these matrices are related to the algebra of SU(n) group. The corresponding representations of the Poincar\\'e group and further symmetry transformations on the obtained equations are discussed. The construction of the related Green functions is suggested.
Haba, Z
2009-02-01
We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.
Symmetries of Differential equations and Applications in Relativistic Physics
Paliathanasis, Andronikos
2015-01-01
In this thesis, we study the one parameter point transformations which leave invariant the differential equations. In particular we study the Lie and the Noether point symmetries of second order differential equations. We establish a new geometric method which relates the point symmetries of the differential equations with the collineations of the underlying manifold where the motion occurs. This geometric method is applied in order the two and three dimensional Newtonian dynamical systems to be classified in relation to the point symmetries; to generalize the Newtonian Kepler-Ermakov system in Riemannian spaces; to study the symmetries between classical and quantum systems and to investigate the geometric origin of the Type II hidden symmetries for the homogeneous heat equation and for the Laplace equation in Riemannian spaces. At last but not least, we apply this geometric approach in order to determine the dark energy models by use the Noether symmetries as a geometric criterion in modified theories of gra...
Essén, Hanno; Nordmark, Arne B.
2016-09-01
The canonical Poisson bracket algebra of four-dimensional relativistic mechanics is used to derive the equation of motion for a charged particle, with the Lorentz force, and the homogeneous Maxwell equations.
Role of retardation in three-dimensional relativistic equations
Lahiff, A.D.; Afnan, I.R. [Department of Physics, The Flinders University of South Australia, GPO Box 2100, Adelaide 5001 (Australia)
1997-11-01
Equal-time Green{close_quote}s function is used to derive a three-dimensional integral equation from the Bethe-Salpeter equation. The resultant equation, in the absence of antiparticles, is identical to the use of time-ordered diagrams, and has been used within the framework of {phi}{sup 2}{sigma} coupling to study the role of energy dependence and nonlocality when the two-body potential is the sum of {sigma} exchange and crossed {sigma} exchange. The results show that nonlocality and energy dependence make a substantial contribution to both the on-shell and off-shell amplitudes. {copyright} {ital 1997} {ital The American Physical Society}
Role of retardation in three-dimensional relativistic equations
Lahiff, A. D.; Afnan, I. R.
1997-11-01
Equal-time Green's function is used to derive a three-dimensional integral equation from the Bethe-Salpeter equation. The resultant equation, in the absence of antiparticles, is identical to the use of time-ordered diagrams, and has been used within the framework of φ2σ coupling to study the role of energy dependence and nonlocality when the two-body potential is the sum of σ exchange and crossed σ exchange. The results show that nonlocality and energy dependence make a substantial contribution to both the on-shell and off-shell amplitudes.
Harko, T
2016-01-01
Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equa...
Relativistic two-, three- and four-body wave equations in scalar QFT
Emami-Razavi, Mohsen; Darewych, Jurij W [Centre for Research in Earth and Space Science and Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3 (Canada)
2005-09-01
We use the variational method within the Hamiltonian formalism of QFT to derive relativistic two-, three- and four-body wave equations for scalar particles interacting via a massive or massless mediating scalar field (the scalar Yukawa model). The Lagrangian of the theory is reformulated by using Green's functions to express the mediating field in terms of the particle fields. The QFT is then constructed from the resulting reformulated Hamiltonian. Simple Fock-space variational trial states are used to derive relativistic two-, three- and four-body equations. The equations are shown to have the Schroedinger non-relativistic limit, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Ground-state solutions of the relativistic equations are obtained approximately for various strengths of coupling, for both massive and massless mediating fields, and a comparison of the two-, three- and four-particle binding energies is presented.
Donker, H. C.; Katsnelson, M. I.; De Raedt, H.; Michielsen, K.
The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space-time data
Donker, H. C.; Katsnelson, M. I.; De Raedt, H.; Michielsen, K.
2016-01-01
The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space-time data colle
Moment equations for chromatography based on Langmuir type reaction kinetics.
Miyabe, Kanji
2014-08-22
Moment equations were derived for chromatography, in which the reaction kinetics between solute molecules and functional ligands on the stationary phase was represented by the Langmuir type rate equation. A set of basic equations of the general rate model of chromatography representing the mass balance, mass transfer rate, and reaction kinetics in the column were analytically solved in the Laplace domain. The moment equations for the first absolute moment and the second central moment in the real time domain were derived from the analytical solution in the Laplace domain. The moment equations were used for predicting the chromatographic behavior under hypothetical HPLC conditions. The influence of the parameters relating to the adsorption equilibrium and to the reaction kinetics on the chromatographic behavior was quantitatively evaluated. It is expected that the moment equations are effective for a detailed analysis of the influence of the mass transfer rates and of the Langmuir type reaction kinetics on the column efficiency.
Relativistic wave equations for interacting massive particles with arbitrary half-intreger spins
Niederle, J
2001-01-01
New formulation of relativistic wave equations (RWE) for massive particles with arbitrary half-integer spins $s$ interacting with external electromagnetic fields are proposed. They are based on wave functions which are irreducible tensors of rank $2n$ ($n=s-\\frac12$) antisymmetric w.r.t. $n$ pairs of indices, whose components are bispinors. The form of RWE is straightforward and free of inconsistencies associated with the other approaches to equations describing interacting higher spin particles.
Kinetic equation for a gas with attractive forces as a functional equation
Ryszard Wojnar
2009-04-01
Full Text Available Diffusion problems studied in the time scale comparable with time of particles collision lead to kinetic equations which for step-wise potentials are functional equations in the velocity space. After a description of meaning of diffusion in biology and survey of derivation of kinetic equations by projective operator method, we pay an attention to the Lorentz gas with step potential. The gas is composed of $N$ particles: $N-1$ of which are immovable between $N-1$ immovable particles-scatterers, particle number 1 is moving, and we describe its movement by means of one-particle distribution function satisfying a kinetic equation. Solutions of the kinetic equation for some simple potentials are given. We derive also a kinetic equation for one-dimensional Lorentz gas, which is a functional equation.
Metamaterial characterization using Boltzmann's kinetic equation for electrons
Novitsky, Andrey; Zhukovsky, Sergei; Novitsky, D.
2013-01-01
Statistical properties of electrons in metals are taken into consideration to describe the microscopic motion of electrons. Assuming degenerate electron gas in metal, we introduce the Boltzmann kinetic equation to supplement Maxwell's equations. The solution of these equations clearly shows the r...
Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity
无
2006-01-01
Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we can see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments.And because of this Newtonian gravitational potential, a quantum particle in the earth's gravitational field may form a gravitationally bound quantized state, which has already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are studied in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, and radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.
A novel fractional technique for the modified point kinetics equations
Ahmed E. Aboanber
2016-10-01
Full Text Available A fractional model for the modified point kinetics equations is derived and analyzed. An analytical method is used to solve the fractional model for the modified point kinetics equations. This methodical technique is based on the representation of the neutron density as a power series of the relaxation time as a small parameter. The validity of the fractional model is tested for different cases of step, ramp and sinusoidal reactivity. The results show that the fractional model for the modified point kinetics equations is the best representation of neutron density for subcritical and supercritical reactors.
Analytic Representation of Relativistic Wave Equations I The Dirac Case
Tepper, L; Zachary, W W
2003-01-01
In this paper we construct an analytical separation (diagonalization) of the full (minimal coupling) Dirac equation into particle and antiparticle components. The diagonalization is analytic in that it is achieved without transforming the wave functions, as is done by the Foldy-Wouthuysen method, and reveals the nonlocal time behavior of the particle-antiparticle relationship. It is well known that the Foldy-Wouthuysen transformation leads to a diagonalization that is nonlocal in space. We interpret the zitterbewegung, and the result that a velocity measurement (of a Dirac particle) at any instant in time is +(-)c, as reflections of the fact that the Dirac equation makes a spatially extended particle appear as a point in the present by forcing it to oscillate between the past and future at speed c. This suggests that although the Dirac Hamiltonian and the square-root Hamiltonian, are mathematically, they are not physically, equivalent. Furthermore, we see that alt! ho! ugh the form of the Dirac equation serve...
Abstract composition rule for relativistic kinetic energy in the thermodynamical limit
Biro, T S
2008-01-01
We demonstrate by simple mathematical considerations that a power-law tailed distribution in the kinetic energy of relativistic particles can be a limiting distribution seen in relativistic heavy ion experiments. We prove that the infinite repetition of an arbitrary composition rule on an infinitesimal amount leads to a rule with a formal logarithm. As a consequence the stationary distribution of energy in the thermodynamical limit follows the composed function of the Boltzmann-Gibbs exponential with this formal logarithm. In particular, interactions described as solely functions of the relative four-momentum squared lead to kinetic energy distributions of the Tsallis-Pareto (cut power-law) form in the high energy limit.
Relativistic quantum mechanical spin-1 wave equation in 2+1 dimensional spacetime
Dernek, Mustafa; Sucu, Yusuf; Unal, Nuri
2016-01-01
In the study, we introduce a relativistic quantum mechanical wave equation of the spin-1 particle as an excited state of the zitterbewegung and show that it is consistent with the 2+1 dimensional Proca theory. At the same time, we see that this equation has two eigenstates, particle and antiparticle states or negative and positive energy eigenstates, respectively, in the rest frame and the spin-1 matrices satisfy $SO(2,1)$ spin algebra. As practical applications, we derive the exact solutions of the equation in the presence of a constant magnetic field and a curved spacetime. From these solutions, we construct the current components of the spin-1 particle.
Solution of the reactor point kinetics equations by MATLAB computing
Singh Sudhansu S.
2015-01-01
Full Text Available The numerical solution of the point kinetics equations in the presence of Newtonian temperature feedback has been a challenging issue for analyzing the reactor transients. Reactor point kinetics equations are a system of stiff ordinary differential equations which need special numerical treatments. Although a plethora of numerical intricacies have been introduced to solve the point kinetics equations over the years, some of the simple and straightforward methods still work very efficiently with extraordinary accuracy. As an example, it has been shown recently that the fundamental backward Euler finite difference algorithm with its simplicity has proven to be one of the most effective legacy methods. Complementing the back-ward Euler finite difference scheme, the present work demonstrates the application of ordinary differential equation suite available in the MATLAB software package to solve the stiff reactor point kinetics equations with Newtonian temperature feedback effects very effectively by analyzing various classic benchmark cases. Fair accuracy of the results implies the efficient application of MATLAB ordinary differential equation suite for solving the reactor point kinetics equations as an alternate method for future applications.
Relativistic kinetic theory and non-gaussian statistical
de Oliveira, Z. B. B.; Silva, R.
2016-12-01
The nonextensive statistical mechanics is extended in the special relativity context through a generalization of H-theorem. We show that the Tsallis framework is compatible with the second law of the thermodynamics when the nonadditive effects are consistently introduced on the collisional term of the Boltzmann equation. The proof of the H-theorem follows from using of q-algebra in the generalization of the molecular chaos hypothesis (Stosszahlansatz). A thermodynamic consistency is possible whether the entropic parameter belongs to interval q ∈ [ 0 , 2 ] .
Crouseilles, Nicolas; Faou, Erwan
2016-01-01
We consider the relativistic Vlasov--Maxwell (RVM) equations in the limit when the light velocity $c$ goes to infinity. In this regime, the RVM system converges towards the Vlasov--Poisson system and the aim of this paper is to construct asymptotic preserving numerical schemes that are robust with respect to this limit. Our approach relies on a time splitting approach for the RVM system employing an implicit time integrator for Maxwell's equations in order to damp the higher and higher frequencies present in the numerical solution. It turns out that the choice of this implicit method is crucial as even $L$-stable methods can lead to numerical instabilities for large values of $c$. A number of numerical simulations are conducted in order to investigate the performances of our numerical scheme both in the relativistic as well as in the classical limit regime. In addition, we derive the dispersion relation of the Weibel instability for the continuous and the discretized problem.
An asymptotic preserving scheme for the relativistic Vlasov-Maxwell equations in the classical limit
Crouseilles, Nicolas; Einkemmer, Lukas; Faou, Erwan
2016-12-01
We consider the relativistic Vlasov-Maxwell (RVM) equations in the limit when the light velocity c goes to infinity. In this regime, the RVM system converges towards the Vlasov-Poisson system and the aim of this paper is to construct asymptotic preserving numerical schemes that are robust with respect to this limit. Our approach relies on a time splitting approach for the RVM system employing an implicit time integrator for Maxwell's equations in order to damp the higher and higher frequencies present in the numerical solution. A number of numerical simulations are conducted in order to investigate the performances of our numerical scheme both in the relativistic as well as in the classical limit regime. In addition, we derive the dispersion relation of the Weibel instability for the continuous and the discretized problem.
Bazow, D.; Denicol, G. S.; Heinz, U.; Martinez, M.; Noronha, J.
2016-12-01
The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe is studied. The mathematical problem of solving the full nonlinear relativistic Boltzmann equation is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. Momentum-space resolution is determined by the number of nonhydrodynamic modes included in the moment hierarchy, i.e., by the truncation order. We show that in the FLRW spacetime the nonhydrodynamic modes decouple completely from the hydrodynamic degrees of freedom. This results in the system flowing as an ideal fluid while at the same time producing entropy. The solutions to the nonlinear Boltzmann equation exhibit transient tails of the distribution function with nontrivial momentum dependence. The evolution of this tail is not correctly captured by the relaxation time approximation nor by the linearized Boltzmann equation. However, the latter probes additional high-momentum details unresolved by the relaxation time approximation. While the expansion of the FLRW spacetime is slow enough for the system to move towards (and not away from) local thermal equilibrium, it is not sufficiently slow for the system to actually ever reach complete local equilibrium. Equilibration is fastest in the relaxation time approximation, followed, in turn, by kinetic evolution with a linearized and a fully nonlinear Boltzmann collision term.
Gan YIN; Wancheng SHENG
2008-01-01
The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.
Inhomogeneous relativistic Boltzmann equation near vacuum in the Robertson-Walker space-time
Takou, Etienne
2016-01-01
In this paper, we consider the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data where the distribution function depends on the time, the position and the impulsion. The collision kernel considered here is for the hard potentials case and the background space-time in which the study is done is the Robertson-Walker space-time. Unique global (in time) mild solution is obtained in a suitable weighted space.
The Relativistic Boltzmann Equation on Bianchi Type I Space Time for Hard Potentials
Noutchegueme, Norbert; Takou, Etienne; Tchuengue, E. Kamdem
2017-08-01
In this paper, we consider the Cauchy problem for the spatially homogeneous relativistic Boltzmann equation with small initial data. The collision kernel considered here is for a hard potentials case. The background space-time in which the study is done is the Bianchi type I space-time. Under certain conditions made on the scattering kernel and on the metric, a uniqueness global (in time) solution is obtained in a suitable weighted functional space.
Gallo, Emanuel
2016-01-01
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. By construction, the model incorporates the back reaction due to gravitational radiation generated by the motion of the particle. Our approach differs from other constructions tackling the same kind of problem.
Figaro, S; Avril, J P; Brouers, F; Ouensanga, A; Gaspard, S
2009-01-30
Adsorption kinetic of molasses wastewaters after anaerobic digestion (MSWD) and melanoidin respectively on activated carbon was studied at different pH. The kinetic parameters could be determined using classical kinetic equations and a recently published fractal kinetic equation. A linear form of this equation can also be used to fit adsorption data. Even with lower correlation coefficients the fractal kinetic equation gives lower normalized standard deviation values than the pseudo-second order model generally used to fit adsorption kinetic data, indicating that the fractal kinetic model is much more accurate for describing the kinetic adsorption data than the pseudo-second order kinetic model.
Fractional Diffusion Limit for Collisional Kinetic Equations
Mellet, Antoine
2010-08-20
This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite variance. We then show that for an appropriate time scale, the small mean free path limit gives rise to a fractional diffusion equation. © 2010 Springer-Verlag.
Kinetic Equations for Describing Phosphorus Transport
无
2001-01-01
@@Studies on kinetics of adsorption and release of phosphorus by soil,a new field in soil chemistry,began only over ten years ago (He et al.,1989; Wang and Zhu,1988;Zhang and Zhang,1991; Lin,1989; Lin and Xue,1989; Jiang,1993; Xue et al.,1995;LU et al.,1997).
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
Kinetic equation for nonlinear resonant wave-particle interaction
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2016-09-01
We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.
Fillion-Gourdeau, F; Herrmann, H J; Mendoza, M; Palpacelli, S; Succi, S
2013-10-18
We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and nonrelativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wave function) propagates in space-time as a classical statistical process (Boltzmann distribution).
Metamaterial characterization using Boltzmann's kinetic equation for electrons
Novitsky, Andrey; Zhukovsky, Sergei; Novitsky, D.;
2013-01-01
Statistical properties of electrons in metals are taken into consideration to describe the microscopic motion of electrons. Assuming degenerate electron gas in metal, we introduce the Boltzmann kinetic equation to supplement Maxwell's equations. The solution of these equations clearly shows the r...... the resonant behavior of electronic response to an external electromagnetic field. We demonstrate the approach for planar and circular geometries of the metamolecules....
On the role of the chaotic velocity in relativistic kinetic theory
Moratto, Valdemar [Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 México D.F. (Mexico); García-Perciante, A. L. [Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana-Cuajimalpa, Prol. Vasco de Quiroga 4871, México D. F. 05348 (Mexico)
2014-01-14
In this paper we revisit the concept of chaotic velocity within the context of relativistic kinetic theory. Its importance as the key ingredient which allows to clearly distinguish convective and dissipative effects is discussed to some detail. Also, by addressing the case of the two component mixture, the relevance of the barycentric comoving frame is established and thus the convenience for the introduction of peculiar velocities for each species. The fact that the decomposition of molecular velocity in systematic and peculiar components does not alter the covariance of the theory is emphasized. Moreover, we show that within an equivalent decomposition into space-like and time-like tensors, based on a generalization of the relative velocity concept, the Lorentz factor for the chaotic velocity can be expressed explicitly as an invariant quantity. This idea, based on Ellis' theorem, allows to foresee a natural generalization to the general relativistic case.
Bazow, D; Heinz, U; Martinez, M; Noronha, J
2016-01-01
The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lema\\^itre-Robertson-Walker (FLRW) universe is studied. The mathematical problem of solving the full nonlinear relativistic Boltzmann equation is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. Momentum-space resolution is determined by the number of non-hydrodynamic modes included in the moment hierarchy, i.e., by the truncation order. We show that in the FLRW spacetime the non-hydrodynamic modes decouple completely from the hydrodynamic degrees of freedom. This results in the system flowing as an ideal fluid while at the same time producing entropy. The solutions to the nonlinear Boltzmann equation exhibit transient tails of the distribution function with nontrivial momentum dependence. The evolution of this tail is not correctly captured by the relaxation time approximation nor by the linearized Boltzmann equation...
Superluminal Neutrinos and a Curious Phenomenon in the Relativistic Quantum Hamilton-Jacobi Equation
Matone, Marco
2011-01-01
OPERA's results, if confirmed, pose the question of superluminal neutrinos. We investigate the kinematics defined by the quantum version of the relativistic Hamilton-Jacobi equation, i.e. E^2=p^2c^2+m^2c^4+2mQc^2, with Q the quantum potential of the free particle. The key point is that the quantum version of the Hamilton-Jacobi equation is a third-order differential equation, so that it has integration constants which are missing in the Schr\\"odinger and Klein-Gordon equations. In particular, a non-vanishing imaginary part of an integration constant leads to a quantum correction to the expression of the velocity which is curiously in agreement with OPERA's results.
Equation of state in relativistic magnetohydrodynamics: variable versus constant adiabatic index
Mignone, A.; McKinney, Jonathan C.
2007-07-01
The role of the equation of state (EoS) for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant Γ-law EoS, commonly adopted in a wide range of astrophysical applications, is compared with a more realistic EoS that better approximates the single-specie relativistic gas. The paper focuses on three different topics. First, the influence of a more realistic EoS on the propagation of fast magnetosonic shocks is investigated. This calls into question the validity of the constant Γ-law EoS in problems where the temperature of the gas substantially changes across hydromagnetic waves. Secondly, we present a new inversion scheme to recover primitive variables (such as rest-mass density and pressure) from conservative ones that allows for a general EoS and avoids catastrophic numerical cancellations in the non-relativistic and ultrarelativistic limits. Finally, selected numerical tests of astrophysical relevance (including magnetized accretion flows around Kerr black holes) are compared using different equations of state. Our main conclusion is that the choice of a realistic EoS can considerably bear upon the solution when transitions from cold to hot gas (or vice versa) are present. Under these circumstances, a polytropic EoS can significantly endanger the solution.
Relativistic equation-of-motion coupled-cluster method using open-shell reference wavefunction
Pathak, Himadri; Nayak, Malaya K; Vaval, Nayana; Pal, Sourav
2016-01-01
The open-shell reference relativistic equation-of-motion coupled-cluster method within its four-component description is successfully implemented with the consideration of single- and double- excitation approximation. The one-body and two-body matrix elements required for the correlation calculation are generated using Dirac-Coulomb Hamiltonian. As a first attempt, the implemented method is employed to calculate a few of the low-lying ionized states of heavy atomic (Ag, Cs, Au, Fr, Lr) and valence ionization potential of molecular (HgH, PbF) systems, where the effect of relativity does really matter to obtain highly accurate results. Not only the relativistic effect, but also the effect of electron correlation is crucial in these heavy atomic and molecular systems. To justify the fact, we have taken two further approximations in the four-component relativistic equation-of-motion framework to quantify how the effect of electron correlation plays a role in the calculated values at different level of the approxi...
Ways to constrain neutron star equation of state models using relativistic disc lines
Bhattacharyya, Sudip
2011-01-01
Relativistic spectral lines from the accretion disc of a neutron star low-mass X-ray binary can be modelled to infer the disc inner edge radius. A small value of this radius tentatively implies that the disc terminates either at the neutron star hard surface, or at the innermost stable circular orbit (ISCO). Therefore an inferred disc inner edge radius either provides the stellar radius, or can directly constrain stellar equation of state (EoS) models using the theoretically computed ISCO radius for the spacetime of a rapidly spinning neutron star. However, this procedure requires numerical computation of stellar and ISCO radii for various EoS models and neutron star configurations using an appropriate rapidly spinning stellar spacetime. We have fully general relativistically calculated about 16000 stable neutron star structures to explore and establish the above mentioned procedure, and to show that the Kerr spacetime is inadequate for this purpose. Our work systematically studies the methods to constrain Eo...
A nondissipative simulation method for the drift kinetic equation
Watanabe, Tomo-Hiko; Sugama, Hideo; Sato, Tetsuya
2001-07-01
With the aim to study the ion temperature gradient (ITG) driven turbulence, a nondissipative kinetic simulation scheme is developed and comprehensively benchmarked. The new simulation method preserving the time-reversibility of basic kinetic equations can successfully reproduce the analytical solutions of asymmetric three-mode ITG equations which are extended to provide a more general reference for benchmarking than the previous work [T.-H. Watanabe, H. Sugama, and T. Sato: Phys. Plasmas 7 (2000) 984]. It is also applied to a dissipative three-mode system, and shows a good agreement with the analytical solution. The nondissipative simulation result of the ITG turbulence accurately satisfies the entropy balance equation. Usefulness of the nondissipative method for the drift kinetic simulations is confirmed in comparisons with other dissipative schemes. (author)
A Pseudo-Kinetic Approach for Helmholtz Equation
Radjesvarane ALEXANDRE; Jie LIAO
2013-01-01
A lattice Boltzmann type pseudo-kinetic model for a non-homogeneous Helmholtz equation is derived in this paper.Numerical results for some model problems show the robustness and efficiency of this lattice Boltzmann type pseudo-kinetic scheme.The computation at each site is determined only by local parameters,and can be easily adapted to solve multiple scattering problems with many scatterers or wave propagation in nonhomogeneous medium without increasing the computational cost.
B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations
Pöschl, W
1997-01-01
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which describe a nuclear system in the framework of relativistic mean field theory. Although, FEM has been applied with great success in nuclear RMF recently, a well known problem is the appearance of spurious solutions in the spectra of the Dirac equation. The question, whether B-splines lead to a reduction of spurious solutions is analyzed. Numerical expenses, precision and behavior of convergence are compared for both methods in view of their use in large scale computation on FEM grids with more dimensions. A B-spline version of the object oriented C++ code for spherical nuclei has been used for this investigation.
Brown, Natalie
In this thesis we solve the Feshbach-Villars equations for spin-zero particles through use of matrix continued fractions. The Feshbach-Villars equations are derived from the Klein-Gordon equation and admit, for the Coulomb potential on an appropriate basis, a Hamiltonian form that has infinite symmetric band-matrix structure. The corresponding representation of the Green's operator of such a matrix can be given as a matrix continued fraction. Furthermore, we propose a finite dimensional representation for the potential operator such that it retains some information about the whole Hilbert space. Combining these two techniques, we are able to solve relativistic quantum mechanical problems of a spin-zero particle in a Coulomb-like potential with a high level of accuracy.
Fractional neutron point kinetics equations for nuclear reactor dynamics
Espinosa-Paredes, Gilberto, E-mail: gepe@xanum.uam.mx [Area de Ingenieria en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico, D.F. 09340 (Mexico); Polo-Labarrios, Marco-A. [Area de Ingenieria en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico, D.F. 09340 (Mexico); Espinosa-Martinez, Erick-G. [Retorno Quebec 6, Col. Burgos de Cuernavaca 62580, Temixco, Mor. (Mexico); Valle-Gallegos, Edmundo del [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Av. Instituto Politecnico Nacional s/n, Col. San Pedro Zacatenco, Mexico, D.F. 07738 (Mexico)
2011-02-15
The fractional point-neutron kinetics model for the dynamic behavior in a nuclear reactor is derived and analyzed in this paper. The fractional model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional order, acting as exponent of the relaxation time, to obtain the best representation of a nuclear reactor dynamics. The physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. The numerical approximation to the solution of the fractional neutron point kinetics model, which can be represented as a multi-term high-order linear fractional differential equation, is calculated by reducing the problem to a system of ordinary and fractional differential equations. The numerical stability of the fractional scheme is investigated in this work. Results for neutron dynamic behavior for both positive and negative reactivity and for different values of fractional order are shown and compared with the classic neutron point kinetic equations. Additionally, a related review with the neutron point kinetics equations is presented, which encompasses papers written in English about this research topic (as well as some books and technical reports) published since 1940 up to 2010.
Retarded versus time-nonlocal quantum kinetic equations
Morawetz, K. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France); Spicka, V.; Lipavsky, P. [Institute of Physics, Academy of Sciences, Praha (Czech Republic)
2000-07-01
The finite duration of the collisions in Fermionic systems as expressed by the retardation time in the non-Markovian Levinson equation is discussed in the quasiclassical limit. The separate individual contributions included in the memory effect resulting in (i) off-shell tails of the Wigner distribution, (ii) renormalization of scattering rates and (iii) of the single-particle energy, (iv) collision delay and (v) related non-local corrections to the scattering integral. In this way we transform the Levison equation into the Landau-Silin equation extended by the non-local corrections known from the theory of dense gases. The derived kinetic equation unifies the Landau theory of quasiparticle transport with the classical kinetic theory of dense gases. The space-time symmetry is discussed versus particle-hole symmetry and a solution is proposed which transforms these two exclusive pictures into each other. (authors)
Harko, T.; Mak, M. K.
2016-09-01
Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index n. The explicit form of the solution is presented for the polytropic index n=1, and for the indexes n=1/2 and n=1/5, respectively. The case of n=3 is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven terms only. The power series representations of the geometric and physical properties of the linear barotropic and polytropic stars are also obtained.
Controllability in hybrid kinetic equations modeling nonequilibrium multicellular systems.
Bianca, Carlo
2013-01-01
This paper is concerned with the derivation of hybrid kinetic partial integrodifferential equations that can be proposed for the mathematical modeling of multicellular systems subjected to external force fields and characterized by nonconservative interactions. In order to prevent an uncontrolled time evolution of the moments of the solution, a control operator is introduced which is based on the Gaussian thermostat. Specifically, the analysis shows that the moments are solution of a Riccati-type differential equation.
The lifespan of 3D radial solutions to the non-isentropic relativistic Euler equations
Wei, Changhua
2017-10-01
This paper investigates the lower bound of the lifespan of three-dimensional spherically symmetric solutions to the non-isentropic relativistic Euler equations, when the initial data are prescribed as a small perturbation with compact support to a constant state. Based on the structure of the hyperbolic system, we show the almost global existence of the smooth solutions to Eulerian flows (polytropic gases and generalized Chaplygin gases) with genuinely nonlinear characteristics. While for the Eulerian flows (Chaplygin gas and stiff matter) with mild linearly degenerate characteristics, we show the global existence of the radial solutions, moreover, for the non-strictly hyperbolic system (pressureless perfect fluid) satisfying the mild linearly degenerate condition, we prove the blowup phenomenon of the radial solutions and show that the lifespan of the solutions is of order O(ɛ ^{-1}), where ɛ denotes the width of the perturbation. This work can be seen as a complement of our work (Lei and Wei in Math Ann 367:1363-1401, 2017) for relativistic Chaplygin gas and can also be seen as a generalization of the classical Eulerian fluids (Godin in Arch Ration Mech Anal 177:497-511, 2005, J Math Pures Appl 87:91-117, 2007) to the relativistic Eulerian fluids.
Denicol, Gabriel S; Martinez, Mauricio; Noronha, Jorge; Strickland, Michael
2014-01-01
We present an exact solution to the Boltzmann equation which describes a system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion for arbitrary shear viscosity to entropy density ratio. This new solution is constructed by considering the conformal map between Minkowski space and the direct product of three dimensional de Sitter space with a line. The resulting solution respects SO(3)_q x SO(1,1) x Z_2 symmetry. We compare the exact kinetic solution with exact solutions of the corresponding macroscopic equations with the same symmetry that were obtained from the kinetic theory in ideal and second-order viscous hydrodynamic approximations.
Leung, Chun Sing; Harko, Tiberiu
2013-01-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation-dissipation theorems. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The Power Spectral Distribution of the luminosity it is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object.
Generalized Langevin Equation Description of Stochastic Oscillations of General Relativistic Disks
Chun Sing Leung; Gabriela Mocanu; Tiberiu Harko
2014-09-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation–dissipation theorems. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and Kerr cases. The power spectral distribution of the luminosity is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object.
Wang Zhi-Yun; Chen Pei-Jie
2016-06-01
A generalized Langevin equation driven by fractional Brownian motion is used to describe the vertical oscillations of general relativistic disks. By means of numerical calculation method, the displacements, velocities and luminosities of oscillating disks are explicitly obtained for different Hurst exponent $H$. The results show that as $H$ increases, the energies and luminosities of oscillating disk are enhanced, and the spectral slope at high frequencies of the power spectrum density of disk luminosity is also increased. This could explain the observational features related to the Intra Day Variability of the BL Lac objects.
Hadron Mass Spectra and Decay Rates in a Potential Model with Relativistic Wave Equations.
Namgung, Wuk
Hadron properties of mass spectra and decay rates are calculated in a quark potential model. Wave equations based on the Klein-Gordon and Todorov equations both of which incorporate the feature of relativistic two-body kinematics are used. The wave equations are modified to contain potentials which transform either like a Lorentz scalar or like a time-component of a four-vector. Potentials based on the Fogleman-Lichtenberg-Wills potential which has the properties suggested by QCD of both confinement and asymptotic freedom are used. The potentials, motivated by QCD but otherwise phenomenological, are further generalized to forms which can apply to any color representation. To break the degeneracy between vector and pseudoscalar mesons or between spin-3/2 and spin-1/2 baryons, the essential feature of spin dependence is included in the potentials. The masses of vector and pseudoscalar mesons are calculated with only a small number of adjustable parameters, and good qualitative agreement with experiment is obtained for both heavy and light mesons. Baryons are treated in this framework by making use of a quark-diquark two-body model of baryons. First, diquark properties are calculated without any additional parameters. The g-factors of diquarks and spin-flavor configuration of baryons, which are necessary for the calculation of baryons, are given. Then baryon masses are calculated also without additional parameters. The results of the masses of ground-state baryons are in good qualitative agreement with experiment. Also effective constituent quark masses are obtained using current quark masses as input. The calculated effective constituent quark masses are in the right range of the values that most theoretical estimates have given. The general qualitative features of hadron spectra are similar with the two relativistic wave equations, although there are differences in detail. The Van Royen-Weisskopf formula for electromagnetic decay widths of vector mesons into lepton
Tidal deformability of neutron and hyperon star with relativistic mean field equations of state
Kumar, Bharat; Patra, S K
2016-01-01
We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field (RMF) equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various love numbers kl (l=2, 3, 4), that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through advanced LIGO detector from the final stages of inspiraling binary neutron star (BNS) merger.
Avron, Joseph
2016-01-01
We derive the relativistically exact Eikonal equation for ring interferometers undergoing adiabatic deformations. The leading term in the adiabatic expansion of the phase shift is independent of the refraction index $n$ and is given by a line integral generalizing results going back to Sagnac to all orders in $\\beta$. The next term in the adiabaticity is of lower order in $\\beta$ and may be as important as the first in nonrelativistic cases. This term is proportional to $n^2$ and has the form of a double integral. It generalizes previous results to fibers with chromatic dispersion and puts Sagnac and Fizeau interferometers under a single umbrella.
Tidal deformability of neutron and hyperon stars within relativistic mean field equations of state
Kumar, Bharat; Biswal, S. K.; Patra, S. K.
2017-01-01
We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various Love numbers kl(l =2 ,3 ,4 ), that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through an advanced LIGO detector from the final stages of an inspiraling binary neutron star merger.
Wells, J C; Eichler, J
1999-01-01
We discuss the two-center, time-dependent Dirac equation describing the dynamics of an electron during a peripheral, relativistic heavy-ion collision at extreme energies. We derive a factored form, which is exact in the high-energy limit, for the asymptotic channel solutions of the Dirac equation, and elucidate their close connection with gauge transformations which transform the dynamics into a representation in which the interaction between the electron and a distant ion is of short range. We describe the implications of this relationship for solving the time-dependent Dirac equation for extremely relativistic collisions.
Amirkhanov, I V; Zhidkova, I E; Vasilev, S A
2000-01-01
Asymptotics of eigenfunctions and eigenvalues has been obtained for a singular perturbated relativistic analog of Schr`dinger equation. A singular convergence of asymptotic expansions of the boundary problems to degenerated problems is shown for a nonrelativistic Schr`dinger equation. The expansions obtained are in a good agreement with a numeric experiment.
Enzyme Kinetics and the Michaelis-Menten Equation
Biaglow, Andrew; Erickson, Keith; McMurran, Shawnee
2010-01-01
The concepts presented in this article represent the cornerstone of classical mathematical biology. The central problem of the article relates to enzyme kinetics, which is a biochemical system. However, the theoretical underpinnings that lead to the formation of systems of time-dependent ordinary differential equations have been applied widely to…
Enzyme Kinetics and the Michaelis-Menten Equation
Biaglow, Andrew; Erickson, Keith; McMurran, Shawnee
2010-01-01
The concepts presented in this article represent the cornerstone of classical mathematical biology. The central problem of the article relates to enzyme kinetics, which is a biochemical system. However, the theoretical underpinnings that lead to the formation of systems of time-dependent ordinary differential equations have been applied widely to…
Relativistic integro-differential form of the Lorentz-Dirac equation in 3D without runaways
Ibison, Michael; Puthoff, Harold E.
2001-04-01
It is well known that the third-order Lorentz-Dirac equation admits runaway solutions wherein the energy of the particle grows without limit, even when there is no external force. These solutions can be denied simply on physical grounds, and on the basis of careful analysis of the correspondence between classical and quantum theory. Nonetheless, one would prefer an equation that did not admit unphysical behavior at the outset. Such an equation - an integro-differential version of the Lorentz-Dirac equation - is currently available either in 1 dimension only, or in 3 dimensions only in the non-relativistic limit. It is shown herein how the Lorentz-Dirac equation may be integrated without approximation, and is thereby converted to a second-order integro-differential equation in 3D satisfying the above requirement. I.E., as a result, no additional constraints on the solutions are required because runaway solutions are intrinsically absent. The derivation is placed within the historical context established by standard works on classical electrodynamics by Rohrlich, and by Jackson.
Modeling the turbulent kinetic energy equation for compressible, homogeneous turbulence
Aupoix, B.; Blaisdell, G. A.; Reynolds, William C.; Zeman, Otto
1990-01-01
The turbulent kinetic energy transport equation, which is the basis of turbulence models, is investigated for homogeneous, compressible turbulence using direct numerical simulations performed at CTR. It is shown that the partition between dilatational and solenoidal modes is very sensitive to initial conditions for isotropic decaying turbulence but not for sheared flows. The importance of the dilatational dissipation and of the pressure-dilatation term is evidenced from simulations and a transport equation is proposed to evaluate the pressure-dilatation term evolution. This transport equation seems to work well for sheared flows but does not account for initial condition sensitivity in isotropic decay. An improved model is proposed.
Relativistic heat conduction and thermoelectric properties of nonuniform plasmas
Honda, M
2003-01-01
Relativistic heat transport in electron-two-temperature plasmas with density gradients has been investigated. The Legendre expansion analysis of relativistically modified kinetic equations shows that strong inhibition of heat flux appears in relativistic temperature regimes, suppressing the classical Spitzer-H{\\"a}rm conduction. The Seebeck coefficient, the Wiedemann-Franz law, and the thermoelectric figure of merit are derived in the relativistic regimes.
Equation of state of a relativistic theory from a moving frame.
Giusti, Leonardo; Pepe, Michele
2014-07-18
We propose a new strategy for determining the equation of state of a relativistic thermal quantum field theory by considering it in a moving reference system. In this frame, an observer can measure the entropy density of the system directly from its average total momentum. In the Euclidean path integral formalism, this amounts to computing the expectation value of the off-diagonal components T(0k) of the energy-momentum tensor in the presence of shifted boundary conditions. The entropy is, thus, easily measured from the expectation value of a local observable computed at the target temperature T only. At large T, the temperature itself is the only scale which drives the systematic errors, and the lattice spacing can be tuned to perform a reliable continuum limit extrapolation while keeping finite-size effects under control. We test this strategy for the four-dimensional SU(3) Yang-Mills theory. We present precise results for the entropy density and its step-scaling function in the temperature range 0.9T(c)-20T(c). At each temperature, we consider four lattice spacings in order to extrapolate the results to the continuum limit. As a by-product, we also determine the ultraviolet finite renormalization constant of T(0k) by imposing suitable Ward identities. These findings establish this strategy as a solid, simple, and efficient method for an accurate determination of the equation of state of a relativistic thermal field theory over several orders of magnitude in T.
Modeling the QCD Equation of State in Relativistic Heavy Ion Collisions on BlueGene/L
Soltz, R; Grady, J; Hartouni, E P; Gupta, R; Vitev, I; Mottola, E; Petreczky, P; Karsch, F; Christ, N; Mawhinney, R; Bass, S; Mueller, B; Vranas, P; Levkova, L; Molnar, D; Teaney, D; De Tar, C; Toussaint, D; Sugar, R
2006-04-10
On 9,10 Feb 2006 a workshop was held at LLNL to discuss how a 10% allocation of the ASC BG/L supercomputer performing a finite temperature Lattice QCD (LQCD) calculation of the equation of state and non-equilibrium properties of the quark-gluon state of matter could lead to a breakthrough in our understanding of recent data from the Relativistic Heavy Ion Collider at Brookhaven National Lab. From this meeting and subsequent discussions we present a detailed plan for this calculation, including mechanisms for working in a secure computing environment and inserting the resulting equation of state into hydrodynamic transport models that will be compared directly to the RHIC data. We discuss expected benefits for DOE Office of Science research programs within the context of the NNSA mission.
Mondal, Ritwik; Berritta, Marco; Oppeneer, Peter M.
2016-10-01
Starting from the Dirac-Kohn-Sham equation, we derive the relativistic equation of motion of spin angular momentum in a magnetic solid under an external electromagnetic field. This equation of motion can be rewritten in the form of the well-known Landau-Lifshitz-Gilbert equation for a harmonic external magnetic field and leads to a more general magnetization dynamics equation for a general time-dependent magnetic field. In both cases there is an electronic spin-relaxation term which stems from the spin-orbit interaction. We thus rigorously derive, from fundamental principles, a general expression for the anisotropic damping tensor which is shown to contain an isotropic Gilbert contribution as well as an anisotropic Ising-like and a chiral, Dzyaloshinskii-Moriya-like contribution. The expression for the spin relaxation tensor comprises furthermore both electronic interband and intraband transitions. We also show that when the externally applied electromagnetic field possesses spin angular momentum, this will lead to an optical spin torque exerted on the spin moment.
Kinetic Equations of Potassium Desorption and the Application of Equation Constants
LUEXIAO－NAN; LUYUN－FU
1995-01-01
Elovich,parabolic diffusion,power function and exponential equations were used to describe K desorption kinetics of 12 soils in a constant electric field of electro-ultrafiltration(EUF),Results showed that the Elovich,parabolic diffusion and power function equations could describe K desorption kinetics well owing to their high correlation coefficients and low standard errors;but the exponential equation was not suitable to be used in this study due to its relatively low correlation coefficients and relatively high standard errors.This work established successfully the relationships between the constants(slope or intercept)of kinetic equations and the barley responses to K fertilizer in the multiple-site field experiments and K-supplying status of soilsk,the constants of Elovich,parabolic diffusion and power function equations were very significantly or significantly correlated to the soil available K,relative yield of barley and K uptake of barley in NP plot.It was suggested that the kinetic equation constants could be used to estimate K-supplying power of soils.
Weberszpil, J; Cherman, A; Helayël-Neto, J A
2012-01-01
The main goal of this paper is to set up the coarse-grained formulation of a fractional Schr\\"odinger equation that incorporates a higher (spatial) derivative term which accounts for relativistic effects at a lowest order. The corresponding continuity equation is worked out and we also identify the contribution of the relativistic correction the quantum potential in the coarse-grained treatment. As a consequence, in the classical regime, we derive the sort of fractional Newtonian law with the quantum potential included and the fractional conterparts of the De Broglies's energy and momentum relations.
Bifurcation in kinetic equation for interacting Fermi systems
Morawetz, Klaus
2003-06-01
The recently derived nonlocal quantum kinetic equation for dense interacting Fermi systems combines time derivatives with finite time stepping known from the logistic mapping. This continuous delay differential equation is a consequence of the microscopic delay time representing the dynamics of the deterministic chaotic system. The responsible delay time is explicitly calculated and discussed for short-range correlations. As a novel feature oscillations in the time evolution of the distribution function itself appear and bifurcations up to chaotic behavior occur. The temperature and density conditions are presented where such oscillations and bifurcations arise indicating an onset of phase transition.
On the drift kinetic equation driven by plasma flows
Shaing, K C [Plasma and Space Science Center and ISAPS, National Cheng Kung University, Tainan 70101, Taiwan (China); Department of Engineering Physics, University of Wisconsin, Madison, WI 53706 (United States)
2010-07-15
A drift kinetic equation that is driven by plasma flows has previously been derived by Shaing and Spong 1990 (Phys. Fluids B 2 1190). The terms that are driven by particle speed that is parallel to the magnetic field B have been neglected. Here, such terms are discussed to examine their importance to the equation and to show that these terms do not contribute to the calculations of plasma viscosity in large aspect ratio toroidal plasmas, e.g. tokamaks and stellarators. (brief communication)
Ghizzo, A. [Institut Jean Lamour UMR 7163, Université de Lorraine, BP 239 F-54506 Vandoeuvre les Nancy (France)
2013-08-15
The saturation of the Weibel instability in the relativistic regime is investigated within the Hamiltonian reduction technique based on the multistream approach developed in paper I in the linear case and in paper II for the nonlinear saturation. In this work, the study is compared with results obtained by full kinetic 1D2V Vlasov-Maxwell simulations based on a semi-Lagrangian technique. For a temperature anisotropy, qualitatively different regimes are realized depending on the excitation of the longitudinal (plasma) electric field, in contrast with the existing theories of the Weibel instability based on their purely transverse characters. The emphasis here is on gaining a better understanding of the nonlinear aspects of the Weibel instability. The multistream model offers an alternate way to make calculations or numerical experiments more tractable, when only a few moments of the velocity distribution of the plasma are considered.
Relativistic equation-of-motion coupled-cluster method for the electron attachment problem
Pathak, Himadri; Nayak, Malaya K; Vaval, Nayana; Pal, Sourav
2016-01-01
The article considers the successful implementation of relativistic equation-of-motion coupled clus- ter method for the electron attachment problem (EA-EOMCC) at the level of single- and double- excitation approximation. The Dirac-Coulomb Hamiltonian is used to generate the single particle orbitals and two-body matrix elements. The implemented relativistic EA-EOMCC method is em- ployed to calculate ionization potential values of alkali metal atoms (Li, Na, K, Rb, Cs, Fr) and the vertical electron affinity values of LiX (X=H, F, Cl, Br), NaY (Y=H, F, Cl) starting from their closed-shell configuration. We have taken C 2 as an example to understand what should be the na- ture of the basis and cut off in the orbital energies that can be used for the correlation calculations without loosing a considerable amount of accuracy in the computed values. Both four-component and X2C calculations are done for all the opted systems to understand the effect of relativity in our calculations as well as to justify the fact tha...
On Some Properties of the Landau Kinetic Equation
Bobylev, Alexander; Gamba, Irene; Potapenko, Irina
2015-12-01
We discuss some general properties of the Landau kinetic equation. In particular, the difference between the "true" Landau equation, which formally follows from classical mechanics, and the "generalized" Landau equation, which is just an interesting mathematical object, is stressed. We show how to approximate solutions to the Landau equation by the Wild sums. It is the so-called quasi-Maxwellian approximation related to Monte Carlo methods. This approximation can be also useful for mathematical problems. A model equation which can be reduced to a local nonlinear parabolic equation is also constructed in connection with existence of the strong solution to the initial value problem. A self-similar asymptotic solution to the Landau equation for large v and t is discussed in detail. The solution, earlier confirmed by numerical experiments, describes a formation of Maxwellian tails for a wide class of initial data concentrated in the thermal domain. It is shown that the corresponding rate of relaxation (fractional exponential function) is in exact agreement with recent mathematically rigorous estimates.
Numerical Comparison of Solutions of Kinetic Model Equations
A. A. Frolova
2015-01-01
Full Text Available The collision integral approximation by different model equations has created a whole new trend in the theory of rarefied gas. One widely used model is the Shakhov model (S-model obtained by expansion of inverse collisions integral in a series of Hermite polynomials up to the third order. Using the same expansion with another value of free parameters leads to a linearized ellipsoidal statistical model (ESL.Both model equations (S and ESL have the same properties, as they give the correct relaxation of non-equilibrium stress tensor components and heat flux vector, the correct Prandtl number at the transition to the hydrodynamic regime and do not guarantee the positivity of the distribution function.The article presents numerical comparison of solutions of Shakhov equation, ESL- model and full Boltzmann equation in the four Riemann problems for molecules of hard spheres.We have considered the expansion of two gas flows, contact discontinuity, the problem of the gas counter-flows and the problem of the shock wave structure. For the numerical solution of the kinetic equations the method of discrete ordinates is used.The comparison shows that solution has a weak sensitivity to the form of collision operator in the problem of expansions of two gas flows and results obtained by the model and the kinetic Boltzmann equations coincide.In the problem of the contact discontinuity the solution of model equations differs from full kinetic solutions at the point of the initial discontinuity. The non-equilibrium stress tensor has the maximum errors, the error of the heat flux is much smaller, and the ESL - model gives the exact value of the extremum of heat flux.In the problems of gas counter-flows and shock wave structure the model equations give significant distortion profiles of heat flux and non-equilibrium stress tensor components in front of the shock waves. This behavior is due to fact that in the models under consideration there is no dependency of the
Complete equation of state for neutron stars using the relativistic Hartree-Fock approximation
Miyatsu, Tsuyoshi; Cheoun, Myung-Ki [Department of Physics, Soongsil University, Seoul 156-743 (Korea, Republic of); Yamamuro, Sachiko; Nakazato, Ken' ichiro [Department of Physics, Faculty of Science and Technology, Tokyo University of Science (TUS), Noda 278-8510 (Japan)
2014-05-02
We construct the equation of state in a wide-density range for neutron stars within relativistic Hartree-Fock approximation. The properties of uniform and nonuniform nuclear matter are studied consistently. The tensor couplings of vector mesons to baryons due to exchange contributions (Fock terms) are included, and the change of baryon internal structure in matter is also taken into account using the quark-meson coupling model. The Thomas-Fermi calculation is adopted to describe nonuniform matter, where the lattice of nuclei and the neutron drip out of nuclei are considered. Even if hyperons exist in the core of a neutron star, we obtain the maximum neutron-star mass of 1.95M{sub ⊙}, which is consistent with the recently observed massive pulsar, PSR J1614-2230. In addition, the strange vector (φ) meson also plays a important role in supporting a massive neutron star.
Very High Order $\\PNM$ Schemes on Unstructured Meshes for the Resistive Relativistic MHD Equations
Dumbser, Michael
2009-01-01
In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space dimensions. The nonlinear system under consideration is purely hyperbolic and contains a source term, the one for the evolution of the electric field, that becomes stiff for low values of the resistivity. For the spatial discretization we propose to use high order $\\PNM$ schemes as introduced in \\cite{Dumbser2008} for hyperbolic conservation laws and a high order accurate unsplit time discretization is achieved using the element-local space-time discontinuous Galerkin approach proposed in \\cite{DumbserEnauxToro} for one-dimensional balance laws with stiff source terms. The divergence free character of the magnetic field is accounted for through the divergence cleaning procedure of Dedner et al. \\cite{Dedneretal}. To validate our high order method we first solve some numerical test c...
Avron, Joseph; Kenneth, Oded
2016-12-01
We derive the relativistically exact eikonal equation for ring interferometers undergoing deformation. For ring interferometers that undergo slow deformation we describe the two leading terms in the adiabatic expansion of the phase shift. The leading term is independent of the refraction index n and is given by a line integral generalizing results going back to Sagnac for nondeforming interferometers to all orders in β =|v |/c . In the nonrelativistic limit this term is O (β ) . The next term in the adiabaticity has the form of a double integral, it is of order β0 and depends on the refractive index n . It accounts for nonreciprocity due to changing circumstances in the fiber. The adiabatic correction is often comparable to the Sagnac term. In particular, this is the case in Fizeau's interferometer. Besides providing a mathematical framework that puts all ring interferometers under a single umbrella, our results strengthen earlier results and generalize them to fibers with chromatic dispersion.
S. W. H. Cowley
2006-03-01
Full Text Available Recent spectroscopic observations of Jupiter's "main oval" auroras indicate that the primary auroral electron beam is routinely accelerated to energies of ~100 keV, and sometimes to several hundred keV, thus approaching the relativistic regime. This suggests the need to re-examine the classic non-relativistic theory of auroral electron acceleration by field-aligned electric fields first derived by Knight (1973, and to extend it to cover relativistic situations. In this paper we examine this problem for the case in which the source population is an isotropic Maxwellian, as also assumed by Knight, and derive exact analytic expressions for the field-aligned current density (number flux and kinetic energy flux of the accelerated population, for arbitrary initial electron temperature, acceleration potential, and field strength beneath the acceleration region. We examine the limiting behaviours of these expressions, their regimes of validity, and their implications for auroral acceleration in planetary magnetospheres (and like astrophysical systems. In particular, we show that for relativistic accelerating potentials, the current density increases as the square of the minimum potential, rather than linearly as in the non-relativistic regime, while the kinetic energy flux then increases as the cube of the potential, rather than as the square.
Semi-relativistic hydrodynamics of three-dimensional and low-dimensional quantum plasma
Andreev, Pavel; Kuz'menkov, Leonid
2014-01-01
Contributions of the current-current and Darwin interactions and weak-relativistic addition to kinetic energy in the quantum hydrodynamic equations are considered. Features of hydrodynamic equations for two-dimensional layer of plasma (two-dimensional electron gas for instance) are described. It is shown that the force fields caused by the Darwin interaction and weak-relativistic addition to kinetic energy are partially reduced. Dispersion of three- and two-dimensional semi-relativistic Langmuir waves is calculated.
M, G. Hafez; N, C. Roy; M, R. Talukder; M Hossain, Ali
2017-01-01
A comparative study is carried out for the nonlinear propagation of ion acoustic shock waves both for the weakly and highly relativistic plasmas consisting of relativistic ions and q-distributed electrons and positions. The Burgers equation is derived to reveal the physical phenomena using the well known reductive perturbation technique. The integration of the Burgers equation is performed by the (G\\prime /G)-expansion method. The effects of positron concentration, ion–electron temperature ratio, electron–positron temperature ratio, ion viscosity coefficient, relativistic streaming factor and the strength of the electron and positron nonextensivity on the nonlinear propagation of ion acoustic shock and periodic waves are presented graphically and the relevant physical explanations are provided.
Mir-Kasimov, R M
1994-01-01
The concept of the one -- dimensional quantum mechanics in the relativistic configurational space (RQM) is reviewed briefly. The Relativistic Schroedinger equation (RSE) arising here is the finite -- difference equation with the step equal to the Compton wave length of the particle. The different generalizations of the Dirac -- Infeld-- Hall factorizarion method for this case are constructed. This method enables us to find out all possible finite-difference generalizations of the most important nonrelativistic integrable case -- the harmonic oscillator. As it was shown in \\cite{kmn},\\cite{mir6} the case of RQM the harmonic oscillator = q -- oscillator. It is also shown that the relativistic and nonrelativistic QM's are different representations of the same theory. The transformation connecting these two representations is found in explicit form. It could be considered as the generalization of the Kontorovich -- Lebedev transformation.
Goncalves, Bruno; Dias Junior, Mario Marcio [Instituto Federal de Educacacao, Ciencia e Tecnologia Sudeste de Minas Gerais, Juiz de Fora, MG (Brazil)
2013-07-01
Full text: The discussion of experimental manifestations of torsion at low energies is mainly related to the torsion-spin interaction. In this respect the behavior of Dirac field and the spinning particle in an external torsion field deserves and received very special attention. In this work, we consider the combined action of torsion and magnetic field on the massive spinor field. In this case, the Dirac equation is not straightforward solved. We suppose that the spinor has two components. The equations have mixed terms between the two components. The electromagnetic field is introduced in the action by the usual gauge transformation. The torsion field is described by the field S{sub μ}. The main purpose of the work is to get an explicit form to the equation of motion that shows the possible interactions between the external fields and the spinor in a Hamiltonian that is independent to each component. We consider that S{sub 0} is constant and is the unique non-vanishing term of S{sub μ}. This simplification is taken just to simplify the algebra, as our main point is not to describe the torsion field itself. In order to get physical analysis of the problem, we consider the non-relativistic approximation. The final result is a Hamiltonian that describes a half spin field in the presence of electromagnetic and torsion external fields. (author)
Fan, Peifeng; Liu, Jian; Xiang, Nong; Yu, Zhi
2016-01-01
A manifestly covariant, or geometric, field theory for relativistic classical particle-field system is developed. The connection between space-time symmetry and energy-momentum conservation laws for the system is established geometrically without splitting the space and time coordinates, i.e., space-time is treated as one identity without choosing a coordinate system. To achieve this goal, we need to overcome two difficulties. The first difficulty arises from the fact that particles and field reside on different manifold. As a result, the geometric Lagrangian density of the system is a function of the 4-potential of electromagnetic fields and also a functional of particles' world-lines. The other difficulty associated with the geometric setting is due to the mass-shell condition. The standard Euler-Lagrange (EL) equation for a particle is generalized into the geometric EL equation when the mass-shell condition is imposed. For the particle-field system, the geometric EL equation is further generalized into a w...
Noutchegueme, N; Noutchegueme, Norbert; Tetsadjio, Mesmin Erick
2003-01-01
We prove, for the relativistic Boltzmann equation in the homogeneous case, on the Minkowski space-time, a global in time existence and uniqueness theorem. The method we develop extends to the cases of some curved space-times such as the flat Robertson-Walker space-time and some Bianchi type I space-times.
Conformational Nonequilibrium Enzyme Kinetics: Generalized Michaelis-Menten Equation.
Piephoff, D Evan; Wu, Jianlan; Cao, Jianshu
2017-08-03
In a conformational nonequilibrium steady state (cNESS), enzyme turnover is modulated by the underlying conformational dynamics. On the basis of a discrete kinetic network model, we use an integrated probability flux balance method to derive the cNESS turnover rate for a conformation-modulated enzymatic reaction. The traditional Michaelis-Menten (MM) rate equation is extended to a generalized form, which includes non-MM corrections induced by conformational population currents within combined cyclic kinetic loops. When conformational detailed balance is satisfied, the turnover rate reduces to the MM functional form, explaining its general validity. For the first time, a one-to-one correspondence is established between non-MM terms and combined cyclic loops with unbalanced conformational currents. Cooperativity resulting from nonequilibrium conformational dynamics can be achieved in enzymatic reactions, and we provide a novel, rigorous means of predicting and characterizing such behavior. Our generalized MM equation affords a systematic approach for exploring cNESS enzyme kinetics.
A boundary matching micro/macro decomposition for kinetic equations
Lemou, Mohammed
2010-01-01
We introduce a new micro/macro decomposition of collisional kinetic equations which naturally incorporates the exact space boundary conditions. The idea is to write the distribution fonction $f$ in all its domain as the sum of a Maxwellian adapted to the boundary (which is not the usual Maxwellian associated with $f$) and a reminder kinetic part. This Maxwellian is defined such that its 'incoming' velocity moments coincide with the 'incoming' velocity moments of the distribution function. Important consequences of this strategy are the following. i) No artificial boundary condition is needed in the micro/macro models and the exact boundary condition on $f$ is naturally transposed to the macro part of the model. ii) It provides a new class of the so-called 'Asymptotic preserving' (AP) numerical schemes: such schemes are consistent with the original kinetic equation for all fixed positive value of the Knudsen number $\\eps$, and if $\\eps \\to 0 $ with fixed numerical parameters then these schemes degenerate into ...
A Second Relativistic Mean Field and Virial Equation of State for Astrophysical Simulations
Shen, G; O'Connor, E
2011-01-01
We generate a second equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions for use in supernovae, neutron star mergers, and black hole formation simulations. We employ full relativistic mean field (RMF) calculations for matter at intermediate density and high density, and the Virial expansion of a non-ideal gas for matter at low density. For this EOS we use the RMF effective interaction FSUGold, whereas our earlier EOS was based on the RMF effective interaction NL3. The FSUGold interaction has a lower pressure at high densities compared to the NL3 interaction. We calculate the resulting EOS at over 100,000 grid points in the temperature range $T$ = 0 to 80 MeV, the density range $n_B$ = 10$^{-8}$ to 1.6 fm$^{-3}$, and the proton fraction range $Y_p$ = 0 to 0.56. We then interpolate these data points using a suitable scheme to generate a thermodynamically consistent equation of state table on a finer grid. We discuss differences between this EOS, our NL3 ba...
Czerw Katarzyna
2016-01-01
Full Text Available The aim of this study was to investigate the ability of kinetic equations to describe the sorption kinetics and expansion rate of solid coal samples. In order to address his issue the sorption kinetics of methane and carbon dioxide on bituminous coals were studied. At the same time, the changes occurring in the sample’s overall dimensions, which accompanied sorption processes, were monitored. Experiments were carried out at high pressure by means of the volumetric method on a cubicoid solid samples. Several literature-based modeling approaches and equations are proposed to fit the kinetic curves of gas deposition, as well as the adequate kinetics of coal swelling. First equation represents the traditional approach to interpret experimental data in terms of fast and slow sorption process and consider the combination of two first-order rate functions. The other empirical kinetic equations are: the pseudo-second-order kinetic equation (PSOE, Elovich equation and the stretched exponential equation (SE. Two of the four equations are suitable to describe the kinetics of methane and carbon dioxide sorption and have been successfully used to quantify the observed dilatometric phenomena rates. The stretched exponential equation gave the best fit to the experimental data.
Kinetic equations modelling wealth redistribution: a comparison of approaches.
Düring, Bertram; Matthes, Daniel; Toscani, Giuseppe
2008-11-01
Kinetic equations modelling the redistribution of wealth in simple market economies is one of the major topics in the field of econophysics. We present a unifying approach to the qualitative study for a large variety of such models, which is based on a moment analysis in the related homogeneous Boltzmann equation, and on the use of suitable metrics for probability measures. In consequence, we are able to classify the most important feature of the steady wealth distribution, namely the fatness of the Pareto tail, and the dynamical stability of the latter in terms of the model parameters. Our results apply, e.g., to the market model with risky investments [S. Cordier, L. Pareschi, and G. Toscani, J. Stat. Phys. 120, 253 (2005)], and to the model with quenched saving propensities [A. Chatterjee, B. K. Chakrabarti, and S. S. Manna, Physica A 335, 155 (2004)]. Also, we present results from numerical experiments that confirm the theoretical predictions.
Al-Hashimi, M H
2015-01-01
We study the relativistic version of Schr\\"odinger equation for a point particle in 1-d with potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultra-violet divergent, and the resultant expression cannot be renormalized in the usual sense. Therefore a general procedure has been developed to derive different physical properties of the system. The procedure is used first on the non-relativistic case for the purpose of clarification and comparisons. The results from the relativistic case show that this system behaves exactly like the delta function potential, which means it also shares the same features with quantum field theories, like being asymptotically free, and in the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point.
Causal kinetic equation of non-equilibrium plasmas
R. A. Treumann
2017-05-01
Full Text Available Statistical plasma theory far from thermal equilibrium is subject to Liouville's equation, which is at the base of the BBGKY hierarchical approach to plasma kinetic theory, from which, in the absence of collisions, Vlasov's equation follows. It is also at the base of Klimontovich's approach which includes single-particle effects like spontaneous emission. All these theories have been applied to plasmas with admirable success even though they suffer from a fundamental omission in their use of the electrodynamic equations in the description of the highly dynamic interactions in many-particle conglomerations. In the following we extend this theory to taking into account that the interaction between particles separated from each other at a distance requires the transport of information. Action needs to be transported and thus, in the spirit of the direct-interaction theory as developed by Wheeler and Feynman (1945, requires time. This is done by reference to the retarded potentials. We derive the fundamental causal Liouville equation for the phase space density of a system composed of a very large number of charged particles. Applying the approach of Klimontovich (1967, we obtain the retarded time evolution equation of the one-particle distribution function in plasmas, which replaces Klimontovich's equation in cases when the direct-interaction effects have to be taken into account. This becomes important in all systems where the distance between two points |Δq| ∼ ct is comparable to the product of observation time and light velocity, a situation which is typical in cosmic physics and astrophysics.
Herschlag, Gregory J; Mitran, Sorin; Lin, Guang
2015-06-21
We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spatial correlations of varying lattice distance; the assumption is that the full system will have finite spatial correlations and thus the behavior of the models within the hierarchy will approach that of the full system. We provide evidence of this convergence in the context of one- and two-dimensional numerical examples. Lower levels within the hierarchy that consider shorter spatial correlations are shown to be up to three orders of magnitude faster than traditional kinetic Monte Carlo methods (KMC) for one-dimensional systems, while predicting similar system dynamics and steady states as KMC methods. We then test the hierarchy on a two-dimensional model for the oxidation of CO on RuO2(110), showing that low-order truncations of the hierarchy efficiently capture the essential system dynamics. By considering sequences of models in the hierarchy that account for longer spatial correlations, successive model predictions may be used to establish empirical approximation of error estimates. The hierarchy may be thought of as a class of generalized phenomenological kinetic models since each element of the hierarchy approximates the master equation and the lowest level in the hierarchy is identical to a simple existing phenomenological kinetic models.
Equation of state of a relativistic theory from a moving frame
Giusti, Leonardo
2014-01-01
We propose a new strategy for determining the equation of state of a relativistic thermal quantum field theory by considering it in a moving reference system. In this frame an observer can measure the entropy density of the system directly from its average total momentum. In the Euclidean path integral formalism, this amounts to compute the expectation value of the off-diagonal components T_{0k} of the energy-momentum tensor in presence of shifted boundary conditions. The entropy is thus easily measured from the expectation value of a local observable computed at the target temperature T only. At large T, the temperature itself is the only scale which drives the systematic errors, and the lattice spacing can be tuned to perform a reliable continuum limit extrapolation while keeping finite-size effects under control. We test this strategy for the four-dimensional SU(3) Yang-Mills theory. We present precise results for the entropy density and its step-scaling function in the temperature range 0.9 T_c - 20 T_c. ...
Murad, Mohammad Hassan; Pant, Neeraj
2014-03-01
In this paper we have studied a particular class of exact solutions of Einstein's gravitational field equations for spherically symmetric and static perfect fluid distribution in isotropic coordinates. The Schwarzschild compactness parameter, GM/ c 2 R, can attain the maximum value 0.1956 up to which the solution satisfies the elementary tests of physical relevance. The solution also found to have monotonic decreasing adiabatic sound speed from the centre to the boundary of the fluid sphere. A wide range of fluid spheres of different mass and radius for a given compactness is possible. The maximum mass of the fluid distribution is calculated by using stellar surface density as parameter. The values of different physical variables obtained for some potential strange star candidates like Her X-1, 4U 1538-52, LMC X-4, SAX J1808.4-3658 given by our analytical model demonstrate the astrophysical significance of our class of relativistic stellar models in the study of internal structure of compact star such as self-bound strange quark star.
Endrizzi, A.; Ciolfi, R.; Giacomazzo, B.; Kastaun, W.; Kawamura, T.
2016-08-01
We present new results of fully general relativistic magnetohydrodynamic simulations of binary neutron star (BNS) mergers performed with the Whisky code. All the models use a piecewise polytropic approximation of the APR4 equation of state for cold matter, together with a ‘hybrid’ part to incorporate thermal effects during the evolution. We consider both equal and unequal-mass models, with total masses such that either a supramassive NS or a black hole is formed after merger. Each model is evolved with and without a magnetic field initially confined to the stellar interior. We present the different gravitational wave (GW) signals as well as a detailed description of the matter dynamics (magnetic field evolution, ejected mass, post-merger remnant/disk properties). Our simulations provide new insights into BNS mergers, the associated GW emission and the possible connection with the engine of short gamma-ray bursts (both in the ‘standard’ and in the ‘time-reversal’ scenarios) and other electromagnetic counterparts.
Endrizzi, Andrea; Giacomazzo, Bruno; Kastaun, Wolfgang; Kawamura, Takumu
2016-01-01
We present new results of fully general relativistic magnetohydrodynamic (GRMHD) simulations of binary neutron star (BNS) mergers performed with the Whisky code. All the models use a piecewise polytropic approximation of the APR4 equation of state (EOS) for cold matter, together with a "hybrid" part to incorporate thermal effects during the evolution. We consider both equal and unequal-mass models, with total masses such that either a supramassive NS or a black hole (BH) is formed after merger. Each model is evolved with and without a magnetic field initially confined to the stellar interior. We present the different gravitational wave (GW) signals as well as a detailed description of the matter dynamics (magnetic field evolution, ejected mass, post-merger remnant/disk properties). Our simulations provide new insights into BNS mergers, the associated GW emission and the possible connection with the engine of short gamma-ray bursts (both in the "standard" and in the "time-reversal" scenarios) and other electro...
Chandra, S.K.
1976-01-01
The perturbation method of Lindstedt is applied to study the relativistic nonlinear effects for an elliptically polarized transverse monochromatic wave in a cold dissipative plasma in the absence of a static magnetic field. Amplitude-dependent wavelength and frequency shifts including relativistic correlations are derived.
Ocean swell within the kinetic equation for water waves
Badulin, Sergei I
2016-01-01
Effects of wave-wave interactions on ocean swell are studied. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation at long times up to $10^6$ seconds are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov-Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring are discussed. Essential drop of wave energy (wave height) due to wave-wave interactions is found to be pronounced at initial stages of swell evolution (of order of 1000 km for typical parameters of the ocean swell). At longer times wave-wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions.
Generalized fractional kinetic equations involving generalized Struve function of the first kind
K.S. Nisar
2016-04-01
Full Text Available In recent paper Dinesh Kumar et al. developed a generalized fractional kinetic equation involving generalized Bessel function of first kind. The object of this paper is to derive the solution of the fractional kinetic equation involving generalized Struve function of the first kind. The results obtained in terms of generalized Struve function of first kind are rather general in nature and can easily construct various known and new fractional kinetic equations.
Uniqueness of Landau-Lifshitz energy frame in relativistic dissipative hydrodynamics.
Tsumura, Kyosuke; Kunihiro, Teiji
2013-05-01
We show that the relativistic dissipative hydrodynamic equation derived from the relativistic Boltzmann equation by the renormalization-group method uniquely leads to the one in the energy frame proposed by Landau and Lifshitz, provided that the macroscopic-frame vector, which defines the local rest frame of the flow velocity, is independent of the momenta of constituent particles, as it should. We argue that the relativistic hydrodynamic equations for viscous fluids must be defined on the energy frame if consistent with the underlying relativistic kinetic equation.
Ocean swell within the kinetic equation for water waves
Badulin, Sergei I.; Zakharov, Vladimir E.
2017-06-01
Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation for long durations of up to 2 × 106 s are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov-Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring is discussed. Essential drop in wave energy (wave height) due to wave-wave interactions is found at the initial stages of swell evolution (on the order of 1000 km for typical parameters of the ocean swell). At longer times, wave-wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions. Weak power-law attenuation of swell within the Hasselmann equation is not consistent with results of ocean swell tracking from satellite altimetry and SAR (synthetic aperture radar) data. At the same time, the relatively fast weakening of wave-wave interactions makes the swell evolution sensitive to other effects. In particular, as shown, coupling with locally generated wind waves can force the swell to grow in relatively light winds.
Marczewski, Adam W
2010-10-05
In the article, a new integrated kinetic Langmuir equation (IKL) is derived. The IKL equation is a simple and easy to analyze but complete analytical solution of the kinetic Langmuir model. The IKL is compared with the nth-order, mixed 1,2-order, and multiexponential kinetic equations. The impact of both equilibrium coverage θ(eq) and relative equilibrium uptake u(eq) on kinetics is explained. A newly introduced Langmuir batch equilibrium factor f(eq) that is the product of both parameters θ(eq)u(eq) is used to determine the general kinetic behavior. The analysis of the IKL equation allows us to understand fully the Langmuir kinetics and explains its relation with respect to the empirical pseudo-first-order (PFO, i.e., Lagergren), pseudo-second-order (PSO), and mixed 1,2-order kinetic equations, and it shows the conditions of their possible application based on the Langmuir model. The dependence of the initial adsorption rate on the system properties is analyzed and compared to the earlier published approximate equations.
Siminos, E; Grech, M; Fülöp, T
2016-01-01
We study kinetic effects responsible for the transition to relativistic self-induced transparency in the interaction of a circularly-polarized laser-pulse with an overdense plasma and their relation to hole-boring and ion acceleration. It is shown, using particle-in-cell simulations and an analysis of separatrices in single-particle phase-space, that this transition is mediated by the complex interplay of fast electron dynamics and ion motion at the initial stage of the interaction. It thus depends on the ion charge-to-mass ratio and can be controlled by varying the laser temporal profile. Moreover, we find a new regime in which a transition from relativistic transparency to hole-boring occurs dynamically during the course of the interaction. It is shown that, for a fixed laser intensity, this dynamic transition regime allows optimal ion acceleration in terms of both energy and energy spread.
Comparison of Seven Kinetic Equations for K Release and Application of Kinetic Parameters
L(U) Xiao-Nan; XU Jian-Ming; MA Wan-Zhu; LU Yun-Fu
2007-01-01
Corn field experiments with two treatments, NP and NPK, where N in the form of urea, P in the form of calcium phosphate, and K in the form of KC1 were applied at rates of 187.5, 33.3, and 125 kg ha-1, respectively, on soils derived from Quaternary red clay were conducted in the hilly red soil region of Zhejiang Province, China. Plant grains and stalks were collected for determination of K content. Seven equations were used to describe the kinetics of K release from surface soil samples taken before the corn experiments under electric field strengths of 44.4 and 88.8 V cm-1 by means of electro-ultrafiltration (EUF) and to determine if their parameters had a practical application. The second-order and Elovich equations excellently described K release; the first-order, power function, and parabolic diffusion equations also described K release well; but the zero-order and exponential equations were not so good at reflecting K release. Five reference standards from the field experiments, including relative grain yield (yield of the NP treatment/yield of the NPK treatment), relative dry matter yield (dry matter of the NP treatment/dry matter of the NPK treatment), quantity of K uptake in the NP treatment (no K application), soil exchangeable K, and soil HNO3-soluble K, were used to test the effectiveness of equation parameters obtained from the slope or intercept of these equations. Correlations of the ymax (the maximum desorbable quantity of K) in the second-order equation and the constant b in the first-order and E lovich equations to all five reference standards were highly significant (P ≤ 0.01). The constant a in the power function equation was highly significant (P ≤ 0.01) for four of the five reference standards with the fifth being significant (P ≤ 0.05). The constant b in the parabolic equation was also significantly correlated (P ≤ 0.05) to the relative grain yield and soil HNO3-solublc K. These suggested that all of these parameters could be used to
New Developments in Relativistic Viscous Hydrodynamics
Romatschke, Paul
2009-01-01
Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized second law of thermodynamics, kinetic theory, and a complete second-order gradient expansion are reviewed. The resulting fluid dynamic equations are shown to be consistent for all these derivations, when properly accounting for the respective region of appl...
Pathak, Himadri; Sasmal, Sudip; Nayak, Malaya K.; Vaval, Nayana; Pal, Sourav
2016-08-01
The open-shell reference relativistic equation-of-motion coupled-cluster method within its four-component description is successfully implemented with the consideration of single- and double- excitation approximations using the Dirac-Coulomb Hamiltonian. At the first attempt, the implemented method is employed to calculate ionization potential value of heavy atomic (Ag, Cs, Au, Fr, and Lr) and molecular (HgH and PbF) systems, where the effect of relativity does really matter to obtain highly accurate results. Not only the relativistic effect but also the effect of electron correlation is crucial in these heavy atomic and molecular systems. To justify the fact, we have taken two further approximations in the four-component relativistic equation-of-motion framework to quantify how the effect of electron correlation plays a role in the calculated values at different levels of theory. All these calculated results are compared with the available experimental data as well as with other theoretically calculated values to judge the extent of accuracy obtained in our calculations.
Chavanis, Pierre-Henri
2014-01-01
Because of their superfluid properties, some compact astrophysical objects such as neutron stars may contain a significant part of their matter in the form of a Bose-Einstein condensate (BEC). We consider a partially-relativistic model of self-gravitating BECs where the relation between the pressure and the rest-mass density is assumed to be quadratic (as in the case of classical BECs) but pressure effects are taken into account in the relation between the energy density and the rest-mass density. At high densities, we get a stiff equation of state similar to the one considered by Zel'dovich (1961) in the context of baryon stars in which the baryons interact through a vector meson field. We determine the maximum mass of general relativistic BEC stars described by this equation of state by using the formalism of Tooper (1965). This maximum mass is slightly larger than the maximum mass obtained by Chavanis and Harko (2012) using a fully-relativistic model. We also consider the possibility that dark matter is ma...
M. G. Hafez
2016-01-01
Full Text Available Two-dimensional three-component plasma system consisting of nonextensive electrons, positrons, and relativistic thermal ions is considered. The well-known Kadomtsev-Petviashvili-Burgers and Kadomtsev-Petviashvili equations are derived to study the basic characteristics of small but finite amplitude ion acoustic waves of the plasmas by using the reductive perturbation method. The influences of positron concentration, electron-positron and ion-electron temperature ratios, strength of electron and positrons nonextensivity, and relativistic streaming factor on the propagation of ion acoustic waves in the plasmas are investigated. It is revealed that the electrostatic compressive and rarefactive ion acoustic waves are obtained for superthermal electrons and positrons, but only compressive ion acoustic waves are found and the potential profiles become steeper in case of subthermal positrons and electrons.
Relativistic kinetic momentum operators, half-rapidities and noncommutative differential calculus
Mir-Kasimov, R. M.
2012-09-01
It is shown that the generating function for the matrix elements of irreps of Lorentz group is the common eigenfunction of the interior derivatives of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions in the Relativistic Configuration Space (RCS). These derivatives commute and can be interpreted as the quantum mechanical operators of the relativistic momentum corresponding to the half of the non-Euclidean distance in the Lobachevsky momentum space (the mass shell).
Electromagnetic fluctuations in magnetized plasmas. I. The rigorous relativistic kinetic theory
Schlickeiser, R., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu [Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Yoon, P. H., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu [Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States); School of Space Research, Kyung Hee University, Yongin-Si, Gyeonggi-Do 446-701 (Korea, Republic of)
2015-07-15
Using the system of the Klimontovich and Maxwell equations, the general linear fluctuation theory for magnetized plasmas is developed. General expressions for the electromagnetic fluctuation spectra (electric and magnetic fields) from uncorrelated plasma particles in plasmas with a uniform magnetic field are derived, which are covariantly correct within the theory of special relativity. The general fluctuation spectra hold for plasmas of arbitrary composition, arbitrary momentum dependences of the plasma particle distribution functions, and arbitrary orientations of the wave vector with respect to the uniform magnetic field. Moreover, no restrictions on the values of the real and the imaginary parts of the frequency are made. The derived fluctuation spectra apply to both non-collective fluctuations and collective plasma eigenmodes in magnetized plasmas. In the latter case, kinetic equations for the components of fluctuating electric and magnetic fields in magnetized plasmas are derived that include the effect of spontaneous emission and absorption. In the limiting case of an unmagnetized plasmas, the general fluctuation spectra correctly reduce to the unmagnetized fluctuation spectra derived before.
A bin integral method for solving the kinetic collection equation
Wang, Lian-Ping; Xue, Yan; Grabowski, Wojciech W.
2007-09-01
A new numerical method for solving the kinetic collection equation (KCE) is proposed, and its accuracy and convergence are investigated. The method, herein referred to as the bin integral method with Gauss quadrature (BIMGQ), makes use of two binwise moments, namely, the number and mass concentration in each bin. These two degrees of freedom define an extended linear representation of the number density distribution for each bin following Enukashvily (1980). Unlike previous moment-based methods in which the gain and loss integrals are evaluated for a target bin, the concept of source-bin pair interactions is used to transfer bin moments from source bins to target bins. Collection kernels are treated by bilinear interpolations. All binwise interaction integrals are then handled exactly by Gauss quadrature of various orders. In essence the method combines favorable features in previous spectral moment-based and bin-based pair-interaction (or flux) methods to greatly enhance the logic, consistency, and simplicity in the numerical method and its implementation. Quantitative measures are developed to rigorously examine the accuracy and convergence properties of BIMGQ for both the Golovin kernel and hydrodynamic kernels. It is shown that BIMGQ has a superior accuracy for the Golovin kernel and a monotonic convergence behavior for hydrodynamic kernels. Direct comparisons are also made with the method of Berry and Reinhardt (1974), the linear flux method of Bott (1998), and the linear discrete method of Simmel et al. (2002).
Kinetic Thomas-Fermi solutions of the Gross-Pitaevskii equation
Ölschläger, M.; Wirth, G.; Smith, C. Morais; Hemmerich, A.
2010-01-01
Approximate solutions of the Gross-Pitaevskii (GP) equation, obtained upon neglection of the kinetic energy, are well known as Thomas-Fermi solutions. They are characterized by the compensation of the local potential by the collisional energy. In this article we consider exact solutions of the GP-equation with this property and definite values of the kinetic energy, which suggests the term "kinetic Thomas-Fermi" (KTF) solutions. We point out that a large class of light-shift potentials gives ...
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
Radhakrishnan, K.
1984-01-01
The efficiency of several algorithms used for numerical integration of stiff ordinary differential equations was compared. The methods examined included two general purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes were applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code available for the integration of combustion kinetic rate equations. It is shown that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient then evaluating the temperature by integrating its time-derivative.
From Langmuir kinetics to first- and second-order rate equations for adsorption.
Liu, Yu; Shen, Liang
2008-10-21
So far, the first- and second-order kinetic equations have been most frequently employed to interpret adsorption data obtained under various conditions, whereas the theoretical origins of these two equations still remain unknown. Using the Langmuir kinetics as a theoretical basis, this study showed that the Langmuir kinetics can be transformed to a polynomial expression of dtheta t /d t = k 1(theta e - theta t ) + k 2(theta e - theta t ) (2), a varying-order rate equation. The sufficient and necessary conditions for simplification of the Langmuir kinetics to the first- and second-order rate equations were put forward, which suggested that the relative magnitude of theta e over k 1/ k 2 governs the simplification of the Langmuir kinetics. In cases where k 1/ k 2 is greater than theta e or k 1/ k 2 is very close to theta e, adsorption kinetics would be reasonably described by the first-order rate equation, whereas the Langmuir kinetics would be reduced to the second-order equation only at k 1/ k 2 Langmuir kinetics indeed is determined by C 0. Detailed C 0-depedent boundary conditions for simplifying the Langmuir kinetics were also established and were verified by experimental data.
On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity
Nikolai N. Bogoliubov (Jr.
2007-01-01
Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.
Bargmann-Michel-Telegdi equation and one-particle relativistic approach
Della Selva, A; Masperi, L
1995-01-01
A reexamination of the semiclassical approach of the relativistic electron indicates a possible variation of its helicity for electric and magnetic static fields applied along its global motion due to zitterbewegung effects, proportional to the anomalous part of the magnetic moment.
Le Bourdiec, S
2007-03-15
Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energetic electrons and the existing electromagnetic waves. This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is chosen in order to obtain the proper velocity resolution. We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv (mono-dimensional for x and three-dimensional for velocity) computations of Weibel and whistler instabilities with one or two electrons species. (author)
Vayenas, C. G.; Fokas, A. S.; Grigoriou, D.
2016-08-01
We compute analytically the masses, binding energies and hamiltonians of gravitationally bound Bohr-type states via the rotating relativistic lepton model which utilizes the de Broglie wavelength equation in conjunction with special relativity and Newton's relativistic gravitational law. The latter uses the inertial-gravitational masses, rather than the rest masses, of the rotating particles. The model also accounts for the electrostatic charge- induced dipole interactions between a central charged lepton, which is usually a positron, with the rotating relativistic lepton ring. We use three rotating relativistic neutrinos to model baryons, two rotating relativistic neutrinos to model mesons, and a rotating relativistic electron neutrino - positron (or electron) pair to model the W± bosons. It is found that gravitationally bound ground states comprising three relativistic neutrinos have masses in the baryon mass range (∼⃒ 0.9 to 1 GeV/c2), while ground states comprising two neutrinos have masses in the meson mass range (∼⃒ 0.4 to 0.8 GeV/c2). It is also found that the rest mass values of quarks are in good agreement with the heaviest neutrino mass value of 0.05 eV/c2 and that the mass of W± bosons (∼⃒ 81 GeV/c2) corresponds to the mass of a rotating gravitationally confined e± — ve pair. A generalized expression is also derived for the gravitational potential energy of such relativistic Bohr-type structures.
Comparative Study on the Kinetic Equations of Potassium Release from Soils
LUXIAO－NAN; LUYUN－FU
1993-01-01
Elovich,two-constant,parabolic diffusion,exponential,second-order,first-order and zero-order equations were used to describe the kinetic characteristics of potassium desorption from six paddy soils of Zhejiang Province in a constant electric field (44.4V/cm) of EUF.Results showed that the second-order and Elovich equations could describe the potassium desorption kinetics best,as evidenced by the highest correlation coefficients (r) and the lowest standard errors (SE).The first-order,two-constant and parabolic diffusion equations also described the K desorption kinetics well,as showed by the relatively high correlation coefficients and relatively low standard errors.The zero-order equation did not describe the K desorption satisfactorily with a relatively low correlation coefficient and relatively high standard error.However,the exponential equation could not be used to describe the K desorption kinetics,due to the lowest correlation coefficient and the highest standarderror.
Kinetic equation for internal oxidation of Cu-Al alloy cylinders
Kexing Song; Jiandong Xing; Baohong Tian; Ping Liu; Qiming Dong
2005-01-01
The kinetics of internal oxidation of Cu-Al alloy cylinders, containing up to 2.214mol% Al, were investigated in the temperature range of 1023 K to 1273 K, and the depth of internal oxidation was measured in the microscopy. A kinetic equation was derived to describe the internal oxidation of Cu-Al alloy cylinders. For the internal oxidation of Cu-Al alloys employed in the synthesis of alumina dispersion strengthened copper, the kinetic equation can be simplified. The derived equation was checked experimentally by means of oxidation depth measurements and the results show that the derived equation is exact enough to describe the kinetics of internal oxidation of Cu-Al alloy cylinders. Based on this equation and the oxidation depth measurements, the permeability of oxygen in solid copper was obtained. Investigation also shows that there is no evidence for preferential diffusion along grain boundaries in the process of internal oxidation.
Wu, Kailiang; Tang, Huazhong
2017-01-01
The ideal gas equation of state (EOS) with a constant adiabatic index is a poor approximation for most relativistic astrophysical flows, although it is commonly used in relativistic hydrodynamics (RHD). This paper develops high-order accurate, physical-constraints-preserving (PCP), central, discontinuous Galerkin (DG) methods for the one- and two-dimensional special RHD equations with a general EOS. It is built on our theoretical analysis of the admissible states for RHD and the PCP limiting procedure that enforce the admissibility of central DG solutions. The convexity, scaling invariance, orthogonal invariance, and Lax–Friedrichs splitting property of the admissible state set are first proved with the aid of its equivalent form. Then, the high-order central DG methods with the PCP limiting procedure and strong stability-preserving time discretization are proved, to preserve the positivity of the density, pressure, specific internal energy, and the bound of the fluid velocity, maintain high-order accuracy, and be L1-stable. The accuracy, robustness, and effectiveness of the proposed methods are demonstrated by several 1D and 2D numerical examples involving large Lorentz factor, strong discontinuities, or low density/pressure, etc.
Itoh, Y
2004-01-01
An equation of motion for relativistic compact binaries is derived through the third post-Newtonian (3 PN) approximation of general relativity. The strong field point particle limit and multipole expansion of the stars are used to solve iteratively the harmonically relaxed Einstein equations. We take into account the Lorentz contraction on the multipole moments defined in our previous works. We then derive a 3 PN acceleration of the binary orbital motion of the two spherical compact stars based on a surface integral approach which is a direct consequence of local energy momentum conservation. Our resulting equation of motion admits a conserved energy (neglecting the 2.5 PN radiation reaction effect), is Lorentz invariant and is unambiguous: there exist no undetermined parameter reported in the previous works. We shall show that our 3 PN equation of motion agrees physically with the Blanchet and Faye 3 PN equation of motion if $\\lambda = - 1987/3080$, where $\\lambda$ is the parameter which is undetermined with...
Cattaneo, Carlo
2011-01-01
This title includes: Pham Mau Quam: Problemes mathematiques en hydrodynamique relativiste; A. Lichnerowicz: Ondes de choc, ondes infinitesimales et rayons en hydrodynamique et magnetohydrodynamique relativistes; A.H. Taub: Variational principles in general relativity; J. Ehlers: General relativistic kinetic theory of gases; K. Marathe: Abstract Minkowski spaces as fibre bundles; and, G. Boillat: Sur la propagation de la chaleur en relativite.
Weibel instability in relativistic quantum plasmas
Mendonça, J. T.; Brodin, G.
2015-08-01
Generation of quasi-static magnetic fields, due to the Weibel instability is studied in a relativistic quantum plasma. This instability is induced by a temperature anisotropy. The dispersion relation and growth rates for low frequency electromagnetic perturbations are derived using a wave-kinetic equation which describes the evolution of the electron Wigner quasi-distribution. The influence of parallel kinetic effects is discussed in detail.
Siminos, Evangelos; Svedung Wettervik, Benjamin; Grech, Mickael; Fülöp, Tünde
2016-10-01
We study kinetic effects responsible for the transition to relativistic self-induced transparency in the interaction of a circularly-polarized laser-pulse with an overdense plasma and their relation to hole-boring and ion acceleration. It is shown, using particle-in-cell simulations and an analysis of separatrices in single-particle phase-space, that this transition is mediated by the complex interplay of fast electron dynamics and ion motion at the initial stage of the interaction. It thus depends on the ion charge-to-mass ratio and can be controlled by varying the laser temporal profile. Moreover, we find a new regime in which a transition from relativistic transparency to hole-boring occurs dynamically during the course of the interaction. It is shown that, for a fixed laser intensity, this dynamic transition regime allows optimal ion acceleration in terms of both energy and energy spread. This work was supported by the Knut and Alice Wallenberg Foundation (pliona project) and the European Research Council (ERC-2014-CoG Grant 647121).
Unitary representations of the Poincaré group and relativistic wave equations
Ohnuki, Yoshio
1976-01-01
This book is devoted to an extensive and systematic study on unitary representations of the Poincaré group. The Poincaré group plays an important role in understanding the relativistic picture of particles in quantum mechanics. Complete knowledge of every free particle states and their behaviour can be obtained once all the unitary irreducible representations of the Poincaré group are found. It is a surprising fact that a simple framework such as the Poincaré group, when unified with quantum theory, fixes our possible picture of particles severely and without exception. In this connection, the
On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind
Dinesh Kumar
2015-01-01
Full Text Available We develop a new and further generalized form of the fractional kinetic equation involving generalized Bessel function of the first kind. The manifold generality of the generalized Bessel function of the first kind is discussed in terms of the solution of the fractional kinetic equation in the paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably new results.
Generalized Klein-Gordon and Dirac Equations from Nonlocal Kinetic Approach
El-Nabulsi, Rami Ahmad
2016-09-01
In this note, I generalized the Klein-Gordon and the Dirac equations by using Suykens's nonlocal-in-time kinetic energy approach, which is motivated from Feynman's kinetic energy functional formalism where the position differences are shifted with respect to one another. I proved that these generalized equations are similar to those obtained in literature in the presence of minimal length based on the Quesne-Tkachuk algebra.
Entropy Analysis of Kinetic Flux Vector Splitting Schemes for the Compressible Euler Equations
Shiuhong, Lui; Xu, Jun
1999-01-01
Flux Vector Splitting (FVS) scheme is one group of approximate Riemann solvers for the compressible Euler equations. In this paper, the discretized entropy condition of the Kinetic Flux Vector Splitting (KFVS) scheme based on the gas-kinetic theory is proved. The proof of the entropy condition involves the entropy definition difference between the distinguishable and indistinguishable particles.
Meliani, Z; Giacomazzo, B
2008-01-01
The deceleration mechanisms for relativistic jets in active galactic nuclei remain an open question, and in this paper we propose a model which could explain sudden jet deceleration, invoking density discontinuities. This is particularly motivated by recent indications from HYMORS. Exploiting high resolution, numerical simulations, we demonstrate that for both high and low energy jets, always at high Lorentz factor, a transition to a higher density environment can cause a significant fraction of the directed jet energy to be lost on reflection. This can explain how one-sided jet deceleration and a transition to FR I type can occur in HYMORS, which start as FR II (and remain so on the other side). For that purpose, we implemented in the relativistic hydrodynamic grid-adaptive AMRVAC code, the Synge-type equation of state introduced in the general polytropic case by Meliani et al. (2004). We present results for 10 model computations, varying the inlet Lorentz factor from 10 to 20, including uniform or decreasin...
Nonlinear relativistic and quantum equations with a common type of solution.
Nobre, F D; Rego-Monteiro, M A; Tsallis, C
2011-04-08
Generalizations of the three main equations of quantum physics, namely, the Schrödinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index q, are considered in such a way that the standard linear equations are recovered in the limit q→1. Interestingly, these equations present a common, solitonlike, traveling solution, which is written in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics. In all cases, the well-known Einstein energy-momentum relation is preserved for arbitrary values of q.
Salhoumi, A.; Galenko, P. K.
2017-04-01
Rapidly moving solid-liquid interface is treated analytically and numerically. Derivation and qualitative analysis of interface propagation kinetics is presented. Quantitative predictions of solutions, which follow from the Kinetic Rate Theory and the solution of Gibbs-Thomson-type equation, are compared with Molecular Dynamics simulation data (MD-data) on crystallization and melting of fcc-lattice of nickel. It is shown in the approximation of a linear behavior of the interface velocity versus undercooling that the Gibbs-Thomson-type equation and kinetic rate theory describe MD-data well enough, in the range of small growth velocity and within the range of relatively small undercooling, with a relative error for the obtained values of kinetic coefficient of the order 1.1%. Within the small-and long range of undercooling, in nonlinear behavior of the interface velocity versus undercooling, the kinetic rate theory disagrees sharply with MD-data, qualitatively and quantitatively, unlike to the Gibbs-Thomson-type equation which is in a good agreement with MD-data within the whole range of undercooling and crystal growth velocity.
Potekhin, A Yu
2000-01-01
The analytic equation of state of nonideal Coulomb plasmas consisting of pointlike ions immersed in a polarizable electron background (physics/9807042) is improved, and its applicability range is considerably extended. First, the fit of the electron screening contribution in the free energy of the Coulomb liquid is refined at high densities where the electrons are relativistic. Second, we calculate the screening contribution for the Coulomb solid (bcc and fcc) and derive an analytic fitting expression. Third, we propose a simple approximation to the internal and free energy of the liquid one-component plasma of ions, accurate within the numerical errors of the most recent Monte Carlo simulations. We obtain an updated value of the coupling parameter at the solid-liquid phase transition for the one-component plasma: Gamma_m = 175.0 (+/- 0.4).
Kinetic theory the Chapman-Enskog solution of the transport equation for moderately dense gases
Brush, S G
1972-01-01
Kinetic Theory, Volume 3: The Chapman-Enskog Solution of the Transport Equation for Moderately Dense Gases describes the Chapman-Enskog solution of the transport equation for moderately dense gases. Topics covered range from the propagation of sound in monatomic gases to the kinetic theory of simple and composite monatomic gases and generalizations of the theory to higher densities. The application of kinetic theory to the determination of intermolecular forces is also discussed. This volume is divided into two sections and begins with an introduction to the work of Hilbert, Chapman, and Ensko
Gholibeigian, Hassan; Amirshahkarami, Abdolazim; Gholibeigian, Kazem
2017-01-01
In special relativity theory, time dilates in velocity of near light speed. Also based on ``Substantial motion'' theory of Sadra, relative time (time flux); R = f (mv , σ , τ) , for each atom is momentum of its involved fundamental particles, which is different from the other atoms. In this way, for modification of the relativistic classical equation of string theory and getting more precise results, we should use effect of dilation and contraction of time in equation. So we propose to add two derivatives of the time's flux to the equation as follows: n.tp∂/R ∂ τ +∂2Xμ/(σ , τ) ∂τ2 = n .tp (∂/R ∂ σ ) +c2∂2Xμ/(σ , τ) ∂σ2 In which, Xμ is space-time coordinates of the string, σ & τ are coordinates on the string world sheet, respectively space and time along the string, string's mass m , velocity of string's motion v , factor n depends on geometry of each hidden extra dimension which relates to its own flux time, and tp is Planck's time. AmirKabir University of Technology, Tehran, Iran.
Relativistic equation of state at subnuclear densities in the Thomas-Fermi approximation
Zhang, Z W
2014-01-01
We study the non-uniform nuclear matter using the self-consistent Thomas--Fermi approximation with a relativistic mean-field model. The non-uniform matter is assumed to be composed of a lattice of heavy nuclei surrounded by dripped nucleons. At each temperature $T$, proton fraction $Y_p$, and baryon mass density $\\rho_B$, we determine the thermodynamically favored state by minimizing the free energy with respect to the radius of the Wigner--Seitz cell, while the nucleon distribution in the cell can be determined self-consistently in the Thomas--Fermi approximation. A detailed comparison is made between the present results and previous calculations in the Thomas--Fermi approximation with a parameterized nucleon distribution that has been adopted in the widely used Shen EOS.
Jagtap, Ameya Dilip
2015-01-01
A novel explicit and implicit Kinetic Streamlined-Upwind Petrov Galerkin (KSUPG) scheme is presented for hyperbolic equations such as Burgers equation and compressible Euler equations. The proposed scheme performs better than the original SUPG stabilized method in multi-dimensions. To demonstrate the numerical accuracy of the scheme, various numerical experiments have been carried out for 1D and 2D Burgers equation as well as for 1D and 2D Euler equations using Q4 and T3 elements. Furthermore, spectral stability analysis is done for the explicit 2D formulation. Finally, a comparison is made between explicit and implicit versions of the KSUPG scheme.
The Existence and Uniqueness Result for a Relativistic Nonlinear Schrödinger Equation
Yongkuan Cheng; Jun Yang
2014-01-01
We study the existence and uniqueness of positive solutions for a class of quasilinear elliptic equations. This model has been proposed in the self-channeling of a high-power ultrashort laser in matter.
Deriglazov, Alexei A
2015-01-01
MPTD-equations in the Lagrangian formulation correspond to the minimal interaction of spin with gravity. Due to the interaction, in the Lagrangian equations instead of the original metric $g$ emerges spin-dependent effective metric $G=g+h(S)$. So we need to decide, which of them the MPTD-particle sees as the space-time metric. We show that MPTD-equations, if considered with respect to original metric, have no physically admissible solutions: acceleration of the particle grows up to infinity as its speed approximates to the speed of light. If considered with respect to $G$, the theory is consistent. But the metric now depends on spin, so there is no unique space-time manifold for the Universe of spinning particles: each particle probes his own three-dimensional geometry. This can be improved by adding a non-minimal interaction, and gives the modified MPTD-equations with reasonable behavior within the original metric.
Kinetic turbulence in relativistic plasma: from thermal bath to non-thermal continuum
Zhdankin, Vladimir; Uzdensky, Dmitri A; Begelman, Mitchell C
2016-01-01
We present results from particle-in-cell simulations of driven turbulence in collisionless, relativistic pair plasma. We find that turbulent fluctuations are consistent with the classical $k_\\perp^{-5/3}$ magnetic energy spectrum at fluid scales and a steeper $k_\\perp^{-4}$ spectrum at sub-Larmor scales, where $k_\\perp$ is the wavevector perpendicular to the mean field. We demonstrate the development of a non-thermal, power-law particle energy distribution, $f(E) \\sim E^{-\\alpha}$, with index well fit by $\\alpha \\sim 1 + C_0 (\\sigma \\rho_e/L)^{-1/2}$, where $C_0$ is a constant, $\\sigma$ is magnetization, and $\\rho_e/L$ is the ratio of characteristic Larmor radius to system size. In the absence of asymptotic system-size independent scalings, our results challenge the viability of turbulent particle acceleration in high-energy astrophysical systems such as pulsar wind nebulae.
Kinetic simulations of the lowest-order unstable mode of relativistic magnetostatic equilibria
Nalewajko, Krzysztof; Yuan, Yajie; East, William E; Blandford, Roger D
2016-01-01
We present the results of particle-in-cell numerical pair plasma simulations of relativistic 2D magnetostatic equilibria known as the 'ABC' fields. In particular, we focus on the lowest-order unstable configuration consisting of two minima and two maxima of the magnetic vector potential. Breaking of the initial symmetry leads to exponential growth of the electric energy and to the formation of two current layers, which is consistent with the picture of 'X-point collapse' first described by Syrovatskii. Magnetic reconnection within the layers heats a fraction of particles to very high energies. After the saturation of the linear instability, the current layers are disrupted and the system evolves chaotically, diffusing the particle energies in a stochastic second-order Fermi process leading to the formation of power-law energy distributions. The power-law slopes harden with the increasing mean magnetization, but they are significantly softer than those produced in simulations initiated from Harris-type layers....
Reaction Kinetic Equation for Char Combustion of Underground Coal Gasification
YU Hong-guan; YANG Lan-he; FENG Wei-min; LIU Shu-qin; SONG Zhen-qi
2006-01-01
Based on the quasi-steady-state approximation, the dynamic equation of char combustion in the oxidation zone of underground coal gasification (UCG) was derived. The parameters of the dynamic equation were determined at 900℃ using a thermo-gravimetric (TG) analyzer connected to a flue gas analyzer and this equation. The equation was simplified for specific coals, including high ash content, low ash content, and low ash fusibility ones. The results show that 1) the apparent reaction rate constant increases with an increase in volatile matter value as dry ash-free basis, 2) the effective coefficient of diffusion decreases with an increase in ash as dry basis, and 3) the mass transfer coefficient is independent of coal quality on the whole. The apparent reaction rate constant, mass-transfer coefficient and effective coefficient of diffusion of six char samples range from 7.51×104 m/s to 8.98×104 m/s, 3.05×106 m/s to 3.23×106 m/s and 5.36×106 m2/s to 8.23×106 m2/s at 900℃, respectively.
The many facets of the (non relativistic) Nuclear Equation of State
Giuliani, G; Bonasera, A
2013-01-01
A nucleus is a quantum many body system made of strongly interacting Fermions, protons and neutrons (nucleons). This produces a rich Nuclear Equation of State whose knowledge is crucial to our understanding of the composition and evolution of celestial objects. The nuclear equation of state displays many different features; first neutrons and protons might be treated as identical particles or nucleons, but when the differences between protons and neutrons are spelled out, we can have completely different scenarios, just by changing slightly their interactions. At zero temperature and for neutron rich matter, a quantum liquid gas phase transition at low densities or a quark-gluon plasma at high densities might occur. Furthermore, the large binding energy of the $\\alpha$ particle, a Boson, might also open the possibility of studying a system made of a mixture of Bosons and Fermions, which adds to the open problems of the nuclear equation of state.
The quantum mechanics based on a general kinetic energy
Wei, Yuchuan
2016-01-01
In this paper, we introduce the Schrodinger equation with a general kinetic energy operator. The conservation law is proved and the probability continuity equation is deducted in a general sense. Examples with a Hermitian kinetic energy operator include the standard Schrodinger equation, the relativistic Schrodinger equation, the fractional Schrodinger equation, the Dirac equation, and the deformed Schrodinger equation. We reveal that the Klein-Gordon equation has a hidden non-Hermitian kinetic energy operator. The probability continuity equation with sources indicates that there exists a different way of probability transportation, which is probability teleportation. An average formula is deducted from the relativistic Schrodinger equation, the Dirac equation, and the K-G equation.
Point-particle effective field theory III: relativistic fermions and the Dirac equation
Burgess, C. P.; Hayman, Peter; Rummel, Markus; Zalavári, László
2017-09-01
We formulate point-particle effective field theory (PPEFT) for relativistic spin-half fermions interacting with a massive, charged finite-sized source using a first-quantized effective field theory for the heavy compact object and a second-quantized language for the lighter fermion with which it interacts. This description shows how to determine the near-source boundary condition for the Dirac field in terms of the relevant physical properties of the source, and reduces to the standard choices in the limit of a point source. Using a first-quantized effective description is appropriate when the compact object is sufficiently heavy, and is simpler than (though equivalent to) the effective theory that treats the compact source in a second-quantized way. As an application we use the PPEFT to parameterize the leading energy shift for the bound energy levels due to finite-sized source effects in a model-independent way, allowing these effects to be fit in precision measurements. Besides capturing finite-source-size effects, the PPEFT treatment also efficiently captures how other short-distance source interactions can shift bound-state energy levels, such as due to vacuum polarization (through the Uehling potential) or strong interactions for Coulomb bound states of hadrons, or any hypothetical new short-range forces sourced by nuclei.
Pedro L. Valencia
2017-04-01
Full Text Available We provide initial rate data from enzymatic reaction experiments and tis processing to estimate the kinetic parameters from the substrate uncompetitive inhibition equation using the median method published by Eisenthal and Cornish-Bowden (Cornish-Bowden and Eisenthal, 1974; Eisenthal and Cornish-Bowden, 1974. The method was denominated the direct linear plot and consists in the calculation of the median from a dataset of kinetic parameters Vmax and Km from the Michaelis–Menten equation. In this opportunity we present the procedure to applicate the direct linear plot to the substrate uncompetitive inhibition equation; a three-parameter equation. The median method is characterized for its robustness and its insensibility to outlier. The calculations are presented in an Excel datasheet and a computational algorithm was developed in the free software Python. The kinetic parameters of the substrate uncompetitive inhibition equation Vmax, Km and Ks were calculated using three experimental points from the dataset formed by 13 experimental points. All the 286 combinations were calculated. The dataset of kinetic parameters resulting from this combinatorial was used to calculate the median which corresponds to the statistic estimator of the real kinetic parameters. A comparative statistical analyses between the median method and the least squares was published in Valencia et al. [3].
Valencia, Pedro L; Astudillo-Castro, Carolina; Gajardo, Diego; Flores, Sebastián
2017-04-01
We provide initial rate data from enzymatic reaction experiments and tis processing to estimate the kinetic parameters from the substrate uncompetitive inhibition equation using the median method published by Eisenthal and Cornish-Bowden (Cornish-Bowden and Eisenthal, 1974; Eisenthal and Cornish-Bowden, 1974). The method was denominated the direct linear plot and consists in the calculation of the median from a dataset of kinetic parameters Vmax and Km from the Michaelis-Menten equation. In this opportunity we present the procedure to applicate the direct linear plot to the substrate uncompetitive inhibition equation; a three-parameter equation. The median method is characterized for its robustness and its insensibility to outlier. The calculations are presented in an Excel datasheet and a computational algorithm was developed in the free software Python. The kinetic parameters of the substrate uncompetitive inhibition equation Vmax , Km and Ks were calculated using three experimental points from the dataset formed by 13 experimental points. All the 286 combinations were calculated. The dataset of kinetic parameters resulting from this combinatorial was used to calculate the median which corresponds to the statistic estimator of the real kinetic parameters. A comparative statistical analyses between the median method and the least squares was published in Valencia et al. [3].
,
2016-01-01
With Einstein's inertial motion (free-falling and non-rotating relative to gyroscopes), geodesics for non-relativistic particles can intersect repeatedly, allowing one to compute the space-time curvature $R^{\\hat{0} \\hat{0}}$ exactly. Einstein's $R^{\\hat{0} \\hat{0}}$ for strong gravitational fields and for relativistic source-matter is identical with the Newtonian expression for the relative radial acceleration of neighboring free-falling test-particles, spherically averaged.--- Einstein's field equations follow from Newtonian experiments, local Lorentz-covariance, and energy-momentum conservation combined with the Bianchi identity.
Luciano, Rezzolla
2013-01-01
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...
An Introduction to Relativistic Quantum Mechanics. I. From Relativity to Dirac Equation
De Sanctis, M
2007-01-01
By using the general concepts of special relativity and the requirements of quantum mechanics, Dirac equation is derived and studied. Only elementary knowledge of spin and rotations in quantum mechanics and standard handlings of linear algebra are employed for the development of the present work.
Itoh, Y; Asada, H; Itoh, Yousuke; Futamase, Toshifumi; Asada, Hideki
2001-01-01
We study the equation of motion appropriate to an inspiralling binary star system whose constituent stars have strong internal gravity. We use the post-Newtonian approximation with the strong field point particle limit by which we can introduce into general relativity a notion of a point-like particle with strong internal gravity without using Dirac delta distribution. Besides this limit, to deal with strong internal gravity we express the equation of motion in surface integral forms and calculate these integrals explicitly. As a result we obtain the equation of motion for a binary of compact bodies accurate through the second and half post-Newtonian (2.5 PN) order. This equation is derived in the harmonic coordinate. Our resulting equation perfectly agrees with Damour and Deruelle 2.5 PN equation of motion. Hence it is found that the 2.5 PN equation of motion is applicable to a relativistic compact binary.
Kinetic Simulations of the Lowest-order Unstable Mode of Relativistic Magnetostatic Equilibria
Nalewajko, Krzysztof; Zrake, Jonathan; Yuan, Yajie; East, William E.; Blandford, Roger D.
2016-08-01
We present the results of particle-in-cell numerical pair plasma simulations of relativistic two-dimensional magnetostatic equilibria known as the “Arnold-Beltrami-Childress” fields. In particular, we focus on the lowest-order unstable configuration consisting of two minima and two maxima of the magnetic vector potential. Breaking of the initial symmetry leads to exponential growth of the electric energy and to the formation of two current layers, which is consistent with the picture of “X-point collapse” first described by Syrovatskii. Magnetic reconnection within the layers heats a fraction of particles to very high energies. After the saturation of the linear instability, the current layers are disrupted and the system evolves chaotically, diffusing the particle energies in a stochastic second-order Fermi process, leading to the formation of power-law energy distributions. The power-law slopes harden with the increasing mean magnetization, but they are significantly softer than those produced in simulations initiated from Harris-type layers. The maximum particle energy is proportional to the mean magnetization, which is attributed partly to the increase of the effective electric field and partly to the increase of the acceleration timescale. We describe in detail the evolving structure of the dynamical current layers and report on the conservation of magnetic helicity. These results can be applied to highly magnetized astrophysical environments, where ideal plasma instabilities trigger rapid magnetic dissipation with efficient particle acceleration and flares of high-energy radiation.
Agostino Marinelli
2010-11-01
Full Text Available Longitudinal space-charge forces from density fluctuations generated by shot noise can be a major source of microbunching instability in relativistic high brightness electron beams. The gain in microbunching due to this effect is broadband, extending at least up to optical frequencies, where the induced structure on the beam distribution gives rise to effects such as coherent optical transition radiation. In the high-frequency regime, theoretical and computational analyses of microbunching formation require a full three-dimensional treatment. In this paper we address the problem of space-charge induced optical microbunching formation in the high-frequency limit when transverse thermal motion due to finite emittance is included for the first time. We derive an analytical description of this process based on the beam’s plasma dielectric function. We discuss the effect of transverse temperature on the angular distribution of microbunching gain and its connection to the physics of Landau damping in longitudinal plasma oscillations. Application of the theory to a relevant experimental scenario is discussed. The analytical results obtained are then compared to the predictions arising from high resolution three-dimensional molecular dynamics simulations.
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 H2 combustion model.
Kinetic Equation for Internal Oxidation of Cu-Al Alloy Spheres
SONG Kexing; GAO Jianxin; XU Xiaofeng; LI Peiquan; TIAN Baohong; GUO Xiuhua
2007-01-01
The kinetics of internal oxidation of Cu-Al alloy spheres, containing up to 2.214% mole fraction Al was investigated in the temperature range 1 023 K to 1 273 K, and the depth of internal oxidation was measured in the microscopy. A kinetic equation was derived to describe the internal oxidation of Cu-Al alloy spheres, which was checked experimentally by means of oxidation depth measurements. The results show that the derived equation is exact enough to describe the kinetics of internal oxidation of Cu-Al alloy spheres.Based on this equation and the oxidation depth measurements, the permeability of oxygen in solid copper has been obtained. Investigation also shows that in the process of internal oxidation, there is no evidence for preferential diffusion along grain boundaries.
Silva, Milena Wollmann da; Vilhena, Marco Tullio M.B.; Bodmann, Bardo Ernst J.; Vasques, Richard, E-mail: milena.wollmann@ufrgs.br, E-mail: vilhena@mat.ufrgs.br, E-mail: bardobodmann@ufrgs.br, E-mail: richard.vasques@fulbrightmail.org [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica
2015-07-01
The neutron point kinetics equation, which models the time-dependent behavior of nuclear reactors, is often used to understand the dynamics of nuclear reactor operations. It consists of a system of coupled differential equations that models the interaction between (i) the neutron population; and (II) the concentration of the delayed neutron precursors, which are radioactive isotopes formed in the fission process that decay through neutron emission. These equations are deterministic in nature, and therefore can provide only average values of the modeled populations. However, the actual dynamical process is stochastic: the neutron density and the delayed neutron precursor concentrations vary randomly with time. To address this stochastic behavior, Hayes and Allen have generalized the standard deterministic point kinetics equation. They derived a system of stochastic differential equations that can accurately model the random behavior of the neutron density and the precursor concentrations in a point reactor. Due to the stiffness of these equations, this system was numerically implemented using a stochastic piecewise constant approximation method (Stochastic PCA). Here, we present a study of the influence of stochastic fluctuations on the results of the neutron point kinetics equation. We reproduce the stochastic formulation introduced by Hayes and Allen and compute Monte Carlo numerical results for examples with constant and time-dependent reactivity, comparing these results with stochastic and deterministic methods found in the literature. Moreover, we introduce a modified version of the stochastic method to obtain a non-stiff solution, analogue to a previously derived deterministic approach. (author)
Double perturbation series in the differential equations of enzyme kinetics
Fraser, Simon J.
1998-07-01
The connection between combined singular and ordinary perturbation methods and slow-manifold theory is discussed using the Michaelis-Menten model of enzyme catalysis as an example. This two-step mechanism is described by a planar system of ordinary differential equations (ODEs) with a fast transient and a slow "steady-state" decay mode. The systems of scaled nonlinear ODEs for this mechanism contain a singular (η) and an ordinary (ɛ) perturbation parameter: η multiplies the velocity component of the fast variable and dominates the fast-mode perturbation series; ɛ controls the decay toward equilibrium and dominates the slow-mode perturbation series. However, higher order terms in both series contain η and ɛ. Finite series expansions partially decouple the system of ODEs into fast-mode and slow-mode ODEs; infinite series expansions completely decouple these ODEs. Correspondingly, any slow-mode ODE approximately describes motion on M, the linelike slow manifold of the system, and in the infinite series limit this description is exact. Thus the perturbation treatment and the slow-manifold picture of the system are closely related. The functional equation for M is solved automatically with the manipulative language MAPLE. The formal η and ɛ single perturbation expansions for the slow mode yield the same double (η,ɛ) perturbation series expressions to given order. Generalizations of this procedure are discussed.
SBMLsqueezer: A CellDesigner plug-in to generate kinetic rate equations for biochemical networks
Schröder Adrian
2008-04-01
Full Text Available Abstract Background The development of complex biochemical models has been facilitated through the standardization of machine-readable representations like SBML (Systems Biology Markup Language. This effort is accompanied by the ongoing development of the human-readable diagrammatic representation SBGN (Systems Biology Graphical Notation. The graphical SBML editor CellDesigner allows direct translation of SBGN into SBML, and vice versa. For the assignment of kinetic rate laws, however, this process is not straightforward, as it often requires manual assembly and specific knowledge of kinetic equations. Results SBMLsqueezer facilitates exactly this modeling step via automated equation generation, overcoming the highly error-prone and cumbersome process of manually assigning kinetic equations. For each reaction the kinetic equation is derived from the stoichiometry, the participating species (e.g., proteins, mRNA or simple molecules as well as the regulatory relations (activation, inhibition or other modulations of the SBGN diagram. Such information allows distinctions between, for example, translation, phosphorylation or state transitions. The types of kinetics considered are numerous, for instance generalized mass-action, Hill, convenience and several Michaelis-Menten-based kinetics, each including activation and inhibition. These kinetics allow SBMLsqueezer to cover metabolic, gene regulatory, signal transduction and mixed networks. Whenever multiple kinetics are applicable to one reaction, parameter settings allow for user-defined specifications. After invoking SBMLsqueezer, the kinetic formulas are generated and assigned to the model, which can then be simulated in CellDesigner or with external ODE solvers. Furthermore, the equations can be exported to SBML, LaTeX or plain text format. Conclusion SBMLsqueezer considers the annotation of all participating reactants, products and regulators when generating rate laws for reactions. Thus, for
Seidi, M.; Behnia, S.; Khodabakhsh, R.
2014-09-01
Point reactor kinetics equations with one group of delayed neutrons in the presence of the time-dependent external neutron source are solved analytically during the start-up of a nuclear reactor. Our model incorporates the random nature of the source and linear reactivity variation. We establish a general relationship between the expectation values of source intensity and the expectation values of neutron density of the sub-critical reactor by ignoring the term of the second derivative for neutron density in neutron point kinetics equations. The results of the analytical solution are in good agreement with the results obtained with numerical solution.
Kinetic theory of spatially homogeneous systems with long-range interactions: II. Basic equations
Chavanis, Pierre-Henri
2013-01-01
We provide a short historic of the early development of kinetic theory in plasma physics and synthesize the basic kinetic equations describing the evolution of systems with long-range interactions derived in Paper I. We describe the evolution of the system as a whole and the relaxation of a test particle in a bath at equilibrium or out-of-equilibrium. We write these equations for an arbitrary long-range potential of interaction in a space of arbitrary dimension d. We discuss the scaling of th...
Formulation of relativistic dissipative fluid dynamics and its applications in heavy-ion collisions
Jaiswal, Amaresh
2014-01-01
Relativistic fluid dynamics finds application in astrophysics, cosmology and the physics of high-energy heavy-ion collisions. In this thesis, we present our work on the formulation of relativistic dissipative fluid dynamics within the framework of relativistic kinetic theory. We employ the second law of thermodynamics as well as the relativistic Boltzmann equation to obtain the dissipative evolution equations. We present a new derivation of the dissipative hydrodynamic equations using the second law of thermodynamics wherein all the second-order transport coefficients get determined uniquely within a single theoretical framework. An alternate derivation of the dissipative equations which does not make use of the two major approximations/assumptions namely, Grad's 14-moment approximation and second moment of Boltzmann equation, inherent in the Israel-Stewart theory, is also presented. Moreover, by solving the Boltzmann equation iteratively in a Chapman-Enskog like expansion, we have derived the form of second-...
Bret, A.; Gremillet, L; Benisti, D.; Lefebvre, E.
2008-01-01
Besides being one of the most fundamental basic issues of plasma physics, the stability analysis of an electron beam-plasma system is of critical relevance in many areas of physics. Surprisingly, decades of extensive investigation had not yet resulted in a realistic unified picture of the multidimensional unstable spectrum within a fully relativistic and kinetic framework. All attempts made so far in this direction were indeed restricted to simplistic distribution functions and/or did not aim...
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.
Generalization of the Analytical Exponential Model for Homogeneous Reactor Kinetics Equations
Abdallah A. Nahla
2012-01-01
Full Text Available Mathematical form for two energy groups of three-dimensional homogeneous reactor kinetics equations and average one group of the precursor concentration of delayed neutrons is presented. This mathematical form is called “two energy groups of the point kinetics equations.” We rewrite two energy groups of the point kinetics equations in the matrix form. Generalization of the analytical exponential model (GAEM is developed for solving two energy groups of the point kinetics equations. The GAEM is based on the eigenvalues and the corresponding eigenvectors of the coefficient matrix. The eigenvalues of the coefficient matrix are calculated numerically using visual FORTRAN code, based on Laguerre’s method, to calculate the roots of an algebraic equation with real coefficients. The eigenvectors of the coefficient matrix are calculated analytically. The results of the GAEM are compared with the traditional methods. These comparisons substantiate the accuracy of the results of the GAEM. In addition, the GAEM is faster than the traditional methods.
Phu, Jack; Al-Saleem, Noha; Kalloniatis, Michael; Khuu, Sieu K
2016-11-01
In the present study, we measured the extent of statokinetic dissociation (SKD) in normal observers and then equated the psychophysical tasks into a two-interval forced choice (2IFC) procedure. In Experiment 1, we used the Humphrey visual field analyzer in static perimetry and automated kinetic perimetry modes to measure contrast sensitivity thresholds and the Goldmann manual kinetic perimeter to measure isopters. This was carried out using a Goldmann size II target. Goldmann kinetic perimetry was performed manually with both inward (peripheral to center) and outward (center to periphery) directions of movement to deduce an "average" isopter. This revealed the presence of SKD when superimposed upon the map of static contrast threshold results. There was no evidence of any contribution of examiner technique or instrument-specific differences to SKD. In Experiment 2, we determined the psychometric curves plotting proportion seen as a function of stimulus eccentricity with static and kinetic stimuli with a 2IFC procedure and method of constant stimuli. In an additional experiment, we also showed that subjects were able to reliably discriminate whether a stimulus was static, moving inward, or moving outward, and hence, comparisons could be made between static and kinetic perimetry tasks. Overall, by making the task objective and reducing criterion bias, eccentricity thresholds were equated across static and kinetic perimetry methods; hence, no evidence of SKD was seen. We suggest SKD is inherent to the differences in methodology of threshold measurement in conventional static and kinetic perimetry and individual criterion bias.
Serov, S A
2013-01-01
In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert's and Enskog's methods are discussed. The equations system of multicomponent non-equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asymptotic) method for solution of the system of kinetic Boltzmann equations. It is shown, that the velocity distribution functions of particles, obtained by the proposed method and by Enskog's method, within Enskog's approach, are equivalent up to the infinitesimal first order terms of the asymptotic expansion, but, generally speaking, differ in the next order. Interpretation of turbulent gas flow is proposed, as stratified on components gas flow, which is described by the derived equations system of multicomponent non-equilibrium gas dynamics.
Static solution of the general relativistic nonlinear $\\sigma$model equation
Lee, C H; Lee, H K; Lee, Chul H; Kim, Joon Ha; Lee, Hyun Kyu
1994-01-01
The nonlinear \\sigma-model is considered to be useful in describing hadrons (Skyrmions) in low energy hadron physics and the approximate behavior of the global texture. Here we investigate the properties of the static solution of the nonlinear \\sigma-model equation coupled with gravity. As in the case where gravity is ignored, there is still no scale parameter that determines the size of the static solution and the winding number of the solution is 1/2. The geometry of the spatial hyperspace in the asymptotic region of large r is explicitly shown to be that of a flat space with some missing solid angle.
Relativistic particle transport in extragalactic jets: I. Coupling MHD and kinetic theory
Casse, F
2003-01-01
Multidimensional magneto-hydrodynamical (MHD) simulations coupled with stochastic differential equations (SDEs) adapted to test particle acceleration and transport in complex astrophysical flows are presented. The numerical scheme allows the investigation of shock acceleration, adiabatic and radiative losses as well as diffusive spatial transport in various diffusion regimes. The applicability of SDEs to astrophysics is first discussed in regards to the different regimes and the MHD code spatial resolution. The procedure is then applied to 2.5D MHD-SDE simulations of kilo-parsec scale extragalactic jets. The ability of SDE to reproduce analytical solutions of the diffusion-convection equation for electrons is tested through the incorporation of an increasing number of effects: shock acceleration, spatially dependent diffusion coefficients and synchrotron losses. The SDEs prove to be efficient in various shock configuration occurring in the inner jet during the development of the Kelvin-Helmholtz instability. ...
Kinetic Flux Vector Splitting Method for the Shallow Water Wave Equations
施卫平; WeiShyy
2003-01-01
Based on the analogy to gas dynamics,the kinetic flux flux vector splitting (KFVS) method is used to stimulate the shallow water wave equations,The flus vectors of the equations are split on the basis of the local equilibrium Maxwell-Boltzmann distribution One dimensional examples including a dam breaking wave and flows over a ridge are calcualted.The solutions exhibit second-order accuracy with no spurious oscillation.
BRIEF COMMUNICATION: On the drift kinetic equation driven by plasma flows
Shaing, K. C.
2010-07-01
A drift kinetic equation that is driven by plasma flows has previously been derived by Shaing and Spong 1990 (Phys. Fluids B 2 1190). The terms that are driven by particle speed that is parallel to the magnetic field B have been neglected. Here, such terms are discussed to examine their importance to the equation and to show that these terms do not contribute to the calculations of plasma viscosity in large aspect ratio toroidal plasmas, e.g. tokamaks and stellarators.
Conformal anisotropic relativistic charged fluid spheres with a linear equation of state
Esculpi, M.; Alomá, E.
2010-06-01
We obtain two new families of compact solutions for a spherically symmetric distribution of matter consisting of an electrically charged anisotropic fluid sphere joined to the Reissner-Nordstrom static solution through a zero pressure surface. The static inner region also admits a one parameter group of conformal motions. First, to study the effect of the anisotropy in the sense of the pressures of the charged fluid, besides assuming a linear equation of state to hold for the fluid, we consider the tangential pressure p ⊥ to be proportional to the radial pressure p r , the proportionality factor C measuring the grade of anisotropy. We analyze the resulting charge distribution and the features of the obtained family of solutions. These families of solutions reproduce for the value C=1, the conformal isotropic solution for quark stars, previously obtained by Mak and Harko. The second family of solutions is obtained assuming the electrical charge inside the sphere to be a known function of the radial coordinate. The allowed values of the parameters pertained to these solutions are constrained by the physical conditions imposed. We study the effect of anisotropy in the allowed compactness ratios and in the values of the charge. The Glazer’s pulsation equation for isotropic charged spheres is extended to the case of anisotropic and charged fluid spheres in order to study the behavior of the solutions under linear adiabatic radial oscillations. These solutions could model some stage of the evolution of strange quark matter fluid stars.
DIFFUSIVE-DISPERSIVE TRAVELING WAVES AND KINETIC RELATIONS IV.COMPRESSIBLE EULER EQUATIONS
无
2003-01-01
The authors consider the Euler equations for a compressible fluid in one space dimensionwhen the equation of state of the fluid does not fulfill standard convexity assumptions andviscosity and capillarity effects are taken into account. A typical example of nonconvex con-stitutive equation for fluids is Van der Waals' equation. The first order terms of these partialdifferential equations form a nonlinear system of mixed (hyperbolic-elliptic) type. For a class ofnonconvex equations of state, an existence theorem of traveling waves solutions with arbitrarylarge amplitude is established here. The authors distinguish between classical (compressive) andnonclassical (undercompressive) traveling waves. The latter do not fulfill Lax shock inequali-ties, and are characterized by the so-called kinetic relation, whose properties are investigatedin this paper.
Gas-kinetic numerical method for solving mesoscopic velocity distribution function equation
Zhihui Li; Hanxin Zhang
2007-01-01
A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and applied to the study of three-dimensional complex flows and micro-channel flows covering various flow regimes. The unified velocity distribution function equation describing gas transport phenomena from rarefied transition to continuumflow regimes can be presented on the basis of the kinetic Boltzmann-Shakhov model equation. The gas-kinetic finite-difference schemes for the velocity distribution function are constructed by developing a discrete velocity ordinate method of gas kinetic theory and an unsteady time-splitting technique from computational fluid dynamics. Gas-kinetic boundary conditions and numerical modeling can be established by directly manipulating on the mesoscopic velocity distribution function. A new Gauss-type discrete velocity numerical integration method can be developed and adopted to attack complex flows with different Mach numbers. HPF parallel strategy suitable for the gas-kinetic numerical method is investigated and adopted to solve three-dimensional complex problems. High Mach number flows around three-dimensional bodies are computed preliminarily with massive scale parallel. It is noteworthy and of practical importance that the HPF parallel algorithm for solving three-dimensional complex problems can be effectively developed to cover various flow regimes. On the other hand, the gas-kinetic numerical method is extended and used to study micro-channel gas flows including the classical Couette flow, the Poiseuillechannel flow and pressure-driven gas flows in twodimensional short micro-channels. The numerical experience shows that the gas-kinetic algorithm may be a powerful tool in the numerical simulation of microscale gas flows occuring in the Micro-Electro-Mechanical System (MEMS).
Zanotti, Olindo; Dumbser, Michael
2015-01-01
We present a new numerical tool for solving the special relativistic ideal MHD equations that is based on the combination of the following three key features: (i) a one-step ADER discontinuous Galerkin (DG) scheme that allows for an arbitrary order of accuracy in both space and time, (ii) an a posteriori subcell finite volume limiter that is activated to avoid spurious oscillations at discontinuities without destroying the natural subcell resolution capabilities of the DG finite element framework and finally (iii) a space-time adaptive mesh refinement (AMR) framework with time-accurate local time-stepping. The divergence-free character of the magnetic field is instead taken into account through the so-called 'divergence-cleaning' approach. The convergence of the new scheme is verified up to 5th order in space and time and the results for a sample of significant numerical tests including shock tube problems, the RMHD rotor problem and the Orszag-Tang vortex system are shown. We also consider a simple case of t...
Kinetic Description for a Suspension of Inelastic Spheres - Boltzmann and BGK Equations
2007-11-02
Kinetic description for a suspension of inelastic spheres - Boltzmann and BGK equations Cedric Croizet and Renee Gatignol Laboratoire de Modelisation ...Organization Name(s) and Address(es) Laboratoire de Modelisation en Mecanique - Universite Pierre et Marie Curie (Paris 6) et CNRS UMR 7607 - 4) place
Quantum-kinetic equations for time correlation functions in higher-order perturbation theory
Leermakers, M.C.J.; Suttorp, L.G.
1981-01-01
The memory kernel of the kinetic equation for the time correlation function of a quantum fluid is determined both in third order of the interaction strength and in the low-density approximation. The results are obtained with the help of a diagram representation for the kernel. The connection with
Kinetic Thomas–Fermi solutions of the Gross–Pitaevskii equation
Ölschläger, M.; Wirth, G.; de Morais Smith, C.; Hemmerich, Andreas
2009-01-01
Approximate solutions of the Gross–Pitaevskii (GP) equation, obtained upon neglection of the kinetic energy, are well known as Thomas–Fermi solutions. They are characterized by the compensation of the local potential by the collisional energy. In this article we consider exact solutions of the
Kinetic Thomas–Fermi solutions of the Gross–Pitaevskii equation
Ölschläger, M.; Wirth, G.; de Morais Smith, C.; Hemmerich, Andreas
2009-01-01
Approximate solutions of the Gross–Pitaevskii (GP) equation, obtained upon neglection of the kinetic energy, are well known as Thomas–Fermi solutions. They are characterized by the compensation of the local potential by the collisional energy. In this article we consider exact solutions of the GP-eq
Explicit Kinetic Flux Vector Splitting Scheme for the 2-D Shallow Water Wave Equations
施卫平; 黄明游; 王婷; 张小江
2004-01-01
Originally, the kinetic flux vector splitting (KFVS) scheme was developed as a numerical method to solve gas dynamic problems. The main idea in the approach is to construct the flux based on the microscopical description of the gas. In this paper, based on the analogy between the shallow water wave equations and the gas dynamic equations, we develop an explicit KFVS method for simulating the shallow water wave equations. A 1D steady flow and a 2D unsteady flow are presented to show the robust and accuracy of the KFVS scheme.
A multi-dimensional kinetic-based upwind solver for the Euler equations
Eppard, W. M.; Grossman, B.
1993-01-01
A multidimensional kinetic fluctuation-splitting scheme has been developed for the Euler equations. The scheme is based on an N-scheme discretization of the Boltzmann equation at the kinetic level for triangulated Cartesian meshes with a diagonal-adaptive strategy. The resulting Euler scheme is a cell-vertex fluctuation-splitting scheme where fluctuations in the conserved-variable vector Q are obtained as moments of the fluctuation in the Maxwellian velocity distribution function at the kinetic level. Encouraging preliminary results have been obtained for perfect gases on Cartesian meshes with first-order spatial accuracy. The present approach represents an improvement to the well-established dimensionally-split upwind schemes.
Relativistic transport theory for simple fluids at first order in the gradients: a stable picture
Sandoval-Villalbazo, A; García-Colin, L S
2008-01-01
In this paper we show how using a relativistic kinetic equation. The ensuing expression for the heat flux can be casted in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so called first order in the gradients theories contend. Since the specific expressions for the transport coefficients are irrelevant for our purposes, the BGK form of the kinetic equation is used. Moreover, from the resulting hydrodynamic equations it is readily seen that no instabilities are present in the transverse hydrodynamic velocity mode of the simple relativistic fluid.
The H-theorem for the physico-chemical kinetic equations with explicit time discretization
Adzhiev, S. Z.; Melikhov, I. V.; Vedenyapin, V. V.
2017-09-01
There is demonstrated in the present paper, that the H-theorem in the case of explicit time discretization of the physico-chemical kinetic equations, generally speaking, is not valid. We prove the H-theorem, when the system of the physico-chemical kinetic equations with explicit time discretization has the form of non-linear analogue of the Markov process with doubly stochastic matrix, and for more general cases. In these cases the proof is reduced to the proof of the H-theorem for Markov chains. The simplest discrete velocity models of the Boltzmann equation with explicit time discretization -the Carleman and Broadwell models are discussed and the H-theorem for them in the case of discrete time is proved.
V.V.Ignatyuk
2004-01-01
Full Text Available Non-Markovian kinetic equations in the second Born approximation are derived for a two-zone semiconductor excited by a short laser pulse. Both collision dynamics and running nonequilibrium correlations are taken into consideration. The energy balance and relaxation of the system to equilibrium are discussed. Results of numerical solution of the kinetic equations for carriers and phonons are presented.
Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation
LI; Zhihui; ZHANG; Hanxin; FU; Song
2005-01-01
The gas-kinetic unified algorithm using Boltzmann model equation have been extended and developed to solve the micro-scale gas flows in Poiseuille-like micro-channels from Micro-Electro-Mechanical Systems (MEMS). The numerical modeling of the gas kinetic boundary conditions suitable for micro-scale gas flows is presented. To test the present method, the classical Couette flows with various Knudsen numbers, the gas flows from short microchannels like plane Poiseuille and the pressure-driven gas flows in two-dimensional short microchannels have been simulated and compared with the approximate solutions of the Boltzmann equation, the related DSMC results, the modified N-S solutions with slip-flow boundary theory, the gas-kinetic BGK-Burnett solutions and the experimental data. The comparisons show that the present gas-kinetic numerical algorithm using the mesoscopic Boltzmann simplified velocity distribution function equation can effectively simulate and reveal the gas flows in microchannels. The numerical experience indicates that this method may be a powerful tool in the numerical simulation of micro-scale gas flows from MEMS.
KINETIC FLUX VECTOR SPLITTING FOR THE EULER EQUATIONS WITH GENERAL PRESSURE LAWS
Hua-zhong Tang
2004-01-01
This paper attempts to develop kinetic flux vector splitting (KFVS) for the Euler equations with general pressure laws. It is well known that the gas distribution function for the local equilibrium state plays an important role in the construction of the gas-kinetic schemes. To recover the Euler equations with a general equation of state (EOS), a new local equilibrium distribution is introduced with two parameters of temperature approximation decided uniquely by macroscopic variables. Utilizing the well-known connection that the Euler equations of motion are the moments of the Boltzmann equation whenever the velocity distribution function is a local equilibrium state, a class of high resolution MUSCL-type KFVS schemes are presented to approximate the Euler equations of gas dynamics with a general EOS. The schemes are finally applied to several test problems for a general EOS. In comparison with the exact solutions, our schemes give correct location and more accurate resolution of discontinuities. The extension of our idea to multidimensional case is natural.
Properties-preserving high order numerical methods for a kinetic eikonal equation
Luo, Songting; Payne, Nicholas
2017-02-01
For the BGK (Bhatnagar-Gross-Krook) equation in the large scale hyperbolic limit, the density of particles can be transformed as the Hopf-Cole transformation, where the phase function converges uniformly to the viscosity solution of an effective Hamilton-Jacobi equation, referred to as the kinetic eikonal equation. In this work, we present efficient high order finite difference methods for numerically solving the kinetic eikonal equation. The methods are based on monotone schemes such as the Godunov scheme. High order weighted essentially non-oscillatory techniques and Runge-Kutta procedures are used to obtain high order accuracy in both space and time. The effective Hamiltonian is determined implicitly by a nonlinear equation given as integrals with respect to the velocity variable. Newton's method is applied to solve the nonlinear equation, where integrals with respect to the velocity variable are evaluated either by a Gauss quadrature formula or as expansions with respect to moments of the Maxwellian. The methods are designed such that several key properties such as the positivity of the viscosity solution and the positivity of the effective Hamiltonian are preserved. Numerical experiments are presented to demonstrate the effectiveness of the methods.
CHEN Ping; LU Zu-shun; YU Da-shu; HU Li-jiang
2005-01-01
Based on three typical mechanisms (second-order, third-order and competitive mechanisms) for the curing reactions of the epoxy resins with amines, a pair of the kinetic equations (for primary and secondary aminations) was presented to explain the uniformity and relationship among the three different kinetic mechanisms of the reactions. The presented macro-equations were deduced from the kinetic micro-equations by the statistics method. And the constitutive equations were verified by experimental data at different reaction times and temperatures (95℃, 60℃ and 39℃), taking diglycidyl ether of bisphenol A (DGEBA) /ethyleneamine (EA) as a model.
Quevedo María
2010-10-01
Full Text Available Abstract Background Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease. Methods The complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type. Results The first stage of complete tumor growth kinetics is highly non linear. The model, at this stage, shows different aspects that agree with those reported theoretically and experimentally. Tumor reversibility and the proportionality between regions before and after electrotherapy are demonstrated. In tumors that reach partial remission, two antagonistic post-treatment processes are induced, whereas in complete remission, two unknown antitumor mechanisms are induced. Conclusion The modified Gompertz equation is likely to lead to insights within cancer research. Such insights hold promise for increasing our understanding of tumors as self-organizing systems and, the possible existence of phase transitions in tumor growth kinetics, which, in turn, may have significant impacts both on cancer research and on clinical practice.
Zhidkov, A.B.; Smirnov, E.P.
1989-02-01
This work is devoted to the study of the kinetics of the reaction of titanium tetrachloride with the hydride functional groups of diamond. The research was performed on submicron powders of ASM 0.7/0.3 grade synthetic diamond with a specific surface area of 8.0 m/sup 2//g as measured from the adsorption of nitrogen. The reaction was carried out in a flow-through quartz reactor in a flow of dry He. The content of the titanium in the samples was determined by a photocolorimetric method. A kinetic equation for the reaction of diamond with titanium tetrachloride was found on the basis of a statistical approach.
Trigonometric Fourier-series solutions of the point reactor kinetics equations
Hamada, Yasser Mohamed, E-mail: yaser_abdelsatar@ci.suez.edu.eg
2015-01-15
Highlights: • A new method based on Fourier series expansion is introduced. • The method provides accurate approximations to the point kinetics equations. • Vandermonde matrix is used to determine the coefficients of the Fourier series. • A new formula is introduced to determine the inverse of the Vandermonde matrix. • The obtained results agree well with those obtained with other conventional codes. - Abstract: In this paper, a new method based on the Fourier series is introduced to obtain approximate solutions to the systems of the point kinetics equations. These systems are stiff involving equations with slowly and rapidly varying components. They are solved numerically using Fourier series expansion over a partition of the total time interval. Approximate solution requires determining the series coefficients over each time step in that partition. These coefficients are determined using the high order derivatives of the dependent variables at the beginning of the time step introducing a system of linear algebraic equations to be solved at each step. The obtained algebraic system is similar to the Vandermonde system. Evaluation of the inverse of the Vandermonde matrix is required to determine the coefficients of the Fourier series. Because the obtained Vandermonde matrix has a special structure, due to the properties of the sine and cosine functions, a new formula is introduced to determine its inverse using standard computations. The new method solves the general linear and non-linear kinetics problems with six groups of delayed neutrons. The validity of the algorithm is tested with five different types of reactivities including step reactivity insertion, ramp input, oscillatory reactivity changes, a reactivity as a function of the neutron density and finally temperature feedback reactivity. Comparisons are made with analytical and conventional numerical methods used to solve the point kinetics equations. The results confirm the theoretical analysis
Itoh, Yousuke
2009-01-01
We report our rederivation of the equations of motion for relativistic compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order approximation to general relativity using the strong field point particle limit to describe self-gravitating stars instead of the Dirac delta functional. The computation is done in harmonic coordinates. Our equations of motion describe the orbital motion of the binary consisting of spherically symmetric non-rotating stars. The resulting equations of motion fully agree with the 3.5 PN equations of motion derived in the previous works. We also show that the locally defined energy of the star has a simple relation with its mass up to the 3.5 PN order.
Linear Landau damping in strongly relativistic quark gluon plasma
Murtaza, G.; Khattak, N.A.D.; Shah, H.A. [Salam Chair in Physics, G C Univ., Lahore (Pakistan)]|[Dept. of Physics, G C Univ., Lahore (Pakistan)
2004-07-01
On the basis of semi classical kinetic Vlasov equation for Quark-Gluon plasma (QGP) and Yang-Mills equation in covariant gauge, linear Landau damping for electrostatic perturbations like Langmuir waves is investigated. For the extreme relativistic case, wherein the thermal speed of the particles exceeds the phase velocity of the perturbations, the linear Landau damping is absent. However, a departure from extreme relativistic case generates an imaginary component of the frequency giving rise to linear Landau damping effect. The relevant integral for the conductivity tensor has been evaluated and the dispersion relation for the longitudinal part of the oscillation obtained. (orig.)
Grima Ramon
2009-10-01
Full Text Available Abstract Background Classical descriptions of enzyme kinetics ignore the physical nature of the intracellular environment. Main implicit assumptions behind such approaches are that reactions occur in compartment volumes which are large enough so that molecular discreteness can be ignored and that molecular transport occurs via diffusion. Though these conditions are frequently met in laboratory conditions, they are not characteristic of the intracellular environment, which is compartmentalized at the micron and submicron scales and in which active means of transport play a significant role. Results Starting from a master equation description of enzyme reaction kinetics and assuming metabolic steady-state conditions, we derive novel mesoscopic rate equations which take into account (i the intrinsic molecular noise due to the low copy number of molecules in intracellular compartments (ii the physical nature of the substrate transport process, i.e. diffusion or vesicle-mediated transport. These equations replace the conventional macroscopic and deterministic equations in the context of intracellular kinetics. The latter are recovered in the limit of infinite compartment volumes. We find that deviations from the predictions of classical kinetics are pronounced (hundreds of percent in the estimate for the reaction velocity for enzyme reactions occurring in compartments which are smaller than approximately 200 nm, for the case of substrate transport to the compartment being mediated principally by vesicle or granule transport and in the presence of competitive enzyme inhibitors. Conclusion The derived mesoscopic rate equations describe subcellular enzyme reaction kinetics, taking into account, for the first time, the simultaneous influence of both intrinsic noise and the mode of transport. They clearly show the range of applicability of the conventional deterministic equation models, namely intracellular conditions compatible with diffusive transport
An equation of state for purely kinetic k-essence inspired by cosmic topological defects
Cordero, Ruben; Queijeiro, Alfonso
2016-01-01
We investigate the physical properties of a purely kinetic k-essence model with an equation of state motivated in superconducting membranes. We compute the equation of state parameter $w$ and discuss its physical evolution via a nonlinear equation of state. Using the adiabatic speed of sound and energy density, we restrict the range of parameters of the model in order to have an acceptable physical behavior. Furthermore, we analyze the evolution of the luminosity distance $d_{L}$ with redshift $z$ by comparing (normalizing) it with the $\\Lambda$CDM model. Since the equation of state parameter is $z$-dependent the evolution of the luminosity distance is also analyzed using the Alcock-Paczy\\'{n}ski test.
An equation of state for purely kinetic k-essence inspired by cosmic topological defects
Cordero, Ruben; Gonzalez, Eduardo L.; Queijeiro, Alfonso [Instituto Politecnico Nacional, Departamento de Fisica, Escuela Superior de Fisica y Matematicas, Ciudad de Mexico (Mexico)
2017-06-15
We investigate the physical properties of a purely kinetic k-essence model with an equation of state motivated in superconducting membranes. We compute the equation of state parameter w and discuss its physical evolution via a nonlinear equation of state. Using the adiabatic speed of sound and energy density, we restrict the range of parameters of the model in order to have an acceptable physical behavior. We study the evolution of the scale factor and address the question of the possible existence of finite-time future singularities. Furthermore, we analyze the evolution of the luminosity distance d{sub L} with redshift z by comparing (normalizing) it with the ΛCDM model. Since the equation of state parameter is z-dependent the evolution of the luminosity distance is also analyzed using the Alcock-Paczynski test. (orig.)
An equation of state for purely kinetic k-essence inspired by cosmic topological defects
Cordero, Rubén; González, Eduardo L.; Queijeiro, Alfonso
2017-06-01
We investigate the physical properties of a purely kinetic k-essence model with an equation of state motivated in superconducting membranes. We compute the equation of state parameter w and discuss its physical evolution via a nonlinear equation of state. Using the adiabatic speed of sound and energy density, we restrict the range of parameters of the model in order to have an acceptable physical behavior. We study the evolution of the scale factor and address the question of the possible existence of finite-time future singularities. Furthermore, we analyze the evolution of the luminosity distance dL with redshift z by comparing (normalizing) it with the Λ CDM model. Since the equation of state parameter is z-dependent the evolution of the luminosity distance is also analyzed using the Alcock-Paczyński test.
Silva, Milena W. Da; Vilhena, Marco T. de; Bodmann, Bardo E., E-mail: milena.wollmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: bardobodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Leite, Sergio B., E-mail: bogado@cnen.gov.br [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RS (Brazil)
2013-07-01
In this work, we report on an analytical representation for the solution of the neutron point kinetics equation, free of stiffness and assuming that the reactivity is a continuous or sectionally continuous function of time. To this end, we cast the point kinetics equation in a first order linear differential equation. Next, we split the corresponding matrix into a diagonal matrix plus a matrix that contains the remaining terms. Expanding the neutron density and the delayed neutron precursors concentrations in a truncated series, allows one to construct a recursive system, in form of a first order matrix differential equation with source. The initialization of the recursion procedure is of diagonal form and has no source, but satisfies the initial conditions. The remaining equations are subject to null initial conditions and include the time dependent diagonal elements together with the off diagonal elements as a source term. The solution is obtained in analytical representation which may be evaluated for any time value, because it is free of stiffness. We present numerical simulations and comparisons against results from the literature, for a constant, a step, a ramp, a quadratic and sine shaped reactivity function. (author)
Arino, O; Kimmel, M
1989-01-01
A model of cell cycle kinetics is proposed, which includes unequal division of cells, and a nonlinear dependence of the fraction of cells re-entering proliferation on the total number of cells in the cycle. The model is described by a nonlinear functional-integral equation. It is analyzed using the operator semigroup theory combined with classical differential equations approach. A complete description of the asymptotic behavior of the model is provided for a relatively broad class of nonlinearities. The nonnegative solutions either tend to a stable steady state, or to zero. The simplicity of the model makes it an interesting step in the analysis of dynamics of nonlinear structure populations.
Numerical solution of point kinetic equations by matrix decomposition and T series expansions
Silva, Jeronimo J.A.; Alvim, Antonio C.M., E-mail: shaolin.jr@gmail.com, E-mail: alvim@nuclear.ufrj.br [Coordenacao dos Programas de Pos-Graduacao de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil); Vilhena, Marco T.M.B., E-mail: vilhena@pq.cnpq.br [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica
2013-07-01
Recently, an analytical solution of the Point Kinetics equations free from stiffness problems has been presented. The equations, cast in matrix form are split into diagonal plus off-diagonal matrices and a series expansion of neutron density and precursor concentrations is done, producing a recurrent system which is then solved analytically. In this paper, a numerical finite differences equivalent of this decomposition plus expansion method is derived and applied to the same problems tested in the analytical case. As a result, the number of terms in the expansions needed for holding steady state is obtained, as well as results for the transient cases, with good agreement between solutions. (author)
Gelß, Patrick, E-mail: p.gelss@fu-berlin.de; Matera, Sebastian, E-mail: matera@math.fu-berlin.de; Schütte, Christof, E-mail: schuette@mi.fu-berlin.de
2016-06-01
In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO{sub 2}(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.
Coupling coefficients and kinetic equation for Rossby waves in multi-layer ocean
T. Soomere
2003-01-01
Full Text Available The kinetic description of baroclinic Rossby waves in multi-layer model ocean is analysed. Explicit analytical expressions for the coupling coefficients describing energy exchange intensity between different modes are obtained and their main properties are established for the three-layer model. It is demonstrated that several types of interactions vanish in the case of simple vertical structures of the ocean, e.g. when all layers have equal depth. These cases correspond to a zero component of the eigenvectors of the potential vorticity equations. The kinetic equation always possesses a fully barotropic solution. If energy is concentrated in the baroclinic modes, the barotropic mode will necessarily be generated. Motion systems consisting of a superposition of the barotropic and a baroclinic mode always transfer energy to other baroclinic modes.
An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit
Wang, Li; Yan, Bokai
2016-05-01
We present a new asymptotic-preserving scheme for the linear Boltzmann equation which, under appropriate scaling, leads to a fractional diffusion limit. Our scheme rests on novel micro-macro decomposition to the distribution function, which splits the original kinetic equation following a reshuffled Hilbert expansion. As opposed to classical diffusion limit, a major difficulty comes from the fat tail in the equilibrium which makes the truncation in velocity space depending on the small parameter. Our idea is, while solving the macro-micro part in a truncated velocity domain (truncation only depends on numerical accuracy), to incorporate an integrated tail over the velocity space that is beyond the truncation, and its major component can be precomputed once with any accuracy. Such an addition is essential to drive the solution to the correct asymptotic limit. Numerical experiments validate its efficiency in both kinetic and fractional diffusive regimes.
Maulidah, Rifa'atul; Purqon, Acep
2016-08-01
Mendong (Fimbristylis globulosa) has a potentially industrial application. We investigate a predictive model for heat and mass transfer in drying kinetics during drying a Mendong. We experimentally dry the Mendong by using a microwave oven. In this study, we analyze three mathematical equations and feed forward neural network (FNN) with back propagation to describe the drying behavior of Mendong. Our results show that the experimental data and the artificial neural network model has a good agreement and better than a mathematical equation approach. The best FNN for the prediction is 3-20-1-1 structure with Levenberg- Marquardt training function. This drying kinetics modeling is potentially applied to determine the optimal parameters during mendong drying and to estimate and control of drying process.
Analysis of atmospheric flow over a surface protrusion using the turbulence kinetic energy equation
Frost, W.; Harper, W. L.; Fichtl, G. H.
1975-01-01
Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Mean-flow results are compared with those given in a previous paper where the same problem was attacked using a Prandtl mixing-length hypothesis. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow. They highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient.
Nandy, D K; Sahoo, B K
2014-01-01
We report the implementation of equation-of-motion coupled-cluster (EOMCC) method in the four-component relativistic framework with the spherical atomic potential to generate the excited states from a closed-shell atomic configuration. This theoretical development will be very useful to carry out high precision calculations of varieties of atomic properties in many atomic systems. We employ this method to calculate excitation energies of many low-lying states in a few Ne-like highly charged ions, such as Cr XV, Fe XVII, Co XVIII and Ni XIX ions, and compare them against their corresponding experimental values to demonstrate the accomplishment of the EOMCC implementation. The considered ions are apt to substantiate accurate inclusion of the relativistic effects in the evaluation of the atomic properties and are also interesting for the astrophysical studies. Investigation of the temporal variation of the fine structure constant (\\alpha) from the astrophysical observations is one of the modern research problems...
Mohammadi, Vahid; Chenaghlou, Alireza
2017-09-01
The two-dimensional Dirac equation with spin and pseudo-spin symmetries is investigated in the presence of the maximally superintegrable potentials. The integrals of motion and the quadratic algebras of the superintegrable quantum E3‧, anisotropic oscillator and the Holt potentials are studied. The corresponding Casimir operators and the structure functions of the mentioned superintegrable systems are found. Also, we obtain the relativistic energy spectra of the corresponding superintegrable systems. Finally, the relativistic energy eigenvalues of the generalized Yang-Coulomb monopole (YCM) superintegrable system (a SU(2) non-Abelian monopole) are calculated by the energy spectrum of the eight-dimensional oscillator which is dual to the former system by Hurwitz transformation.
Chiba, G.; Tsuji, M.; Narabayashi, T.
2014-04-01
In order to better predict a kinetic behavior of a nuclear fission reactor, an improvement of the delayed neutron parameters is essential. The present paper specifies important nuclear data for a reactor kinetics: Fission yield and decay constant data of 86Ge, some bromine isotopes, 94Rb, 98mY and some iodine isotopes. Their importance is quantified as sensitivities with a help of the adjoint kinetic equation, and it is found that they are dependent on an inserted reactivity (or a reactor period). Moreover, dependence of sensitivities on nuclear data files is also quantified using the latest files. Even though the currently evaluated data are used, there are large differences among different data files from a view point of the delayed neutrons.
SBMLsqueezer 2: context-sensitive creation of kinetic equations in biochemical networks
Draeger, Andreas; Zielinski, Daniel C.; Keller, Roland
2015-01-01
Background: The size and complexity of published biochemical network reconstructions are steadily increasing, expanding the potential scale of derived computational models. However, the construction of large biochemical network models is a laborious and error-prone task. Automated methods have...... during kinetic model construction would thus benefit from automated methods for rate law assignment. Results: We present a high-throughput algorithm to automatically suggest and create suitable rate laws based upon reaction type according to several criteria. The criteria for choices made...... simplified the network reconstruction process, but building kinetic models for these systems is still a manually intensive task. Appropriate kinetic equations, based upon reaction rate laws, must be constructed and parameterized for each reaction. The complex test-and-evaluation cycles that can be involved...
Yang Xue
2009-01-01
Full Text Available The fourth order Rosenbrock method with an automatic step size control feature was described and applied to solve the reactor point kinetics equations. A FORTRAN 90 program was developed to test the computational speed and algorithm accuracy. From the results of various benchmark tests with different types of reactivity insertions, the Rosenbrock method shows high accuracy, high efficiency and stable character of the solution.
Brun-Battistini, D; Sandoval-Villalbazo, A
2016-01-01
Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolman\\textquoteright s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by \\textquotedblleft suppressing\\textquotedblright{} the molecular acceleration in Boltzmann\\textquoteright s equation, that a gravitational field drives a heat flux. This procedure corresponds to the description of particle motion through geodesics, in which a Newtonian limit to the Schwarzschild metric is assumed. The effect vanishes in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit.
Polko, Peter; Markoff, Sera
2012-01-01
We present a new, approximate method for modelling the acceleration and collimation of relativistic jets in the presence of gravity. This method is self-similar throughout the computational domain where gravitational effects are negligible and, where significant, self-similar within a flux tube. These solutions are applicable to jets launched from a small region (e.g., near the inner edge of an accretion disk). As implied by earlier work, the flow can converge onto the rotation axis, potentially creating a collimation shock. In this first version of the method, we derive the gravitational contribution to the relativistic equations by analogy with non-relativistic flow. This approach captures the relativistic kinetic gravitational mass of the flowing plasma, but not that due to internal thermal and magnetic energies. A more sophisticated treatment, derived from the basic general relativistic magnetohydrodynamical equations, is currently being developed. Here we present an initial exploration of parameter space...
Relativistic neoclassical radial fluxes in the 1/nu regime
Marushchenko, I; Marushchenko, N B
2013-01-01
The radial neoclassical fluxes of electrons in the 1/nu-regime are calculated with relativistic effects taken into account and compared with those in the non-relativistic approach. The treatment is based on the relativistic drift-kinetic equation with the thermodynamic equilibrium given by the relativistic J\\"uttner-Maxwellian distribution function. It is found that for the range of fusion temperatures, T_e < 100 keV, the relativistic effects produce a reduction of the radial fluxes which does not exceed 10%. This rather small effect is a consequence of the non-monotonic temperature dependence of the relativistic correction caused by two counteracting factors: a reduction of the contribution from the bulk and a significant broadening with the temperature growth of the energy range of electrons contributing to transport. The relativistic formulation for the radial fluxes given in this paper is expressed in terms a set of relativistic thermodynamic forces which is not identical to the canonical set since it ...
Kinetic Formulation of the Kohn-Sham Equations for ab initio Electronic Structure Calculations
Mendoza, M; Herrmann, H J
2013-01-01
We introduce a new approach to density functional theory based on kinetic theory, showing that the Kohn-Sham equations can be derived as a macroscopic limit of a suitable Boltzmann kinetic equation in the limit of small mean free path versus the typical scale of density gradients (Chapman-Enskog expansion). To derive the approach, we first write the Schr\\"odinger equation as a special case of a Boltzmann equation for a gas of quasi-particles, with the potential playing the role of an external source that generates and destroys particles, so as to drive the system towards the ground state. The ions are treated as classical particles, using the Born-Oppenheimer dynamics, or by imposing concurrent evolution with the electronic orbitals. In order to provide quantitative support to our approach, we implement a discrete (lattice) model and compute, the exchange and correlation energies of simple atoms, and the geometrical configuration of the methane molecule. Excellent agreement with values in the literature is fo...
Proton-pumping mechanism of cytochrome c oxidase: A kinetic master-equation approach
Kim, Young C.; Hummer, Gerhard
2011-01-01
Cytochrome c oxidase (CcO) is an efficient energy transducer that reduces oxygen to water and converts the released chemical energy into an electrochemical membrane potential. As a true proton pump, CcO translocates protons across the membrane against this potential. Based on a wealth of experiments and calculations, an increasingly detailed picture of the reaction intermediates in the redox cycle has emerged. However, the fundamental mechanism of proton pumping coupled to redox chemistry remains largely unresolved. Here we examine and extend a kinetic master-equation approach to gain insight into redox-coupled proton pumping in CcO. Basic principles of the CcO proton pump emerge from an analysis of the simplest kinetic models that retain essential elements of the experimentally determined structure, energetics, and kinetics, and that satisfy fundamental physical principles. The master-equation models allow us to address the question of how pumping can be achieved in a system in which all reaction steps are reversible. Whereas proton pumping does not require the direct modulation of microscopic reaction barriers, such kinetic gating greatly increases the pumping efficiency. Further efficiency gains can be achieved by partially decoupling the proton uptake pathway from the ative-site region. Such a mechanism is consistent with the proposed Glu valve, in which the side chain of a key glutamic acid shuttles between the D channel and the active-site region. We also show that the models predict only small proton leaks even in the absence of turnover. The design principles identified here for CcO provide a blueprint for novel biology-inspired fuel cells, and the master-equation formulation should prove useful also for other molecular machines. PMID:21946020
Proton-pumping mechanism of cytochrome c oxidase: a kinetic master-equation approach.
Kim, Young C; Hummer, Gerhard
2012-04-01
Cytochrome c oxidase is an efficient energy transducer that reduces oxygen to water and converts the released chemical energy into an electrochemical membrane potential. As a true proton pump, cytochrome c oxidase translocates protons across the membrane against this potential. Based on a wealth of experiments and calculations, an increasingly detailed picture of the reaction intermediates in the redox cycle has emerged. However, the fundamental mechanism of proton pumping coupled to redox chemistry remains largely unresolved. Here we examine and extend a kinetic master-equation approach to gain insight into redox-coupled proton pumping in cytochrome c oxidase. Basic principles of the cytochrome c oxidase proton pump emerge from an analysis of the simplest kinetic models that retain essential elements of the experimentally determined structure, energetics, and kinetics, and that satisfy fundamental physical principles. The master-equation models allow us to address the question of how pumping can be achieved in a system in which all reaction steps are reversible. Whereas proton pumping does not require the direct modulation of microscopic reaction barriers, such kinetic gating greatly increases the pumping efficiency. Further efficiency gains can be achieved by partially decoupling the proton uptake pathway from the active-site region. Such a mechanism is consistent with the proposed Glu valve, in which the side chain of a key glutamic acid shuttles between the D channel and the active-site region. We also show that the models predict only small proton leaks even in the absence of turnover. The design principles identified here for cytochrome c oxidase provide a blueprint for novel biology-inspired fuel cells, and the master-equation formulation should prove useful also for other molecular machines. .
Relativistic Corrections to the Bohr Model of the Atom
Kraft, David W.
1974-01-01
Presents a simple means for extending the Bohr model to include relativistic corrections using a derivation similar to that for the non-relativistic case, except that the relativistic expressions for mass and kinetic energy are employed. (Author/GS)
Kolobov, Vladimir [CFD Research Corporation, Huntsville, AL 35805, USA and The University of Alabama in Huntsville, Huntsville, AL 35805 (United States); Arslanbekov, Robert [CFD Research Corporation, Huntsville, AL 35805 (United States); Frolova, Anna [Computing Center of the Russian Academy of Sciences, Moscow, 119333 (Russian Federation)
2014-12-09
The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers.
Relativistic radiative transfer in relativistic spherical flows
Fukue, Jun
2017-02-01
Relativistic radiative transfer in relativistic spherical flows is numerically examined under the fully special relativistic treatment. We first derive relativistic formal solutions for the relativistic radiative transfer equation in relativistic spherical flows. We then iteratively solve the relativistic radiative transfer equation, using an impact parameter method/tangent ray method, and obtain specific intensities in the inertial and comoving frames, as well as moment quantities, and the Eddington factor. We consider several cases; a scattering wind with a luminous central core, an isothermal wind without a core, a scattering accretion on to a luminous core, and an adiabatic accretion on to a dark core. In the typical wind case with a luminous core, the emergent intensity is enhanced at the center due to the Doppler boost, while it reduces at the outskirts due to the transverse Doppler effect. In contrast to the plane-parallel case, the behavior of the Eddington factor is rather complicated in each case, since the Eddington factor depends on the optical depth, the flow velocity, and other parameters.
Kinetic Thomas-Fermi solutions of the Gross-Pitaevskii equation
Ölschläger, M.; Wirth, G.; Smith, C. Morais; Hemmerich, A.
2009-04-01
Approximate solutions of the Gross-Pitaevskii (GP) equation, obtained upon neglection of the kinetic energy, are well known as Thomas-Fermi solutions. They are characterized by the compensation of the local potential by the collisional energy. In this article we consider exact solutions of the GP-equation with this property and definite values of the kinetic energy, which suggests the term "kinetic Thomas-Fermi" (KTF) solutions. Despite their formal simplicity, KTF-solutions can possess complex current density fields with unconventional topology. We point out that a large class of light-shift potentials gives rise to KTF-solutions. As elementary examples, we consider one-dimensional and two-dimensional optical lattice scenarios, obtained by means of the superposition of two, three and four laser beams, and discuss the stability properties of the corresponding KTF-solutions. A general method is proposed to excite two-dimensional KTF-solutions in experiments by means of time-modulated light-shift potentials.
Relativistic Remnants of Non-Relativistic Electrons
Kashiwa, Taro
2015-01-01
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \\mapsto \\infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.
Schramm, Marcelo; Bodmann, Bardo E.J.; Vilhena, Marco T.M.B., E-mail: marceloschramm@hotmail.com, E-mail: bardo.bodmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica; Petersen, Claudio Z., E-mail: claudiopetersen@yahoo.com.br [Universidade Federal de Pelotas (UFPel), RS (Brazil). Departamento de Matematica; Alvim, Antonio C.M., E-mail: alvim@nuclear.ufrj.br [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Instituto Alberto Luiz Coimbra de Pos-Graduacao e Pesquisa em Engenharia
2013-07-01
Following the quest to find analytical solutions, we extend the methodology applied successfully to timely fractional neutron point kinetics (FNPK) equations by adding the effects of temperature. The FNPK equations with temperature feedback correspond to a nonlinear system and “stiff” type for the neutron density and the concentration of delayed neutron precursors. These variables determine the behavior of a nuclear reactor power with time and are influenced by the position of control rods, for example. The solutions of kinetics equations provide time information about the dynamics in a nuclear reactor in operation and are useful, for example, to understand the power fluctuations with time that occur during startup or shutdown of the reactor, due to adjustments of the control rods. The inclusion of temperature feedback in the model introduces an estimate of the transient behavior of the power and other variables, which are strongly coupled. Normally, a single value of reactivity is used across the energy spectrum. Especially in case of power change, the neutron energy spectrum changes as well as physical parameters such as the average cross sections. However, even knowing the importance of temperature effects on the control of the reactor power, the character of the set of nonlinear equations governing this system makes it difficult to obtain a purely analytical solution. Studies have been published in this sense, using numerical approaches. Here the idea is to consider temperature effects to make the model more realistic and thus solve it in a semi-analytical way. Therefore, the main objective of this paper is to obtain an analytical representation of fractional neutron point kinetics equations with temperature feedback, without having to resort to approximations inherent in numerical methods. To this end, we will use the decomposition method, which has been successfully used by the authors to solve neutron point kinetics problems. The results obtained will
Shtykov, N. M., E-mail: nshtykov@mail.ru; Palto, S. P.; Umanskii, B. A. [Russian Academy of Sciences, Shubnikov Institute of Crystallography (Russian Federation)
2013-08-15
We report on the results of calculating the conditions for light generation in cholesteric liquid crystals doped with fluorescent dyes using kinetic equations. Specific features of spectral properties of the chiral cholesteric medium as a photonic structure and spatially distributed type of the feedback in the active medium are taken into account. The expression is derived for the threshold pump radiation intensity as a function of the dye concentration and sample thickness. The importance of taking into account the distributed loss level in the active medium for calculating the optimal parameters of the medium and for matching the calculated values with the results of experiments is demonstrated.
Theory of warm ionized gases: equation of state and kinetic Schottky anomaly.
Capolupo, A; Giampaolo, S M; Illuminati, F
2013-10-01
Based on accurate Lennard-Jones-type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analog in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed. In particular, the predicted plasma electron density in a sonoluminescent bubble turns out to be in good agreement with the value measured in recent experiments.
Theory of warm ionized gases: equation of state and kinetic Schottky anomaly
Capolupo, Antonio; Illuminati, Fabrizio
2013-01-01
Based on accurate Lennard-Jones type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analogue in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed.
Kierkels, A. H. M.; Velázquez, J. J. L.
2016-06-01
We construct a family of self-similar solutions with fat tails to a quadratic kinetic equation. This equation describes the long time behaviour of weak solutions with finite mass to the weak turbulence equation associated to the nonlinear Schrödinger equation. The solutions that we construct have finite mass, but infinite energy. In Kierkels and Velázquez (J Stat Phys 159:668-712, 2015) self-similar solutions with finite mass and energy were constructed. Here we prove upper and lower exponential bounds on the tails of these solutions.
Phonon Boltzmann equation-based discrete unified gas kinetic scheme for multiscale heat transfer
Guo, Zhaoli
2016-01-01
Numerical prediction of multiscale heat transfer is a challenging problem due to the wide range of time and length scales involved. In this work a discrete unified gas kinetic scheme (DUGKS) is developed for heat transfer in materials with different acoustic thickness based on the phonon Boltzmann equation. With discrete phonon direction, the Boltzmann equation is discretized with a second-order finite-volume formulation, in which the time-step is fully determined by the Courant-Friedrichs-Lewy (CFL) condition. The scheme has the asymptotic preserving (AP) properties for both diffusive and ballistic regimes, and can present accurate solutions in the whole transition regime as well. The DUGKS is a self-adaptive multiscale method for the capturing of local transport process. Numerical tests for both heat transfers with different Knudsen numbers are presented to validate the current method.
L. Alfonso
2010-03-01
Full Text Available The kinetic collection equation (KCE has been widely used to describe the evolution of the average droplet spectrum due to the collection process that leads to the development of precipitation in warm clouds. This deterministic, integro-differential equation only has analytic solution for very simple kernels. For more realistic kernels, the KCE needs to be integrated numerically. In this study, the validity time of the KCE for the hydrodynamic kernel is estimated by a direct comparison of Monte Carlo simulations with numerical solutions of the KCE. The simulation results show that when the largest droplet becomes separated from the smooth spectrum, the total mass calculated from the numerical solution of the KCE is not conserved and, thus, the KCE is no longer valid. This result confirms the fact that for realistic kernels appropriate for precipitation development within warm clouds, the KCE can only be applied to the continuous portion of the mass distribution.
Generalized kinetics of overall phase transition in terms of logistic equation
Avramov, I
2015-01-01
We summarize and to discuss briefly the geometrical practice of modeling attitudes so far popular in treating reaction kinetics of solid-state processes. The model equations existing in the literature have been explored to describe the thermal decomposition and crystallization data and are deeply questioned and analyzed showing that under such a simple algebraic representation, the reacting system is thus classified as a set of geometrical bodies (spheres) where each and every one reaction interface is represented by similar and smooth characteristics of reaction curve. It brings an unsolved question whether the sharp and even boundary factually exists or if it resides jointly just inside the global whole of the sample entirety preventing individual particles from having their individual reaction front. Most of the derived expressions are specified in an averaged generalization in terms of the three and two parameters equation (so called JMAK and SB models) characterized by a combination of power exponents m,...
Relativistic magnetohydrodynamics
Hernandez, Juan; Kovtun, Pavel
2017-05-01
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).
Ten-no, Seiichiro; Yamaki, Daisuke
2012-10-07
We propose explicitly correlated Ansatz for four-component relativistic methods within the framework of the no-pair approximation. Kinetically balanced geminal basis is derived to satisfy the cusp conditions in the non-relativistic limit based on the Lévy-Leblend-like equation. Relativistic variants of strong-orthogonality projection operator (Ansätze 2α and 2β) suitable for practical calculations are introduced by exploiting the orthogonal complement of the large-component basis. A pilot implementation is performed for the second order Møller-Plesset perturbation theory.
Klinman, Judith P
2014-01-01
The final arbiter of enzyme mechanism is the ability to establish and test a kinetic mechanism. Isotope effects play a major role in expanding the scope and insight derived from the Michaelis-Menten equation. The integration of isotope effects into the formalism of the Michaelis-Menten equation began in the 1970s and has continued until the present. This review discusses a family of eukaryotic copper proteins, including dopamine β-monooxygenase, tyramine β-monooxygenase and peptidylglycine α-amidating enzyme, which are responsible for the synthesis of neuroactive compounds, norepinephrine, octopamine and C-terminally carboxamidated peptides, respectively. The review highlights the results of studies showing how combining kinetic isotope effects with initial rate parameters permits the evaluation of: (a) the order of substrate binding to multisubstrate enzymes; (b) the magnitude of individual rate constants in complex, multistep reactions; (c) the identification of chemical intermediates; and (d) the role of nonclassical (tunnelling) behaviour in C-H activation. © 2013 FEBS.
Marta Cecilia Quicazán
2012-12-01
Full Text Available Legume soaking is an important practice in food processing; the characteristics of beverages and tofu mainly depend on this operation regarding soybeans. Peleg’s equation has been used in this work to describe the kinetics of water absorption and solid loss during soaking at 20°C, 40°C and 80°C. The moisture content of grain and solids in the remaining water was measured for 10 hours. Variance analysis and principal components analysis showed high fitting of kinetics to Peleg's equation for predicting both transference phenomena. This work found that the value of k1 (rate depended on temperature according to a polynomial function while k2 (capacity did not, meaning that the value of equilibrium moisture content was independent of soaking temperature. k1 had the minimum value for the migration of solids to soaking water at 40°C; this was related to lost solids’ high speed and the microbial degradation of carbohydrates; the values obtained for k2, showed that it was possible to lose total soluble solids at 20°C, while further migration of insoluble compounds occurred at 80°C.
Bayesian inference for kinetic models of biotransformation using a generalized rate equation.
Ying, Shanshan; Zhang, Jiangjiang; Zeng, Lingzao; Shi, Jiachun; Wu, Laosheng
2017-03-06
Selecting proper rate equations for the kinetic models is essential to quantify biotransformation processes in the environment. Bayesian model selection method can be used to evaluate the candidate models. However, comparisons of all plausible models can result in high computational cost, while limiting the number of candidate models may lead to biased results. In this work, we developed an integrated Bayesian method to simultaneously perform model selection and parameter estimation by using a generalized rate equation. In the approach, the model hypotheses were represented by discrete parameters and the rate constants were represented by continuous parameters. Then Bayesian inference of the kinetic models was solved by implementing Markov Chain Monte Carlo simulation for parameter estimation with the mixed (i.e., discrete and continuous) priors. The validity of this approach was illustrated through a synthetic case and a nitrogen transformation experimental study. It showed that our method can successfully identify the plausible models and parameters, as well as uncertainties therein. Thus this method can provide a powerful tool to reveal more insightful information for the complex biotransformation processes.
Polo L, M. A.; Espinosa P, G. [Universidad Autonoma Metropolitana, Unidad Iztapalapa, Area de Ingenieria en Recursos Energeticos, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 Mexico D. F. (Mexico)], e-mail: gepe@xanum.uam.mx
2009-10-15
In this work is presented the deduction and solution of punctual equation of neutronic kinetics of second order, which is obtained applying the fundamental principles of nuclear reactor physics. The work hypothesis consisted on considering that the temporary dependence of current vector is not worthless in the constitutive law for the approach of neutronic processes with the diffusion equation. As results of work eight roots of analytical solution of punctual equation of neutronic kinetics of second order are obtained for case of six groups of slowed neutrons, a root more respect the classic pattern of punctual equation of neutronic kinetics. This theory can be used when appear highly heterogeneous configurations in the nuclear reactor. (Author)
About and beyond the Henri-Michaelis-Menten rate equation for single-substrate enzyme kinetics.
Bajzer, Zeljko; Strehler, Emanuel E
2012-01-20
For more than a century the simple single-substrate enzyme kinetics model and related Henri-Michaelis-Menten (HMM) rate equation have been thoroughly explored in various directions. In the present paper we are concerned with a possible generalization of this rate equation recently proposed by F. Kargi (BBRC 382 (2009) 157-159), which is assumed to be valid both in the case that the total substrate or enzyme is in excess and the quasi-steady-state is achieved. We demonstrate that this generalization is grossly inadequate and propose another generalization based on application of the quasi-steady-state condition and conservation equations for both enzyme and substrate. The standard HMM equation is derived by (a) assuming the quasi-steady-state condition, (b) applying the conservation equation only for the enzyme, and (c) assuming that the substrate concentration at quasi-steady-state can be approximated by the total substrate concentration [S](0). In our formula the rate is already expressed through [S](0), and we only assume that when quasi-steady-state is achieved the amount of product formed is negligible compared to [S](0). Numerical simulations show that our formula is generally more accurate than the HMM formula and also can provide a good approximation when the enzyme is in excess, which is not the case for the HMM formula. We show that the HMM formula can be derived from our expression by further assuming that the total enzyme concentration is negligible compared to [S](0). Copyright © 2011 Elsevier Inc. All rights reserved.
On the Rate of Relaxation for the Landau Kinetic Equation and Related Models
Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong
2017-08-01
We study the rate of relaxation to equilibrium for Landau kinetic equation and some related models by considering the relatively simple case of radial solutions of the linear Landau-type equations. The well-known difficulty is that the evolution operator has no spectral gap, i.e. its spectrum is not separated from zero. Hence we do not expect purely exponential relaxation for large values of time t>0. One of the main goals of our work is to numerically identify the large time asymptotics for the relaxation to equilibrium. We recall the work of Strain and Guo (Arch Rat Mech Anal 187:287-339 2008, Commun Partial Differ Equ 31:17-429 2006), who rigorously show that the expected law of relaxation is \\exp (-ct^{2/3}) with some c > 0. In this manuscript, we find an heuristic way, performed by asymptotic methods, that finds this "law of two thirds", and then study this question numerically. More specifically, the linear Landau equation is approximated by a set of ODEs based on expansions in generalized Laguerre polynomials. We analyze the corresponding quadratic form and the solution of these ODEs in detail. It is shown that the solution has two different asymptotic stages for large values of time t and maximal order of polynomials N: the first one focus on intermediate asymptotics which agrees with the "law of two thirds" for moderately large values of time t and then the second one on absolute, purely exponential asymptotics for very large t, as expected for linear ODEs. We believe that appearance of intermediate asymptotics in finite dimensional approximations must be a generic behavior for different classes of equations in functional spaces (some PDEs, Boltzmann equations for soft potentials, etc.) and that our methods can be applied to related problems.
Bret, A; Benisti, D; Lefebvre, E
2008-01-01
Besides being one of the most fundamental basic issues of plasma physics, the stability analysis of an electron beam-plasma system is of critical relevance in many areas of physics. Surprisingly, decades of extensive investigation had not yet resulted in a realistic unified picture of the multidimensional unstable spectrum within a fully relativistic and kinetic framework. All attempts made so far in this direction were indeed restricted to simplistic distribution functions and/or did not aim at a complete mapping of the beam-plasma parameter space. The present paper comprehensively tackles this problem by implementing an exact linear model. We show that three kinds of modes compete in the linear phase, which can be classified according to the direction of their wavenumber with respect to the beam. We then determine their respective domain of preponderance in a three-dimensional parameter space. All these results are supported by multidimensional particle-in-cell simulations.
Improving Solution of Euler Equations by a Gas-Kinetic BGK Method
Liu Ya; Gao Chao; F. Liu
2009-01-01
Aim. The well known JST(Jameson-Schmidt-Turkel) scheme requires the use of a dissipation term. We propose using gas-kinetic BGK (Bhatnagar-Gross-Krook) method, which is based on the more fundamental Boltzmann equation, in order to obviate the use of dissipation term and obtain, we believe, an improved solution. Section 1 deals essentially with three things: (1) as analytical solution of molecular probability density function at the ceil interface has been obtained by the Bohzmann equation with BGK model, we can compute the flux term by integrating the density function in the phase space; eqs. (8) and (11) require careful attention; (2) the integrations can be expressed as the moments of Maxwellian distribution with different limits according to the analytical solution; eqs. (9) and (10) require careful attention; (3) the discrete equation by finite volume method can be solved using the time marching method. Computations are performed by the BGK method for the Sod's shock tube problem and a two-dimensional shock reflection problem. The results are compared with those of the conventional JST scheme in Figs. 1 and 2. The BGK method provides better resolution of shock waves and other features of the flow fields.
Solution of fractional kinetic equation by a class of integral transform of pathway type
Kumar, Dilip
2013-04-01
Solutions of fractional kinetic equations are obtained through an integral transform named Pα-transform introduced in this paper. The Pα-transform is a binomial type transform containing many class of transforms including the well known Laplace transform. The paper is motivated by the idea of pathway model introduced by Mathai [Linear Algebra Appl. 396, 317-328 (2005), 10.1016/j.laa.2004.09.022]. The composition of the transform with differential and integral operators are proved along with convolution theorem. As an illustration of applications to the general theory of differential equations, a simple differential equation is solved by the new transform. Being a new transform, the Pα-transform of some elementary functions as well as some generalized special functions such as H-function, G-function, Wright generalized hypergeometric function, generalized hypergeometric function, and Mittag-Leffler function are also obtained. The results for the classical Laplace transform is retrieved by letting α → 1.
Modeling Adsorption Kinetics of Magnesium and Phosphate Ions on Goethite by Empirical Equations
Malihe Talebi Atouei
2017-06-01
Full Text Available Introduction: Natural environments, including soils and sediments, are open and complex systems in which physico-chemical reactions are in semi equilibrium state. In these systems, bioavailability of plant nutrients, like phosphate, is influenced by environmental conditions and concentrations of other ions such as calcium and magnesium. Magnesium is a dominant cation in irrigation water and in the soil solution of calcareous soils. Recent evidences show relative increase in the concentration of magnesium in irrigation water. Because of the importance of chemical kinetics in controlling concentrations of these ions in the soil solution and for understanding their effects of adsorption kinetics of magnesium and phosphate ions, in this research, adsorption kinetics of these two ions on goethite is investigated as function of time and pH in single ion and binary ion systems. The experimental data are described by using the adsorption kinetics equations. These data are of the great importance in better understanding adsorption interactions and ion adsorption mechanism.With respect to the importance of these interactions from both economical and environmental point of view, in this research, the kinetics and thermodynamics of phosphate and Mg2adsorption interactions were investigated as function of pH on soil model mineral goethite in both single and binary ion systems. Materials and Methods: Kinetics experiments were performed in the presence of 0.2 mM magnesium and 0.4 mM phosphate in 0.1 M NaCl background solution and 3 g L-1 goethite concentration as function of pH and time (1, 5, 14, 24, 48. 72 and 168 h in single ion and binary ion systems. After reaction time, the suspensions were centrifuged and a sample of supernatant was taken for measuring ions equilibrium concentrations.Phosphate concentration was measured calorimetrically with the ammonium molybdate blue method by spectrophotometer (Jenway-6505 UV/Vis. Magnesium concentration was
A refined way of solving reactor point kinetics equations for imposed reactivity insertions
Ganapol Barry D.
2009-01-01
Full Text Available We apply the concept of convergence acceleration, also known as extrapolation, to find the solution of the reactor kinetics equations (RKEs. The method features simplicity in that an approximate finite difference formulation is constructed and converged to high accuracy from knowledge of the error term. Through the Romberg extrapolation, we demonstrate its high accuracy for a variety of imposed reactivity insertions found in the literature. The unique feature of the proposed algorithm, called RKE/R(omberg, is that no special attention is given to the stiffness of the RKEs. Finally, because of its simplicity and accuracy, the RKE/R algorithm is arguably the most efficient numerical solution of the RKEs developed to date.
Tumelero, Fernanda; Petersen, Claudio Zen; Goncalves, Glenio Aguiar [Universidade Federal de Pelotas, Capao do Leao, RS (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Schramm, Marcelo [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica
2016-12-15
In this work, we report a solution to solve the Neutron Point Kinetics Equations applying the Polynomial Approach Method. The main idea is to expand the neutron density and delayed neutron precursors as a power series considering the reactivity as an arbitrary function of the time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions and the analytical continuation is used to determine the solutions of the next intervals. A genuine error control is developed based on an analogy with the Rest Theorem. For illustration, we also report simulations for different approaches types (linear, quadratic and cubic). The results obtained by numerical simulations for linear approximation are compared with results in the literature.
Wu, Fuke; Tian, Tianhai; Rawlings, James B.; Yin, George
2016-05-01
The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766-1793 (1996); ibid. 56, 1794-1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence.
Liao, Fei; Tian, Kao-Cong; Yang, Xiao; Zhou, Qi-Xin; Zeng, Zhao-Chun; Zuo, Yu-Ping
2003-03-01
The reliability of kinetic substrate quantification by nonlinear fitting of the enzyme reaction curve to the integrated Michaelis-Menten equation was investigated by both simulation and preliminary experimentation. For simulation, product absorptivity epsilon was 3.00 mmol(-1) L cm(-1) and K(m) was 0.10 mmol L(-1), and uniform absorbance error sigma was randomly inserted into the error-free reaction curve of product absorbance A(i) versus reaction time t(i) calculated according to the integrated Michaelis-Menten equation. The experimental reaction curve of arylesterase acting on phenyl acetate was monitored by phenol absorbance at 270 nm. Maximal product absorbance A(m) was predicted by nonlinear fitting of the reaction curve to Eq. (1) with K(m) as constant. There were unique A(m) for best fitting of both the simulated and experimental reaction curves. Neither the error in reaction origin nor the variation of enzyme activity changed the background-corrected value of A(m). But the range of data under analysis, the background absorbance, and absorbance error sigma had an effect. By simulation, A(m) from 0.150 to 3.600 was predicted with reliability and linear response to substrate concentration when there was 80% consumption of substrate at sigma of 0.001. Restriction of absorbance to 0.700 enabled A(m) up to 1.800 to be predicted at sigma of 0.001. Detection limit reached A(m) of 0.090 at sigma of 0.001. By experimentation, the reproducibility was 4.6% at substrate concentration twice the K(m), and A(m) linearly responded to phenyl acetate with consistent absorptivity for phenol, and upper limit about twice the maximum of experimental absorbance. These results supported the reliability of this new kinetic method for enzymatic analysis with enhanced upper limit and precision.
Barik, N; Mohanty, D K; Panda, P K; Frederico, T
2013-01-01
We have calculated the properties of nuclear matter in a self-consistent manner with quark-meson coupling mechanism incorporating structure of nucleons in vacuum through a relativistic potential model; where the dominant confining interaction for the free independent quarks inside a nucleon, is represented by a phenomenologically average potential in equally mixed scalar-vector harmonic form. Corrections due to spurious centre of mass motion as well as those due to other residual interactions such as the one gluon exchange at short distances and quark-pion coupling arising out of chiral symmetry restoration; have been considered in a perturbation manner to obtain the nucleon mass in vacuum. The nucleon-nucleon interaction in nuclear matter is then realized by introducing additional quark couplings to sigma and omega mesons through mean field approximations. The relevant parameters of the interaction are obtained self consistently while realizing the saturation properties such as the binding energy, pressure a...
Wachter, H
2007-01-01
The aim of these three papers (I, II, and III) is to develop a q-deformed version of non-relativistic Schroedinger theory. Paper I introduces the fundamental mathematical and physical concepts. The braided line and the three-dimensional q-deformed Euclidean space play the role of position space. For both cases the algebraic framework is extended by a time element. A short review of the elements of q-deformed analysis on the spaces under consideration is given. The time evolution operator is introduced in a consistent way and its basic properties are discussed. These reasonings are continued by proposing q-deformed analogs of the Schroedinger and the Heisenberg picture.
Conditions for critical effects in the mass action kinetics equations for water radiolysis
Wittman, Richard S.; Buck, Edgar C.; Mausolf, Edward J.; McNamara, Bruce K.; Smith, Frances N.; Soderquist, Chuck Z.
2014-12-26
We report on a subtle global feature of the mass action kinetics equations for water radiolysis that results in predictions of a critical behavior in H2O2 and associated radical concentrations. While radiolysis kinetics has been studied extensively in the past, it is only in recent years that high speed computing has allowed the rapid exploration of the solution over widely varying dose and compositional conditions. We explore the radiolytic production of H2O2 under various externally fixed conditions of molecular H2 and O2 that have been regarded as problematic in the literature – specifically, “jumps” in predicted concentrations, and inconsistencies between predictions and experiments have been reported for alpha radiolysis. We computationally map-out a critical concentration behavior for alpha radiolysis kinetics using a comprehensive set of reactions. We then show that all features of interest are accurately reproduced with 15 reactions. An analytical solution for steady-state concentrations of the 15 reactions reveals regions in [H2] and [O2] where the H2O2 concentration is not unique – both stable and unstable concentrations exist. The boundary of this region can be characterized analytically as a function of G-values and rate constants independent of dose rate. Physically, the boundary can be understood as separating a region where a steady-state H2O2 concentration exists, from one where it does not exist without a direct decomposition reaction. We show that this behavior is consistent with reported alpha radiolysis data and that no such behavior should occur for gamma radiolysis. We suggest experiments that could verify or discredit a critical concentration behavior for alpha radiolysis and could place more restrictive ranges on G-values from derived relationships between them.
Conditions for critical effects in the mass action kinetics equations for water radiolysis
Wittman, Richard S.; Buck, Edgar C.; Mausolf, Edward J.; McNamara, Bruce K.; Smith, Frances N.; Soderquist, Chuck Z.
2014-11-25
We report on a subtle global feature of the mass action kinetics equations for water radiolysis that results in predictions of a critical behavior in H2O2 and associated radical concentrations. While radiolysis kinetics has been studied extensively in the past, it is only in recent years that high speed computing has allowed the rapid exploration of the solution over widely varying dose and compositional conditions. We explore the radiolytic production of H2O2 under various externally fixed conditions of molecular H2 and O2 that have been regarded as problematic in the literature – specifically, “jumps” in predicted concentrations, and inconsistencies between predictions and experiments have been reported for alpha radiolysis. We computationally map-out a critical concentration behavior for alpha radiolysis kinetics using a comprehensive set of reactions. We then show that all features of interest are accurately reproduced with 15 reactions. An analytical solution for steady-state concentrations of the 15 reactions reveals regions in [H2] and [O2] where the H2O2 concentration is not unique – both stable and unstable concentrations exist. The boundary of this region can be characterized analytically as a function of G-values and rate constants independent of dose rate. Physically, the boundary can be understood as separating a region where a steady-state H2O2 concentration exists, from one where it does not exist without a direct decomposition reaction. We show that this behavior is consistent with reported alpha radiolysis data and that no such behavior should occur for gamma radiolysis. We suggest experiments that could verify or discredit a critical concentration behavior for alpha radiolysis and could place more restrictive ranges on G-values from derived relationships between them.
V.G. Morozov
2009-01-01
Full Text Available We present a kinetic theory of radiative processes in many-component plasmas with relativistic electrons and nonrelativistic heavy particles. Using the non-equilibrium Green's function technique in many-particle QED, we show that the transverse field correlation functions can be naturally decomposed into sharply peaked (non-Lorentzian parts that describe resonant (propagating photons and off-shell parts corresponding to virtual photons in the medium. Analogous decompositions are obtained for the longitudinal field correlation functions and the correlation functions of relativistic electrons. We derive a kinetic equation for the resonant photons with a finite spectral width and show that the off-shell parts of the particle and field correlation functions are essential to calculate the local radiating power in plasmas and recover the results of vacuum QED. The plasma effects on radiative processes are discussed.
Relativistic hadrons and the origin of relativistic outflows in active galactic nuclei
Contopoulos, John; Kazanas, D.
1995-01-01
We examine the hydrodynamic origin of relativistic outflows in active galactic nuclei (AGN). Specifically, we propose that the presence of a population of relativistic hadrons in the AGN 'central engine' and the associated neutron production suffices to produce outflows which under rather general conditions could be relativistic. The main such condition is that the size of the neutron production region be larger than the neutron flight path tau(sub n) approximately 3 x 10(exp 13) cm. This condition guarantees that the mean energy per particle in the proton fluid, resulting from the decay of the neutrons outside their production region, be greater than the proton rest mass. The expansion of this fluid can then lead naturally to a relativistic outflow by conversion of its internal energy to directed motion. We follow the development of such flows by solving the mass, energy as well as the kinetic equation for the proton gas in steady state, taking into account the source terms due to compute accurately the adiabatic index of the expanding gas, and in conjunction with Bernoulli's equation the detailed evolution of the bulk Lorentz factor. We further examine the role of large-scale magnetic fields in confining these outflows to produce the jets observed at larger scales.
Tumelero, Fernanda, E-mail: fernanda.tumelero@yahoo.com.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Petersen, Claudio Z.; Goncalves, Glenio A.; Lazzari, Luana, E-mail: claudiopeteren@yahoo.com.br, E-mail: gleniogoncalves@yahoo.com.br, E-mail: luana-lazzari@hotmail.com [Universidade Federal de Pelotas (DME/UFPEL), Capao do Leao, RS (Brazil). Instituto de Fisica e Matematica
2015-07-01
In this work, we present a solution of the Neutron Point Kinetics Equations with temperature feedback effects applying the Polynomial Approach Method. For the solution, we consider one and six groups of delayed neutrons precursors with temperature feedback effects and constant reactivity. The main idea is to expand the neutron density, delayed neutron precursors and temperature as a power series considering the reactivity as an arbitrary function of the time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions of the problem and the analytical continuation is used to determine the solutions of the next intervals. With the application of the Polynomial Approximation Method it is possible to overcome the stiffness problem of the equations. In such a way, one varies the time step size of the Polynomial Approach Method and performs an analysis about the precision and computational time. Moreover, we compare the method with different types of approaches (linear, quadratic and cubic) of the power series. The answer of neutron density and temperature obtained by numerical simulations with linear approximation are compared with results in the literature. (author)
Xu, Peng
2016-01-01
With continuous advances in technologies related to deep space ranging and satellite gravity gradiometry, corrections from general relativity to the dynamics of relative orbital motions will certainly become important. In this work, we extend,in a systematic way, the Hill-Clohessy-Wiltshire Equations to include the complete first order post-Newtonian effects from general relativity. Within certain short time limit, post-Newtonian corrections to general periodic solutions of the Hill-Clohessy-Wiltshire Equations are also worked out.
Pastor, J
2004-07-01
We have determined the equation of state of nuclear matter according to relativistic non-linear models. In particular, we are interested in regions of high density and/or high temperature, in which the thermodynamic functions have very different behaviours depending on which model one uses. The high-density behaviour is, for example, a fundamental ingredient for the determination of the maximum mass of neutron stars. As an application, we have studied the process of two-pion annihilation into e{sup +}e{sup -} pairs in dense and hot matter. Accordingly, we have determined the way in which the non-linear terms modify the meson propagators occurring in this process. Our results have been compared with those obtained for the meson propagators in free space. We have found models that give an enhancement of the dilepton production rate in the low invariant mass region. Such an enhancement is in good agreement with the invariant mass dependence of the data obtained in heavy ions collisions at CERN/SPS energies. (author)
Soliton propagation in relativistic hydrodynamics
Fogaça, D A; 10.1016/j.nuclphysa.2007.03.104
2013-01-01
We study the conditions for the formation and propagation of Korteweg-de Vries (KdV) solitons in nuclear matter. In a previous work we have derived a KdV equation from Euler and continuity equations in non-relativistic hydrodynamics. In the present contribution we extend our formalism to relativistic fluids. We present results for a given equation of state, which is based on quantum hadrodynamics (QHD).
Barik, N.; Mishra, R. N.; Mohanty, D. K.; Panda, P. K.; Frederico, T.
2013-07-01
We have calculated the properties of nuclear matter in a self-consistent manner with a quark-meson coupling mechanism incorporating the structure of nucleons in vacuum through a relativistic potential model; where the dominant confining interaction for the free independent quarks inside a nucleon is represented by a phenomenologically average potential in equally mixed scalar-vector harmonic form. Corrections due to spurious center of mass motion as well as those due to other residual interactions, such as the one gluon exchange at short distances and quark-pion coupling arising out of chiral symmetry restoration, have been considered in a perturbative manner to obtain the nucleon mass in vacuum. The nucleon-nucleon interaction in nuclear matter is then realized by introducing additional quark couplings to σ and ω mesons through mean field approximations. The relevant parameters of the interaction are obtained self-consistently while realizing the saturation properties such as the binding energy, pressure, and compressibility of the nuclear matter. We also discuss some implications of chiral symmetry in nuclear matter along with the nucleon and nuclear σ term and the sensitivity of nuclear matter binding energy with variations in the light quark mass.
Li, Zhihui; Wu, Junlin; Ma, Qiang; Jiang, Xinyu; Zhang, Hanxin
2014-12-01
Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.
Li, Zhihui; Ma, Qiang [Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, P.O.Box 211, Mianyang 621000, China and National Laboratory for Computational Fluid Dynamics, No.37 Xueyuan Road, Beijing 100191 (China); Wu, Junlin; Jiang, Xinyu [Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, P.O.Box 211, Mianyang 621000 (China); Zhang, Hanxin [National Laboratory for Computational Fluid Dynamics, No.37 Xueyuan Road, Beijing 100191 (China)
2014-12-09
Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.
Speeds of Propagation in Classical and Relativistic Extended Thermodynamics
Müller Ingo
1999-01-01
Full Text Available The Navier-Stokes-Fourier theory of viscous, heat-conducting fluids provides parabolic equations and thus predicts infinite pulse speeds. Naturally this feature has disqualified the theory for relativistic thermodynamics which must insist on finite speeds and, moreover, on speeds smaller than $c$. The attempts at a remedy have proved heuristically important for a new systematic type of thermodynamics: Extended thermodynamics. That new theory has symmetric hyperbolic field equations and thus it provides finite pulse speeds. Extended thermodynamics is a whole hierarchy of theories with an increasing number of fields when gradients and rates of thermodynamic processes become steeper and faster. The first stage in this hierarchy is the 14-field theory which may already be a useful tool for the relativist in many applications. The 14 fields -- and further fields -- are conveniently chosen from the moments of the kinetic theory of gases. The hierarchy is complete only when the number of fields tends to infinity. In that case the pulse speed of non-relativistic extended thermodynamics tends to infinity while the pulse speed of relativistic extended thermodynamics tends to $c$, the speed of light. In extended thermodynamics symmetric hyperbolicity -- and finite speeds -- are implied by the concavity of the entropy density. This is still true in relativistic thermodynamics for a privileged entropy density which is the entropy density of the rest frame for non-degenerate gases.
Relativistic stars in scalar-tensor theories with disformal coupling
Silva, Hector O.; Minamitsuji, Masato
2017-01-01
We discuss a general formulation to study the structure of slowly-rotating relativistic stars in a broad class of scalar-tensor theories including disformal coupling to matter. Our approach includes as particular cases theories with generalized kinetic terms and generic scalar field potentials, and contains theories with conformal coupling as particular limits. We propose a minimal model to investigate the role of the disformal coupling on the non-perturbative effect known as spontaneous scalarization, which causes relativistic star solutions in certain classes of scalar-tensor theories to differ dramatically from their general relativistic counterparts. Moreover, we show that the moment of inertia and compactness of stars are equation of state independent, which can potentially be used to constrain the model observationally.
Acoustic perturbations in special-relativistic parallel flows
Rogava, A D; Mahajan, S M
1996-01-01
Acoustic perturbations in a parallel relativistic flow of an inviscid fluid are considered. The general expression for the frequency of the sound waves in a uniformly (with zero shear) moving medium is derived. It is shown that relativity evokes a difference in the frequencies of the sound-type perturbations propagating along and against the current. Besides, it is shown that the perturbations are not purely irrotational as they are in nonrelativistic case. For a non-uniformly (with nonzero shear) moving fluid a general set of equations, describing the evolution of the acoustic perturbations in relativistic sheared flows, is obtained and analysed when the temperature is nonrelativistic. It is shown that, like the nonrelativistic case, in the new system: (a) the excitation of vortical, transiently growing perturbations, and (b) the excitation of sound-type perturbations, extracting the kinetic energy of the background flow, are possible. It is demonstrated that the relativistic character of the motion signific...
Relativistic viscoelastic fluid mechanics.
Fukuma, Masafumi; Sakatani, Yuho
2011-08-01
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
Applications of nonlinear science and kinetic equations to the spread of epidemics
Macinnis, David Robert
The study of the spread of epidemics is currently growing into a successful subfield of a combination of nonlinear science and statistical mechanics. Topics studied in this field include kinetic and mean field levels of epidemiological models. This thesis consists of the analysis of such topics and specifically directed at the Hantavirus, West Nile virus, and the Bubonic Plague. A successful reaction-diffusion equation approach developed recently by Abramson and Kenkre was able to describe spatiotemporal patterns of the Hantavirus model. From measurements of the parameters of their model it was found that the mice, the carriers of the infection, must be regarded as moving diffusively within attractive potentials representative of home ranges. Several attempts have been made to incorporate home ranges into their model. Two of these attempts are discussed within this thesis. A model to explain the transmission of the West Nile virus within bird and mosquito populations was recently developed by Kenkre, Parmenter, Peixoto, and Sadasiv who showed how spatially resolved issues could be discussed but restricted their analysis to mean field considerations. This thesis extends that study by investigating spatial resolution of the infected populations. Traveling waves of the bird and mosquito populations are found in the West Nile context. Infection control of various epidemics has become increasingly important to limit the potential force of infection into the human population. This thesis contains a quantitative attempt at a theory of such control (for the West Nile virus) via spraying of the mosquito population. Mean field and kinetic level models are proposed in this thesis to describe the transmission of the Bubonic Plague which involves flea and mammal populations. The various populations are found to undergo a variety of bifurcations as well as hysteresis in their steady state regime. Spatially resolved analysis of the populations is also presented.
Kim, Song Hyun; Woo, Myeong Hyun; Shin, Chang Ho [Hanyang University, Seoul (Korea, Republic of); Pyeon, Cheol Ho [Kyoto University, Osaka (Japan)
2015-10-15
In this study, a new balance equation to overcome the problems generated by the previous methods is proposed using source-based balance equation. And then, a simple problem is analyzed with the proposed method. In this study, a source-based balance equation with the time dependent fission kernel was derived to simplify the kinetics equation. To analyze the partial variations of reactor characteristics, two representative methods were introduced in previous studies; (1) quasi-statics method and (2) multipoint technique. The main idea of quasistatics method is to use a low-order approximation for large integration times. To realize the quasi-statics method, first, time dependent flux is separated into the shape and amplitude functions, and shape function is calculated. It is noted that the method has a good accuracy; however, it can be expensive as a calculation cost aspect because the shape function should be fully recalculated to obtain accurate results. To improve the calculation efficiency, multipoint method was proposed. The multipoint method is based on the classic kinetics equation with using Green's function to analyze the flight probability from region r' to r. Those previous methods have been used to analyze the reactor kinetics analysis; however, the previous methods can have some limitations. First, three group variables (r{sub g}, E{sub g}, t{sub g}) should be considered to solve the time dependent balance equation. This leads a big limitation to apply large system problem with good accuracy. Second, the energy group neutrons should be used to analyze reactor kinetics problems. In time dependent problem, neutron energy distribution can be changed at different time. It can affect the change of the group cross section; therefore, it can lead the accuracy problem. Third, the neutrons in a space-time region continually affect the other space-time regions; however, it is not properly considered in the previous method. Using birth history of the
Lee, Roman N
2016-01-01
We apply the differential equation method to the calculation of the total Born cross section of the process $Z_1Z_2\\to Z_1Z_2e^+e^-$. We obtain explicit expression for the cross section exact in the relative velocity of the nuclei.
Luo, Songting; Payne, Nicholas
2017-07-01
We present an effective asymptotic method for approximating the density of particles for kinetic equations with a Bhatnagar-Gross-Krook (BGK) relaxation operator in the large scale hyperbolic limit. The density of particles is transformed via a Hopf-Cole transformation, where the phase function is expanded as a power series with respect to the Knudsen number. The expansion terms can be determined by solving a sequence of equations. In particular, it has been proved in [3] that the leading order term is the viscosity solution of an effective Hamilton-Jacobi equation, and we show that the higher order terms can be formally determined by solving a sequence of transport equations. Both the effective Hamilton-Jacobi equation and the transport equations are independent of the Knudsen number, and are formulated in the physical space, where the effective Hamiltonian is obtained as the solution of a nonlinear equation that is given as an integral in the velocity variable, and the coefficients of the transport equations are given as integrals in the velocity variable. With appropriate Gauss quadrature rules for evaluating these integrals effectively, the effective Hamilton-Jacobi equation and the transport equations can be solved efficiently to obtain the expansion terms for approximating the density function. In this work, the zeroth, first and second order terms in the expansion are used to obtain second order accuracy with respect to the Knudsen number. The proposed method balances efficiency and accuracy, and has the potential to deal with kinetic equations with more general BGK models. Numerical experiments verify the effectiveness of the proposed method.
Kiernan, D; Malone, A; O'Brien, T; Simms, C K
2015-01-01
Regression equations based on pelvic anatomy are routinely used to estimate the hip joint centre during gait analysis. While the associated errors have been well documented, the clinical significance of these errors has not been reported. This study investigated the clinical agreement of three commonly used regression equation sets (Bell et al., Davis et al. and Orthotrak software) against the equations of Harrington et al. Full 3-dimensional gait analysis was performed on 18 healthy paediatric subjects. Kinematic and kinetic data were calculated using each set of regression equations and compared to Harrington et al. In addition, the Gait Profile Score and GDI-Kinetic were used to assess clinical significance. Bell et al. was the best performing set with differences in Gait Profile Score (0.13°) and GDI-Kinetic (0.84 points) falling below the clinical significance threshold. Small deviations were present for the Orthotrak set for hip abduction moment (0.1 Nm/kg), however differences in Gait Profile Score (0.27°) and GDI-Kinetic (2.26 points) remained below the clinical threshold. Davis et al. showed least agreement with a clinically significant difference in GDI-Kinetic score (4.36 points). It is proposed that Harrington et al. or Bell et al. regression equation sets are used during gait analysis especially where inverse dynamic data are calculated. Orthotrak is a clinically acceptable alternative however clinicians must be aware of the effects of error on hip abduction moment. The Davis et al. set should be used with caution for inverse dynamic analysis as error could be considered clinically meaningful.
Bambang Rusdiarso
2016-12-01
Full Text Available Extraction and purification of humic acid from dry horse dung powder (HD-HA was performed successfully and the purified HD-HA was then applied as sorbent to adsorb Zn2+. Extraction and purification were performed based on procedure of Stevenson (1994 under atmospheric air. Parameters investigated in this work consist of effect of medium sorption acidity, sorption rate (ka and desorption rate constant (kd, Langmuir (monolayer and Freundlich (multilayer sorption capacities, and energy (E of sorption. The ka and kd were determined according to the kinetic model of second order sorption reaching equilibrium, monolayer sorption capacity (b and energy (E were determined according to Langmuir isotherm model, and multilayer sorption capacity (B was determined based on Freundlich isotherm model. Sorption of Zn2+ on purified HD-HA was maximum at pH 5.0. The novel kinetic expression resulted from proposed kinetic model has been shown to be more applicable than the commonly known Lagergren equation obtained from the pseudo-first order sorption model. The application of the equation revealed that the intercept of Lagergren equation, ln qe was more complex function of initial concentration of Zn2+ (a, Langmuir sorption capacity (b, and sorbed Zn2+ at equilibrium (xe.
Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation
Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui
2014-01-01
Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904
Adaptive change of basis in entropy-based moment closures for linear kinetic equations
Alldredge, Graham W; O'Leary, Dianne P; Tits, André L
2013-01-01
Entropy-based (M_N) moment closures for kinetic equations are defined by a constrained optimization problem that must be solved at every point in a space-time mesh, making it important to solve these optimization problems accurately and efficiently. We present a complete and practical numerical algorithm for solving the dual problem in one-dimensional, slab geometries. The closure is only well-defined on the set of moments that are realizable from a positive underlying distribution, and as the boundary of the realizable set is approached, the dual problem becomes increasingly difficult to solve due to ill-conditioning of the Hessian matrix. To improve the condition number of the Hessian, we advocate the use of a change of polynomial basis, defined using a Cholesky factorization of the Hessian, that permits solution of problems nearer to the boundary of the realizable set. We also advocate a fixed quadrature scheme, rather than adaptive quadrature, since the latter introduces unnecessary expense and changes th...
Study of carbon dioxide gas treatment based on equations of kinetics in plasma discharge reactor
Abedi-Varaki, Mehdi
2017-08-01
Carbon dioxide (CO2) as the primary greenhouse gas, is the main pollutant that is warming earth. CO2 is widely emitted through the cars, planes, power plants and other human activities that involve the burning of fossil fuels (coal, natural gas and oil). Thus, there is a need to develop some method to reduce CO2 emission. To this end, this study investigates the behavior of CO2 in dielectric barrier discharge (DBD) plasma reactor. The behavior of different species and their reaction rates are studied using a zero-dimensional model based on equations of kinetics inside plasma reactor. The results show that the plasma reactor has an effective reduction on the CO2 density inside the reactor. As a result of reduction in the temporal variations of reaction rate, the speed of chemical reactions for CO2 decreases and very low concentration of CO2 molecules inside the plasma reactor is generated. The obtained results are compared with the existing experimental and simulation findings in the literature.
Zakharov, A Yu
2016-01-01
The exact closed equation of motion for microscopic distribution function of classical many-body system with account of interactions retardation between particles is derived. It is shown that interactions retardation leads to irreversible behaviour of many-body systems.
Modelling early stages of relativistic heavy-ion collisions
Ruggieri M.
2016-01-01
Full Text Available In this study we model early time dynamics of relativistic heavy ion collisions by an initial color-electric field which then decays to a plasma by the Schwinger mechanism. The dynamics of the many particles system produced by the decay is described by relativistic kinetic theory, taking into account the backreaction on the color field by solving self-consistently the kinetic and the field equations. Our main results concern isotropization and thermalization for a 1+1D expanding geometry. In case of small η/s (η/s ≲ 0.3 we find τisotropization ≈ 0.8 fm/c and τthermalization ≈ 1 fm/c in agreement with the common lore of hydrodynamics.
Costa, Rafael S.; Machado, Daniel; Rocha, Isabel
2010-01-01
, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis–Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action...... using the hybrid model composed of Michaelis–Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown....
QE+QSS for Derivation of Kinetic Equations and Stiffness Removing
Gorban, A N
2010-01-01
We present the general formalism of the Quasiequilibrium approximation (QE) with the proof of the persistence of entropy production in the QE approximation. We demonstrate, how to apply this formalism to chemical kinetics and describe the difference between QE and Quasi--Steady--State (QSS) approximations. The celebrated QSS "Michaelis--Menten" kinetics is, as a matter of fact, the "Briggs-Haldane" kinetics. Michaelis and Menten used the QE assumption that all intermediate complexes are in fast equilibrium with free substrates and enzyme. Similar approach was developed by Stuekelberg (1952) for the Boltzmann kinetics. Following them, we combine the QE (fast equilibria) and the QSS (small amounts) approaches and study the general kinetics with fast intermediates present in small amount. We prove the representation of the rate of an elementary reaction as a product of the Boltzmann factor (purely thermodynamic) and the kinetic factor, and found the basic relations between kinetic factors. In the practice of mod...
A reduced model for relativistic electron beam transport in solids and dense plasmas
Touati, M.; Feugeas, J.-L.; Nicolaï, Ph; Santos, J. J.; Gremillet, L.; Tikhonchuk, V. T.
2014-07-01
A hybrid reduced model for relativistic electron beam transport based on the angular moments of the relativistic kinetic equation with a special closure is presented. It takes into account collective effects with the self-generated electromagnetic fields as well as collisional effects with the slowing down of the relativistic electrons by plasmons, bound and free electrons and their angular scattering on both ions and electrons. This model allows for fast computations of relativistic electron beam transport while describing their energy distribution evolution. Despite the loss of information concerning the angular distribution of the electron beam, the model reproduces analytical estimates in the academic case of a monodirectional and monoenergetic electron beam propagating through a warm and dense plasma and hybrid particle-in-cell simulation results in a realistic laser-generated electron beam transport case.
Demianski, Marek
2013-01-01
Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity
Sun, Wenjun; Jiang, Song; Xu, Kun; Li, Shu
2015-12-01
This paper presents an extension of previous work (Sun et al., 2015 [22]) of the unified gas kinetic scheme (UGKS) for the gray radiative transfer equations to the frequency-dependent (multi-group) radiative transfer system. Different from the gray radiative transfer equations, where the optical opacity is only a function of local material temperature, the simulation of frequency-dependent radiative transfer is associated with additional difficulties from the frequency-dependent opacity. For the multiple frequency radiation, the opacity depends on both the spatial location and the frequency. For example, the opacity is typically a decreasing function of frequency. At the same spatial region the transport physics can be optically thick for the low frequency photons, and optically thin for high frequency ones. Therefore, the optical thickness is not a simple function of space location. In this paper, the UGKS for frequency-dependent radiative system is developed. The UGKS is a finite volume method and the transport physics is modeled according to the ratio of the cell size to the photon's frequency-dependent mean free path. When the cell size is much larger than the photon's mean free path, a diffusion solution for such a frequency radiation will be obtained. On the other hand, when the cell size is much smaller than the photon's mean free path, a free transport mechanism will be recovered. In the regime between the above two limits, with the variation of the ratio between the local cell size and photon's mean free path, the UGKS provides a smooth transition in the physical and frequency space to capture the corresponding transport physics accurately. The seemingly straightforward extension of the UGKS from the gray to multiple frequency radiation system is due to its intrinsic consistent multiple scale transport modeling, but it still involves lots of work to properly discretize the multiple groups in order to design an asymptotic preserving (AP) scheme in all
S. Yamoah
2012-04-01
Full Text Available The understanding of the time-dependent behaviour of the neutron population in a nuclear reactor in response to either a planned or unplanned change in the reactor conditions is of great importance to the safe and reliable operation of the reactor. In this study two analytical methods have been presented to solve the point kinetic equations of average one-group of delayed neutrons. These methods which are both approximate solution of the point reactor kinetic equations are compared with a numerical solution using the Euler’s first order method. To obtain accurate solution for the Euler method, a relatively small time step was chosen for the numerical solution. These methods are applied to different types of reactivity to check the validity of the analytical method by comparing the analytical results with the numerical results. From the results, it is observed that the analytical solution agrees well with the numerical solution.
Two corrections to the drift-wave kinetic equation in the context of zonal-flow physics
Ruiz, D E; Shi, E L; Dodin, I Y
2016-01-01
The drift-wave (DW) kinetic equation, that is commonly used in studies of zonal flows (ZF), excludes the exchange of enstrophy between DW and ZF and also effects beyond the geometrical-optics limit. Using the quasilinear approximation of the generalized Hasegawa--Mima model, we propose a modified theory that accounts for these effects within a wave kinetic equation (WKE) of the Wigner--Moyal type, which is commonly known in quantum mechanics. In the geometrical-optics limit, this theory features additional terms beyond the traditional WKE that ensure exact conservation of the \\textit{total} enstrophy and energy in the DW-ZF system. Numerical simulations are presented to illustrate the importance of these additional terms. The proposed theory can be viewed as a reformulation of the second-order cumulant expansion (also known as the CE2) in a more intuitive manner, namely, in terms of canonical phase-space variables.
Frost, W.; Harper, W. L.
1975-01-01
Flow over surface obstructions can produce significantly large wind shears such that adverse flying conditions can occur for aeronautical systems (helicopters, STOL vehicles, etc.). Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow and highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient. Discussion of the effects of the disturbed wind field in CTOL and STOL aircraft flight path and obstruction clearance standards is given. The results indicate that closer inspection of these presently recommended standards as influenced by wind over irregular terrains is required.
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Zhang, Dong-Rui; Wei, Si-Na; Yang, Rong-Yao; Xiang, Qian-Fei
2016-01-01
It has been a puzzle whether quarks may exist in the interior of massive neutron stars, since the hadron-quark phase transition softens the equation of state (EOS) and reduce the neutron star (NS) maximum mass very significantly. In this work, we consider the light U-boson that increases the NS maximum mass appreciably through its weak coupling to fermions. The inclusion of the U-boson may thus allow the existence of the quark degrees of freedom in the interior of large mass neutron stars. Unlike the consequence of the U-boson in hadronic matter, the stiffening role of the U-boson in the hybrid EOS is not sensitive to the choice of the hadron phase models. In addition, we have also investigated the effect of the effective QCD correction on the hybrid EOS. This correction may reduce the coupling strength of the U-boson that is needed to satisfy NS maximum mass constraint. While the inclusion of the U-boson also increases the NS radius significantly, we find that appropriate in-medium effects of the U-boson may...
Zhang, Dong-Rui; Jiang, Wei-Zhou; Wei, Si-Na; Yang, Rong-Yao [Southeast University, Department of Physics, Nanjing (China); Xiang, Qian-Fei [Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China)
2016-05-15
It has been a puzzle whether quarks may exist in the interior of massive neutron stars, since the hadron-quark phase transition softens the equation of state (EOS) and reduce the neutron star (NS) maximum mass very significantly. In this work, we consider the light U-boson that increases the NS maximum mass appreciably through its weak coupling to fermions. The inclusion of the U-boson may thus allow the existence of the quark degrees of freedom in the interior of large mass neutron stars. Unlike the consequence of the U-boson in hadronic matter, the stiffening role of the U-boson in the hybrid EOS is not sensitive to the choice of the hadron phase models. In addition, we have also investigated the effect of the effective QCD correction on the hybrid EOS. This correction may reduce the coupling strength of the U-boson that is needed to satisfy NS maximum mass constraint. While the inclusion of the U-boson also increases the NS radius significantly, we find that appropriate in-medium effects of the U-boson may reduce the NS radii significantly, satisfying both the NS radius and mass constraints well. (orig.)
Tomaschewski, Fernanda K.; Segatto, Cynthia F., E-mail: fernandasls_89@hotmail.com, E-mail: cynthia.segatto@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada; Barros, Ricardo C., E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Departamento de Modelagem Computacional
2015-07-01
Presented here is a decomposition method based on series representation of the group angular fluxes and delayed neutron precursors in smoothly continuous functions for energy multigroups, slab-geometry discrete ordinates kinetics equations supplemented with a prescribed number of delayed neutron precursors. Numerical results to a non-reflected sub-critical slab stabilized by steady-state sources are given to illustrate the accuracy and efficiency of the o offered method. (author)
Costa, Rafael S; Machado, Daniel; Rocha, Isabel; Ferreira, Eugénio C
2010-05-01
The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis-Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action, convenience kinetics, lin-log and power-law). Using the mechanistic model for Escherichia coli central carbon metabolism as a benchmark, we investigate the alternative modeling approaches through comparative simulations analyses. The good dynamic behavior and the powerful predictive capabilities obtained using the hybrid model composed of Michaelis-Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown. 2010 Elsevier Ireland Ltd. All rights reserved.
A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations
Liu, Chang; Xu, Kun; Sun, Quanhua; Cai, Qingdong
2016-06-01
Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region
Utilization of Integrated Michaelis-Menten Equation to Determine Kinetic Constants
Bezerra, Rui M. F.; Dias, Albino A.
2007-01-01
Students of biochemistry and related biosciences are urged to solve problems where kinetic parameters are calculated from initial rates obtained at different substrate concentrations. Troubles begin when they go to the laboratory to perform kinetic experiments and realize that usual laboratory instruments do not measure initial rates but only…
Utilization of Integrated Michaelis-Menten Equation to Determine Kinetic Constants
Bezerra, Rui M. F.; Dias, Albino A.
2007-01-01
Students of biochemistry and related biosciences are urged to solve problems where kinetic parameters are calculated from initial rates obtained at different substrate concentrations. Troubles begin when they go to the laboratory to perform kinetic experiments and realize that usual laboratory instruments do not measure initial rates but only…
Analogy betwen dislocation creep and relativistic cosmology
J.A. Montemayor-Aldrete; J.D. Muñoz-Andrade; Mendoza-Allende, A.; Montemayor-Varela, A.
2005-01-01
A formal, physical analogy between plastic deformation, mainly dislocation creep, and Relativistic Cosmology is presented. The physical analogy between eight expressions for dislocation creep and Relativistic Cosmology have been obtained. By comparing the mathematical expressions and by using a physical analysis, two new equations have been obtained for dislocation creep. Also, four new expressions have been obtained for Relativistic Cosmology. From these four new equations, one may determine...
Relativistic suppression of wave packet spreading.
Su, Q; Smetanko, B; Grobe, R
1998-03-30
We investigate numerically the solution of Dirac equation and analytically the Klein-Gordon equation and discuss the relativistic motion of an electron wave packet in the presence of an intense static electric field. In contrast to the predictions of the (non-relativistic) Schroedinger theory, the spreading rate in the field's polarization direction as well as in the transverse directions is reduced.
Relativistic theories of materials
Bressan, Aldo
1978-01-01
The theory of relativity was created in 1905 to solve a problem concerning electromagnetic fields. That solution was reached by means of profound changes in fundamental concepts and ideas that considerably affected the whole of physics. Moreover, when Einstein took gravitation into account, he was forced to develop radical changes also in our space-time concepts (1916). Relativistic works on heat, thermodynamics, and elasticity appeared as early as 1911. However, general theories having a thermodynamic basis, including heat conduction and constitutive equations, did not appear in general relativity until about 1955 for fluids and appeared only after 1960 for elastic or more general finitely deformed materials. These theories dealt with materials with memory, and in this connection some relativistic versions of the principle of material indifference were considered. Even more recently, relativistic theories incorporating finite deformations for polarizable and magnetizable materials and those in which couple s...
The Einstein-Vlasov System/Kinetic Theory
Håkan Andréasson
2011-05-01
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 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.
Relativistic Electron Experiment for the Undergraduate Laboratory
Marvel, Robert E
2011-01-01
We have developed an undergraduate laboratory experiment to make independent measurements of the momentum and kinetic energy of relativistic electrons from a \\beta -source. The momentum measurements are made with a magnetic spectrometer and a silicon surface-barrier detector is used to measure the kinetic energy. A plot of the kinetic energy as a function of momentum compared to the classical and relativistic predictions clearly shows the relativistic nature of the electrons. Accurate values for the rest mass of the electron and the speed of light are also extracted from the data.
Lewin, Mathieu
2011-01-01
In a recent paper published in Nonlinear Analysis: Theory, Methods & Applications, C. Argaez and M. Melgaard studied excited states for pseudo-relativistic multi-configuration methods. Their paper follows a previous work of mine in the non-relativistic case (Arch. Rat. Mech. Anal., 171, 2004). The main results of the paper of C. Argaez and M. Melgaard are correct, but the proofs are both wrong and incomplete.
Steady-state benchmarks of DK4D: A time-dependent, axisymmetric drift-kinetic equation solver
Lyons, B. C. [Princeton University, Princeton, New Jersey 08544 (United States); Jardin, S. C. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543-0451 (United States); Ramos, J. J. [Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 (United States)
2015-05-15
The DK4D code has been written to solve a set of time-dependent, axisymmetric, finite-Larmor-radius drift-kinetic equations (DKEs) for the non-Maxwellian part of the electron and ion distribution functions using the full, linearized Fokker–Planck–Landau collision operator. The plasma is assumed to be in the low- to finite-collisionality regime, as is found in the cores of modern and future magnetic confinement fusion experiments. Each DKE is formulated such that the perturbed distribution function carries no net density, parallel momentum, or kinetic energy. Rather, these quantities are contained within the background Maxwellians and would be evolved by an appropriate set of extended magnetohydrodynamic (MHD) equations. This formulation allows for straight-forward coupling of DK4D to existing extended MHD time evolution codes. DK4D uses a mix of implicit and explicit temporal representations and finite element and spectral spatial representations. These, along with other computational methods used, are discussed extensively. Steady-state benchmarks are then presented comparing the results of DK4D to expected analytic results at low collisionality, qualitatively, and to the Sauter analytic fits for the neoclassical conductivity and bootstrap current, quantitatively. These benchmarks confirm that DK4D is capable of solving for the correct, gyroaveraged distribution function in stationary magnetic equilibria. Furthermore, the results presented demonstrate how the exact drift-kinetic solution varies with collisionality as a function of the magnetic moment and the poloidal angle.
Fractional Dynamics of Relativistic Particle
Tarasov, Vasily E
2011-01-01
Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to a non-potential four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u_{\\mu} u^{\\mu}+c^2=0, where c is a speed of light in vacuum. In the general case, the fractional dynamics of relativistic particle is described as non-Hamiltonian and dissipative. Conditions for fractional relativistic particle to be a Hamiltonian system are considered.
Generalization of the Dirac’s Equation and Sea
Javadi, Hossein; Forouzbakhsh, Farshid; Daei Kasmaei, Hamed
2016-01-01
Newton's second law is motion equation in classic mechanics that does not say anything about the nature of force. The equivalent formulations and their extensions such as Lagrangian and Hamiltonian do not explain about mechanism of converting Potential energy to Kinetic energy and Vice versa. In quantum mechanics, Schrodinger equation is similar to Newton's second law in classic mechanics. Quantum mechanics is also extension of Newtonian mechanics to atomic and subatomic scales and relativist...
Pratt, D. T.; Radhakrishnan, K.
1986-01-01
The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.
Relativistic elastic differential cross sections for equal mass nuclei
C.M. Werneth
2015-10-01
Full Text Available The effects of relativistic kinematics are studied for nuclear collisions of equal mass nuclei. It is found that the relativistic and non-relativistic elastic scattering amplitudes are nearly indistinguishable, and, hence, the relativistic and non-relativistic differential cross sections become indistinguishable. These results are explained by analyzing the Lippmann–Schwinger equation with the first order optical potential that was employed in the calculation.
Relativistic elastic differential cross sections for equal mass nuclei
Werneth, C.M., E-mail: charles.m.werneth@nasa.gov [NASA Langley Research Center, 2 West Reid Street, Hampton, VA 23681 (United States); Maung, K.M.; Ford, W.P. [The University of Southern Mississippi, 118 College Drive, Box 5046, Hattiesburg, MS 39406 (United States)
2015-10-07
The effects of relativistic kinematics are studied for nuclear collisions of equal mass nuclei. It is found that the relativistic and non-relativistic elastic scattering amplitudes are nearly indistinguishable, and, hence, the relativistic and non-relativistic differential cross sections become indistinguishable. These results are explained by analyzing the Lippmann–Schwinger equation with the first order optical potential that was employed in the calculation.
Quantum Potential Via General Hamilton - Jacobi Equation
Mollai, Maedeh; Jami, Safa; Ahanj, Ali
2011-01-01
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The interpretation of QP in terms of independent entity is discussed along with the introduction of quantum kinetic energy. The method has been extended to relativistic regime, and same results have been concluded.
Special Relativistic Hydrodynamics with Gravitation
Hwang, Jai-chan; Noh, Hyerim
2016-12-01
Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.
Special relativistic hydrodynamics with gravitation
Hwang, Jai-chan
2016-01-01
The special relativistic hydrodynamics with weak gravity is hitherto unknown in the literature. Whether such an asymmetric combination is possible was unclear. Here, the hydrodynamic equations with Poisson-type gravity considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit are consistently derived from Einstein's general relativity. Analysis is made in the maximal slicing where the Poisson's equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the {\\it general} hypersurface condition. Our formulation includes the anisotropic stress.
Investigation on shock waves stability in relativistic gas dynamics
Alexander Blokhin
1993-05-01
Full Text Available This paper is devoted to investigation of the linearized mixed problem of shock waves stability in relativistic gas dynamics. The problem of symmetrization of relativistic gas dynamics equations is also discussed.
Wang, Jia X; Uribe, Francisco A; Springer, Thomas E; Zhang, Junliang; Adzic, Radoslav R
2008-01-01
According to Sergio Trasatti, "A true theory of electrocatalysis will not be available until activity can be calculated a priori from some known properties of the materials." Toward this goal, we developed intrinsic kinetic equations for the hydrogen oxidation reaction (HOR) and the oxygen reduction reaction (ORR) using as the kinetic parameters the free energies of adsorption and activation for elementary reactions. Rigorous derivation retained the intrinsic connection between the intermediates' adsorption isotherms and the kinetic equations, affording us an integrated approach for establishing the reaction mechanisms based upon various experimental and theoretical results. Using experimentally deduced free energy diagrams and activity-and-barriers plot for the ORR on Pt(111), we explained why the Tafel slope in the large overpotential region is double that in the small overpotential region. For carbon-supported Pt nanoparticles (Pt/C), the polarization curves measured with thin-film rotating disk electrodes also exhibit the double Tafel slope, albeit Pt(111) is several times more active than the Pt nanoparticles when the current is normalized by real surface area. An analytic method was presented for the polarization curves measured with H2 in proton exchange membrane fuel cells (PEMFCs). The fit to a typical iR-free polarization curve at 80 degrees C revealed that the change of the Tafel slope occurs at about 0.77 V that is the reversible potential for the transition between adsorbed O and OH on Pt/C. This is significant because it predicts that the Butler-Volmer equation can only fit the data above this potential, regardless the current density. We also predicted a decrease of the Tafel slope from 70 to 65 mV dec(-1) at 80 degrees C with increasing oxygen partial pressure, which is consistent with the observation reported in literature.
Fillion-Gourdeau, F; Bandrauk, A D
2015-01-01
A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron-molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.
Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis
Fillion-Gourdeau, F., E-mail: filliong@CRM.UMontreal.ca [Université du Québec, INRS – Énergie, Matériaux et Télécommunications, Varennes, J3X 1S2 (Canada); Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 (Canada); Lorin, E., E-mail: elorin@math.carleton.ca [School of Mathematics and Statistics, Carleton University, Ottawa, K1S 5B6 (Canada); Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 (Canada); Bandrauk, A.D., E-mail: andre.bandrauk@usherbrooke.ca [Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, J1K 2R1 (Canada); Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 (Canada)
2016-02-15
A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron–molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.
无
2002-01-01
The apparent activation energies and frequency factors of the double reversible transformations occurring in heating CuZnAlMnNi shape memory alloy (SMA) were deduced as AEx .M = 62.597 8 kJ/mol, AEm.A 153.92 kJ'mol,Ax-m = 5.223 2 × 109s 1, and AM-A = 2.325 1 × l023 s 1, respectively. The kinetic equations of the two transfornations during heating were established simultaneously.
Relativistic Hydrodynamics with Wavelets
DeBuhr, Jackson; Anderson, Matthew; Neilsen, David; Hirschmann, Eric W
2015-01-01
Methods to solve the relativistic hydrodynamic equations are a key computational kernel in a large number of astrophysics simulations and are crucial to understanding the electromagnetic signals that originate from the merger of astrophysical compact objects. Because of the many physical length scales present when simulating such mergers, these methods must be highly adaptive and capable of automatically resolving numerous localized features and instabilities that emerge throughout the computational domain across many temporal scales. While this has been historically accomplished with adaptive mesh refinement (AMR) based methods, alternatives based on wavelet bases and the wavelet transformation have recently achieved significant success in adaptive representation for advanced engineering applications. This work presents a new method for the integration of the relativistic hydrodynamic equations using iterated interpolating wavelets and introduces a highly adaptive implementation for multidimensional simulati...
Sánchez, Ana; Vázquez, José A; Quinteiro, Javier; Sotelo, Carmen G
2013-04-10
Real-time PCR is the most sensitive method for detection and precise quantification of specific DNA sequences, but it is not usually applied as a quantitative method in seafood. In general, benchmark techniques, mainly cycle threshold (Ct), are the routine method for quantitative estimations, but they are not the most precise approaches for a standard assay. In the present work, amplification data from European hake (Merluccius merluccius) DNA samples were accurately modeled by three sigmoid reparametrized equations, where the lag phase parameter (λc) from the Richards equation with four parameters was demonstrated to be the perfect substitute for Ct for PCR quantification. The concentrations of primers and probes were subsequently optimized by means of that selected kinetic parameter. Finally, the linear correlation among DNA concentration and λc was also confirmed.
Relativistic cosmological hydrodynamics
Hwang, J
1997-01-01
We investigate the relativistic cosmological hydrodynamic perturbations. We present the general large scale solutions of the perturbation variables valid for the general sign of three space curvature, the cosmological constant, and generally evolving background equation of state. The large scale evolution is characterized by a conserved gauge invariant quantity which is the same as a perturbed potential (or three-space curvature) in the comoving gauge.
Tian, C T; Chan, K L; Deng, L C
2007-01-01
This paper extends the gas-kinetic scheme for one-dimensional inviscid shallow water equations (J. Comput. Phys. 178 (2002), pp. 533-562) to multidimensional gas dynamic equations under gravitational fields. Four important issues in the construction of a well-balanced scheme for gas dynamic equations are addressed. First, the inclusion of the gravitational source term into the flux function is necessary. Second, to achieve second-order accuracy of a well-balanced scheme, the Chapman-Enskog expansion of the Boltzmann equation with the inclusion of the external force term is used. Third, to avoid artificial heating in an isolated system under a gravitational field, the source term treatment inside each cell has to be evaluated consistently with the flux evaluation at the cell interface. Fourth, the multidimensional approach with the inclusion of tangential gradients in two-dimensional and three-dimensional cases becomes important in order to maintain the accuracy of the scheme. Many numerical examples are used ...
Wu, Zhen; Zhang, Xian; Zhou, Chunjiao; Pang, Jing-Lin; Zhang, Panyue
2017-02-22
Single-molecule aluminum salt AlCl3, medium polymerized polyaluminum chloride (PAC), and high polymerized polyaluminum chloride (HPAC) were prepared in a laboratory. The characteristics and coagulation properties of these prepared aluminum salts were investigated. The Langmuir, Freundlich, and Sips adsorption isotherms were first used to describe the adsorption neutralization process in coagulation, and the Boltzmann equation was used to fit the reaction kinetics of floc growth in flocculation. It was novel to find that the experimental data fitted well with the Sips and Boltzmann equation, and the significance of parameters in the equations was discussed simultaneously. Through the Sips equation, the adsorption neutralization reaction was proved to be spontaneous and the adsorption neutralization capacity was HPAC > PAC > AlCl3. Sips equation also indicated that the zeta potential of water samples would reach a limit with the increase of coagulant dosage, and the equilibrium zeta potential values were 30.25, 30.23, and 27.25 mV for AlCl3, PAC, and HPAC, respectively. The lower equilibrium zeta potential value of HPAC might be the reason why the water sample was not easy to achieve restabilization at a high coagulant dosage. Through the Boltzmann equation modeling, the maximum average floc size formed by AlCl3, PAC, and HPAC were 196.0, 188.0, and 203.6 μm, respectively, and the halfway time of reactions were 31.23, 17.08, and 9.55 min, respectively. The HPAC showed the strongest floc formation ability and the fastest floc growth rate in the flocculation process, which might be caused by the stronger adsorption and bridging functions of Alb and Alc contained in HPAC.
Introduction to relativistic statistical mechanics classical and quantum
Hakim, Rémi
2011-01-01
This is one of the very few books focusing on relativistic statistical mechanics, and is written by a leading expert in this special field. It started from the notion of relativistic kinetic theory, half a century ago, exploding into relativistic statisti
Magnetic Dissipation in Relativistic Jets
Yosuke Mizuno
2016-10-01
Full Text Available The most promising mechanisms for producing and accelerating relativistic jets, and maintaining collimated structure of relativistic jets involve magnetohydrodynamical (MHD processes. We have investigated the magnetic dissipation mechanism in relativistic jets via relativistic MHD simulations. We found that the relativistic jets involving a helical magnetic field are unstable for the current-driven kink instability, which leads to helically distorted structure in relativistic jets. We identified the regions of high current density in filamentary current sheets, indicative of magnetic reconnection, which are associated to the kink unstable regions and correlated to the converted regions of magnetic to kinetic energies of the jets. We also found that an over-pressured relativistic jet leads to the generation of a series of stationary recollimation shocks and rarefaction structures by the nonlinear interaction of shocks and rarefaction waves. The differences in the recollimation shock structure due to the difference of the magnetic field topologies and strengths may be observable through mm-VLBI observations and space-VLBI mission.
Blazar flares powered by plasmoids in relativistic reconnection
Petropoulou, Maria; Sironi, Lorenzo
2016-01-01
Powerful flares from blazars with short ($\\sim$ min) variability timescales are challenging for current models of blazar emission. Here, we present a physically motivated ab initio model for blazar flares based on the results of recent particle-in-cell (PIC) simulations of relativistic magnetic reconnection. PIC simulations demonstrate that quasi-spherical plasmoids filled with high-energy particles and magnetic fields are a self-consistent by-product of the reconnection process. By coupling our PIC-based results (i.e., plasmoid growth, acceleration profile, particle and magnetic content) with a kinetic equation for the evolution of the electron distribution function we demonstrate that relativistic reconnection in blazar jets can produce powerful flares whose temporal and spectral properties are consistent with the observations. In particular, our model predicts correlated synchrotron and synchrotron self-Compton flares of duration of several hours--days powered by the largest and slowest moving plasmoids th...
Validity of the Onsager relations in relativistic binary mixtures.
Moratto, Valdemar; Garcia-Perciante, A L; Garcia-Colin, L S
2011-08-01
In this work we study the properties of a relativistic mixture of two nonreacting dilute species in thermal local equilibrium. Following the conventional ideas in kinetic theory, we use the concept of chaotic velocity. In particular, we address the nature of the density, or pressure gradient term that arises in the solution of the linearized Boltzmann equation in this context. Such an effect, also present for the single component problem, has, so far, not been analyzed from the point of view of the Onsager resciprocity relations. To address this matter, we propose two alternatives for the onsagerian matrix which comply with the corresponding reciprocity relations. The implications of both representations are briefly analyzed.
Entropy current for non-relativistic fluid
Banerjee, Nabamita; Jain, Akash; Roychowdhury, Dibakar
2014-01-01
We study transport properties of a parity-odd, non-relativistic charged fluid in presence of background electric and magnetic fields. To obtain stress tensor and charged current for the non-relativistic system we start with the most generic relativistic fluid, living in one higher dimension and reduce the constituent equations along the light-cone direction. We also reduce the equation satisfied by the entropy current of the relativistic theory and obtain a consistent entropy current for the non-relativistic system (we call it "canonical form" of the entropy current). Demanding that the non-relativistic fluid satisfies the second law of thermodynamics we impose constraints on various first order transport coefficients. For parity even fluid, this is straight forward; it tells us positive definiteness of different transport coefficients like viscosity, thermal conductivity, electric conductivity etc. However for parity-odd fluid, canonical form of the entropy current fails to confirm the second law of thermody...
Feng, Xin; Ye, Xingyou; Park, Jun-Bom; Lu, Wenli; Morott, Joe; Beissner, Brad; Lian, Zhuoyang John; Pinto, Elanor; Bi, Vivian; Porter, Stu; Durig, Tom; Majumdar, Soumyajit; Repka, Michael A
2015-01-01
The recrystallization of an amorphous drug in a solid dispersion system could lead to a loss in the drug solubility and bioavailability. The primary objective of the current research was to use an improved kinetic model to evaluate the recrystallization kinetics of amorphous structures and to further understand the factors influencing the physical stability of amorphous solid dispersions. Amorphous solid dispersions of fenofibrate with different molecular weights of hydroxypropylcellulose, HPC (Klucel™ LF, EF, ELF) were prepared utilizing hot-melt extrusion technology. Differential scanning calorimetry was utilized to quantitatively analyze the extent of recrystallization in the samples stored at different temperatures and relative humidity (RH) conditions. The experimental data were fitted into the improved kinetics model of a modified Avrami equation to calculate the recrystallization rate constants. Klucel LF, the largest molecular weight among the HPCs used, demonstrated the greatest inhibition of fenofibrate recrystallization. Additionally, the recrystallization rate (k) decreased with increasing polymer content, however exponentially increased with higher temperature. Also k increased linearly rather than exponentially over the range of RH studied.
On the convexity of Relativistic Hydrodynamics
Ibáñez, José María; Martí, José María; Miralles, Juan Antonio; 10.1088/0264-9381/30/5/057002
2013-01-01
The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 {\\it Relativistic Fluids and Magneto-Fluids} (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr 1989 {\\it Rev. Mod. Phys.} {\\bf 61} 75). The classical limit is recovered.
Fisher, Harvey F
2016-08-01
The transient-state kinetic approach has failed to reach its full potential despite its advantage over the steady-state approach in its ability to observe mechanistic events directly and in real time. This failure has been due in part to the lack of any rigorously derived and readily applicable body of theory corresponding to that which currently characterizes the steady-state approach. In order to clarify the causes of this discrepancy and to suggest a route to its solution we examine the capabilities and limitations of the various forms of transient-state kinetic approaches to the mathematical resolution of enzymatic reaction mechanisms currently available. We document a lack of validity inherent in their basic assumptions and suggest the need for a potentially more rigorous analytic approach.
Relativistic Cyclotron Instability in Anisotropic Plasmas
López, Rodrigo A.; Moya, Pablo S.; Navarro, Roberto E.; Araneda, Jaime A.; Muñoz, Víctor; Viñas, Adolfo F.; Alejandro Valdivia, J.
2016-11-01
A sufficiently large temperature anisotropy can sometimes drive various types of electromagnetic plasma micro-instabilities, which can play an important role in the dynamics of relativistic pair plasmas in space, astrophysics, and laboratory environments. Here, we provide a detailed description of the cyclotron instability of parallel propagating electromagnetic waves in relativistic pair plasmas on the basis of a relativistic anisotropic distribution function. Using plasma kinetic theory and particle-in-cell simulations, we study the influence of the relativistic temperature and the temperature anisotropy on the collective and noncollective modes of these plasmas. Growth rates and dispersion curves from the linear theory show a good agreement with simulations results.
Regularization of Grad’s 13 -Moment-Equations in Kinetic Gas Theory
2011-01-01
Struchtrup, H. (2009). Couette and poiseuille microflows: Analytical solutions for regularized 13-moment equations. Phys. Fluids, 21:017102. Takata, S., Sone...C3 − 1 45 F 2 Kn2 y4 − 2 5 σyy (y) . (70) For σyy = 0 this is the classical temperature profile in Poiseuille flow due to dissipation. Due to...which, of course, is not valid at these Knudsen numbers. 4.3.3 Full Simulation The R13 equations have been solved for Poiseuille flow in the full non
Non-Relativistic Spacetimes with Cosmological Constant
Aldrovandi, R.; Barbosa, A. L.; Crispino, L.C.B.; Pereira, J. G.
1998-01-01
Recent data on supernovae favor high values of the cosmological constant. Spacetimes with a cosmological constant have non-relativistic kinematics quite different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of Einstein's equations with a cosmological constant, reduce in the non-relativistic limit to Newton-Hooke spacetimes, which are non-metric homogeneous spacetimes with non-vanishing curvature. The whole non-relativistic kinematics would then be modified, with possible ...
Relativistic non-equilibrium thermodynamics revisited
García-Colin, L S
2006-01-01
Relativistic irreversible thermodynamics is reformulated following the conventional approach proposed by Meixner in the non-relativistic case. Clear separation between mechanical and non-mechanical energy fluxes is made. The resulting equations for the entropy production and the local internal energy have the same structure as the non-relativistic ones. Assuming linear constitutive laws, it is shown that consistency is obtained both with the laws of thermodynamics and causality.
Fu, Mingkun; Perlman, Michael; Lu, Qing; Varga, Csanad
2015-03-25
An accelerated stress approach utilizing the moisture-modified Arrhenius equation and JMP statistical software was utilized to quantitatively assess the solid state stability of an investigational oncology drug MLNA under the influence of temperature (1/T) and humidity (%RH). Physical stability of MLNA under stress conditions was evaluated by using XRPD, DSC, TGA, and DVS, while chemical stability was evaluated by using HPLC. The major chemical degradation product was identified as a hydrolysis product of MLNA drug substance, and was subsequently subjected to an investigation of kinetics based on the isoconversion concept. A mathematical model (ln k=-11,991×(1/T)+0.0298×(%RH)+29.8823) based on the initial linear kinetics observed for the formation of this degradant at all seven stress conditions was built by using the moisture-modified Arrhenius equation and JMP statistical software. Comparison of the predicted versus experimental lnk values gave a mean deviation value of 5.8%, an R(2) value of 0.94, a p-value of 0.0038, and a coefficient of variation of the root mean square error CV(RMSE) of 7.9%. These statistics all indicated a good fit to the model for the stress data of MLNA. Both temperature and humidity were shown to have a statistically significant impact on stability by using effect leverage plots (p-valueArrhenius equation modeling theory. The model was found to be of value to aid setting of specifications and retest period, and storage condition selection. A model was also generated using only four conditions, as an example from a resource saving perspective, which was found to provide a good fit to the entire set of data. Copyright © 2015 Elsevier B.V. All rights reserved.
Maslov, Lev A.; Chebotarev, Vladimir I.
2017-02-01
The generalized logistic equation is proposed to model kinetics and statistics of natural processes such as earthquakes, forest fires, floods, landslides, and many others. This equation has the form dN(A)/dA = s dot (1-N(A)) dot N(A)q dot A-α, q>0q>0 and A>0A>0 is the size of an element of a structure, and α≥0. The equation contains two exponents α and q taking into account two important properties of elements of a system: their fractal geometry, and their ability to interact either to enhance or to damp the process of aggregation. The function N(A)N(A) can be understood as an approximation to the number of elements the size of which is less than AA. The function dN(A)/dAdN(A)/dA where N(A)N(A) is the general solution of this equation for q=1 is a product of an increasing bounded function and power-law function with stretched exponential cut-off. The relation with Tsallis non-extensive statistics is demonstrated by solving the generalized logistic equation for q>0q>0. In the case 01q>1 it models sub-additive structures. The Gutenberg-Richter (G-R) formula results from interpretation of empirical data as a straight line in the area of stretched exponent with small α. The solution is applied for modeling distribution of foreshocks and aftershocks in the regions of Napa Valley 2014, and Sumatra 2004 earthquakes fitting the observed data well, both qualitatively and quantitatively.
Long wavelength unstable modes in the far upstream of relativistic collisionless shocks
Rabinak, Itay; Waxman, Eli
2010-01-01
The growth rate of long wavelength kinetic instabilities arising due to the interaction of a collimated beam of relativistic particles and a cold unmagnetized plasma are calculated in the ultra relativistic limit. For sufficiently culminated beams, all long wave-length modes are shown to be Weibel-unstable, and a simple analytic expression for their growth rate is derived. For large transverse velocity spreads, these modes become stable. An analytic condition for stability is given. These analytic results, which generalize earlier ones given in the literature, are shown to be in agreement with numerical solutions of the dispersion equation and with the results of novel PIC simulations in which the electro-magnetic fields are restricted to a given k-mode. The results may describe the interaction of energetic cosmic rays, propagating into the far upstream of a relativistic collisionless shock, with a cold unmagnetized upstream. The long wavelength modes considered may be efficient in deflecting particles and co...
Non-Newtonian Properties of Relativistic Fluids
Koide, Tomoi
2010-01-01
We show that relativistic fluids behave as non-Newtonian fluids. First, we discuss the problem of acausal propagation in the diffusion equation and introduce the modified Maxwell-Cattaneo-Vernotte (MCV) equation. By using the modified MCV equation, we obtain the causal dissipative relativistic (CDR) fluid dynamics, where unphysical propagation with infinite velocity does not exist. We further show that the problems of the violation of causality and instability are intimately related, and the relativistic Navier-Stokes equation is inadequate as the theory of relativistic fluids. Finally, the new microscopic formula to calculate the transport coefficients of the CDR fluid dynamics is discussed. The result of the microscopic formula is consistent with that of the Boltzmann equation, i.e., Grad's moment method.
Sahoo, Raghunath
2016-01-01
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students working in the related areas.
Thermostatted kinetic equations as models for complex systems in physics and life sciences.
Bianca, Carlo
2012-12-01
Statistical mechanics is a powerful method for understanding equilibrium thermodynamics. An equivalent theoretical framework for nonequilibrium systems has remained elusive. The thermodynamic forces driving the system away from equilibrium introduce energy that must be dissipated if nonequilibrium steady states are to be obtained. Historically, further terms were introduced, collectively called a thermostat, whose original application was to generate constant-temperature equilibrium ensembles. This review surveys kinetic models coupled with time-reversible deterministic thermostats for the modeling of large systems composed both by inert matter particles and living entities. The introduction of deterministic thermostats allows to model the onset of nonequilibrium stationary states that are typical of most real-world complex systems. The first part of the paper is focused on a general presentation of the main physical and mathematical definitions and tools: nonequilibrium phenomena, Gauss least constraint principle and Gaussian thermostats. The second part provides a review of a variety of thermostatted mathematical models in physics and life sciences, including Kac, Boltzmann, Jager-Segel and the thermostatted (continuous and discrete) kinetic for active particles models. Applications refer to semiconductor devices, nanosciences, biological phenomena, vehicular traffic, social and economics systems, crowds and swarms dynamics.
Al-Hashimi, M H; Shalaby, A M
2016-01-01
A general method has been developed to solve the Schr\\"odinger equation for an arbitrary derivative of the $\\delta$-function potential in 1-d using cutoff regularization. The work treats both the relativistic and nonrelativistic cases. A distinction in the treatment has been made between the case when the derivative $n$ is an even number from the one when $n$ is an odd number. A general gap equations for each case has been derived. The case of $\\delta^{(2)}$-function potential has been used as an example. The results from the relativistic case show that the $\\delta^{(2)}$-function system behaves exactly like the $\\delta$-function and the $\\delta'$-function potentials, which means it also shares the same features with quantum field theories, like being asymptotically free, in the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. As a result the evidence of universality of contact interactions has been extended further to include the $\\delta^{(2)}$-functi...
黄时中; 方燕
2011-01-01
用一种简洁的数学形式给出了受恒力作用的粒子的相对论动力学方程的解,解决了相对论中的抛体运动问题,详细讨论了相对论粒子的加速度、速度和运动方程与牛顿力学中对应物理量的区别和联系.%A concise solution to the dynamic equation for a relativistic particle acted by a constant force is presented,which is corresponding to the projectile motion in special relativity,the acceleration,velocity and equation of motion are expressed by easy functions,the differences and relations between special relativity and Newton's Mechanics are analyzed in detail.
Relativistic top in the Ostrohrads'kyj dynamics
Matsyuk, Roman
2015-01-01
A variational equation of the fourth order for the free relativistic top is developed starting from the Dixon's system of equations for the motion of the relativistic dipole. The obtained equation is then cast into the homogeneous space-time Hamiltonian form.
On the maximum-entropy method for kinetic equation of radiation, particle and gas
El-Wakil, S.A. [Mansoura Univ. (Egypt). Phys. Dept.; Madkour, M.A. [Mansoura Univ. (Egypt). Phys. Dept.; Degheidy, A.R. [Mansoura Univ. (Egypt). Phys. Dept.; Machali, H.M. [Mansoura Univ. (Egypt). Phys. Dept.
1995-02-01
The maximum-entropy approach is used to calculate some problems in radiative transfer and reactor physics such as the escape probability, the emergent and transmitted intensities for a finite slab as well as the emergent intensity for a semi-infinite medium. Also, it is employed to solve problems involving spherical geometry, such as luminosity (the total energy emitted by a sphere), neutron capture probability and the albedo problem. The technique is also employed in the kinetic theory of gases to calculate the Poiseuille flow and thermal creep of a rarefied gas between two plates. Numerical calculations are achieved and compared with the published data. The comparisons demonstrate that the maximum-entropy results are good in agreement with the exact ones. (orig.).
Manning, Robert M.
2009-01-01
Based on a theoretical model of the propagation of electromagnetic waves through a hypersonically induced plasma, it has been demonstrated that the classical radiofrequency communications blackout that is experienced during atmospheric reentry can be mitigated through the appropriate control of an external magnetic field of nominal magnitude. The model is based on the kinetic equation treatment of Vlasov and involves an analytical solution for the electric and magnetic fields within the plasma allowing for a description of the attendant transmission, reflection and absorption coefficients. The ability to transmit through the magnetized plasma is due to the magnetic windows that are created within the plasma via the well-known whistler modes of propagation. The case of 2 GHz transmission through a re-entry plasma is considered. The coefficients are found to be highly sensitive to the prevailing electron density and will thus require a dynamic control mechanism to vary the magnetic field as the plasma evolves through the re-entry phase.
Morii, Youhi; Terashima, Hiroshi; Koshi, Mitsuo; Shimizu, Taro; Shima, Eiji
2016-10-01
We herein propose a fast and robust Jacobian-free time integration method named as the extended robustness-enhanced numerical algorithm (ERENA) to treat the stiff ordinary differential equations (ODEs) of chemical kinetics. The formulation of ERENA is based on an exact solution of a quasi-steady-state approximation that is optimized to preserve the mass conservation law through use of a Lagrange multiplier method. ERENA exhibits higher accuracy and faster performance in homogeneous ignition simulations compared to existing popular explicit and implicit methods for stiff ODEs such as VODE, MTS, and CHEMEQ2. We investigate the effects of user-specified threshold values in ERENA, to provide trade-off information between the accuracy and the computational cost.
CHARACTERIZATIONS ON THE THIXOTROPY-LOOP TESTS USING UCM MODEL WITH A RATE-TYPE KINETIC EQUATION
Shu-xin Huang; Chuan-jing Lu
2006-01-01
The theoretical characterizations on the triangular-form thixotropy-loop tests of an LDPE melt (PE-FSB23D022/Q200) were conducted in the present paper by using a new thixotropy model, which is constituted by the upper convected Maxwell model and a rate-type kinetic equation. The new thixotropic Maxwell model can partially describe well three reported thixotropy-loop experiments by comparison with the previous calculations of the variant form of the thixotropy-type Huang model. It is noted that the stress deviations between the experiments and the predictions of the new thixotropic Maxwell model are much slighter than those deviations obtained by using the variant Huang model at the same condition, although both models include five parameters. The constitution of the new thixotropic Maxwell model is more reasonable than that of the variant Huang model.
Geochemical kinetics via the Swift-Connick equations and solution NMR
Harley, Steven J.; Ohlin, C. André; Casey, William H.
2011-07-01
Signal analysis in Nuclear Magnetic Resonance spectroscopy is among the most powerful methods to quantify reaction rates in aqueous solutions. To this end, the Swift-Connick approximations to the Bloch-McConnell equations have been used extensively to estimate rate parameters for elementary reactions. The method is primarily used for 17O NMR in aqueous solutions, but the list of geochemically relevant nuclei that can be used is long, and includes 29Si, 27Al, 19F, 13C and many others of particular interest to geochemists. Here we review the derivation of both the Swift-Connick and Bloch-McConnell equations and emphasize assumptions and quirks. For example, the equations were derived for CW-NMR, but are used with modern pulse FT-NMR and can be applied to systems that have exchange rates that are shorter than the lifetime of a typical pulse. The method requires a dilute solution where the minor reacting species contributes a negligible amount of total magnetization. We evaluate the sensitivity of results to this dilute-solution requirement and also highlight the need for chemically well-defined systems if reliable data are to be obtained. The limitations in using longitudinal relaxation to estimate reaction rate parameters are discussed. Finally, we provide examples of the application of the method, including ligand exchanges from aqua ions and hydrolysis complexes, that emphasize its flexibility. Once the basic requirements of the Swift-Connick method are met, it allows geochemists to establish rates of elementary reactions. Reactions at this scale lend themselves well to methods of computational simulation and could provide key tests of accuracy.
Mohamad, Nur Ikhwan; Cronin, John B; Nosaka, Ken K
2012-01-01
Although it is generally accepted that a high load is necessary for muscle hypertrophy, it is possible that a low load with a high velocity results in greater kinematics and kinetics than does a high load with a slow velocity. The purpose of this study was to determine if 2 training loads (35 and 70% 1 repetition maximum [1RM]) equated by volume, differed in terms of their session kinematic and kinetic characteristics. Twelve subjects were recruited in this acute randomized within-subject crossover design study. Two bouts of a half-squat exercise were performed 1 week apart, one with high load-low velocity (HLLV = 3 sets of 12 reps at 70% 1RM) and the other with low-load high-velocity (LLHV = 6 sets of 12 reps at 35% 1RM). Time under tension (TUT), average force, peak force (PF), average power (AP), peak power (PP), work (TW), and total impulse (TI) were calculated and compared between loads for the eccentric and concentric phases. For average eccentric and concentric single repetition values, significantly (p eccentric and concentric TUT, PF, AP, PP, and TW. The only variable that was significantly greater for the HLLV protocol than for the LLHV protocol was TI (∼20-24%). From these results, it seems that the LLHV protocol may offer an equal if not better training stimulus for muscular adaptation than the HLLV protocol, because of the greater time under tension, power, force, and work output when the total volume of the exercise is equated.
Quasirelativistic Langevin equation.
Plyukhin, A V
2013-11-01
We address the problem of a microscopic derivation of the Langevin equation for a weakly relativistic Brownian particle. A noncovariant Hamiltonian model is adopted, in which the free motion of particles is described relativistically while their interaction is treated classically, i.e., by means of action-to-a-distance interaction potentials. Relativistic corrections to the classical Langevin equation emerge as nonlinear dissipation terms and originate from the nonlinear dependence of the relativistic velocity on momentum. On the other hand, similar nonlinear dissipation forces also appear as classical (nonrelativistic) corrections to the weak-coupling approximation. It is shown that these classical corrections, which are usually ignored in phenomenological models, may be of the same order of magnitude, if not larger than, relativistic ones. The interplay of relativistic corrections and classical beyond-the-weak-coupling contributions determines the sign of the leading nonlinear dissipation term in the Langevin equation and thus is qualitatively important.
A two-fluid model for relativistic heat conduction
López-Monsalvo, César S. [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México (Mexico)
2014-01-14
Three years ago it was presented in these proceedings the relativistic dynamics of a multi-fluid system together with various applications to a set of topical problems [1]. In this talk, I will start from such dynamics and present a covariant formulation of relativistic thermodynamics which provides us with a causal constitutive equation for the propagation of heat in a relativistic setting.
Gravitationally confined relativistic neutrinos
Vayenas, C. G.; Fokas, A. S.; Grigoriou, D.
2017-09-01
Combining special relativity, the equivalence principle, and Newton’s universal gravitational law with gravitational rather than rest masses, one finds that gravitational interactions between relativistic neutrinos with kinetic energies above 50 MeV are very strong and can lead to the formation of gravitationally confined composite structures with the mass and other properties of hadrons. One may model such structures by considering three neutrinos moving symmetrically on a circular orbit under the influence of their gravitational attraction, and by assuming quantization of their angular momentum, as in the Bohr model of the H atom. The model contains no adjustable parameters and its solution, using a neutrino rest mass of 0.05 eV/c2, leads to composite state radii close to 1 fm and composite state masses close to 1 GeV/c2. Similar models of relativistic rotating electron - neutrino pairs give a mass of 81 GeV/c2, close to that of W bosons. This novel mechanism of generating mass suggests that the Higgs mass generation mechanism can be modeled as a latent gravitational field which gets activated by relativistic neutrinos.
Malkov, Ewgenij A.; Poleshkin, Sergey O.; Kudryavtsev, Alexey N.; Shershnev, Anton A.
2016-10-01
The paper presents the software implementation of the Boltzmann equation solver based on the deterministic finite-difference method. The solver allows one to carry out parallel computations of rarefied flows on a hybrid computational cluster with arbitrary number of central processor units (CPU) and graphical processor units (GPU). Employment of GPUs leads to a significant acceleration of the computations, which enables us to simulate two-dimensional flows with high resolution in a reasonable time. The developed numerical code was validated by comparing the obtained solutions with the Direct Simulation Monte Carlo (DSMC) data. For this purpose the supersonic flow past a flat plate at zero angle of attack is used as a test case.
Watkins, N. W.; Rosenberg, S.; Sanchez, R.; Chapman, S. C.; Credgington, D.
2008-12-01
Since the 1960s Mandelbrot has advocated the use of fractals for the description of the non-Euclidean geometry of many aspects of nature. In particular he proposed two kinds of model to capture persistence in time (his Joseph effect, common in hydrology and with fractional Brownian motion as the prototype) and/or prone to heavy tailed jumps (the Noah effect, typical of economic indices, for which he proposed Lévy flights as an exemplar). Both effects are now well demonstrated in space plasmas, notably in the turbulent solar wind. Models have, however, typically emphasised one of the Noah and Joseph parameters (the Lévy exponent μ and the temporal exponent β) at the other's expense. I will describe recent work in which we studied a simple self-affine stable model-linear fractional stable motion, LFSM, which unifies both effects and present a recently-derived diffusion equation for LFSM. This replaces the second order spatial derivative in the equation of fBm with a fractional derivative of order μ, but retains a diffusion coefficient with a power law time dependence rather than a fractional derivative in time. I will also show work in progress using an LFSM model and simple analytic scaling arguments to study the problem of the area between an LFSM curve and a threshold. This problem relates to the burst size measure introduced by Takalo and Consolini into solar-terrestrial physics and further studied by Freeman et al [PRE, 2000] on solar wind Poynting flux near L1. We test how expressions derived by other authors generalise to the non-Gaussian, constant threshold problem. Ongoing work on extension of these LFSM results to multifractals will also be discussed.
Hakim, Rémi
1994-01-01
Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.
Pireaux, S
2008-01-01
The Relativistic Motion Integrator (RMI) consists in integrating numerically the EXACT relativistic equations of motion, with respect to the appropriate gravitational metric, instead of Newtonian equations plus relativistic corrections. The aim of the present paper is to validate the method, and to illustrate how RMI can be used for space missions to produce relativistic ephemerides of satellites. Indeed, nowadays, relativistic effects have to be taken into account, and comparing a RMI ephemeris with a classical keplerian one helps to quantify such effects. LISA is a relevant example to use RMI. This mission is an interferometer formed by three spacecraft which aims at the detection of gravitational waves. Precise ephemerides of LISA spacecraft are needed not only for the sake of the orbitography but also to compute the photon flight time in laser links between spacecraft, required in LISA data pre-processing in order to reach the gravitational wave detection level. Relativistic effects in LISA orbitography n...
Jones, Bernard J. T.; Markovic, Dragoljub
1997-06-01
Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.
Qureshi, Mumnuna A.; Zhong, Johnny; Betouras, Joseph J.; Zagoskin, Alexandre M.
2017-03-01
Theoretical description and simulation of large quantum coherent systems out of equilibrium remains a daunting task. Here we are developing an approach to it based on the Pechukas-Yukawa formalism, which is especially convenient in the case of an adiabatically slow external perturbation, though it is not restricted to adiabatic systems. In this formalism the dynamics of energy levels in an externally perturbed quantum system as a function of the perturbation parameter is mapped on that of a fictitious one-dimensional classical gas of particles with cubic repulsion. Equilibrium statistical mechanics of this Pechukas gas allows us to reproduce the random matrix theory of energy levels. In the present work, we develop the nonequilibrium statistical mechanics of the Pechukas gas, starting with the derivation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) chain of equations for the appropriate generalized distribution functions. Sets of approximate kinetic equations can be consistently obtained by breaking this chain at a particular point (i.e., approximating all higher-order distribution functions by the products of the lower-order ones). When complemented by the equations for the level occupation numbers and interlevel transition amplitudes, they allow us to describe the nonequilibrium evolution of the quantum state of the system, which can describe better a large quantum coherent system than the currently used approaches. In particular, we find that corrections to the factorized approximation of the distribution function scale as 1 /N , where N is the number of the "Pechukas gas particles" (i.e., energy levels in the system).
Theory of symmetry for a rotational relativistic Birkhoff system
罗绍凯; 陈向炜; 郭永新
2002-01-01
The theory of symmetry for a rotational relativistic Birkhoff system is studied. In terms of the invariance of therotational relativistic Pfaff-Birkhoff-D'Alembert principle under infinitesimal transformations, the Noether symmetriesand conserved quantities of a rotational relativistic Birkhoff system are given. In terms of the invariance of rotationalrelativistic Birkhoff equations under infinitesimal transformations, the Lie symmetries and conserved quantities of therotational relativistic Birkhoff system are given.
Chaos and Maps in Relativistic Dynamical Systems
Horwitz, L P
1999-01-01
The basic work of Zaslavskii et al showed that the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on the phase space; the resulting evolution contains a stochastic flow to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistic charged particle in interaction with the electromagnetic field. We review the structure of the covariant Lorentz force used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field, establishing a connection between these equations and mass shell constraints. We argue that these relativistic generalizations of the problem are intrinsically inaccurate due to an inconsistency in the structure of the relativistic Lorentz force, and show that a reformulation of the relativistic problem, permitting variations (classically) in both the particle mass and the effective...
Relativistic gas in a Schwarzschild metric
Kremer, Gilberto M
2013-01-01
A relativistic gas in a Schwarzschild metric is studied within the framework of a relativistic Boltzmann equation in the presence of gravitational fields, where Marle's model for the collision operator of the Boltzmann equation is employed. The transport coefficients of bulk and shear viscosities and thermal conductivity are determined from the Chapman-Enskog method. It is shown that the transport coefficients depend on the gravitational potential. Expressions for the transport coefficients in the presence of weak gravitational fields in the non-relativistic (low temperatures) and ultra-relativistic (high temperatures) limiting cases are given. Apart from the temperature gradient the heat flux has two relativistic terms. The first one, proposed by Eckart, is due to the inertia of energy and represents an isothermal heat flux when matter is accelerated. The other, suggested by Tolman, is proportional to the gravitational potential gradient and indicates that -- in the absence of an acceleration field -- a stat...
Babintsev, I. A.; Adzhemyan, L. Ts.; Shchekin, A. K.
2017-08-01
Relaxation of micellar systems can be described with the help of the Becker-Döring kinetic difference equations for aggregate concentrations. Passing in these equations to continual description, when the aggregation number is considered as continuous variable and the concentration difference is replaced by the concentration differential, allows one to find analytically the eigenvalues (to whom the inverse times of micellar relaxation are related) and eigenfunctions (or the modes of fast relaxation) of the linearized differential operator of the kinetic equation corresponding to the Fokker-Planck approximation. At this the spectrum of eigenvalues appears to be degenerated at some surfactant concentrations. However, as has been recently found by us, there is no such a degeneracy at numerical determination of the eigenvalues of the matrix of coefficients for the linearized difference Becker-Döring equations. It is shown in this work in the frameworks of the perturbation theory, that taking into account the corrections to the kinetic equation produced by second derivatives at transition from differences to differentials and by deviation of the aggregation work from a parabolic form in the vicinity of the work minimum, lifts the degeneracy of eigenvalues and improves markedly the agreement of concentration-dependent fast relaxation time with the results of the numerical solution of the linearized Becker-Döring difference equations.
Comment on "Fractional quantum mechanics" and "Fractional Schroedinger equation"
Wei, Yuchuan
2016-01-01
In this comment, we point out some shortcomings in two papers "Fractional quantum mechanics" [Phys. Rev. E 62, 3135 (2000)] and "Fractional Schroedinger equation" [Phys. Rev. E 66, 056108 (2002)]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from one place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to a destination.
Komissarov, S S; Lyutikov, M
2015-01-01
In this paper we describe a simple numerical approach which allows to study the structure of steady-state axisymmetric relativistic jets using one-dimensional time-dependent simulations. It is based on the fact that for narrow jets with v~c the steady-state equations of relativistic magnetohydrodynamics can be accurately approximated by the one-dimensional time-dependent equations after the substitution z=ct. Since only the time-dependent codes are now publicly available this is a valuable and efficient alternative to the development of a high-specialized code for the time-independent equations. The approach is also much cheaper and more robust compared to the relaxation method. We tested this technique against numerical and analytical solutions found in literature as well as solutions we obtained using the relaxation method and found it sufficiently accurate. In the process, we discovered the reason for the failure of the self-similar analytical model of the jet reconfinement in relatively flat atmospheres a...
Equation with the many fathers
Kragh, Helge
1984-01-01
In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...
Relativistic Radiation Mediated Shocks
Budnik, Ran; Sagiv, Amir; Waxman, Eli
2010-01-01
The structure of relativistic radiation mediated shocks (RRMS) propagating into a cold electron-proton plasma is calculated and analyzed. A qualitative discussion of the physics of relativistic and non relativistic shocks, including order of magnitude estimates for the relevant temperature and length scales, is presented. Detailed numerical solutions are derived for shock Lorentz factors $\\Gamma_u$ in the range $6\\le\\Gamma_u\\le30$, using a novel iteration technique solving the hydrodynamics and radiation transport equations (the protons, electrons and positrons are argued to be coupled by collective plasma processes and are treated as a fluid). The shock transition (deceleration) region, where the Lorentz factor $ \\Gamma $ drops from $ \\Gamma_u $ to $ \\sim 1 $, is characterized by high plasma temperatures $ T\\sim \\Gamma m_ec^2 $ and highly anisotropic radiation, with characteristic shock-frame energy of upstream and downstream going photons of a few~$\\times\\, m_ec^2$ and $\\sim \\Gamma^2 m_ec^2$, respectively.P...
Corinaldesi, Ernesto
1963-01-01
Geared toward advanced undergraduate and graduate students of physics, this text provides readers with a background in relativistic wave mechanics and prepares them for the study of field theory. The treatment originated as a series of lectures from a course on advanced quantum mechanics that has been further amplified by student contributions.An introductory section related to particles and wave functions precedes the three-part treatment. An examination of particles of spin zero follows, addressing wave equation, Lagrangian formalism, physical quantities as mean values, translation and rotat
Density perturbations with relativistic thermodynamics
Maartens, R
1997-01-01
We investigate cosmological density perturbations in a covariant and gauge- invariant formalism, incorporating relativistic causal thermodynamics to give a self-consistent description. The gradient of density inhomogeneities splits covariantly into a scalar part, a rotational vector part that is determined by the vorticity, and a tensor part that describes the shape. We give the evolution equations for these parts in the general dissipative case. Causal thermodynamics gives evolution equations for viswcous stress and heat flux, which are coupled to the density perturbation equation and to the entropy and temperature perturbation equations. We give the full coupled system in the general dissipative case, and simplify the system in certain cases.
DYNAMICS OF RELATIVISTIC FLUID FOR COMPRESSIBLE GAS
无
2011-01-01
In this paper the relativistic fluid dynamics for compressible gas is studied.We show that the strict convexity of the negative thermodynamical entropy preserves invariant under the Lorentz transformation if and only if the local speed of sound in this gas is strictly less than that of light in the vacuum.A symmetric form for the equations of relativistic hydrodynamics is presented,and thus the local classical solutions to these equations can be deduced.At last,the non-relativistic limits of these local cla...
Light Cone analysis of relativistic first-order in the gradients hydrodynamics
Brun-Battistini, D
2010-01-01
This work applies a Rayleigh-Brillouin light spectrum analysis in order to establish a causality test by means of a frequency cone. This technique allows to identify forbidden and unforbidden regions in light scattering experiments and establishes if a set of linearized transport equations admits causal solutions. It is shown that, when studying a relativistic fluid with its acoustic modes interacting with light, Eckart's formalism yields a non causal behavior. In this case the solutions describing temperature, density and pressure fluctuations are located outside the frequency cone. In contrast, the set of equations that arises from modified Eckart's theory (based on relativistic kinetic theory) yields solutions that lie within the cone, so that they are causal.
Pais, Helena
2016-01-01
The Vlasov formalism is extended to relativistic mean-field hadron models with non-linear terms up to fourth order and applied to the calculation of the crust-core transition density. The effect of the nonlinear $\\omega\\rho$ and $\\sigma\\rho$ coupling terms on the crust-core transition density and pressure, and on the macroscopic properties of some families of hadronic stars is investigated. For that purpose, six families of relativistic mean field models are considered. Within each family, the members differ in the symmetry energy behavior. For all the models, the dynamical spinodals are calculated, and the crust-core transition density and pressure, and the neutron star mass-radius relations are obtained. The effect on the star radius of the inclusion of a pasta calculation in the inner crust is discussed. The set of six models that best satisfy terrestrial and observational constraints predicts a radius of 13.6$\\pm$0.3 km and a crust thickness of $1.36\\pm 0.06$km for a 1.4 $M_\\odot$ star.
Wu, Hui-Chun [Los Alamos National Laboratory; Hegelich, B.M. [Los Alamos National Laboratory; Fernandez, J.C. [Los Alamos National Laboratory; Shah, R.C. [Los Alamos National Laboratory; Palaniyappan, S. [Los Alamos National Laboratory; Jung, D. [Los Alamos National Laboratory; Yin, L [Los Alamos National Laboratory; Albright, B.J. [Los Alamos National Laboratory; Bowers, K. [Guest Scientist of XCP-6; Huang, C. [Los Alamos National Laboratory; Kwan, T.J. [Los Alamos National Laboratory
2012-06-19
Two new experimental technologies enabled realization of Break-out afterburner (BOA) - High quality Trident laser and free-standing C nm-targets. VPIC is an powerful tool for fundamental research of relativistic laser-matter interaction. Predictions from VPIC are validated - Novel BOA and Solitary ion acceleration mechanisms. VPIC is a fully explicit Particle In Cell (PIC) code: models plasma as billions of macro-particles moving on a computational mesh. VPIC particle advance (which typically dominates computation) has been optimized extensively for many different supercomputers. Laser-driven ions lead to realization promising applications - Ion-based fast ignition; active interrogation, hadron therapy.
Kaganovich, Igor D; Polomarov, Oleg
2003-08-01
In low-pressure discharges, where the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially nonlocal. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the nonlocal conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study, a self-consistent system of equations for the kinetic description of nonlocal, nonuniform, nearly collisionless plasmas of low-pressure discharges is derived. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. The importance of accounting for the nonuniform plasma density profile on both the current density profile and the EEDF is demonstrated.
Berim, Gersh O.; Ruckenstein, Eli
2003-11-01
A generalized kinetic Ising model is applied to the description of phase transformations in lattice systems. A procedure, based on the conjecture that the probability distribution function of the states of the system is similar to the equilibrium one, is used for closing the infinite chain of kinetic equations. The method is illustrated by treating as an example the one-dimensional Ising model. The predicted rate of phase transformation (RPT) demonstrates various time behaviors dependent upon the details of the interactions between spins and a heat bath. If the parameters W0 and W the reciprocals of which characterize, respectively, the time scales of growth (decay) and splitting (coagulation) of clusters have the same order of magnitude, then the RPT is constant during almost the entire transformation process. For the case W=0, which corresponds to the absence of splitting and coagulation of clusters, the phase transformation follows an exponential law in the final stage and is linear with respect to time during the initial one. It has a similar behavior for W0≫W≠0; however, the RPT in the final stage is much smaller in the last case than for W=0. In the absence of supersaturation, RPT decreases to zero as T→Tc, where Tc(=0 K) is the phase transition temperature for a one-dimensional model. The time-dependent size distribution of clusters is for all times exponential with respect to the cluster size. The average size of the cluster far from both equilibrium and initial state grows linearly in time. Both the above quantities behave in a manner similar to those obtained by Monte Carlo simulations for systems of higher dimension.
Algebraic structure and Poisson integrals of a rotational relativistic Birkhoff system
罗绍凯; 陈向炜; 郭永新
2002-01-01
We have studied the algebraic structure of the dynamical equations of a rotational relativistic Birkhoff system. It is proven that autonomous and semi-autonomous rotational relativistic Birkhoff equations possess consistent algebraic structure and Lie algebraic structure. In general, non-autonomous rotational relativistic Birkhoff equations possess no algebraic structure, but a type of special non-autonomous rotational relativistic Birkhoff equation possesses consistent algebraic structure and consistent Lie algebraic structure. Then, we obtain the Poisson integrals of the dynamical equations of the rotational relativistic Birkhoff system. Finally, we give an example to illustrate the application of the results.
Winter, Pierre M.; Rheaume, Michael; Cooksy, Andrew L.
2017-08-01
We have calculated the temperature-dependent rate coefficients of the addition reactions of butadien-2-yl (C4H5) and acroylyl (C3H3O) radicals with ethene (C2H4), carbon monoxide (CO), formaldehyde (H2CO), hydrogen cyanide (HCN), and ketene (H2CCO), in order to explore the balance between kinetic and thermodynamic control in these combustion-related reactions. For the C4H5 radical, the 1,3-diene form of the addition products is more stable than the 1,2-diene, but the 1,2-diene form of the radical intermediate is stabilized by an allylic delocalization, which may influence the relative activation energies. For the reactions combining C3H3O with C2H4, CO, and HCN, the opposite is true: the 1,2-enone form of the addition products is more stable than the 1,3-enone, whereas the 1,3-enone is the slightly more stable radical species. Optimized geometries and vibrational modes were computed with the QCISD/aug-cc-pVDZ level and basis, followed by single-point CCSD(T)-F12a/cc-pVDZ-F12 energy calculations. Our findings indicate that the kinetics in all cases favor reaction along the 1,3 pathway for both the C4H5 and C3H3O systems. The Rice-Ramsperger-Kassel-Marcus (RRKM) microcanonical rate coefficients and subsequent solution of the chemical master equation were used to predict the time-evolution of our system under conditions from 500 K to 2000 K and from 10-5 bar to 10 bars. Despite the 1,3 reaction pathway being more favorable for the C4H5 system, our results predict branching ratios of the 1,2 to 1,3 product as high as 0.48 at 1 bar. Similar results hold for the acroylyl system under these combustion conditions, suggesting that under kinetic control the branching of these reactions may be much more significant than the thermodynamics would suggest. This effect may be partly attributed to the low energy difference between 1,2 and 1,3 forms of the radical intermediate. No substantial pressure-dependence is found for the overall forward reaction rates until pressures
Relativistic RPA in axial symmetry
Arteaga, D Pena; 10.1103/PhysRevC.77.034317
2009-01-01
Covariant density functional theory, in the framework of self-consistent Relativistic Mean Field (RMF) and Relativistic Random Phase approximation (RPA), is for the first time applied to axially deformed nuclei. The fully self-consistent RMF+RRPA equations are posed for the case of axial symmetry and non-linear energy functionals, and solved with the help of a new parallel code. Formal properties of RPA theory are studied and special care is taken in order to validate the proper decoupling of spurious modes and their influence on the physical response. Sample applications to the magnetic and electric dipole transitions in $^{20}$Ne are presented and analyzed.
José Gilson Louzada Regadas Filho
2011-09-01
Full Text Available This study aimed at estimating the kinetic parameters of ruminal degradation of neutral detergent fiber from agroindustrial byproducts of cashew (pulp and cashew nut, passion fruit, melon, pineapple, West Indian cherry, grape, annatto and coconut through the gravimetric technique of nylon bag, and to evaluate the prediction equation of indigestible fraction of neutral detergent fiber suggested by the Cornell Net Carbohydrate and Protein System. Samples of feed crushed to 2 mm were placed in 7 × 14 cm nylon bags with porosity of 50 µm in a ratio of 20 g DM/cm² and incubated in duplicate in the rumen of a heifer at 0, 3, 6, 9, 12, 16, 24, 36, 48, 72, 96 and 144 hours. The incubation residues were analyzed for NDF content and evaluated by a non-linear logistic model. The evaluation process of predicting the indigestible fraction of NDF was carried out through adjustment of linear regression models between predicted and observed values. There was a wide variation in the degradation parameters of NDF among byproducts. The degradation rate of NDF ranged from 0.0267 h-1 to 0.0971 h-1 for grape and West Indian cherry, respectively. The potentially digestible fraction of NDF ranged from 4.17 to 90.67%, respectively, for melon and coconut byproducts. The CNCPS equation was sensitive to predict the indigestible fraction of neutral detergent fiber of the byproducts. However, due to the high value of the mean squared error of prediction, such estimates are very variable; hence the most suitable would be estimation by biological methods.
A New Kinetic Equation for Non-Isothermal Reaction Process%非等温反应过程中新的动力学方程
成一
2006-01-01
For the kinetic equation in non-isothermal process, the temperature integral for Arrhenius Equation should be from T2 to T1, but the integral of many current kinetic equations is from T to 0 K, such as Ozawa Equation. Our work shows that the activation energies from these equations are with larger error for some reactions and a new kinetic equation has been established. By the isoconversional method, the activation energy of chemical reaction in linear or nonlinear heating process can be calculated more accurately by the new equation. The results by the new equation for two classic reactions, the degradation of Polyamide (PA6) and decomposition of Ca er error.%对于非等温过程中的动力学方程,正确的Arrhenius方程的温度积分应该是从T2到T1,但是许多动力学方程中的温度积分是从T到0 K,例如Ozawa等方程.我们的研究指出对于某些反应,这些方程中的活化能存在较大的误差,因此我们提出了一个新的动力学方程.凭借等转化率法,应用新的方程可以精确求解线性或非线性加热过程中化学反应的活化能.用新方程对2个经典反应(聚酰胺的热裂解和一水草酸钙的热分解)的研究表明:Ozawa方程的活化能有时是精确的,有时偏差太大.
Cyclic integrals and reduction of rotational relativistic Birkhoffian system
罗绍凯
2003-01-01
The order reduction method of the rotational relativistic Birkhoffian equations is studied. For a rotational relativistic Birkhoffian system, the cyclic integrals can be found by using the perfect differential method. Through these cyclic integrals, the order of the system can be reduced. If the rotational relativistic Birkhoffian system has a cyclic integral, then the Birkhoffian equations can be reduced at least two degrees and the Birkhoffian form can be kept. An example is given to illustrate the application of the results.
Pratt, D. T.
1984-01-01
Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.
Whittaker Order Reduction Method of Relativistic Birkhoffian Systems
LUOShao-Kai; HUANGFei-Jiang; LUYi-Bing
2004-01-01
The order reduction method of the relativistic Birkhollian equations is studied. For a relativistic autonomous Birkhotffian system, if the conservative law of the Birkhotffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the relativisticBirkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least twodegrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics and the relativistic Lagrangian mechanics are discussed, and the Whittaker order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of theresult.
Whittaker Order Reduction Method of Relativistic Birkhoffian Systems
LUO Shao-Kai; HUANG Fei-Jiang; LU Yi-Bing
2004-01-01
The order reduction method of the relativistic Birkhoffian equations is studied. For a relativistic autonomous Birkhoffian system, if the conservative law of the Birkhoffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the relativistic Birkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least two degrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics and the relativistic Lagrangian mechanics are discussed, and the Whittaker order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of the result.
Routh Order Reduction Method of Relativistic Birkhoffian Systems
LUO Shao-Kai; GUO Yong-Xin
2007-01-01
Routh order reduction method of the relativistic Birkhoffian equations is studied.For a relativistic Birkhoffian system,the cyclic integrals can be found by using the perfect differential method.Through these cyclic integrals,the order of the system can be reduced.If the relativistic Birkhoffian system has a cyclic integral,then the Birkhoffian equations can be reduced at least by two degrees and the Birkhoffian form can be kept.The relations among the relativistic Birkhoffian mechanics,the relativistic Hamiltonian mechanics,and the relativistic Lagrangian mechanics are discussed,and the Routh order reduction method of the relativistic Lagrangian system is obtained.And an example is given to illustrate the application of the result.
Relativistic differential-difference momentum operators and noncommutative differential calculus
Mir-Kasimov, R. M.
2013-09-01
The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics (QM) in the Relativistic Configuration Space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated as the independent term of the total Hamiltonian. This relativistic kinetic energy term is not distinguishing in form from its nonrelativistic counterpart. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generating function for the matrix elements of the unitary irreps of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS.
Leardini, Fabrice
2013-01-01
This manuscript presents a problem on special relativity theory (SRT) which embodies an apparent paradox relying on the concept of simultaneity. The problem is represented in the framework of Greek epic poetry and structured in a didactic way. Owing to the characteristic properties of Lorenz transformations, three events which are simultaneous in a given inertial reference system, occur at different times in the other two reference frames. In contrast to the famous twin paradox, in the present case there are three, not two, different inertial observers. This feature provides a better framework to expose some of the main characteristics of SRT, in particular, the concept of velocity and the relativistic rule of addition of velocities.
On the relativistic anisotropic configurations
Shojai, F. [University of Tehran, Department of Physics, Tehran (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), Foundations of Physics Group, School of Physics, Tehran (Iran, Islamic Republic of); Kohandel, M. [Alzahra University, Department of Physics and Chemistry, Tehran (Iran, Islamic Republic of); Stepanian, A. [University of Tehran, Department of Physics, Tehran (Iran, Islamic Republic of)
2016-06-15
In this paper we study anisotropic spherical polytropes within the framework of general relativity. Using the anisotropic Tolman-Oppenheimer-Volkov equations, we explore the relativistic anisotropic Lane-Emden equations. We find how the anisotropic pressure affects the boundary conditions of these equations. Also we argue that the behavior of physical quantities near the center of star changes in the presence of anisotropy. For constant density, a class of exact solution is derived with the aid of a new ansatz and its physical properties are discussed. (orig.)
Henrice Junior, Edson; Goncalves, Alessandro da Cruz, E-mail: ejunior@nuclear.ufrj.br, E-mail: alessandro@nuclear.ufrj.br [Coordenacao dos Programas de Pos-Graduacao em Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Energia Nuclear; Palma, Daniel Artur Pinheiro, E-mail: dapalma@cnen.gov.br [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil); Mesquita, Amir Zacarias, E-mail: amir@cdtn.br [Centro de Desenvolvimento da Tecnologia Nuclear (CDTN/CNEN-MG), Belo Horizonte, MG (Brazil)
2015-07-01
This paper provides a comparison between the reactivity calculated by the approximation based on the multiplication factor (K{sub eff}) and a new approach for the reactivity calculation to be used in the kinetics point equation for subcritical systems. To obtain the necessary kinetic parameters as well and the reference Power value calculation and validation, a subcritical system was simulated with the Monte Carlo code Serpent. This study is important for determining nuclear Power in such systems. The results shown consistent values with the validation method and new in-depth studies to calculate the reactivity should be performed to such systems, making the issue a very current theme. (author)
Schwanz, Daphne, E-mail: daphne_schwanz@yahoo.com.b [Universidade Estadual do Rio Grande do Sul, Novo Hamburgo, RS (Brazil); Petersen, Claudio Z., E-mail: claudiopetersen@yahoo.com.b [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Leite, Sargio Q.B., E-mail: bogado@cnen.gov.b [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil). Coordenacao Geral de Reatores e Ciclo do Combustivel
2009-07-01
In this work, the punctual kinetic equation, which consists of a Stiff type ordinary equation system, will be solved by the technique of Laplace Transformation with numerical inversion. The punctual kinetic equation will be written in a matrix form assuming constant reactivity. The inversion of the Laplace Transformation will be solved by the gaussian quadrature method. We will perform numerical simulation and will make comparisons with obtained results in the literature for constant reactivity
André, Raíla
2014-01-01
In this work we analyze the dynamics of collisionless self-gravitating systems described by the f(R)-gravity and Boltzmann equation in the weak field approximation, focusing on the Jeans instability for theses systems. The field equations in this approximation were obtained within the Palatini formalism. Through the solution of coupled equations we achieved the collapse criterion for infinite homogeneous fluid and stellar systems, which is given by a dispersion relation. This result is compared with the results of the standard case and the case for f(R)-gravity in metric formalism, in order to see the difference among them. The limit of instability varies according to which theory of gravity is adopted.
Relativistic Runaway Electrons
Breizman, Boris
2014-10-01
This talk covers recent developments in the theory of runaway electrons in a tokamak with an emphasis on highly relativistic electrons produced via the avalanche mechanism. The rapidly growing population of runaway electrons can quickly replace a large part of the initial current carried by the bulk plasma electrons. The magnetic energy associated with this current is typically much greater than the particle kinetic energy. The current of a highly relativistic runaway beam is insensitive to the particle energy, which separates the description of the runaway current evolution from the description of the runaway energy spectrum. A strongly anisotropic distribution of fast electrons is generally prone to high-frequency kinetic instabilities that may cause beneficial enhancement of runaway energy losses. The relevant instabilities are in the frequency range of whistler waves and electron plasma waves. The instability thresholds reported in earlier work have been revised considerably to reflect strong dependence of collisional damping on the wave frequency and the role of plasma non-uniformity, including radial trapping of the excited waves in the plasma. The talk also includes a discussion of enhanced scattering of the runaways as well as the combined effect of enhanced scattering and synchrotron radiation. A noteworthy feature of the avalanche-produced runaway current is a self-sustained regime of marginal criticality: the inductive electric field has to be close to its critical value (representing avalanche threshold) at every location where the runaway current density is finite, and the current density should vanish at any point where the electric field drops below its critical value. This nonlinear Ohm's law enables complete description of the evolving current profile. Work supported by the U.S. Department of Energy Contract No. DEFG02-04ER54742 and by ITER contract ITER-CT-12-4300000273. The views and opinions expressed herein do not necessarily reflect those of
Komorovsky, Stanislav; Repisky, Michal; Malkin, Elena; Demissie, Taye B; Ruud, Kenneth
2015-08-11
We present an implementation of the nuclear spin-rotation (SR) constants based on the relativistic four-component Dirac-Coulomb Hamiltonian. This formalism has been implemented in the framework of the Hartree-Fock and Kohn-Sham theory, allowing assessment of both pure and hybrid exchange-correlation functionals. In the density-functional theory (DFT) implementation of the response equations, a noncollinear generalized gradient approximation (GGA) has been used. The present approach enforces a restricted kinetic balance condition for the small-component basis at the integral level, leading to very efficient calculations of the property. We apply the methodology to study relativistic effects on the spin-rotation constants by performing calculations on XHn (n = 1-4) for all elements X in the p-block of the periodic table and comparing the effects of relativity on the nuclear SR tensors to that observed for the nuclear magnetic shielding tensors. Correlation effects as described by the density-functional theory are shown to be significant for the spin-rotation constants, whereas the differences between the use of GGA and hybrid density functionals are much smaller. Our calculated relativistic spin-rotation constants at the DFT level of theory are only in fair agreement with available experimental data. It is shown that the scaling of the relativistic effects for the spin-rotation constants (varying between Z(3.8) and Z(4.5)) is as strong as for the chemical shieldings but with a much smaller prefactor.
D. Baumgardner
2013-01-01
Full Text Available Warm rain in real clouds is produced by the collision and coalescence of an initial population of small droplets. The production of rain in warm cumulus clouds is still one of the open problems in cloud physics, and although several mechanisms have been proposed in the past, at present there is no complete explanation for the rapid growth of cloud droplets within the size range of diameters from 10 to 50 μm. By using a collection kernel enhanced by turbulence and a fully stochastic simulation method, the formation of a runaway droplet is modeled through the turbulent collection process. When the runaway droplet forms, the traditional calculation using the kinetic collection equation is no longer valid, since the assumption of a continuous distribution breaks down. There is in essence a phase transition in the system from a continuous distribution to a continuous distribution plus a runaway droplet. This transition can be associated to gelation (also called sol–gel transition and is proposed here as a mechanism for the formation of large droplets required to trigger warm rain development in cumulus clouds. The fully stochastic turbulent model reveals gelation and the formation of a droplet with mass comparable to the mass of the initial system. The time when the sol–gel transition occurs is estimated with a Monte Carlo method when the parameter ρ (the ratio of the standard deviation for the largest droplet mass over all the realizations to the averaged value reaches its maximum value. Moreover, we show that the non-turbulent case does not exhibit the sol–gel transition that can account for the impossibility of producing raindrop embryos in such a system. In the context of cloud physics theory, gelation can be interpreted as the formation of the "lucky droplet" that grows at a much faster rate than the rest of the population and becomes the embryo for runaway raindrops.
L. Alfonso
2012-01-01
Full Text Available In a coagulating system, a sol-gel transition occurs when a single giant particle (a gel arises under certain conditions and begins to consume the mass of smaller but higher populated fraction (the sol. This single giant particle (also known as a runaway particle is detached from the continuous spectrum. Since the kinetic collection equation (KCE only models the evolution of the continuous size of the spectrum, as the largest particle continue to grow by accretion of smaller ones, the liquid water content predicted by the KCE will decrease.
In this paper, the sol-gel transition is proposed as the mechanism that forms the large droplets that are needed to trigger warm rain development in cumulus clouds. By using a collection kernel enhanced by turbulence and a stochastic simulation method, the formation of a runaway droplet is modeled through the turbulent collection process. The model results show that the sol-gel transition (also called gelation leads to the formation of a droplet with mass comparable to the mass of the initial system. The time when the sol-gel transition occurs is estimated with a Monte Carlo method when the parameter ρ (the ratio of the standard deviation for the largest droplet mass over all the realizations to the averaged value reaches its maximum value. Moreover, we show that without turbulence, the sol-gel transition will not occur. In the context of theoretical cloud microphysics, gelation can be interpreted as the formation of the "lucky droplet" that grows at a much faster rate than the rest of the droplet population and subsequently becomes the embryo for raindrops.
EL Safadi, M
2007-03-15
We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C{sup {infinity}} regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)
Bezerra, Rui M F; Fraga, Irene; Dias, Albino A
2013-01-01
Enzyme kinetic parameters are usually determined from initial rates nevertheless, laboratory instruments only measure substrate or product concentration versus reaction time (progress curves). To overcome this problem we present a methodology which uses integrated models based on Michaelis-Menten equation. The most severe practical limitation of progress curve analysis occurs when the enzyme shows a loss of activity under the chosen assay conditions. To avoid this problem it is possible to work with the same experimental points utilized for initial rates determination. This methodology is illustrated by the use of integrated kinetic equations with the well-known reaction catalyzed by alkaline phosphatase enzyme. In this work nonlinear regression was performed with the Solver supplement (Microsoft Office Excel). It is easy to work with and track graphically the convergence of SSE (sum of square errors). The diagnosis of enzyme inhibition was performed according to Akaike information criterion. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.
Liao, Fei; Zhu, Xiao-Yun; Wang, Yong-Mei; Zuo, Yu-Ping
2005-01-31
The estimation of enzyme kinetic parameters by nonlinear fitting reaction curve to the integrated Michaelis-Menten rate equation ln(S(0)/S)+(S(0)-S)/K(m)=(V(m)/K(m))xt was investigated and compared to that by fitting to (S(0)-S)/t=V(m)-K(m)x[ln(S(0)/S)/t] (Atkins GL, Nimmo IA. The reliability of Michaelis-Menten constants and maximum velocities estimated by using the integrated Michaelis-Menten equation. Biochem J 1973;135:779-84) with uricase as the model. Uricase reaction curve was simulated with random absorbance error of 0.001 at 0.075 mmol/l uric acid. Experimental reaction curve was monitored by absorbance at 293 nm. For both CV and deviation kinetic parameters and applicable for the characterization of enzyme inhibitors.
Relativistic MHD with Adaptive Mesh Refinement
Anderson, M; Liebling, S L; Neilsen, D; Anderson, Matthew; Hirschmann, Eric; Liebling, Steven L.; Neilsen, David
2006-01-01
We solve the relativistic magnetohydrodynamics (MHD) equations using a finite difference Convex ENO method (CENO) in 3+1 dimensions within a distributed parallel adaptive mesh refinement (AMR) infrastructure. In flat space we examine a Balsara blast wave problem along with a spherical blast wave and a relativistic rotor test both with unigrid and AMR simulations. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. We also investigate the impact of hyperbolic divergence cleaning for the spherical blast wave and relativistic rotor. We include unigrid and mesh refinement parallel performance measurements for the spherical blast wave.
Relativistic diffusive motion in random electromagnetic fields
Haba, Z, E-mail: zhab@ift.uni.wroc.pl [Institute of Theoretical Physics, University of Wroclaw, 50-204 Wroclaw, Plac Maxa Borna 9 (Poland)
2011-08-19
We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Juettner equilibrium at the inverse temperature {beta}{sup -1} = mc{sup 2}. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).
Double Relativistic Electron Accelerating Mirror
Saltanat Sadykova
2013-02-01
Full Text Available In the present paper, the possibility of generation of thin dense relativistic electron layers is shown using the analytical and numerical modeling of laser pulse interaction with ultra-thin layers. It was shown that the maximum electron energy can be gained by optimal tuning between the target width, intensity and laser pulse duration. The optimal parameters were obtained from a self-consistent system of Maxwell equations and the equation of motion of electron layer. For thin relativistic electron layers, the gaining of maximum electron energies requires a second additional overdense plasma layer, thus cutting the laser radiation off the plasma screen at the instant of gaining the maximum energy (DREAM-schema.
Fluctuations in Relativistic Causal Hydrodynamics
Kumar, Avdhesh; Mishra, Ananta P
2013-01-01
The formalism to calculate the hydrodynamics fluctuation using the quasi-stationary fluctuation theory of Onsager to the relativistic Navier-Stokes hydrodynamics is already known. In this work we calculate hydrodynamic fluctuations in relativistic causal theory of Muller, Israel and Stewart and other related causal hydrodynamic theories. We show that expressions for the Onsager coefficients and the correlation functions have form similar to the ones obtained by using Navier-Stokes equation. However, temporal evolution of the correlation functions obtained using MIS and the other causal theories can be significantly different than the correlation functions obtained using the Navier-Stokes equation. Finally, as an illustrative example, we explicitly plot the correlation functions obtained using the causal-hydrodynamics theories and compare them with correlation functions obtained by earlier authors using the expanding boost-invariant (Bjorken) flows.
Entropy production for a relativistic simple fluid in a weak electromagnetic field
García-Perciante, A. L.; Sandoval-Villalbazo, A.; Brun-Battistini, D.
2016-11-01
Thermal dissipation in plasmas includes a variety of effects, most of them arising from the fact that these gases are usually composed of at least two species. In the case of a mild temperature single component charged fluid kinetic theory indicates that the temperature gradient is the only source of vector-type dissipation. However, if the temperature increases to a point in which the molecule's velocities approach the speed of light, electrothermal dissipation is possible even for the single component charged gas. The modification to the structure of the entropy production introduced by this effect is established in order to address the second law of thermodynamics for such a system. The entropy balance equation is obtained from the relativistic Boltzmann equation and the vector contribution to the entropy production is calculated in terms of the thermodynamic forces and the electromagnetic field using Chapman-Enskog's expansion. It is shown that the structure is consistent with the constitutive equation previously reported, in which a thermoelectric effect was found for a single component relativistic fluid. This effect does not have a non-relativistic counterpart and presents no ambiguity regarding the frame chosen as the comoving frame, which is an issue in the mixture case.