20,720 research outputs found
Relativistic hydrodynamics - causality and stability
Causality and stability in relativistic dissipative hydrodynamics are
important conceptual issues. We argue that causality is not restricted to
hyperbolic set of differential equations. E.g. heat conduction equation can be
causal considering the physical validity of the theory. Furthermore we propose
a new concept of relativistic internal energy that clearly separates the
dissipative and non-dissipative effects. We prove that with this choice we
remove all known instabilities of the linear response approximation of viscous
and heat conducting relativistic fluids. In this paper the Eckart choice of the
velocity field is applied.Comment: 14 pages, 2 figures, completely revise
Stochastic foundations of undulatory transport phenomena: Generalized Poisson-Kac processes - Part I Basic theory
This article introduces the notion of Generalized Poisson-Kac (GPK) processes
which generalize the class of "telegrapher's noise dynamics" introduced by Marc
Kac in 1974, usingPoissonian stochastic perturbations. In GPK processes the
stochastic perturbation acts as a switching amongst a set of stochastic
velocity vectors controlled by a Markov-chain dynamics. GPK processes possess
trajectory regularity (almost everywhere) and asymptotic Kac limit, namely the
convergence towards Brownian motion (and to stochastic dynamics driven by
Wiener perturbations), which characterizes also the long-term/long-distance
properties of these processes. In this article we introduce the structural
properties of GPK processes, leaving all the physical implications to part II
and part III
Diffuse-interface model for rapid phase transformations in nonequilibrium systems
A thermodynamic approach to rapid phase transformations within a diffuse
interface in a binary system is developed. Assuming an extended set of
independent thermodynamic variables formed by the union of the classic set of
slow variables and the space of fast variables, we introduce finiteness of the
heat and solute diffusive propagation at the finite speed of the interface
advancing. To describe the transformation within the diffuse interface, we use
the phase-field model which allows us to follow the steep but smooth change of
phases within the width of diffuse interface. The governing equations of the
phase-field model are derived for the hyperbolic model, model with memory, and
for a model of nonlinear evolution of transformation within the
diffuse-interface. The consistency of the model is proved by the condition of
positive entropy production and by the outcomes of the fluctuation-dissipation
theorem. A comparison with the existing sharp-interface and diffuse-interface
versions of the model is given.Comment: 15 pages, regular article submitted to Physical Review
Production of a sterile species: quantum kinetics
Production of a sterile species is studied within an effective model of
active-sterile neutrino mixing in a medium in thermal equilibrium. The quantum
kinetic equations for the distribution functions and coherences are obtained
from two independent methods: the effective action and the quantum master
equation. The decoherence time scale for active-sterile oscillations is
, but the evolution of the distribution functions
is determined by the two different time scales associated with the damping
rates of the quasiparticle modes in the medium: \Gamma_1=\Gamma_{aa}\cos^2\tm
; \Gamma_2=\Gamma_{aa}\sin^2\tm where is the interaction rate of
the active species in absence of mixing and \tm the mixing angle in the
medium. These two time scales are widely different away from MSW resonances and
preclude the kinetic description of active-sterile production in terms of a
simple rate equation. We give the complete set of quantum kinetic equations for
the active and sterile populations and coherences and discuss in detail the
various approximations. A generalization of the active-sterile transition
probability \emph{in a medium} is provided via the quantum master equation. We
derive explicitly the usual quantum kinetic equations in terms of the
``polarization vector'' and show their equivalence to those obtained from the
quantum master equation and effective action.Comment: To appear in Phys. Rev.
Evolutionary Poisson Games for Controlling Large Population Behaviors
Emerging applications in engineering such as crowd-sourcing and
(mis)information propagation involve a large population of heterogeneous users
or agents in a complex network who strategically make dynamic decisions. In
this work, we establish an evolutionary Poisson game framework to capture the
random, dynamic and heterogeneous interactions of agents in a holistic fashion,
and design mechanisms to control their behaviors to achieve a system-wide
objective. We use the antivirus protection challenge in cyber security to
motivate the framework, where each user in the network can choose whether or
not to adopt the software. We introduce the notion of evolutionary Poisson
stable equilibrium for the game, and show its existence and uniqueness. Online
algorithms are developed using the techniques of stochastic approximation
coupled with the population dynamics, and they are shown to converge to the
optimal solution of the controller problem. Numerical examples are used to
illustrate and corroborate our results
A quantum hydrodynamics approach to the formation of new types of waves in polarized two-dimension systems of charged and neutral particles
In this paper we explicate a method of quantum hydrodynamics (QHD) for the
study of the quantum evolution of a system of polarized particles. Though we
focused primarily on the two-dimension physical systems, the method is valid
for three-dimension and one-dimension systems too. The presented method is
based upon the Schr\"{o}dinger equation. Fundamental QHD equations for charged
and neutral particles were derived from the many-particle microscopic
Schr\"{o}dinger equation. The fact that particles possess the electric dipole
moment (EDM) was taken into account. The explicated QHD approach was used to
study dispersion characteristics of various physical systems. We analyzed
dispersion of waves in a two-dimension (2D) ion and hole gas placed into an
external electric field which is orthogonal to the gas plane. Elementary
excitations in a system of neutral polarized particles were studied for 1D, 2D
and 3D cases. The polarization dynamics in systems of both neutral and charged
particles is shown to cause formation of a new type of waves as well as changes
in the dispersion characteristics of already known waves. We also analyzed wave
dispersion in 2D exciton systems, in 2D electron-ion plasma and 2D
electron-hole plasma. Generation of waves in 3D system neutral particles with
EDM by means of the beam of electrons and neutral polarized particles is
investigated.Comment: 15 pages, 7 figure
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