656 research outputs found
Validity of path thermodynamics in reactive systems
Path thermodynamic formulation of nonequilibrium reactive systems is considered. It is shown through simple practical examples that this approach can lead to results that contradict well established thermodynamic properties of such systems. Rigorous mathematical analysis confirming this fact is presented
Reply to "Comment on `Validity of path thermodynamic description of reactive systems: Microscopic simulations'
The Comment's author argues that a correct description of reactive systems
should incorporate the explicit interaction with reservoirs, leading to a
unified system-reservoirs entity. However, this proposition has two major
flaws. Firstly, as we will emphasize, this entity inherently follows a
thermodynamic equilibrium distribution. In the Comment, no indication is
provided on how to maintain such a system-reservoirs entity in a
non-equilibrium state. Secondly, contrary to the author's claim, the inclusion
of system-reservoir interaction in traditional stochastic modeling of reactive
systems does not automatically alter the limited applicability of path
thermodynamics to problematic reactive systems. We will provide a simple
demonstration to illustrate that certain elementary reactions may not involve
any changes in reservoir components, which seems to have been overlooked by the
author.Comment: To appear in Physical Review
Hydrodynamic fluctuations in the Kolmogorov flow: Linear regime
The Landau-Lifshitz fluctuating hydrodynamics is used to study the
statistical properties of the linearized Kolmogorov flow. The relative
simplicity of this flow allows a detailed analysis of the fluctuation spectrum
from near equilibrium regime up to the vicinity of the first convective
instability threshold. It is shown that in the long time limit the flow behaves
as an incompressible fluid, regardless of the value of the Reynolds number.
This is not the case for the short time behavior where the incompressibility
assumption leads in general to a wrong form of the static correlation
functions, except near the instability threshold. The theoretical predictions
are confirmed by numerical simulations of the full nonlinear fluctuating
hydrodynamic equations.Comment: 20 pages, 4 figure
Spurious diffusion in particle simulations of the Kolmogorov flow
Particle simulations of the Kolmogorov flow are analyzed by the
Landau-Lifshitz fluctuating hydrodynamics. It is shown that a spurious
diffusion of the center of mass corrupts the statistical properties of the
flow. The analytical expression for the corresponding diffusion coefficient is
derived.Comment: 10 pages, no figure
Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh-Benard instability
Starting from the linearized fluctuating Boussinesq equations we derive an
expression for the structure factor of fluids in stationary convection-free
thermal nonequilibrium states, taking into account both gravity and finite-size
effects. It is demonstrated how the combined effects of gravity and finite size
causes the structure factor to go through a maximum value as a function of the
wave number . The appearance of this maximum is associated with a crossover
from a dependence for larger to a dependence for very small
. The relevance of this theoretical result for the interpretation of light
scattering and shadowgraph experiments is elucidated. The relationship with
studies on various aspects of the problem by other investigators is discussed.
The paper thus provides a unified treatment for dealing with fluctuations in
fluid layers subjected to a stationary temperature gradient regardless of the
sign of the Rayleigh number , provided that is smaller than the critical
value associated with the appearance of Rayleigh-B\'{e}nard
convection.Comment: 33 pages, 6 figures, accepted for publication: Physica
A discretized integral hydrodynamics
Using an interpolant form for the gradient of a function of position, we
write an integral version of the conservation equations for a fluid. In the
appropriate limit, these become the usual conservation laws of mass, momentum
and energy. We also discuss the special cases of the Navier-Stokes equations
for viscous flow and the Fourier law for thermal conduction in the presence of
hydrodynamic fluctuations. By means of a discretization procedure, we show how
these equations can give rise to the so-called "particle dynamics" of Smoothed
Particle Hydrodynamics and Dissipative Particle Dynamics.Comment: 10 pages, RevTex, submitted to Phys. Rev.
Non-Newtonian Couette-Poiseuille flow of a dilute gas
The steady state of a dilute gas enclosed between two infinite parallel
plates in relative motion and under the action of a uniform body force parallel
to the plates is considered. The Bhatnagar-Gross-Krook model kinetic equation
is analytically solved for this Couette-Poiseuille flow to first order in the
force and for arbitrary values of the Knudsen number associated with the shear
rate. This allows us to investigate the influence of the external force on the
non-Newtonian properties of the Couette flow. Moreover, the Couette-Poiseuille
flow is analyzed when the shear-rate Knudsen number and the scaled force are of
the same order and terms up to second order are retained. In this way, the
transition from the bimodal temperature profile characteristic of the pure
force-driven Poiseuille flow to the parabolic profile characteristic of the
pure Couette flow through several intermediate stages in the Couette-Poiseuille
flow are described. A critical comparison with the Navier-Stokes solution of
the problem is carried out.Comment: 24 pages, 5 figures; v2: discussion on boundary conditions added; 10
additional references. Published in a special issue of the journal "Kinetic
and Related Models" dedicated to the memory of Carlo Cercignan
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