163 research outputs found
Poisson-Bracket Approach to the Dynamics of Nematic Liquid Crystals. The Role of Spin Angular Momentum
Nematic liquid crystals are well modeled as a fluid of rigid rods. Starting
from this model, we use a Poisson-bracket formalism to derive the equations
governing the dynamics of nematic liquid crystals. We treat the spin angular
momentum density arising from the rotation of constituent molecules about their
centers of mass as an independent field and derive equations for it, the mass
density, the momentum density, and the nematic director. Our equations reduce
to the original Leslie-Ericksen equations, including the inertial director term
that is neglected in the hydrodynamic limit, only when the moment of inertia
for angular momentum parallel to the director vanishes and when a dissipative
coefficient favoring locking of the angular frequencies of director rotation
and spin angular momentum diverges. Our equations reduce to the equations of
nematohydrodynamics in the hydrodynamic limit but with dissipative coefficients
that depend on the coefficient that must diverge to produce the Leslie-Ericksen
equations.Comment: 10 pages, to be published in Phys. Rev. E 72(5
Geometrical dissipation for dynamical systems
On a Riemannian manifold we consider the functions
and construct the vector fields that conserve and
dissipate with a prescribed rate. We study the geometry of these vector
fields and prove that they are of gradient type on regular leaves corresponding
to . By using these constructions we show that the cubic Morrison
dissipation and the Landau-Lifschitz equation can be formulated in a unitary
form
An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics
A general method for deriving closed reduced models of Hamiltonian dynamical
systems is developed using techniques from optimization and statistical
estimation. As in standard projection operator methods, a set of resolved
variables is selected to capture the slow, macroscopic behavior of the system,
and the family of quasi-equilibrium probability densities on phase space
corresponding to these resolved variables is employed as a statistical model.
The macroscopic dynamics of the mean resolved variables is determined by
optimizing over paths of these probability densities. Specifically, a cost
function is introduced that quantifies the lack-of-fit of such paths to the
underlying microscopic dynamics; it is an ensemble-averaged, squared-norm of
the residual that results from submitting a path of trial densities to the
Liouville equation. The evolution of the macrostate is estimated by minimizing
the time integral of the cost function. The value function for this
optimization satisfies the associated Hamilton-Jacobi equation, and it
determines the optimal relation between the statistical parameters and the
irreversible fluxes of the resolved variables, thereby closing the reduced
dynamics. The resulting equations for the macroscopic variables have the
generic form of governing equations for nonequilibrium thermodynamics, and they
furnish a rational extension of the classical equations of linear irreversible
thermodynamics beyond the near-equilibrium regime. In particular, the value
function is a thermodynamic potential that extends the classical dissipation
function and supplies the nonlinear relation between thermodynamics forces and
fluxes
Spinodal Decomposition in Binary Gases
We carried out three-dimensional simulations, with about 1.4 million
particles, of phase segregation in a low density binary fluid mixture,
described mesoscopically by energy and momentum conserving Boltzmann-Vlasov
equations. Using a combination of Direct Simulation Monte Carlo(DSMC) for the
short range collisions and a version of Particle-In-Cell(PIC) evolution for the
smooth long range interaction, we found dynamical scaling after the ratio of
the interface thickness(whose shape is described approximately by a hyperbolic
tangent profile) to the domain size is less than ~0.1. The scaling length R(t)
grows at late times like t^alpha, with alpha=1 for critical quenches and
alpha=1/3 for off-critical ones. We also measured the variation of temperature,
total particle density and hydrodynamic velocity during the segregation
process.Comment: 11 pages, Revtex, 4 Postscript figures, submitted to PR
Thermodynamically admissible form for discrete hydrodynamics
We construct a discrete model of fluid particles according to the GENERIC
formalism. The model has the form of Smoothed Particle Hydrodynamics including
correct thermal fluctuations. A slight variation of the model reproduces the
Dissipative Particle Dynamics model with any desired thermodynamic behavior.
The resulting algorithm has the following properties: mass, momentum and energy
are conserved, entropy is a non-decreasing function of time and the thermal
fluctuations produce the correct Einstein distribution function at equilibrium.Comment: 4 page
Deriving effective models for multiscale systems via evolutionary -convergence
We discuss possible extensions of the recently established theory of evolutionary Gamma convergence for gradient systems to nonlinear dynamical systems obtained by perturbation of a gradient systems. Thus, it is possible to derive effective equations for pattern forming systems with multiple scales. Our applications include homogenization of reaction-diffusion systems, the justification of amplitude equations for Turing instabilities, and the limit from pure diffusion to reaction-diffusion. This is achieved by generalizing the Gamma-limit approaches based on the energy-dissipation principle or the evolutionary variational estimate
Heavy Ions at LHC: A Quest for Quark-Gluon Plasma
Quantum Chromo Dynamics (QCD), the theory of strong interactions, predicts a
transition of the usual matter to a new phase of matter, called Quark-Gluon
Plasma (QGP), at sufficiently high temperatures. The non-perturbative technique
of defining a theory on a space-time lattice has been used to obtain this and
other predictions about the nature of QGP. Heavy ion collisions at the Large
Hadron Collider in CERN can potentially test these predictions and thereby test
our theoretical understanding of confinement. This brief review aims at
providing a glimpse of both these aspects of QGP.Comment: 26 pages, 31 Figures, Invited article for the volume on LHC physics
to celebrate the Platinum Jubilee of the Indian National Science Academy,
edited by Amitava Datta, Biswarup Mukhopadhyaya and Amitava Raychaudhuri.
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Mechanics and thermodynamics of a new minimal model of the atmosphere
The understanding of the fundamental properties of the climate system has long benefitted from the use of simple numerical models able to parsimoniously represent the essential ingredients of its processes. Here, we introduce a new model for the atmosphere that is constructed by supplementing the now-classic Lorenz â96 one-dimensional lattice model with temperature-like variables. The model features an energy cycle that allows for energy to be converted between the kinetic form and the potential form and for introducing a notion of efficiency. The modelâs evolution is controlled by two contributionsâa quasi-symplectic and a gradient one, which resemble (yet not conforming to) a metriplectic structure. After investigating the linear stability of the symmetric fixed point, we perform a systematic parametric investigation that allows us to define regions in the parameters space where at steady-state stationary, quasi-periodic, and chaotic motions are realised, and study how the terms responsible for defining the energy budget of the system depend on the external forcing injecting energy in the kinetic and in the potential energy reservoirs. Finally, we find preliminary evidence that the model features extensive chaos. We also introduce a more complex version of the model that is able to accommodate for multiscale dynamics and that features an energy cycle that more closely mimics the one of the Earthâs atmosphere
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