54 research outputs found
A statistical mechanical approach to fluid dynamics: Thermodynamically consistent equations for simple dissipative fluids
In this paper, a statistical mechanical derivation of thermodynamically
consistent fluid dynamical equations is presented for non-isothermal viscous
molecular fluids. The coarse-graining process is based on the combination of
key concepts from earlier works, including the Dirac-delta formalism of Irving
and Kirkwood, the identity of statistical physical ensemble averages by
Khinchin, and a first-order Taylor expansion around the leading-order solution
of the Chapman-Enskog theory. The non-equilibrium thermodynamic quantities and
constitutive relations directly emerge in the proposed coarse-graining process,
which results in a completion of the phenomenological theory. We show that (i)
the variational form of the thermodynamic part of the reversible stress is
already encoded on the level of the Hamiltonian many-body problem, (ii) the
dynamics monotonically maximizes the entropy at constant energy, and (iii) that
the phenomenological energy balance equation obtained in the adiabatic
approximation lacks the contribution of non-local interactions, which is
crucial in modelling the gas-liquid transition in near-critical fluids
Nonlinear hydrodynamic theory of crystallization
We present an isothermal fluctuating nonlinear hydrodynamic theory of
crystallization in molecular liquids. A dynamic coarse-graining technique is
used to derive the velocity field, a phenomenology, which allows a direct
coupling between the free energy functional of the classical Density Functional
Theory and the Navier-Stokes equation. Contrary to the Ginzburg-Landau type
amplitude theories, the dynamic response to elastic deformations is described
by parameter-free kinetic equations. Employing our approach to the free energy
functional of the Phase-Field Crystal model, we recover the classical spectrum
for the phonons and the steady-state growth fronts. The capillary wave spectrum
of the equilibrium crystal-liquid interface is in a good qualitative agreement
with the molecular dynamics simulations
Phase field theory of interfaces and crystal nucleation in a eutectic system of fcc structure: II. Nucleation in the metastable liquid immiscibility region
The official version of this Article can be accessed from the link below - Copyright @ 2007 American Institute of PhysicsIn the second part of our paper, we address crystal nucleation in the metastable liquid miscibility region of eutectic systems that is always present, though experimentally often inaccessible. While this situation resembles the one seen in single component crystal nucleation in the presence of a metastable vapor-liquid critical point addressed in previous works, it is more complex because of the fact that here two crystal phases of significantly different compositions may nucleate. Accordingly, at a fixed temperature below the critical point, six different types of nuclei may form: two liquid-liquid nuclei: two solid-liquid nuclei; and two types of composite nuclei, in which the crystalline core has a liquid "skirt," whose composition falls in between the compositions of the solid and the initial liquid phases, in addition to nuclei with concentric alternating composition shells of prohibitively high free energy. We discuss crystalline phase selection via exploring/identifying the possible pathways for crystal nucleation.This work has been supported by the Hungarian Academy of Sciences under contract No. OTKA-K-62588 and by the ESA PECS Nos. 98021 and 98043
Free energy of the bcc-liquid interface and the Wulff shape as predicted by the Phase-Field Crystal model
The Euler-Lagrange equation of the phase-field crystal (PFC) model has been
solved under appropriate boundary conditions to obtain the equilibrium free
energy of the body centered cubic crystal-liquid interface for 18 orientations
at various reduced temperatures in the range .
While the maximum free energy corresponds to the
orientation for all values, the minimum is realized by the direction for small , and by the orientation for higher . The predicted dependence on
the reduced temperature is consistent with the respective mean field critical
exponent. The results are fitted with an eight-term Kubic harmonic series, and
are used to create stereographic plots displaying the anisotropy of the
interface free energy. We have also derived the corresponding Wulff shapes that
vary with increasing from sphere to a polyhedral form that differs
from the rhombo-dodecahedron obtained previously by growing a bcc seed until
reaching equilibrium with the remaining liquid
Faceting and branching in 2D crystal growth
The official published version of the Article can be accessed from the link below - Copyright @ 2011 APSUsing atomic scale time-dependent density functional calculations we confirm that both diffusion-controlled and diffusionless crystallization modes exist in simple 2D systems. We provide theoretical evidence that a faceted to nonfaceted transition is coupled to these crystallization modes, and faceting is governed by the local supersaturation at the fluid-crystalline interface. We also show that competing modes of crystallization have a major influence on mesopattern formation. Irregularly branched and porous structures are emerging at the crossover of the crystallization modes. The proposed branching mechanism differs essentially from dendritic fingering driven by diffusive instability.This work has been supported by the EU FP7
Collaborative Project ENSEMBLE under Grant
Agreement NMP4-SL-2008-213669 and by the
Hungarian Academy of Sciences under Contract
No. OTKA-K-62588
Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility
Wigner functions, allowing for a reformulation of quantum mechanics in phase
space, are of central importance for the study of the quantum-classical
transition. A full understanding of the quantum-classical transition, however,
also requires an explanation for the absence of macroscopic superpositions to
solve the quantum measurement problem. Stochastic reformulations of quantum
mechanics based on spontaneous collapses of the wavefunction are a popular
approach to this issue. In this article, we derive the dynamic equations for
the four most important spontaneous collapse models - Ghirardi-Rimini-Weber
(GRW) theory, continuous spontaneous localization (CSL) model, Di\'osi-Penrose
model, and dissipative GRW model - in the Wigner framework. The resulting
master equations are approximated by Fokker-Planck equations. Moreover, we use
the phase-space form of GRW theory to test, via molecular dynamics simulations,
David Albert's suggestion that the stochasticity induced by spontaneous
collapses is responsible for the emergence of thermodynamic irreversibility.
The simulations show that, for initial conditions leading to anti-thermodynamic
behavior in the classical case, GRW-type perturbations do not lead to
thermodynamic behavior. Consequently, the GRW-based equilibration mechanism
proposed by Albert is not observed.Comment: 22 pages, 2 figure
Thermodynamics, formation dynamics and structural correlations in the bulk amorphous phase of the phase-field crystal model
We investigate bulk thermodynamic and microscopic structural properties of
amorphous solids in the framework of the phase-field crystal (PFC) model. These
are metastable states with a non-uniform density distribution having no
long-range order. From extensive numerical simulations we determine the
distribution of free energy density values in varying size amorphous systems
and also the point-to-set correlation length, which is the radius of the
largest volume of amorphous one can take while still having the particle
arrangements within the volume determined by the particle ordering at the
surface of the chosen volume. We find that in the thermodynamic limit, the free
energy density of the amorphous tends to a value that has a slight dependence
on the initial state from which it was formed -- i.e.\ it has a formation
history dependence. The amorphous phase is observed to form on both sides of
the liquid linear-stability limit, showing that the liquid to amorphous
transition is first order, with an associated finite free energy barrier when
the liquid is metastable. In our simulations this is demonstrated when noise in
the initial density distribution is used to induce nucleation events from the
metastable liquid. Depending on the strength of the initial noise, we observe a
variety of nucleation pathways, in agreement with previous results for the PFC
model, and which show that amorphous precursor mediated multi-step crystal
nucleation can occur in colloidal systems.Comment: 13 pages, 16 figure
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