546 research outputs found
Mesoscopic Model for Diffusion-Influenced Reaction Dynamics
A hybrid mesoscopic multi-particle collision model is used to study
diffusion-influenced reaction kinetics. The mesoscopic particle dynamics
conserves mass, momentum and energy so that hydrodynamic effects are fully
taken into account. Reactive and non-reactive interactions with catalytic
solute particles are described by full molecular dynamics. Results are
presented for large-scale, three-dimensional simulations to study the influence
of diffusion on the rate constants of the A+CB+C reaction. In the limit of
a dilute solution of catalytic C particles, the simulation results are compared
with diffusion equation approaches for both the irreversible and reversible
reaction cases. Simulation results for systems where the volume fraction of
catalytic spheres is high are also presented, and collective interactions among
reactions on catalytic spheres that introduce volume fraction dependence in the
rate constants are studied.Comment: 9 pages, 5 figure
Decoherence and Quantum-Classical Master Equation Dynamics
The conditions under which quantum-classical Liouville dynamics may be
reduced to a master equation are investigated. Systems that can be partitioned
into a quantum-classical subsystem interacting with a classical bath are
considered. Starting with an exact non-Markovian equation for the diagonal
elements of the density matrix, an evolution equation for the subsystem density
matrix is derived. One contribution to this equation contains the bath average
of a memory kernel that accounts for all coherences in the system. It is shown
to be a rapidly decaying function, motivating a Markovian approximation on this
term in the evolution equation. The resulting subsystem density matrix equation
is still non-Markovian due to the fact that bath degrees of freedom have been
projected out of the dynamics. Provided the computation of non-equilibrium
average values or correlation functions is considered, the non-Markovian
character of this equation can be removed by lifting the equation into the full
phase space of the system. This leads to a trajectory description of the
dynamics where each fictitious trajectory accounts for decoherence due to the
bath degrees of freedom. The results are illustrated by computations of the
rate constant of a model nonadiabatic chemical reaction.Comment: 13 pages, 6 figures, revision includes: Added references on mixed
quantum-classical Liouville theory, and some minor details that address the
comments of the reviewe
Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations
Pattern formation often occurs in spatially extended physical, biological and
chemical systems due to an instability of the homogeneous steady state. The
type of the instability usually prescribes the resulting spatio-temporal
patterns and their characteristic length scales. However, patterns resulting
from the simultaneous occurrence of instabilities cannot be expected to be
simple superposition of the patterns associated with the considered
instabilities. To address this issue we design two simple models composed by
two asymmetrically coupled equations of non-conserved (Swift-Hohenberg
equations) or conserved (Cahn-Hilliard equations) order parameters with
different characteristic wave lengths. The patterns arising in these systems
range from coexisting static patterns of different wavelengths to traveling
waves. A linear stability analysis allows to derive a two parameter phase
diagram for the studied models, in particular revealing for the Swift-Hohenberg
equations a co-dimension two bifurcation point of Turing and wave instability
and a region of coexistence of stationary and traveling patterns. The nonlinear
dynamics of the coupled evolution equations is investigated by performing
accurate numerical simulations. These reveal more complex patterns, ranging
from traveling waves with embedded Turing patterns domains to spatio-temporal
chaos, and a wide hysteretic region, where waves or Turing patterns coexist.
For the coupled Cahn-Hilliard equations the presence of an weak coupling is
sufficient to arrest the coarsening process and to lead to the emergence of
purely periodic patterns. The final states are characterized by domains with a
characteristic length, which diverges logarithmically with the coupling
amplitude.Comment: 9 pages, 10 figures, submitted to Chao
Spot deformation and replication in the two-dimensional Belousov-Zhabotinski reaction in water-in-oil microemulsion
In the limit of large diffusivity ratio, spot-like solutions in the
two-dimensional Belousov-Zhabotinski reaction in water-in-oil microemulsion are
studied. It is shown analytically that such spots undergo an instability as the
diffusivity ratio is decreased. An instability threshold is derived. For spots
of small radius, it is shown that this instability leads to a spot splitting
into precisely two spots. For larger spots, it leads to deformation, fingering
patterns and space-filling curves. Numerical simulations are shown to be in
close agreement with the analytical predictions.Comment: To appear, PR
Renormalized Equilibria of a Schloegl Model Lattice Gas
A lattice gas model for Schloegl's second chemical reaction is described and
analyzed. Because the lattice gas does not obey a semi-detailed-balance
condition, the equilibria are non-Gibbsian. In spite of this, a self-consistent
set of equations for the exact homogeneous equilibria are described, using a
generalized cluster-expansion scheme. These equations are solved in the
two-particle BBGKY approximation, and the results are compared to numerical
experiment. It is found that this approximation describes the equilibria far
more accurately than the Boltzmann approximation. It is also found, however,
that spurious solutions to the equilibrium equations appear which can only be
removed by including effects due to three-particle correlations.Comment: 21 pages, REVTe
Role of an intermediate state in homogeneous nucleation
We explore the role of an intermediate state (phase) in homogeneous
nucleation phenomenon by examining the decay process through a doubly-humped
potential barrier. As a generic model we use the fourth- and sixth-order Landau
potentials and analyze the Fokker-Planck equation for the one-dimensional
thermal diffusion in the system characterized by a triple-well potential. In
the low temperature case we apply the WKB method to the decay process and
obtain the decay rate which is accurate for a wide range of depth and curvature
of the middle well. In the case of a deep middle well, it reduces to a
doubly-humped-barrier counterpart of the Kramers escape rate: the barrier
height and the curvature of an initial well in the Kramers rate are replaced by
the arithmetic mean of higher(or outer) and lower(or inner) partial barriers
and the geometric mean of curvatures of the initial and intermediate wells,
respectively. It seems to be a universal formula. In the case of a
shallow-enough middle well, Kramers escape rate is alternatively evaluated
within the standard framework of the mean-first-passage time problem, which
certainly supports the WKB result. The criteria whether or not the existence of
an intermediate state can enhance the decay rate are revealed.Comment: 9pages, 11figure
Modeling of solvent flow effects in enzyme catalysis under physiological conditions
A stochastic model for the dynamics of enzymatic catalysis in explicit,
effective solvents under physiological conditions is presented.
Analytically-computed first passage time densities of a diffusing particle in a
spherical shell with absorbing boundaries are combined with densities obtained
from explicit simulation to obtain the overall probability density for the
total reaction cycle time of the enzymatic system. The method is used to
investigate the catalytic transfer of a phosphoryl group in a phosphoglycerate
kinase-ADP-bis phosphoglycerate system, one of the steps of glycolysis. The
direct simulation of the enzyme-substrate binding and reaction is carried out
using an elastic network model for the protein, and the solvent motions are
described by multiparticle collision dynamics, which incorporates hydrodynamic
flow effects. Systems where solvent-enzyme coupling occurs through explicit
intermolecular interactions, as well as systems where this coupling is taken
into account by including the protein and substrate in the multiparticle
collision step, are investigated and compared with simulations where
hydrodynamic coupling is absent. It is demonstrated that the flow of solvent
particles around the enzyme facilitates the large-scale hinge motion of the
enzyme with bound substrates, and has a significant impact on the shape of the
probability densities and average time scales of substrate binding for
substrates near the enzyme, the closure of the enzyme after binding, and the
overall time of completion of the cycle.Comment: 15 pages in double column forma
Pattern Formation by Boundary Forcing in Convectively Unstable, Oscillatory Media With and Without Differential Transport
Motivated by recent experiments and models of biological segmentation, we
analyze the exicitation of pattern-forming instabilities of convectively
unstable reaction-diffusion-advection (RDA) systems, occuring by means of
constant or periodic forcing at the upstream boundary. Such boundary-controlled
pattern selection is a generalization of the flow-distributed oscillation (FDO)
mechanism that can include Turing or differential flow instability (DIFI)
modes. Our goal is to clarify the relationships among these mechanisms in the
general case where there is differential flow as well as differential
diffusion. We do so by analyzing the dispersion relation for linear
perturbations and showing how its solutions are affected by differential
transport. We find a close relationship between DIFI and FDO, while the Turing
mechanism gives rise to a distinct set of unstable modes. Finally, we
illustrate the relevance of the dispersion relations using nonlinear
simulations and we discuss the experimental implications of our results.Comment: Revised version with added content (new section and figures added),
changes to wording and organizatio
Surface Structure and Catalytic Oxidation Oscillations
A cellular automaton model is used to describe the dynamics of the catalytic
oxidation of on a surface. The cellular automaton rules account
for the structural phase transformations of the substrate, the reaction
kinetics of the adsorbed phase and diffusion of adsorbed species. The model is
used to explore the spatial structure that underlies the global oscillations
observed in some parameter regimes. The spatiotemporal dynamics varies
significantly within the oscillatory regime and depends on the harmonic or
relaxational character of the global oscillations. Diffusion of adsorbed
plays an important role in the synchronization of the patterns on the substrate
and this effect is also studied.Comment: Latex file with six postscript figures. To appear in Physica
Stress Tensors of Multiparticle Collision Dynamics Fluids
Stress tensors are derived for the multiparticle collision dynamics
algorithm, a particle-based mesoscale simulation method for fluctuating fluids,
resembling those of atomistic or molecular systems. Systems with periodic
boundary conditions as well as fluids confined in a slit are considered. For
every case, two equivalent expressions for the tensor are provided, the
internal stress tensor, which involves all degrees of freedom of a system, and
the external stress, which only includes the interactions with the confining
surfaces. In addition, stress tensors for a system with embedded particles are
determined. Based on the derived stress tensors, analytical expressions are
calculated for the shear viscosity. Simulations illustrate the difference in
fluctuations between the various derived expressions and yield very good
agreement between the numerical results and the analytically derived expression
for the viscosity
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