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 COCO Oxidation Oscillations

A cellular automaton model is used to describe the dynamics of the catalytic oxidation of $CO$ on a $Pt(100)$ surface. The cellular automaton rules account for the structural phase transformations of the $Pt$ 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 $CO$ 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