Raymond Kapral

Chemical waves and patterns

Spiral Waves. Lingering Mysteries about Organizing Centers in the Belousov-Zhabotinsky Medium and its Oregonator Model A. Winfree. Spiral Wave Dynamics S. Muller, T. Plesser. A Theory of Rotating Scroll Waves in Excitable Media J. Tyson, J. Keener. Spiral Waves in Weakly Excitable Media A.S. Mikhailov, V.S. Zykov. Spiral Meandering D. Barkley. Spiral and Target Waves in Finite and Discontinuous Media A.-A. Sepulchre, A. Babloyantz. Turing and Turing-like Patterns. Turing Patterns: from Myth to Reality J. Boissonade, E. Dulos, P. DeKepper. Onset and Beyond Turing Pattern Formation Q. Ouyang, H.L. Swinney. The Chemistry behind the First Experimental Chemical Examples of Turing Patterns I. Lengyel, I.R. Epstein. Turing Bifurcations and Pattern Selection P. Borckmans, G. Dewel, A. De Witt, D. Walgraef. The Differential Flow Instabilities M. Menzinger, A. Rovinsky. Chemical Wave Dynamics. Wave Propagation and Pattern Formation in Nonuniform Reaction-Diffusion Systems A. Zhabotinsky. Chemical Front Propagation: Initiation and Stability E. Mori, X. Chu, J. Ross. Pattern Formation on Catalytic Surfaces M. Eiswirth, G. Ertl. Simple and Complex Reaction-Diffusion Fronts S.K. Scott, K. Showalter. Modeling Front Pattern Formation and Intermittent Bursting Phenomena in the Couette Flow Reactor A. Arneodo, J. Elegaray. Fluctuations and Chemical Waves. Probabilistic Approach to Chemical Instabilities and Chaos G. Nicolis, F. Baras, P. Geysermans, P. Peeters. Internal Noise, Oscillations, Chaos and Chemical Patterns R. Kapral, X.-G. Wu. Index.

Constrained reaction coordinate dynamics for the simulation of rare events

Abstract A computationally efficient molecular dynamics method for estimating the rates of rare events that occur by activated processes is described. The system is constrained at “bottleneck” regions on a general many-body reaction coordinate in order to generate a biased configurational distribution. Suitable reweighting of this biased distribution, along with correct momentum distribution sampling, provides a new ensemble, the constrained-reaction-coordinate-dynamics ensemble, with which to study rare events of this type. Applications to chemical reaction rates are made.

Mesoscopic model for solvent dynamics

Complex fluids such as polymers in solution or multispecies reacting systems in fluid flows often can be studied only by employing a simplified description of the solvent motions. A stochastic model utilizing a synchronous, discrete-time dynamics with continuous velocities and local multiparticle collisions is developed for this purpose. An H theorem is established for the model and the hydrodynamic equations and transport coefficients are derived. The results of simulations are presented which verify the properties of the model and demonstrate its utility as a hydrodynamics medium for the study of complex fluids.

Mixed quantum-classical dynamics

Mixed quantum-classical equations of motion are derived for a quantum subsystem of light (mass m) particles coupled to a classical bath of massive (mass M) particles. The equation of motion follows from a partial Wigner transform over the bath degrees of freedom of the Liouville equation for the full quantum system, followed by an expansion in the small parameter μ=(m/M)1/2 in analogy with the theory of Brownian motion. The resulting mixed quantum-classical Liouville equation accounts for the coupled evolution of the subsystem and bath. The quantum subsystem is represented in an adiabatic (or other) basis and the series solution of the Liouville equation leads to a representation of the dynamics in an ensemble of surface-hopping trajectories. A generalized Pauli master equation for the evolution of the diagonal elements of the density matrix is derived by projection operator methods and its structure is analyzed in terms of surface-hopping trajectories.

Quantum dynamics in open quantum-classical systems

Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.

Solute molecular dynamics in a mesoscale solvent

A hybrid molecular dynamics (MD) algorithm which combines a full MD description of solute–solute and solute–solvent interactions with a mesoscale treatment of solvent-solvent interactions is developed. The solvent dynamics is modeled on a mesoscale level by coarse graining the system into cells and updating the velocities of the solvent molecules by multiparticle collisions within each cell. The solvent dynamics is such that the correct hydrodynamic equations are obtained in the macroscopic limit and a Boltzmann distribution of velocities is established in equilibrium. Discrete-time versions of the hydrodynamic equations and Green–Kubo autocorrelation functions are derived. Between the discrete-time solvent–solvent collisions the system evolves by the classical equations of motion. The hybrid MD scheme is illustrated by an application to the Brownian motion of a nanocolloidal particle in the mesoscale solvent and concentrated nanocolloidal suspensions.

Constrained molecular dynamics and the mean potential for an ion pair in a polar solvent

Abstract A constrained molecular dynamics (MD) method for the calculation of the potential of mean force is described, and applied to study the solvent-separated and contact ion pair equilibrium in a polar solvent. The method uses holonomic constraints on the MD to fix ion pair internuclear separation. The average force exerted on the ions by the solvent is computed as a function of ion separation, and the potential of mean force follows from an integration of the mean force. The ion pair mean potential, the reaction equilibrium constant and the solvent structure in the vicinity of the ions are examined for two model solvents with differing molecular dipole moments. The relevance of this study for the dynamics of the contact ion pair-solvent separated ion pair reaction is pointed out.

Catalytic Nanomotors: Self‐Propelled Sphere Dimers

Experimental and theoretical studies of the self-propelled motional dynamics of a new genre of catalytic sphere dimer, which comprises a non-catalytic silica sphere connected to a catalytic platinum sphere, are reported for the first time. Using aqueous hydrogen peroxide as the fuel to effect catalytic propulsion of the sphere dimers, both quasi-linear and quasi-circular trajectories are observed in the solution phase and analyzed for different dimensions of the platinum component. In addition, well-defined rotational motion of these sphere dimers is observed at the solution-substrate interface. The nature of the interaction between the sphere dimer and the substrate in the aqueous hydrogen peroxide phase is discussed. In computer simulations of the sphere dimer in solution and the solution-substrate interface, sphere-dimer dynamics are simulated using molecular-dynamics methods and solvent dynamics are modeled by mesoscopic multiparticle collision methods taking hydrodynamic interactions into account. The rotational and translational dynamics of the sphere dimer are found to be in good accord with the predictions of computer simulations.

Molecular rotation and reorientation: Microscopic and hydrodynamic contributions

The relative roles of microscopic and hydrodynamic contributions to molecular rotation and reorientation are examined within the framework of the microscopic boundary layer theory recently proposed by the authors. The theory is applied to rough spheres, for which computer simulation data are available and to experimental results on spherical top molecules. Attention is focused on rotational diffusion constants, the kappa parameter introduced by Kivelson et al., and orientational relaxation times. It is shown that, while collective effects are present and often nonnegligible, the motion of small molecules is dominated by its microscopic aspects. Experimental trends which can incorrectly suggest dominance by hydrodynamic contributions are discussed in some detail. Finally, the transition to the regime where collective effects are dominant is considered.

Discrete models for chemically reacting systems

Nonequilibrium spatially distributed chemically reacting systems are usually described in terms of reaction-diffusion equations. In this article, a hierarchy of discrete models is studied that show similar spatio-temporal structure and can be used to explore the complex phenomena occurring in these systems. We consider cellular automaton models where space, time and chemical concentrations are discrete and the dynamics is embodied in a simple updating rule, coupled map lattices where space and time are discrete variables but chemical concentrations are continuous and the dynamics is given by a nonlinear function and, lastly, lattice gas cellular automaton models that view the system on a microscopic or mesoscopic level where space, time and particle velocities are discrete.