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

Effects of cluster diffusion on the island density and size distribution in submonolayer island growth

The effects of cluster diffusion on the submonolayer island density and island-size distribution are studied for the case of irreversible growth of compact islands on a 2D substrate. In our model, we assume instantaneous coalescence of circular islands, while the cluster mobility is assumed to exhibit power-law decay as a function of island-size with exponent mu. Results are presented for mu = 1/2, 1, and 3/2 corresponding to cluster diffusion via Brownian motion, correlated evaporation-condensation, and edge-diffusion respectively, as well as for higher values including mu = 2,3, and 6. We also compare our results with those obtained in the limit of no cluster mobility corresponding to mu = infinity. In agreement with theoretical predictions of power-law behavior of the island-size distribution (ISD) for mu < 1, for mu = 1/2 we find Ns({\theta}) ~ s^{-\tau} (where Ns({\theta}) is the number of islands of size s at coverage {\theta}) up to a cross-over island-size S_c. However, the value of {\tau} obtained in our simulations is higher than the mean-field (MF) prediction {\tau} = (3 - mu)/2. Similarly, the value of the exponent {\zeta} corresponding to the dependence of S_c on the average island-size S (e.g. S_c ~ S^{\zeta}) is also significantly higher than the MF prediction {\zeta} = 2/(mu+1). A generalized scaling form for the ISD is also proposed for mu < 1, and using this form excellent scaling is found for mu = 1/2. However, for finite mu >= 1 neither the generalized scaling form nor the standard scaling form Ns({\theta}) = {\theta} /S^2 f(s/S) lead to scaling of the entire ISD for finite values of the ratio R of the monomer diffusion rate to deposition flux. Instead, the scaled ISD becomes more sharply peaked with increasing R and coverage. This is in contrast to models of epitaxial growth with limited cluster mobility for which good scaling occurs over a wide range of coverages.Comment: 12 pages, submitted to Physical Review

Quantum Collapse and the Second Law of Thermodynamics

A heat engine undergoes a cyclic operation while in equilibrium with the net result of conversion of heat into work. Quantum effects such as superposition of states can improve an engine's efficiency by breaking detailed balance, but this improvement comes at a cost due to excess entropy generated from collapse of superpositions on measurement. We quantify these competing facets for a quantum ratchet comprised of an ensemble of pairs of interacting two-level atoms. We suggest that the measurement postulate of quantum mechanics is intricately connected to the second law of thermodynamics. More precisely, if quantum collapse is not inherently random, then the second law of thermodynamics can be violated. Our results challenge the conventional approach of simply quantifying quantum correlations as a thermodynamic work deficit.Comment: 11 pages, 2 figure

Nonequilibrium fluctuations in a resistor

In small systems where relevant energies are comparable to thermal agitation, fluctuations are of the order of average values. In systems in thermodynamical equilibrium, the variance of these fluctuations can be related to the dissipation constant in the system, exploiting the Fluctuation-Dissipation Theorem (FDT). In non-equilibrium steady systems, Fluctuations Theorems (FT) additionally describe symmetry properties of the probability density functions (PDFs) of the fluctuations of injected and dissipated energies. We experimentally probe a model system: an electrical dipole driven out of equilibrium by a small constant current $I$, and show that FT are experimentally accessible and valid. Furthermore, we stress that FT can be used to measure the dissipated power $\bar{\cal P}=RI^2$ in the system by just studying the PDFs symmetries.Comment: Juillet 200

Diffusion, Fragmentation and Coagulation Processes: Analytical and Numerical Results

We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the rate equation exactly leading to size distributions of Bessel type which fall off as $\exp(-x^{3/2})$ for large $x$-values. Moreover, we provide explicit formulas for the expansion coefficients in terms of Airy functions. Introducing the coagulation term, the full non-linear model is mapped exactly onto a Riccati equation that enables us to derive various asymptotic solutions for the distribution function. In particular, we find a standard exponential decay, $\exp(-x)$, for large $x$, and observe a crossover from the Bessel function for intermediate values of $x$. These findings are checked by numerical simulations and we find perfect agreement between the theoretical predictions and numerical results.Comment: (28 pages, 6 figures, v2+v3 minor corrections

Reaction Pathways Based on the Gradient of the Mean First-Passage Time

Finding representative reaction pathways is necessary for understanding mechanisms of molecular processes, but is considered to be extremely challenging. We propose a new method to construct reaction paths based on mean first-passage times. This approach incorporates information of all possible reaction events as well as the effect of temperature. The method is applied to exemplary reactions in a continuous and in a discrete setting. The suggested approach holds great promise for large reaction networks that are completely characterized by the method through a pathway graph.Comment: v2; 4 pages including 5 figure

DNA-Protein Binding Rates: Bending Fluctuation and Hydrodynamic Coupling Effects

We investigate diffusion-limited reactions between a diffusing particle and a target site on a semiflexible polymer, a key factor determining the kinetics of DNA-protein binding and polymerization of cytoskeletal filaments. Our theory focuses on two competing effects: polymer shape fluctuations, which speed up association, and the hydrodynamic coupling between the diffusing particle and the chain, which slows down association. Polymer bending fluctuations are described using a mean field dynamical theory, while the hydrodynamic coupling between polymer and particle is incorporated through a simple heuristic approximation. Both of these we validate through comparison with Brownian dynamics simulations. Neither of the effects has been fully considered before in the biophysical context, and we show they are necessary to form accurate estimates of reaction processes. The association rate depends on the stiffness of the polymer and the particle size, exhibiting a maximum for intermediate persistence length and a minimum for intermediate particle radius. In the parameter range relevant to DNA-protein binding, the rate increase is up to 100% compared to the Smoluchowski result for simple center-of-mass motion. The quantitative predictions made by the theory can be tested experimentally.Comment: 21 pages, 11 figures, 1 tabl

Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes

We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates proportional to their sizes, conserving the total mass. The total number of clusters grows continuously but the full time-dependent distribution can be rescaled over at least 15 decades onto a universal curve which we derive analytically. This curve includes a scale free solution with a scaling exponent of -3/2 for the cluster sizes.Comment: 4 pages, 3 figure

Smoluchowski's equation for cluster exogenous growth

We introduce an extended Smoluchowski equation describing coagulation processes for which clusters of mass s grow between collisions with $ds/dt=As^\beta$. A physical example, dropwise condensation is provided, and its collision kernel K is derived. In the general case, the gelation criterion is determined. Exact solutions are found and scaling solutions are investigated. Finally we show how these results apply to nucleation of discs on a planeComment: Revtex, 4 pages (multicol.sty), 1 eps figures (uses epsfig