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

How the asymmetry of internal potential influences the shape of I-V characteristic of nanochannels

Ion transport in biological and synthetic nanochannels is characterized by such phenomena as ion current fluctuations, rectification, and pumping. Recently, it has been shown that the nanofabricated synthetic pores could be considered as analogous to biological channels with respect to their transport characteristics \cite{Apel, Siwy}. The ion current rectification is analyzed. Ion transport through cylindrical nanopores is described by the Smoluchowski equation. The model is considering the symmetric nanopore with asymmetric charge distribution. In this model, the current rectification in asymmetrically charged nanochannels shows a diode-like shape of $I-V$ characteristic. It is shown that this feature may be induced by the coupling between the degree of asymmetry and the depth of internal electric potential well. The role of concentration gradient is discussed

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

Asymptotic behavior of the generalized Becker-D\"oring equations for general initial data

We prove the following asymptotic behavior for solutions to the generalized Becker-D\"oring system for general initial data: under a detailed balance assumption and in situations where density is conserved in time, there is a critical density $\rho_s$ such that solutions with an initial density $\rho_0 \leq \rho_s$ converge strongly to the equilibrium with density $\rho_0$, and solutions with initial density $\rho_0 > \rho_s$ converge (in a weak sense) to the equilibrium with density $\rho_s$. This extends the previous knowledge that this behavior happens under more restrictive conditions on the initial data. The main tool is a new estimate on the tail of solutions with density below the critical density

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

The Effect of the Third Dimension on Rough Surfaces Formed by Sedimenting Particles in Quasi-Two-Dimensions

The roughness exponent of surfaces obtained by dispersing silica spheres into a quasi-two-dimensional cell is examined. The cell consists of two glass plates separated by a gap, which is comparable in size to the diameter of the beads. Previous work has shown that the quasi-one-dimensional surfaces formed have two distinct roughness exponents in two well-defined length scales, which have a crossover length about 1cm. We have studied the effect of changing the gap between the plates to a limit of about twice the diameter of the beads.Comment: 4 pages, 4 figures, submitted to IJMP

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

A Note on the Smoluchowski-Kramers Approximation for the Langevin Equation with Reflection

According to the Smoluchowski-Kramers approximation, the solution of the equation ${\mu}\ddot{q}^{\mu}_t=b(q^{\mu}_t)-\dot{q}^{\mu}_t+{\Sigma}(q^{\mu}_t)\dot{W}_t, q^{\mu}_0=q, \dot{q}^{\mu}_0=p$ converges to the solution of the equation $\dot{q}_t=b(q_t)+{\Sigma}(q_t)\dot{W}_t, q_0=q$ as {\mu}->0. We consider here a similar result for the Langevin process with elastic reflection on the boundary.Comment: 14 pages, 2 figure

Survival probability of a diffusing test particle in a system of coagulating and annihilating random walkers

We calculate the survival probability of a diffusing test particle in an environment of diffusing particles that undergo coagulation at rate lambda_c and annihilation at rate lambda_a. The test particle dies at rate lambda' on coming into contact with the other particles. The survival probability decays algebraically with time as t^{-theta}. The exponent theta in d<2 is calculated using the perturbative renormalization group formalism as an expansion in epsilon=2-d. It is shown to be universal, independent of lambda', and to depend only on delta, the ratio of the diffusion constant of test particles to that of the other particles, and on the ratio lambda_a/lambda_c. In two dimensions we calculate the logarithmic corrections to the power law decay of the survival probability. Surprisingly, the log corrections are non-universal. The one loop answer for theta in one dimension obtained by setting epsilon=1 is compared with existing exact solutions for special values of delta and lambda_a/lambda_c. The analytical results for the logarithmic corrections are verified by Monte Carlo simulations.Comment: 8 pages, 8 figure

The Equilibrium Distribution of Gas Molecules Adsorbed on an Active Surface

We evaluate the exact equilibrium distribution of gas molecules adsorbed on an active surface with an infinite number of attachment sites. Our result is a Poisson distribution having mean $X = {\mu P P_s \over P_e}$, with $\mu$ the mean gas density, $P_s$ the sticking probability, $P_e$ the evaporation probability in a time interval $\tau$, and $P$ Smoluchowski's exit probability in time interval $\tau$ for the surface in question. We then solve for the case of a finite number of attachment sites using the mean field approximation, recovering in this case the Langmuir isotherm.Comment: 14 pages done in late