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In many practically important problems which rely on particles' transport in realistic corrugated channels, one is interested in knowing the probability that either of the extremities (e.g., the one containing a chemically active site, or connected to a broader channel) is reached before the other one. In mathematical literature, the latter are called the "splitting" probabilities (SPs). Here, within the Fick-Jacobs approach, we study analytically the SPs as functions of system's parameters for dynamics in three-dimensional corrugated channels, confronting standard diffusion and active Brownian motion. Our analysis reveals some similarities in the behavior and also some markedly different features, which can be seen as fingerprints of the activity of particles. [ABSTRACT FROM AUTHOR]

Using scaling arguments and extensive numerical simulations, we study the dynamics of a tracer particle in a corrugated channel represented by a periodic sequence of broad chambers and narrow funnel-like bottlenecks enclosed by a hard-wall boundary. The tracer particle is affected by an external force pointing along the channel, and performs an unbiased diffusion in the perpendicular direction. We present a detailed analysis (a) of the distribution function of the height above the funnel's boundary at which the first crossing of a given bottleneck takes place, and (b) of the distribution function of the first passage time to such an event. Our analysis reveals several new features of the dynamical behaviour that are overlooked in the studies based on the Fick–Jacobs approach. In particular, trajectories passing through a funnel concentrate predominantly on its boundary, which makes first-crossing events very sensitive to the presence of binding sites and microscopic roughness. [ABSTRACT FROM AUTHOR]

We analyze the mean time tapp that a randomly moving particle spends in a bounded domain (sphere) before it escapes through a small window in the domain’s boundary. A particle is assumed to diffuse freely in the bulk until it approaches the surface of the domain where it becomes weakly adsorbed, and then wanders diffusively along the boundary for a random time until it desorbs back to the bulk, etc. Using a mean-field approximation, we define tapp analytically as a function of the bulk and surface diffusion coefficients, the mean time it spends in the bulk between two consecutive arrivals to the surface and the mean time it wanders on the surface within a single round of the surface diffusion. [ABSTRACT FROM AUTHOR]

We study theoretically the effects of spatial confinement on the phoretic motion of a dissolved particle driven by composition gradients generated by chemical reactions of their solvent, which are active only on certain parts of the particle surface. We show that the presence of confining walls increases in a similar way both the composition gradients and the viscous friction, and the overall result of these competing effects is an increase in the phoretic velocity of the particle. For the case of steric repulsion only between the particle and the product molecules of the chemical reactions, the absolute value of the velocity remains nonetheless rather small. [ABSTRACT FROM AUTHOR]

We study the kinetics of diffusion-limited catalytically activated A+B→B reactions taking place in three-dimensional systems, in which an annihilation of diffusive A particles by diffusive traps B may happen only if the encounter of an A with any of the Bs happens within a special catalytic subvolumen: these subvolumens being immobile and uniformly distributed within the reaction bath. Suitably extending the classical approach of Wilemski and Fixman [J. Chem. Phys. 58, 4009 (1973)] to such three-molecular diffusion-limited reactions, we calculate analytically an effective reaction constant and show that it comprises several terms associated with the residence and joint residence times of Brownian paths in finite domains. The effective reaction constant exhibits a nontrivial dependence on the reaction radii, the mean density of catalytic subvolumens, and particles’ diffusion coefficients. Finally, we discuss the fluctuation-induced kinetic behavior in such systems. [ABSTRACT FROM AUTHOR]

For diffusion-limited reversible A+A⇋B reactions we reexamine two fundamental concepts of classical chemical kinetics—the notion of “chemical equilibrium” and the “law of mass action.” We consider a general model with distance-dependent reaction rates, such that any pair of A particles, performing standard random walks on sites of a d-dimensional lattice and being at a distance μ apart of each other at time moment t, may associate forming a B particle at the rate k+(μ). In turn, any randomly moving B particle may spontaneously dissociate at the rate k-(λ) into a geminate pair of As “born” at a distance λ apart of each other. Within a formally exact approach based on Gardiner’s Poisson representation method we show that the asymptotic t=∞ state attained by such diffusion-limited reactions is generally not a true thermodynamic equilibrium, but rather a nonequilibrium steady state, and that the law of mass action is invalid. The classical concepts hold only in case when the ratio k+(μ)/k-(μ) does not depend on μ for any μ. [ABSTRACT FROM AUTHOR]

In the present paper we analyze the kinetics of irreversible A+B→0 reactions in situations appropriate to electrolyte solutions. We consider diffusing species which experience short-range repulsive (attractive) interactions between like (unlike) particles and we highlight the role of fluctuations in the particles’ spatial distributions. We focus mainly on one-dimensional systems and devise a many-particle description of the reaction kinetics. In terms of our analytical approach we show that at intermediate times the interplay between fluctuations and short-ranged interactions gives rise to unusual behaviors, characterized by novel dynamical exponents of the particles’ mean concentrations. For batch reactions at longer times, when the concentrations drop off significantly, the usual fluctuation-induced behavior is recovered. We also analyze systems with external, steady sources of particles and we show that in such situations the effects of the interactions become decisive at long times. Our analytical findings are in good agreement with the results of numerical simulations, which we also present. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We study the direct incoherent energy transfer in systems, in which the molecules involved in the transfer process are attached to ideal (Gaussian) polymers, randomly arranged in a viscous solvent. In what the molecules’ attachment to polymers is concerned we consider two different situations: (a) each polymer chain contains at its opposite ends a donor and an acceptor molecule, (b) the donor molecules are dispersed randomly in the solvent and all acceptors are attached to polymers. In both cases we derive the donors’ decay forms exactly. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this work we report first analytical results on the dynamics and conformational properties of polyampholytes (PAs, polymers containing positive and negative charges) in the presence of external electrical fields. In terms of the Rouse model of polymer dynamics and in the so-called weak coupling limit we obtain for PAs explicitly the mean-square displacement both of the center of mass and of individual beads, and also determine the PAs’ equilibrium end-to-end distance. For a singly charged PA we also relate the findings to a fractional differential equation. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We discuss the influence of transport limitations on the kinetics of homopolymerization reactions. We show that in the systems in which the polymer’s diffusivity decreases faster than the first inverse power of its radius of gyration, the transport limitations represent the rate-controlling step and induce anomalous behavior of the characteristics of the process. For such systems we compute the evolution of the molecular weight distribution and its zeroth moment explicitly. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Examines the kinetic conditions of bimolecular based on catalytically activated reactions (CAR). Identification of elementary reaction act between reactants; Association between CAR and Collins Kimball type idea; Discussion on the characteristics of the catalytic site.

The article focuses on the comparison between the Asian and European stock option. It says that the underlying asset on which the Asian option is based is equal to a stock with price St in the classical Black-Scholes settings. It adds that the payoff in the European-and American-style option is determined by the underlying price at maturity as compared to the Asian option, which is established by the average underlying price over some pre-set period of time.

We study the distribution function P(ω) of the random variable ω = τ,1/(τ1 +…+ τN), where τk's are the partial Wigner delay times for chaotic scattering in a disordered system with N independent, statistically equivalent channels. In this case, τk's are independent and identically distributed random variables with a distribution Ψ(τ) characterized by a "fat" power-law intermediate tail ~1/τ1+μ, truncated by an exponential (or a log-normal) function of τ. For N = 2 and N = 3, we observe a surprisingly rich behavior of P(ω), revealing a breakdown of the symmetry between identical independent channels. For N = 2, numerical simulations of the quasi-one-dimensional Anderson model confirm our findings. [ABSTRACT FROM AUTHOR]

We study an outcome of a vote in a population of voters exposed to an externally applied bias in favour of one of two potential candidates. The population consists of ordinary individuals, that are in majority and tend to align their opinion with the external bias, and some number of contrarians – individuals who are always hostile to the bias but are not in a conflict with ordinary voters. The voters interact among themselves, all with all, trying to find an opinion reached by the community as a whole. We demonstrate that for a sufficiently weak external bias, the opinion of ordinary individuals is always decisive and the outcome of the vote is in favour of the preferential candidate. On the contrary, for an excessively strong bias, the contrarians dominate in the population's opinion, producing overall a negative response to the imposed bias. We also show that for sufficiently strong interactions within the community, either of two subgroups can abruptly change an opinion of the other group. [ABSTRACT FROM AUTHOR]