Diffusion of a Janus nanoparticle in an explicit solvent: A molecular dynamics simulation study

Molecular dynamics simulations are carried out to study the translational and rotational diffusion of a single Janus particle immersed in a dense Lennard-Jones fluid. We consider a spherical particle with two hemispheres of different wettability. The analysis of the particle dynamics is based on the time-dependent orientation tensor, particle displacement, as well as the translational and angular velocity autocorrelation functions. It was found that both translational and rotational diffusion coefficients increase with decreasing surface energy at the nonwetting hemisphere, provided that the wettability of the other hemisphere remains unchanged. We also observed that in contrast to homogeneous particles, the nonwetting hemisphere of the Janus particle tends to rotate in the direction of the displacement vector during the rotational relaxation time.Comment: Web reference added for animations:http://www.wright.edu/~nikolai.priezjev/janus/janus.htm

Weak Disorder in Fibonacci Sequences

We study how weak disorder affects the growth of the Fibonacci series. We introduce a family of stochastic sequences that grow by the normal Fibonacci recursion with probability 1-epsilon, but follow a different recursion rule with a small probability epsilon. We focus on the weak disorder limit and obtain the Lyapunov exponent, that characterizes the typical growth of the sequence elements, using perturbation theory. The limiting distribution for the ratio of consecutive sequence elements is obtained as well. A number of variations to the basic Fibonacci recursion including shift, doubling, and copying are considered.Comment: 4 pages, 2 figure

Cocliques of maximal size in the prime graph of a finite simple group

In this paper we continue our investgation of the prime graph of a finite simple group started in http://arxiv.org/abs/math/0506294 (the printed version appeared in [1]). We describe all cocliques of maximal size for all finite simple groups and also we correct mistakes and misprints from our previous paper. The list of correction is given in Appendix of the present paper.Comment: published version with correction

Infinitesimals without Logic

We introduce the ring of Fermat reals, an extension of the real field containing nilpotent infinitesimals. The construction takes inspiration from Smooth Infinitesimal Analysis (SIA), but provides a powerful theory of actual infinitesimals without any need of a background in mathematical logic. In particular, on the contrary with respect to SIA, which admits models only in intuitionistic logic, the theory of Fermat reals is consistent with classical logic. We face the problem to decide if the product of powers of nilpotent infinitesimals is zero or not, the identity principle for polynomials, the definition and properties of the total order relation. The construction is highly constructive, and every Fermat real admits a clear and order preserving geometrical representation. Using nilpotent infinitesimals, every smooth functions becomes a polynomial because in Taylor's formulas the rest is now zero. Finally, we present several applications to informal classical calculations used in Physics: now all these calculations become rigorous and, at the same time, formally equal to the informal ones. In particular, an interesting rigorous deduction of the wave equation is given, that clarifies how to formalize the approximations tied with Hook's law using this language of nilpotent infinitesimals.Comment: The first part of the preprint is taken directly form arXiv:0907.1872 The second part is new and contains a list of example

Nonlinear Dynamics of Capacitive Charging and Desalination by Porous Electrodes

The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by super-capacitors, water desalination and purification by capacitive deionization (or desalination), and capacitive extraction of renewable energy from a salinity difference. Here, we present a unified mean-field theory for capacitive charging and desalination by ideally polarizable porous electrodes (without Faradaic reactions or specific adsorption of ions) in the limit of thin double layers (compared to typical pore dimensions). We illustrate the theory in the case of a dilute, symmetric, binary electrolyte using the Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae are available for salt adsorption and capacitive charging of the diffuse part of the double layer. We solve the full GCS mean-field theory numerically for realistic parameters in capacitive deionization, and we derive reduced models for two limiting regimes with different time scales: (i) In the "super-capacitor regime" of small voltages and/or early times where the porous electrode acts like a transmission line, governed by a linear diffusion equation for the electrostatic potential, scaled to the RC time of a single pore. (ii) In the "desalination regime" of large voltages and long times, the porous electrode slowly adsorbs neutral salt, governed by coupled, nonlinear diffusion equations for the pore-averaged potential and salt concentration