Development of non-linear finite element computer code

Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows finite element analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional finite element code, TEXLESP-S, which is documented herein

Comment on "Generalized exclusion processes: Transport coefficients"

In a recent paper Arita et al. [Phys. Rev. E 90, 052108 (2014)] consider the transport properties of a class of generalized exclusion processes. Analytical expressions for the transport-diffusion coefficient are derived by ignoring correlations. It is claimed that these expressions become exact in the hydrodynamic limit. In this Comment, we point out that (i) the influence of correlations upon the diffusion does not vanish in the hydrodynamic limit, and (ii) the expressions for the self- and transport diffusion derived by Arita et al. are special cases of results derived in [Phys. Rev. Lett. 111, 110601 (2013)].Comment: (citation added, published version

Diffusion of interacting particles in discrete geometries

We evaluate the self-diffusion and transport diffusion of interacting particles in a discrete geometry consisting of a linear chain of cavities, with interactions within a cavity described by a free-energy function. Exact analytical expressions are obtained in the absence of correlations, showing that the self-diffusion can exceed the transport diffusion if the free-energy function is concave. The effect of correlations is elucidated by comparison with numerical results. Quantitative agreement is obtained with recent experimental data for diffusion in a nanoporous zeolitic imidazolate framework material, ZIF-8.Comment: 5 pages main text (3 figures); 9 pages supplemental material (2 figures). (minor changes, published version

Adsorption and desorption in confined geometries: a discrete hopping model

We study the adsorption and desorption kinetics of interacting particles moving on a one-dimensional lattice. Confinement is introduced by limiting the number of particles on a lattice site. Adsorption and desorption are found to proceed at different rates, and are strongly influenced by the concentration-dependent transport diffusion. Analytical solutions for the transport and self-diffusion are given for systems of length 1 and 2 and for a zero-range process. In the last situation the self- and transport diffusion can be calculated analytically for any length.Comment: Published in EPJ ST volume "Brownian Motion in Confined Geometries

Quantum Gravity Corrections for Schwarzschild Black Holes

We consider the Matrix theory proposal describing eleven-dimensional Schwarzschild black holes. We argue that the Newtonian potential between two black holes receives a genuine long range quantum gravity correction, which is finite and can be computed from the supergravity point of view. The result agrees with Matrix theory up to a numerical factor which we have not computed.Comment: 14 pages, Tex, no figure

Exhaustion of Nucleation in a Closed System

We determine the distribution of cluster sizes that emerges from an initial phase of homogeneous aggregation with conserved total particle density. The physical ingredients behind the predictions are essentially classical: Super-critical nuclei are created at the Zeldovich rate, and before the depletion of monomers is significant, the characteristic cluster size is so large that the clusters undergo diffusion limited growth. Mathematically, the distribution of cluster sizes satisfies an advection PDE in "size-space". During this creation phase, clusters are nucleated and then grow to a size much larger than the critical size, so nucleation of super-critical clusters at the Zeldovich rate is represented by an effective boundary condition at zero size. The advection PDE subject to the effective boundary condition constitutes a "creation signaling problem" for the evolving distribution of cluster sizes during the creation era. Dominant balance arguments applied to the advection signaling problem show that the characteristic time and cluster size of the creation era are exponentially large in the initial free-energy barrier against nucleation, G_*. Specifically, the characteristic time is proportional to exp(2 G_*/ 5 k_B T) and the characteristic number of monomers in a cluster is proportional to exp(3G_*/5 k_B T). The exponentially large characteristic time and cluster size give a-posteriori validation of the mathematical signaling problem. In a short note, Marchenko obtained these exponentials and the numerical pre-factors, 2/5 and 3/5. Our work adds the actual solution of the kinetic model implied by these scalings, and the basis for connection to subsequent stages of the aggregation process after the creation era.Comment: Greatly shortened paper. Section on growth model removed. Added a section analyzing the error in the solution of the integral equation. Added reference

Chiral Zeromodes on Vortex-type Intersecting Heterotic Five-branes

We solve the gaugino Dirac equation on a smeared intersecting five-brane solution in E_8\times E_8 heterotic string theory to search for localized chiral zeromodes on the intersection. The background is chosen to depend on the full two-dimensional overall transverse coordinates to the branes. Under some appropriate boundary conditions, we compute the complete spectrum of zeromodes to find that, among infinite towers of Fourier modes, there exist only three localized normalizable zeromodes, one of which has opposite chirality to the other two. This agrees with the result previously obtained in the domain-wall type solution, supporting the claim that there exists one net chiral zeromode localized on the heterotic five-brane system.Comment: 10 pages, 2 figure