Another characterization of homogeneous Poisson processes

For a general renewal process N (allowing delay, defect and multiple simultaneous arrivals) the independence of the first renewal epochs of the marked processes got from N by Bernoulli 0/1 thinning is characterized. This independence is well-known to hold true in the case of homogeneous Poisson processes; by way of corollary one obtains the interesting observation that, when coupled with some minimal extra conditions, it in fact already identifies them. The proof is analytic in character.     

Probabilistic interpretation of a system of quasilinear parabolic PDEs

Using a forward–backward stochastic differential equations (FBSDE) associated to a transmutation process driven by a finite sequence of Poisson processes, we obtain a probabilistic interpretation for a non-degenerate system of quasilinear parabolic partial differential equations (PDEs). The novetly is that the linear second order differential operator is different on each line of the system.     

Continuous development of schemes for parallel computing of the electrostatics in biological systems: Implementation in DelPhi

Due to the enormous importance of electrostatics in molecular biology, calculating the electrostatic potential and corresponding energies has become a standard computational approach for the study of biomolecules and nano‐objects immersed in water and salt phase or other media. However, the electrostatics of large macromolecules and macromolecular complexes, including nano‐objects, may not be obtainable via explicit methods and even the standard continuum electrostatics methods may not be applicable due to high computational time and memory requirements. Here, we report further development of the parallelization scheme reported in our previous work (Li, et al., J. Comput. Chem. 2012, 33, 1960) to include parallelization of the molecular surface and energy calculations components of the algorithm. The parallelization scheme utilizes different approaches such as space domain parallelization, algorithmic parallelization, multithreading, and task scheduling, depending on the quantity being calculated. This allows for efficient use of the computing resources of the corresponding computer cluster. The parallelization scheme is implemented in the popular software DelPhi and results in speedup of several folds. As a demonstration of the efficiency and capability of this methodology, the electrostatic potential, and electric field distributions are calculated for the bovine mitochondrial supercomplex illustrating their complex topology, which cannot be obtained by modeling the supercomplex components alone. © 2013 Wiley Periodicals, Inc.     

An Approximate Expression for the Degree of Counterion Binding of Dressed Micelles

A simple formula for calculating the degree of counterion binding of dressed micelles is presented. This approximate expression for the spherical micelle is derived from the extending Langmuir's method in the case of high surface potentials. It works quite well for the estimation of the degree of counterion binding of micelles. The simple form is very convenient for practical use.     

Interpolating solutions of the Poisson equation in the disk based on Radon projections

We consider an algebraic method for reconstruction of a function satisfying the Poisson equation with a polynomial right-hand side in the unit disk. The given data, besides the right-hand side, is assumed to be in the form of a finite number of values of Radon projections of the unknown function. We first homogenize the problem by finding a polynomial which satisfies the given Poisson equation. This leads to an interpolation problem for a harmonic function, which we solve in the space of harmonic polynomials using a previously established method. For the special case where the Radon projections are taken along chords that form a regular convex polygon, we extend the error estimates from the harmonic case to this Poisson problem. Finally we give some numerical examples.     

Existence of global weak solutions for Navier‐Stokes‐Poisson equations with quantum effect and convergence to incompressible Navier‐Stokes equations

In this paper, we consider a three dimensional quantum Navier‐Stokes‐Poisson equations. Existence of global weak solutions is obtained, and convergence toward the classical solution of the incompressible Navier‐Stokes equation is rigorously proven for well prepared initial data. Furthermore, the associated convergence rates are also obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

Mathematical model of electromigration allowing the deviation from electroneutrality

The structure of the double layer on the boundary between solid and liquid phases is described by various models, of which the Stern–Gouy–Chapman model is still commonly accepted. Generally, the solid phase is charged, which also causes the distribution of the electric charge in the adjacent diffuse layer in the liquid phase. We propose a new mathematical model of electromigration considering the high deviation from electroneutrality in the diffuse layer of the double layer when the liquid phase is composed of solution of weak multivalent electrolytes of any valence and of any complexity. The mathematical model joins together the Poisson equation, the continuity equation for electric charge, the mass continuity equations, and the modified G-function. The model is able to calculate the volume charge density, electric potential, and concentration profiles of all ionic forms of all electrolytes in the diffuse part of the double layer, which consequently enables to calculate conductivity, pH, and deviation from electroneutrality. The model can easily be implemented into the numerical simulation software such as Comsol. Its outcome is demonstrated by the numerical simulation of the double layer composed of a charged silica surface and an adjacent liquid solution composed of weak multivalent electrolytes. The validity of the model is not limited only to the diffuse part of the double layer but is valid for electromigration of electrolytes in general.     

A Lagrangian for Hamiltonian vector fields on singular Poisson manifolds

On a manifold equipped with a bivector field, we introduce for every Hamiltonian a Lagrangian on paths valued in the cotangent space whose stationary points project onto Hamiltonian vector fields. We show that the remaining components of those stationary points tell whether the bivector field is Poisson or at least defines an integrable distribution—a class of bivector fields generalizing twisted Poisson structures that we study in detail.     

Anisotropic Poisson Effect and Deformation-Induced Fluorescence Change of Elastic 9,10-Dibromoanthracene Single Crystals

Elastic organic crystals have attracted considerable attention as next-generation flexible smart materials. However, the detailed information on both molecular packing change and macroscopic mechanical crystal deformations upon applied stress is still insufficient. Herein, we report that fluorescent single crystals of 9,10-dibromoanthracene are elastically bendable and stretchable, which allows a detailed investigation of the deformation behavior. We clearly observed a Poisson effect for the crystal, where the short axes (b and c-axes) of the crystal are contracted upon elongation along the long axis (a-axis). Moreover, we found that the Poisson's ratios along the b-axis and c-axis are largely different. Theoretical molecular simulation suggests that the tilting motion of the anthracene may be responsible for the large deformation along the c-axis. Spatially resolved photoluminescence (PL) measurement of the bent elastic crystals reveals that the PL spectra at the outer (elongated), central (neutral), and inner (contracted) sides are different from each other.