We have modeled the electric potential profile, across the membranes of the ganglion neuron and neuroblastoma cells. We considered the resting and action potential states, and analyzed the influence of fixed charges of the membrane on the electric potential of the surface of the membranes of these cells, based on experimental values of membrane properties. The ganglion neuron portrays a healthy...

We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space Hn. This enables us to find asymptotic properties of the kernel. Our starting point is the formula for its Fourier transform. When n = 3, 4 or 6 we give an explicit formula for the Poisson kernel itself. In the general case we give various asymptotics and show convergence to the Poi...

We consider a gas in a horizontal slab in which the top and bottom walls are kept at different temperatures. The system is described by the Boltzmann equation (BE) with Maxwellian boundary conditions specifying the wall temperatures. We study the behavior of the system when the Knudsen number e. is small and the temperature difference between the walls as well as the velocity field is of order ...

Let ω(·) = ω(·, x) denote the harmonic measure associated to the Laplace operator and defined with respect to Ω and x ∈ Ω. A classical result concerning the harmonic measure, due to Lavrentiev [22], states that if Ω ⊂ R is a chord arc domain, then ω is mutually absolutely continuous with respect to σ, i.e., dω = kdσ, where k is the associated Poisson kernel. Moreover, Lavrentiev [22] proved tha...

In this paper we consider the Gaussian Besov-Lipschitz B α p,q (γ d) and Gaussian Triebel-Lizorkin F α p,q (γ d) spaces, for any α > 0, studying the inclusion relations among them, proving that the Gaussian Sobolev spaces L p α (γ d) are contained in them, giving some interpolation results and studying the continuity properties of the Ornstein-Uhlenbeck semigroup, the Poisson-Hermite semigroup ...

We prove the uniqueness of the self-similar profile solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard spheres such that, whenever two particles meet, they either annihilate with probability α ∈ (0, 1) or they undergo an elastic collision with probability 1 − α. The existence of a self-similar profile for α smaller...

Higher-order intergrid transfer operators used within cell-centered multigrid can improve the convergence properties of the multigrid method compared to low-order operators. In this thesis those operators are analyzed and incorporated into the LSE (linear systems of equation) module of the waLBerla software framework. The aim is to provide a solver for Poisson and Poisson-Boltzmann partial di e...

We give an overview of the Stein{Chen method for establishing Poisson approximations of various random variables. Couplings of certain variables are used to gives explicit bounds for the total variation distance between the distribution of a random variable and a Poisson variable. Some applications are given. In some cases, explicit couplings may be used to obtain good estimates; in other appli...

1 The Boltzmann equation 6 1.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Physical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Fluid limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Other collis...

We assume a flat brane located at y = 0, surrounded by an AdS space, and consider the 5D Einstein equations when the energy flux component of the energy-momentum tensor is related to the Hubble parameter through a constant Q. We calculate the metric tensor, as well as the Hubble parameter on the brane, when Q is small. As a special case, if the brane is tensionless, the influence from Q on the ...