A nonlocal inhomogeneous dispersal process

AbstractThis article in devoted to the study of the nonlocal dispersal equationut(x,t)=∫RJ(x−yg(y))u(y,t)g(y)dy−u(x,t)in R×[0,∞), and its stationary counterpart. We prove global existence for the initial value problem, and under suitable hypothesis on g and J, we prove that positive bounded stationary solutions exist. We also analyze the asymptotic behavior of the finite mass solutions as t→∞, showing that they converge locally to zero

Origin of conductivity cross over in entangled multi-walled carbon nanotube network filled by iron

A realistic transport model showing the interplay of the hopping transport between the outer shells of iron filled entangled multi-walled carbon nanotubes (MWNT) and the diffusive transport through the inner part of the tubes, as a function of the filling percentage, is developed. This model is based on low-temperature electrical resistivity and magneto-resistance (MR) measurements. The conductivity at low temperatures showed a crossover from Efros-Shklovski (E-S) variable range hopping (VRH) to Mott VRH in 3 dimensions (3D) between the neighboring tubes as the iron weight percentage is increased from 11% to 19% in the MWNTs. The MR in the hopping regime is strongly dependent on temperature as well as magnetic field and shows both positive and negative signs, which are discussed in terms of wave function shrinkage and quantum interference effects, respectively. A further increase of the iron percentage from 19% to 31% gives a conductivity crossover from Mott VRH to 3D weak localization (WL). This change is ascribed to the formation of long iron nanowires at the core of the nanotubes, which yields a long dephasing length (e.g. 30 nm) at the lowest measured temperature. Although the overall transport in this network is described by a 3D WL model, the weak temperature dependence of inelastic scattering length expressed as L_phi ~T^-0.3 suggests the possibility for the presence of one-dimensional channels in the network due to the formation of long Fe nanowires inside the tubes, which might introduce an alignment in the random structure.Comment: 29 pages,10 figures, 2 tables, submitted to Phys. Rev.

Finite to infinite steady state solutions, bifurcations of an integro-differential equation

We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid--solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is varied to examine the transition from an infinite number of steady states to three for the continuum limit of the semi--discretised system. We show how the symmetry of the problem is responsible for the generation and stabilisation of equilibria and comment on the puzzling connection between continuity and stability that exists in this problem

Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem

We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB) equations, i.e. scalar conservation laws with diffusive-dispersive regularization. We review the existence of traveling wave solutions for these two classes of evolution equations. For classical equations the traveling wave problem (TWP) for a local KdVB equation can be identified with the TWP for a reaction-diffusion equation. In this article we study this relationship for these two classes of evolution equations with nonlocal diffusion/dispersion. This connection is especially useful, if the TW equation is not studied directly, but the existence of a TWS is proven using one of the evolution equations instead. Finally, we present three models from fluid dynamics and discuss the TWP via its link to associated reaction-diffusion equations

Pushed traveling fronts in monostable equations with monotone delayed reaction

We study the existence and uniqueness of wavefronts to the scalar reaction-diffusion equations $u_{t}(t,x) = \Delta u(t,x) - u(t,x) + g(u(t-h,x)),$ with monotone delayed reaction term $g: \R_+ \to \R_+$ and $h >0$. We are mostly interested in the situation when the graph of $g$ is not dominated by its tangent line at zero, i.e. when the condition $g(x) \leq g'(0)x,$ $x \geq 0$, is not satisfied. It is well known that, in such a case, a special type of rapidly decreasing wavefronts (pushed fronts) can appear in non-delayed equations (i.e. with $h=0$). One of our main goals here is to establish a similar result for $h>0$. We prove the existence of the minimal speed of propagation, the uniqueness of wavefronts (up to a translation) and describe their asymptotics at $-\infty$. We also present a new uniqueness result for a class of nonlocal lattice equations.Comment: 17 pages, submitte

New species of Mesoplia (Hymenoptera, Apidae) from Mesoamerica.

36 p. : ill. (some col.) ; 26 cm.This paper investigates the bionomics of the cleptoparasitic bee Mesoplia sapphirina Melo and Rocha-Filho, sp. nov. (described in the appendix), and of its ground-nesting host Centris flavofasciata Friese found along the Pacific coast of Guanacaste Province, Costa Rica. We explore the host-nest searching behavior, egg deposition, and hospicidal behavior of M. sapphirina. Anatomical accounts of its egg, first, second, and fifth larval instars are presented and compared with published descriptions of other ericrocidine taxa. Nests of the host bee as well as its egg and method of eclosion are also described