Qualitative properties of pulsating fronts for reaction–advection–diffusion equations in periodic excitable media

In this paper, we study the pulsating fronts of reaction–advection-diffusion equations with two types of nonlinear term in periodic excitable media. Firstly, for the case with combustion nonlinearity, the unique front is proved to decay exponentially when it approaches the unstable limiting state. Secondly, for the degenerate monostable type nonlinearity, it is shown that the front with critical speed is unique, monotone and decays exponentially at negative end, while the fronts of noncritical speeds decay to zero non-exponentially.     

Leray–Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress–strain relation

We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba–Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. We prove the existence of global-in-time weak solutions satisfying an energy inequality under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.     

Spectra of graphs and fractal dimensions II

This paper continues the study of exponentsd(x), d (x), d _R (x) andd (x) for graphG; and the nearest neighbor random walk {X _n } _nN onG, if the starting pointX ₀=x is fixed. These exponents are responsible for the geometric, resistance, diffusion and spectral properties of the graph. The main concern of this paper is the relation of these exponents to the spectral density of the transition matrix. A series of new exponentse, e ,e _R ,e are introduced by allowingx to vary along the vertices. The results suggest that the geometric and resistance properties of the graph are responsible for the diffusion speed on the graph.     

New results for diffusion in Lorentz lattice gas cellular automata

New calculations to over ten million time steps have revealed a more complex diffusive behavior than previously reported of a point particle on a square and triangular lattice randomly occupied by mirror or rotator scatterers. For the square lattice fully occupied by mirrors where extended closed particle orbits occur, anomalous diffusion was still found. However, for a not fully occupied lattice the superdiffusion, first noticed by Owczarek and Prellberg for a particular concentration, obtains for all concentrations. For the square lattice occupied by rotators and the triangular lattice occupied by mirrors or rotators, an absence of diffusion (trapping) was found for all concentrations, except on critical lines, where anomalous diffusion (extended closed orbits) occurs and hyperscaling holds for all closed orbits withuniversal exponentsd _f =7/4 and =15/7. Only one point on these critical lines can be related to a corresponding percolation problem. The questions arise therefore whether the other critical points can be mapped onto a new percolation-like problem and of the dynamical significance of hyperscaling.     

Diffusion on the torus for Hamiltonian maps

For a mapping of the torusT ² we propose a definition of the diffusion coefficientD suggested by the solution of the diffusion equation ofT ². The definition ofD, based on the limit of moments of the invariant measure, depends on the set where an initial uniform distribution is assigned. For the algebraic automorphism of the torus the limit is proved to exist and to have the same value for almost all initial sets in the subfamily of parallelograms. Numerical results show that it has the same value for arbitrary polygons and for arbitrary moments.     

Polymer diffusion in quenched disorder: A renormalization group approach

We study the diffusion of polymers through quenched short-range correlated random media by renormalization group (RG) methods, which allow us to derive universal predictions in the limit of long chains and weak disorder. We take local quenched random potentials with second momentv and the excluded-volume interactionu of the chain segments into account. We show that our model contains the relevant features of polymer diffusion in random media in the RG sense if we focus on the local entropic effects rather than on the topological constraints of a quenched random medium. The dynamic generating functional and the general structure of its perturbation expansion inu andv are derived. The distribution functions for the center-of-mass motion and the internal modes of one chain and for the correlation of the center of mass motions of two chains are calculated to one-loop order. The results allow for sufficient cross-checks to have trust in the one-loop renormalizability of the model. The general structure as well as the one-loop results of the integrated RG flow of the parameters are discussed. Universal results can be found for the effective static interactionwu–v0 and for small effective disorder coupling on the intermediate length scalel. As a first physical prediction from our analysis, we determine the general nonlinear scaling form of the chain diffusion constant and evaluate it explicitly as for .     

An energy-transport model for semiconductors derived from the Boltzmann equation

An energy-transport model is rigorously derived from the Boltzmann transport equation of semiconductors under the hypothesis that the energy gain or loss of the electrons by the phonon collisions is weak. Retaining at leading order electron-electron collisions and elastic collisions (i.e., impurity scattering and the elastic part of phonon collisions), a rigorous diffusion limit of the Boltzmann equation can be carried over, which leads to a set of diffusion equations for the electron density and temperature. The derivation is given in both the degenerate and nondegenerate cases.     

Intradiffusion coefficients in perchloric acid solutions: Water at 5°C; water and perchlorate ion at 25°C

Intradiffusion coefficients for tritiated water (³HHO) and perchlorate ion (³⁶ClO ₄ ^- ) were measured in perchloric acid solutions. At 5°C the diffusion coefficient measured for the tritiated species increases to a maximum near 1.3 mol-dm^–3. The data at 25°C have been used to calculate distinct diffusion coefficients, D _ij ^d . As a precursor for those calculations, new estimates were made of the Onsager phenomenological coefficients, l _ij . The l _ij and D _ij ^d are similar to the respective coefficients in hydrochloric acid solutions.     

不对称合成中手性磷配体催化剂的研究进展（I）（待续）

评述了作为配体催化剂的手性三配位及四配位磷化合物的合成及其在某些不对称的合反应中的应用。     

用环形扩散管和滤纸联用采样技术采集空气中氨和铵盐

建立了环形扩散管和滤纸采样夹联用，分形态同时采集空气中所态氨和颗粒态铵盐的方法。在同一气流中，采用涂渍１．５％草酸乙醇水溶液的环形扩散管采集气态氨，用浸渍上述试剂的玻璃纤维纸和慢速定量滤纸分别采集颗粒安和第一层滤纸上的铵盐挥发产生的氨气。用靛酚蓝比色法分别测定氨和铵盐。当采气流速为１．０Ｌ／ｍｉｎ时，采样效率高于９８．２％。将本法测得的氨气和铵盐的总量与标准采样方法的测定结果比较。无显著性差异（Ｐ