Darcy's law as long-time limit of adiabatic porous media flow

It is conjectured that Darcy's law governs the motion of compressible porous media flow in large time. This has been justified for one-dimensional isentropic flows. In this work, we show the conjecture is true for one-dimensional adiabatic flows with generic small smooth initial data.     

Ordered K-groups associated to substitutional dynamics

The Matsumoto K₀-group is an interesting invariant of flow equivalence for symbolic dynamical systems. Because of its origin as the K-theory of a certain C^∗-algebra, which is also a flow invariant, this group comes equipped with a flow invariant order structure. We emphasize this order structure and demonstrate how methods from operator algebra and symbolic dynamics combine to allow a computation of it in certain cases, including Sturmian and primitive substitutional shifts. In the latter case we show by example that the ordered group is a strictly finer invariant than the group itself.     

Optical properties and g factors of GaAs quantum rods

The Hamiltonian of the zinc-blende quantum rods in the framework of eight-band effective-mass approximation in the presence of external homogeneous magnetic field is given. The electronic structure, optical properties and electron g factors of GaAs quantum rods are investigated. We found that the electron g factors are very sensitively dependent on the dimensions of the quantum rods. As some of the three dimensions increase, the electron g factors decrease. The more the dimensions increase, the more the electron g factors decrease. The dimensions perpendicular to the direction of the magnetic field affect the electron g factors more than the other dimension.     

Valence bands spin splitting in GaAs/AlGaAs quantum wells

A quantitative comparison between different model calculations of valence band states in GaAs/AlGaAs heterostructures is presented. We demonstrate that a 14-band k.p Hamiltonian using a completely new parameterization based on fits of the tight-binding band structure leads to energy dispersion relations in excellent agreement with experiment, whereas previous parameterizations result in significant deviations. The relevance of the present results to the calculation of spin-related phenomena is discussed.     

Magneto optics of single photons emitted from single InAs/GaAs self-assembled quantum dots in a planar microcavity

We fully characterize the fine spectral structure of neutral and negatively charged single microcavity quantum dot excitons, using polarization-sensitive magneto-photoluminescence spectroscopy. We show that the microcavity allows the simultaneous detection of both the bright and dark excitons using Faraday configuration. Thus, we were able to fully determine the fine structure and the g-factors of the neutral and negatively charged single exciton states within the same single quantum dot. Our measurements are in excellent agreement with novel, many carrier model calculations, which take into account Coulomb and exchange interactions among all the confined e–h pair states.     

Travelling wave solutions for the nonlinear dispersion Drinfel’d–Sokolov () system

In this paper, travelling wave solutions for the nonlinear dispersion Drinfel’d–Sokolov system (called D(m,n) system) are studied by using the Weierstrass elliptic function method. As a result, more new exact travelling wave solutions to the D(m,n) system are obtained including not only all the known solutions found by Xie and Yan but also other more general solutions for different parameters m,n. Moreover, it is also shown that the D(m,1) system with linear dispersion possess compacton and solitary pattern solutions. Besides that, it should be pointed out that the approach is direct and easily carried out without the aid of mathematical software if compared with other traditional methods. We believe that the method can be widely applied to other similar types of nonlinear partial differential equations (PDEs) or systems in mathematical physics.     

具源项的奇异扩散方程解的存在性及渐近性

讨论了一类具源项的奇异扩散方程的第二初边值问题,证明了经典解的存在性以及时间充分大时解的渐近性质.     

Hopscotch method: The numerical solution of the Frank-Kamenetskii partial differential equation

Numerical solutions to the Frank-Kamenetskii partial differential equation modelling a thermal explosion in a cylindrical vessel are obtained using the hopscotch scheme. We observe that a nonlinear source term in the equation leads to numerical difficulty and hence adjust the scheme to accommodate such a term. Numerical solutions obtained via MATLAB, MATHEMATICA and the Crank-Nicolson implicit scheme are employed as a means of comparison. To gain insight into the accuracy of the hopscotch scheme the solution is compared to a power series solution obtained via the Lie group method. The numerical solution is also observed to converge to a well-known steady state solution. A linear stability analysis is performed to validate the stability of the results obtained.     

Independence polynomials of k-tree related graphs

An independent set of a graph G is a set of pairwise non-adjacent vertices. Let α(G) denote the cardinality of a maximum independent set and f_s(G) for 0≤s≤α(G) denote the number of independent sets of s vertices. The independence polynomial defined first by Gutman and Harary has been the focus of considerable research recently. Wingard bounded the coefficients f_s(T) for trees T with n vertices: for s≥2. We generalize this result to bounds for a very large class of graphs, maximal k-degenerate graphs, a class which includes all k-trees. Additionally, we characterize all instances where our bounds are achieved, and determine exactly the independence polynomials of several classes of k-tree related graphs. Our main theorems generalize several related results known before.