A class of differentiable toral maps which are topologically mixing

We show that on the 2-torus there exists a open set of regular maps such that every map belonging to is topologically mixing but is not Anosov. It was shown by Mañé that this property fails for the class of toral diffeomorphisms, but that the property does hold for the class of diffeomorphisms on the 3-torus . Recently Bonatti and Diaz proved that the second result of Mañé is also true for the class of diffeomorphisms on the -torus ().

     

Strongly confined semiconductor quantum dots: Pair excitations and optical properties

This paper reviews a microscopic model of basic electron-hole pair excitation processes in strongly confined semiconductor quantum dots (QD) and their influence on the optical QD properties. The effects of valence band mixing, Coulomb interaction, and surface polarization are taken into account. The exciton and biexciton wave functions and energies are obtained using a numerical diagonalization method. The computed optical spectra, such as absorption, gain, pump-probe, and two-photon absorption, agree well with experiments.     

Dynamical chiral-symmetry breaking at T = 0 and T ≠ 0 in the Schwinger-Dyson equation with lattice QCD data

Dynamical chiral-symmetry breaking (DCSB) in QCD is investigated in the Schwinger-Dyson (SD) formalism based on lattice QCD data. From the quenched lattice data for the quark propagator in the Landau gauge, we extract the SD integral kernel function, the product of the quark-gluon vertex and the polarization factor in the gluon propagator, in an Ansatz-independent manner. We find that the SD kernel function exhibits the characteristic behavior of nonperturbative physics, such as infrared vanishing and strong enhancement at the intermediate-energy region around p 0.6GeV. The infrared and intermediate energy region (0.4GeV < p < 1.5GeV) is found to be most relevant for DCSB from analysis on the relation between the SD kernel and the quark mass function. We apply the lattice-QCD-based SD equation to thermal QCD, and calculate the quark mass function at the finite temperature. Spontaneously broken chiral symmetry is found to be restored at high temperature above 110 MeV.     

A model to explain varying Λ, <Emphasis Type="Italic">G</Emphasis> and σ<Superscript>2</Superscript> simultaneously

Models with varying cosmic parameters, which were earlier regarded constant, are getting attention. However, different models are usually invoked to explain the evolution of different parameters. We argue that whatever physical process is responsible for the evolution of one parameter, should also be responsible for the evolution of others. This means that the different parameters are coupled together somehow. Based on this guiding principle, we investigate a Bianchi type I model with variable Λ and G, in which Λ, G and the shear parameter σ², all are coupled. It is interesting that the resulting model reduces to the FLRW model for large t with G approaching a constant.     

Computation of Dispersion in Microstrip Line with Anisotropic Substrate and Overlay

This paper presents an analysis of frequency dependent propagation characteristics of microstrip lines with anisotropic substrate and overlay. The method involves setting up of the Greens functions corresponding to the structure and formulating a dispersion relation in Fourier transform domain. The dispersion relation is constructed in a Galerkins procedure. Numerical results are also presented.     

Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes

In this paper an anisotropic interpolation theorem is presentedthat can be easily used to check the anisotropy of an element.A kind of quasi-Wilson element is considered for second-orderproblems on narrow quadrilateral meshes for which the usualregularity condition _K/h_K c₀ > 0 is not satisfied, whereh_K is the diameter of the element K and _K is the radius of thelargest inscribed circle in K. Anisotropic error estimates ofthe interpolation error and the consistency error in the energynorm and the L²-norm are given. Furthermore, we give a Poincaréinequality on a trapezoid which improves a result of eniek.     

A non-conforming finite element method with anisotropic mesh grading for the Stokes problem in domains with edges

The solution of the Stokes problem in three-dimensional domainswith edges has anisotropic singular behaviour which is treatednumerically by using anisotropic finite element meshes. Thevelocity is approximated by Crouzeix–Raviart (nonconformingP₁ ) elements and the pressure by piecewise constants. Thismethod is stable for general meshes (without minimal or maximalangle condition). Denoting by N_e the number of elements in themesh, the interpolation and consistency errors are of the optimalorder h N_e^–1/3 which is proved for tensor product meshes.As a by-product, we analyse also nonconforming prismatic elementswith P₁ [oplus ] span {x₃²} as the local space for the velocitywhere x₃ is the direction of the edge.     

A posteriori L2 error estimation on anisotropic tetrahedral finite element meshes

A new a posteriori L₂ norm error estimator is proposed for thePoisson equation. The error estimator can be applied to anisotropictetrahedral or triangular finite element meshes. The estimatoris rigorously analysed for Dirichlet and Neumann boundary conditions. The lower error bound relies on specifically designed anisotropicbubble functions and the corresponding inverse inequalities.The upper error bound utilizes non-standard anisotropic interpolationestimates. Its proof requires H² regularity of the Poisson problem,and its quality depends on how good the anisotropic mesh resolvesthe anisotropy of the problem. This is measured by a so-called‘matching function’. A numerical example supports the anisotropic error analysis.     

Average widths of anisotropic Besov-Wiener classes

This paper concerns the problem of average σ-K width and average σ-L width of some anisotropic Besov-Wiener classes Srp q θb(Rd) and Srp q θB(Rd) in Lq(Rd) (1≤q≤p＜∞). The weak asymptotic behavior is established for the corresponding quantities.