In order to evaluate the energy distribution (due to matter and fields including gravitation) associated with a space-time model of Szekeres class I and II metrics, we consider the Einstein, Bergmann-Thomson and LandauLifshitz energy and/or momentum definitions in the tele-parallel gravity (the tetrad theory of gravitation). We find the same energy distribution using Einstein and Bergmann-Thoms...

Suppose that ω ⊂ Ω ⊂ R. In the annular domain A = Ω \ ω̄ we consider the class J of complex valued maps having degree 1 on ∂Ω and ∂ω. It was conjectured in [5] that the existence of minimizers of the Ginzburg-Landau energy Eκ in J is completely determined by the value of the H-capacity cap(A) of the domain and the value of the Ginzburg-Landau parameter κ. The existence of minimizers of Eκ for al...

The rearrangement of the Fermi surface of a homogeneous Fermi system upon approach to a second-order phase transition is studied at zero temperature. The analysis begins with an investigation of solutions of the equation ǫ(p) = μ, a condition that ordinarily has the Fermi momentum pF as a single root. The emergence of a bifurcation point in this equation is found to trigger a qualitative altera...

In a simply connected two dimensional domain Ω, we consider Ginzburg-Landau minimizers u with zero degree Dirichlet boundary condition g ∈ H1/2(∂Ω;S1). We prove uniqueness of u whenever either the energy or the Ginzburg-Landau parameter are small. This generalizes a result of Ye and Zhou requiring smoothness of g. We also obtain uniqueness when Ω is multiply connected and the degrees of the vor...

Let Ω be a 2D simply connected domain, ω be a simply connected subdomain of Ω and set A = Ω\ω. In the annular type domain A, we consider the class J of complex valued maps having degrees 1 on ∂Ω and on ∂ω. We investigate whether the minimum of the Ginzburg-Landau energy Eλ is attained in J , as well as the asymptotic behavior of minimizers as the coherency length λ−1/2 tends to 0. We show that ...

We study the propagation of molecular wave packets through the simplest two types of avoided crossings of electronic energy levels in a limit where the gap between the eigenvalues shrinks as the nuclear masses are increased. For these types of avoided crossings, the electron energy levels essentially depend on only one of the nuclear configuration parameters, as is the case for all diatomic mol...

The photon bremsstrahlung rate from a quark jet produced in deep-inelastic scattering (DIS) off a large nucleus is studied in the collinear limit. The leading medium-enhanced higher twist corrections that describe the multiple scattering of the jet in the nucleus are re-summed to all orders of twist. The propagation of the jet in the absence of further radiative energy loss is shown to be gover...

In this paper, we present the mathematical analysis of a covolume method for the approximations of the Ginzburg–Landau (GL) model for superconductivity. A nice feature of this approach is that the gauge invariance properties are retained in discrete approximations based on triangular grids. We also use properties of discrete vector fields to study issues such as the gauge choices and their enfo...

The objective of this paper is to perform, by means of Γ -convergence and two-scale convergence, a rigorous derivation of the homogenized GIBBS-LANDAU free energy functional associated to a composite periodic ferromagneticmaterial, i.e. a ferromagneticmaterial in which the heterogeneities are periodically distributed inside the media. We thus describe the Γ -limit of the GIBBS-LANDAU free energ...