Magnetpolaron effect in two-dimensional anisotropic parabolic quantum dot in a perpendicular magnetic field

We study the two-dimensional weak-coupling Frohlich polaron in a completely anisotropic quantum dot in a perpendicular magnetic field. By performing a unitary transformation, we first transform the Hamiltonian into a new one which describes an anisotropic harmonic oscillator with new mass and trapping frequencies interacting with the same phonon bath but with different interaction form and strength. Then employing the second-order Rayleigh–Schrodinger perturbation theory, we obtain the polaron correction to the ground-state energy. The magnetic field and anisotropic effects on the polaron correction to the ground-state energy are discussed.

A REMARK ON THE REGULARITY OF VECTOR-VALUED MAPPINGS DEPENDING ON TWO VARIABLES WHICH MINIMIZE SPLITTING-TYPE VARIATIONAL INTEGRALS

We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u： Ω→^R^N of splitting-type variational integrals provided Ω is a domain in R^2.

Interaction energy of interface dislocation loops in piezoelectric bi-crystals

Interface dislocations may dramatically change the electric properties, such as polarization, of the piezoelectric crystals. In this paper, we study the linear interactions of two interface dislocation loops with arbitrary shape in generally anisotropic piezoelectric bi-crystals. A simple formula for calculating the interaction energy of the interface dislocation loops is derived and given by a double line integral along two closed dislocation curves. Particularly, interactions between two straight segments of the interface dislocations are solved analytically, which can be applied to approximate any curved loop so that an analytical solution can be also achieved. Numerical results show the influence of the bi-crystal interface as well as the material orientation on the interaction of interface dislocation loops.

AN ENERGY-STABLE PARAMETRICFINITE ELEMENT METHOD FOR SIMULATING SOLID-STATE DEWETTING PROBLEMS INTHREE DIMENSIONS

We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space.The model describes the motion of the film/vapor interface with contact line migration and is governed by the surface diffusion equation with proper boundary conditions at the contact line.We present a weak formulation for the problem,in which the contact angle condition is weakly enforced.By using piecewise linear elements in space and backward Euler method in time,we then discretize the formulation to obtain a parametric finite element approximation,where the interface and its contact line are evolved simultaneously.The resulting numerical method is shown to be well-posed and unconditionally energystable.Furthermore,the numerical method is generalized to the case of anisotropic surface energies in the Riemannian metric form.Numerical results are reported to show the convergence and efficiency of the proposed numerical method as well as the anisotropic effects on the morphological evolution of thin films in solid-state dewetting.

A θ-L APPROACH FOR SOLVING SOLID-STATE DEWETTING PROBLEMS

We propose a θ-L approach for solving a sharp-interface model about simulating solid-state dewetting of thin films with isotropic/weakly anisotropic surface energies.The sharp-interface model is governed by surface diffusion and contact line migration.For solving the model,traditional numerical methods usually suffer from the severe stability constraint and/or the mesh distribution trouble.In the θ-L approach,we introduce a useful tangential velocity along the evolving interface and utilize a new set of variables(i.e.,the tangential angle 6 and the total length L of the interface curve),so that it not only could reduce the stiffness resulted from the surface tension,but also could ensure the mesh equidistri-bution property during the evolution.Furthermore,it can achieve second-order accuracy when implemented by a semi-implicit linear finite element method.Numerical results are reported to demonstrate that the proposed θ-L approach is efficient and accurate.