Highlighting non-parabolic bands in semiconductors

The parabolic approximation to the dispersion relation is a simplification that has often been adopted for the electronic band structure of most semiconductors near the edges of the fundamental bandgap. A non-parabolic approximation can be justified which will better describe the properties of semiconductors of narrow bandgaps for which a reduction to a quadratic form is not accurate enough, nor always warranted. It also stands for a better approximation in III–V compounds and for more complex thermoelectric materials. Some of the consequences of adopting non-parabolic bands will be highlighted, as well as approximate expressions for statistical properties. It is emphasized that many properties of semiconductors are not difficult to calculate with non-parabolic bands, which may have a wider range of applications in actual materials. These calculations can then be introduced in solid state physics and statistical physics courses through projects and homework problem sets. Specific examples are discussed designed to clarify basic physics concepts in semiconductors.

Calculating Multiple Scattering from a Time-Varying, Undulating Sea Surface Using a Full-Wavefield Multistage Algorithm

The sea surface interface between ocean and air is time varying and can be spatially rough as a result of wind, tides and currents; the shape of this interface changes over time considering the influence of wind, tides, etc. As a result, waves impinging on the sea surface are continuously scattered. In the case of marine seismic, the multiple scattered waves propagate downward into the underwater formation and result in complex seismic responses. To understand the structure of the responses, we propose a multistage algorithm for computing the scattered waves at the sea surface. Specifically, we first extrapolate the upgoing incident waves stepwise using the thin-slab approximation from the scattering theory based on the De Wolf approximation of the Lippmann–Schwinger equation. Then, we implement the air-water boundary condition at the sea surface. Finally, we use the irregular boundary processing technique to compute the time-varying undulating sea-surface scattered waves from different scattering stages. To overcome the angular limitation of the original parabolic approximation, we introduce a multi-directional parabolic approximation based on computational electromagnetics. Numerical tests show that the multistage algorithm presented here can accurately calculate the sea surface scattered waves and should be useful in investigating the structure of marine seismic responses.

Diffusive limits of 2D well-balanced schemes\\for kinetic models of neutron transport

Two-dimensional dissipative and isotropic kinetic models, like the ones used in neutron transport theory, are considered. Especially, steady-states are expressed for constant opacity and damping, allowing to derive a scattering $S$-matrix and corresponding ``truly 2D well-balanced'' numerical schemes. A first scheme is obtained by directly implementing truncated Fourier-Bessel series, whereas another proceeds by applying an exponential modulation to a former, conservative, one. Consistency with the asymptotic damped parabolic approximation is checked for both algorithms. These findings are confirmed by means of practical benchmarks carried out on coarse Cartesian computational grids.

Kinetic solutions for nonlocal stochastic conservation laws

This work is devoted to examining the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal super-critical diffusion operator and a multiplicative noise. Our proof for uniqueness is based upon the analysis on double variables method and the existence is enabled by a parabolic approximation.

Orlicz–Minkowski flows

We study the long-time existence and behavior for a class of anisotropic non-homogeneous Gauss curvature flows whose stationary solutions, if they exist, solve the regular Orlicz–Minkowski problems. As an application, we obtain old and new existence results for the regular even Orlicz–Minkowski problems; the corresponding $$L_p$$ L p version is the even $$L_p$$ L p -Minkowski problem for $$p>-n-1$$ p > - n - 1 . Moreover, employing a parabolic approximation method, we give new proofs of some of the existence results for the general Orlicz–Minkowski problems; the $$L_p$$ L p versions are the even $$L_p$$ L p -Minkowski problem for $$p>0$$ p > 0 and the $$L_p$$ L p -Minkowski problem for $$p>1$$ p > 1 . In the final section, we use a curvature flow with no global term to solve a class of $$L_p$$ L p -Christoffel–Minkowski type problems.

Модельные оценки свойств флюорографена

Green’s function method together with the tight-binding approach are used to get analytical estimations for the electron bands dispersions. The parabolic approximation is proposed which permits to find carriers effective masses and quantum capacitance. With the use of the Koster – Slater and Haldane – Anderson models the problem on the local states of vacancies is considered. Analytical estimates of the specific phonon frequencies and elastic constants are given. The obtained results are compared with the data available.