Hugoniót–Maslov Chains for Singular Vortical Solutions to Quasilinear Hyperbolic Systems and Typhoon Trajectory

According to Maslov, many 2D quasilinear systems of PDE possess only three algebras of singular solutions with properties of structural self-similarity and stability. They are the algebras of shock waves, narrow solitons, and square-root point singularities (solitary vortices). Their propagation is described by infinite chains of ODE (the Hugoniót–Maslov chains). We consider the Hugoniót-Maslov chain for the square-root point singularities of the shallow water equations. We discuss different related mathematical questions (in particular, unexpected integrability effects) as well as their possible application to the problem of typhoon dynamics.     

Heat kernel bounds and desingularizing weights

We study the parabolic operator ∂_t−Δ_x+V(t,x), in d?1, with a potential V=V+−V−,V±?0 assumed to be from a parabolic Kato class, and obtain two-sided Gaussian bounds on the associated heat kernel. The constraints on the Kato norms of V⁺ and V⁻ are completely asymmetric, as they should be. Further improvements to our heat kernel bounds are obtained in the case of time-independent potentials.If V has singularities of the type ±c|x|⁻² with a suitably small constant c, we obtain new lower and (sharp) upper weighted heat kernel bounds. The rate of growth of the weights depends (explicitly) on the constant c. The standard bounds and methods (estimates in L^p-spaces without desingularizing weights) fail for singular potentials.     

Manifestation of many-electron correlations in photoionization of the K shell of N2

It is demonstrated theoretically in the random phase approximation (RPA) that due to the intershell many-electron correlations the sigma(*) shape resonance in the photoionization of K shells of the N2 molecule appears not only in the 1sigma(g)-->varepsilonsigma(u) channel as it was believed earlier on the basis of single particle calculations, but in both 1sigma(g)-->varepsilonsigma(u) and 1sigma(u)-->varepsilonsigma(g) channels. As a confirmation of this phenomenon we show that the experimental angular distributions of photoelectrons ejected from fixed-in-space N2 molecules can be reproduced theoretically only after taking into account many-electron correlations.     

Study of dissipative tunneling controllability in systems of interacting quantum molecules

Controlled 2D dissipative tunneling in systems of coupled quantum molecules is studied in the quasi-classical (instanton) approximation. It is shown that, with allowance for the electron tunneling trajectory bifurcation, the effect of two-particle wave function blocking in a system of coupled quantum molecules is observed when the radii of quantum dots (making up the quantum molecules) coincide. If the influence of a thermostat medium is neglected, blocking is replaced by a “kink” in the tunneling probability as a function of the asymmetry parameter of quantum molecules.     

InSb/InAsSb nanostructures for Mid-IR optoelectronics

The technique of preparation of nanostructures with InSb quantum dots in an InAs(Sb) matrix, emitting in the mid-IR range upon optical and injection pumping, by molecular beam epitaxy is considered and the structural and optical properties of these nanostructures are investigated. The characteristics of the first injection lasers based on III–V/II–VI hybrid heterostructures with InSb/InAs(Sb) quantum dots in the active region are reported.     

Ermittlung der Molekulargewichtsverteilung der linearen und verzweigten Polyvinyltrimethylsilane

Ohne Zusammenfassung