Confinement in bilayer graphene via intra- and inter-layer interactions

We consider confinement of Dirac fermions in AB-stacked bilayer graphene by inhomogeneous on-site interactions, (pseudo-)magnetic field or inter-layer interaction. Working within the framework of four-band approximation, we focus on the systems where the stationary equation is reducible into two stationary equations with 2x2 Dirac-type Hamiltonians and auxiliary interactions. We show that the localized states are given in terms of solutions of an effective Schrodinger equation with energy-dependent potential. We consider several scenarios where bilayer graphene is subject to inhomogneous (pseudo-)magnetic field, on-site interactions or inter-layer coupling. In explicit examples, we provide analytical solutions for the states localized by local fluctuations or periodicity defects of the interactions.

Determination of the bottom scattering coefficient discontinuity lines in the multibeam ocean sounding

In this paper the problems of constructing sonar images of the seabed according to measurements of the multibeam side scan sonar are considered. The inverse problem for the non-stationary equation of radiation transfer with the diffuse reflection conditions at the boundary which consists in finding the discontinuity lines of the bottom scattering coefficient is investigated. A numerical algorithm for solving the inverse problem is developed, and an analysis of the quality of reconstructing the boundaries of inhomogeneities of the seabed is carried out, depending on the number of views and the width of a radiation pattern and the sounding range.

On an Inverse Problem for the Stationary Equation with a Boundary Condition of the Third Type

The identification of an unknown coefficient in the lower term of elliptic second-order differential equation Mu + ku = f with the boundary condition of the third type is considered. The identification of the coefficient is based on integral boundary data. The local existence and uniqueness of the strong solution for the inverse problem is proved

Stationary currents in long-range interacting magnetic systems

We construct a solution for the 1d integro-differential stationary equation derived from a finite-volume version of the mesoscopic model proposed in Giacomin and Lebowitz (J. Stat. Phys. 87(1), 37–61, 1997). This is the continuous limit of an Ising spin chain interacting at long range through Kac potentials, staying in contact at the two edges with reservoirs of fixed magnetizations. The stationary equation of the model is introduced here starting from the Lebowitz-Penrose free energy functional defined on the interval [−ε− 1, ε− 1], ε > 0. Below the critical temperature, and for ε small enough, we obtain a solution that is no longer monotone when opposite in sign, metastable boundary conditions are imposed. Moreover, the mesoscopic current flows along the magnetization gradient. This can be considered as an analytic proof of the existence of diffusion along the concentration gradient in one-component systems undergoing a phase transition, a phenomenon generally known as uphill diffusion. In our proof uniqueness is lacking, and we have clues that the stationary solution obtained is not unique, as suggested by numerical simulations.

OPTIMIZINGAND ADJUSTMENTOF PARAMETER OF THEDISCHARGE OF WASTEWATER SUE "LENOBLVODOKANAL TIKHVIN" ON THE BASIS OF MATHEMATICAL MODELING

The description of the process and treatment facilities GUP "LenoblmolokoTikhvin". A mathematical model of the convective-diffusive transport and transformation of pollutants for the river Tikhvinka in the area of wastewater sue "LenoblmolokoTikhvin". The obtained two-dimensional stationary equation of convective-diffusion transfer of a nonconservative impurity is solved by the finite difference method. According to the developed model, the calculation of the anthropogenic load exerted by the water channel on the Tikhvinkariver was carried out with three variants of the design of the scattering water outlet for the following pollutants: ammonium-ion, nitrate-ion, nitrite-ion and phosphorus total. The maximum concentration of pollutants in the control range and the degree of mixing of pollutants were chosen as criteria for choosing the optimal design. According to the results of mathematical modeling it is shown that the optimal design of the scattering outlet consists of 7 scattering nozzles with a diameter of 200 mm, providing a reduction of the maximum concentrations in the control section by 12% compared to the scattering outlet with 4 drainage pipes.

Linking supernovae and supernova remnants. Time-dependent injection in SN1987A and gamma-ray spectrum of IC443

Acceleration times of particles responsible for the gamma-rays in supernova remnants (SNRs) are comparable with SNR age. If the number of particles starting acceleration was varying during early times after the supernova explosion then this variation should be reflected in the shape of the gamma-ray spectrum. In order to analyse this effect, we consider the time variation of the radio spectral index in SN1987A and solution of the non-stationary equation for particle acceleration. We reconstruct evolution of the particle injection in SN1987A, apply it to derive the particle momentum distribution in IC443 and model its gamma-ray spectrum. We show that: i) observed break in the proton spectrum around 50 GeV in IC443 is a consequence of the variation of the cosmic ray injection; ii) shape of the hadronic gamma-ray spectrum in SNRs critically depends on the temporal variation of the cosmic ray injection in the immediate post explosion phases.

A Few New 2+1-Dimensional Nonlinear Dynamics and the Representation of Riemann Curvature Tensors

We first introduced a linear stationary equation with a quadratic operator in ∂xand ∂y, then a linear evolution equation is given byN-order polynomials of eigenfunctions. As applications, by takingN=2, we derived a (2+1)-dimensional generalized linear heat equation with two constant parameters associative with a symmetric space. When takingN=3, a pair of generalized Kadomtsev-Petviashvili equations with the same eigenvalues with the case ofN=2 are generated. Similarly, a second-order flow associative with a homogeneous space is derived from the integrability condition of the two linear equations, which is a (2+1)-dimensional hyperbolic equation. WhenN=3, the third second flow associative with the homogeneous space is generated, which is a pair of new generalized Kadomtsev-Petviashvili equations. Finally, as an application of a Hermitian symmetric space, we established a pair of spectral problems to obtain a new (2+1)-dimensional generalized Schrödinger equation, which is expressed by the Riemann curvature tensors.