The Stationary Nonlinear Boltzmann Equation in a Couette Setting with Multiple, Isolated L q -solutions and Hydrodynamic Limits

This paper studies the stationary nonlinear Boltzmann equation for hard forces, in a Couette setting between two coaxial, rotating cylinders with given indata of Maxwellian type on the cylinders. A priori estimates are obtained mainly in L², leading to multiple, isolated solutions together with a hydrodynamic limit control, based on asymptotic expansions together with a rest term.     

New exact solutions of Einstein—Maxwell equations for magnetostatic fields

The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions.     

Growth of large La2−xSrxCuO4 single crystals using tilting-mirror-type infrared heating image furnace

Large single crystals of La_2−xSr_xCuO₄ (LSCO) high-T_c superconductors were grown by the infrared heating floating zone (IR-FZ) method using a tilting-mirror-type image furnace. The maximum diameter of the LSCO crystals increased to 10 mm in the tilting-mirror-type image furnace from 6 mm in the conventional image furnace. CuO rich feeds were required for the crystal growth using the tilting-mirror-type image furnace to compensate for the lack of CuO caused by the significant evaporation of CuO during the growth. The evaporation of CuO was affected by the tilting angle of the mirrors of the image furnace and by feed diameter. The optimized growth conditions were as follows: mirror tilting angle, 20°; feed diameter, 10 mm∅; and feed composition 50.7 mol% CuO.     

Generalized isothermal models with strange equation of state

We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein-Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal Universe. We show that the mass corresponds to the values obtained previously for quark stars when anisotropy and charge are present.      

The Fifth Order Peregrine Breather and Its Eight-Parameter Deformations Solutions of the NLS Equation

We construct here explicitly new deformations of the Peregrine breather of order 5 with 8 real parameters. This gives new families of quasi-rational solutions of the NLS equation and thus one can describe in a more precise way the phenomena of appearance of multi rogue waves. With this method, we construct new patterns of different types of rogue waves. We get at the same time, the triangular configurations as well as rings isolated. Moreover, one sees appearing for certain values of the parameters, new configurations of concentric rings.     

Studying effect of MHD on thin films of a micropolar fluid

This paper deals with the study of the effect of MHD on thin films of a micropolar fluid. These thin films are considered for three different geometries, namely: (i) flow down an inclined plane, (ii) flow on a moving belt and (iii) flow down a vertical cylinder. The transformed boundary layer governing equations of a micropolar fluid and the resulting system of coupled non-linear ordinary differential equations are solved numerically by using shooting method. Numerical results were presented for velocity and micro-rotation profiles within the boundary layer for different parameters of the problem including micropolar fluid parameters, magnetic field parameter, etc., which are also discussed numerically and illustrated graphically.     

Motzkin numbers out of Random Domino Automaton

Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes. It is also a generalisation of 1D Drossel–Schwabl forest-fire model. A solution of the set of equations describing stationary state of Random Domino Automaton in inverse-power case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton.     

Annular billiards with position-dependent mass

We present exact solutions for the position-dependent mass Schrödinger equation (PDMSE) in an annular billiard with impenetrable walls where the mass is allowed to depend on the radial position, i.e., μ=μ(r)$\mu =\mu \left(r\right)$. Exact wavefunctions are calculated explicitly for four mass distributions.     

Symmetry Analysis of Two Types of （2＋1）-Dimensional Nonlinear Klein-Gorden Equation

By means of the classical symmetry method, we investigate two types of the （2＋1）-dimensional nonlinear Klein-Gorden equation. For the wave equation, we give out its symmetry group analysis in detail. For the second type of the （2＋1）-dimensional nonlinear Klein-Gorden equation, an optimal system of its one-dimensional subalgebras is constructed and some corresponding two-dimensional symmetry reductions are obtained.