Exact Travelling Wave Solutions of Some Nonlinear Nonlocal Evolutionary Equations

Direct algebraic method of obtaining exact solutions to nonlinear PDE's is applied to certain set of nonlinear nonlocal evolutionary equations, including nonlinear telegraph equation, hyperbolic generalization of Burgers equation and some spatially nonlocal hydrodynamic-type model. Special attention is paid to the construction of the kink-like and soliton-like solutions.Comment: 13 pages, LaTeX2

Analytical description of the coherent structures within the hyperbolic generalization of Burgers equation

We present new periodic, kink-like and soliton-like travelling wave solutions to the hyperbolic generalization of Burgers equation. To obtain them, we employ the classical and generalized symmetry methods and the ansatz-based approachComment: 12 pages, 8 figure

Damage production in atomic displacement cascades in beryllium

AbstractThe paper presents the results of a molecular dynamics simulation of cascade damage production in beryllium caused by self-ion recoils in the energy range of 0.5–3keV. It is demonstrated that point defects are produced in Be preferentially in well-separated subcascades generated by secondary and higher order recoils. A linear dependence of the point defect number on the primary recoil energy is obtained with the slope that corresponds to formal atom displacement energy of ∼21eV. Most of the damage is created as single defects and the relatively high part of created point defects (∼50%) survives the correlated recombination following the ballistic cascade stage and becomes freely-migrating

On the localized wave patterns supported by convection-reaction-diffusion equation

A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary waves within this family for wide range of parameter values

Exact Solution of the Hyperbolic Generalization of Burgers Equation, Describing Travelling Fronts and their Interaction

We present new analytical solutions to the hyperbolic generalization of Burgers equation, describing interaction of the wave fronts. To obtain them, we employ a modified version of the Hirota method.Comment: 12 pages, 3 figure

Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology

We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these wave patterns is carried out by means of our modification of the direct algebraic balance method. In the case when the analytical description fails, we propose to approximate invariant travelling wave solutions by means of an infinite series of exponential functions. The effectiveness of the method of approximation is demonstrated on a hyperbolic modification of Burgers equation

Compacton-like solutions of the hydrodynamic system describing relaxing media

We show the existence of a compacton-like solutions within the relaxing hydrodynamic-type model and perform numerical study of attracting features of these solutions

On the motifs distribution in random hierarchical networks

The distribution of motifs in random hierarchical networks defined by nonsymmetric random block--hierarchical adjacency matrices, is constructed for the first time. According to the classification of U. Alon et al of network superfamilies by their motifs distributions, our artificial directed random hierarchical networks falls into the superfamily of natural networks to which the class of neuron networks belongs. This is the first example of ``handmade'' networks with the motifs distribution as in a special class of natural networks of essential biological importance.Comment: 7 pages, 5 figure

Nuclear emulsion with molybdenum filling for observation of ββ\beta\beta decay

The usage of nuclear emulsion with molybdenum filling for observation of $\beta\beta$ decay are shown to be possible. Estimates for 1 kg of $^{100}$Mo with zero background give the sensitivity for the $0\nu\beta\beta$ decay of $^{100}$Mo at the level of $\sim 1.5\cdot 10^{24}$ y for 1 year of measurement.Comment: 7 pages, 3 figure

Supersymmetric null-surfaces

Single trace operators with the large R-charge in supersymmetric Yang-Mills theory correspond to the null-surfaces in $AdS_5\times S^5$. We argue that the moduli space of the null-surfaces is the space of contours in the super-Grassmanian parametrizing the complex $(2|2)$-dimensional subspaces of the complex $(4|4)$-dimensional space. The odd coordinates on this super-Grassmanian correspond to the fermionic degrees of freedom of the superstring.Comment: v4: added a reference to the earlier work; corrected the formula for the stabilizer of the BMN vacuum; added the discussion of the complex structure of the odd coordinates in Section 3.