Alexander M. Samsonov

Bio: Alexander M. Samsonov is an academic researcher from Ioffe Institute. The author has contributed to research in topics: Soliton & Longitudinal wave. The author has an hindex of 16, co-authored 70 publications receiving 827 citations. Previous affiliations of Alexander M. Samsonov include Saint Petersburg State Polytechnic University & Russian Academy of Sciences.

Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures

Abstract: We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.

Fission of a longitudinal strain solitary wave in a delaminated bar.

Abstract: The aim of the paper is to show that splitting of a waveguide leads to fission of bulk solitons in solids. We study the dynamics of a longitudinal bulk solitary wave in a delaminated, symmetric layered elastic bar. First, we consider a two-layered bar and assume that there is a perfect interface when x 0 and complete debonding splitting when x 0, where the axis Ox is directed along the bar. We derive the so-called doubly dispersive equation DDE for a long nonlinear longitudinal bulk wave propagating in an elastic bar of rectangular cross section. We formulate the problem for a delaminated two-layered bar in terms of the DDE with piecewise constant coefficients, subject to continuity of longitudinal displacement and normal stress across the “jump” at x=0. We find the weakly nonlinear solution to the problem and consider the case of an incident solitary wave. The solution describes both the reflected and transmitted waves in the far field, as well as the diffraction in the near field in the vicinity of the jump . We generalize the solution to the case of a symmetric n-layered bar. We show that delamination can lead to the fission of an incident solitary wave, and obtain explicit formulas for the number, amplitudes, velocities, and positions of the secondary solitary waves propagating in each layer of the split waveguide. We establish that generally there is a higher-order reflected wave even when the leading order reflected wave is absent.

Longitudinal-strain soliton focusing in a narrowing nonlinearly elastic rod

Abstract: The evolution of a longitudinal-strain solitary wave (a soliton) is studied theoretically and in experiments in a nonlinearly elastic tapered rod. Amplification (focusing) of the soliton is predicted and observed in the rod with decreasing cross section. An asymmetric soliton deformation when focused is observed. An approach is developed to obtain analytical relationships between longitudinal and shear nonlinear strains, and an asymptotic solution to the problem is found, accurately satisfying the boundary conditions on the lateral rod's surface. The explicit relationship is obtained for the soliton amplitude dependence upon the cross section radius' variations of the nonlinearly elastic rod. An allowed interval of soliton velocities is shown to exist that is dependent on elasticity. It was proved in experiments that the elastic strain soliton is not absorbed even at distances much greater than the typical linear dissipation length for linear waves in polystyrene.

Mechanisms of gap gene expression canalization in the Drosophila blastoderm

Abstract: Extensive variation in early gap gene expression in the Drosophila blastoderm is reduced over time because of gap gene cross regulation. This phenomenon is a manifestation of canalization, the ability of an organism to produce a consistent phenotype despite variations in genotype or environment. The canalization of gap gene expression can be understood as arising from the actions of attractors in the gap gene dynamical system. In order to better understand the processes of developmental robustness and canalization in the early Drosophila embryo, we investigated the dynamical effects of varying spatial profiles of Bicoid protein concentration on the formation of the expression border of the gap gene hunchback. At several positions on the anterior-posterior axis of the embryo, we analyzed attractors and their basins of attraction in a dynamical model describing expression of four gap genes with the Bicoid concentration profile accounted as a given input in the model equations. This model was tested against a family of Bicoid gradients obtained from individual embryos. These gradients were normalized by two independent methods, which are based on distinct biological hypotheses and provide different magnitudes for Bicoid spatial variability. We showed how the border formation is dictated by the biological initial conditions (the concentration gradient of maternal Hunchback protein) being attracted to specific attracting sets in a local vicinity of the border. Different types of these attracting sets (point attractors or one dimensional attracting manifolds) define several possible mechanisms of border formation. The hunchback border formation is associated with intersection of the spatial gradient of the maternal Hunchback protein and a boundary between the attraction basins of two different point attractors. We demonstrated how the positional variability for hunchback is related to the corresponding variability of the basin boundaries. The observed reduction in variability of the hunchback gene expression can be accounted for by specific geometrical properties of the basin boundaries. We clarified the mechanisms of gap gene expression canalization in early Drosophila embryos. These mechanisms were specified in the case of hunchback in well defined terms of the dynamical system theory.

Differential Evolution: A Survey of the State-of-the-Art

Abstract: Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Annual Review of Ecology, Evolution and Systematics

Abstract: Twenty-four articles by biologists, ecologists, and other scientists represent a year's progress in the field. Among the topics addressed: the effects of introduced species, paleobiogeography, genetics and geographic structure, marine fisheries management, time as an ecological resource, genetic var

The topology of the regulatory interactions predics the expression pattern of the segment polarity genes in Drosophila melanogaster

Abstract: Expression of the Drosophila segment polarity genes is initiated by a prepattern of pair-rule gene products and maintained by a network of regulatory interactions throughout several stages of embryonic development. Analysis of a model of gene interactions based on differential equations showed that wild-type expression patterns of these genes can be obtained for a wide range of kinetic parameters, which suggests that the steady states are determined by the topology of the network and the type of regulatory interactions between components, not the detailed form of the rate laws. To investigate this, we propose and analyze a Boolean model of this network which is based on a binary ON/OFF representation of transcription and protein levels, and in which the interactions are formulated as logical functions. In this model the spatial and temporal patterns of gene expression are determined by the topology of the network and whether components are present or absent, rather than the absolute levels of the mRNAs and proteins and the functional details of their interactions. The model is able to reproduce the wild type gene expression patterns, as well as the ectopic expression patterns observed in over-expression experiments and various mutants. Furthermore, we compute explicitly all steady states of the network and identify the basin of attraction of each steady state. The model gives important insights into the functioning of the segment polarity gene network, such as the crucial role of the wingless and sloppy paired genes, and the network's ability to correct errors in the prepattern.