Reductions of integrable equations on A.III-type symmetric spaces

We study a class of integrable non-linear differential equations related to the A.III-type symmetric spaces. These spaces are realized as factor groups of the form SU(N)/S(U(N-k) x U(k)). We use the Cartan involution corresponding to this symmetric space as an element of the reduction group and restrict generic Lax operators to this symmetric space. The symmetries of the Lax operator are inherited by the fundamental analytic solutions and give a characterization of the corresponding Riemann-Hilbert data.Comment: 14 pages, 1 figure, LaTeX iopart styl

Dynamical clustering in oscillator ensembles with time-dependent interactions

We consider an ensemble of coupled oscillators whose individual states, in addition to the phase, are characterized by an internal variable with autonomous evolution. The time scale of this evolution is different for each oscillator, so that the ensemble is inhomogeneous with respect to the internal variable. Interactions between oscillators depend on this variable and thus vary with time. We show that as the inhomogeneity of time scales in the internal evolution grows, the system undergoes a critical transition between ordered and incoherent states. This transition is mediated by a regime of dynamical clustering, where the ensemble recurrently splits into groups formed by varying subpopulations.Comment: 4 pages, 3 figure

Nonequilibrium pattern formation in chiral Langmuir monolayers with transmembrane flows

Nonequilibrium Langmuir monolayers including a fraction of chiral molecules and subject to transmembrane flow are considered. The flow induces coherent collective precession of chiral molecules. Our theoretical study shows that splay interactions in this system lead to spatial redistribution of chiral molecules and formation of spiral waves and target patterns observed in experiments

From Development To Evolution: The Re-Establishment Of The Alexander Kowalevsky Medal

The Saint Petersburg Society of Naturalists has reinstated the Alexander O. Kowalevsky Medal. This article announces the winners of the first medals and briefly reviews the achievements of A.O. Kowalevsky,the Russian comparative embryologist whose studies on amphioxus, tunicates and germ layer homologies pioneered evolutionary embryology and confirmed the evolutionary continuity between invertebrates and vertebrates. In re-establishing this international award, the Society is pleased to recognize both the present awardees and the memory of Kowalevsky, whose work pointed to that we now call evolutionary developmental biology

Inter-valley plasmons in graphene

The spectrum of two-dimensional (2D) plasma waves in graphene has been recently studied in the Dirac fermion model. We take into account the whole dispersion relation for graphene electrons in the tight binding approximation and the local field effects in the electrodynamic response. Near the wavevectors close to the corners of the hexagon-shaped Brillouin zone we found new low-frequency 2D plasmon modes with a linear spectrum. These "inter-valley" plasmon modes are related to the transitions between the two nearest Dirac cones.Comment: 4 pages, 2 figures; submitted in PR

Design of oscillator networks with enhanced synchronization tolerance against noise

Can synchronization properties of a network of identical oscillators in the presence of noise be improved through appropriate rewiring of its connections? What are the optimal network architectures for a given total number of connections? We address these questions by running the optimization process, using the stochastic Markov Chain Monte Carlo method with replica exchange, to design the networks of phase oscillators with the increased tolerance against noise. As we find, the synchronization of a network, characterized by the Kuramoto order parameter, can be increased up to 40 %, as compared to that of the randomly generated networks, when the optimization is applied. Large ensembles of optimized networks are obtained and their statistical properties are investigated.Comment: 9 pages, 8 figure

Numerics of boundary-domain integral and integro-differential equations for BVP with variable coefficient in 3D

This is the post-print version of the article. The official published version can be accessed from the links below - Copyright @ 2013 Springer-VerlagA numerical implementation of the direct boundary-domain integral and integro-differential equations, BDIDEs, for treatment of the Dirichlet problem for a scalar elliptic PDE with variable coefficient in a three-dimensional domain is discussed. The mesh-based discretisation of the BDIEs with tetrahedron domain elements in conjunction with collocation method leads to a system of linear algebraic equations (discretised BDIE). The involved fully populated matrices are approximated by means of the H-Matrix/adaptive cross approximation technique. Convergence of the method is investigated.This study is partially supported by the EPSRC grant EP/H020497/1:"Mathematical Analysis of Localised-Boundary-Domain Integral Equations for Variable-Coefficients Boundary Value Problems"

Microwave-induced magnetotransport phenomena in two-dimensional electron systems: Importance of electrodynamic effects

We discuss possible origins of recently discovered microwave induced photoresistance oscillations in very-high-electron-mobility two-dimensional electron systems. We show that electrodynamic effects -- the radiative decay, plasma oscillations, and retardation effects, -- are important under the experimental conditions, and that their inclusion in the theory is essential for understanding the discussed and related microwave induced magnetotransport phenomena.Comment: 5 pages, including 2 figures and 1 tabl

History-sensitive accumulation rules for life-time prediction under variable loading

This is the post-print version of the article. The official published version can be obtained from the link below - Copyright @ 2011 SpringerA general form of temporal strength conditions under variable creep loading is employed to formulate several new phenomenological accumulation rules based on the constant-loading durability diagram. Unlike the well-known Robinson rule of linear accumulation of partial life-times, the new rules allow to describe the life-time sensibility to the load sequence, observed in experiments. Comparison of the new rules with experimental data shows that they fit the data much more accurately than the Robinson rule