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

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

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

Algebraic entropy for semi-discrete equations

We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of integrability for this type of equations

Propagation of small perturbations in synchronized oscillator networks

We study the propagation of a harmonic perturbation of small amplitude on a network of coupled identical phase oscillators prepared in a state of full synchronization. The perturbation is externally applied to a single oscillator, and is transmitted to the other oscillators through coupling. Numerical results and an approximate analytical treatment, valid for random and ordered networks, show that the response of each oscillator is a rather well-defined function of its distance from the oscillator where the external perturbation is applied. For small distances, the system behaves as a dissipative linear medium: the perturbation amplitude decreases exponentially with the distance, while propagating at constant speed. We suggest that the pattern of interactions may be deduced from measurements of the response of individual oscillators to perturbations applied at different nodes of the network