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

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

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

Ridges and Soft Jet Components in Untriggered Di-hadron Correlations in Pb+Pb Collisions at 2.76 TeV

We study untriggered di-hadron correlations in Pb+Pb at 2.76 TeV, based on an event-by-event simulation of a hydrodynamic expansion starting from flux tube initial conditions. The correlation function shows interesting structures as a function of the pseudorapidity difference $\Delta\eta$ and the azimuthal angle difference $\Delta\phi$, in particular comparing different centralities. We can clearly identify a peak-like nearside structure associated with very low momentum components of jets for peripheral collisions, which disappears towards central collisions. On the other hand, a very broad ridge structure from asymmetric flow seen at central collisions, gets smaller and finally disappears towards peripheral collisions

Bose-Einstein Correlations in a Fluid Dynamical Scenario for Proton-Proton Scattering at 7 TeV

Using a fluid dynamical scenario for $pp$ scattering at 7 TeV, we compute correlation functions for $\pi^+\pi^+$ pairs. Femtoscopic radii are extracted based on three-dimensional parametrizations of the correlation functions. We study the radii as a function of the transverse momenta of the pairs, for different multiplicity classes, corresponding to recent experimental results from ALICE. We find the same decrease of the radii with $k_T$, more and more pronounced with increasing multiplicity, but absent for the lowest multiplicities. In the model we understand this as transition from string expansion (low multiplicity) towards a three-dimensional hydrodynamical expansion (high multiplicity)

Analysis of some localized boundary-domain integral equations for transmission problems with variable coefficients

This is the post-print version of the Article. The official published version can be found at the links below - Copyright @ 2011 Birkhäuser Boston.Some segregated systems of direct localized boundary-domain integral equations (LBDIEs) associated with several transmission problems for scalar PDEs with variable coefficients are formulated and analyzed for a bounded domain composed of two subdomains with a coefficient jump over the interface. The main results established in the paper are the LBDIE equivalence to the original transmission problems and the invertibility of the corresponding localized boundary-domain integral operators in corresponding Sobolev spaces function spaces.This research was supported by the EPSRC grant EP/H020497/1: ”Mathematical analysis of Localized Boundary-Domain Integral Equations for Variable-Coefficient Boundary Value Problems” and partly by the Georgian Technical University grant in the case of the third author

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"

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

Russian comparative embryology takes form: a conceptual metamorphosis toward “evo-devo”

[Abstract] This essay recapitulates major paths followed by the Russian tradition of what we refer to today as evolutionary developmental biology (“evo-devo”). The article addresses several questions regarding the conceptual history of evolutionary embryological thought in its particularly Russian perspective: (1) the assertion by the St. Petersburg academician Wolff regarding the possible connections between environmental modifications during morphogenesis and the “transformation” of species, (2) the discovery of shared “principles” underlying animal development by von Baer, (3) the experimental expression of Baer's principles by Kowalevsky and Mechnikoff, (4) Severtsov's theory of phylembryogenesis, (5) Filatov's approach to the study of evolution using comparative “developmental mechanics”, and (6) Shmalgausen's concept of “stabilizing” selection as an attempt to elucidate the evolution of developmental mechanisms. The focus on comparative evolutionary embryology, which was established by Kowalevsky and Mechnikoff, still continues to be popular in present-day “evo-devo” research in Russia.Ministerio de Ciencia e Innovación; SAF2008-00337Galicia. Consellería de Economía e Industria; 08CSA008161P