The structure of decomposition of a triconnected graph

We describe the structure of triconnected graph with the help of its decomposition by 3-cutsets. We divide all 3-cutsets of a triconnected graph into rather small groups with a simple structure, named complexes. The detailed description of all complexes is presented. Moreover, we prove that the structure of a hypertree could be introduced on the set of all complexes. This structure gives us a complete description of the relative disposition of the complexes. Keywords: connectivity, triconneted graphs.Comment: 49 pages, 8 figures. Russian version published in Zap. Nauchn. Sem. POMI v.391 (2011), http://www.pdmi.ras.ru/znsl/2011/v391/abs090.htm

Polariton condensation in photonic crystals with high molecular orientation

We study Frenkel exciton-polariton Bose-Einstein condensation in a two-dimensional defect-free triangular photonic crystal with an organic semiconductor active medium containing bound excitons with dipole moments oriented perpendicular to the layers. We find photonic Bloch modes of the structure and consider their strong coupling regime with the excitonic component. Using the Gross- Pitaevskii equation for exciton polaritons and the Boltzmann equation for the external exciton reservoir, we demonstrate the formation of condensate at the points in reciprocal space where photon group velocity equals zero. Further, we demonstrate condensation at non-zero momentum states for TM-polarized photons in the case of a system with incoherent pumping, and show that the condensation threshold varies for different points in the reciprocal space, controlled by detuning.Comment: 6 pages, 4 figure

Local anisotropy and giant enhancement of local electromagnetic fields in fractal aggregates of metal nanoparticles

We have shown within the quasistatic approximation that the giant fluctuations of local electromagnetic field in random fractal aggregates of silver nanospheres are strongly correlated with a local anisotropy factor S which is defined in this paper. The latter is a purely geometrical parameter which characterizes the deviation of local environment of a given nanosphere in an aggregate from spherical symmetry. Therefore, it is possible to predict the sites with anomalously large local fields in an aggregate without explicitly solving the electromagnetic problem. We have also demonstrated that the average (over nanospheres) value of S does not depend noticeably on the fractal dimension D, except when D approaches the trivial limit D=3. In this case, as one can expect, the average local environment becomes spherically symmetrical and S approaches zero. This corresponds to the well-known fact that in trivial aggregates fluctuations of local electromagnetic fields are much weaker than in fractal aggregates. Thus, we find that, within the quasistatics, the large-scale geometry does not have a significant impact on local electromagnetic responses in nanoaggregates in a wide range of fractal dimensions. However, this prediction is expected to be not correct in aggregates which are sufficiently large for the intermediate- and radiation-zone interaction of individual nanospheres to become important.Comment: 9 pages 9 figures. No revisions from previous version; only figure layout is change

Semiorthogonal decompositions of derived categories of equivariant coherent sheaves

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of bounded derived category of G-equivariant coherent sheaves on X into components, equivalent to derived categories of twisted representations of the group. If the group is finite or reductive over the algebraically closed field of zero characteristic, this gives a full exceptional collection in the derived equivariant category. We apply our results to particular varieties such as projective spaces, quadrics, Grassmanians and Del Pezzo surfaces.Comment: 28 pages, uses XY-pi

The role of localization in glasses and supercooled liquids

This is the publisher's version, also available electronically from http://scitation.aip.org/content/aip/journal/jcp/104/13/10.1063/1.471147.Localized excitations (tunneling modes, soft harmonic vibrations) are believed to play a dominant role in the thermodynamics and transport properties of glasses at low temperature. Using instantaneous normal‐mode (INM) analysis, we explore the role that such localization plays in determining the behavior of such systems in the vicinity of the glass transition. Building on our previous study [Phys. Rev. Lett. 74, 936 (1995)] we present evidence that the glass transition in two simple model systems is associated with a transition temperature below which all un‐ stable INM’s become localized. This localization transition is a possible mechanism for the change in diffusion mechanism from continuous flow to localized hopping that is believed to occur in fragile glass formers at a temperature just above T g