REFLECTIVE AND QUASI-REFLECTIVE BIANCHI GROUPS

A discrete subgroup of the group of isometries of the hyperbolic space is called reflective if up to a finite index it is generated by reflections in hyperplanes. The main result of this paper is a complete classification of the reflective (and quasi-reflective) subgroups among the Bianchi groups and their extensions.     

Rotational relaxation rates in CO-He mixtures

The rotational level populations of CO molecules were measured in CO(<10%) + He free jets by electron beam fluorescence (in a stationary jet) and resonantly enhanced multiphoton ionization (in a pulsed jet). The measured evolution of the non-equilibrium rotational energy was used to derive the rotational relaxation cross-sections in the temperature range from 6 K to 140 K. To compare and analyse on a common basis all available experimental data (ours and others) on rotational relaxation of CO in He, the infinite order sudden approximation was explored. The following quantities were investigated: integral rotationally inelastic cross-sections, state-to-state rate coefficients, rotational relaxation times, line broadening coefficients, and non-equilibrium rotational energy distributions in a free jet.     

Rotational energy relaxation in CH4 and CH4-He,Ar collisions calculated from coherent and stimulated Raman spectroscopy data

Theoretical treatment of the evolution of the methane Q branch contour with pressure is given in the framework of a quantum model of rotational relaxation with allowance for the tetra-hedral symmetry of rotational levels. The results obtained are compared in detail with available experimental data. As a result, rotational energy relaxation cross-sections for methane and its mixtures with helium and argon have been determined.     

Stochastic Modeling of Congress

We analyze the dynamics of growth of the number of congressmen supporting the resolution HR1207 to audit the Federal Reserve. The plot of the total number of cosponsors as a function of time is of the “Devil's staircase” type. The distribution of the numbers of new cosponsors joining during a particular day (step height) follows a power law. The distribution of the length of intervals between additions of new cosponsors (step length) also follows a power law. We use a modification of Bak-Tang-Wiesenfeld sandpile model to simulate the dynamics of Congress and obtain good agreement with the data.     

𝔾a-ACTIONS ON AFFINE CONES

An affine algebraic variety X is called cylindrical if it contains a principal Zariski dense open cylinder U ? Z × A1. A polarized projective variety (Y, H) is called cylindrical if it contains a cylinder U = Y \ supp D, where D is an effective Q-divisor on Y such that [D] ∈ Q+[H] in PicQ(Y ). We show that cylindricity of a polarized projective variety is equivalent to that of a certain Veronese affine cone over this variety. This gives a criterion of the existence of a unipotent group action on an affine cone.     

SYMMETRIC AND EXTERIOR POWERS OF CATEGORIES

We define symmetric and exterior powers of categories, fitting into categorified Koszul complexes. We discuss examples and calculate the effect of these power operations on the categorical characters of matrix 2-representations.     

Thermal conductivity of nonlinear waves in disordered chains

We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity κ(T). We find indications for an asymptotic low-temperature κ ∼ T ⁴ and intermediate temperature κ ∼ T ² laws. These findings are in accord with theoretical studies of wave packet spreading, where a regime of strong chaos is found to be intermediate, followed by an asymptotic regime of weak chaos (Laptyeva et al, Europhys. Lett. 91, 30001 (2010)).