Tropical eigenwave and intermediate Jacobians

Tropical manifolds are polyhedral complexes enhanced with certain kind of affine structure. This structure manifests itself through a particular cohomology class which we call the eigenwave of a tropical manifold. Other wave classes of similar type are responsible for deformations of the tropical structure. If a tropical manifold is approximable by a 1-parametric family of complex manifolds then the eigenwave records the monodromy of the family around the tropical limit. With the help of tropical homology and the eigenwave we define tropical intermediate Jacobians which can be viewed as tropical analogs of classical intermediate Jacobians.Comment: 38 pages, 8 figure

Two dimensional periodic box-ball system and its fundamental cycle

We study a 2-dimensional Box-Ball system which is a ultradiscrete analog of the discrete KP equation. We construct an algorithm to calculate the fundamental cycle, which is an important conserved quantity of the 2-dim. Box-Ball system with periodic boundary condition, by using the tropical curve theory.Comment: 16 pages, 5 figure

Enhancement of the Raman lidar sensitivity using overtones of vibrational-rotational Raman bands of oxygen or nitrogen as the reference signals

Influence of the vibrational-rotational Raman bands of molecules of the main components of the atmosphere (oxygen and nitrogen) on the sensitivity of Raman lidar is considered. A method is proposed of using the first overtones of the vibrational-rotational Raman bands of oxygen and nitrogen molecules as the reference signals for the measurement of low concentrations of chemicals in the atmosphere by the Raman method

Mathematical model of a two-stage process of laser fragmentation of nitrocompound molecules and subsequent laser-induced fluorescence of characteristic fragments

The paper presents a mathematical model describing the kinetics of the two-stage process of laser fragmentation of vapors of nitrocompounds and subsequent nitric oxide (NO-fragments) laser-induced fluorescence. The use of the developed model in the lidar equation for the case of fluorescent objects allows to calculate the expected value of the lidar signal for a particular nitrocompound on the basis of spectroscopic information about the object of detection, parameters of the radiation propagation medium, and transceiver equipment parameter

Remote detection of traces of high energetic materials

The possibility of remote detection of traces of high energetic materials using laser fragmentation/laser-induced fluorescence (LF/LIF) method is studied. Experimental data on the remote visualization of traces of trinitrotoluene, hexogen, composition B, octogen, and tetryl obtained at a distance of 5 m with a scanning lidar detector of traces of high energetic materials are presented

Engineering geological characteristics of artificial soils in Kazan city (Russia)

© SGEM 2014. Zoning by type and thickness of artificial soils was conducted in 2012. Following categories of artificial soils were identified : sandy and loamy fill-up soils, sandy hydraulically filled soils, soils from industrial dumps, modern dissimilar fill-up soils, which contain household and construction debris, cultural layer soils. Special attention in this article is given to geological and engineering assessment of heterogeneous fill-up soils and industrial wastes. Our investigations show that these soils are characterized by high chemical and microbiological aggressiveness to underground constructions, which undoubtedly require anti-corrosion actions

Exact analytical solution of the problem of current-carrying states of the Josephson junction in external magnetic fields

The classical problem of the Josephson junction of arbitrary length W in the presence of externally applied magnetic fields (H) and transport currents (J) is reconsidered from the point of view of stability theory. In particular, we derive the complete infinite set of exact analytical solutions for the phase difference that describe the current-carrying states of the junction with arbitrary W and an arbitrary mode of the injection of J. These solutions are parameterized by two natural parameters: the constants of integration. The boundaries of their stability regions in the parametric plane are determined by a corresponding infinite set of exact functional equations. Being mapped to the physical plane (H,J), these boundaries yield the dependence of the critical transport current Jc on H. Contrary to a wide-spread belief, the exact analytical dependence Jc=Jc(H) proves to be multivalued even for arbitrarily small W. What is more, the exact solution reveals the existence of unquantized Josephson vortices carrying fractional flux and located near one of the junction edges, provided that J is sufficiently close to Jc for certain finite values of H. This conclusion (as well as other exact analytical results) is illustrated by a graphical analysis of typical cases.Comment: 21 pages, 9 figures, to be published in Phys. Rev.

The formation of Uranus and Neptune among Jupiter and Saturn

The outer giant planets, Uranus and Neptune, pose a challenge to theories of planet formation. They exist in a region of the Solar System where long dynamical timescales and a low primordial density of material would have conspired to make the formation of such large bodies ($\sim$ 15 and 17 times as massive as the Earth, respectively) very difficult. Previously, we proposed a model which addresses this problem: Instead of forming in the trans-Saturnian region, Uranus and Neptune underwent most of their growth among proto-Jupiter and -Saturn, were scattered outward when Jupiter acquired its massive gas envelope, and subsequently evolved toward their present orbits. We present the results of additional numerical simulations, which further demonstrate that the model readily produces analogues to our Solar System for a wide range of initial conditions. We also find that this mechanism may partly account for the high orbital inclinations observed in the Kuiper belt.Comment: Submitted to AJ; 38 pages, 16 figure