Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on Z^3, and square root Klein-Gordon operators on Z^n

Essential spectra of difference operators on \sZ^n-periodic graphs

Let (\cX, \rho) be a discrete metric space. We suppose that the group \sZ^n acts freely on $X$ and that the number of orbits of $X$ with respect to this action is finite. Then we call $X$ a \sZ^n-periodic discrete metric space. We examine the Fredholm property and essential spectra of band-dominated operators on $l^p(X)$ where $X$ is a \sZ^n-periodic discrete metric space. Our approach is based on the theory of band-dominated operators on \sZ^n and their limit operators. In case $X$ is the set of vertices of a combinatorial graph, the graph structure defines a Schr\"{o}dinger operator on $l^p(X)$ in a natural way. We illustrate our approach by determining the essential spectra of Schr\"{o}dinger operators with slowly oscillating potential both on zig-zag and on hexagonal graphs, the latter being related to nano-structures

ПРЕДЕЛЬНЫЕ ПАРАМЕТРЫ АДСОРБЦИОННО-ХИМИЧЕСКОГО ПРЕОБРАЗОВАНИЯ ТЕПЛОВОЙ ЭНЕРГИИ В УСЛОВИЯХ ИДЕАЛЬНОГО ТЕПЛООБМЕНА ВНУТРИ АДСОРБЕРА

The limiting case of operation of an adsorption refrigerator, in which the temperature and concentration are uniform over the cross-section due to a uniform distribution of heat transfer fluid within an adsorber and a high rate of heat exchange between sorbent and heat transfer fluid, is examined. The influence of various parameters on the efficiency of the considered device is investigated and their optimum values are found.Рассмотрен предельный случай работы адсорбционного холодильника, в котором благодаря равномерному распределению теплоносителя внутри адсорбера и высокой скорости теплообмена между теплоносителем и сорбентом достигнута однородность температур и концентраций в поперечном сечении. Исследовано влияние различных параметров на эффективность рассматриваемого устройства и установлены их оптимальные значения

Оптимизация работы адсорбционного холодильника в условиях конденсации/испарения газа в низкотемпературном адсорбенте

The optimization of the adsorption refrigerator in working gas condensation/evaporation into the low-temperature ad-sorber on some operating and design parameters is conducted. The optimum values of these parameters are determined.Проведена оптимизация работы адсорбционного холодильника в условиях конденсации/ испарения рабочего газа в низкотемпературном адсорбере по некоторым режимным и конструктивным параметрам. Определены их оптимальные значения

УСТОЙЧИВОСТЬ ПЛОСКОГО ФРОНТА ФИЛЬТРАЦИОННОГО ГОРЕНИЯ ТВЕРДОГО ТОПЛИВА

Analysis of thermal-hydrodynamic instability of plane filtration combustion front of solid fuel is performed. The boundaries of stable region for co-flow combustion wave are determined by numerical modeling. Possible scenarios of plane combustion front evolution o new steady-state or oscillating structures are investigated. The results are expressed in terms of dimensionless parameters.Проведен анализ тепло-гидродинамической неустойчивости плоского фронта фильтрационного горения твердого топлива. С использованием численного моделирования определены границы области устойчивых режимов для спутных волн горения. Исследованы возможные сценарии перестройки плоского фронта горения в новые стационарные или колебательные структуры. Результаты сформулированы в терминах безразмерных параметров

Thermodynamic aspects of materials' hardness: prediction of novel superhard high-pressure phases

In the present work we have proposed the method that allows one to easily estimate hardness and bulk modulus of known or hypothetical solid phases from the data on Gibbs energy of atomization of the elements and corresponding covalent radii. It has been shown that hardness and bulk moduli of compounds strongly correlate with their thermodynamic and structural properties. The proposed method may be used for a large number of compounds with various types of chemical bonding and structures; moreover, the temperature dependence of hardness may be calculated, that has been performed for diamond and cubic boron nitride. The correctness of this approach has been shown for the recently synthesized superhard diamond-like BC5. It has been predicted that the hypothetical forms of B2O3, diamond-like boron, BCx and COx, which could be synthesized at high pressures and temperatures, should have extreme hardness

Two Scenarios of Breaking Chaotic Phase Synchronization

Two types of phase synchronization (accordingly, two scenarios of breaking phase synchronization) between coupled stochastic oscillators are shown to exist depending on the discrepancy between the control parameters of interacting oscillators, as in the case of classical synchronization of periodic oscillators. If interacting stochastic oscillators are weakly detuned, the phase coherency of the attractors persists when phase synchronization breaks. Conversely, if the control parameters differ considerably, the chaotic attractor becomes phase-incoherent under the conditions of phase synchronization break.Comment: 8 pages, 7 figure

Proper orthogonal decomposition of solar photospheric motions

The spatio-temporal dynamics of the solar photosphere is studied by performing a Proper Orthogonal Decomposition (POD) of line of sight velocity fields computed from high resolution data coming from the MDI/SOHO instrument. Using this technique, we are able to identify and characterize the different dynamical regimes acting in the system. Low frequency oscillations, with frequencies in the range 20-130 microHz, dominate the most energetic POD modes (excluding solar rotation), and are characterized by spatial patterns with typical scales of about 3 Mm. Patterns with larger typical scales of 10 Mm, are associated to p-modes oscillations at frequencies of about 3000 microHz.Comment: 8 figures in jpg in press on PR

Journeying through Dementia: the story of a 14 year design-led research enquiry

Consider a linear ordering equipped with a finite sequence of monadic predicates. If the ordering contains an interval of order type \omega or -\omega, and the monadic second-order theory of the combined structure is decidable, there exists a non-trivial expansion by a further monadic predicate that is still decidable.Comment: 18 page

Spatial representation of temporal information through spike timing dependent plasticity

We suggest a mechanism based on spike time dependent plasticity (STDP) of synapses to store, retrieve and predict temporal sequences. The mechanism is demonstrated in a model system of simplified integrate-and-fire type neurons densely connected by STDP synapses. All synapses are modified according to the so-called normal STDP rule observed in various real biological synapses. After conditioning through repeated input of a limited number of of temporal sequences the system is able to complete the temporal sequence upon receiving the input of a fraction of them. This is an example of effective unsupervised learning in an biologically realistic system. We investigate the dependence of learning success on entrainment time, system size and presence of noise. Possible applications include learning of motor sequences, recognition and prediction of temporal sensory information in the visual as well as the auditory system and late processing in the olfactory system of insects.Comment: 13 pages, 14 figures, completely revised and augmented versio