The <Emphasis Type="Bold">±</Emphasis><Emphasis Type="Bold">J</Emphasis> spin glass in Migdal-Kadanoff approximation

We study the low-temperature phase of the three-dimensional ± J Ising spin glass in Migdal-Kadanoff approximation. At zero temperature, T = 0, the properties of the spin glass result from the ground-state degeneracy and can be elucidated using scaling arguments based on entropy. The approach to the asymptotic scaling regime is very slow, and the correct exponents are only visible beyond system sizes around 64. At T > 0, a crossover from the zero-temperature behaviour to the behaviour expected from the droplet picture occurs at length scales proportional to T ^-2/ds where d_s is the fractal dimension of a domain wall. Canonical droplet behaviour is not visible at any temperature for systems whose linear dimension is smaller than 16 lattice spacings, because the data are either affected by the zero-temperature behaviour or the critical point behaviour. Received 18 February 2001     

Darboux First Integral Conditions and Integrability of the 3D Lotka-Volterra System

Abstract

We apply the Darboux theory of integrability to polynomial ODE’s of dimension 3. Using this theory and computer algebra, we study the existence of first integrals for the 3–dimensional Lotka–Volterra systems with polynomial invariant algebraic solutions linear and quadratic and determine numerous cases of integrability.     

Diluted generalized random energy model

A layered random spin model, equivalent to the generalized random energy model (GREM), is introduced. In analogy with diluted spin systems, a diluted GREM (DGREM) is constructed. It can be applied to calculate approximately the thermodynamic properties of spin glass models in low dimensions. For the Edwards-Anderson model it gives the correct critical dimension and 5% accuracy for the ground state energy in two dimensions. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 6, 415–419 (25 March 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Improved analysis of dispersion compensation using differential time delay for high-speed long-span optical link

Abstract

A dispersion-compensation technique using differential time delay has been analyzed for a high bit rate dispersive limited system using higher order dispersion terms. The technique is based on splitting the power spectrum into upper and lower parts, corresponding to the two modulation sidebands, and delaying one of these with respect to the other. RMS, phase deviation, dimension free chirp parameter, and figure of merit have been evaluated due to higher order dispersion terms for ideal and realistic optical communication systems. It has been shown that the transmission distance could be enhanced to fourfold, sixfold, and eightfold when the compensation has been performed using second-, third-, and fourth-order dispersion (20D, 30D, and 40D) terms.     

Lateral transport in quasiperiodically ordered layered media with isotropic randomness

Abstract

We investigate the lateral wave transport in quasiperiodically ordered layer media with isotropic randomness. As an example, we consider the case of the Fibonacci sequence and study the ergodic properties in such systems. From the results of the channel occupation number of nine generations, we find that the wave transport in such systems falls between the transport of anisotropic hopping systems and that of randomly layered media and can be associated with a fractal dimension that can be tuned according to the strength of the layer coupling. The origin of this fractal dimensionality is attributed to the interplay between the quasiperiodic ordering in the layer direction and the presence of isotropic randomness in the system.     

Theory of one-dimensional and quasi-one-dimensional heat conduction

It is shown that the heat conduction process in a one-dimensional flow of a fluid moving with a velocity V in a constant temperature field follows a law that is considerably more complicated than an “ordinary” exponential law. It is demonstrated that in the quasi-one-dimensional case the heat conduction process in an abstract space of dimension 1+ɛ, where ɛ varies from zero to unity, is described by a modified Fourier equation. Its solution for an infinite space is found. Zh. Tekh. Fiz. 67, 8–12 (July 1997)     

Analysis of fractals with dependent branching by box counting, P-adic coverages, and systems of equations of P-adic coverages

Concept of the dimension of space-time in the general relativity theory and quantum theory is discussed. It is emphasized that the dimension of a discrete space can be defined based on the Hausdorff measure. The noninteger dimension is a typical characteristic of a fractal. The process of hadron formation in interactions between high-energy particles and nuclei is supposed to possess fractal properties. The following methods for analyzing fractals are considered: box counting (BC), method of P-adic coverages (PaC), and method of systems of equations of P-adic coverages (SePaC), for determining the fractal dimension. A comparative analysis of fractals with dependent branching is performed using these methods. We determine the optimum values of parameters permitting one to determine the fractal dimension D _F , number of levels N _lev, and the fractal structure with maximal efficiency. It is noted that the SePaC method has advantages in analyzing fractals with dependent branching.     

On the similarity of the sensitivity functions of methane combustion models

It is widely known that detailed kinetic mechanisms with identical reaction steps but with very different rate parameters may provide similar simulation results in combustion calculations. This phenomenon is related to the similarity of sensitivity functions, which arises if low-dimensional manifolds in the space of variables, and autocatalytic processes are present. We demonstrated the similarity of sensitivity functions for adiabatic explosions and burner-stabilized laminar flames of stoichiometric methane–air mixtures. The cause of similarities was investigated by calculating the dimension of the corresponding manifolds, and the pseudo-homogeneous property of the sensitivity ordinary differential equation (ODE). The methane explosion model showed global similarity, which means that different parameter sets could provide the same simulation results. This was demonstrated by numerical experiments, in which two significantly different parameter sets resulted in identical concentration profiles for all species. This phenomenon is important from a practical point of view in the fields of ‘validation’ of complex reaction mechanisms and parameter estimation of chemical kinetic systems.     

Four-Wave Mixing in Microwires to All-Optical Signal Processing in Mode-Division Multiplexing Systems

Abstract

Mode-division multiplexing requires all-optical signal processing techniques that are able to deal with a new coding dimension, the spatial mode. In this context, optical microwires emerge as a potential highly non-linear and multi-modal waveguide envisioning the development of all-optical signal processing devices to mode-division multiplexing systems based on the four-wave mixing process. The inter- and intramodal phase-matching conditions for the four-wave mixing process are mapped as a function of the microwire diameter and the wavelength of signals. Moreover, the efficiency of four-wave mixing considering a strong guiding regime is investigated in the multi-modal regime.     

Degenerate Integrability of the Spin Calogero–Moser Systems and the Duality with the Spin Ruijsenaars Systems

It is shown that spin Calogero–Moser systems are completely integrable in a sense of degenerate integrability. Their Liouville tori have dimension less than half of the dimension of the phase space. It is also shown that rational spin Ruijsenaars systems are degenerately integrable and dual to spin Calogero–Moser systems in a sense that action-angle variables of one are angle-action variables of the other.     

How to test for diagonalizability: the discretized PT-invariant square-well potential

Given a non-Hermitian matrix M, the structure of its minimal polynomial encodes whether M is diagonalizable or not. This note explains how to determine the minimal polynomial of a matrix without going through its characteristic polynomial. The approach is applied to a quantum mechanical particle moving in a square well under the influence of a piece-wise constant PT-symmetric potential. Upon discretizing the configuration space, the system is described by a matrix of dimension three which turns out not to be diagonalizable for a critical strength of the interaction. The systems develops a three-fold degenerate eigenvalue, and two of the three eigenfunctions disappear at this exceptional point, giving a difference between the algebraic and geometric multiplicity of the eigenvalue equal to two. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Gas pressure cell for electroluminescence and photoconductivity measurements

Abstract

High-pressure studies of electroluminescence and photoconductivity are commonly carried out using liquid pressure systems. The wider application of a gas pressure system (with its substantial advantages) in this kind of studies is limited by the difficulties in the construction of a suitable sample cell. Such a cell, in addition to electric and optical access, must be provided with a high-pressure inlet, and the overall dimension of the cell should allow it to fit most standard cryostats. In this paper a high gas pressure optical cell is described which enables electroluminescence or photoconductivity measurements at pressures up to 1.0 GPa and at temperatures down to 1K.     

Generalized Physical and SRB Measures for Hyperbolic Diffeomorphisms

In this paper we introduce the notion of generalized physical and SRB measures. These measures naturally generalize classical physical and SRB measures to measures which are supported on invariant sets that are not necessarily attractors. We then perform a detailed case study of these measures for hyperbolic Hènon maps. For this class of systems we are able to develop a complete theory about the existence, uniqueness, finiteness, and properties of these natural measures. Moreover, we derive a classification for the existence of a measure of full dimension. We also consider general hyperbolic surface diffeomorphisms and discuss possible extensions of, as well as the differences to, the results for Hènon maps. Finally, we study the regular dependence of the dimension of the generalized physical/SRB measure on the diffeomorphism. For the proofs we apply various techniques from smooth ergodic theory including the thermodynamic formalism. 2000 Mathematics Subject Classification. Primary: 37C45, 37D20, 37D35, Secondary: 37A35, 37E30     

Modification of the theory of diffracted channeling radiation for axial electron and positron channeling

A new type of combinational channeling radiation induced by subbarrier (interband) transitions for the transverse motion of relativistic electrons (positrons) is studied. It is known as diffracted channeling radiation (DCR). The formula describing the DCR angular distribution in the case of axial channeling is obtained by taking into account the band structure of energy levels for the transverse motion of electrons (positrons). It is shown that, in the two-wave approximation of the wave function A(r) of virtual photons, the DCR matrix elements in the dipole approximation for axial and plane channeling coincide formally (with the dimension of the problem taken into account). However, the formulas for DCR angular distributions in the cases of axial and plane channeling differ considerably.     

Growth of piezoelectric quartz crystals of large dimension on seeds parallel to the (10–11) face and lengthened along the Y-axis

Abstract

We have grown crystals on seeds parallel to the side of the negative rhombohedron by the hydrothermal method. Their dimension was equal to the projection one along the Y-axis to the plane (01–11) and approximately exceeded the size of the crystal along the X-axis by one order. In Russia these crystals are referred to as - ry′. The maximal sizes of ry′ -cryszals are 410mm and 120mm along the Y- and X-axes, respectively. It is established that each crystal increases its dimension along the X-axis due to the formation of the sides of the sharpest rhombohedron (20–21). These faces form the pyramids of growth by which it is possible to get the plates from an average part of each crystal. Their dimension exceeds the initial one by 15-20mm along the X-axis. We have studied the structural and morphological properties of ry′ -crystals grown at different rates at the temperature of crystallization of 330-410°C and a pressure up to 150 MPa.     

Second virial coefficient in one dimension as a function of asymptotic quantities

A result from Dodd and Gibbs (J. Math. Phys., 15, 41 (1974)) for the second virial coefficient of particles in one dimension, subject to delta-function interactions, has been obtained by direct integration of the wave functions. It is shown that this result can be obtained from a phase shift formalism, if one also includes the contribution of oscillating terms. The result is important in work to follow, for the third virial coefficient, for which a similar formalism is being developed. We examine a number of fine points in the quantum mechanical formalisms.     

Absence of long-range order in certain random systems

It is proved that a classical X-Y model where the field conjugate to the order parameter is static and random shows no long-range order at any temperature for spatial dimensions d ? 4. The proof can be extended to systems with higher order parameter dimension n.     

Method of systems of equations of P-adic coverages for fractal analysis of events

Self-similarity in high-energy multiparticle production processes is discussed. A parton shower and hadronization are assumed to give rise to a set of particle with a fractal structure. It is noted that the box counting (BC) and P-adic coverage (PaC) methods determine the fractal dimension with permissible 1/k ranges. A new method of systems of equations of P-adic coverages (SePaC) is proposed that extends the PaC method to fractals with permissible m/k ranges. The SePaC method is shown to determine the fractal dimension of a shower with a prescribed accuracy, the number of fractal levels, the type of the cascade (random or regular), and its structure.     

Dynamic and fractal properties of SP-28 steel under high-speed loading conditions

Using an interferometric method to record the velocity of the free surface of a target subjected to two-dimensional shock loading, it is shown experimentally that the decrease in the compression pulse amplitude is due to the nonstationary nature of mesoscale processes — the amplitude decrease is progressively larger for higher rates of change of the variance of the mesoparticle velocity. It is shown theoretically that the loading rate influences the spallation strength of a material in a planar collision only if the variance of the particle velocity is nonzero. A fractal analysis of the spallation surfaces of steel samples is performed by quantitative fractography methods. An expression relating the fractal dimension of the spallation fracture surface and the variance of the mesoparticle velocity is derived. For typical values of the load pulse parameters for which back-side spallation occurs the fractal dimension agrees satisfactorily with the fractal dimensions for triadic Koch islands. Zh. Tekh. Fiz. 68, 43–49 (October 1998)