High-field vs. low-field magneto-transport in a percolating medium

Recent theoretical and numerical work on high-field magneto-transport in a percolating medium is described and compared to earlier work on weak-field magneto-transport in such systems. While the weak-field behavior is well described by the simple nodes-links picture, which ignores blobs and loops on a scale smaller than the percolation correlation length ξ_p, the strong-field behavior is extremely sensitive to those features. The critical behavior at strong magnetic fields H near the percolation threshold is governed by competition between the usual H=0 fixed point and a new H=∞ fixed point. Which of those fixed points dominates the behavior is determined by the relative sizes of two characteristic lenghts: the percolation correlation length ξ_p and a new, magnetic field dependent length ξ_H.     

Dynamic characterization of hysteresis elements in mechanical systems. II. Experimental validation

The industrial demand for machine tools with ever increasing speed and accuracy calls for a closer look at the physical phenomena that are present at small movements of those machine's slides. One of these phenomena, and probably the most dominant one, is the dependence of the friction force on displacement that can be described by a rate-independent hysteresis function with nonlocal memory. The influence of this highly nonlinear effect on the dynamics of the system has been theoretically analyzed in Part I of this paper. This part (II) aims at verifying these theoretical results on three experimental setups. Two setups, consisting of linearly driven rolling element guideways, have been built to specifically study the hysteretic friction behavior. The experiments performed on these specially designed setups are then repeated on one axis of an industrial pick-and-place device, driven by a linear motor and guided by commercial guideways. The results of the experiments on all the setups agree qualitatively well with the theoretically predicted ones and point to the inherent difficulty of accurate quantitative identification of the hysteretic behavior. They further show that the hysteretic friction behavior has a direct bearing on the dynamics of machine tools and its presence should therefore be carefully considered in the dynamic identification process of these systems.     

Consecutive reactions in a countercurrent plug-flow reactor. Gas-liquid system

A mathematical model of a bimolecular two-step consecutive exothermic reaction in the liquid phase of a gas-step consecutive exothermic reaction in the liquid phase of a gas-flow reactor is proposed. Spatial profiles of the heatings and relative concentrations of the reactants in both phases for the steady state of the system are presented. The behavior of the reaction intermediate product is examined. The kinetic characteristics of the reaction are demonstrated to substantially influence the behavior of the system in the reactor.     

Ergodic properties and thermodynamic behavior of elementary reversible cellular automata. I. Basic properties

This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of fully-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems.     

Radiation-induced changes in physical properties of bulk polyethylene. I. Effect of crystallization conditions

Melt crystallized polyethylenes with different crystallization histories were irradiated with γ-rays and examined for various properties. These include solubility (gel content), melting and recrystallization behavior, load extension behavior, and creep properties. Even for the same dose, very significant differences were observed for the different sample types. Although such differences have been reported previously, the present work reveals that these differences can be unusually large and that they are displayed by a range of different tests with a consistent correlation between them. The underlying trend is that in poorly crystallized samples the radiation is much more effective in forming networks than in samples of highly developed crystallinity. This finding may merely indicate that cross-linking is more abundant in the amorphous region than in the crystallites; nevertheless, analogy with single crystals suggests that in addition details of the fold surface morphology and the nature of the lamellar contact may also have a part to play. Among other properties, the elasticity of cross-linked melt was analyzed and found to be consistent with simple rubber elasticity theory, leading to an estimate of both the number of effective cross-links and of intrinsic entanglements acting as cross-links. The most conspicuous effects were observed in the creep behavior where different sample types irradiated to the same dose could behave as viscous liquids and true rubbers according to crystallization history. The relevance of such findings for the technological irradiation of polyethylene should be self-evident, particularly as the doses involved were those commonly employed in industrial applications.     

Recurrence time statistics in chaotic dynamics. I. Discrete time maps

The dynamics of transitions between the cells of a finite-phase-space partition in a variety of systems giving rise to chaotic behavior is analyzed, with special emphasis on the statistics of recurrence times. In the case of one-dimensional piecewise Markow maps the recurrence problem is cast into a-renewal process. In the presence of intermittency, transitions between cells define a non-Markovian, non-renewal process reflected in the presence of power-law probability distributions and of divergent variances and mean values.     

On polymeric materials containing fibrils with a phase transition. II. The mechanical consequences of matrix shear

The mechanical behavior of a system of parallel fibrils, capable of a phase change and embedded in a matrix, is analyzed by considering a simplified model. The model consists of a single infinitely long isolated fibril together with its associated matrix. Furthermore, it is assumed that slippage cannot occur at the fibril-matrix interface but that the matrix deforms in both tension and in shear. The phase change occurring in the fibrils gives rise to large discontinuous local strains in the fibril and is characterized by a “critical stress” and an “equilibrium stress.” Analysis of the model shows that distinct zones of the secondary phase will form consecutively along the fibril length when the system is extended. These zones are mobile and the stress fields in the matrix associated with each zone result in the mutual repulsion of adjacent zones. Stress-strain curves for both extension and recovery are calculated using linear and nonlinear forms of the system parameters. It is suggested that the model studied is relevant to the mechanical behavior of keratin fibers.     

Macromolecular conformations in solutions. II. Thermodynamics of interactions

The model of polymeric chains in solution developed in the preceding paper (this issue) is examined. Results of some numerical calculations are reported. Predictions of chain behavior are derived from the model in terms of the exchange interaction energy parameterX ₁₂, polymer concentration, number of segments in a bundle, molecular mass, and temperature.     

Spin-spin correlation function in the two-dimensional Ising model with linear defects. I.T<T c

The dispersion expansion for the spin correlation function in the two-dimensional Ising model with linear defects belowT _c is derived. The asymptotic behavior is computed by a steepest descent analysis. The lattice is divided into four domains with different asymptotic behaviors. In particular, the correlation length inside certain domains is a function of the defect.     

Spin-spin correlation function in the two-dimensional Ising model with linear defects. II.T>T c

The dispersion expansion for the spin correlation function in the two-dimensional Ising model with linear defects aboveT _c is derived. The asymptotic behavior is computed by a steepest descent analysis. The lattice is divided into four domains with different asymptotic behaviors. In particular, the correlation length inside certain domains is a function of the defect.     

A.C. electrical conductivity of pure and doped potassium perchlorate

A.C. electrical conductivity of potassium perchlorate (KP) has been measured in the temperature range 25–325°C at frequencies ranging from 50–500 Hz using an automated technique. The results are interpreted in terms of a novel mechanism involving Schottky defects in the anion sublattice and Frenkel defects in the cation sublattice. The conductivity behavior of KP is compared with literature data on similar low-symmetry systems containing polyatomic ions.     

Solitonic gravitational waves in Bianchi II cosmologies. 2. One solitonic perturbations

This paper is a continuation of a previous one, in which the general framework for constructing solitonic perturbations on Bianchi II background was described. Here we calculate the exact solitonic perturbation corresponding to one (real) pole and we investigate in detail some of its main features. Its asymptotic behavior in time is discussed with the aid of a modified oscillatory approach to the singularity.     

Lattice gas generalization of the hard hexagon model. II. The local densities as elliptic functions

In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.Supported in part by the National Science Foundation Grant MCS 8201733.     

Interacting Quantum and Classical Continuous Systems II. Asymptotic Behavior of the Quantum Subsystem

In the framework of event-enhanced quantum theory the dynamical equation for the reduced density matrix of a quantum system interacting with a continuous classical system is derived. The asymptotic behavior of the corresponding dynamical semigroup is discussed. The example of a quantum–classical coupling on Lobatchevski space is presented.     

Quasisteady aero-acoustic response of orifices.

The low frequency response of orifices (slit, circular diaphragm, and perforated plate) in the presence of mean flow is well predicted by a quasisteady theory. A refinement is brought to the theory by considering a Mach number dependent vena contracta coefficient. The measurements of the vena contracta coefficient of a slit agree well with the simple analytical expression existing in the case of the Borda tube orifice. The measured scattering matrix coefficients do not depend strongly on the geometry of the element. If the frequency is increased the moduli remain relatively unaffected while the arguments exhibit a complex behavior which depends on the geometry. From these considerations an anechoic termination efficient at high mass flow is designed.     

Stabilization of perceived echo amplitudes in echolocating bats. II. The acoustic behavior of the big brown bat, Eptesicus fuscus, when tracking moving prey.

Big brown bats, Eptesicus fuscus, can be trained to use echolocation to track a small microphone with a food reward attached when it is moved rapidly toward them. This situation mimics prey interception in the wild while allowing very precise recording of the sonar pulses emitted during tracking behavior. The results show that E. fuscus intensity compensates, reducing emitted intensity by 6 dB per halving of target range so that the intensity incident upon the target is constant and echo intensity increases by 6 dB per halving of range. This increase in echo intensity is effectively canceled by the reduction in auditory sensitivity due to automatic gain control (AGC) of 6 to 7 dB per halving of range. Intensity compensation behavior and AGC therefore form a dual-component, symmetrical system that stabilizes perceived echo amplitudes during target approach. The same system is present in the fishing bat, Noctilio leporinus, suggesting that it may be widespread in echolocating bats. Correlation analysis shows that, despite large changes in the duration of the pulses emitted by E. fuscus during an approach, the pulse frequency structure is such that the spatial image of the target perceived along the range axis is highly stable. Pulse duration is not reduced in the manner theoretically necessary to eliminate potential echo distortion effects due to AGC, but is reduced in such a way that this distortion is insignificant. During the terminal buzz, a high degree of temporal overlap (relative to pulse duration) occurs between emitted pulse and returning echo.     

A.C. and D.C. conductivity of NiZn ferrite nanoparticles in wet and dry conditions

Promising future applications of ferrite nanoparticles in medicine, drug delivery, sensors and ferrofluids are expected to be in wet or humid environments. Therefore nanostructured powders of ferrites having the chemical compositions.Ni_xZn _(1−x)Fe₂O₄ with (x=0.0, 0.25, 0.5, 0.75, and 1) were pressed immediately after preparation - by the co-precipitation method - without any drying to simulate a humid environment. The nanoparticles were characterized by X-ray diffraction analysis (XRD) to be sure of the formation of the ferrite in nanoscale. The infrared (IR) spectroscopy of the samples ensures the existence of water as well as the characteristic absorption bands of ferrites. The ac and dc conductivity of the samples had been investigated immediately after preparation (the as-prepared samples). Then, the samples were dried at 200 °C for about 12 h and reinvestigated. The behavior of conductivity differs significantly in the two cases showing a noticeable effect due to humidity. Also, the magnetic induction of the as-prepared samples was investigated by using the vibrating sample magnetometer (VSM). The samples show superparamagnetic behavior.     

Translation drag coefficient of a self-similar assembly of spheres immersed in an incompressible fluid.

On the basis of deterministic fractals and the Rotne-Prager hydrodynamic interaction tensor, we confirm the asymptotic as well as the finite size scaling of the friction coefficient lambda of a self-similar structure. The fractal assembly is made of N spheres with its dimension varying from D < 1 to D = 3. The number of spheres can be as high as N approximately O(10(4)). The asymptotic scaling behavior of the friction coefficient per sphere is lambda approximately N(1/D-1) for D > 1, lambda approximately (lnN)(-1) for D = 1, and lambda approximately N(0) for D < 1. The crossover behavior indicates that while in the regime of D > 1 the hydrodynamic screening effect grows with the size, for D<1 it is limited in a finite range, which decays with decreasing D.     

Asymptotic properties of multistate random walks. I. Theory

A calculation is presented of the long-time behavior of various random walk properties (moments, probability of return to the origin, expected number of distinct sites visited) formultistate random walks on periodic lattices. In particular, we consider inhomogeneous periodic lattices, consisting of a periodically repeated unit cell which contains a finite number of internal states (sites). The results are identical to those for perfect lattices except for a renormalization of coefficients. For walks without drift, it is found that all the asymptotic random walk properties are determined by the diffusion coefficients for the multistate random walk. The diffusion coefficients can be obtained by a simple matrix algorithm presented here. Both discrete and continuous time random walks are considered. The results are not restricted to nearest-neighbor random walks but apply as long as the single-step probability distributions associated with each of the internal states have finite means and variances.