Influence of Inhomogeneity on Critical Behavior of Earthquake Model on Random Graph

We consider the earthquake model on a random graph. A detailed analysis of the probability distribution of the size of the avalanches will be given. The model with different inhomogeneities is studied in order to compare the critical behavior of different systems. The results indicate that with the increase of the inhomogeneities, the avalanche exponents reduce, i.e., the different numbers of defects cause different critical behaviors of the system. This is virtually ascribed to the dynamical perturbation.     

The influence of inhomogeneous properties of a system on the percolation process in two-dimensional space

The percolation process in a two-dimensional inhomogeneous lattice is studied by the Monte Carlo method. The inhomogeneous lattice is simulated by a random distribution of inhomogeneities differing in size and number. The influence of inhomogeneities on the parameters (critical concentration, average number of sites in finite clusters, percolation probability, critical exponents, and fractal dimension of an infinite cluster) characterizing the percolation in the system is analyzed. It is demonstrated that all these parameters essentially depend on the linear size of inhomogeneities and their relative area.     

Free energies of supercritical solvation from molecular dynamics simulation and integral equation studies

We present here molecular dynamics (MD) simulation and integral equation (IE) studies on free energies of solvation of a non-polar solute in a dilute supercritical solvent to estimate the contribution of inhomogeneities in solvent density to the free energy of solvation. The solvation of a Xe-like solute in an Ne-like solvent as well as that of naphthalene in CO₂ have been investigated. At state points in the compressible region in the neighborhood of the solvent critical point, we have utilized the IE estimates of free energies to model the ideal situation where local density inhomogeneities would be absent. The difference between the free energies in the presence (as derived from MD simulation) and in the absence (from IE) of local density inhomogeneities was studied as a function of density along an isotherm close to the critical point. Although for low density supercritical solvents, a marked difference is observed, a study of the density dependence of this difference across the critical density does not directly reveal any signature of local density enhancement on the thermodynamics of solvation.     

Computer modeling of sound propagation in the ocean with fractal inhomogeneities

The wave-field computer code based on the wide-angle parabolic equation is modified and adapted to the problems of sound scattering in a medium with anisotropic inhomogeneities of fractal type. To verify the computer code, a model numerical experiment on determining the angular dependence of the scattered sound field is performed for different anisotropy coefficients of the sound speed inhomogeneities. The comparison of the computed data with the theoretical dependences shows their rather good agreement and indicates that the computer code can be applied to calculations of sound propagation in the ocean with fine-structure inhomogeneities possessing fractal properties.     

Effects of impurities on heat capacities at paramagnetic to ferromagnetic transitions

The influence of controlled impurities upon the detailed shape of the heat capacity of Gd near the Curie temperature is studied experimentally. The experimental results can be interpreted in terms of Watson's theoretical analyses which show that small scale, random inhomogeneities do not alter the shape of the heat capacity curve, whereas large scale inhomogeneities are found to reduce the sharpness of the critical singularities.     

A Simple Mean Field Model for Social Interactions: Dynamics,Fluctuations, Criticality

We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in the limit of infinitely many interacting individuals, and show that phase transition occurs. Then, after having obtained the dynamics of normal fluctuations around this limit, we analyze long time fluctuations for critical values of the parameters. We show that random inhomogeneities produce critical fluctuations at a shorter time scale compared to the homogeneous system.     

Equivalent Josephson junctions

The magnetic field dependences of critical current are numerically constructed for a long Josephson junction with a shunt-or resistor-type microscopic inhomogeneities and compared to the critical curve of a junction with exponentially varying width. The numerical results show that it is adequate to replace the distributed inhomogeneity of a long Josephson junction by an inhomogeneity localized at one of its ends, which has certain technological advantages. It is also shown that the critical curves of junctions with exponentially varying width and inhomogeneities localized at the ends are unaffected by the mixed fluxon-antifluxon distributions of the magnetic flow. This fact may explain the improvement of the spectra of microwave radiation noted in the literature.     

On one mechanism of magnetization reversal in crystals with combined anisotropy

The effect of a magnetic field on the stability of null domain walls is considered in terms of a variational model. The walls are localized near defects in a (001)-oriented plate. The critical fields at which the inhomogeneities exist are found, and their role in magnetization processes taking place in the crystals under study is considered.     

Investigation of statistical characteristics of waves in layered media with regular and random inhomogeneities based on the invariant imbedding method

We consider a model of a stationary problem of wave propagation in a layered half-space with regular and random inhomogeneities. The choice of regular perturbation corresponds to a linear profile of the wave velocity. Random inhomogeneities are simulated in the framework of the white noise model. We analyse the influence of inhomogeneities on the probability distribution of the reflection-coefficient phase and the imaginary value of the average wavefield at the boundary of the half-space.     

Coulomb-frustrated phase separation phase diagram in systems with short-range negative compressibility

Using numerical techniques and asymptotic expansions we obtain the phase diagram of a paradigmatic model of Coulomb-frustrated phase separation in systems with negative short-range compressibility. The transition from the homogeneous phase to the inhomogeneous phase is generically first order in isotropic three-dimensional systems except for a critical point. Close to the critical point, inhomogeneities are predicted to form a bcc lattice with subsequent transitions to a triangular lattice of rods and a layered structure. Inclusion of a strong anisotropy allows for second- and first-order transition lines joined by a tricritical point.     

Effects of the mixture of one-and three-dimensional inhomogeneities on the wave spectrum of superlattices

Dependences of the dispersion laws and damping of waves in an initially sinusoidal superlattice on the dimensionality of inhomogeneities modulating the period of the superlattice are studied. The cases of one-and three-dimensional modulations, as well as modulation by a mixture of inhomogeneities of both of these dimensionalities, are considered. The correlation function of the superlattice K(r) has the form of a product of the same periodic function and a decreasing function that is significantly different for these different cases. The decreasing part of the correlation function for the mixture of inhomogeneities of different dimensionalities has the form of a product of the decreasing parts of the correlation functions of the components of the mixture. This leads to the nonadditivity of the contributions of the components of different dimensionalities to the resulting modification of the parameters of the wave spectrum that are due to the inhomogeneities (the damping of waves for the mixture of these components is smaller than the sum of the dampings of the components, the maximum gap in the spectrum corresponds to the simultaneous presence of both components of the mixture, not only of the three-dimensional inhomogeneities).     

Effect of cosmic backreaction on the future evolution of an accelerating universe

We investigate the effect of backreaction due to inhomogeneities on the evolution of the present universe by considering a two-scale model within the Buchert framework. Taking the observed present acceleration of the universe as an essential input, we study the effect of inhomogeneities in the future evolution. We find that the backreaction from inhomogeneities causes the acceleration to slow down in the future for a range of initial configurations and model parameters. The present acceleration ensures formation of the cosmic event horizon, and our analysis brings out how the effect of the event horizon could further curtail the global acceleration, and even lead in certain cases to the emergence of a future decelerating epoch.     

Sound scattering by random fractal inhomogeneities in the ocean

Sound scattering by random volume inhomogeneities (fluctuations of the refraction index in a medium) with an arbitrary anisotropy is considered using the small perturbation method (Born’s approximation). Surfaces (boundaries) of the inhomogeneities are deemed to be fractal ones: the energy spectra of the refraction index fluctuations follow the power law with a nonintegral exponent. Formulas are obtained for the volume scattering coefficient. Frequency and angular dependences of the scattering coefficient and their relations to the fractal dimension of inhomogeneities with different kinds of anisotropy and different sizes (on the sound wavelength scale) are presented. The fractal dimension of the inhomogeneities is estimated.     

A state space model for cochlear mechanics

The stability of a linear model of the active cochlea is difficult to determine from its calculated frequency response alone. A state space model of the cochlea is presented, which includes a discretized set of general micromechanical elements coupled via the cochlear fluid. The stability of this time domain model can be easily determined in the linear case, and the same framework used to simulate the time domain response of nonlinear models. Examples of stable and unstable behavior are illustrated using the active micromechanical model of Neely and Kim. The stability of this active cochlea is extremely sensitive to abrupt spatial inhomogeneities, while smoother inhomogeneities are less likely to cause instability. The model is a convenient tool for investigating the presence of instabilities due to random spatial inhomogeneities. The number of unstable poles is found to rise sharply with the relative amplitude of the inhomogeneities up to a few percent, but to be significantly reduced if the spatial variation is smoothed. In a saturating nonlinear model, such instabilities generate limit cycles that are thought to produce spontaneous otoacoustic emissions. An illustrative time domain simulation is presented, which shows how an unstable model evolves into a limit cycle, distributed along the cochlea.     

Effect of the correlation properties of one-and three-dimensional inhomogeneities on the high-frequency magnetic susceptibility of sinusoidal superlattices

The effect of one-(1D) and three-dimensional (3D) inhomogeneities on the high-frequency magnetic susceptibility at the boundary of the first Brillouin zone of a ferromagnetic superlattice is studied. The study is performed with an earlier developed method of random spatial modulation (RSM) of the superlattice period. In this method, structural inhomogeneities are described in terms of the random-phase model, in which the phase depends on three coordinates in the general case. The frequency spacing Δν_m between two peaks in the imaginary part of the averaged Green’s function, which characterizes the gap width in the frequency spectrum at the boundary of the Brillouin zone, is calculated as a function of both the root-mean-square fluctuations γ_i and the correlation wavenumbers η_i of phase inhomogeneities (i = 1 and 3 for 1D and 3D inhomogeneities, respectively). The function Δν_m(γ₁, η₁) for 1D inhomogeneities is shown to be symmetric with respect to interchanging the variables γ ₁ ² and η₁, whereas the function Δν_m(γ₃, η₃) for 3D inhomogeneities is strongly asymmetric with respect to interchanging γ ₂ ³ and η₃. This effect is associated with the difference in form between the correlation functions of 1D and 3D inhomogeneities and can be used to determine the dimensionality of inhomogeneities from the results of spectral studies of such superlattices.     

Simulation of the electrophysical characteristics of a biological tissue with allowance for large-scale inhomogeneities

An electrodynamic model of reflection of a plane wave from a layer simulating a biological structure with a slowly varying thickness is constructed with allowance for roughness in the case when the characteristic size of inhomogeneities on the surface is much larger than the wavelength. The model makes it possible to vary the size of inhomogeneities on the rough surface, the electrophysical parameters of the biological sample under investigation, and the geometrical parameters and to establish the dependences between these parameters and the biological properties of the biotissue being simulated.     

Nonlinear dynamics of DNA systems with inhomogeneity effects

We investigate the nonlinear dynamics of the Peyrard–Bishop DNA model taking into account site dependent inhomogeneities. By means of the multiple-scale expansion in the semi-discrete approximation, the dynamics is governed by the perturbed nonlinear Schrödinger equation. We carry out a multiple-scale soliton perturbation analysis to find the effects of the variety of nonlinear inhomogeneities on the breatherlike soliton solution. During the crossing of the inhomogeneities, the coherent structure of the soliton is found stable. The global shape of the inhomogeneous molecule is merged with the shape of the homogeneous molecule. However, the velocity, the wavenumber and the angular frequency undergo a time-dependent correction that is proportional to initial width of the soliton and depends on the nature of the inhomogeneities.     

Scroll-wave dynamics in the presence of ionic and conduction inhomogeneities in an anatomically realistic mathematical model for the pig heart

Nonlinear waves of the reaction–diffusion (RD) type occur in many biophysical systems, including the heart, where they initiate cardiac contraction. Such waves can form vortices called scroll waves, which result in the onset of life-threatening cardiac arrhythmias. The dynamics of scroll waves is affected by the presence of inhomogeneities, which, in a very general way, can be of (i) ionic type; i.e., they affect the reaction part, or (ii) conduction type, i.e., they affect the diffusion part of an RD-equation. We demonstrate, for the first time, by using a state-of-the-art, anatomically realistic model of the pig heart, how differences in the geometrical and biophysical nature of such inhomogeneities can influence scroll-wave dynamics in different ways. Our study reveals that conduction-type inhomogeneities become increasingly important at small length scales, i.e., in the case of multiple, randomly distributed, obstacles in space at the cellular scale (0.2–0.4 mm). Such configurations can lead to scroll-wave break up. In contrast, ionic inhomogeneities affect scroll-wave dynamics significantly at large length scales, when these inhomogeneities are localized in space at the tissue level (5–10 mm). In such configurations, these inhomogeneities can attract scroll waves, by pinning them to the heterogeneity, or lead to scroll-wave breakup.     

Single-layer and multilayered films for perpendicular recording based on a Co-Cr alloy

Results of materials research into the dependence of the magnetic properties of Co-Cr recording media on the structural properties are discussed in relation with results from recording experiments. The magnetic properties depend strongly on the preparation conditions. An increase in substrate temperature results in an increase of the coercivity, but also gives rise to inhomogeneities of the Co-Cr film in the growth direction and to lateral inhomogeneities due to Cr segregation. The inhomogeneities in the growth direction are suppressed by the application of a non-magnetic, amorphous Ge layer between the substrate and the Co-Cr layer, resulting in a magnetic layer with a large perpendicular anisotropy. From the slope of the hysteresis loops we obtain, using a model proposed by Kooy and Enz, an estimate for the mean size of the stripe domains, which is found to increase with increasing layer thickness and decrease with increasing substrate temperature. The change in the size of the stripe domains is consistent with the trends calculated from noise spectra obtained in recording experiments. Multilayers of thin Co-Cr layers alternated with non-magnetic Ge layers are also discussed.