Inhomogeneity Length Research Articles

Effect of Critical Slowing Down on Local-Density Dynamics

Through molecular dynamics simulation we demonstrate that the time scale for local solvent reorganizations, which may control solute dynamics, can become very long for low- and near-critical-density supercritical fluids. We show that this can be ascribed to two processes, the first being due to direct, interparticle potential interactions, and the second, which dominates on all but the shortest length scales, being due to a coupling between the dynamics of the local solvent environment and those of the long-length-scale density fluctuations which are present in compressible supercritical fluids. Specifically, as the critical point is approached and the correlation length of these density inhomogeneities increases, we find that the associated slowing of these extended collective fluctuations, known as “critical slowing down”, generates a concomitant slowing of the local reorganization time.

Nonlinear percolation conductivity and negative differential resistivity in microcrystalline PbTe layers with an adjustable potential well

The effect of electric fields on the electrical conductivity of PbTe films with block sizes smaller than the Debye screening length is studied. As the temperature is varied, a readjustment of the potential well is observed due to thermal spread of barriers with height ϕkT and the expansion of higher barriers. Spatial ensembles, which consist of several blocks that increase rapidly with temperature, are established for each T. This process leads to an increase in the height of the potential barriers as the linear size of these ensembles increases. This determines the potential well in these films and their nonlinear properties, which originate in the nonlinear percolation conductivity of a microscopic crystalline system with intergranular barriers. A comparison with the experimental data of Shklovskii shows that the scale length of the spatial inhomogeneity a=3.7×10−6 cm at T=4.2 K corresponds to the average block size. The value of a increases with temperature, reaching 5×10−4 cm at T=240 K. This mechanism for electrical conductivity is compared with the hopping conductivity with a variable hopping length. The negative differential resistance in the structures examined here is found to be electrothermal in nature.

A method based on singularity theory to predict edge delamination of laminates

Delamination starting from a stress free edge is the main mode of failure of cross-ply laminates. The analysis of singularities and resulting stress concentrations at interfaces along these edges are not sufficient to provide a satisfying model of onset mechanisms. In particular, the model is by far less sensitive to the layers thickness than observed in traction experiments. A refined asymptotic process is proposed which takes into account the existence of surface flaws (micro-cracks or notches). Numerical results prove that this model is much more in agreement with the experiments. Moreover, the knowledge of the interface toughness, in addition with the experiments, allows to estimate a characteristic fracture length, a kind of process zone. It is a material property and in a first approximation it arises to be of the same order of magnitude than the characteristic inhomogeneity length of the components, i.e. the fibers diameter.

Wake potentials in nonuniform dusty magnetoplasmas

It is shown that the presence of equilibrium density gradients in a magnetized dusty plasma can introduce new types of drift-like waves. These give rise to oscillatory wake-potentials, which can focus ions and attract dust grains of similar polarity. Using a test particle approach, typical profiles for wake-potentials are obtained in several interesting cases. It is found that the effective attraction length is independent of the magnetic field strength for high density dusty plasmas, whereas it is larger for larger magnetic fields in a low-density dusty plasma. Furthermore, the dust attraction takes place predominantly in the inhomogeneous region of the dusty plasma having smaller lattice periodicity for smaller scale length of the density inhomogeneity.

Pressure Fields Generated by Acoustical Pulses Propagating in Randomly Layered Media

This paper investigates the pressure field generated at the bottom of a high-contrast randomly layered slab by an acoustical pulse emitted at the surface of the slab. This analysis takes place in the framework introduced by Asch et al. [SIAM Rev., 33 (1991), pp. 519--625], where the incident pulse wave length is long compared to the correlation length of the random inhomogeneities but short compared to the size of the slab. This problem has been studied in the one-dimensional case simultaneously by Clouet and Fouque [Ann. Appl. Probab., 4 (1994), pp. 1083--1097] and Lewicki, Burridge, and Papanicolaou [Wave Motion, 20 (1994), pp. 177--195] and also for multimode plane wave pulses by Lewicki, Burridge, and De Hoop [SIAM J. Appl. Math., 56 (1996), pp. 256--276]. These situations require only the use of classical diffusion-approximation results whereas the point-source problem studied in this paper requires a nontrivial combination of diffusion-approximation results with stationary phase methods. The stationary phase method has been used by De Hoop, Chang, and Burridge [Geophys. J. Int., 104 (1991), pp. 489--506] for weakly fluctuating media and by Asch et al. for the study of the reflected pressure. The main statement of this paper is that, in order to simultaneously apply diffusion-approximation and stationary phase results, it is correct to apply them consecutively. We believe that this situation will be encountered again and again in this field and the goal of this paper is to present a clear statement in the most simple case of an acoustical pulse propagating in a randomly layered medium. In that case, the main result gives a formula describing the spreading of the pulse around its arrival time at the bottom of the slab which is obviously not contained in the classical geometrical acoustic approximation.

A new parametric reflection mechanism for ducted whistlers and an explanation of precursors

Abstract A new reflection mechanism of ducted whistler-mode waves in the magnetosphere, which can be defined as a parametric reflection, is discussed. Unlike the well-known process of backscattering, parametric reflection occurs when the scale length of electron density inhomogeneities is much less than the whistler wave-length; the reflected whistler wave appears simultaneously with the excitation of short-scale lower hybrid resonance (LHR) plasma waves. The efficiency of such a parametric reflection is higher than that of traditional backscattering. Two cases are analysed. The first is when a reflected whistler wave arises via the process of the parametric decay instability of a sufficiently intense whistler wave into two quasielectrostatic short-scale waves, that is a LHR wave and an ionic (ion cyclotron or sound) wave. The second case is when the initial whistler interacts with naturally occurring ionic waves. Quantitative estimates show that both cases can exist in the magnetosphere. In the case of ducted whistler, generated by a lightning discharge, reflected signals at a given frequency are formed near two points along the magnetic field line where this frequency coincides with the local LHR frequency. This leads to appearance on a spectrogram of signals with a hook-like shape, which precede the whistler. It is shown that these signals can be associated with different types of whistler precursors.

Studies of the generalized Ohm's law

Within the generalized Ohm's law, we present a tranformation which it similar to a thermoelectronic transport problem in a 2D nonhomogeneous medium/ For a general class of films with any number of different components, the resulting equations can be decoupled by a universal transformation. For the purpose of studying the applicability of the generalized Ohm's law, we consider the problem of an electromagnetic plane-wave scattered from a film which, although materially homogeneous, has a corrugated surface, in the regime where the wavelength is larger than the inhomogeneity length scales. The optical response of such a film is calculated by applying the generalized Ohm's law, and indendently by solving the three-dimensional Maxwell's equations and invoking the physical boundary conditions at the surface (Rayleigh method).

Decoupling and testing of the generalized Ohm's law

The generalized Ohm's law is an approximation formulated for the description of optical properties of nonhomogeneous thin films beyond the quasistatic approximation, when the inhomogeneity length scale is still much smaller than the wavelength, but is not smaller than the skin depth. Within this approximation, we transform the problem to a form that is similar to a thermoelectric transport problem in a two-dimensional (2D) nonhomogeneous medium. We show that for a general class of nonhomogeneous films with any number of different components, the resulting equations can be decoupled by a universal transformation. This simplifies practical application of the theory by reducing the coupled-field problem in a nonhomogeneous 2D system to two uncoupled conductivitylike problems with the same microgeometry, for which extensive theory already exists. For the purpose of studying the applicability of the generalized Ohm's law, we consider the problem of an electromagnetic plane wave scattered from a film that, although materially homogeneous, has a corrugated surface in the regime where the wavelength is larger than the inhomogeneity length scales. The optical response of such a film is calculated by applying the generalized Ohm's law, and independently by solving the three-dimensional Maxwell's equations, invoking the physical boundary conditions at the surface (Rayleigh method). We compare results of the two approaches for several configurations and materials and thus learn about the range of parameter values for which the generalized Ohm's law can provide a good description of the optical properties of a thin film.

Characteristics of electrons at the trapping boundary of the radiation belt

New measurements are presented of the L‐dependent energy threshold for electron flux isotropy observed near midnight from low‐altitude satellites. These data provide the basis for an important remote sensing of the geomagnetic field configurations near the outer edge of the radiation belt. The threshold energy for isotropy observed at low altitudes is interpreted as providing a measure of the effective scale length of inhomogeneity of the geomagnetic field near the equator at high altitude. The data presented were obtained with electron spectrometers on the UARS satellite providing flux and energy spectrum measurements for energies between 30 keV and 5 MeV simultaneously at a variety of pitch angles. On certain orbits the UARS satellite achieved fine L shell resolution and nearly simultaneous measurements at different local times. With this previously unavailable L shell resolution the threshold energy for isotropy versus L shell curves near midnight have shown slopes steeper than 20 MeV per unit L on 20% of the cases, using the International Geomagnetic Reference Field (IGRF) 85 magnetic field model. On 66% of the satellite passes the slopes at the two boundary crossings within 01 to 06 hours in magnetic local time and about 10 min in elapsed time were within a factor of 3 of each other. The L shell at which isotropy occurs above a given threshold energy is found to be generally lower and the slope steeper at times of high geomagnetic disturbance. For the analysis presented here, if isotropy occurs when the radius of field line curvature is less than 10 times the gyroradius of the particles, the scale lengths of inhomogeneities were always found to be less than 2900 km, and in 99% of the cases the scale lengths were greater than 73 km.

Phenomenological analysis of microphase separation in relation to SAXS investigations of polymer blend fibres

Based on the Takayanagi models, the phenomenological analysis of microphase separation for PE/ABS and PS/PMMA blend fibres is presented. The supermolecular structure parameters, including the value of the long period, the thickness of the transition layer between phases and the average inhomogeneity lengths, were determined by means SAXS. The changes in parameters of the supermolecular structure correspond well with conclusions drawn from phenomenological analysis.

Deterministic and stochastic analyses of acoustic plane-wave reflection from inhomogeneous porous seafloor

The propagator matrix technique for the acoustic plane-wave reflection in layered, porous, anisotropic seafloor is combined with Monte Carlo simulation to investigate the layering effect of the sediment. Statistical data from a geologically known site are processed and used as a benchmark. Realizations of sediment property profiles are generated using a spectral technique. A deterministic analysis demonstrates that the amplitude and phase of reflection coefficient is highly dependent on the variation of porosity. In a stochastic analysis, the effect of randomness is examined. It is found that the fluctuation of the sediment physical properties around a mean profile has a significant influence on the seabed reflectivity, particularly for the incident angles near and above the critical value. Frequency behavior of reflectivity is strongly dependent on the correlation length of medium inhomogeneities. This behavior is attributed to the interaction among different waves that propagate in the porous sediment layers, suggesting the possibility of obtaining the properties using the reflection loss data.

Non-stationary resonant Alfvén surface waves in one-dimensional magnetic plasmas

This paper uses incompressible visco-resistive MHD to study the propagation of linear resonant waves in an inhomogeneous plasma. The background density and magnetic field are assumed to depend only on one spartial Cartesian coordinate, and the magnetic field is taken to be unidirectional and perpendicular to the direction of inhomogeneity. The equation that governs the component of the velocity normal to the plane formed by the direction of the inhomogeneity and the magnetic field is derived under the assumption that the coefficients of viscosity and resistivity are sufficiently small that dissipation of energy is confined to a narrow dissipative layer. The solutions to this equation are obtained in the form of decaying normal surface modes with wavelengths much larger than the characteristic scale of the inhomogeneity. The effect of non-stationarity inside the dissipative layer is taken into account, and valid solutions are found even when the ratio of the thickness of the dissipative layer to the inhomogeneity length scale is of the order of or smaller than the ratio of the inhoinogeneity length scale to the wavelength. These solutions are the generalization of the solutions obtained by Mok and Einaudi, which are only valid when the first ratio is much larger than the second. The rate of wave damping is shown to be independent of the values of the viscosity and the resistivity. However, the behaviour of the solutions in the dissipative layer depends strongly on the viscosity and the resistivity. In the case that the effect of dissipation dominates the effect of non-stationarity, the solutions behave in the dissipative layer as found by Mok and Einaudi. When the effect of dissipation is steadily decreased in comparison with the effect of nonstationarity, the solutions become more and more oscillatory, and their amplitudes grow very rapidly in the dissipative layer. Eventually, when nonstationarity dominates dissipation, the amplitudes of the solutions become so large in the dissipative layer in comparison with those outside the dissipative layer that practically all the energy of the perturbations is concentrated in the dissipative layer.

Stability analysis of electromagnetic interchange modes in toroidal geometry

An investigation is presented of how the stability of collisionless electromagnetic interchange modes depends on εn (the ratio of the magnetic drift frequency to the diamagnetic drift frequency), the ion temperature gradient and the electron temperature gradient. A linear two fluid model in toroidal geometry is used. The eigenvalue problem is solved analytically and then the complex frequency is solved numerically from the dispersion relation. Comparison is made with Mercier's criterion, in the magnetohydrodynamic limit. The most important observed effects are:1. When εn increases Mercier's criterion becomes increasingly incorrect. The toroidal system becomes more stable than Mercier's criterion predicts. εn is large in regions where we have flat density profiles, Ln » LB (the characteristic scale length of density and magnetic field inhomogeneities).2. Finite ηi (Ln/LTi) may cause instability below the critical pressure gradient in the Mercier criterion.

The influence of sediment scattering and variability on acoustic intensity including data comparisons

Previous work [Howell et al., 2928 (1994)] has shown that statistics of multimodal intensity could be matched using a three-layer isospeed model that included effects of scattering. To more accurately estimate scattering effects on intensity over a broad frequency range, additional bottom information must be included. In this paper, an analytic treatment of a shallow channel consisting of n isospeed layers is developed for a wide-angle PE propagation model. A scattering layer is introduced at a horizontal water-bottom interface to model effects of attenuation due to interface and sediment scattering. The local mean of intensity is determined and its sensitivity to parameters such as the number of layers, frequency, scattering layer thickness, and correlation length of inhomogeneities is investigated. The standard deviation of intensity is also examined. Comparisons are made between intensity statistics for the multilayer models and depth-dependent profile models consistent with data from a New Jersey Shelf experiment. Additional emphasis is directed toward the number of isospeed layers needed to match experimental intensity over a range of frequencies. [Work supported by ONR.]

Scaling theory for the optical properties of thick percolative metal-insulator films

The 2D scaling approach for the optical properties of semicontinuous metal films is generalized to thick (3D) percolative films. Model calculations demonstrate that the scaling model is qualitatively different from any effective medium approach, and should be used whenever the inhomogeneity length scale is larger than the optical one.

Mechanical and geometrical properties of the rat semimembranosus lateralis muscle during isometric contractions

The orientation of the line of pull and geometrical characteristics of rat semimembranousus lateralis muscle (SM1) were measured in a plane during isometric contractions at different muscle lengths. The orientation of the line of pull was always similar in our plane of analysis. It was always aligned with the external tendon but not with the aponeurosis. Muscle and fiber length changes were similar. Aponeurosis length changes were very small. Angular changes of aponeurosis with respect to the line of pull were larger than those of muscle fibers. Functional implications of angular effects on muscle length changes were negligible in SM1. The muscle fiber was modelled as a slanted cylinder to test the hypothesis whether angular changes of fibers with the attachment area during muscle shortening are related to the constancy of fiber volume. Accommodation of the change in fiber cross-sectional area which accompanies fiber shortening was insufficient at the bony attachment area. It is concluded that during muscle shortening fiber volume displacement toward the bony origin is reduced as a smaller cross-sectional area needs to be accommodated. Angular changes of fibers with the proximal and distal part of the aponeurosis were so large that they cannot be related to the constancy of volume of a fiber with a homogeneous cross-sectional area. When angular changes of fibers are related to their length changes it is suggested that volume displacement and inhomogeneous length changes along the aponeurosis can explain the experimental results at the aponeurosis.

Wave equations for a relativistic magnetoplasma

The linearized relativistic Vlasov-Maxwell system for a hot inhomogeneous relativistic magnetized electron plasma is studied through particle orbit theory using the techniques of Fourier transform. An analytical integral expression in the (k, omega )-space is obtained for the current density for waves propagating across an externally applied uniform static magnetic field (k is the wavenumber and omega is the wave frequency). After applying inverse Fourier transform, differential equations for the electric field are obtained from the expression for the current density combined with Maxwell's equations. These fully relativistic equations are correct up to second order in rc/L. where rc is the electron gyroradius and L is the gradient length of the plasma inhomogeneity.

Thermal stability and intermixing of ultrathin Fe films on a Au(001) surface

Thermal stabilities and atomic intermixing of ultrathin ferromagnetic Fe films grown on a Au(001) surface have been studied using high-resolution low-energy electron diffraction (HRLEED). Both the average terrace size and the average inhomogeneity length can be quantitatively determined as a function of temperature by properly decomposing the energy dependent angular profiles of the (00) beam measured from Fe/Au(001) films at various temperatures. Atomic place exchange between Au and Fe is processed in Fe films up to ~ 2.5 ML thick at room temperature. For higher coverage Fe films (3.5–5.0 ML), the Fe adatoms bury the intermixed interface (⩽ 2.5 ML thick) formed at room temperature. For all the films studied (1.5–5.0 ML), the occurrence of intermixing — i.e., intermixed Fe and Au patches due to interdiffusion of Fe adatoms into Au bulk and exchanges of Au atoms to the surface — is observed clearly in different elevated temperature ranges. This conclusion is supported by the results that dominant surface steps for the thicker Fe films change from Fe/Fe steps to Au/Fe steps, and eventually, to Au/Au steps as the annealing temperature is increased. The average inhomogeneity length as a result of intermixing is extracted and is in the order of 20 Å over a wide range of temperatures.

In-Situ Characterization of Growth and Intermixing at a Heteroepitaxial Interface: Fe on Au(001)

ABSTRACTThe growth and chemical intermixing of submonolayer and a few monolayer thick Fe films on a Au(001) surface was studied by High Resolution Low Energy Electron Diffraction (HRLEED) technique. Through the analysis of the energy dependent angular profiles as a function of time, we obtained the distribution of islands and distribution of spacings during submonolayer growth. The interference of electron waves from different chemical elements in terraces at different heights in the surface contributes to the background intensity and broadening in the angular profiles of diffraction beams. A subsurface Fe capped by Au islands as a result of atomic place exchange was observed at the initial stage of monolayer growth. From the energy dependent angular profiles as a function of temperature, we determine the quantitative change of inhomogeneity length (∼20 Å) at the interface of ultrathin films at elevated temperatures due to intermixing.

Heating of oxygen ions by resonant absorption of Alfvén waves in a multicomponent plasma

Conical distributions of oxygen ions are commonly observed at high altitudes above the auroral zone and in the cusp and cleft regions. The occurrence of these oxygen conics is well correlated with the intensity of waves in the ULF frequency range (of the order of a few hertz). It is shown that the inhomogeneity along the geomagnetic field lines allows a mode coupling between downgoing Alfvén waves (either proton cyclotron or magnetosonic) and upgoing oxygen cyclotron waves. Thus the electromagnetic energy flux carried downward with a large phase velocity can be transferred into a low phase velocity left‐handed mode that resonates with oxygen ions and heats them. We estimate the corresponding rate of absorption of the incident Alfvén waves as a function of the incidence angle and of the parameter ηO+, which is essentially the product of the O+ relative concentration and the characteristic length of inhomogeneity of the magnetic field, normalized to the typical wavelength of the Alfvén waves, at the O+ gyrofrequency. For an incident magnetosonic wave (type II branch) the rate of absorption can be quite large (up to 20%), for ηO+ < 10−2. This peak in the absorption coefficient, however, is obtained for a relatively narrow angular range, when the incidence angle is close to 90°. An incident proton cyclotron wave (type III branch) is more likely to lead to efficient O+ heating because (1) two regimes, either at small or at large incidence angle, lead to an absorption rate up to 20%, (2) these maxima are only slightly dependent on the incidence angle, and (3) large absorption rates are expected over a relatively broad range of values of ηO+ (5 × 10−3 < ηO+ < 10−1), compatible with those values that are expected throughout the magnetosphere.