Weak Inhomogeneity Research Articles

Magnetic zenith effect and some features of the multifractal structure of the small-scale artificial ionospheric turbulence

We present the results of the experiment on studying the multifractal structure (with inhomogeneity sizes from tens to hundreds of meters across the Earth’s magnetic field) of the artificial ionospheric turbulence when the midlatitude ionosphere is affected by high-power HF radio waves. The experimental studies were performed on the basis of the “Sura” heating facility with the help of radio sounding of the disturbed region of the ionospheric plasma by signals from the Earth’s orbital satellites. The influence of the magnetic zenith effect on measured multifractal characteristics of the small-scale artificial turbulence of the midlatitude ionosphere was examined. In the case of vertical radio sounding of the disturbed ionosphere region, the measured multipower and generalized multifractal spectra of turbulence coincide well with similar multifractal characteristics of the ionospheric turbulence under natural conditions. This result is explained by the fact that the scattering of signals by weak quasi-isotropic small-scale inhomogeneities of the electron number density in a thick layer with a typical size of several hundred kilometers above the region of reflection of high-power HF radio waves gives the major contribution to the observed amplitude fluctuations of received signals. In the case of oblique sounding of the disturbance region at small angles between the line of sight to the satellite and the direction of the Earth’s magnetic field, the nonuniform structure of the small-scale turbulence with a relatively narrow multipower spectrum and small variations in the generalized multifractal spectrum of the electron number density was detected. Such a fairly well ordered structure of the turbulence is explained by the influence of the magnetic zenith effect on the generation of anisotropic small-scale artificial turbulence in a thin layer having a typical size of several ten kilometers and located below the pump-wave reflection height in the upper ionosphere.

BREATHERS IN INHOMOGENEOUS NONLINEAR LATTICES: AN ANALYSIS VIA CENTER MANIFOLD REDUCTION

We consider an infinite chain of particles linearly coupled to their nearest neighbors and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous, i.e. coupling constants, particle masses and on-site potentials can have small variations along the chain. We look for small amplitude and time-periodic solutions, and, in particular, spatially localized ones (discrete breathers). The problem is reformulated as a nonautonomous recurrence in a space of time-periodic functions, where the dynamics is considered along the discrete spatial coordinate. Generalizing to nonautonomous maps a center manifold theorem previously obtained for infinite-dimensional autonomous maps [44], we show that small amplitude oscillations are determined by finite-dimensional nonautonomous mappings, whose dimension depends on the solutions frequency. We consider the case of two-dimensional reduced mappings, which occur for frequencies close to the edges of the phonon band (computed for the unperturbed homogeneous chain). For an homogeneous chain, the reduced map is autonomous and reversible, and bifurcations of reversible homoclinic orbits or heteroclinic solutions are found for appropriate parameter values. These orbits correspond respectively to discrete breathers for the infinite chain, or "dark" breathers superposed on a spatially extended standing wave. Breather existence is shown in some cases for any value of the coupling constant, which generalizes (for small amplitude solutions) an existence result obtained by MacKay and Aubry at small coupling [57]. For an inhomogeneous chain, the study of the nonautonomous reduced map is in general far more involved. Here, the problem is considered when the chain presents a finite number of defects. For the principal part of the reduced recurrence, using the assumption of weak inhomogeneity, we show that homoclinics to 0 exist when the image of the unstable manifold under a linear transformation (depending on the defect sequence) intersects the stable manifold. This provides a geometrical understanding of tangent bifurcations of discrete breathers commonly observed in classes of systems with impurities as defect strengths are varied. The case of a mass impurity is studied in detail, and our geometrical analysis is successfully compared with direct numerical simulations. In addition, a class of homoclinic orbits is shown to persist for the full reduced mapping and yields a family of discrete breathers with maximal amplitude at the impurity site.

Method for super Fresnel resolution in electromagnetic diagnostics of inhomogeneous plasma

The method of electromagnetic diagnostics is suggested, which promises to perform super Fresnel resolution of plasma inhomogeneities, that is resolution, distinguishing details smaller than Fresnel radius. To realize super Fresnel resolution it is suggested to represent the wave field of the source in the form of double weighted Fourier transform (DWFT), deals with Fourier transform simultaneously in coordinates of the sources and in coordinates of receivers. Important property of DWFT is that DWFT transfers into geometrical optics (GO) approximation for smooth inhomogeneous media and becomes equivalent to the Rytov or to small angle Born approximation in the case of weak inhomogeneities. As a result, inverse DWFT allows obtaining linear integral of plasma density both for large scale inhomogeneities, as in GO approximation, and also for inhomogeneities, whose transverse sizes are small as compared with Fresnel radius. DWFT embraces also the results of the phase screen method and allows to take into account phenomenon of micro-multirayness and to describe strong amplitude fluctuations. Using inverse DWFT algorithm, the authors study resolution of systems consisting of discrete sources and receivers. Both analytical estimates and the results of numerical modeling evidence opportunity to observe small scale plasma inhomogeneities with super Fresnel resolution.

On the influence of sea‐ice inhomogeneities onto roll convection in cold‐air outbreaks

In this study we use large‐eddy simulations (LES) to model roll convection within the convective atmospheric boundary‐layer (CBL) during strong cold‐air outbreaks (CAO). Previous LES were mostly unsuccessful in reproducing clear signals of roll convection, especially in case of strong surface heating and weak vertical wind shear in the CBL. In nature however, this phenomenon is very robust and roll convection can be observed as cloud streets in satellite pictures of almost any CAO. Previous LES studies assumed homogeneous sea‐ice, unlike the current study, where under strong surface heating clear signals of rolls appear only when introducing sea‐ice inhomogeneities in the marginal ice zone. For weaker surface heating, rolls also appear without sea‐ice inhomogeneities. The results of this study suggest that in case of strong surface heating and weak vertical wind shear surface inhomogeneities increase the chance of roll formation.

Pulsating wave for mean curvature flow in inhomogeneous medium

We prove the existence and uniqueness of pulsating waves for the motion by mean curvature of ann-dimensional hypersurface in an inhomogeneous medium, represented by a periodic forcing. The main difficulty is caused by the degeneracy of the equation and the fact the forcing is allowed to change sign. Under the assumption of weak inhomogeneity, we obtain uniform oscillation and gradient bounds so that the evolving surface can be written as a graph over a reference hyperplane. The existence of an effective speed of propagation is established for any normal direction. We further prove the Lipschitz continuity of the speed with respect to the normal and various stability properties of the pulsating wave. The results are related to the homogenisation of mean curvature flow with forcing.

Quantum kinetic theory of trapped particles in a strong electromagnetic field

The idea of treating quantum systems by semiclassical representations using effective quantum potentials (forces) has been successfully applied in equilibrium by many authors, see e.g. [D. Bohm, Phys. Rev. 85 (1986) 166 and 180; D.K. Ferry, J.R. Zhou, Phys. Rev. B 48 (1993) 7944; A.V. Filinov, M. Bonitz, W. Ebeling, J. Phys. A 36 (2003) 5957 and references cited therein]. Here, this idea is extended to nonequilibrium quantum systems in an external field. A gauge-invariant quantum kinetic theory for weakly inhomogeneous charged particle systems in a strong electromagnetic field is developed within the framework of nonequilibrium Green’s functions. The equation for the spectral density is simplified by introducing a classical (local) form for the kinetics. Nonlocal quantum effects are accounted for in this way by replacing the bare external confinement potential with an effective quantum potential. The equation for this effective potential is identified and solved for weak inhomogeneity in the collisionless limit. The resulting nonequilibrium spectral function is used to determine the density of states and the modification of the Born collision operator in the kinetic equation for the Wigner function due to quantum confinement effects.

Suppression ofd-wave superconductivity in the checkerboard Hubbard model

Using a dynamical cluster quantum Monte Carlo approximation, we investigate the $d$-wave superconducting transition temperature ${T}_{c}$ in the doped two-dimensional repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings ${t}^{\ensuremath{'}}$ and $t$ in the form of a checkerboard pattern where $t$ is the hopping within a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette, and ${t}^{\ensuremath{'}}$ is the hopping between the plaquettes. We find inhomogeneity suppresses ${T}_{c}$. The characteristic spin excitation energy and the strength of $d$-wave pairing interaction decrease with decreasing ${T}_{c}$, suggesting a strong correlation between these quantities.

A mean-field model of extrinsic line broadening in ferromagnetic resonance

A model of ferromagnetic resonance in inhomogeneous films is described, which includes interactions in a mean-field approximation. The mean-field model yields linewidth values that span the range from intrinsic linewidth for strong interactions to fully broadened local resonance linewidths for weak interactions. For weak inhomogeneity, the mean-field model does not follow the quadratic dependence of broadening on inhomogeneity predicted by the two-magnon model. For weakly interacting regions with strong inhomogeneity, the mean-field model fills a gap in the modeling of ferromagnetic resonance spectra where only computationally intensive models have been available previously.

Field‐theoretic simulations of polyelectrolyte complexation

Field‐theoretic simulations of polyelectrolyte complexation

Linear multifrequency-grey acceleration recast for preconditioned Krylov iterations

The linear multifrequency-grey acceleration (LMFGA) technique is used to accelerate the iterative convergence of multigroup thermal radiation diffusion calculations in high energy density simulations. Although it is effective and efficient in one-dimensional calculations, the LMFGA method has recently been observed to significantly degrade under certain conditions in multidimensional calculations with large discontinuities in material properties. To address this deficiency, we recast the LMFGA method in terms of a preconditioned system that is solved with a Krylov method (LMFGK). Results are presented demonstrating that the new LMFGK method always requires fewer iterations than the original LMFGA method. The reduction in iteration count increases with both the size of the time step and the inhomogeneity of the problem. However, for reasons later explained, the LMFGK method can cost more per iteration than the LMFGA method, resulting in lower but comparable efficiency in problems with small time steps and weak inhomogeneities. In problems with large time steps and strong inhomogeneities, the LMFGK method is significantly more efficient than the LMFGA method.

On a leveraging effect of weak azimuthal inhomogeneities explaining the nonuniqueness of critical Maier-Saupe order parameters

The Maier--Saupe theory of liquid crystals predicts a unique critical order parameter for the transition point of isotropic--nematic phase transitions. Experimental studies have shown that critical order parameters are shifted away from that unique value. We show that micro-defects and weak azimuthal inhomogeneities can result due to a leveraging effect in the experimentally observed macro-shifts of the critical order parameter. We demonstrate the leveraging effect by computing the corresponding micro-shifts of the order parameter in the isotropic phase with the help of an effective order parameter. Our approach accounts for critical order parameters observed in experimental studies which is explicitly demonstrated for methyl-deuterated para-azoxyanisole (PAA-d6), 4-n-pentyl-4′-cyanobiphenyl (5CB), N-(4-methoxybenzylidene)-4-butylaniline (MBBA). Finally, in line with the effective order parameter approach and the dynamical mean field approaches by Hess, Doi, and Edwards, predictions are derived that provide novel testbeds for experimental studies.

Equilibrium spin currents in the Rashba medium

We analyze equilibrium spin currents in a 2D electron gas with Rashba spin-orbit interaction (Rashba medium). In a uniform Rashba medium these currents are constant, and their ability to really transport spin is not evident. But even weak inhomogeneity of the Rashba medium allows to reveal that equilibrium spin currents can transport spin from areas where spin is produced to areas where spin is absorbed.

Charge and Spin Order on the Triangular Lattice:NaxCoO2atx=0.5

The nature of electronic states due to strong correlation and geometric frustration on the triangular lattice is investigated in connection to the unconventional insulating state of NaxCoO2 at x=0.5. We study an extended Hubbard model using a spatially unrestricted Gutzwiller approximation. We find a new class of charge and spin ordered states at x=1/3 and x=0.5 where antiferromagnetic (AFM) frustration is alleviated via weak charge inhomogeneity. At x=0.5, we show that the square root of 3a x 2a off-plane Na dopant order induces weak square root of 3a x 1a charge order in the Co layer. The symmetry breaking enables successive square root of 3a x 1a AFM and 2a x 2a charge- or spin-ordering transitions at low temperatures. The Fermi surface is truncated by the 2a x 2a hexagonal zone boundary into small electron and hole pockets. We study the phase structure and compare to recent experiments.

Torsional oscillations of longitudinally inhomogeneous coronal loops

We explore the effect of an inhomogeneous mass density field on frequencies and wave profiles of torsional Alfven oscillations in solar coronal loops. Dispersion relations for torsional oscillations are derived analytically in limits of weak and strong inhomogeneities. These analytical results are verified by numerical solutions, which are valid for a wide range of inhomogeneity strength. It is shown that the inhomogeneous mass density field leads to the reduction of a wave frequency of torsional oscillations, in comparison to that of estimated from mass density at the loop apex. This frequency reduction results from the decrease of an average Alfven speed as far as the inhomogeneous loop is denser at its footpoints. The derived dispersion relations and wave profiles are important for potential observations of torsional oscillations which result in periodic variations of spectral line widths. Torsional oscillations offer an additional powerful tool for a development of coronal seismology.

Vlasov-Maxwell plasma equilibria with temperature and density gradients: Weak inhomogeneity limit

Stationary self-consistent solutions of the Vlasov-Maxwell system in a magnetized plasma (so called Vlasov equilibria) with both density and temperature gradients are investigated analytically in the limit of weak inhomogeneities. These solutions provide a simple class of self-consistent equilibria that can be used as a convenient starting point for numerical studies such as the study of the effects of temperature gradient and temperature anisotropy on the nonlinear development of reconnection instabilities in a kinetic plasma regime.

Heat conduction in laminates with a weak transversal inhomogeneity

AbstractThe purpose of this contribution is to formulate a tolerance model, [1], for periodically laminated media with a weak transversal inhomogeneity. Laminates in which layers are of the same material but one of them is reinforced by thin fibers in parallel to the interfaces are this kind of media. Taking into account the weak transversal inhomogeneity makes possible to separate model equations for the averaged temperature and temperature fluctuations. To analyse and solve these equations we apply asymptotic expansions. Using the proposed model selected initial‐boundary value problems were solved. Results were verified by direct numerical solutions obtained in the framework of the Fourier model. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dynamic inverse problem in a weakly laterally inhomogeneous medium: theory and numerical experiment

An inverse problem of wave propagation into a weakly laterally inhomogeneous medium occupying a half-space is considered in the acoustic approximation. The half-space consists of an upper layer and a semi-infinite bottom separated with an interface. An assumption of a weak lateral inhomogeneity means that the velocity of wave propagation and the shape of the interface depend weakly on the horizontal coordinates, x = (x1, x2), in comparison with the strong dependence on the vertical coordinate, z, giving rise to a small parameter ε ≪ 1. Expanding the velocity in power series with respect to ε, we obtain a recurrent system of 1D inverse problems. We provide algorithms to solve these problems for the zero and first-order approximations. In the zero-order approximation, the corresponding 1D inverse problem is reduced to a system of non-linear Volterra-type integral equations. In the first-order approximation, the corresponding 1D inverse problem is reduced to a system of coupled linear Volterra integral equations. These equations are used for the numerical reconstruction of the velocity in both layers and the interface up to O(ε2).

Impact of localized inhomogeneity on the surface-wave velocity and bulk-wave reflection in solids

The effect of a weak surface, near-surface and interfacial inhomogeneity on the frequency dependence of the surface wave velocity and of the SH (shear horizontal) wave reflectivity in isotropic elastic media is studied analytically and numerically. The inhomogeneity is modeled as an infinite planar layer with continuously varying properties. Weak inhomogeneity may markedly affect the dispersion of the Rayleigh velocity and especially of the reflectivity. It is demonstrated how this effect, particularly pronounced at high frequency, depends on the extent of inhomogeneity. The material data for damaged and ideal concrete and several simple examples of inhomogeneity profiles are utilized for the numerical calculations based on the Peano expansion. The use of explicit low- and high-frequency approximations is also exemplified. Among these, simple WKB asymptotics are shown to be particularly helpful for the Rayleigh velocity in the case of a prominent inhomogeneity attached to the surface and for the reflection on weak interfaces.

Recovering inhomogeneities in a waveguide using eigensystem decomposition

We present an eigensystem decomposition method to recover weak inhomogeneities in a waveguide from knowledge of the far-field scattered acoustic fields. Due to the particular geometry of the waveguide, which supports only a finite number of propagating modes, the problem of recovering inhomogeneities in a waveguide has a different set of challenges than the corresponding problem in free space. Our method takes advantage of the spectral properties of the far-field matrix, and by using its eigenvalues and its eigenvectors we obtain a representation of the linearized solution to the inverse problem in terms of products of fields which are linear combinations of the propagating modes of the waveguide with weights given by the eigenvectors of the far-field matrix. The problem of finding the unknown inhomogeneity reduces to a problem of determining some coefficients in a finite system of linear equations, whose coefficients depend on the background medium and the eigenvalues and the eigenvectors of the far-field matrix. By numerically implementing our inverse algorithm we reconstructed the inhomogeneities present in the waveguide. We show that (1) even with as few as seven propagating modes we obtain a good recovery of the size and shape of the inhomogeneity; (2) multiple inhomogeneities can be well recovered and, as expected, (3) the recovery improves when the number of propagating modes increases.

Reflectivity of a stratified half-space: the limit of weak inhomogeneity and anisotropy

Analytical expressions for the reflectivity of a weakly inhomogeneous and weakly anisotropic half-space are derived. The calculation uses the well-known 4 × 4 matrix formalism of stratified media in a perturbation-theoretical approach, with the deviation of the dielectric tensor from a spatially constant scalar being treated as the perturbation. As a result, we find simple first-order expressions for the elements of the reflection matrix, which can readily be applied without any need for further numerical analysis. Their practical usefulness is illustrated by two simple examples.