Smooth Inhomogeneity Research Articles

Scarf for Lifshitz

Polarization of a vacuum as well as of dispersive and dissipative dielectric media with piece-wise and smooth inhomogeneities is studied with the goal to clarify the question of renormalizability of diverging electromagnetic stress-energy tensor. First, the stress tensor is computed with the Lifshitz approach to London forces in the non-retarded limit, which after the substraction of the leading free space ultraviolet divergencies still retains the divergencies associated with the presence of sharp boundaries between piece-wise inhomogeneities. We call these contributions finite because they become renormalized after a sharp interface is replaced with a dielectric permittivity changing according to a smooth function of spatial coordinates. In addition, such a smoothed out interface exhibits new subleading ultraviolet divergencies that appear due to its internal structure. To systematically deal with the polarization of inhomogeneous media, the Hadamard expansion is applied to single out both finite and subleading contributions and to unequivocally demonstrate incomplete renormalizability of the Lifshitz theory. The above approach also allows us to reveal the nature of surface tension, which proves to be purely quantum mechanical. The deduced theory of surface tension and its calculations for real dielectric media are favorably compared to the available experimental data. While the sharp interface limit recovers the classical boundary conditions for the electric field and uncovers the origin of the apparent local divergencies of the renormalized stresses in the sharp interface formulation previously pointed out in the literature, the problem of surface tension proves to be of a distinguished limit type because the sharp interface formulation loses the information about the internal structure of an interface and hence cannot explain the origin of surface tension.

Longitudinal Fracture Analysis of Inhomogeneous Beams with a Continuously Varying Height

Longitudinal fracture behavior of nonlinear elastic inhomogeneous beam configurations with a continuously varying height along its length is analyzed. The general solution of the strain energy release rate problem is obtained by considering the energy balance. Beam configurations with the longitudinal crack located arbitrarily along the height are analyzed. The beams exhibit smooth material inhomogeneity in the height direction. The solution derived is valid within the arbitrary law of continuous beam height variations. Longitudinal fracture in a simply supported nonlinear elastic inhomogeneous beam with a height that varies in a parabolic law is investigated by applying the general solution of the strain energy release rate problem. The J-integral approach is used to verify this solution. The effect of various geometrical and material parameters on the longitudinal fracture of the simply supported beam configuration is evaluated and discussed in detail.

Unified bulk semiclassical theory for intrinsic thermal transport and magnetization currents

We reveal the unexpected role of the material inhomogeneity in unifying the formulation of intrinsic thermal and thermoelectric transport as well as magnetization currents. The smooth inhomogeneity leads to the position dependent local band dispersion and phase-space Berry curvature, enabling a general and rapid access to transport and magnetization currents displaying the momentum-space Berry curvature physics. Our theory does not invoke the boundary current, the thermodynamic approach to magnetization or any mechanical counterpart of statistical forces. By introducing a fictitious inhomogeneity, it applies to homogeneous samples as well, promoting the inhomogeneity to be a basic trick in semiclassical transport theories. Such a trick works regardless of the driving force of transport, e.g., temperature gradient, in contrast to the trick of fictitious gravitational field in quantum transport theories. We thus include more general mechanical driving forces and establish the Mott relation between the resulting transport thermal and electric currents, whereas this relation for these two currents was previously only known when an electric field is the driving force.

Longitudinal fracture of inhomogeneous beams with material non-linearity: An analytical investigation

This paper describes an analytical approach for analysing of longitudinal fracture in beam structures which exhibit smooth material inhomogeneity along the height and length. A solution to the strain energy release rate is derived for a general loading scheme assuming non-linear mechanical behaviour of the material. The Ramberg-Osgood stress-strain relation is used to model the material non-linearity. It is assumed that the three material properties which are involved in the Ramberg-Osgood stress-strain relation vary continuously along the height and length of the beam (exponential laws are applied for describing the distribution of these properties along the height and length of the beam). The solution derived is valid for a longitudinal crack located arbitrary along the beam height. It is shown that the approach developed can be applied for evaluating the effects of material inhomogeneity along the height and length of the beam, non-linear mechanical behaviour of the material, crack location along the beam height and the crack length on the longitudinal fracture.

Dynamic water/fat separation and inhomogeneity mapping-joint estimation using undersampled triple-echo multi-spoke radial FLASH.

To achieve dynamic water/fat separation and field inhomogeneity mapping via model-based reconstructions of undersampled triple-echo multi-spoke radial FLASH acquisitions. This work introduces an undersampled triple-echo multi-spoke radial FLASH sequence, which uses (i) complementary radial spokes per echo train for faster spatial encoding, (ii) asymmetric echoes for flexible and nonuniform echo spacing, and (iii) a golden angle increment across frames for optimal k-space coverage. Joint estimation of water, fat, inhomogeneity, and coil sensitivity maps from undersampled triple-echo data poses a nonlinear and non-convex inverse problem which is solved by a model-based reconstruction with suitable regularization. The developed methods are validated using phantom experiments with different degrees of undersampling. Real-time MRI studies of the knee, liver, and heart are conducted without prospective gating or retrospective data sorting at temporal resolutions of 70, 158, and 40ms, respectively. Up to 18-fold undersampling is achieved in this work. Even in the presence of rapid physiological motion, large field inhomogeneities, and phase wrapping, the model-based reconstruction yields reliably separated water/fat maps in conjunction with spatially smooth inhomogeneity maps. The combination of a triple-echo acquisition and joint reconstruction technique provides a practical solution to time-resolved and motion robust water/fat separation at high spatial and temporal resolution.

Quantifying wave-function overlaps in inhomogeneous Majorana nanowires

A key property of Majorana zero modes is their protection against local perturbations. In the standard picture, this protection is guaranteed by a high degree of spatial nonlocality of the Majoranas, namely a suppressed wave-function overlap, in the topological phase. However, a careful characterisation of resilience to local noise goes beyond mere spatial separation, and must also take into account the projection of wave-function spin. By considering the susceptibility of a given zero mode to different local perturbations, we find the relevant forms of spin-resolved wave-function overlaps that measure its resilience. We quantify these overlaps and study their dependence with nanowire parameters in several classes of experimentally relevant configurations. These include nanowires with inhomogeneous depletion and induced pairing, barriers and quantum dots. Smooth inhomogeneities have been shown to produce near-zero modes, so-called pseudo-Majoranas, below the critical Zeeman field in the bulk. Surprisingly, their resilience is found to be comparable or better than that of topological Majoranas in realistic systems. We further study how accurately their overlaps can be estimated using a purely local measurement on one end of the nanowire, accessible through conventional transport experiments. In uniform nanowires this local estimator is remarkably accurate. In inhomogeneous cases it is less accurate but can still provide reasonable estimates for potential inhomogeneities of the order of the superconducting gap. We further analyse the zero mode wave-function structure, spin texture and spectral features associated with each type of inhomogeneity. All our results highlight the strong connection between internal wave-function degrees of freedom, nonlocality and protection in smoothly inhomogeneous nanowires.

Theory of acoustooptical filtration of light beams in the inhomogeneous acoustic field

The theory of acoustooptical (AO) interaction between light beams in the longitudinally inhomogeneous acoustic field is constructed with allowance for conditions typical of AO filtration. In the case of smooth acoustic inhomogeneities, analytical expressions for the spatially spectral characteristic relating the spatial spectra of incident and diffracted light beams are derived. The situation where a Gaussian light beam undergoes filtration in the acoustic field excited by a rectangular transducer is discussed in detail. The narrowband quasi-collinear AO filter based on a paratellurite crystal is simulated. It is demonstrated that the maximum diffraction efficiency and transmission-function shape distortion (with respect to the plane-wave model) of the given device depend to the greatest extent on the misalignment between the directions of the group velocities of interacting light beams.

Quantitative Evaluation of Intensity Inhomogeneity Correction Methods for Structural MR Brain Images

The correction of intensity non-uniformity (INU) in magnetic resonance (MR) images is extremely important to ensure both within-subject and across-subject reliability. Here we tackled the problem of objectively comparing INU correction techniques for T1-weighted images, which are the most commonly used in structural brain imaging. We focused our investigations on the methods integrated in widely used software packages for MR data analysis: FreeSurfer, BrainVoyager, SPM and FSL. We used simulated data to assess the INU fields reconstructed by those methods for controlled inhomogeneity magnitudes and noise levels. For each method, we evaluated a wide range of input parameters and defined an enhanced configuration associated with best reconstruction performance. By comparing enhanced and default configurations, we found that the former often provide much more accurate results. Accordingly, we used enhanced configurations for a more objective comparison between methods. For different levels of INU magnitude and noise, SPM and FSL, which integrate INU correction with brain segmentation, generally outperformed FreeSurfer and BrainVoyager, whose methods are exclusively dedicated to INU correction. Nonetheless, accurate INU field reconstructions can be obtained with FreeSurfer on images with low noise and with BrainVoyager for slow and smooth inhomogeneity profiles. Our study may prove helpful for an accurate selection of the INU correction method to be used based on the characteristics of actual MR data.Electronic supplementary materialThe online version of this article (doi:10.1007/s12021-015-9277-2) contains supplementary material, which is available to authorized users.

Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions

We investigate the effects of smooth inhomogeneities at first-order quantum transitions (FOQTs), such as those arising in the presence of a space-dependent external field, which smooths out the discontinuities of the low-energy properties at the transition. We argue that a universal scaling behavior emerges in the space transition region close to the point in which the external field takes the value for which the homogeneous system undergoes the FOQT. We verify the general theory in two model systems. We consider the quantum Ising chain in the ferromagnetic phase and the q-state Potts chain for q=10, investigating the scaling behavior which arises in the presence of an additional inhomogeneous parallel and transverse magnetic field, respectively. Numerical results are in full agreement with the general theory.

Universal scaling effects of a temperature gradient at first-order transitions.

We study the effects of smooth inhomogeneities at first-order transitions. We show that a temperature gradient at a thermally driven first-order transition gives rise to nontrivial universal scaling behaviors with respect to the length scale l_{t} of the variation of the local temperature T_{x}. We propose a scaling ansatz to describe the crossover region at the surface where T_{x}=T_{c}, where the typical discontinuities of a first-order transition are smoothed out. The predictions of this scaling theory are checked, and get strongly supported, by numerical results for the two-dimensional (2D) Potts models, for a sufficiently large number of states to have first-order transitions. Comparing with analogous results at the 2D Ising transition, we note that the scaling behaviors induced by a smooth inhomogeneity appear quite similar in first-order and continuous transitions.

Compatibility conditions for Dirichlet and Neumann problems of Poisson's equation on a rectangle

It is a well-known fact that the solution of Poisson's equation on a rectangle lacks regularity. Even for a smooth inhomogeneity, corner singularities arise in the derivatives of the solution. The very form of these singularities is of particular interest in numerical analysis; more precisely for the analysis of dimension splitting methods applied to parabolic equations. In this work, necessary and sufficient conditions on the inhomogeneity are derived which ensure a higher regularity of the solution of the Dirichlet or the Neumann problem – the so called compatibility conditions.

Surface waves in plasma waveguides with a smooth transverse inhomogeneity

A theory of cylindrical surface waves in a circular waveguide filled with a smoothly inhomogeneous plasma is presented. For a special radial profile of the plasma density, dispersion relations for the complex frequencies of surface waves are derived analytically. The dispersion relations are solved numerically (in the long-wavelength limit) and numerically. It is shown that there are two types of surface waves. When passing to the case of a sharply bounded plasma, one of the waves becomes an ordinary surface wave, while the other becomes strongly damped.

The magnetic penetration depth influenced by the proximity to the surface

The effect of smooth inhomogeneities near a superconductor boundary on the magnetic penetration depth λ is studied with emphasis on the proximity-induced spatial dependence of the Cooper pair amplitude. The influence of surface pair breaking or pair formation on λ is described within the Ginzburg–Landau theory, with no model assumptions, for both strongly type-II and strongly type-I homogeneous superconductors. Generic values of λ, which can differ greatly from the London penetration depth, are identified and demonstrated to be induced by large-scale inhomogeneities, when superconductivity is strongly suppressed on the surface.

Dirac-like Plasmons in Honeycomb Lattices of Metallic Nanoparticles

We consider a two-dimensional honeycomb lattice of metallic nanoparticles, each supporting a localized surface plasmon, and study the quantum properties of the collective plasmons resulting from the near-field dipolar interaction between the nanoparticles. We analytically investigate the dispersion, the effective Hamiltonian, and the eigenstates of the collective plasmons for an arbitrary orientation of the individual dipole moments. When the polarization points close to the normal to the plane, the spectrum presents Dirac cones, similar to those present in the electronic band structure of graphene. We derive the effective Dirac Hamiltonian for the collective plasmons and show that the corresponding spinor eigenstates represent Dirac-like massless bosonic excitations that present similar effects to electrons in graphene, such as a nontrivial Berry phase and the absence of backscattering off smooth inhomogeneities. We further discuss how one can manipulate the Dirac points in the Brillouin zone and open a gap in the collective plasmon dispersion by modifying the polarization of the localized surface plasmons, paving the way for a fully tunable plasmonic analogue of graphene.

Scattering of two-dimensional dark quasi-solitons by smooth inhomogeneities in a Bose-Einstein condensate

It is theoretically shown that creation of artificial inhomogeneities allows one to control dynamics of two-dimensional dark quasi-solitons in a Bose-Einstein condensate. A method to calculate trajectories of these quasi-solitons is proposed. It allows control parameters to be selected for the potentials responsible for formation of the Bose gas density distributions required for the scattering through the given angle.

SAUSAGE OSCILLATIONS OF CORONAL PLASMA STRUCTURES

The dependence of the period of sausage oscillations of coronal loops on length together with the depth and steepness of the radial profile are determined. We performed a parametric study of linear axisymmetric fast magnetoacoustic (sausage) oscillations of coronal loops modeled as a field-aligned low-β plasma cylinder with a smooth inhomogeneity of the plasma density in the radial direction. The density decreases smoothly in the radial direction. Sausage oscillations are impulsively excited by a perturbation of the radial velocity, localized at the cylinder axis and with a harmonic dependence on the longitudinal coordinate. The initial perturbation results in either a leaky or a trapped sausage oscillation, depending upon whether the longitudinal wavenumber is smaller or greater than a cutoff value, respectively. The period of the sausage oscillations was found to always increase with increasing longitudinal wavelength, with the dependence saturating in the long-wavelength limit. Deeper and steeper radial profiles of the Alfven speed correspond to more efficient trapping of sausage modes: the cutoff value of the wavelength increases with the steepness and the density (or Alfven speed) contrast ratio. In the leaky regime, the period is always longer than the period of a trapped mode of a shorter wavelength in the same cylinder. For shallow density profiles and shorter wavelengths, the period increases with wavelength. In the long-wavelength limit, the period becomes independent of the wavelength and increases with the depth and steepness of the radial profile of the Alfven speed.

Subluminal and superluminal parametric doppler effects in the case of light reflection from a moving smooth medium inhomogeneity

The reflection of test radiation from a smooth inhomogeneity of medium characteristics propagating with a subluminal or superluminal velocity is analyzed. The equations describing the propagation of the forward- and counter-propagating waves in such an inhomogeneous medium are derived. Quasi-phase conjugation is demonstrated in the case of superluminal inhomogeneities. The Bragg resonance conditions are formulated and the conditions for increasing the reflection coefficient of radiation from an inhomogeneity are discussed.

The parametric Doppler effect upon reflection of light from a moving smooth inhomogeneity of a medium

The reflection of probe radiation from a smooth inhomogeneity of characteristics of a medium that propagates with a relativistic velocity is analyzed. Equations that describe the propagation of forward and backward waves in an inhomogeneous medium are derived, conditions of occurrence of a Bragg resonance are formulated, and conditions for increasing the coefficient of reflection from the inhomogeneity are discussed.

On the anomalous diffusion in nonisothermal plasma

In nonisothermal plasmas at temperature Te≫Ti diffusion plays a decisive role at conditions of smooth inhomogeneity when the inhomogeneity size is much larger than Te/Ti times the Debye radius. When the inhomogeneity is rather abrupt and this condition is violated, then during the spreading process the Maxwellian relaxation of ion charges becomes significant. Here, we consider these two phenomena together and refer to the anomalous character of diffusion, i.e., anomalous diffusion.

An algorithm for determination of the amplitudes of reflected and transmitted waves in the case when counterpropagating waves are incident on a multilayer stepwise inhomogeneous structure

A simple algorithm is proposed for derivimg analytical expressions for the amplitudes of reflected and transmitted waves in the case when two 1D counterpropagating waves are incident on a multilayer stepwise inhomogeneous structure. Wave amplitudes are analytically expressed for structures consisting of three, four, and five layers. The proposed algorithm is applied to solve numerically the problem of wave propagation in an inhomogeneous structure where the wave number linearly changes along the structure’s length. The algorithm involves approximation of a smooth inhomogeneity by a step one. A criterion and conditions are obtained for the applicability of the step approximation for the investigation of wave propagation through inhomogeneous media with smoothly varying parameters. It is shown that the algorithm can be applied to problems on propagation of electromagnetic waves in the cases of the normal and oblique incidence.