Presence Of Strong Inhomogeneities Research Articles

On small local equilibrium systems

Abstract Even for large nonequilibrium systems, local equilibrium subsystems in the presence of strong inhomogeneities may be very small. Such situations typically arise either in the presence of large gradients of temperature, velocity or pressure, or in transition zones between different phases. For small thermodynamic systems, the Euler equation of macroscopic thermodynamics does not hold. One less equation implies one additional degree of freedom, which is the hallmark of small thermodynamic systems. I would like to offer some remarks on the description and role of small local equilibrium subsystems in nonequilibrium thermodynamics.

Excess pressure and electric fields in nonideal plasma hydrodynamics.

Nonideal plasmas have nontrivial space and time correlations, which simultaneously impact both the excess thermodynamic quantities as well as the collision processes. However, hydrodynamics models for designing and interpreting nonideal plasma experiments, such as inertial-confinement fusion experiments, typically neglect electrodynamics, although some models include electric fields indirectly through a generalized Fick's law. However, because most transport models are not computed self-consistently with the equation of state, there is double counting of the forces in the excess thermodynamic quantities and the collision terms. Here we employ the statistical mechanical hydrodynamic theory of Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)JCPSA60021-960610.1063/1.1747782] to examine inhomogeneous, nonideal plasmas that contain electric fields. We show that it is not possible to simultaneously separate terms that correspond to electric fields and excess pressure; rather, these quantities arise from the same interparticle Coulomb forces. Moreover, new terms associated with nonlocality appear in the presence of strong inhomogeneities.

Resolving estimation uncertainties of chemical shift encoded fat-water imaging using magnetization transfer effect.

B0 field inhomogeneity may cause significant errors in chemical shift encoding-based fat-water (F/W) separation. We describe a new approach to improve its robustness using novel B0 field map pre-estimation. Our method exploits insensitivity of fat to magnetization transfer effect, which allows generating fat-insensitive B0 field priors with full or partial spatial support using a low-resolution magnetization transfer-weighted scan. The full prior can be employed by most F/W separation methods for initialization or data demodulation. We also propose a modified region-growing algorithm in which the partial prior is utilized for its initial seeding. The magnetization transfer-based B0 priors significantly reduced F/W errors of three representative F/W separation methods in all cases. In cases with moderate B0 inhomogeneity, the full prior allowed error-free separation even with basic, voxel-independent processing. When coupled with methods exploiting B0 field smoothness, it significantly improved separation accuracy even in the presence of strong inhomogeneities. Seeding the region-growing with the partial prior significantly improved performance of F/W separation, including cases with spatially disconnected tissues. Magnetization transfer-based B0 field pre-estimation provides valuable prior information for F/W separation, which may significantly improve its robustness at the expense of nominal (< 5%-10%) scan time increase.

Transverse magnetoresistance peculiarities of thermoelectric Lu-doped Bi2Te3 compound due to strong electrical disorder

The n-type thermoelectric Bi1.9Lu0.1Te3 was prepared by microwave-solvothermal method and spark plasma sintering. The magnetic field and temperature dependences of transverse magnetoresistance measured within temperature 2–200 K interval allow finding the peculiarities characteristic for strongly disordered and inhomogeneous semiconductors. The first peculiarity is due to appearance of linear-in-magnetic field contribution to the total magnetoresistance reflected in a crossover from quadratic magnetoresistance at low magnetic fields to linear magnetoresistance at high magnetic fields. The linear magnetoresistance can result from the Hall resistance picked up from macroscopically distorted current paths due to local variations in stoichiometry of the compound studied. The second peculiarity is that both linear magnetoresistance magnitude and crossover field are functions of carrier mobility which is in agreement with the Parish and Littlewood model developed for disordered and inhomogeneous semiconductors. An increase in the mobility due to a decrease in temperature is accompanied by an increase in the magnetoresistance magnitude and a decrease in the crossover field. Finally, the third peculiarity is related to the remarkable deviation of the total magnetoresistance measured at various temperatures from the Kohler's rule. Presence of strong inhomogeneity and disorder in the Bi1.9Lu0.1Te3 structure concluded from the magnetoresistance peculiarities can be responsible for the remarkable reduction in the total thermal conductivity of this compound.

The effective increase in atomic scale disorder by doping and superconductivity in Ca3Rh4Sn13

A comprehensive study of the electronic structure, thermodynamic and electrical transport properties reveals the existence of inhomogeneous superconductivity due to structural disorder in Ca3Rh4Sn13 doped with La (Ca3−xLaxRh4Sn13) or Ce (Ca3−xCexRh4Sn13) with superconducting critical temperatures higher than those (Tc) observed in the parent compounds. The T − x diagrams and the entropy S(x)T isotherms document well the relation between the degree of atomic disorder and separation of the high-temperature and Tc-bulk phases. In these dirty superconductors, with the mean free path much smaller than the coherence length, the Werthamer–Helfand–Hohenber theoretical model does not fit well the Hc2(T) data. We demonstrate that this discrepancy can result from the presence of strong inhomogeneity or from two-band superconductivity in these systems. Both the approaches very well describe the H − T dependencies, but the present results as well as our previous studies give stronger arguments for the scenario based on the presence of nanoscopic inhomogeneity of the superconducting state. A comparative study of La-doped and Ce-doped Ca3Rh4Sn13 showed that in the disordered Ca3−xCexRh4Sn13 alloys the presence of spin-glass effects is the cause of the additional increase of in respect to the critical temperatures of disordered Ca3−xLaxRh4Sn13. We also revisited the nature of structural phase transition at K and documented that there might be another precursor transition at higher temperatures. Raman spectroscopy and thermodynamic properties suggest that this structural transition may be associated with a CDW-type instability.

An efficient level set method for simultaneous intensity inhomogeneity correction and segmentation of MR images

Intensity inhomogeneity (bias field) is a common artefact in magnetic resonance (MR) images, which hinders successful automatic segmentation. In this work, a novel algorithm for simultaneous segmentation and bias field correction is presented. The proposed energy functional allows for explicit regularization of the bias field term, making the model more flexible, which is crucial in presence of strong inhomogeneities. An efficient minimization procedure, attempting to find the global minimum, is applied to the energy functional. The algorithm is evaluated qualitatively and quantitatively using a synthetic example and real MR images of different organs. Comparisons with several state-of-the-art methods demonstrate the superior performance of the proposed technique. Desirable results are obtained even for images with strong and complicated inhomogeneity fields and sparse tissue structures.

Determining the wavelength of Langmuir wave packets at the Earth's bow shock

Abstract. The propagation of Langmuir waves in plasmas is known to be sensitive to density fluctuations. Such fluctuations may lead to the coexistence of wave pairs that have almost opposite wave-numbers in the vicinity of their reflection points. Using high frequency electric field measurements from the WIND satellite, we determine for the first time the wavelength of intense Langmuir wave packets that are generated upstream of the Earth's electron foreshock by energetic electron beams. Surprisingly, the wavelength is found to be 2 to 3 times larger than the value expected from standard theory. These values are consistent with the presence of strong inhomogeneities in the solar wind plasma rather than with the effect of weak beam instabilities.

Solitary waves on manifolds of integrate-and-fire neurons

Abstract We investigate lattices of interacting integrate-and-fire neurons. Excitatory short-range interactions lead to coherent firing patterns such as moving stripes on a two-dimensional surface. They have been suggested as possible explanations of hallucinatory phenomena. Other known formations include rotating spirals and expanding concentric rings. We obtain all of them using a novel two-variable description of integrate-and-fire neurons that allows for a continuum formulation of neural fields. Within our model we can formulate a topological constraint that explains why all the moving coherent patterns have a dimension lower by one unit from that of the manifold. In the presence of strong inhomogeneity, neural continuity breaks down, and the field approximation no longer holds. In that case, one obtains incoherent firing patterns driven by the excitatory interactions.

Solitary waves of integrate-and-fire neural fields.

Arrays of interacting identical neurons can develop coherent firing patterns, such as moving stripes that have been suggested as possible explanations of hallucinatory phenomena. Other known formations include rotating spirals and expanding concentric rings. We obtain all of them using a novel two-variable description of integrate-and-fire neurons that allows for a continuum formulation of neural fields. One of these variables distinguishes between the two different states of refractoriness and depolarization and acquires topological meaning when it is turned into a field. Hence, it leads to a topologic characterization of the ensuing solitary waves, or excitons. They are limited to pointlike excitations on a line and linear excitations, including all the examples noted above, on a two-dimensional surface. A moving patch of firing activity is not an allowed solitary wave on our neural surface. Only the presence of strong inhomogeneity that destroys the neural field continuity allows for the appearance of patchy incoherent firing patterns driven by excitatory interactions.

Spatial patterns of sound propagation in sand.

This paper addresses the problem of how sound propagates in a granular medium composed of noncohesive particles. This propagation has many unusual aspects which are due to the fragile nature of the contacts between grains. Sound propagation in a granular material is very sensitive to the exact position of each of the grains. The thermal expansion of a single bead of about 3000 \AA{} can produce a change as large as 25% in the total transmission of the sound even though this expansion is 4 to 5 orders of magnitude smaller than the wavelength of the sound or the size of a bead (5 mm). I interpret this as being due to sound propagating predominantly along force chains within the medium. By replacing some of the beads with local heaters, I have used this effect to investigate the spatial properties of the low-amplitude vibrations. The disturbance of a single heater can be characterized by a time scale ${\mathrm{\ensuremath{\tau}}}_{\mathit{h}}$ which reveals the elapsed time of the signal traveling along a path via the heater. Two heaters placed symmetrically with respect to the source and detector can produce very different disturbances. Finally, I show that the spatial pattern caused by heaters placed at different positions within the medium is very irregular in that two adjacent heaters can give very different responses. These experiments all indicate the presence of strong inhomogeneities and the existence of force chains within the medium along which the sound predominantly travels.