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A growing body of applied mathematics literature in recent years has focussed on the application of fractional calculus to problems of anomalous transport. In these analyses, the anomalous transport (of charge, tracers, fluid, etc.) is…
We use the high sensitivity to magnetic flux of mesoscopic conductance fluctuations in large quantum dots to investigate changes in the two-dimensional electron dispersion caused by an in-plane magnetic field. In particular, changes in…
We develop a time dependent random matrix theory describing the influence of a time-dependent perturbation on mesoscopic conductance fluctuations in open quantum dots. The effect of external field is taken into account to all orders of…
The influence of fluctuating conductivity on the coefficients known from the mean-field electrodynamics is considered. If the conductivity fluctuations are assumed as uncorrelated with the turbulent velocity field then only the effective…
We consider the induction of magnetic field in flows of electrically conducting fluid at low magnetic Prandtl number and large kinetic Reynolds number. Using the separation between the magnetic and kinetic diffusive lengthscales, we propose…
We consider the convected Helmholtz equation modeling linear acoustic propagation at a fixed frequency in a subsonic flow around a scattering object. The flow is supposed to be uniform in the exterior domain far from the object, and…
We propose a phenomenological theory of strong incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale external magnetic field. We argue that in the inertial range of scales, magnetic-field and velocity-field…
In this paper, we focus on a new wave equation described wave propagation in the attenuation medium. In the first part of this paper, based on the time-domain space fractional wave equation, we formulate the frequency-domain equation named…
The effect of fluctuations on the transport and thermodynamic properties of two-dimensional superconductors in a magnetic field is studied at low temperature. The fluctuation conductivity is calculated in the framework of the perturbation…
Quantum interference phenomena in the conductivity of mesoscopic ferromagnets are considered, particularly with regard to the effects of geometric phases acquired by electrons propagating through regions of spatially varying magnetization…
In this paper, we consider an inverse conductivity problem on a bounded domain $\Omega\subset\mathbb{R}^n$, $n\geq2$, also known as Electrical Impedance Tomography (EIT), for the case where unknown impenetrable obstacles are embedded into…
The non-Ohmic effect of a high electric field on the out-of-plane magneto-conductivity of a layered superconductor near the superconducting transition is studied in the frame of the Langevin approach to the time-dependent Ginzburg-Landau…
This paper concerns the inverse problem of determining a planar conductivity inclusion. Our aim is to analytically recover from the generalized polarization tensors (GPTs), which can be obtained from exterior measurements, a homogeneous…
Quantum transport in inhomogeneous magnetic fields is investigated numerically in two-dimensional systems using the equation of motion method. In particular, the diffusion of electrons in random magnetic fields in the presence of additional…
A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…
We consider the bilocal conductivity tensor, the two-probe conductance and its fluctuations for a disordered phase-coherent two-dimensional system of non-interacting electrons in the presence of a magnetic field, including correctly the…
In this letter we analyze the effects of an externally applied electric field on thermal fluctuations for a fluid containing charged species. We show in particular that the fluctuating Poisson-Nernst-Planck equations for charged…
We study mesoscopic fluctuations of the conductance through a quantum dot at the wings of the Coulomb blokade peaks. At low temperatures, the main mechanism of conduction is the elastic cotunneling. The conductance strongly fluctuates with…
We present a new method for the analysis of electromagnetic scattering from homogeneous penetrable bodies. Our approach is based on a reformulation of the governing Maxwell equations in terms of two uncoupled vector Helmholtz systems: one…
This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint…