Thermal Fluctuations of the Electric Field in the Presence of Carrier Drift

We consider a semiconductor in a non-equilibrium steady state, with a dc current. On top of the stationary carrier motion there are fluctuations. It is shown that the stationary motion of the carriers (i.e., their drift) can have a profound effect on the electromagnetic field fluctuations in the bulk of the sample as well as outside it, close to the surface (evanescent waves in the near field). The effect is particularly pronounced near the plasma frequency. This is because drift leads to a significant modification of the dispersion relation for the bulk and surface plasmons.Comment: Comments are welcom

Analytic model for a frictional shallow-water undular bore

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by friction. This is derived in Riemann variables using a modified finite-gap integration technique for the AKNS scheme. The Whitham system is then reduced to a simple first-order differential equation which is integrated numerically to obtain an asymptotic profile of the undular bore, with the local oscillatory structure described by the periodic solution of the unperturbed Kaup-Boussinesq system. This solution of the Whitham equations is shown to be consistent with certain jump conditions following directly from conservation laws for the original system. A comparison is made with the recently studied dissipationless case for the same system, where the undular bore is unsteady.Comment: 24 page

Whitham systems and deformations

We consider the deformations of Whitham systems including the "dispersion terms" and having the form of Dubrovin-Zhang deformations of Frobenius manifolds. The procedure is connected with B.A. Dubrovin problem of deformations of Frobenius manifolds corresponding to the Whitham systems of integrable hierarchies. Under some non-degeneracy requirements we suggest a general scheme of the deformation of the hyperbolic Whitham systems using the initial non-linear system. The general form of the deformed Whitham system coincides with the form of the "low-dispersion" asymptotic expansions used by B.A. Dubrovin and Y. Zhang in the theory of deformations of Frobenius manifolds.Comment: 27 pages, Late

Towards an ASM thesis for reflective sequential algorithms

Starting from Gurevich's thesis for sequential algorithms (the so-called "sequential ASM thesis"), we propose a characterization of the behaviour of sequential algorithms enriched with reflection. That is, we present a set of postulates which we conjecture capture the fundamental properties of reflective sequential algorithms (RSAs). Then we look at the plausibility of an ASM thesis for the class of RSAs, defining a model of abstract state machine (which we call reflective ASM) that we conjecture captures the class of RSAs as defined by our postulates

Multifocusing imaging over an irregular topography

If seismic data are acquired over an irregular topography, standard elevation statics methods may be inaccurate because the assumption of vertical raypaths will no longer be valid. An effective solution to the problem of irregular topography can be found through the use of the multifocusing method, in which large supergathers of seismic traces are stacked, each of which can span many common midpoint (CMP) gathers. This can be done by extending the multifocusing moveout formula to explicitly account for nonzero elevations of the source and receiver, as well as their horizontal coordinates.Implementation of this formula into the multifocusing algorithm is straightforward because estimating the necessary raypath information (i.e., emergence angles) is an integral part of the algorithm. The extended multifocusing moveout correction can be applied directly to the data acquired in areas of irregular topography without the need for prior elevation static corrections. Synthetic tests on such data show that the proposed technique results in a better alignment of reflection events

Flux flow of Abrikosov-Josephson vortices along grain boundaries in high-temperature superconductors

We show that low-angle grain boundaries (GB) in high-temperature superconductors exhibit intermediate Abrikosov vortices with Josephson cores, whose length $l$ along GB is smaller that the London penetration depth, but larger than the coherence length. We found an exact solution for a periodic vortex structure moving along GB in a magnetic field $H$ and calculated the flux flow resistivity $R_F(H)$, and the nonlinear voltage-current characteristics. The predicted $R_F(H)$ dependence describes well our experimental data on $7^{\circ}$ unirradiated and irradiated $YBa_2Cu_3O_7$ bicrystals, from which the core size $l(T)$, and the intrinsic depairing density $J_b(T)$ on nanoscales of few GB dislocations were measured for the first time. The observed temperature dependence of $J_b(T)=J_{b0}(1-T/T_c)^2$ indicates a significant order parameter suppression in current channels between GB dislocation cores.Comment: 5 pages 5 figures. Phys. Rev. Lett. (accepted

Magnetic cloaking by a paramagnet/superconductor cylindrical tube in the critical state

Cloaking of static magnetic fields by a finite thickness type-II superconductor tube being in the full critical state and surrounded by a coaxial paramagnet shell is studied. On the basis of exact solutions to the Maxwell equations, it is shown that, additionally to previous studies assuming the Meissner state of the superconductor constituent, perfect cloaking is still realizable at fields higher than the field of full flux penetration into the superconductor and for arbitrary geometrical parameters of both constituents. It is also proven that simultaneously the structure is fully undetectable under the cloaking conditions. Differently from the case of the Meissner state the cloaking properties in the application relevant critical state are realized, however, only at a certain field magnitude.Comment: 5 pages, 4 figures; to be published in Applied Physics Letters. arXiv admin note: substantial text overlap with arXiv:1401.356

Descriptive Complexity of Deterministic Polylogarithmic Time and Space

We propose logical characterizations of problems solvable in deterministic polylogarithmic time (PolylogTime) and polylogarithmic space (PolylogSpace). We introduce a novel two-sorted logic that separates the elements of the input domain from the bit positions needed to address these elements. We prove that the inflationary and partial fixed point vartiants of this logic capture PolylogTime and PolylogSpace, respectively. In the course of proving that our logic indeed captures PolylogTime on finite ordered structures, we introduce a variant of random-access Turing machines that can access the relations and functions of a structure directly. We investigate whether an explicit predicate for the ordering of the domain is needed in our PolylogTime logic. Finally, we present the open problem of finding an exact characterization of order-invariant queries in PolylogTime.Comment: Submitted to the Journal of Computer and System Science

Cavity solitons in vertical-cavity surface-emitting lasers

We investigate a control of the motion of localized structures of light by means of delay feedback in the transverse section of a broad area nonlinear optical system. The delayed feedback is found to induce a spontaneous motion of a solitary localized structure that is stationary and stable in the absence of feedback. We focus our analysis on an experimentally relevant system namely the Vertical-Cavity Surface-Emitting Laser (VCSEL). In the absence of the delay feedback we present experimental evidence of stationary localized structures in a 80 $\mu$m aperture VCSEL. The spontaneous formation of localized structures takes place above the lasing threshold and under optical injection. Then, we consider the effect of the time-delayed optical feedback and investigate analytically the role of the phase of the feedback and the carrier lifetime on the self-mobility properties of the localized structures. We show that these two parameters affect strongly the space time dynamics of two-dimensional localized structures. We derive an analytical formula for the threshold associated with drift instability of localized structures and a normal form equation describing the slow time evolution of the speed of the moving structure.Comment: 7 pages, 5 figure