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51.
In a bounded domain with smooth boundary in ?3 we consider the stationary Maxwell equations for a function u with values in ?3 subject to a nonhomogeneous condition (u, v)x = u0 on the boundary, where v is a given vector field and u0 a function on the boundary. We specify this problem within the framework of the Riemann-Hilbert boundary value problems for the Moisil-Teodorescu system. This latter is proved to satisfy the Shapiro-Lopaniskij condition if an only if the vector v is at no point tangent to the boundary. The Riemann-Hilbert problem for the Moisil-Teodorescu system fails to possess an adjoint boundary value problem with respect to the Green formula, which satisfies the Shapiro-Lopatinskij condition. We develop the construction of Green formula to get a proper concept of adjoint boundary value problem. 相似文献
52.
Roberta Citro Emanuele G. Dalla Torre Luca D’Alessio Anatoli Polkovnikov Mehrtash Babadi Takashi Oka Eugene Demler 《Annals of Physics》2015
We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine–Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculation. Classical and quantum experiments are proposed to verify the validity of our results. 相似文献
53.
We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like an atmosphere. The engine first gets an energy intake, which can be done in an arbitrary nonequilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits their efficiency. For ergodic engines we find a rigorous upper bound for the efficiency, which is strictly smaller than the equivalent Carnot efficiency. I.e. the Carnot efficiency can be never achieved in single reservoir heat engines. For non-ergodic engines the efficiency can be higher and can exceed the equilibrium Carnot bound. By extending the fundamental thermodynamic relation to nonequilibrium processes, we find a rigorous thermodynamic bound for the efficiency of both ergodic and non-ergodic engines and show that it is given by the relative entropy of the nonequilibrium and initial equilibrium distributions. These results suggest a new general strategy for designing more efficient engines. We illustrate our ideas by using simple examples. 相似文献
54.
A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum systems. We study this quantity after an interaction quench in lattice hard-core bosons and spinless fermions, and after a local chemical potential quench in a system of hard-core bosons in a superlattice potential. The former systems have a chaotic regime, where the diagonal entropy becomes equivalent to the equilibrium microcanonical entropy, coinciding with the onset of thermalization. The latter system is integrable. We show that its diagonal entropy is additive and different from the entropy of a generalized Gibbs ensemble, which has been introduced to account for the effects of conserved quantities at integrability. 相似文献
55.
A. D. Akhsakhalyan E. B. Kluenkov A. Ya. Lopatin V. I. Luchin A. N. Nechay A. E. Pestov V. N. Polkovnikov N. N. Salashchenko M. V. Svechnikov M. N. Toropov N. N. Tsybin N. I. Chkhalo A. V. Shcherbakov 《Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques》2017,11(1):1-19
A real opportunity for applying traditional optical methods to soft X-ray and extreme UV (ultraviolet) radiation bands has appeared thanks to recent successes in the area of multilayer-mirror deposition and procedures for fabricating supersmooth and highly precise substrates of mirrors. The implementation of this opportunity opens up fundamentally new prospectss in the nanodiagnostics of substances, micro- and nanoelectronics, microbiology, solar astronomy and other applications. The main directions in multilayer X-ray optics developed at the Institute for the Physics of Microstructures, Russian Academy of Sciences, are presented and the aspects of the use thereof in science and technology are considered. The main problems arising during the fabrication of multilayer interference structures for the soft X-ray and extreme UV bands are discussed. The main results obtained recently in the scope of each direction of investigation are presented. Plans for the future development of these directions are discussed. 相似文献
56.
We discuss necessary and sufficient conditions for a sensing matrix to be “s-good”—to allow for exact ℓ
1-recovery of sparse signals with s nonzero entries when no measurement noise is present. Then we express the error bounds for imperfect ℓ
1-recovery (nonzero measurement noise, nearly s-sparse signal, near-optimal solution of the optimization problem yielding the ℓ
1-recovery) in terms of the characteristics underlying these conditions. Further, we demonstrate (and this is the principal
result of the paper) that these characteristics, although difficult to evaluate, lead to verifiable sufficient conditions
for exact sparse ℓ
1-recovery and to efficiently computable upper bounds on those s for which a given sensing matrix is s-good. We establish also instructive links between our approach and the basic concepts of the Compressed Sensing theory, like
Restricted Isometry or Restricted Eigenvalue properties. 相似文献
57.
58.
Phil Howlett Charles Pearce Anatoli Torokhti 《Journal of Computational Analysis and Applications》2003,5(3):273-297
In this paper, we provide a state-of-the-art survey of some recent methods in nonlinear operator approximation theory and its applications. We give existence theorems for approximating operators. and discuss corresponding numerical schemes. The new results are natural but very specific extensions of known techniques to the so-called realistic operator approximation. 相似文献
59.
We prove that the solution of the Neumann problem for the Helmholtz equation in a plane angle Ω with boundary conditions from the space H−1/2(Γ), where Γ is the boundary of Ω, which is provided by the well‐known Sommerfeld integral, belongs to the Sobolev space H1(Ω) and depends continuously on the boundary values. To this end, we use another representation of the solution given by the inverse two‐dimensional Fourier transform of an analytic function depending on the Cauchy data of the solution. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
60.
Yuli K. Godovsky Irina A. Volegova Elena V. Konyukhova Anatoli E. Chalykh Vladimir K. Gerasimov Faina A. Avgonova 《Macromolecular Symposia》2000,149(1):113-118
Temperature transitions and structural transformations were studied for blends of two thermotropic mesophase cyclolinear polymethylsiloxanes with linear PDMS of various molecular weights by means of DSC, optical polarizing microscopy, and optical interferometry. Compatibility of the components which depends on the chemical structure of cyclolinear polymethylsiloxanes, molecular weight of PDMS, composition, and temperature affect formation of mesophase in cyclolinear polymethylsiloxanes. The most interesting aspect of the phase behaviour consists in the fact that it is possible to reach compatibility of the components in the mesomorphic state for the blends of two cyclolinear polymethylsiloxanens due to various annealing regimes in one‐phase molten state. 相似文献