Renormalization group calculation of the critical temperature dependence on longitudinal magnetic field for a disordered superconductor model

We describe a calculation ofT _c (P, H) in a model of a disordered superconductor which is based on the de Gennes-Skal-Shklovskii (dGSS) picture of the large cluster in a percolation system. The calculation is done by carrying out successive decimations on the Landau-Ginzburg Hamiltonian describing the links in the model. We calculateT _c (P, H) in the presence of longitudinal magnetic field by evaluating the renormalized Landau-Ginzburg coupling when the renormalized Landau-Ginzburg length equals the percolation link length in the dGSS picture and obtain the approximate analytic form ofT _c (P, H).Work supported by China Natural Science Foundation     

Nonlinear properties of surface “screw” instability in symmetric semiconductor plates

For the first time we study the nonlinear properties of the surface screw instability (SSI) when waves are excited at both faces of a plate and the interaction between them must be taken into account. The nature of the SSI development and the stability of surface screw waves against modulation are examined. Diagrams of the regions where the SSI development is soft and explosive as well as the regions of modulated waves are given in the space of parameters characterizing the electro-hole plasma and external fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 30–34, April 1990.     

Erbium:YAG (2.94 mum) laser effects on dental tissues

Past trials with soft and calcified tissues have demonstrated that long pulse train (2.5 mus) Er:YAG (2.94 mum) laser may be used to ablate tooth structure of human teeth. Determination of physical and thermal damage to surrounding tissue during removal of enamel and dentin is a primary objective of this study. Extracted human teeth with thermal probes imbedded in the pulp chambers were submitted to cavity preparation using an Erbium YAG laser with water mist. Wavelength selection as well as use of a water mist during the procedure resulted in efficient tissue removal without significant surrounding damage. Ground sections and SEM sections of teeth showed little or no melting or ash formation in adjacent dentin and enamel and no visible change in the pulp chamber. The surfaces produced by laser ablation were rough and irregular with craters and grooves. Average temperature change in the pulp chamber monitored during tooth preparation was 2.2 degrees Centigrade. These findings suggest that constantly available water aids vaporization and microexplosions, increasing the efficiency of tooth structure removal, and aids in cooling of the tooth structures. The long pulse Er:YAG (2.94 mum) laser may be an effective method for tooth reduction applications when used with a water mist.     

Behavior of effective charges in e6 grand unification theory in curved spacetime

The behavior of effective charges _i(t) corresponding to the parameters of nonminimal coupling of scalar and gravitational fields in E₆ Grand Unification Theory (GUT) in curve spacetimes is studied. It is shown that in a strong gravitational field ¦_i(t)¦ grows indefinitely.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 74–11, September, 1990.     

Excitation spectrum of anisotropic non-dissipative elastic-plastic medium

The simplest gauge theory of an elastic-plastic medium is considered in this paper that takes account of just translational plasticity. The equations of motion for such a model turn out to be linear and permit the normal modes spectrum of a medium to be obtained. Taking account of plasticity results in a cardinal transformation of the elastic branches of the spectrum and the appearance of a group of plasma oscillations of a dislocation gas.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 64–68, June, 1990.     

Dependence of “Reststrahlen” bands in far-infrared reflectivity on configuration of GaAs/AlAs multiple quantum well heterostructures

Far infrared reflectivity measurements are performed on a series of GaAs/AlAs multiple quantum well (MQW) heterostructures with systematically varied thicknesses of the constituent layers. In addition to the artificial anisotropy we observe two distinct bulk-like Reststrahlen regions. The widths of the GaAs-like and the AlAs-like Reststrahlen bands strongly depend on the relative thicknesses of the constituent layers of the MQW heterostructures, in excellent agreement with the predictions of the effective-medium theory.Prof. Aldo Cingolani passed away just before the publication of this article. We would like to dedicate this paper to his memory     

A Dynamic location problem for graphs

We introduce a class of optimization problems, calleddynamic location problems, involving the processing of requests that occur sequentially at the nodes of a graphG. This leads to the definition of a new parameter of graphs, called the window indexWX(G), that measures how large a window into the future is needed to solve every instance of the dynamic location problem onG optimally on-line. We completely characterize this parameter:WX(G)k if and only ifG is a weak retract of a product of complete graphs of size at mostk. As a byproduct, we obtain two (polynomially recognizable) structural characterizations of such graphs, extending a result of Bandelt.     

Algorithms for proportional matrices in reals and integers

LetR be the set of nonnegative matrices whose row and column sums fall between specific limits and whose entries sum to some fixedh > 0. Closely related axiomatic approaches have been developed to ascribe meanings to the statements: the real matrixf R and the integer matrixa R are proportional to a given matrixp 0.These approaches are described, conditions under which proportional solutions exist are characterized, and algorithms are given for finding proportional solutions in each case.     

Metastable patterns in solutions of ut = ϵ2uxx − f(u)

We consider the equation in question on the interval 0 ≦ x ≦ 1 having Neumann boundary conditions, with f(u) = F(u), where F is a double well energy density with equal minima at u = ±1. The only stable states of the system are patternless constant solutions. But given two-phase initial data, a pattern of interfacial layers typically forms far out of equilibrium. The ensuing nonlinear relaxation process is extremely slow: patterns persist for exponentially long times proportional to exp{A_±l/?, where A = F(±1) and l is the minimum distance between layers. Physically, a tiny potential jump across a layer drives its motion. We prove the existence and persistence of these metastable patterns, and characterise accurately the equations governing their motion. The point of view is reminiscent of center manifold theory: a manifold parametrising slowly evolving states is introduced, a neighbourhood is shown to be normally attracting, and the parallel flow is characterised to high relative accuracy. Proofs involve a detailed study of the Dirichlet problem, spectral gap analysis, and energy estimates.