Solutions in Sobolev spaces of vector refinement equations with a general dilation matrix

In this paper, we present a necessary and sufficient condition for the existence of solutions in a Sobolev space W_p^k(ℝ^s) (1≤p≤∞) to a vector refinement equation with a general dilation matrix. The criterion is constructive and can be implemented. Rate of convergence of vector cascade algorithms in a Sobolev space W_p^k(ℝ^s) will be investigated. When the dilation matrix is isotropic, a characterization will be given for the L_p (1≤p≤∞) critical smoothness exponent of a refinable function vector without the assumption of stability on the refinable function vector. As a consequence, we show that if a compactly supported function vector φ∈L_p(ℝ^s) (φ∈C(ℝ^s) when p=∞) satisfies a refinement equation with a finitely supported matrix mask, then all the components of φ must belong to a Lipschitz space Lip(ν,L_p(ℝ^s)) for some ν>0. This paper generalizes the results in R.Q. Jia, K.S. Lau and D.X. Zhou (J. Fourier Anal. Appl. 7 (2001) 143–167) in the univariate setting to the multivariate setting. Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 42C20, 41A25, 39B12. Research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) under Grant G121210654.     

Tunneling Radiation of a Torus-Like Black Hole in Anti-de Sitter Space-Time

An extension of the Parikh-Wilczek's semi-classical quantum tunneling method, the tunneling radiation of the charged particle from a torus-like black hole is investigated. Difference from the uncharged mass-less particle, the geodesics of the charged massive particle tunneling from the black hole is not light-like, but determined by the phase velocity. The derived result shows that the tunneling rate depends on the emitted particle's energy and electric charge, and takes the same functional form as uncharged particle. It proves also that the exact emission spectrum is not strictly pure thermal, but is consistent with the underlying unitary theory. PACS Numbers: 04.70.Dy, 97.60.Lf, 05.30.Ch.     

Dynamics of liquid membranes. II: Adaptive finite difference methods

Two domain-adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time-dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time-dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non-linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non-conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non-adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies.     

时分复用倍乘光脉冲重复率的新型光纤耦合器环状连接法分析

提出并详细分析了一种基于时分复用技术倍乘光脉冲重复率的方法：在２×２光纤耦合器的一个输入口与一个输出口间，接入时延为脉冲列半周期奇数倍的一段光纤使之形成环状连接循环耦合，而在另一输出口获得光脉冲。详细分析了该系统中光纤耦合器耦合比、插入损耗、时延光纤长度的要求，偏差的影响及其调节法，给出了理论公式、结果的计算机模拟与实验介绍；与经典的马赫陈德尔干涉仪接法及近年提出的Ｓａｇｎａｃ环接法进行了比较。该方法特别适用于对窄脉冲列进行串接复用实现重复率的多次倍乘，从而得到数千兆赫至上百千兆赫的高重复率光脉冲     

THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

1IntroductionThispaperisconcernedwithpositivesolutionOfthesemilinearheatequationswithlocalizedreactionssubjecttoeitherinitialconditions(Cauchyproblem)ortheinitialandboundary-value(DirichletorNeumanntype)conditionswherenisaboundeddomaininRe,icEO.Equations(1.1)canbethoughtofasamodeltodescribesomephysicalphenomena(heatpropagation,chemicalreaction)inwhichthenonlinearreactionsinadynndcalsystemtakesplaceonlyatasinglesite.InthesequelforconvenienceweshallsamplycalltheCauchy,initial-Direchlet,orini…     

Coulomb blockade in molecular quantum dots

The rate-equation approach is used to describe sequential tunneling through a molecular junction in the Coulomb blockade regime. Such device is composed of molecular quantum dot (with discrete energy levels) coupled with two metallic electrodes via potential barriers. Based on this model, we calculate nonlinear transport characteristics (conductance-voltage and current-voltage dependences) and compare them with the results obtained within a self-consistent field approach. It is shown that the shape of transport characteristics is determined by the combined effect of the electronic structure of molecular quantum dots and by the Coulomb blockade. In particular, the following phenomena are discussed in detail: the suppression of the current at higher voltages, the charging-induced rectification effect, the charging-generated changes of conductance gap and the temperature-induced as well as broadening-generated smoothing of current steps.     

Critical points in the Bragg glass phase of a weakly pinned crystal of Ca3Rh4Sn13

New experimental data are presented on the scan rate dependence of the magnetization hysteresis width ΔM(H) (∞ critical current densityJ _c(H)) in isothermalMH scans in a weakly pinned single crystal of Ca₃Rh₄Sn₁₃, which displays second magnetization peak (SMP) anomaly as distinct from the peak effect (PE). We observe an interesting modulation in the field dependence of a parameter which purports to measure the dynamical annealing of the disordered bundles of vortices injected through the sample edges towards the destined equilibrium vortex state at a givenH. These data, in conjunction with the earlier observations made while studying the thermomagnetic history dependence inJ _c(H) in the tracing of the minor hysteresis loops, imply that the partially disordered state heals towards the more ordered state between the peak field of the SMP anomaly and the onset field of the PE. The vortex phase diagram in the given crystal of Ca₃Rh₄Sn₁₃ has been updated in the context of the notion of the phase coexistence of the ordered and disordered regions between the onset field of the SMP anomaly and the spinodal line located just prior to the irreversibility line. A multi-critical point and a critical point in the (H,T) region of the Bragg glass phase have been marked in this phase diagram and the observed behavior is discussed in the light of recent data on multi-critical point in the vortex phase diagram in a single crystal of Nb.     

Evaluation of the drag force by integrating the energy dissipation rate in stokes flow for 2D domains using the FEM

The total drag force on the surface of a body, which is the sum of the form drag and the skin friction drag in a 2D domain, is numerically evaluated by integrating the energy dissipation rate in the whole domain for an incompressible Stokes fluid. The finite element method is used to calculate both the energy dissipation rate in the whole domain as well as the drag on the boundary of the body. The evaluation of the drag and the energy dissipation rate are post-processing operations which are carried out after the velocity field and the pressure field for the flow over a particular profile have been obtained. The results obtained for the flow over three different but constant area profiles—a circle, an ellipse and a cross-section of a prolate spheroid—with uniform inlet velocity are presented and it is shown that the total drag force times the velocity is equal to the total energy dissipation rate in the entire finite flow domain. Hence, by calculating the energy dissipation rate in the domain with unit velocity specified at the far-field boundary enclosing the domain, the drag force on the boundary of the body can be obtained.     

硼中子俘获治疗的蒙特卡罗方法模拟

用通用蒙特卡罗程序MCNP模拟了粒子在人脑中的输运过程. 吸收剂量率主要来自以下四个反应:¹⁰B(n,α)⁷Li,¹⁴N(n,p)¹⁴C,¹H(n,γ)²D,快中子弹性散射反应.对肿瘤区的贡献主要来自硼中子吸收反应.结果表明,超热中子比热中子适合于深肿瘤的治疗,而热中子对浅肿瘤的治疗有优越性,比如皮肤癌.同确定论方法的结果相比,蒙特卡罗方法不失为一种模拟中子俘获治疗的好工具.     

Representing the mean residual life in terms of the failure rate

In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Whereas the failure rate can be expressed quite simply in terms of the mean residual life and its derivative, the inverse problem—namely that of expressing the mean residual life in terms of the failure rate—typically involves an integral of a complicated expression. In this paper, we obtain simple expressions for the mean residual life in terms of the failure rate for certain classes of distributions which subsume many of the standard cases. Several results in the literature can be obtained using our approach. Additionally, we develop an expansion for the mean residual life in terms of Gaussian probability functions for a broad class of ultimately increasing failure rate distributions. Some examples are provided to illustrate the procedure.