A new formulation of regularized meshless method applied to interior and exterior anisotropic potential problems

This paper proposes a new formulation of regularized meshless method (RMM), which differs from the traditional RMM in that the traditional formulation generates the diagonal elements of influence matrix via null-field integral equations, while our new one directly employs the boundary integral equations at the domain point to evaluate the diagonal elements. We test the present RMM formulation to two-dimensional anisotropic potential problems in finite and infinite domains in comparison with the traditional RMM. Numerical results show that the present RMM sharply outperforms the traditional RMM in the solution of interior problems, while the latter is clearly superior for exterior problems. A rigorous theoretical analysis of circular domain case also corroborates such numerical experiment observations and is provided in the appendix of this paper.     

Crossing in the magnetic force-gap hysteresis curve of magnetic levitation systems with a high-Tc superconductor

For the magnetic levitation system consisting of a high-T_c superconductor and permanent magnet, the relation curve of magnetic force with gap between these two components is known as a hysteresis loop, that is, the approaching and departing portions envelop a complete one, and generally these two portions do not cross each other. However, in some special cases this crossing arises, and makes the complete loop broken. In this paper, by the numerical simulation of the magnetic force-gap curve in large numbers of physical and geometrical parameters, two typical crossings were found. To investigate the crossing and explore its physical causes, for one of the crossings, the current density in the superconductor was further calculated and its magnitude and vector distribution at the gaps nearby where the crossing arises were obtained. Based on these calculation results and an adequate discussion, the conclusion was induced that the crossing in the magnetic force-gap hysteresis curve results from applied magnetic field’s incomplete and insufficient penetrating in superconductor.     

Comparison of performance characterization of asphalt mastic prepared by foamed and unfoamed asphalt binders

Journal of Thermal Analysis and Calorimetry - Applying foamed warm-mix asphalt in pavement has attracted great attention, but its effects on asphalt mastic are not clear. This research investigated...     

Homotopy analysis method for fractional IVPs

In this paper, the homotopy analysis method is applied to solve linear and nonlinear fractional initial-value problems (fIVPs). The fractional derivatives are described by Caputo’s sense. Exact and/or approximate analytical solutions of the fIVPs are obtained. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the approach.     

Density Functional Study of Two Seven-Membered Unconventional Fullerenes C58F17CF3 and C58F18

The density functional method is used to study the structure, electronic properties, static linear polarizabilities, and optical absorption spectra of two seven‐membered unconventional fullerene derivatives C₅₈F₁₇CF₃ and C₅₈F₁₈. It is calculated that three sites chosen to locate the CF₃ are isoenergetic. The energy gaps of C₅₈F₁₈ and C₅₈F₁₇CF₃ are much larger than that of C₅₈, indicating the fluorination and trifluoromethylation of C₅₈ can remarkably enhance the kinetic stability. The density of states explore that the influence of CF₃ to the energy levels is mainly distributed in the energy range from ?10 to ?2 eV. However, when the CF₃ substitutes for F in C₅₈F₁₈, the bond lengths, energy gaps, static linear polarizabilities, and optical absorption spectra all show small variety.     

具线性退化特征场对角型方程组Goursat问题的奇性形成机制

For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.     

扰动Nizhnik-Novikov-Veselov系统分形孤子渐近解

文章研究了一类扰动Nizhnik-Novikov-Veselov非线性系统, 利用特殊的渐近方法得到了相应系统分形孤子渐近解. 关键词： 孤子 渐近解 扰动     

Dynamics of non-autonomous parabolic problems with subcritical and critical nonlinearities

This is a subsequent work of our previous one in [25]. Let the nonlinear terms of non-autonomous parabolic problems with singular initial data satisfy subcritical and critical growth conditions. We first establish the existence of uniform attractors in W^1,r(Ω)$W^{1,r}(\Omega )$, 1<r<N$1<r<N$, for the family of processes corresponding to the equations with external forces being translation bounded but not translation compact. Then, we prove the existence of pullback attractors in L^r(Ω)$L^r(\Omega )$ and W^1,r(Ω)$W^{1,r}(\Omega )$, respectively, for the process corresponding to the equation with the weaker assumption on the external force than previous one. Finally, we investigate the robust of attractors and establish the existence of pullback exponential attractors for the process acting in L^r(Ω)$L^r(\Omega )$ and W^1,r(Ω)$W^{1,r}(\Omega )$, respectively.     

Fractional derivatives: Probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.     

Mechanism of the formation of singularities for quasilinear hyperbolic systems with linearly degenerate characteristic fields

One often believes that there is no shock formation for the Cauchy problem of quasilinear hyperbolic systems (of conservation laws) with linearly degenerate characteristic fields. It has been a conjecture for a long time (see Arch. Rational Mech. Anal. 2004; 172 :65–91; Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Springer: New York, 1984) and it is still an open problem in the general situation up to now. In this paper, a framework to justify this conjecture is proposed, and, by means of the concept such as the strict block hyperbolicity, the part richness and the successively block‐closed system, some general kinds of quasilinear hyperbolic systems, which verify the conjecture, are given. Copyright © 2007 John Wiley & Sons, Ltd.