Extended radial epiderivatives of non-convex vector-valued maps and parametric quasiconvex programming

In this paper, we consider extended vector-valued mappings defined on a normed linear space. Based on the recent semicontinuous regularizations related to hypographical and/or epigraphical profile mappings of the considered function introduced, we define semicontinuous radial epiderivatives. We, then, demonstrate that the properties of these epiderivatives amount to properties of hypographical and/or epigraphical profile mappings of the corresponding difference quotient of the underlying function, which simplify fairly well the proofs in the radial epiderivative formulaes. In particular, we stress the impact of semicontinuity, hence, we characterize with new arguments the radial epiderivatives in terms of the suprema and/or infima of the interiorly radial cone of the hypograph and/or epigraph of the considered function. Finally, we obtain optimality conditions for general non-convex constrained vector optimization problems. We apply thereafter the obtained pattern to a parametric quasiconvex programming problem for which we derive necessary and sufficient optimality conditions that are not sensitive to perturbation at the nominal level, yielding henceforth more – and strong at least under asymptotically regular constraints – information than the recent stability results obtained under additional conditions on the regularity of the normal cone to the adjusted sublevel sets of the underlying function.     

Observation of defect clustering in Gd-doped calcium fluoride

Abstract

Solid solutions Ca_1-xGd_xF_2+x for 3 × 10^?7≤ x ≤10^?1 have been studied by electron paramagnetic resonance (EPR) and ionic thermal currents (ITC). The EPR experiments show the presence of two single-ion sites a cubic and a tetragonal Gd³⁺ center which co-exist with comparable abundances for intermediate impurity concentrations. The cubic center predominates at very low and high concentrations. Seven different relaxation processes have been identified from the ITC spectra and the variation of their intensity vs. x was measured. The absolute concentrations of the cubic and nn Gd³⁺ dipoles were calculated. The scavenging of interstitial fluorines by the neutral clusters explains both the abundance of cubic sites at high concentration and the variety of orientable clusters detected by ITC.     

Symmetry and stability of asymptotic profiles for fast diffusion equations in annuli

This paper is concerned with stability analysis of asymptotic profiles for (possibly sign-changing) solutions vanishing in finite time of the Cauchy–Dirichlet problems for fast diffusion equations in annuli. It is proved that the unique positive radial profile is not asymptotically stable, and moreover, it is unstable for the two-dimensional annulus. Furthermore, the method of stability analysis presented here will be also applied to exhibit symmetry breaking of least energy solutions.     

蒸发器支撑板板孔精密测量系统

建立了蒸发器支撑板板孔精密测量系统,并提出了基于边缘约束条件的轮廓参量测量方法.首先采用图像处理技术将待测目标转化为二维离散坐标点,计算其最小外接矩形并对轮廓进行预定位;然后将轮廓分割成相互重合的"扩展邻域轮廓",建立以曲率角为原则的边缘约束算法对各轮廓段精确定界,实现对轮廓参量的精密测量.实验和误差分析表明,该系统测量准确度优于0.02mm,对具有复杂轮廓的零件参量测量有参考价值.     

Alternating-current losses in two-layer superconducting cables consisting of second-generation superconductors coated by U-shaped ferromagnetic materials

Alternating-current losses in a two-layer superconducting cable, each layer being composed of 15 closely-spaced rectangular wires made up of second-generation superconductors when the ends of wires are coated by either a non-magnetic or strong ferromagnetic material having a U profile is numerically investigated. Computations are carried out through the finite-element method. The alternating-current losses do not increase significantly if the relative permeability of the coating is increased three orders of magnitude, provided that the current amplitude is less than half of the critical current in a superconducting wire. However, the losses are much higher for ferromagnetic coating if the amplitude of the applied current oscillating at 50 Hz is close to the critical current. The ferromagnetic coating is seen to accumulate the magnetic field lines normally on its surfaces, while the field lines are parallel to the long axes of the wires, leading to more significant flux penetration in the coated regions. This facilitates a uniform low-loss current flow in the uncoated regions of the wires. In contrast, coating with a non-magnetic material gives rise to a considerably smaller current flow in the uncoated regions, whereas the low-loss flow is maintained in the coated regions. Moreover, the current flows in opposite directions in the coated and uncoated regions, where the direction in each region is converse for the two materials.     

Poisson–Boltzmann for oppositely charged bodies: an explicit derivation

The interaction between two parallel charged plates in ionic solution is a general starting point for studying colloidal complexes. An intuitive expression of the pressure exerted on the plates is usually proposed, which includes an electrostatic plus an osmotic contribution. We present here an explicit and self-consistent derivation of this formula in the only framework of the Poisson–Boltzmann (PB) theory. We also show that, depending on external constraints, the correct thermodynamic potential can differ from the usual PB free energy. For asymmetric, oppositely charged plates, the resulting expression predicts a non-trivial equilibrium position with the plates separated by a finite distance. The depth of this energy minimum is decisive for the stability of the complex. It is therefore crucial to obtain its explicit dependence on the charge densities of the plates and on the ion concentration. Analytic expressions for the position and depth of the energy minimum were derived in 1975 by Ohshima [Colloid Polym. Sci. 253, 150 (1975)] but, surprisingly, these important results seem to have been overlooked. We retrieve these expressions in a simpler formalism, more familiar to the physics community, and give a physical interpretation of the observed behavior.     

Investigation of a UV-laser generated waveguide in a planar polymer chip using an improved interferometric method

Polymeric integrated-optical waveguides are prepared in a planar polymer chip by UV-laser lithographic methods. The waveguide samples are irradiated by an excimer laser at a wavelength Λ=248 nm with various irradiation parameters (different fluencies and irradiation doses). Mach-Zehnder interferometer is employed and the refractive index depth profiles of the waveguide samples are obtained. This profile covers two regions having exponential and Gaussian shapes. The model field distributions strongly depend on the refractive index of each region. The mode field distribution and the effective mode indices for each region have been calculated on the basis of a theoretical model and the experimentally measured data.     

Dispersion Stability of Fluorinated Multi-Walled Carbon Nanotubes in FC-27 Refrigerant

In order to achieve the dispersion stability of multi-walled carbon nanotubes (MWCNT) in a fluorinated refrigerant (FC-72) used in various cooling purposes, fluorinated MWCNT (MWCNT-F) was prepared by a combined process of oxidation and fluorination. As a fluorine source, (tridecafluoro-1,1,2,2-tetrahydrooctyl)trichlorosilane was used to react with hydroxyl groups on MWCNT (MWCNT-OH) generated by chemical oxidation. Pristine MWCNT, MWCNT-OH, and MWCNT-F were dispersed in FC-72 and MWCNT-F was also dispersed in polar and nonpolar solvents. The MWCNT-F has excellent colloidal stability in FC-72 because of the chemical affinity between FC-72 and functional groups (-CF_n) on the side walls of MWCNT. Through surface modifications, we could obtain the enhanced dispersion stability of MWCNT in a refrigerant. This homogenous MWCNT solution in FC-72 may be used to increase the heat transfer in FC-72 based nanofluids.     

Monodisperse Crosslinked Microsphere Polymer Particles by Dispersion Copolymerization of Glycidyl Methacrylate and Divinylbenzene

Monodisperse polyglycidyl methacrylate (PGMA) microsphere particles crosslinked with divinylbenzene crosslinker were prepared by single-stage dispersion copolymerization in ethanol medium. 1 wt% of DVB was successfully incorporated due to the costabilizing effect of GMA as a surface-active monomer. This behavior may indicate that the fast formation of stable primary particle leads to monodispersity. The average particle sizes and the particle size distributions increased with the DVB crosslinker concentration. The effects of two different variables (initiator concentration, crosslinker concentration) on the rate of dispersion copolymerization have been investigated. With the initiator concentration, the polymerization procedure mainly depended on the dual natures of general dispersion polymerization, in the crosslinked state. Up to 1 wt% DVB, the particle growth was controlled by the monomer diffusion from the continuous phase into the particle phase.     

Stable blow-up dynamics in the -critical and -supercritical generalized Hartree equation

We study stable blow-up dynamics in the generalized Hartree equation with radial symmetry, which is a Schrödinger-type equation with a nonlocal, convolution-type nonlinearity: First, we consider the -critical case in dimensions and obtain that a generic blow-up has a self-similar structure and exhibits not only the square root blowup rate , but also the log-log correction (via asymptotic analysis and functional fitting), thus, behaving similarly to the stable blow-up regime in the -critical nonlinear Schrödinger equation. In this setting, we also study blow-up profiles and show that generic blow-up solutions converge to the rescaled , a ground state solution of the elliptic equation . We also consider the -supercritical case in dimensions . We derive the profile equation for the self-similar blow-up and establish the existence and local uniqueness of its solutions. As in the NLS -supercritical regime, the profile equation exhibits branches of nonoscillating, polynomially decaying (multi-bump) solutions. A numerical scheme of putting constraints into solving the corresponding ordinary differential equation is applied during the process of finding the multi-bump solutions. Direct numerical simulation of solutions to the generalized Hartree equation by the dynamic rescaling method indicates that the is the profile for the stable blow-up. In this supercritical case, we obtain the blow-up rate without any correction. This blow-up happens at the focusing level , and thus, numerically observable (unlike the -critical case). In summary, we find that the results are similar to the behavior of stable self-similar blowup solutions in the corresponding settings for the nonlinear Schrödinger equation. Consequently, one may expect that the form of the nonlinearity in the Schrödinger-type equations is not essential in the stable formation of singularities.