Narrow Results

We have investigated the residual in-plane strain and width of the surface misfit dislocation free zone in linearly-graded GaAs_1-yP_y metamorphic buffer layers as approximated by a finite number of sublayers. For this purpose we have developed an electric circuit model approach for the equilibrium analysis of these structures, in which each sublayer may be represented by an analogous configuration involving a current source, a resistor, a voltage source, and an ideal diode. The resulting node voltages in the analogous electric circuit correspond to the equilibrium strains in the original epitaxial structure. Utilizing this new approach, we show that the residual surface strain in linearly-graded epitaxial structures increases monotonically with grading coefficient as well as the number of sublayers, and is strongly dependent on the width of the misfit dislocation free zone, which diminishes with an increasing grading coefficient.

In this paper we address a relaxation theorem for a new integral functional of the calculus of variations defined on the space of functions in whose gradient is an L^p-vector field with distributional divergence given by a Radon measure. The result holds for integrand of type f(x, Δu) without any coerciveness condition, with respect to the second variable, and C¹-continuity assumptions with respect to the spatial variable x.

Using the new supercomputer JUMP at the Research Center Jülich, we were able to simulate large lattices (up to L=2·10⁶, a new world record) for long times (up to T=6000 for L=1.5·10⁵). Using this data, we examined the dynamical critical exponent z. The old assumption of z=2 with logarithmic corrections seems very unlikely according to our data, leaving the asymptotic value of z≃2.167.

In this paper we compare the relaxation in several versions of the Sznajd model (SM) with random sequential updating on the chain and square lattice. We start by reviewing briefly all proposed one-dimensional versions of SM. Next, we compare the results obtained from Monte Carlo simulations with the mean field results obtained by Slanina and Lavicka. Finally, we investigate the relaxation on the square lattice and compare two generalizations of SM, one suggested by Stauffer et al. and another by Galam. We show that there are no qualitative differences between these two approaches, although the relaxation within the Galam rule is faster than within the well known Stauffer et al. rule.

In this paper, we have studied theoretically the effects of gold adsorption on the Al(001) surface, using ab initio pseudo-potential method in the framework of the density functional theory. Having found the hollow sites at the Al(001) surface as the most preferred adsorption sites, we have investigated the effects of the Au adsorption with different coverages (Θ =0.11, 0.25, 0.50, 0.75, 1.00 ML) on the geometry, adsorption energy, surface dipole moment, and the work function of the Al(001) surface. The results show that even though the work function of the Au substrate increases with the Au coverage, the surface dipole moment decreases with the changes in coverage from Θ =0.11 to 0.25 ML. We have explained this behavior by analyzing the electronic and ionic charge distributions. Furthermore, by studying the diffusion of Au atoms into the substrate, we have shown that at room temperature the diffusion rate of Au atoms into the substrate is negligible but increasing the temperature to about 200°C the Au atoms significantly diffuse into the substrate, in agreement with the experiment.

The standard Ising model in two and three dimensions was simulated with Metropolis-Glauber kinetics on the Intel Hypercube with 32 MIMD processors of i860 type, each with 16 megabytes of distributed memory, and on 8 such processors of the Alliant FX with shared memory. The nucleation time in reverse magnetic fields h. was found to increase as 1/h² in three dimensions, for times up to millions of iterations. The relaxation towards the equilibrium spontaneous magnetization was a simple exponential in three dimensions and a stretched exponential in two below the critical temperature; its power-law decay at the critical point lead to z=2.18(d=2) and =2.09 (d=3). The Becker-Döring equation for the growth of microdroplets leads at the critical temperature to a growth rate vanishing with some power of the time.

Simulations at the critical point for short times t agree in part with the expected logarithmic powers for systems up to 336⁴.

The principle of indirect elimination states that an algorithm for solving discretized differential equations can be used to identify its own bad-converging modes. When the number of bad-converging modes of the algorithm is not too large, the modes thus identified can be used to strongly improve the convergence. The method presented here is applicable to any linear algorithm like relaxation or multigrid. An example from theoretical physics, the Dirac equation in the presence of almost-zero-modes arising from instantons, is studied. Using the principle, bad-converging modes are removed efficiently. It is sketched how the method can be used for a Conjugate Gradient algorithm. Applied locally, the principle is one of the main ingredients of the Iteratively Smoothing Unigrid algorithm.

Iterative transportation microsimulations adjust traveler route plans by iterating between a microsimulation and a route planner. At each iteration, the route planner adjusts individuals' route choices based on the preceding microsimulations. Empirically, this process yields good results, but it is usually unclear when to stop the iterative process when modeling real-world traffic. This paper investigates several criteria to judge relaxation of the iterative process, emphasizing criteria related to traveler decision-making.

In this paper a new formulation of the simple plant location problem (SPLP) is given that uses the style of Sharma and Sharma (European Journal of Operational Research, 122(3), 37–48). When the integer restrictions are relaxed, it results in a new relaxation of SPLP that is different from the already well known "strong" and "weak" relaxation of SPLP. It is shown that the bound given by the new relaxation is worse than the bound given by "strong relaxation" of SPLP. However, a numerical example illustrates that the bound given by the new relaxation can at times be better than the bound given by "weak relaxation" (already known) of SPLP. In this paper a new proof [which is different from the one given by Bilde and Krarup (Annals of Discrete Mathematics, 1, 79–97)] is given to establish relative strengths of various relaxations of SPLP.

This paper concentrates on improving the convergence properties of the relaxation schemes introduced by Kadrani et al. and Kanzow and Schwartz for mathematical program with equilibrium constraints (MPEC) by weakening the original constraint qualifications. It has been known that MPEC relaxed constant positive-linear dependence (MPEC-RCPLD) is a class of extremely weak constraint qualifications for MPEC, which can be strictly implied by MPEC relaxed constant rank constraint qualification (MPEC-RCRCQ) and MPEC relaxed constant positive-linear dependence (MPEC-rCPLD), of course also by the MPEC constant positive-linear dependence (MPEC-CPLD). We show that any accumulation point of stationary points of these two approximation problems is M-stationarity under the MPEC-RCPLD constraint qualification, and further show that the accumulation point can even be S-stationarity coupled with the asymptotically weak nondegeneracy condition.

Experimental data on the field and time dependencies of the isothermal magnetization hysteresis for Tl₂Ba₂CaCu₂O₈ single crystals with fields applied parallel to the c-axis are reported. From the M–H measurements, we determined the first peak field (H_p), the onset field of the second peak (H_on), the second peak field (H_sp), and the irreversible field (H_irr). Using these physical parameters, we have drawn a vortex phase diagram for this system. As observed in BSCCO(2212) system, below the irreversibility line, the H–T plane is divided into three distinct phases: the vortex lattice, the entangle phase, and the quasi 2D pancake vortex states in the temperature interval 30 K≤T≤60 K.¹ From the relaxation of remanent magnetization measurements, we have obtained the flux creep activation barrier U(j) as a function of j using the method developed by Malay et al. Within the collective pinning theory, it is argued that T≤30 K, the pancake vortices are pinned individually, while for T≥42 K, the vortex state is characterized by individually pinned 3D vortex strings. At T~30 K, a crossover from 2D pancake to 3D collectively pinned state was observed and shows a smooth crossover to 3D single vortex state at higher temperatures.

Samples with the nominal composition Bi₂Sr₂GdCu₂O_y in Bi-2212 where Gd replaces Ca as well as samples without Gd were prepared by solid-state reaction method. From the room temperature X-ray diffraction data, the samples were found to be similar to the single phase Bi-2212 structure. Impedance studies were performed from room temperature to 423 K at different frequencies in the range of 10 to 700 KHz. The AC conductivity increases with temperature and frequency, exhibiting frequency dispersion at low temperature region. The activation energy from AC conductivity in the high temperature region is found to be 0.432 eV. The permitivity increases with the increase in temperature and at 373 K it shows a maximum value exhibiting a dielectric loss. Complex impedance spectra are analyzed in terms of bulk relaxation and interfacial effects. The activation energy of the dipoles involved in the relaxation was estimated to be 0.482 eV. The universal power law of Jonscher is verified in the present system.

The strong scattering limit of the magnetic field dependence of the local phonon-assisted nuclear spin relaxation rate, (NSRR), in two dimensional electron systems, (2DES) with magnetic impurities is calculated. It is shown that the NSRR can be tuned resonantly, by external magnetic field, due to the possibility of matching the electron Zeeman splitting with the energy spacing between the localized vibrational modes created by the lattice distortion around the impurity. This new resonance phenomenon could be used to manipulate, with high precision, the relaxation and decoherence times of nuclear spin based quantum information processing devices.

Five samples of mixed Y₂O₃/CaO doped ZrO₂ electrolytes, with the same nominal chemical composition of (ZrO₂)_0.90–(Y₂O₃)_0.04-( CaO)_0.06, were sintered at 1600^°C for 2, 4, 6, 8 and 10 h, respectively. The frequency dependence of the grain-boundary conductivity of each sample was measured using complex impedance method in the temperature range from 773 to 1073 K and experimental results were analyzed according to a power law, which was frequently referred to as the so-called universal dynamic response (UDR). Results indicated the apparent ac grain-boundary conductivity can be well-described by the power law and some useful information about the grain-boundary effect, such as the activation energy of the grain-boundary conduction and the dissociated energy of the charge carrier in the space charge layer, can be obtained by analyzing the temperature dependence of the power law parameters.

The polycrystalline sample of KPb₂V₅ O₁₅ was prepared by a mixed-oxide method relatively at low temperature (i.e., 550°C). X-ray diffraction studies of the compound showed the formation of single phase orthorhombic crystal structure at room temperature. SEM micrograph showed the homogeneous distribution of grains throughout the sample. Electric properties were analyzed using the complex impedance spectroscopy. The modulus plot showed the presence of both the grain and grain boundary effect. The bulk impedance evaluated from the Nyquist plots was observed to decrease with the rise in temperature, showing a negative temperature coefficient of resistance. The variation of AC electrical conductivity (σ_AC) was measured in a wide temperature (30–500°C) and frequency (10²–10⁶ Hz) range. The activation energy of the compound calculated from both the impedance and modulus spectrum was found to be the same.

We present the detailed dynamics of the particles in the $\beta$-Fermi–Pasta–Ulam–Tsingou (FPUT) chain after the initiation of a localized nonlinear excitation (LNE) by squeezing a central bond in the monodispersed chain at time $t$ = 0 while all other particles remain in their original relaxed positions. In the absence of phonons in the system, the LNE appears to initiate its relaxation process by symmetrically emitting two very weak solitary waves. The next stage involves the spreading of the LNE and the formation of nonsolitary wave-like objects to broaden the excitation region until a stage is reached when many weak solitary wave-like objects can be emitted as the system begins its journey to quasi-equilibrium and then to equilibrium. In addition to being of fundamental interest, these systems may be realized using cantilever systems and could well hold the key to constructing the next generation of broadband energy harvesting systems.

This paper provides information on a self-consistent model of an anomalously slow relaxation of nonwetting liquid–nanoporous medium systems with a random size distribution of pores, which introduces changes in interaction between local liquid cluster configurations in the process of liquid outflow from the porous medium. A self-consistent equation was deduced, the solution of which determines a functional connection of porous medium filling degree or time $𝜃(t)$. It is shown that the anomalously slow relaxation is presented as a process of decay of interacting local metastable configurations, initialized by thermal fluctuations. As time increments, relaxation acceleration takes place with subsequent avalanche fluid outflow from the porous medium, which is connected with interaction decrease between local configurations. The dependence of the fraction of volume of liquid remaining in a porous medium changes by the power law $𝜃(t)\sim t^{-\alpha (T,t)}$. It is shown that for a system of water–L23 at the initial stage in the time range of $10s<t<{10}^{3}s$, an index assumes a constant value $\alpha \approx \mathrm{\text{const}}(T)$, while at the following stage the acceleration of relaxation and the increase of parameter $\alpha (T,t)$ are observed.

Polyvinyl chloride (PVC) is widely used as insulator in electrical engineering especially as cable insulation sheaths. In order to improve the dielectric properties, polymers are mixed with ceramics. In this paper, PVC composites with different weight percentages 2 wt.%, 5 wt.%, 8 wt.% and 10 wt.% were prepared and investigated. Loss index (${𝜀}^{″}$) and dielectric constant (${𝜀}^{\prime }$) have been measured using an impedance analyzer RLC. Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy (SEM) equipped with energy dispersive X-ray (EDX) have been used as characterization techniques. The incorporation of BaTiO₃ does not modify the crystallinity and the morphology of the PVC but reduces the space charges, therefore the dielectric losses. The frequency response analysis has been followed in the frequency ranges (20–140 Hz and 115–1 MHz). Relaxation frequencies have been evaluated in each frequency range. Experimental measurements have been validated using Cole–Cole’s model. Experimental results show well that BaTiO₃ as a filler improves the dielectric properties of PVC.

The evolution of the current-voltage characteristic in K_0.3MoO₃ was observed intuitively with the presence of current cycling. No variation of the ohmic conductivity was distinguished, while the threshold field for the charge density waves depinning exhibited distinct enhancement with the current cycling. These results were attributed to the electric field-assisted metastable states' relaxation of the charge density waves.