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101.
Fabrizio Colombo Samuele Mongodi Marco Peloso Stefano Pinton 《Mathematical Methods in the Applied Sciences》2019,42(5):1662-1686
Let e?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory. 相似文献
102.
In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) on undirected graphs. He proved that there exists an EMSO sentence ? such that does not converge as (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices ). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-one law holds. In this paper, we disprove this conjecture. 相似文献
103.
We propose a discrete-time model of opinion dynamics. The neighborhood relationship is decided by confidence radius and influence radius of each agent. We investigate the influence of heterogeneity in confidence/influence distribution on the behavior of the network. The simulations suggest that the heterogeneity of single confidence or influence networks can promote the opinions to achieve consensus. It is shown that the heterogeneous influence radius systems converge in fewer time steps and more often in finite time than the heterogeneous confidence radius systems. We find that heterogeneity does not always promote consensus, and there is an optimal heterogeneity so that the relative size of the largest consensus cluster reaches maximum in heterogeneous confidence and influence networks. 相似文献
104.
Antonio M. Scarfone Hiroki Suyari Tatsuaki Wada 《Central European Journal of Physics》2009,7(3):414-420
We reformulate the Gauss’ law of error in presence of correlations which are taken into account by means of a deformed product
arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product
and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an
asymptotic power-law behavior.
相似文献
105.
S. Yasin P. F. Luckham T. Iqbal M. Zafar 《Journal of Dispersion Science and Technology》2013,34(2):268-272
For making stable dispersions of graphitic carbon black (Monarch 700), the effectiveness of three dispersants/polymers (hypermer LP1, hypermer B246, and OLOA 11000) in xylene is investigated. Hypermer LP1 (polyhydroxystearic acid) is a homopolymer and hypermer B246 (PEG 30-dipolyhydroxystearate) is a polyhydroxystearic acid/polyethylene oxide/polyhydroxystearic acid ABA block copolymer, while OLOA 11000 (polyisobutylene succinimide) has a polar head group (polyamine) attached to a hydrocarbon chain (polyisobutylene). Well-dispersed graphitic carbon black dispersions were prepared using dispersants at optimum concentrations. Percolation threshold and rheological threshold were determined by analyzing the variations in electrical conductivity and elastic modulus with concentration of carbon black. Above threshold concentration, scaling law was applied to experimental data of rheology (dynamic measurements) and electrical conductivity measurements to evaluate quality of the system. Effectiveness of polymers was investigated on the basis of value of critical exponent (t and t′, respectively) in scaling power law. Hypermer LP1 was proved to be a poor dispersant for Monarch 700 dispersions while other two polymers were found to be effective stabilizers. 相似文献
106.
本文研究了可加稳定过程的自相交局部时的问题.利用Borel–Canteil引理等方法,得到可加稳定过程的自相交局部时的Hlder上界,推广了文献[5]中的结果. 相似文献
107.
The focus of this article is on the analysis of repairable systems that are subject to multiple sources of recurrence. The event of interest at the system level is assumed to be caused by the earliest occurrence of a source, thereby conforming to a series system competing risks framework. Parametric inference is carried out under the power law process model that has found significant attention in industrial applications. Dependence among the cause‐specific recurrent processes is induced via a shared frailty structure. The theoretical inference results are implemented to a warranty database for a fleet of automobiles, for which the warranty repair is triggered by the failure of one of many components. Extensive finite‐sample simulation is carried out to supplement the asymptotic findings. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
108.
Yan Guan Dayu Zhou Jin Xu Xiaohua Liu Fei Cao Xianlin Dong Johannes Müller Tony Schenk Uwe Schroeder 《固体物理学:研究快报》2015,9(10):589-593
A wealth of studies have confirmed that the low‐field hysteresis behaviour of ferroelectric bulk ceramics and thin films can be described using Rayleigh relations, and irreversible domain wall motion across the array of pining defects has been commonly accepted as the underlying micro‐mechanism. Recently, HfO2 thin films incorporated with various dopants were reported to show pronounced ferroelectricity, however, their microscopic domain structure remains unclear till now. In this work, the effects of the applied electric field amplitude, frequency and temperature on the sub‐coercive polarization reversal properties were investigated for 10 nm thick Si‐doped HfO2 thin films. The applicability of the Rayleigh law to ultra‐thin ferroelectric films was first confirmed, indicating the existence of a multi‐domain structure. Since the grain size is about 20–30 nm, a direct observation of domain walls within the grains is rather challenging and this indirect method is a feasible approach to resolve the domain structure. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim) 相似文献
109.
110.
《Wave Motion》2020
Acoustoelastic effect describes the change of ultrasound velocity due to the initial stress. Its simulation involves a numerical analysis of nonlinear elastodynamics and requires high accuracy in the time domain. A time–space finite element formulation, derived from the quadratic interpolation of the acceleration within a time segment, is proposed for an accurate simulation of the acoustoelastic effect in the present study. Ten different integration schemes are generated based on this formulation and nine of them are found to be conditionally stable. Among the nine stable schemes, one is found to obtain a spectral radius of one when the normalized step ratio is less than 5.477, indicating no numerical dissipation or numerical divergence. Compared with integration schemes from previous studies, this integration scheme demonstrates better performance in calculation accuracy and energy conservation. A two-stage approach, namely the static stage and the dynamic stage, has been employed in the simulation of the acoustoelastic effect. The former stage is adopted to obtain the initial stress and the latter stage, where the proposed integration scheme is implemented, is adopted to simulate the ultrasound propagation in an initial stress state. The simulation results of the dynamic stage show that the ultrasound velocity increases in a compression stress state and decreases in a tension stress state for aluminum alloy, which is in good agreement with previous experimental studies. Together with the simulation result of the static stage, it is conjectured that the acoustoelastic effect results from the stress-dependent elastic modulus. 相似文献