Well-posedness of an evolution problem with nonlocal diffusion

We prove the well-posedness of a general evolution reaction–nonlocal diffusion problem under two sets of assumptions. In the first set, the main hypothesis is the Lipschitz continuity of the range kernel and the bounded variation of the spatial kernel and the initial datum. In the second set of assumptions, we relax the Lipschitz continuity of the range kernel to Hölder continuity, and assume monotonic behavior. In this case, the spatial kernel and the initial data can be just integrable functions. The main applications of this model are related to the fields of Image Processing and Population Dynamics.     

Stochastic modeling of quality of systems operating in a heterogeneous environment

We consider systems that are subject to an external mixed Poisson shock process. Each shock can result in a failure of a system with a given probability and is survived with the complementary probability. Each shock additionally decreases the quality function that describes the performance of a system, thus forming the corresponding stochastic process. Expectations (unconditional and conditional on survival) and relevant variability characteristics for the stochastic quality function are derived. Some monotonicity properties of the conditional quality function are investigated and the future values of this function are derived.     

Statistical inference for Vasicek-type model driven by Hermite processes

Let $Z$ denote a Hermite process of order $q\ge 1$ and self-similarity parameter $H\in (\frac{1}{2},1)$. This process is $H$-self-similar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $q?2$. In this paper, we deal with a Vasicek-type model driven by $Z$, of the form $d{X}_t=a(b?X_t)dt+d{Z}_t$. Here, $a>0$ and $b\in \mathbb{R}$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations.     

基于ANP法的股权激励模式选择研究

本文对企业如何科学合理地选择股权激励模式问题进行研究探讨。不仅考虑到以往研究中的企业特征因素,同时也考虑了激励对象特征因素和外部实施环境因素,建立股权激励模式选择指标体系,并分析各指标间的依存关系,基于此构建了ANP网络结构模型,并选取两个代表性样本企业进行算例验证和应用,最终使得不同企业可根据自身的实际情况选择合适的股权激励模式,验证了该模型的合理性与可行性。     

The formation of dead zones in nonisothermal porous catalyst with temperature-dependent diffusion coefficient

This paper considers the formation of dead zones in the porous catalyst pellets due to the chemical reaction and diffusion. We established and investigated the model with nonisothermal reaction of fractional order and activated temperature-dependent diffusivity. The effects of process parameters, catalyst shape, and reaction and diffusion parameters on the formation of the dead zone are studied numerically and characterized by the critical Thiele modulus. The lower bounds for the critical Thiele modulus are derived analytically in terms of process parameters for exothermic and endothermic reactions and verified numerically. The critical Thiele modulus increases with increasing Arrhenius number for diffusion and decreasing Arrhenius number for reaction in the case of exothermic reactions, whereas the opposite trends hold for the endothermic reactions. The critical Thiele modulus also increases with increasing fractional reaction order as well as with decreasing energy generation function, and increasing Biot numbers for heat and mass transfer. Moreover, the critical Thiele modulus is the highest for spherical pellets and the lowest for pellets with planar shape.     

Physics-based plasticity model incorporating microstructure changes for severe plastic deformation

During machining processes, materials undergo severe deformations that lead to different behavior than in the case of slow deformation. The microstructure changes, as a consequence, affect the materials properties and therefore influence the functionality of the component. Developing material models capable of capturing such changes is therefore critical to better understand the interaction process–materials. In this paper, we introduce a new physics model associating Mechanical Threshold Stress (MTS) with Dislocation Density (DD) models. The modeling and the experimental results of a series of large strain experiments on polycrystalline copper (OFHC) involving sequences of shear deformation and strain rate (varying from quasi-static to dynamic) are very similar to those observed in processes such as machining. The Kocks–Mecking model, using the mechanical threshold stress as an internal state variable, correlates well with experimental results and strain rate jump experiments. This model was compared to the well-known Johnson–Cook model that showed some shortcomings in capturing the stain jump. The results show a high effect of rate sensitivity of strain hardening at large strains. Coupling the mechanical threshold stress dislocation density (MTS–DD), material models were implemented in the Abaqus/Explicit FE code. The model shows potentialities in predicting an increase in dislocation density and a reduction in cell size. It could ideally be used in the modeling of machining processes.     

Fractional powers of the noncommutative Fourier's law by the S‐spectrum approach

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.