Gradient‐based nodal limiters for artificial diffusion operators in finite element schemes for transport equations

This paper presents new linearity‐preserving nodal limiters for enforcing discrete maximum principles in continuous (linear or bilinear) finite element approximations to transport problems with steep fronts. In the process of algebraic flux correction, the oscillatory antidiffusive part of a high‐order base discretization is decomposed into a set of internodal fluxes and constrained to be local extremum dim inishing. The proposed nodal limiter functions are designed to be continuous and satisfy the principle of linearity preservation that implies the preservation of second‐order accuracy in smooth regions. The use of limited nodal gradients makes it possible to circumvent angle conditions and guarantee that the discrete maximum principle holds on arbitrary meshes. A numerical study is performed for linear convection and anisotropic diffusion problems on uniform and distorted meshes in two space dimensions. Copyright © 2017 John Wiley & Sons, Ltd.     

Adhesion,atomic structure,and bonding variation at TiN/VN interface by chemical segregation

Introduction of alloying elements often alters properties of materials. In the technologically significant multilayered superlattice coatings, interfaces are known to play a key role in the deformation mechanisms, especially in the phenomenon of interface‐induced superhardness at nanoscale. Here, we elucidate, by first‐principles calculations, atomic structure of TiN/VN interface and its relationship to adhesion upon introducing Cr, Mo, Ta, Y, Al, Nb, Zr, and Sc, the very commonly occurring alloying elements in the coating. We find that the elements Cr, Mo, Ta, Y weaken substantially interfacial adhesion, whereas the others modify adhesion only slightly. The bond length, charge transfer, and interactions between atoms at interface are found to be the key factors to understanding the origin of shift in properties in the coatings with the chemical alloying. Using several methods of analysis, we have clarified electronic mechanism behind the variation induced by alloying elements and determined the interfacial bonding nature to be mainly ionic with a certain degree of covalency. The theoretical calculations presented provide insight into the complex electronic properties of the TiN/VN interfaces with alloying elements. Our findings help enhance performances of the multilayered coatings for wide‐ranging applications. Copyright © 2012 John Wiley & Sons, Ltd.     

On the coupling of plastic slip and deformation-induced twinning in magnesium: A variationally consistent approach based on energy minimization

The present paper is concerned with the analysis of the deformation systems in single crystal magnesium at the micro-scale and with the resulting texture evolution in a polycrystal representing the macroscopic mechanical response. For that purpose, a variationally consistent approach based on energy minimization is proposed. It is suitable for the modeling of crystal plasticity at finite strains including the phase transition associated with deformation-induced twinning. The method relies strongly on the variational structure of crystal plasticity theory, i.e., an incremental minimization principle can be derived which allows to determine the unknown slip rates by computing the stationarity conditions of a (pseudo) potential. Phase transition associated with twinning is modeled in a similar fashion. More precisely, a solid-solid phase transition corresponding to twinning is assumed, if this is energetically favorable. Mathematically speaking, the aforementioned transition can be interpreted as a certain rank-one convexification. Since such a scheme is computationally very expensive and thus, it cannot be applied to the analysis of a polycrystal, a computationally more efficient approximation is elaborated. Within this approximation, the deformation induced by twinning is decomposed into the reorientation of the crystal lattice and simple shear. The latter is assumed to be governed by means of a standard Schmid-type plasticity law (pseudo-dislocation), while the reorientation of the crystal lattice is considered, when the respective plastic shear strain reaches a certain threshold value. The underlying idea is in line with experimental observations, where dislocation slip within the twinned domain is most frequently seen, if the twin laminate reaches a critical volume. The resulting model predicts a stress-strain response in good agreement with that of a rank-one convexification method, while showing the same numerical efficiency as a classical Taylor-type approximation. Consequently, it combines the advantages of both limiting cases. The model is calibrated for single crystal magnesium by means of the channel die test and finally applied to the analysis of texture evolution in a polycrystal. Comparisons of the predicted numerical results to their experimental counterparts show that the novel model is able to capture the characteristic mechanical response of magnesium very well.     

基于雨课堂智慧教学工具的化工原理课堂教学改革与实践*

化工原理是化工及其相关专业的一门专业基础课,存在内容多、计算量大、课堂互动难等情况。在教学中引入雨课堂智慧教学工具,有助于解决教学中存在的普遍问题。从课前教学设计、课中互动和测验、课后复习和信息反馈、课程评价机制等方面介绍了雨课堂智慧教学工具在化工原理教学中的应用,实现以学生为中心、科学地评价学生的学习过程与学习效果。基于雨课堂的智慧教学模式对教学的促进作用显著,出勤率明显提升,课堂气氛活跃,信息反馈及时,有助于教师掌握每位学生的学习情况,能使教学更具个性化。     

生物工程专业化工原理理论教学的改革与探索

在当前高等学校注重创新创业人才培养的教育改革背景下,从生物工程专业化工原理理论教学如何从教学内容的载体、教学方法、考核方式等方面改革出发,探讨了适合工科院校化工原理教学加强实践和创新能力,培养创新型人才的新途径。     

Moderate deviations for marked Hawkes processes

We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu [Stoch. Models, 31, 433–451 (2015)]. In this paper, we obtain a moderate deviation principle for marked Hawkes processes.     

Hybrid organic–inorganic CH3NH3PbI3 perovskite building blocks: Revealing ultra‐strong hydrogen bonding and mulliken inner complexes and their implications in materials design

Methylammonium lead iodide (CH₃NH₃PbI₃) perovskite compound has produced a remarkable breakthrough in the photovoltaic history of solar cell technology because of its outstanding device‐based performance as a light‐harvesting semiconductor. Whereas the experimental and theoretical studies of this system in the solid state have been numerously reported in the last 4 years, its fundamental cluster physics is yet to be exploited. To this end, this study has performed theoretical investigations using DFT‐M06‐2X/ADZP to examine the principal geometrical, electronic, topological, and orbital properties of the CH₃NH₃PbI₃ molecular building block. The intermolecular hydrogen bonded interactions examined for the most important conformers of the system are found to be unusually strong, with binding energies lying between −93.53 and −125.11 kcal mol⁻¹ (beyond the covalent limit, −40 kcal mol⁻¹), enabling us to classify the underlying interactions as ultra‐strong type since their characteristic properties are unidentical with those have already been proposed as very strong, strong, moderate, weak, and van der Waals. Based on this, together with the unusually high charge transfers, strong hyperconjugative interactions, sophisticated topologies of the charge density, and short intermolecular distances of separation, we have characterized the conformers of CH₃NH₃PbI₃ as Mulliken inner complexes. The consequences of these, as well as of the ultra‐strong interactions, in designing novel functional nanomaterials are outlined. © 2017 Wiley Periodicals, Inc.     

On a free boundary problem for a class of anisotropic equations

This paper deals with a certain condenser capacity in an anisotropic environment. More precisely, we are going to investigate a free boundary problem for a class of anisotropic equations on a ring domain N≥2. Our aim is to show that if the problem admits a solution in a suitable weak sense, then the underlying domain Ω is a Wulff‐shaped ring. The proof makes use of a maximum principle for an appropriate P‐function, in the sense of L. E. Payne, a Rellich type identity and some geometric arguments involving the anisotropic mean curvature of the free boundary. Copyright © 2016 John Wiley & Sons, Ltd.     

On stability of discontinuous systems via vector Lyapunov functions

This paper deals with the stability of systems with discontinuous right- hand side(with solutions in Filippov's sense)via locally Lipschitz continuous and regular vector Lyapunov functions.A new type of"set-valued derivative"of vector Lyapunov functions is introduced,some generalized comparison principles on discontinuous systems are shown.Furthermore,Lyapunov stability theory is developed for a class of discontinu- ous systems based on locally Lipschitz continuous and regular vector Lyapunov functions.     

On Substitution Principles in Ideal Magneto-Gasdynamics by Means of Lie Group Analysis

The equations governing the flow of an inviscid thermally non-conducting fluid of infinite electrical conductivity in the presence of a magnetic field and subject to no extraneous forces are considered within the framework of Lie group analysis. It is shown how to recover and extend some results, known in literature as substitution principles, by conveniently requiring the invariance of the basic governing equations under a one-parameter Lie group of point transformations. Moreover, a new substitution principle for the equations ruling the plane motion of a fluid with adiabatic index Γ = 2 subjected to a transverse magnetic field is given. Some applications of the results are also given.