Parametric error bounds for convex approximations of two-stage mixed-integer recourse models with a random second-stage cost vector

We consider two-stage recourse models with integer restrictions in the second stage. These models are typically non-convex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q. In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the ${?}_1$-norm of q.     

A priori bounds and multiplicity for fully nonlinear equations with quadratic growth in the gradient

We consider fully nonlinear uniformly elliptic equations with quadratic growth in the gradient, such as

$?F(x,u,Du,D^{2}u)=\lambda c(x)u+〈M(x)Du,Du〉+h(x)$

in a bounded domain with a Dirichlet boundary condition; here $\lambda \in \mathbb{R}$, $c,h\in L^p(\mathrm{\Omega })$, $p>n\ge 1$, $c?0$ and the matrix M satisfies $0<{\mu }_{1}I\le M\le {\mu }_{2}I$. Recently this problem was studied in the “coercive” case $\lambda c\le 0$, where uniqueness of solutions can be expected; and it was conjectured that the solution set is more complex for noncoercive equations. This conjecture was verified in 2015 by Arcoya, de Coster, Jeanjean and Tanaka for equations in divergence form, by exploiting the integral formulation of the problem. Here we show that similar phenomena occur for general, even fully nonlinear, equations in nondivergence form. We use different techniques based on the maximum principle.We develop a new method to obtain the crucial uniform a priori bounds, which permit to us to use degree theory. This method is based on basic regularity estimates such as half-Harnack inequalities, and on a Vázquez type strong maximum principle for our kind of equations.     

Effective permittivity of liquid crystal nanodispersions and composites with different pore structure

The volume filling fraction dependence of the effective permittivity of the nematic liquid crystal 4-n-pentyl-4’-cyanobiphenyl embedded in different porous membranes and dispersed with aerosil nanoparticles was determined using broadband dielectric spectroscopy in the frequency range from 10⁶ to 10⁹ Hz. The experimental data were analyzed and compared with some existing theories based on the effective medium approximation and their modifications. The obtained effective permittivities as a function of the volume filling fraction lie between the lower limits of the Wiener and Hashin–Shtrikman bounds. The observed shift of the experimental points reflects the changes in the structure of the investigated composites.     

Shape morphing and topology optimization of fluid channels by explicit boundary tracking

An integrated shape morphing and topology optimization approach based on the deformable simplicial complex methodology is developed to address Stokes and Navier‐Stokes flow problems. The optimized geometry is interpreted by a set of piecewise linear curves embedded in a well‐formed triangular mesh, resulting in a physically well‐defined interface between fluid and impermeable regions. The shape evolution is realized by deforming the curves while maintaining a high‐quality mesh through adaption of the mesh near the structural boundary, rather than performing global remeshing. Topological changes are allowed through hole merging or splitting of islands. The finite element discretization used provides smooth and stable optimized boundaries for simple energy dissipation objectives. However, for more advanced problems, boundary oscillations are observed due to conflicts between the objective function and the minimum length scale imposed by the meshing algorithm. A surface regularization scheme is introduced to circumvent this issue, which is specifically tailored for the deformable simplicial complex approach. In contrast to other filter‐based regularization techniques, the scheme does not introduce additional control variables, and at the same time, it is based on a rigorous sensitivity analysis. Several numerical examples are presented to demonstrate the applicability of the approach.     

Comparison of implicit and explicit AUSM‐family schemes for compressible multiphase flows

This paper makes the first attempt of extending implicit AUSM‐family schemes to multiphase flow simulations. Water faucet, air–water shock tube and oscillating manometer problems are used as benchmark tests with the generic four‐equation two‐fluid model. For solving the equations implicitly, Newton's method along with a sparse matrix solver (UMFPACK solver) is employed, and the numerical Jacobian matrix is calculated. Comparison between implicit and explicit AUSM‐family schemes is presented, indicating that similarly accurate results are obtained with both schemes. Furthermore, the water faucet problem is solved using both staggered and collocated grids. This investigation helps integrate high‐resolution schemes into staggered‐grid‐based computational algorithms. The influence of the interface pressure correction on the simulation results is also examined. Results show that the interfacial pressure correction introduces numerical dissipation. However, this dissipation cannot eliminate the overshoots because of the incompatibility of numerical discretization of the conservative and non‐conservative terms in the governing equations. The comparison of CPU time between implicit and explicit schemes is also studied, indicating that the implicit scheme is capable of improving the computational efficiency over its explicit counterpart. Copyright © 2014 John Wiley & Sons, Ltd.     

Explicit H1-Estimate for the Solution of the Lamé System with Mixed Boundary Conditions

In this paper we consider the Lamé system on a polygonal convex domain with mixed boundary conditions of Dirichlet-Neumann type. An explicit L² norm estimate for the gradient of the solution of this problem is established. This leads to an explicit bound of the H¹ norm of this solution. Note that the obtained upper-bound is not optimal.     

基于显示连通贝叶斯网络的机场塔台地震易损性分析

将基于性能的多维易损性分析方法,结合显示连通贝叶斯网络,应用于机场塔台的多维易损性分析。考虑地震激励的不确定性,通过非线性时程分析获得结构响应数据;将塔台结构分为三个层次,每个层次按包含的层数分为相应的子层次。根据功能特性确定子层次的评价指标和极限状态,建立服从多元对数正态分布的概率地震需求模型;考虑各种极限状态之间的相关性,建立极限状态方程,确定失效域,通过蒙特卡洛法求得构件的超越概率;建立塔台结构的显示连通贝叶斯网络模型,利用层次分析法获得中间节点的条件概率表,利用MATLAB进行贝叶斯网络的推理计算,实现从单一层次的易损性到整体易损性的推理。     

Comprehensive Mechanism for CO Electroreduction on Dual-Atom-Catalyst-Anchored N-Doped Graphene

Carbon neutrality has drawn increasing attention for realizing the carbon cyclization and reducing the greenhouse effect. Although the C1 products, such as CO, can be achieved with a high Faraday efficiency, the targeted production of C2 fuels as well as the mechanism have not been systematically investigated. In this work, we carry out a first-principles study to screen dual-atom catalysts (DACs) for producing C2 fuels through the electrocatalytic carbon monoxide reduction reaction (e-CORR). We find that methanol, ethanol and ethylene can be produced on both DAC−Co and DAC−Cu, while acetate can be achieved on DAC−Cu only. Importantly, methanol and ethylene are preferred on DAC−Co, while acetate and ethylene on DAC−Cu. Furthermore, we show that the explicit solvent can enhance the adsorption and influence the protonation steps, which subsequently affects the protonation and dimerization behavior as well as the performance and selectivity of e-CORR on DACs. We further demonstrate that the C−C coupling is easy to be formed and stabilized if the Integrated Crystal Orbital Hamilton Population (ICOHP) is low because of the low energy barrier. Our findings provide not only guidance on the design of novel catalysts for e-CORR, but an insightful understanding on the reduction mechanism.     

Stability of ion triplets in ionic liquid/lithium salt solutions: Insights from implicit and explicit solvent models and molecular dynamics simulations

Binding energies of ion triplets formed in ionic liquids by Li⁺ with two anions have been studied using quantum‐chemical calculations with implicit and explicit solvent supplemented by molecular dynamics (MD) simulations. Explicit solvent approach confirms variation of solute‐ionic liquid interactions at distances up to 2 nm, resulting from structure of solvation shells induced by electric field of the solute. Binding energies computed in explicit solvent and from the polarizable continuum model approach differ largely, even in sign, but relative values generally agree between these two models. Stabilities of ion triplets obtained in quantum‐chemical calculations for some systems disagree with MD results; the discrepancy is attributed to the difference between static optimized geometries used in quantum chemical modeling and dynamic structures of triplets in MD simulations. © 2015 Wiley Periodicals, Inc.