对称向量拟均衡问题有效解的存在性

利用标量化方法建立对称向量拟均衡问题有效解的存在性定理。作为标量化方法的应用，利用这一方法得到向量变分不等式和拟向量变分不等式有效解的存在性定理。     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

硫化镉反蛋白石光子晶体制备及光解水制氢

对硫化镉反蛋白石结构光子晶体薄膜进行了可控合成,用巯基乙酸修饰的纳米晶和P(St-MMA-SPMAP)高分子小球共组装,成功地构筑了反蛋白石结构并用于可见光光解水产氢。结果表明,在可见光(λ≥420 nm)照射下,Cd S-310反蛋白石结构薄膜的光解水产氢性能比硫化镉纳米颗粒提高了一倍。这主要是因为等级孔结构反蛋白石光子晶体特性对催化剂的光催化性能的提升:首先,反蛋白石的周期性结构增加了光子在材料中的传播,提高了催化剂对太阳光的利用率;同时,大孔孔壁是由纳米颗粒堆积而成的,在反应中提供了更多的反应活性位点;此外,孔结构有利于物质的传输和分子的吸附。     

Time reversal for obstacle location in elastodynamics from acoustic recording

The Note is concerned with a feasibility study of time reversal in a non-homogeneous elastic medium, from data recorded in an acoustic medium. Our aim here is to determine the presence and some physical properties of elastic “inclusions” (unknown, not observable solid objects, characterized by their elastic properties) from partial observations of acoustic waves scattered by these inclusions. A finite element numerical method, based on a variational acousto-elastodynamics formulation, is derived and used to solve the forward, and then, the time-reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help construct images of the inclusions to be determined. Numerical illustrations on configurations that mimic the breast cancer configuration are proposed, and show that one can differentiate between two inclusions, even with different properties.     

NIFTy 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters

NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy  3, a major upgrade to the original NIFTy  framework. NIFTy  3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy  3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy  3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 .     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.