Impact resistance analysis of flexible fabric by 3D shape of impact basin in low-speed impact test

Hopkinson non-penetrating low-speed impact test was carried out on Kevlar flexible fabrics. The impact basin was formed by the clay on the back of the fabric, and the ultimate deformation of the fabric was recorded completely. The 3D shape of the clay impact basin was measured by fringe projection profilometry and converted into the impact basin volume. At the same time, the relationship between the indentation volume and the deformation energy of the clay was calibrated using the clay intrusion test. The clay impact basin volume is then converted into the residual energy of the flexible fabric subjected to the low-speed impact, and a new index of the impact basin volume is established to evaluate the energy absorption efficiency of fabric under the low-speed impact. Finally, combined with the deformation of single-layer fabric, the stress wave propagation in the impact deformation process of fabric is discussed, which is helpful to understand the impact energy absorption mechanism of flexible fabric.     

“Weakley型稀土多金属氧酸盐的制备与发光性质”在无机化学实验教学中的应用

采用理论与实验相结合的方法对稀土多金属氧酸盐的发光性质进行探究。首先,通过常规水溶液法合成了一系列稀土多金属氧簇Na9LnW10O36(Ln^3+=Sm^3+、Eu^3+、Tb^3+、Dy^3+);其次,利用粉末X射线衍射、红外光谱、拉曼光谱对簇合物的结构进行表征;最后,利用紫外-可见光谱、荧光光谱对簇合物的光学性质进行考查。通过系统性的实验使学生对稀土簇合物的结构表征以及发光性质有全面、深刻的认识。     

Analysis of energy consumption in microwave and convective drying process of multi-layered porous material inside a rectangular wave guide

This work applies the first law of thermodynamics to estimate the ratio of energy utilization in microwave drying process using a rectangular waveguide. Two porous packed bed systems are considered such as attaching fine bed on coarse bed (F-C) and attaching coarse bed on fine bed (C-F). The effects of layered configuration and layered thickness on drying rate, power absorbed efficiency, specific energy consumption (SEC), and energy efficiency are studied in detail. The results show that the variations of all parameters have strongly affected on microwave penetration depth and power absorbed within the packed bed. Furthermore, F-C bed with equal layer thickness corresponds to great energy efficiency.     

Characterization of energy minimizers in micromagnetics

We present a new characterization of minimizing sequences and possible minimizers (all called the minimizing magnetizations) for a nonlocal micromagnetic-like energy (without the exchange energy). Our method is to replace the nonlocal energy functional and its relaxation with certain local integral functionals on divergence-free fields obtained by a two-step minimization of some auxiliary augmented functionals. Through this procedure, the minimization problem becomes equivalent to the minimization of a new local variational functional, called the dual variational functional, which has a unique minimizer. We then precisely characterize the minimizing magnetizations of original nonlocal functionals in terms of the unique minimizer of the dual variational functional. Finally, we give some remarks and ideas on solving the dual minimization problem.     

Energy decay rates of elastic waves in unbounded domain with potential type of damping

In this paper we first show that the total energy of solutions for a semilinear system of elastic waves in Rn with a potential type of damping decays in an algebraic rate to zero. We study the critical potential case and we assume that the initial data have a compact support. An application for the Euler-Poisson-Darboux type dissipation V(t,x) is obtained and in this case the compactness of the support on the initial data is not necessary. Finally, we shall discuss the energy concentration region for the linear system of elastic waves in an exterior domain.     

Global Existence of the Equilibrium Diffusion Model in Radiative Hydrodynamics

This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta condition holds. Then, based on these structure properties, the well-posedness close to a constant state can be proved by using fine energy estimates. The asymptotic decay of the solutions are also investigated.     

Climate change and optimal energy technology R&D policy

Public policy response to global climate change presents a classic problem of decision making under uncertainty. Theoretical work has shown that explicitly accounting for uncertainty and learning in climate change can have a large impact on optimal policy, especially technology policy. However, theory also shows that the specific impacts of uncertainty are ambiguous. In this paper, we provide a framework that combines economics and decision analysis to implement probabilistic data on energy technology research and development (R&D) policy in response to global climate change. We find that, given a budget constraint, the composition of the optimal R&D portfolio is highly diversified and robust to risk in climate damages. The overall optimal investment into technical change, however, does depend (in a non-monotonic way) on the risk in climate damages. Finally, we show that in order to properly value R&D, abatement must be included as a recourse decision.     

Energy bands: Chern numbers and symmetry

Energy bands formed by rotation–vibrational states of molecules in the presence of symmetry and their qualitative modifications under variation of some control parameters are studied within the semi-quantum model. Rotational variables are treated as classical whereas a finite set of vibrational states is considered as quantum. In the two-state approximation the system is described in terms of a fiber bundle with the base space being a two-dimensional sphere, the classical phase space for rotational variables. Generically this rank 2 complex vector bundle can be decomposed into two complex line bundles characterized by a topological invariant, the first Chern class. A general method of explicit calculation of Chern classes and of their possible modifications under variation of control parameters in the presence of symmetry is suggested. The construction of iso-Chern diagrams which split the space of control parameters into connected domains with fixed Chern numbers is suggested. A detailed analysis of the rovibrational model Hamiltonian for a D₃ invariant molecule possessing two vibrational states transforming according to the two-dimensional irreducible representation is done to illustrate non-trivial restrictions imposed by symmetry on possible values of Chern classes.     

Energy law preserving C finite element schemes for phase field models in two-phase flow computations

We use the idea in [33] to develop the energy law preserving method and compute the diffusive interface (phase-field) models of Allen–Cahn and Cahn–Hilliard type, respectively, governing the motion of two-phase incompressible flows. We discretize these two models using a C⁰ finite element in space and a modified midpoint scheme in time. To increase the stability in the pressure variable we treat the divergence free condition by a penalty formulation, under which the discrete energy law can still be derived for these diffusive interface models. Through an example we demonstrate that the energy law preserving method is beneficial for computing these multi-phase flow models. We also demonstrate that when applying the energy law preserving method to the model of Cahn–Hilliard type, un-physical interfacial oscillations may occur. We examine the source of such oscillations and a remedy is presented to eliminate the oscillations. A few two-phase incompressible flow examples are computed to show the good performance of our method.     

The energy conserving particle-in-cell method

A new particle-in-cell (PIC) method, that conserves energy exactly, is presented. The particle equations of motion and the Maxwell’s equations are differenced implicitly in time by the midpoint rule and solved concurrently by a Jacobian-free Newton Krylov (JFNK) solver. Several tests show that the finite grid instability is eliminated in energy conserving PIC simulations, and the method correctly describes the two-stream and Weibel instabilities, conserving exactly the total energy. The computational time of the energy conserving PIC method increases linearly with the number of particles, and it is rather insensitive to the number of grid points and time step. The kinetic enslavement technique can be effectively used to reduce the problem matrix size and the number of JFNK solver iterations.