泡沫铝在SHPB高温动态下的变形过程研究

利用分离式Hopkinson压杆(SHPB)实验装置研究轻质泡沫铝在动态压缩下的温度相关性,重点设计了一种基于SHPB的可视化高温炉,在此基础上通过高速摄影观测泡沫铝试件在高低温且动态压缩下的变形过程。动态加载下的实验结果表明：常温下,胞壁在变形过程中易于观察到屈曲失稳、撕裂、弯曲等现象,且在压缩的过程中碎片飞溅;高温下材料软化较明显,呈现出更多的塑性弯曲现象,但是屈曲失稳与撕裂的现象并不显著,变形过程中并无碎片产生。     

Dual Bounds and Optimality Cuts for All-Quadratic Programs with Convex Constraints

A central problem of branch-and-bound methods for global optimization is that often a lower bound do not match with the optimal value of the corresponding subproblem even if the diameter of the partition set shrinks to zero. This can lead to a large number of subdivisions preventing the method from terminating in reasonable time. For the all-quadratic optimization problem with convex constraints we present optimality cuts which cut off a given local minimizer from the feasible set. We propose a branch-and-bound algorithm using optimality cuts which is finite if all global minimizers fulfill a certain second order optimality condition. The optimality cuts are based on the formulation of a dual problem where additional redundant constraints are added. This technique is also used for constructing tight lower bounds. Moreover we present for the box-constrained and the standard quadratic programming problem dual bounds which have under certain conditions a zero duality gap.     

Vehicle routing with split deliveries

This paper considers a relaxation of the classical vehicle routing problem (VRP), in which split deliveries are allowed. As the classical VRP, this problem is NP-hard, but nonetheless it seems more difficult to solve exactly. It is first formulated as an integer linear program. Several new classes of valid constraints are derived, and a hierarchy between these is established. A constraint relaxation branch and bound algorithm for the problem is then described. Computational results indicate that by using an appropriate combination of constraints, the gap between the lower and upper bounds at the root of the search tree can be reduced considerably. These results also confirm the quality of a previously published heuristic for this problem.     

Polar cographs

Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s,k)-polar if there exists a partition A,B of its vertex set such that A induces a complete s-partite graph (i.e., a collection of at most s disjoint stable sets with complete links between all sets) and B a disjoint union of at most k cliques (i.e., the complement of a complete k-partite graph).Recognizing a polar graph is known to be NP-complete. These graphs have not been extensively studied and no good characterization is known. Here we consider the class of polar graphs which are also cographs (graphs without induced path on four vertices). We provide a characterization in terms of forbidden subgraphs. Besides, we give an algorithm in time O(n) for finding a largest induced polar subgraph in cographs; this also serves as a polar cograph recognition algorithm. We examine also the monopolar cographs which are the (s,k)-polar cographs where min(s,k)?1. A characterization of these graphs by forbidden subgraphs is given. Some open questions related to polarity are discussed.     

Valid inequalities for mixed integer linear programs

This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these families. The tutorial also discusses computational aspects of generating the cuts and their strength. Supported by NSF grant DMI-0352885, ONR grant N00014-03-1-0188 and ANR grant BLAN06-1-138894.     

Split-step orthogonal spline collocation methods for nonlinear Schrödinger equations in one, two, and three dimensions

Split-step orthogonal spline collocation (OSC) methods are proposed for one-, two-, and three-dimensional nonlinear Schrödinger (NLS) equations with time-dependent potentials. Firstly, the NLS equation is split into two nonlinear equations, and one or more one-dimensional linear equations. Commonly, the nonlinear subproblems could be integrated directly and accurately, but it fails when the time-dependent potential cannot be integrated exactly. In this case, we propose three approximations by using quadrature formulae, but the split order is not reduced. Discrete-time OSC schemes are applied for the linear subproblems. In numerical experiments, many tests are carried out to prove the reliability and efficiency of the split-step OSC (SSOSC) methods. Solitons in one, two, and three dimensions are well simulated, and conservative properties and convergence rates are demonstrated. We also apply the ways of solving the nonlinear subproblems to the split-step finite difference (SSFD) methods and the time-splitting spectral (TSSP) methods, and the approximate ways still work well. Finally, we apply the SSOSC methods to solve some problems of Bose-Einstein condensates.     

Phase-shift, refraction and focusing based on the metamaterial technologies

We address the problem of positive phase-shifting, negative refraction and focusing via a flat lens on the basis of the metamaterial technologies. With this aim, three examples are considered which differ by the technology employed and the operating frequency. The first one concerns negative-zero-positive refraction by using a prism-shaped electromagnetic metamaterial which consists of omega-type inclusion arrays operating at microwaves. The experimental verification was done in this case by angle-resolved transmission measurements. Second, we report on the phase-shift properties of a negative index transmission line which operates at Terahertz frequencies. In order to experimentally demonstrate the left-handed character of the propagation along the line, resulting in a phase advance, we used time domain experiments. At last, focusing by double refraction in a flat negative index lens was demonstrated by the theoretical and experimental mapping of the intensity of the electric field. Such a mapping of the E-field was carried out at near infrared (1.5 μm) by analysis in the time domain and scanning by near field optical microscopy. To cite this article: D. Lippens, C. R. Physique 10 (2009).     

Screw split ring resonator as building block of three-dimensional chiral metamaterials

We proposed and numerically investigated the influence of spatial topology on the infrared frequency region response of chiral metamaterials based on discrete deformed split ring resonators. Compared with the well studied continuous helix, the proposed metamaterials with discrete topology exhibit broad band chiral electromagnetic response. It is shown that the conversion between left and right circular polarization waves for our model is much broader than the continuous helix model. The observed cross-coupling between electric and magnetic fields results from the chiral electric currents on the resonators due to the broken mirror symmetry. The findings are useful for the design of future real three-dimensional chiral metamaterials with tunable optical response.     

Study on the resonance properties of combinations of different split ring resonator cells

We combine different split ring resonator (SRR) unit cells along three axes respectively and study the electromagnetic behaviors of combinations numerically, with the purpose of broadening the frequency band of negative permeability. When combining SRRs in z-direction, the wave propagation direction, it is found that the bandwidth of negative permeability is broadened by 0.22 GHz. The same bandwidth expansion effects, however, are not observed along the other two axes. In addition, it is feasible to obtain two isolated frequency bands with negative permeability by combining SRRs along three axes.