Minimal interatomic distance in Morse clusters

In this paper we derive a lower bound, independent from the number of atoms N, for the minimal interatomic distances between atoms in a cluster whose total energy is modelled by means of the so called Morse potential. A similar result was previously proven for Lennard–Jones clusters but the proof can not be extended to Morse clusters. Besides the theoretical interest, the derivation of this lower bound is important for the definition of efficient procedures for the computation of the total energy of clusters with a large number of atoms.     

孤立不变集的强连续延拓性

利用拓扑分析方法讨论孤立不变集的吸引子，排斥子及Morse分解的强连续延拓性，给出的结论推广了ConleyC在1978年和SalamonD在1985年的部分结果。     

The Morse Index of Wente Tori

We find various lower and upper bounds for the index of Wente tori that contain a continuous family of planar principal curves. We then prove a result that gives an algorithm for computing the index sharply.     

Floer Homology and the Heat Flow

We study the heat flow in the loop space of a closed Riemannian manifold M as an adiabatic limit of the Floer equations in the cotangent bundle. Our main application is a proof that the Floer homology of the cotangent bundle, for the Hamiltonian function kinetic plus potential energy, is naturally isomorphic to the homology of the loop space. J.W. received partial financial support from TH-Projekt 00321. Received: December 2004 Revision: September 2005 Accepted: September 2005     

Light propagation in polytype Thue–Morse structures made of porous silicon

For the first time, two different sets of polytype Thue–Morse multilayered porous silicon structures are studied to investigate the reflection of light in aperiodic dielectrics. The optical response of the samples was studied before and after oxidation. The results were compared with the classical periodic structure, and an enhancement in the number of photonic bandgaps with a significant blue shift in reflectance peaks, in some of the structures, were observed. Numerical simulation along the lines of the transfer matrix approach is also presented.     

Morse Decompositions and Spectra on Flag Bundles

For linear flows on vector bundles, the chain recurrent components of the induced flows on flag bundles are described and a corresponding Morse spectrum is constructed.     

Index theory, nontrivial solutions, and asymptotically linear second-order Hamiltonian systems

In this paper, we consider the existence and multiplicity of solutions of second-order Hamiltonian systems. We propose a generalized asymptotically linear condition on the gradient of Hamiltonian function, classify the linear Hamiltonian systems, prove the monotonicity of the index function, and obtain some new conditions on the existence and multiplicity for generalized asymptotically linear Hamiltonian systems by global analysis methods such as the Leray-Schauder degree theory, the Morse theory, the Ljusternik-Schnirelman theory, etc.     

Morse势阱中的光检波效应

利用量子力学中的密度矩阵算符理论和迭代方法，得到Morse势阱中的光检波系数的解析表达式。并以典型的GaAs/AlGaAs莫尔斯量子阱为例进行数值计算。研究结果表明，较大的光检波系数与系统的非对称性有关，系统的非对称性越大，光检波系数越大。     

Conformational ensembles and sampled energy landscapes: Analysis and comparison

We present novel algorithms and software addressing four core problems in computational structural biology, namely analyzing a conformational ensemble, comparing two conformational ensembles, analyzing a sampled energy landscape, and comparing two sampled energy landscapes. Using recent developments in computational topology, graph theory, and combinatorial optimization, we make two notable contributions. First, we present a generic algorithm analyzing height fields. We then use this algorithm to perform density‐based clustering of conformations, and to analyze a sampled energy landscape in terms of basins and transitions between them. In both cases, topological persistence is used to manage (geometric) frustration. Second, we introduce two algorithms to compare transition graphs. The first is the classical earth mover distance metric which depends only on local minimum energy configurations along with their statistical weights, while the second incorporates topological constraints inherent to conformational transitions. Illustrations are provided on a simplified protein model (BLN69), whose frustrated potential energy landscape has been thoroughly studied. The software implementing our tools is also made available, and should prove valuable wherever conformational ensembles and energy landscapes are used. © 2015 Wiley Periodicals, Inc.