The Picone identity: A device to get optimal uniqueness results and global dynamics in Population Dynamics

This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence state in two generalized diffusive prototypes of the symbiotic and competing species models of Lotka–Volterra. The optimality of these uniqueness theorems reveals the tremendous strength of the Picone identity.     

Dynamics of Bacteriorhodopsin in the Dark-Adapted State from Solution Nuclear Magnetic Resonance Spectroscopy

To achieve efficient proton pumping in the light-driven proton pump bacteriorhodopsin (bR), the protein must be tightly coupled to the retinal to rapidly convert retinal isomerization into protein structural rearrangements. Methyl group dynamics of bR embedded in lipid nanodiscs were determined in the dark-adapted state, and were found to be mostly well ordered at the cytosolic side. Methyl groups in the M145A mutant of bR, which displays only 10 % residual proton pumping activity, are less well ordered, suggesting a link between side-chain dynamics on the cytosolic side of the bR cavity and proton pumping activity. In addition, slow conformational exchange, attributed to low frequency motions of aromatic rings, was indirectly observed for residues on the extracellular side of the bR cavity. This may be related to reorganization of the water network. These observations provide a detailed picture of previously undescribed equilibrium dynamics on different time scales for ground-state bR.     

Mass distribution and skewness for passive scalar transport in pipes with polygonal and smooth cross sections

We extend our previous results characterizing the loading properties of a diffusing passive scalar advected by a laminar shear flow in ducts and channels to more general cross‐sectional shapes, including regular polygons and smoothed corner ducts originating from deformations of ellipses. For the case of the triangle and localized, cross‐wise uniform initial distributions, short‐time skewness is calculated exactly to be positive, while long‐time asymptotics shows it to be negative. Monte Carlo simulations confirm these predictions, and document the timescale for sign change. The equilateral triangle appears to be the only regular polygon with this property—all others possess positive skewness at all times. Alternatively, closed‐form flow solutions can be constructed for smooth deformations of ellipses, and illustrate how both nonzero short‐time skewness and the possibility of multiple sign switching in time is unrelated to domain corners. Exact conditions relating the median and the skewness to the mean are developed which guarantee when the sign for the skewness implies front (more mass to the right of the mean) or back (more mass to the left of the mean) “loading” properties of the evolving tracer distribution along the pipe. Short‐ and long‐time asymptotics confirm this condition, and Monte Carlo simulations verify this at all times. The simulations are also used to examine the role of corners and boundaries on the distribution for short‐time evolution of point source , as opposed to cross‐wise uniform, initial data.     

Excited-State Dynamics of Non-Luminescent and Luminescent π-Radicals

Recently, the potential use of organic π-radicals and related spin systems has been expanded to modern technological applications. The unique excited-state dynamics of organic π-radicals can be useful to improve the stability of photochemically unstable organic compounds, make the polarization transfer applicable to information technology, and achieve effective up-conversion of interest for luminescence bioimaging, among others. Furthermore, highly luminescent stable π-radicals have been recently reported, which are especially interesting for application in organic light-emitting devices owing to their potential to provide an internal quantum efficiency of 100 %. Thus, the excited-state nature of stable π-radicals as well as the control of their excited-state spin dynamics are emerging topics both in terms of fundamental science and related technological applications. In this minireview, we focus on the excited-state dynamics of both photostable non(weakly)-luminescent and luminescent π-radicals, which are opposites of each other. In particular, we cover the following topics: 1) effective generation of high-spin photoexcited states and control of the excited-state dynamics by using non-luminescent π-radicals, 2) unique excited-state dynamics of luminescent π-radicals and radical excimers, and 3) applications utilizing excited-state dynamics of π-radicals.     

THE QUALITATIVE CONTENT OF RENEWABLE RESOURCE MODELS

This paper analyzes the extent to which standard dynamic renewable resource models possess refutable implications. Both the steady state comparative static and local comparative dynamic properties of the standard model are studied. A unified framework is developed which enables one to analyze the qualitative properties of any standard renewable resource model. This is achieved by explicitly linking the local stability, steady state comparative static, and local comparative dynamic properties of the model.     

A new rule of vibration sampling for predicting acoustical radiation from rectangular plates

Structural surface velocity distribution is often used to predict structural borne sound radiation. However the sampling interval of velocity should be chosen carefully to increase the prediction accuracy and to reduce the system cost. In this paper, several factors affecting the sampling interval are theoretically analyzed and discussed for a vibrating baffled rectangular plate. A new rule for the determination of the sampling interval is formulated. Using this rule, the results from both numerical simulations and experiments may be explained well.     

Investigations of Solid State Dynamics at the NRSSR Beamline at PETRA II. An Overview

The present status of the new nuclear resonance beamline PETRA 1 at HASYLAB, DESY, Hamburg is described. Besides an overview of the experimental setup some examples of recent experiments are given. Those cover the main applications, i.e., inelastic scattering from iron alloys and quasielastic scattering from glass-forming liquids. This revised version was published online in August 2006 with corrections to the Cover Date.     

On Quantum Team Games

Recently Liu and Simaan (2004) convex static multi-team classical games have been introduced. Here they are generalized to both nonconvex, dynamic and quantum games. Puu's incomplete information dynamical systems are modified and applied to Cournot team game. The replicator dynamics of the quantum prisoner's dilemma game is also studied.     

Field Theory Methods in Classical Dynamics

A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger–Feynman–Dyson perturbation expansion and detailed rules are derived for computations. Complexification formalisms are given for the time evolution operator suitable for phase space analyses, and then extended to a two-dimensional setting for a study of the geometrical Berry phase as an example. Finally a direct integration of Hamilton's equations is shown to lead naturally to a path integral expression, as a resolution of the identity, as applied to arbitrary functions of generalized coordinates and momenta.     

面心立方晶体外延膜沉积生长中失配位错的结构与形成过程

用分子动力学方法对5%负失配条件下面心立方晶体铝薄膜的原子沉积外延生长进行了三维模拟.铝原子间的相互作用采用嵌入原子法(EAM)多体势计算.模拟结果再现了失配位错的形成现象.分析表明，失配位错在形成之初即呈现为Shockley扩展位错，即由两个伯格斯矢量为〈211〉/6的部分位错和其间的堆垛层错组成，两个部分位错的间距、即层错宽度为1.8 nm,与理论计算结果一致；外延晶体薄膜沉积生长中，位错对会发生滑移，但其间距保持稳定.进一步观察发现，该扩展位错产生于一种类似于“局部熔融-重结晶”的表层局部无序紊乱- 关键词： 失配位错 外延生长 薄膜 分子动力学 铝