Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems

In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the chosen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan–Yorke dimension of the attractor. Preliminary numerical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.     

Intermolecular hybridization governs molecular electrical doping

Current models for molecular electrical doping of organic semiconductors are found to be at odds with other well-established concepts in that field, like polaron formation. Addressing these inconsistencies for prototypical systems, we present experimental and theoretical evidence for intermolecular hybridization of organic semiconductor and dopant frontier molecular orbitals. Common doping-related observations are attributed to this phenomenon, and controlling the degree of hybridization emerges as a strategy for overcoming the present limitations in the yield of doping-induced charge carriers.     

A review of boundary and finite element methods in fracture mechanics

Reviewed in this work are the methods of finite and boundary element as applied to solve fracture mechanics problems. The former requires the discretization of the interior of the domain while the latter involves computing an integral equation over the boundary of the domain. Applications of these methods are made to two-dimensional elastic crack problems. Efficiency and accuracy of different approaches are discussed and compared by examples. The boundary element procedure employing special Green's functions for the plane crack problem is shown to be superior. The correlation between the hybrid element formulations and boundary element regions embedded into a finite element model is also given.     

Quantum dynamical system with hyperbolic instabilities

An analysis of a quantum counterpart of a parametrically kicked nonlinear oscillator is given. The method, using as a basic criterion the recently introduced quantum characteristic exponents, is analogous to the technique developed in classical dynamical system theory. However, our approach to the characterization of the stability of an observable's evolution is done in pure quantum terms.     

Simulation of Crack Propagation under Small-Scale Yielding by means of a Non-local GTN-Model

Today, the local approach to fracture is widely applied to simulate the failure of specimens. For ductile damage processes the Gurson-Tvergaard-Needleman model is the quasi-standard. In the last time non-local extensions allowed a mesh-size independent simulation of crack growth. However, most publications dealing with this subject focus upon the convergence regarding global quantities such as the load-displacement relation. Minor attention is paid to the fields directly at the crack tip. Correspondingly, the interrelationship between the intrinsic length of the model and relevant microscopic damage processes at the crack tip is only partly established until now. In the present study the crack propagation is simulated for an implicitly gradient enriched GTN-model within a boundary layer in order to overcome influences of the specimen geometry. The different stages of damage evolution are resolved by a fine mesh. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A novel constitutive law for Silicon under contact loading

Silicon (Si) remains the most important semiconductor material to date. The understanding of its deformation behavior under contact (indenter-) loading is crucial to improving technologically relevant abrasive machining techniques (lapping, sawing, grinding). While it has been long established that Si undergoes a series of stress driven phase transitions upon compression and subsequent pressure release, to the authors' knowledge, no material model is available that adequately captures this behavior. In particular, reverse transformation in unloading has received too little attention. A novel phenomenological, thermomechanical model based on experimental observations and MD predictions is presented in this work. It captures both the cd-Si → β-Si transition upon compression and the β-Si → a-Si transition upon rapid decompression, which are most relevant for indenter loading. To control inelasticity in unloading, the dissipation function was augmented by a kinematic constraint on the tensorial internal variable. In stress space, the transformation surfaces are hyperboloids of revolution aligned along the hydrostatic axis. The non-linear model was numerically implemented in a finite element code using an iterative implicit algorithm and successfully applied to simple loading cases. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

锦灯笼果实的化学成分研究

从锦灯笼中分离得到5个甾体类化合物,分别鉴定为酸浆素A(1,alkekengilin A)、酸浆素B(2,alkekengilin B)、酸浆苦素D(3,physalin D)、酸浆苦素P(4,physalin P)、4,7-二去氢新酸浆苦素B(5,4,7-didehydro-neophysalin B).其中酸浆素A(1,alkekengilin A)和酸浆素B(2,alkekengilin B)为新的天然产物.运用现代波谱技术对上述化合物的结构进行了确证.     

Confocal microscopy as a tool for the study of the emission characteristics of high-power LEDs

We report on an experimental set-up based on a confocal principle in order to acquire the light-intensity distribution (XZ and XY optical sections) of high-power LEDs. To be able to record the emission characteristics of millimeter-sized LEDs and to carry out the measurements with high precision the set-up consists of a moving stage and stationary rather than scanning optics, along with a lock-in amplifier in combination with a photodiode as a detection unit. The optical sections recorded provide valuable information on the light-intensity distribution and the light propagation both within transparent substrates (in case of flip-chip LEDs) as well as in the ambient of the LEDs. In order to evaluate the accuracy of the measurement technique, the impact of the numerical aperture of the objective lens on the shape of the optical sections recorded was tested for a set of different objective lenses. The method reported provides new opportunities for a direct determination not only of the amount but also the directionality of the light extraction from LEDs that are processed in order to improve the light-extraction efficiency.