Canonical transformations and exact invariants for time‐dependent Hamiltonian systems

An exact invariant is derived for n‐degree‐of‐freedom non‐relativistic Hamiltonian systems with general time‐dependent potentials. To work out the invariant, an infinitesimalcanonical transformation is performed in the framework of the extended phase‐space. We apply this approach to derive the invariant for a specific class of Hamiltonian systems. For the considered class of Hamiltonian systems, the invariant is obtained equivalently performing in the extended phase‐space a finitecanonical transformation of the initially time‐dependent Hamiltonian to a time‐independent one. It is furthermore shown that the invariant can be expressed as an integral of an energy balance equation. The invariant itself contains a time‐dependent auxiliary function ξ (t) that represents a solution of a linear third‐order differential equation, referred to as the auxiliary equation. The coefficients of the auxiliary equation depend in general on the explicitly known configuration space trajectory defined by the system's time evolution. This complexity of the auxiliary equation reflects the generally involved phase‐space symmetry associated with the conserved quantity of a time‐dependent non‐linear Hamiltonian system. Our results are applied to three examples of time‐dependent damped and undamped oscillators. The known invariants for time‐dependent and time‐independent harmonic oscillators are shown to follow directly from our generalized formulation.     

Static and dynamic light scattering in turbid suspensions

The application of static and dynamic light scattering to many colloidal systems of practical interest has often been considered too complicated due to strong multiple scattering. There are two new approaches to overcome this problem. One of them aims at suppressing contributions from multiple scattering using novel cross‐correlation schemes. While this relies on the suppression of multiple scattering, the so‐called diffusing wave spectroscopy (DWS) works in the limit of very strong multiple scattering. DWS can be used for the characterization of dynamic and static properties of colloidal systems on a large range of time and length scales ranging from a few Ångstroms to hundreds of nanometers. We demonstrate that a wealth of information can be obtained from these methods on the structure, dynamics, interaction effects, stability, aggregation, and sol‐gel transition in colloidal dispersions.     

1H‐Benzotriazole as Synthetic Auxiliary in a Facile Route to N6‐(Arylmethyl)‐2′‐deoxyadenosines: DNA Intercalators Inserted into Three‐Way Junctions

The 2′‐deoxy‐N⁶‐(naphthalen‐1‐ylmethyl)‐ ( 5a ) and N⁶‐(pyren‐1‐ylmethyl)adenosine ( 5b ) were synthesized in two steps from 2′‐deoxyadenosine and the adequate arenecarbaldehyde with 1H‐benzotriazole as a synthetic auxiliary (Scheme). When the N⁶‐(arylmethyl)‐2′‐deoxyadenosines were inserted into the junction region of a DNA three‐way junction, its thermal stability increased.     

Development of 1,3-acetonedicarboxylate-derived glucoside amphiphiles (ACAs) for membrane protein study

Detergents are extensively used for membrane protein manipulation. Membrane proteins solubilized in conventional detergents are prone to denaturation and aggregation, rendering downstream characterization of these bio-macromolecules difficult. Although many amphiphiles have been developed to overcome the limited efficacy of conventional detergents for protein stabilization, only a handful of novel detergents have so far proved useful for membrane protein structural studies. Here, we introduce 1,3-acetonedicarboxylate-derived amphiphiles (ACAs) containing three glucose units and two alkyl chains as head and tail groups, respectively. The ACAs incorporate two different patterns of alkyl chain attachment to the core detergent unit, generating two sets of amphiphiles: ACA-As (asymmetrically alkylated) and ACA-Ss (symmetrically alkylated). The difference in the attachment pattern of the detergent alkyl chains resulted in minor variation in detergent properties such as micelle size, critical micelle concentration, and detergent behaviors toward membrane protein extraction and stabilization. In contrast, the impact of the detergent alkyl chain length on protein stability was marked. The two C11 variants (ACA-AC11 and ACA-SC11) were most effective at stabilizing the tested membrane proteins. The current study not only introduces new glucosides as tools for membrane protein study, but also provides detergent structure–property relationships important for future design of novel amphiphiles.

Newly developed amphiphiles, designated ACAs, are not only efficient at extracting G protein-coupled receptors from the membranes, but also conferred enhanced stability to the receptors compared to the gold standards (DDM and LMNG).     

Krull–Remak–Schmidt Fails for Artinian Modules over Local Rings

Let R be a ring. Any R-module M which is Artinian or Noetherian can be written as the direct sum of a finite number of indecomposable R-modules. The theorem of Krull–Remak–Schmidt asserts that in the case where M is of finite length, such a decomposition is unique up to isomorphism. On the other hand, examples of Noetherian R-modules which have essentially different decompositions have been known for a long time. The first examples of Artinian R-modules with essentially different decompositions were published only in 1995 by Facchini, Herbera, Levy and Vámos. In order to construct such examples, one needs to deal with suitable rings R. Note that for R Noetherian or commutative, all the Artinian modules have the Krull–Remak–Schmidt property. In 1998, Facchini raised the problem of whether the same is true in the case where R is a local ring. The aim of this note is to show that this is not so: we are going to present a local ring R and Artinian R-modules M with essentially different direct decompositions into indecomposables. The military importance of these results has been discussed during the NATO meeting at Constantia (August 2000) which was organized by K. W. Roggenkamp.     

In Situ Observation of Adiabatic Shear Band Formation in Aluminum Alloys

We used high-speed X-ray phase contrast imaging and infrared thermal imaging techniques to study the formation processes of adiabatic shear bands in aluminum 7075-T6 and 6061-T6 alloys. A modified compression Kolsky bar setup was used to apply the dynamic loading. A flat hat-shaped specimen design was adopted for generating the shear bands at the designated locations. Experimental results show that 7075-T6 exhibits less ductility and a narrower shear band than 6061-T6. Maximum temperatures of 720 K and 770 K were locally determined within the shear band zones for 7075-T6 and 6061-T6 respectively. This local high temperature zone and the resulting thermal instability were found to relate to the shear band formation in these aluminum alloys.

     

M-seminorms on spaces of continuous functions

Let U be a realcompact completely regular Hausdorff space, C(U) the vector lattice of all continuous functions on U. We consider representations of M-seminorms on C(U) and some subspaces) by semicontinuous functions on U.     

Phenomenological and Numerical Simulation of Shape Memory Alloys at Finite Strains

A phenomenological material law for pseudo elastic NiTi shape memory alloys (SMA) is presented. The model was derived from a thermodynamical framework and is well-suited to describe the thermomechanical coupled behaviour of the material. The material law, which was originally derived for small deformations, was extended to finite deformations using the Eulerian frame, in particular Hencky's logarithmic strain and the logarithmic rate. A first emphasis is on the physical interpretation of the material parameters and their identification. A second focus lies in the presentation of a structural example for the implementation of the material law into a commercial Finite Element code. Additionally a comparison of the numerical and experimental data of the presented example is performed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)