A finite volume cell‐centered Lagrangian hydrodynamics approach for solids in general unstructured grids

A finite volume cell‐centered Lagrangian hydrodynamics approach, formulated in Cartesian frame, is presented for solving elasto‐plastic response of solids in general unstructured grids. Because solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum, and energy conservation laws. The total stress is split into deviatoric shear stress and dilatational components. The dilatational response of the material is modeled using the Mie‐Grüneisen equation of state. A predicted trial elastic deviatoric stress state is evolved assuming a pure elastic deformation in accordance with the hypo‐elastic stress‐strain relation. The evolution equations are advanced in time by constructing vertex velocity and corner traction force vectors using multi‐dimensional Riemann solutions erected at mesh vertices. Conservation of momentum and total energy along with the increase in entropy principle are invoked for computing these quantities at the vertices. Final state of deviatoric stress is effected via radial return algorithm based on the J‐2 von Mises yield condition. The scheme presented in this work is second‐order accurate both in space and time. The suitability of the scheme is evinced by solving one‐ and two‐dimensional benchmark problems both in structured grids and in unstructured grids with polygonal cells. Copyright © 2013 John Wiley & Sons, Ltd.     

Singularity Structure of Third-Order Dynamical Systems. I

A general third-order dynamical system with polynomial right-hand sides of finite degrees in the dependent variables is analyzed to unravel the singularity structure of its solutions about a movable singular point. To that end, the system is first transformed to a second-order Briot–Bouquet system and a third auxiliary equation via a transformation, similar to one used earlier by R. A. Smith in 1973–1974 for a general second-order dynamical system. This transformation imposes some constraints on the coefficients appearing in the general third-order system. The known results for the second-order Briot–Bouquet system are used to explicitly write out Laurent or psi-series solutions of the general third-order system about a movable singularity. The convergence of the relevant series solutions in a deleted neighborhood of the singularity is ensured. The theory developed here is illustrated with the help of the May–Leonard system.     

Reaction-based two-photon probes for in vitro analysis and cellular imaging of monoamine oxidase activity

Reaction-based fluorescent probes for monoamine oxidases A and B are developed based on a new two-photon absorbing compound and its precursor. The probes show turn-on fluorescence response to the enzymes owing to the two-photon absorbing compound produced by the enzymatic activity, as monitored by one- as well as two-photon microscopy for the first time.     

A structural remedy toward bright dipolar fluorophores in aqueous media

The donor–acceptor (D–A) type dipolar fluorophores, an important class of luminescent dyes with two-photon absorption behaviour, generally emit strongly in organic solvents but poorly in aqueous media. To understand and enhance the poor emission behaviour of dipolar dyes in aqueous media, we undertake a rational approach that includes a systematic structure variation of the donor, amino substituent of acedan, an important two-photon dye. We identify several factors that influence the emission behaviour of the dipolar dyes in aqueous media through computational and photophysical studies on new acedan derivatives. As a result, we can make acedan dyes emit bright fluorescence under one- and two-photon excitation in aqueous media by suppressing the liable factors for poor emission: 1,3-allylic strain, rotational freedom, and hydrogen bonding with water. We also validate that these findings can be generally extended to other dipolar fluorophores, as demonstrated for naphthalimide, coumarin and (4-nitro-2,1,3-benzoxadiazol-7-yl)amine (NBD) dyes. The new acedan and naphthalimide dyes thus allow us to obtain much brighter two-photon fluorescent images in cells and tissues than in their conventional forms. As an application of these findings, a thiol probe is synthesized based on a new naphthalimide dye, which shows greatly enhanced fluorescence from the widely used N,N-dimethyl analogue. The results disclosed here provide essential guidelines for the development of efficient dipolar dyes and fluorescence probes for studying biological systems, particularly by two-photon microscopy.     

Screening rhodium metallopeptide libraries "on bead": asymmetric cyclopropanation and a solution to the enantiomer problem

Searching with a beady eye: A high-throughput, on-bead screen of rhodium metallopeptide catalysts was developed in a 96-well format for asymmetric cyclopropanation. Different sequences of natural L-amino acids have been identified that produce opposite product enantiomers. In addition to styrene derivatives, high enantioselectivity is observed for vinyl ether and vinyl amine derivatives.     

Multilayer mirror fluorescence detection system for photon‐in photon‐out in‐situ carbon k‐edge NEXAFS

The Second International Workshop on Imaging Techniques with Synchrotron Radiation (ITSR) was held November 6–10, 2009, at the beautiful beach resort city of Sanya on the tropical island of Hainan province in the south of China, and followed on from a similar successful meeting in Hefei in December 2008. The meeting was supported by the National Natural Science Foundation of China, National Synchrotron Radiation Laboratory (NSRL) in Hefei, Institute of High Energy Physics (IHEP) in Beijing, INFN, Xradia Inc., and the Italian Ministry of Foreign Affairs based on an agreement for bilateral collaboration. This enthusiasm for collaboration is a reflection of the increasing interest in synchrotron-based research, particularly in the area of imaging and microscopy, which has been stimulated by the successful commissioning of various projects in China, such as the new Shanghai synchrotron light source and the upgrade of the Hefei synchrotron sources. Some further new projects are proposed that will focus even more on advancing the imaging capability in China and its application in different domains of science and technology. The Sanya meeting was therefore held at an important time and designed to bring world experts together to help build the user community, foster new scientific applications, and nurture young scientists. It is encouraging to witness that more than 10 students participated in the meeting, which included 25 oral presentations contributed by 40 delegates from 8 countries including China, Australia, the U.S., France, Germany, Italy, Japan, and the Netherlands.     

Measuring molecular order in poly(3-alkylthiophene) thin films with polarizing spectroscopies

We measured the molecular order of poly(3-alkylthiophene) chains in thin films before and after melting through the combination of several polarized photon spectroscopies: infrared (IR) absorption, variable angle spectroscopic ellipsometry (SE), and near-edge X-ray absorption fine structure (NEXAFS). The data from the various techniques can be uniformly treated in the context of the dielectric constant tensor epsilon for the film. The combined spectroscopies allow determination of the orientation distribution of the main-chain axis (SE and IR), the conjugated pi system normal (NEXAFS), and the side-chain axis (IR). We find significant improvement in the backbone order of the films after recrystallization of the material at temperatures just below the melting temperature. Less aggressive thermal treatments are less effective. IR studies show that the changes in backbone structure occur without significant alteration of the structure of the alkyl side chains. The data indicate that the side chains exhibit significant disorder for all films regardless of the thermal history of the sample.     

Singularity Structure of Third-Order Dynamical Systems. II

The singularity structure of the solutions of a general third-order system, with polynomial right-hand sides of degree less than or equal to two, is studied about a movable singular point. An algorithm for transforming the given third-order system to a third-order Briot–Bouquet system is presented. The dominant behavior of a solution of the given system near a movable singularity is used to construct a transformation that changes the given system directly to a third-order Briot–Bouquet system. The results of Horn for the third-order Briot–Bouquet system are exploited to give the complete form of the series solutions of the given third-order system; convergence of these series in a deleted neighborhood of the singularity is ensured. This algorithm is used to study the singularity structure of the solutions of the Lorenz system, the Rikitake system, the three-wave interaction problem, the Rabinovich system, the Lotka–Volterra system, and the May–Leonard system for different sets of parameter values. The proposed approach goes far beyond the ARS algorithm.