Reflection of plane waves from the boundary of a pre-stressed compressible elastic half-space

The effect of pre-stress on the propagation and reflection ofplane waves in an incompressible isotropic elastic half-spacehas been examined recently by the authors (Ogden & Sotiropoulos,1997). In the present paper the corresponding analysis for compressiblematerials is detailed. In the two-dimensional context consideredfor incompressible materials the (homogeneous) plane waves werenecessarily shear waves. By contrast, in the compressible contextpure shear waves can propagate only in specific directions inthe considered principal plane and, in a general direction,a quasi-shear wave may be accompanied by a quasi-longitudinalwave, as is the case in the anisotropic linear theory. The dependenceof the (in-plane) slowness section on the pre-stress (and finitedeformation) and on the choice of constitutive law is elucidated.This information is used to determine the reflection coefficientsfor reflection of either a (quasi-) shear wave or a (quasi-)longitudinal wave from the boundary of the half-space and tocharacterize the different cases which arise depending on thegeometry of the slowness section. The theoretical results are illustrated by numerical calculationsfor the range of possible types of behaviour with referenceforms of strain-energy function and different states of finitedeformation and to the question of stability of the half-space.     

Optimal design of trusses with geometric imperfections: Accounting for global instability

A topology optimization method is proposed for the design of trusses with random geometric imperfections due to fabrication errors. This method is a generalization of a previously developed perturbation approach to topology optimization under geometric uncertainties. The main novelty in the present paper is that the objective function includes the nonlinear effects of potential buckling due to misaligned structural members. Solutions are therefore dependent on the magnitude of applied loads and the direction of resulting internal member forces (whether they are compression or tension). Direct differentiation is used in the sensitivity analysis, and analytical expressions for the associated derivatives are derived in a form that is computationally efficient. A series of examples illustrate how the effects of geometric imperfections and buckling may have substantial influence on truss design. Monte Carlo simulation together with second-order elastic analysis is used to verify that solutions offer improved performance in the presence of geometric uncertainties.     

Ruthenium hydride complexes of the hindered phosphine ligand tris(3-diisopropylphosphinopropyl)phosphine

The synthesis and characterization of the novel hindered tripodal phosphine ligand P(CH(2)CH(2)CH(2)P(i)Pr(2))(3) (P(3)P(3)(iPr)) (1) are reported, along with the synthesis and characterization of ruthenium chloro and hydrido complexes of 1. Complexes [RuCl(P(3)P(3)(i)Pr)][BPh(4)] (2[BPh(4)]), RuH(2)(P(3)P(3)(i)Pr) (3), and [Ru(H(2))(H)(P(3)P(3)(iPr))][BPh(4)] (4[BPh(4)]) were characterized by crystallography. Complex 2 is fluxional in solution, and low-temperature NMR spectroscopy of the complex correlates well with two dynamic processes, an exchange between stereoisomers and a faster turnstile-type exchange within one of the stereoisomers.     

Emergence of excited-state plasmon modes in linear hydrogen chains from time-dependent quantum mechanical methods

Explicitly time-dependent configuration-interaction theory is used to predict a new type of plasmonic behavior in linear hydrogen chains. After an intense ultrashort laser pulse brings the system into a broad superposition of excited states, the electronic dipole of the entire chain oscillates coherently, and the system is predicted to emit radiation at energies significantly lower than the first absorption band. A simple classical model accurately predicts the energy of this plasmon resonance for different hydrogen chain lengths and electron densities, demonstrating that collective, free-electron-like behavior can arise in chains of as few as 20 hydrogen atoms. The excitation mechanism for this plasmonic resonance is a highly nonlinear, multiphoton process, different from the linear excitation of ordinary surface plasmons.     

Satellite peaks in the high energy photoelectron spectra of some small first row molecules

The gas phase high energy photoelectron spectra of CH₄, NH₃, H₂O, N₂, O₂, CO and CO₂ have been recorded, and in all cases weak satellite peaks to high binding energy of the main ionization peak are observed. These peaks are assigned to transitions to ionic states in which valence electron excitation as well as core ionization has occurred. The intensity and position of these peaks, relative to the main ionization peak have been estimated from ab initio UHF calculations on the core hole states, which in general allow assignment of the satellite peaks in terms of orbital transitions of the core hole ion.     

Editorial

I am pleased to accept an invitation from Professor Qihua Wang at Chinese Academy of Sciences to serve as a guest editor for a special issue on statistical methods for evaluation of diagnostic tests and biomarkers in SCIENCE CHINA Mathematics. Diagnostic tests and biomarkers play an important role in medicine. They can be used not only as diagnostic tools for the diagnosis of a particular disease but also as companion tools for therapeutic     

Electronically excited states of disulphur dinitride (S2N2) and its conversion to the metallic polymer (SN)x

Ab initio configuration interaction calculations with a double zeta basis augmented by polarisation functions have been carried out for all the lowest singlet and triplet states of S₂N₂ and (SN)₂) - a unit of the polymer (SN)_x. The results satisfactory account for the UV-absorption spectrum of S₂N₂ which is probably dominated by ¹B_2u. There are low-lying singlet and triplet states for (SN)₂, and one of these a σσ* triplet seems likely to be the polymerisation precursor.     

Tunneling resonances and coherence in an optical lattice

The center-of-mass quantization of atoms trapped in a gray optical lattice is observed to manifest itself in the steady-state properties of the atoms. Modulations in the lifetime and macroscopic magnetization as a function of an applied B field are attributed to quantum mechanical tunneling resonances and are shown to exist only under conditions which afford spatial coherence of the trapped atoms over several lattice wells and coherence times that exceed the tunneling period.     

High-angular-momentum states in cold Rydberg gases

Cold, dense Rydberg gases produced in a cold-atom trap are investigated using spectroscopic methods and time-resolved electron counting. Optical excitation on the discrete Rydberg resonances reveals long-lasting electron emission from the Rydberg gas ( >20 ms). Our observations are explained by lm-mixing collisions between Rydberg atoms and slow electrons that lead to the population of long-lived high-angular-momentum Rydberg states. These atoms thermally ionize slowly and with large probabilities.