Variational response-function formulation of vibrational circular dichroism

The atomic axial tensor (AAT) of vibrational circular dichroism is expressed as the frequency derivative at zero frequency of a linear response function for operators referencing a nuclear displacement and a magnetic field. This is used in the density matrix-based quasienergy derivative Lagrangian approach of Thorvaldsen et al. [J. Chem. Phys., 2008, 129, 214108] to express the AAT in a form where the need to solve response equations for the nuclear displacements is removed, significantly reducing the computation cost compared to existing formulations. The density matrix-based quasienergy derivative Lagrangian approach also allows us straightforwardly to use London atomic orbitals to remove the gauge-origin dependence and to account for the atomic orbitals' dependence on the nuclear coordinates. The formalism is entirely based on atomic-orbital density and integral matrices and therefore amenable to linear scaling for sufficiently sparse matrices and given a linearly scaling response solver.     

Thin noble metal films on Si (111) investigated by optical second-harmonic generation and photoemission

Thin noble metal films (Ag, Au and Cu) on Si (111) have been investigated by optical second-harmonic generation (SHG) in combination with synchrotron radiation photoemission spectroscopy. The valence band spectra of Ag films show a quantization of the sp-band in the 4-eV energy range from the Fermi level down to the onset of the d-bands. For Cu and Au the corresponding energy range is much narrower and quantization effects are less visible. Quantization effects in SHG are observed as oscillations in the signal as a function of film thickness. The oscillations are strongest for Ag and less pronounced for Cu, in agreement with valence band photoemission spectra. In the case of Au, a reacted layer floating on top of the Au film masks the observation of quantum well levels by photoemission. However, SHG shows a well-developed quantization of levels in the Au film below the reacted layer. For Ag films, the relation between film thickness and photon energy of the SHG resonances indicates different types of resonances, some of which involve both quantum well and substrate states. Received: 16 October 2001 / Revised version: 14 March 2002 / Published online: 29 May 2002     

Dynamical approach to complex regional economic growth based on Keynesian model for China

The paper addresses the problem of complex regional economic growth by using nonlinear Keynesian model with focusing on direct foreign investments effects. We investigate the dynamics of the model for the broad range of parameters which, in particular, contains the parameter values obtained recently by econometric analysis of the data for economic growth in China. For the single-region model we give conditions for which the dynamics of the model will be chaotic or regular. The parameters which prevent the economic stagnation are indicated. Further, we consider the model for two regions with a common trade as a coupling factor. The conditions are given for the two trading systems to exhibit chaotic synchronization, in-phase and out-of-phase behavior.     

Up to 30 mW of broadly tunable CW green-to-orange light, based on sum-frequency mixing of Cr:forsterite and Nd:YVO4 lasers

Efficient generation of continuous-wave (CW) tunable light in the yellow region is reported. The method is based on sum-frequency mixing of a tunable Cr⁴⁺:forsterite laser with a Nd:YVO₄ laser. A periodically poled lithium niobate crystal was placed intra-cavity in a Nd:YVO₄ laser, and the Cr⁴⁺:forsterite laser was single-passed through the non-linear media. With this setup, it was possible to generate up to 3 mW of yellow light smoothly tunable from 573 to 587 nm. This is the highest output demonstrated to date for a tunable diode pumped solid-state CW laser in this wavelength region. The ways to improve the efficiency further are discussed.     

On the rate of convergence of spatial birth-and-death processes

Sufficient conditions for geometrical fast convergence of general spatial birth-and-death processes to equilibrium are established.     

The Anisotropic Hooke's Law for Cancellous Bone and Wood

A method of data analysis for a set of elastic constant measurements is applied to data bases for wood and cancellous bone. For these materials the identification of the type of elastic symmetry is complicated by the variable composition of the material. The data analysis method permits the identification of the type of elastic symmetry to be accomplished independent of the examination of the variable composition. This method of analysis may be applied to any set of elastic constant measurements, but is illustrated here by application to hardwoods and softwoods, and to an extraordinary data base of cancellous bone elastic constants. The solid volume fraction or bulk density is the compositional variable for the elastic constants of these natural materials. The final results are the solid volume fraction dependent orthotropic Hooke's law for cancellous bone and a bulk density dependent one for hardwoods and softwoods. This revised version was published online in August 2006 with corrections to the Cover Date.     

Novel retinylidene iminium salts for defining opsin shifts: synthesis and intrinsic chromophoric properties

Retinal Schiff bases serve as chromophores in many photoactive proteins that carry out functions such as signalling and light-induced ion translocation. The retinal Schiff base can be found as neutral or protonated, as all-trans, 11-cis or 13-cis isomers and can adopt different conformations in the protein binding pocket. Here we present the synthesis and characterisation of isomeric retinylidene iminium salts as mimics blocked towards isomerisation at the C11 position and conformationally restrained. The intrinsic chromophoric properties are elucidated by gas phase absorption studies. These studies reveal a small blue-shift in the S0-->S1 absorption for the 11-locked derivative as compared to the unlocked one. The gas phase absorption spectra of all the cationic mimics so far investigated show almost no absorption in the blue region. This observation stresses the importance of protein interactions for colour tuning, which allows the human eye to perceive blue light.     

Toward superlensing with metal–dielectric composites and multilayers

We report on the fabrication of two types of adjustable, near-field superlens designs: metal–dielectric composites and metal–dielectric multilayer films. We fabricated a variety of films with different materials, thicknesses and compositions. These samples were characterized physically and optically to determine their film composition, quality, and optical responses. Our results on metal–dielectric composites indicate that although the real part of the effective permittivity generally follows effective medium theory predictions, the imaginary part does not and substantially higher losses are observed. Going forward, it appears that multilayer metal–dielectric designs are more suitable for sub-diffraction imaging applications because they could provide both tunability and low loss.     

Relaxation of signed integral functionals in BV

For integral functionals initially defined for ${u \in {\rm W}^{1,1}(\Omega; \mathbb{R}^m)}$ by $$\int_{\Omega} f(\nabla u) \, {\rm d}x$$ we establish strict continuity and relaxation results in ${{\rm BV}(\Omega; \mathbb{R}^m)}$ . The results cover the case of signed continuous integrands ${f : \mathbb{R}^{m \times d} \to \mathbb{R}}$ of linear growth at infinity. In particular, it is not excluded that the integrands are unbounded below.     

BMO and uniform estimates for multi-well problems

We establish optimal local regularity results for vector-valued extremals and minimizers of variational integrals whose integrand is the squared distance function to a compact set K in matrix space ${{{\mathbb M}^{N \times n}}}$ . The optimality is illustrated by explicit examples showing that, in the nonconvex case, minimizers need not be locally Lipschitz. This is in contrast to the case when the set K is suitably convex, where we show that extremals are locally Lipschitz continuous. The results rely on the special structure of the integrand and elementary Cordes–Nirenberg type estimates for elliptic systems.