Gaussian Schell-model beams and general shape invariance

We present two six-parameter families of anisotropic Gaussian Schell-model beams that propagate in a shape-invariant manner, with the intensity distribution continuously twisting about the beam axis. The two families differ in the sense or helicity of this beam twist. The propagation characteristics of these shape-invariant beams are studied, and the restrictions on the beam parameters that arise from the optical uncertainty principle are brought out. Shape invariance is traced to a fundamental dynamical symmetry that underlies these beams. This symmetry is the product of spatial rotation and fractional Fourier transformation.

Constitutive modeling of shape memory alloy wire with non-local rate kinetics

A constitutive modeling approach for shape memory alloy (SMA) wire by taking into account the microstructural phase inhomogeneity and the associated solid-solid phase transformation kinetics is reported in this paper. The approach is applicable to general thermomechanical loading. Characterization of various scales in the non-local rate sensitive kinetics is the main focus of this paper. Design of SMA materials and actuators not only involve an optimal exploitation of the hysteresis loops during loading-unloading, but also accounts for fatigue and training cycle identifications. For a successful design of SMA integrated actuator systems, it is essential to include the microstructural inhomogeneity effects and the loading rate dependence of the martensitic evolution, since these factors play predominant role in fatigue. In the proposed formulation, the evolution of new phase is assumed according to Weibull distribution. Fourier transformation and finite difference methods are applied to arrive at the analytical form of two important scaling parameters. The ratio of these scaling parameters is of the order of 10(6) for stress-free temperature-induced transformation and 10(4) for stress-induced transformation. These scaling parameters are used in order to study the effect of microstructural variation on the thermo-mechanical force and interface driving force. It is observed that the interface driving force is significant during the evolution. Increase in the slopes of the transformation start and end regions in the stress-strain hysteresis loop is observed for mechanical loading with higher rates.

Diffusion Anomaly in Silicalite and VPI-5 from Molecular Dynamics Simulations

Molecular dynamics (MD) simulations on rigid and flexible framework models of silicalite and a rigid framework model of the aluminophosphate VPI-5 for different sorbate diameters are reported. The sorbate-host interactions are modeled in terms of simple atom-atom Lennard-Jones interactions. The results suggest that the diffusion coefficient exhibits an anomaly as gamma approaches unity. The MD results confirm the existence of a linear regime for sorbate diameters significantly smaller than the channel diameter and an anomalous regime observed for sorbate diameters comparable to the channel diameter. The power spectra obtained by Fourier transformation of the velocity autocorrelation function indicate that there is an increase in the intensity of the low-frequency component for the velocity component parallel to the direction of motion for the sorbate diameter in the anomalous regime. The present results suggest that the diffusion anomaly is observed irrespective of (1) the geometry and topology of the pore structure and (2) the nature of the host material. The results are compared with the work of Derouane and co-workers, who have suggested the existence of ''floating molecules'' on the basis of earlier theoretical and computational approaches.

Transformation formula for exponential sums involving fourier coefficients of modular forms

In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular group SL(2, Z). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups of SL(2, Z) and prove similar estimates for the corresponding Dirichlet series.

Paraxial Maxwell beams: transformation by general linear optical systems

Extending the work of earlier papers on the relativistic-front description of paraxial optics and the formulation of Fourier optics for vector waves consistent with the Maxwell equations, we generalize the Jones calculus of axial plane waves to describe the action of the most general linear optical system on paraxial Maxwell fields. Several examples are worked out, and in each case it is shown that the formalism leads to physically correct results. The importance of retaining the small components of the field vectors along the axis of the system for a consistent description is emphasized.

Ordering transformation in icosahedral quasicrystals and related crystalline phases

Arcs of diffuse intensity appear in various shapes and positions in the diffraction patterns from the icosahedral phase, violating the parity rule for simple icosahedral (SI) symmetry. In the process of annealing treatment, the diffuse spots also evolve in the centre of the arcs and become sharp. These extra diffuse spots change the symmetry of the quasilattice from P-type to F-type. The ordered and disordered structures in quasicrystal have been linked to the ordered and disordered structures present in the crystalline alpha (Al-Mn-Si) and alpha (Al-Fe-Si) alloys.

Preparation of lamellar and hexagonal forms of mesoporous silica and zirconiaby the neutral amine route: lamellar-hexagonal transformation in the solid state

The chain length of the surfactant and the solvent composition are two of the factors that determine whether the lamellar or the hexagonal form of mesoporous SiO2 (or ZrO2) is formed by the neutral amine route; a lamellar-hexagonal transformation occurs on removal of the amine from the former.

Study of texture evolution in metastable beta-Ti alloy as a function of strain path and its effect on alpha transformation texture

Texture evolution in a low cost beta titanium alloy was studied for different modes of rolling and heat treatments. The alloy was cold rolled by unidirectional and multi-step cross rolling. The cold rolled material was either aged directly or recrystallized and then aged. The evolution of texture in alpha and beta phases were studied. The rolling texture of beta phase that is characterized by the gamma fiber is stronger for MSCR than UDR; while the trend is reversed on recrystallization. The mode of rolling affects alpha transformation texture on aging with smaller alpha lath size and stronger alpha texture in UDR than in MSCR. The defect structure in beta phase influences the evolution of a texture on aging. A stronger defect structure in beta phase leads to variant selection with the rolled samples showing fewer variants than the recrystallized samples.

DSC studies on the phase transformation of hydrazonium sulfate

The high temperature phase transformation of hydrazonium sulfate, N2H6SO4 has been studied using DSC. The enthalpy of phase transition is found to be 3.63 ± 0.1 kJ mole−1. The phase transition temperature is found to decrease with the increase of particle size. It appears that the strain energy and not surface energy, is responsible for the phase transformation. The molar volume of the salt increases during the transformation as found by the dilatometric experiment involving percentage of linear thermal expansion. On cooling, the transformation from the high temperature modification to orthorhombic form is incomplete and extends over a wide range of temperature.

Paraxial-wave optics and relativistic front description .1. The scalar theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Small-amplitude cyclic voltammetry: Part I. A simple fourier synthesis approach

Current-potential relationships are derived for small-amplitude periodic inputs for linear electrochemical systems using a Fourier synthesis procedure. Specific results have been obtained for a triangular potential waveform for two simple model systems.

Stress-induced martensitic phase transformation in Cu-Zr nanowires

A novel stress-induced martensitic phase transformation in an initial < 100 >/{100} B2-CuZr nanowire is reported for the first time in this letter. Such behavior is observed in a nanowire with cross-sectional dimensions of 19.44 x 19.44 angstrom(2) over a temperature range of 100-400 K and at a strain rate of 1 x 10(9) s(-1) using atomistic simulations. Phase transformation from an initial B2 phase to a BCT (Body-Centered-Tetragonal) phase is observed via nucleation and propagation of {100} twinning plane under high strain rate tensile deformation. (C) 2009 Elsevier B.V. All rights reserved.

Determination of chemical shift anisotropy without a reference and of direct and indirect spin-spin couplings between heteronuclei

A method employing two liquid crystals of opposite diamagnetic anisotropies to determine chemical shift anisotropy without using any reference compound is described. It also provides individual values of the direct and the indirect spin-spin coupling constants between heteronuclei. The parameters for acetonitrile are reported.

Microbial transformation of a fungicide-derived amine, dimethyl-p-phenylene diamine by Alcaligenes DM4

Abstract Microbial transformation of N, N-dimethyl-p-phenylene diamine (DMPDA), a microbial product formed from the fungicide fenaminosulf (p-dimethylaminobenzenediazo sodium sulfonate) was studied by enriching microbes in soils treated with the amine. Microorganisms isolated from DMPDA-treated soil belonged to the genera of Micrococcus, Alcaligenes, and Corynebacterium. Of the various isolates, Alcaligenes DM4 showed maximal growth on DMPDA utilizing it as sources of carbon and nitrogen. When grown in mineral salts basal medium containing 0.05% DMPDA to serve as carbon and nitrogen sources, Alcaligenes DM4 grew exponentially up to 18 h. Even though the characterization of the complete pathway of microbial degradation of DMPDA could not be carried out due to the auto-oxidation of the compound, the initial transformation product of DMPDA by Alcaligenes DM4 has been identified as a dimer. The dimer is generated into the culture medium presumably by the extra-cellular oxidase of Alcaligenes DM4. It is suggested that the risk-benefit evaluation on the use of fenaminosulf is to be made taking into consideration the microbial transformations of the fungicide.