Twist phase in Gaussian-beam optics

The recently discovered twist phase is studied in the context of the full ten-parameter family of partially coherent general anisotropic Gaussian Schell-model beams. It is shown that the nonnegativity requirement on the cross-spectral density of the beam demands that the strength of the twist phase be bounded from above by the inverse of the transverse coherence area of the beam. The twist phase as a two-point function is shown to have the structure of the generalized Huygens kernel or Green's function of a first-order system. The ray-transfer matrix of this system is exhibited. Wolf-type coherent-mode decomposition of the twist phase is carried out. Imposition of the twist phase on an otherwise untwisted beam is shown to result in a linear transformation in the ray phase space of the Wigner distribution. Though this transformation preserves the four-dimensional phase-space volume, it is not symplectic and hence it can, when impressed on a Wigner distribution, push it out of the convex set of all bona fide Wigner distributions unless the original Wigner distribution was sufficiently deep into the interior of the set.

Void Geometry Driven Spin Crossover in Zeolite-Encapsulated Cobalt Tris(bipyridyl) Complex Ion

The cobalt(II) tris(bipyridyl) complex ion encapsulated in zeolite-Y supercages exhibits a thermally driven interconversion between a low-spin and a high-spin state-a phenomenon not observed for this ion either in solid state or in solution. From a comparative study of the magnetism and optical spectroscopy of the encapsulated and unencapsulated complex ion, supported by molecular modeling, such spin behavior is shown to be intramolecular in origin. In the unencapsulated or free state, the [Co(bipy)(3)](2+) ion exhibits a marked trigonal prismatic distortion, but on encapsulation, the topology of the supercage forces it to adopt a near-octahedral geometry. An analysis using the angular overlap ligand field model with spectroscopically derived parameters shows that the geometry does indeed give rise to a low-spin ground state, and suggests a possible scenario for the spin state interconversion.

Effect of ion nitriding on the microstructure and properties of Maraging steel (250 Grade)

In the present investigation, ion nitriding of Maraging steel (250 grade) has been carried out at three different temperatures i.e., at 435 degrees C, 450 degrees C and 465 degrees C for 10 h duration in order to achieve good wear resistance along with high strength required for the slat track component of aircraft. The microstructure of the base material and the nitrided layer was examined by optical and scanning electron microscope, and various phases present were determined by X-ray diffraction. Various properties, such as, hardness, case depth, tensile, impact, fatigue properties and corrosion resistance were investigated for both un-nitrided and ion-nitrided materials. It is observed that the microstructure of the core material remains unaltered and Fe4N is formed in the hardened surface layer after ion nitriding at all the three temperatures employed. Surface hardness increases substantially after ion nitriding. Surface hardness remains almost the same but case depth increases with the increase in ion nitriding temperature due to greater diffusivity at higher temperatures. Tensile strength, fatigue strength and corrosion resistance are improved but ductility and energy absorbed in impact test decrease on ion nitriding. These results are explained on the basis of microstructural observations. The properties obtained after ion nitriding at 450 degrees C for 10 h are found to be optimum when compared to the other two ion nitriding temperatures.

High-Temperature Phase Transition Studies in a Novel Fast Ion Conductor, Na2Cd(SO4)2, Probed by Raman Spectroscopy

Temperature-dependent Raman spectroscopic studies were carried out on Na2Cd(SO4)(2) from room temperature to 600 degrees C. We observe two transitions at around 280 and 565 degrees C. These transitions are driven by the change in the SO4 ion. On the basis of these studies, one can explain the changes in the conductivity data observed around 280 and 565 degrees C. At 280 degrees C, spontaneous tilting of the SO4 ion leads to restriction of Na+ mobility. Above 565 degrees C, the SO4 ion starts to rotate freely, leading to increased mobility of Na+ ion in the channel.

The influence of the gas environment on morphology and chemical composition of surfaces micro-machined with a femtosecond laser

We investigated the influence of different gas environments on the fabrication of surfaces, homogeneously covered with equally sized and spaced micro-structures. Two types of structures have been successfully micro-machined with a femtosecond laser on titanium surfaces in various atmospheres. The surface chemistry of samples machined in oxygen and helium shows TiO2, while machining in nitrogen leads to an additional share of TiN. The actual surface structure was found to vary significantly as a function of the gas environment. We found that the ablated particles and their surface triggered two consecutive events: The optical properties of the gas environment became non-isotropic which then led to the pulse intensity being redistributed throughout the cross section of the laser beam. Additionally, the effective intensity was further reduced for TiN surfaces due to TiN's high reflectivity. Thus, the settings for the applied raster-scanning machining method had to be adjusted for each gas environment to produce comparable structures. In contrast to previous studies, where only noble gases were found suitable to produce homogeneous patches, we obtained them in an oxygen environment.

Field imperfection induced axial secular frequency shifts in nonlinear ion traps

This article develops a simple analytical expression that relates ion axial secular frequency to field aberration in ion trap mass spectrometers. Hexapole and octopole aberrations have been considered in the present computations. The equation of motion of the ions in a pseudopotential well with these superpositions has the form of a Duffing-like equation and a perturbation method has been used to obtain the expression for ion secular frequency as a function of field imperfections. The expression indicates that the frequency shift is sensitive to the sign of the octopole superposition and insensitive to the sign of the hexapole superposition. Further, for weak multipole superposition of the same magnitude, octopole superposition causes a larger frequency shift in comparison to hexapole superposition.

Effect of spatial dispersion of the dielectric on the binding energy of D- ion in Si and Ge

Using a multivalley effective mass theory, we obtain the binding energy of a D- ion in Si and Ge taking into account the spatial variation of the host dielectric function. We find that on comparison with experimental results the effect of spatial dispersion is important in the estimation of binding energy for the D- formed by As in Si and Ge. The effect is less significant for the case of D- formed by P and Sb donors.

Gel-coated ion-exchange resin: A new kinetic model

Regenerable 'gel-coated' cationic resins with fast sorption kinetics and high sorption capacity have application potential for removal of trace metal ions even in large-scale operations. Poly(acrylic acid) has been gel-coated on high-surface area silica (pre-coated with ethylene-vinyl acetate copolymer providing a thin barrier layer) and insolubilized by crosslinking with a low-molecular-weight diepoxide (epoxy equivalent 180 g) in the presence of benzyl dimethylamine catalyst at 70 degrees C, In experiments performed for Ca2+ sorption from dilute aqueous solutions of Ca(NO,),, the gel-coated acrylic resin is found to have nearly 40% higher sorption capacity than the bead-form commercial methacrylic resin Amberlite IRC-50 and also several limes higher rate of sorption. The sorption on the gel-coated sorbent under vigorous agitation has the characteristics of particle diffusion control with homogeneous (gel) diffusion in resin phase. A new mathematical model is proposed for such sorption on gel-coated ion-exchange resin in finite bath and solved by applying operator-theoretic methods. The analytical solution so obtained shows goad agreement with experimental sorption kinetics at relatively low levels (< 70%) of resin conversion.

Reconstruction from incomplete data in cone-beam tomography

A method for reconstruction of an object f(x) x=(x,y,z) from a limited set of cone-beam projection data has been developed. This method uses a modified form of convolution back-projection and projection onto convex sets (POCS) for handling the limited (or incomplete) data problem. In cone-beam tomography, one needs to have a complete geometry to completely reconstruct the original three-dimensional object. While complete geometries do exist, they are of little use in practical implementations. The most common trajectory used in practical scanners is circular, which is incomplete. It is, however, possible to recover some of the information of the original signal f(x) based on a priori knowledge of the nature of f(x). If this knowledge can be posed in a convex set framework, then POCS can be utilized. In this report, we utilize this a priori knowledge as convex set constraints to reconstruct f(x) using POCS. While we demonstrate the effectiveness of our algorithm for circular trajectories, it is essentially geometry independent and will be useful in any limited-view cone-beam reconstruction.

Evaluation of ion exchange as a pre-treatment option for coal seam gas water

The Coal Seam Gas (CSG) industry in Australia has grown significantly in recent years. During the gas extraction process, water is also recovered which is brackish in character. In order to facilitate beneficial reuse of the water, the CSG industry has primarily invested in Reverse Osmosis (RO) as the primary method for associated water desalination. However, the presence of alkaline earth ions in the water combined with the inherent alkalinity of the water may result in RO membrane scaling. Consequently, weak acid cation (WAC) synthetic ion exchange resins were investigated as a potential solution to this potential problem. It was shown that resins were indeed highly efficient at treating single and multi-component solutions of alkaline earth ions. The interaction of the ions with the resin was found to be considerably more complex that previously reported.

A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization

While frame-invariant solutions for arbitrarily large rotational deformations have been reported through the orthogonal matrix parametrization, derivation of such solutions purely through a rotation vector parametrization, which uses only three parameters and provides a parsimonious storage of rotations, is novel and constitutes the subject of this paper. In particular, we employ interpolations of relative rotations and a new rotation vector update for a strain-objective finite element formulation in the material framework. We show that the update provides either the desired rotation vector or its complement. This rules out an additive interpolation of total rotation vectors at the nodes. Hence, interpolations of relative rotation vectors are used. Through numerical examples, we show that combining the proposed update with interpolations of relative rotations yields frame-invariant and path-independent numerical solutions. Advantages of the present approach vis-a-vis the updated Lagrangian formulation are also analyzed.

Metal-Ion-Dependent Oxidative DNA Cleavage by Transition Metal Complexes of a New Water-Soluble Salen Derivative

A new water-soluble, salen [salen = bis(salicylidene) ethylenediamine]-based ligand, 3 was developed. Two of the metal complexes of this ligand, i.e., 3a, [Mn(III)] and 3b, [Ni(II)], in the presence of cooxidant magnesium monoperoxyphthalate (MMPP) cleaved plasmid DNA pTZ19R efficiently and rapidly at a concentration similar to 1 mu M. In contrast, under comparable conditions, other metal complexes 3c, [Cu(II)] or 3d, [Cr(III)] could not induce any significant DNA nicking. The findings with Ni(II) complex suggest that the DNA cleavage processes can be modulated by the disposition of charges around the ligand.

Ultrafast Solvation Dynamics of an Ion in the gamma-Cyclodextrin Cavity: The Role of Restricted Environment

A detailed study of the solvation dynamics of a charged coumarin dye molecule in gamma-cyclodextrin/water has been carried out by using two different theoretical approaches. The first approach is based on a multishell continuum model (MSCM). This model predicts the time scales of the dynamics rather well, provided an accurate description of the frequency-dependent dielectric function is supplied. The reason for this rather surprising agreement is 2-fold. First, there is a cancellation of errors, second, the two-zone model mimics the heterogeneous microenvironment surrounding the ion rather well. The second approach is based on the molecular hydrodynamics theory (MI-IT). In this molecular approach, the solvation dynamics has been studied by restricting the translational motion of the solvent molecules enclosed within the cavity. The results from the molecular theory are also in good agreement with the experimental results. Our study indicates that, in the present case, the restricted environment affects only the long time decay of the solvation time correlation function. The short time dynamics is still governed by the librational (and/or vibrational) modes present in bulk water.

Response And Stability Of A Stochastic Beam-Column Using Stochastic Fem

A beam-column resting on continuous Winkler foundation and discrete elastic supports is considered. The beam-column is of variable cross-section and the variation of sectional properties along the axis of the beam-column is deterministic. Young's modulus, mass per unit length and distributed axial loadings of the beam-column have a stochastic distribution. The foundation stiffness coefficient of the Winkler model, the stiffnesses of discrete elastic supports, stiffnesses of end springs and the end thrust, are all considered as random parameters. The material property fluctuations and distributed axial loadings are considered to constitute independent, one-dimension uni-variate homogeneous real stochastic fields in space. The foundation stiffness coefficient, stiffnesses of the discrete elastic supports, stiffnesses of end springs and the end thrust are considered to constitute independent random variables. Static response, free vibration and stability behaviour of the beam-column are studied. Hamilton's principle is used to formulate the problem using stochastic FEM. Sensitivity vectors of the response and stability parameters are evaluated. Using these statistics of free vibration frequencies, mode shapes, buckling parameters, etc., are evaluated. A numerical example is given.

Ion conductance in electrolyte solutions

We develop a new theoretical formulation to study ion conductance in electrolyte solutions, based on a mode coupling theory treatment of the electrolyte friction. The new theory provides expressions for both the ion atmosphere relaxation and electrophoretic contributions to the total electrolyte friction that acts on a moving ion. While the ion atmosphere relaxation term arises from the time-dependent microscopic interaction of the moving ion with the surrounding ions in the solution, the electrophoretic term originates from the coupling of the ion's velocity to the collective current mode of the ion atmosphere. Mode coupling theory, combined with time-dependent density functional theory of ion atmosphere fluctuations, leads to self-consistent expressions for these two terms which also include the effects of self-motion of the ion under consideration. These expressions have been solved for the concentration dependence of electrolyte friction and ion conductance. It is shown that in the limit of very low ion concentration, the present theory correctly reduces to the well-known Debye-Huckel-Onsager limiting law which predicts a linear dependence of conductance on the square root of ion concentration (c). At moderate and high concentrations, the present theory predicts a significant nonlinear and weaker dependence on root c which is in very good agreement with experimental results. The present theory is self-contained and does not involve any adjustable parameter.