Ultrafast Raman loss spectroscopy: a new approach to vibrational structure determination

The rapid data acquisition, natural fluorescence rejection and experimental ease are the advantages of the ultra-fast Raman loss scattering (URLS) which makes it a unique and valuable molecular structure-determining technique. URLS is an analogue of stimulated Raman scattering (SRS) but far more sensitive than SRS. It involves the interaction of two laser sources, viz. a picosecond (ps) pulse and white light, with the sample leading to the generation of loss signal on the higher energy (blue) side with respect to the wavelength of the ps pulse, unlike the gain signal observed on the red side in SRS. These loss signals are at least 1.5 times more intense than the SRS signals. Also, the very prerequisite of the experimental protocol for signal detection to be on the higher energy side by design eliminates the interference from fluorescence, which always appears on the red side. Unlike coherent anti-Stokes Raman scattering, URLS signals are not precluded by non-resonant background under resonance condition and also being a self-phase matched process, it is experimentally easier.

A chitotetrose specific lectin from Luffa acutangula :Physico-chemical properties and the assignment of orientation of sugars in the lectin binding site

A chitooligosaccharide specific lectin (Luffa acutangula agglutinin) has been purified from the exudate of ridge gourd fruits by affinity chromatography on soybean agglutininglycopeptides coupled to Sepharose-6B. The affinity purified lectin was found homogeneous by polyacrylamide gel electrophoresis, in sodium dodecyl sulphate-polyacrylamide gels, by gel filtration on Sephadex G-100 and by sedimentation velocity experiments. The relative molecular weight of this lectin is determined to be 48,000 ± 1,000 by gel chromatography and sedimentation equilibrium experiments. The sedimentation coefficient (S20, w) was obtained to be 4·06 S. The Stokes’ radius of the protein was found to be 2·9 nm by gel filtration. In sodium dodecyl sulphate-polyacrylamide gel electrophoresis the lectin gave a molecular weight of 24,000 in the presence as well as absence of 2-mercaptoethanol. The subunits in this dimeric lectin are therefore held by non-covalent interactions alone. The lectin is not a glycoprotein and circular dichroism spectral studies indicate that this lectin has 31% α-helix and no ß-sheet. The lectin is found to bind specifically to chitooligosaccharides and the affinity of the lectin increases with increasing oligosaccharide chain length as monitored by near ultra-violetcircular dichroism and intrinsic fluorescence titration. The values of ΔG, ΔΗ and ΔS for the binding process showed a pronounced dependence on the size of the oligosaccharide. The values for both ΔΗ and ΔS show a significant increase with increase in the oligosaccharide chain length showing that the binding of higher oligomers is progressively more favoured thermodynamically than chitobiose itself. The thermodynamic data is consistent with an extended binding site in the lectin which accommodates a tetrasaccharide. Based on the thermodynamic data, blue shifts and fluorescence enhancement, spatial orientation of chitooligosaccharides in the combining site of the lectin is assigned.

A complete characterization of pre-Mueller and Mueller matrices in polarization optics

The Mueller-Stokes formalism that governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could require of a 4 x 4 real matrix M in order that it qualify to be the Mueller matrix of some physical system would be that M map Omega((pol)), the positive solid light cone of Stokes vectors, into itself. In view of growing current interest in the characterization of partially coherent partially polarized electromagnetic beams, there is a need to extend this formalism to such beams wherein the polarization and spatial dependence are generically inseparably intertwined. This inseparability brings in additional constraints that a pre-Mueller matrix M mapping Omega((pol)) into itself needs to meet in order to be an acceptable physical Mueller matrix. These additional constraints are motivated and fully characterized. (C) 2010 Optical Society of America

Diffusion of flexible, charged, nanoscopic molecules in solution: Size and pH dependence for PAMAM dendrimer

In order to understand self-diffusion (D) of a charged, flexible, and porous nanoscopic molecule in water, we carry out very long, fully atomistic molecular dynamics simulation of PAMAM dendrimer up to eight generations in explicit salt water under varying pH. We find that while the radius of gyration (R-g) varies as N-1/3, the self-diffusion constant (D) scales, surprisingly, as N-alpha, with alpha=0.39 at high pH and 0.5 at neutral pH, indicating a dramatic breakdown of Stokes-Einstein relation for diffusion of charged nanoscopic molecules. The variation in D as a function of radius of gyration demonstrates the importance of treating water and ions explicitly in the diffusion process of a flexible nanoscopic molecule. In agreement with recent experiments, the self-diffusion constant increases with pH, revealing the importance of dielectric friction in the diffusion process. The shape of a dendrimer is found to fluctuate on a nanosecond time scale. We argue that this flexibility (and also the porosity) of the dendrimer may play an important role in determining the mean square displacement of the dendrimer and the breakdown of the Stokes-Einstein relation between diffusion constant and the radius.

Hanle-Zeeman redistribution matrix. I. Classical theory expressions in the laboratory frame

Polarized scattering in spectral lines is governed by a 4; 4 matrix that describes how the Stokes vector is scattered and redistributed in frequency and direction. Here we develop the theory for this redistribution matrix in the presence of magnetic fields of arbitrary strength and direction. This general magnetic field case is called the Hanle- Zeeman regime, since it covers both of the partially overlapping weak- and strong- field regimes in which the Hanle and Zeeman effects dominate the scattering polarization. In this general regime, the angle-frequency correlations that describe the so-called partial frequency redistribution (PRD) are intimately coupled to the polarization properties. We develop the theory for the PRD redistribution matrix in this general case and explore its detailed mathematical properties and symmetries for the case of a J = 0 -> 1 -> 0 scattering transition, which can be treated in terms of time-dependent classical oscillator theory. It is shown how the redistribution matrix can be expressed as a linear superposition of coherent and noncoherent parts, each of which contain the magnetic redistribution functions that resemble the well- known Hummer- type functions. We also show how the classical theory can be extended to treat atomic and molecular scattering transitions for any combinations of quantum numbers.

Dust Deposition on Single Cylinders

The inertial impaction of Lycopodium spores on single wires lying transverse to the direction of flow has been studied. The equations of particle motion in a potential flow field have been modified for the case when Stokes' law is inapplicable. Solutions to the above equations have been obtained by digital computation. Rec, the Reynolds number based on cylinder diameter, varied from 4 to 240; particle trajectories in a flow field at Rec = 10 have been determined for inertia parameter K = 1, 2, 4, 6, and 10. Ten trajectories were developed for the above cases by the numerical stepwise method. Experiments were performed by depositing Lycopodium spores on adhesive-coated wires of various diameters and at different velocities. The weight of dust deposited was determined with a microbalance. The experimental conditions were:. Wire diameters: 345, 457, 1500 μ. Particle diameter: 35 μ. Air velocities: 20-250 cm/sec. Inertia parameter: 1-60. The particle was considered as a point mass in the theoretical analysis. But in the experiments the ratio of particle size to wire size was not negligible (rp/rc = 0·1) and hence the effect of finite size of particle on collection efficiency due to the direct interception effect has been estimated. The effect of particle size distribution on collection efficiency has also been estimated. The experimental efficiencies obtained compare well with the calculated efficiencies at Rec = 10 when direct interception is taken into account.

A general treatment of two dimensional plane flows, for a micropolar fluid

In this paper we have studied the flow of a micropolar fluid, whose constitutive equations were given by Eringen, in two dimensional plane flow. In two notes, we have discussed the validity of the boundary condition v=a ω and its effect on the entire flow field. We have restricted our study to the case when Stokes' approximation is valid, i. e. slow motion for it is difficult to uncouple the equations in the most general case.

Solvation dynamics in dipolar liquids

The time dependent response of a polar solvent to a changing charge distribution is studied in solvation dynamics. The change in the energy of the solute is measured by a time domain Stokes shift in the fluorescence spectrum of the solute. Alternatively, one can use sophisticated non-linear optical spectroscopic techniques to measure the energy fluctuation of the solute at equilibrium. In both methods, the measured dynamic response is expressed by the normalized solvation time correlation function, S(t). The latter is found to exhibit uniquefeatures reflecting both the static and dynamic characteristics of each solvent. For water, S(t) consists of a dominant sub-50 fs ultrafast component, followed by a multi-exponential decay. Acetonitrile exhibitsa sub-100 fs ultrafast component, followed by an exponential decay. Alcohols and amides show features unique to each solvent and solvent series. However, understanding and interpretation of these results have proven to be difficult, and often controversial. Theoretical studiesand computer simulations have greatly facilitated the understanding ofS(t) in simple systems. Recently solvation dynamics has been used extensively to explore dynamics of complex systems, like micelles and reverse micelles, protein and DNA hydration layers, sol-gel mixtures and polymers. In each case one observes rich dynamical features, characterized again by multi-exponential decays but the initial and final time constants are now widely separated. In this tutorial review, we discuss the difficulties in interpreting the origin of the observed behaviour in complex systems.

Interfacial microrheology as a tool to study viscoelastic transitions in nanoconfined soft matter

We present a method to perform in situ microrheological measurements on monolayers of soft materials undergoing viscoelastic transitions under compression. Using the combination of a Langmuir trough mounted on the inverted microscope stage of a laser scanning confocal microscope we track the motion of individual fluorescent quantum dots partly dispersed in monolayers spread at the air-water interface. From the calculated mean square displacement of the probe particles and extending a well established scheme of the generalized Stokes-Einstein relation in bulk to the interface we arrive at the viscoelastic modulus for the respective monolayers as a function of surface density. Measurements on monolayers of glassy as well as nonglassy polymers and a standard fatty acid clearly show sensitivity of our technique to subtle variations, in the viscoelastic properties of the highly confined materials under compression. Evidence for possible spatial variations of such viscoelastic properties at a given surface density for the fatty acid monolayer is also provided.

Extending lagrange interpolation to develop a 4-node quadrilateral element

Today finite element method is a well established tool in engineering analysis and design. Though there axe many two and three dimensional finite elements available, it is rare that a single element performs satisfactorily in majority of practical problems. The present work deals with the development of 4-node quadrilateral element using extended Lagrange interpolation functions. The classical univariate Lagrange interpolation is well developed for 1-D and is used for obtaining shape functions. We propose a new approach to extend the Lagrange interpolation to several variables. When variables axe more than one the method also gives the set of feasible bubble functions. We use the two to generate shape function for the 4-node arbitrary quadrilateral. It will require the incorporation of the condition of rigid body motion, constant strain and Navier equation by imposing necessary constraints. The procedure obviates the need for isoparametric transformation since interpolation functions are generated for arbitrary quadrilateral shapes. While generating the element stiffness matrix, integration can be carried out to the accuracy desired by dividing the quadrilateral into triangles. To validate the performance of the element which we call EXLQUAD4, we conduct several pathological tests available in the literature. EXLQUAD4 predicts both stresses and displacements accurately at every point in the element in all the constant stress fields. In tests involving higher order stress fields the element is assured to converge in the limit of discretisation. A method thus becomes available to generate shape functions directly for arbitrary quadrilateral. The method is applicable also for hexahedra. The approach should find use for development of finite elements for use with other field equations also.

Interfacial microrheology as a tool to study viscoelastic transitions in nanoconfined soft matter

We present a method to perform in situ microrheological measurements on monolayers of soft materials undergoing viscoelastic transitions under compression. Using the combination of a Langmuir trough mounted on the inverted microscope stage of a laser scanning confocal microscope we track the motion of individual fluorescent quantum dots partly dispersed in monolayers spread at the air-water interface. From the calculated mean square displacement of the probe particles and extending a well established scheme of the generalized Stokes-Einstein relation in bulk to the interface we arrive at the viscoelastic modulus for the respective monolayers as a function of surface density. Measurements on monolayers of glassy as well as nonglassy polymers and a standard fatty acid clearly show sensitivity of our technique to subtle variations, in the viscoelastic properties of the highly confined materials under compression. Evidence for possible spatial variations of such viscoelastic properties at a given surface density for the fatty acid monolayer is also provided.

A mathematical analysis of nonlinear waves in a fluid filled visco-elastic tube

Our investigations in this paper are centred around the mathematical analysis of a ldquomodal waverdquo problem. We have considered the axisymmetric flow of an inviscid liquid in a thinwalled viscoelastic tube under certain simplifying assumptions. We have first derived the propagation space equations in the long wave limit and also given a general procedure to derive these equations for arbitrary wave length, when the flow is irrotational. We have used the method of operators of multiple scales to derive the nonlinear Schrödinger equation governing the modulation of periodic waves and we have elaborated on the ldquolong modulated wavesrdquo and the ldquomodulated long wavesrdquo. We have also examined the existence and stability of Stokes waves in this system. This is followed by a discussion of the progressive wave solutions of the long wave equations. One of the most important results of our paper is that the propagation space equations are no longer partial differential equations but they are in terms of pseudo-differential operators.Die vorliegenden Untersuchungen beziehen sich auf die mathematische Behandlung des ldquorModalwellenrdquo-Problems. Die achsensymmetrische Strömung einer nichtviskosen Flüssigkeit in einem dünnwandigen viskoelastischen Rohr, unter bestimmten vereinfachenden Annahmen, wird betrachtet. Zuerst werden die Gleichungen des Ausbreitungsraumes im Langwellenbereich abgeleitet und eine allgemeine Methode zur Herleitung dieser Gleichungen für beliebige Wellenlängen bei nichtrotierender Strömung angegeben. Eine Operatorenmethode mit multiplem Maßstab wird verwendet zur Herleitung der nichtlinearen Schrödinger-Gleichung für die Modulation der periodischen Wellen, und die ldquorlangmodulierten Wellenrdquo sowie die ldquormodulierten Langwellenrdquo werden aufgezeigt. Weiters wird die Existenz und die Stabilität der Stokes-Wellen im System untersucht. Anschließend werden die progressiven Wellenlösungen der Langwellengleichungen diskutiert. Eines der wichtigsten Ergebnisse dieser Arbeit ist, daß die Gleichungen des Ausbreitungsraumes keine partiellen Differentialgleichungen mehr sind, sondern Ausdrücke von Pseudo-Differentialoperatoren.

Solvent effect on the spectroscopic properties of 6MAMC and 7MAMC

The absorption and emission spectra of two dyes namely 6MAMC and 7MAMC have been recorded at room temperature in solvents of different polarities. The ground-state dipole moments (mu(g)) of these two were determined experimentally by Guggenheim method and were compared with theoretical values obtained using quantum chemical method. The exited state (mu(e))dipole moments were estimated from Lippert's, Bakhshiev's and Chamma-Viallet's equations by using the variation of the Stokes shift with the solvent dielectric constant and refractive index. The ground and excited-state dipole moments were calculated by means of the solvatochromic shift method and also the excited-state dipole moments are determined in combination with ground-state dipole moments. It was observed that dipole moments of excited state were higher than those of the ground state, indicating a substantial redistribution of the pi-electron densities in a more polar excited state for these two dyes. (C) 2010 Elsevier B.V. All rights reserved.

Solid finite elements through three decades

conventionally, solid finite elements have been looked upon as just generalizations of two-dimensional finite elements. In this article we trace their development starting from the days of their inception. Keeping in tune with our perceptions on developing finite elements, without taking recourse to any extra variational techniques, we discuss a few of the techniques which have been applied to solid finite elements. Finally we critically examine our own work on formulating solid finite elements based on the solutions to the Navier equations.

Shear-induced enhancement of self-diffusion in interacting colloidal suspensions

We set up the generalized Langevin equations describing coupled single-particle and collective motion in a suspension of interacting colloidal particles in a shear how and use these to show that the measured self-diffusion coefficients in these systems should be strongly dependent on shear rate epsilon. Three regimes are found: (i) an initial const+epsilon(.2), followed by (ii) a large regime of epsilon(.1/2) behavior, crossing over to an asymptotic power-law approach (iii) D-o - const x epsilon(.-1/2) to the Stokes-Einstein value D-o. The shear dependence is isotropic up to very large shear rates and increases with the interparticle interaction strength. Our results provide a straightforward explanation of recent experiments and simulations on sheared colloids.