Microscopic expression for frequency and wave vector dependent dielectric constant of a dipolar liquid

A microscopic expression for the frequency and wave vector dependent dielectric constant of a dense dipolar liquid is derived starting from the linear response theory. The new expression properly takes into account the effects of the translational modes in the polarization relaxation. The longitudinal and the transverse components of the dielectric constant show vastly different behavior at the intermediate values of the wave vector k. We find that the microscopic structure of the dense liquid plays an important role at intermediate wave vectors. The continuum model description of the dielectric constant, although appropriate at very small values of wave vector, breaks down completely at the intermediate values of k. Numerical results for the longitudinal and the transverse dielectric constants are obtained by using the direct correlation function from the mean‐spherical approximation for dipolar hard spheres. We show that our results are consistent with all the limiting expressions known for the dielectric function of matter.

Microwave Assisted Synthesis of Nanostructured Titanium Dioxide with High Photocatalytic Activity

TiO2 (anatase) was synthesized using a microwave-irradiation-assisted chemical method. The reaction conditions were varied to obtain unique nanostructures of TiO2 comprising nanometric spheres giving the materials a very porous morphology. The oxide was characterized by X-ray diffraction (XRD), Raman spectroscopy, transmission electron microscopy (TEM), scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), Fourier transform infrared (FTIR) spectroscopy, and thermogravimetric analysis (TGA). The specific surface area and porosity were quantified by the BET method, and the degradation of dyes was carried out using these materials. The photocatalytic activity of the nanometric TiO2 was significantly higher than that of commercially available TiO2 (Degussa P25) for the degradation of the dyes.

Facile hydrothermal synthesis and observation of bubbled growth mechanism in nano-ribbons aggregated microspherical Covellite blue-phosphor

Well uniform microspheres of phase pure Covellite were synthesized through a simple hydrothermal approach using poly vinyl pyrrolidone (PVP) as surfactant. The micro-spheres were constituted of numerous self-organized knitted nano-ribbons of similar to 30 nm thickness. The effect of conc. PVP in the hydrothermal precursor solution on the product morphology was investigated. Based on the out-coming product micro-architecture a growth mechanism was proposed which emphasized bubbled nucleation inside the hydrothermal reactor. In a comparative study on linear optical properties, enhancement of luminescent intensity was observed for nano-ribbon clung microspheres rather than that of agglomerates of distorted particles, which may be attributed to better crystallinity as well as reduced surface defects and ionic vacancies for ribbon-like nano-structures.

Time-Dependent Dynamics of a Planar Galaxy Model

Time-dependent models of collisionless stellar systems with harmonic potentials allowing for an essentially exact analytic description have recently been described. These include oscillating spheres and spheroids. This paper extends the analysis to time-dependent elliptic discs. Although restricted to two space dimensions, the systems are richer in that their parameters form a 10-dimensional phase space (in contrast to six for the earlier models). Apart from total energy and angular momentum, two additional conserved quantities emerge naturally. These can be chosen as the areas of extremal sections of the ellipsoidal region of phase space occupied by the system (their product gives the conserved volume). The present paper describes the construction of these models. An application to a tidal encounter is given which allows one to go beyond the impulse approximation and demonstrates the effects of rotation of the perturbed system on energy and angular-momentum transfer. The angular-momentum transfer is shown to scale inversely as the cube of the encounter velocity for an initial configuration of the perturbed galaxy with zero quadrupole moment.

Relationship between microscopic and macroscopic orientational relaxation times in polar liquids

Microscopic relations between single-particle orientational relaxation time (T, ) , dielectric relaxation time ( T ~ )a,n d many-body orientational relaxation time ( T ~o)f a dipolar liquid are derived. We show that both T~ and T~ are influenced significantly by many-body effects. In the present theory, these many-body effects enter through the anisotropic part of the two-particle direct correlation function of the polar liquid. We use mean-spherical approximation (MSA) for dipolar hard spheres for explicit numerical evaluation of the relaxation times. We find that, although the dipolar correlation function is biexponential, the frequency-dependent dielectric constant is of simple Debye form, with T~ equal to the transverse polarization relaxation time. The microscopic T~ falls in between Debye and Onsager-Glarum expressions at large values of the static dielectric constant.

Combustion studies on concentrated distillery effluents

Studies on ignition and combustion of distillery effluent containing solids consisting of 38 +/- 2% inorganics and 62 +/- 2% of organics (cane sugar derivatives) have been carried out in order to investigate the role of droplet size and ambient temperature in the process of combustion. Experiments were conducted on in liquid droplets of effluent having solids concentration 65% and (2) spheres of died (100% solids) effluent of diameters ranging from 0.5 to 25 mm. These spheres were introduced into a furnace where air temperature ranged from 500 to 1000 degrees C, and they burned with two distinct regimes of combustion-flaming and glowing. The ignition delay of the 65% concentration effluent increases with diameter as in the case of nonvolatile droplets, while that of dried spheres appears to be independent of size. The ignition delay shows Arrhenius dependence on temperature. The flaming combustion involves a weight loss of 50-80%, depending on ambient temperature, and the flaming time is given by t(f) similar to d(0)(2), as in the case of liquid fuel droplets and wood spheres. Char glowing involves weight loss of an additional 10-20%, with glowing time behaving as t(c) similar to d(0)(2) as in the case of wood char, even though the inert content of effluent char is as large as 50% compared to 2-3% in wood char Char combustion has been modeled, and the results of this model compare well with the experimental results.

Phase Separation in Binary Nearly-Hard-Sphere Colloids: Evidence for the Depletion Force

A binary aqueous suspension of large (L) and small (S) nearly-hard-sphere colloidal polystyrene spheres is shown to segregate spontaneously into L-rich and S-rich regions for suitable choices of volume fraction and size ratio. This is the first observation of such purely entropic phase separation of chemically identical species in which at least one component remains fluid. Simple theoretical arguments are presented to make this effect plausible.

Variational principles in evolution

For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a straightforward generalization of the one-locus case, but (iii) that in two-locus or more general models there is no straightforward extension of this principle if linkage and epistasis are present. The population trajectories can be constructed as trajectories of steepest ascent in a Riemannian metric space. A general method is formulated to find the metric tensor and the surface-in the metric space on which the trajectories, which characterize the variations in the gene structure of the population, lie. The local optimality principle holds good in such a space. In the special case when all possible linkage disequilibria are zero, the phase point of the n-locus genetic system moves on the surface of the product space of n higher dimensional unit spheres in a certain Riemannian metric space of gene frequencies so that the rate of change of mean fitness is maximum along the trajectory. In the two-locus case the corresponding surface is a hyper-torus.

Structure-potential relationship and nature of disorder in liquids and glassy solids

A method based on the minimal-spanning tree is extended to a collection of points in three dimensions. Two parameters, the average edge length and its standard deviation characterize the disorder. The structural phase diagram for a monatomic system of particles and the characteristic values for the uniform random distribution of points have been obtained. The method is applied to hard spheres and Lennard-Jones systems. These systems occupy distinct regions in the structural phase diagram. The structure of the Lennard-Jones system approaches that of the defective close-packed arrangements at low temperatures whereas in the liquid regime, it deviates from the close-packed configuration.

On Walkup's class K (d) and a minimal triangulation of (S-3 (sic) S-1)(#3)

For d >= 2, Walkup's class K (d) consists of the d-dimensional simplicial complexes all whose vertex-links are stacked (d - 1)-spheres. Kalai showed that for d >= 4, all connected members of K (d) are obtained from stacked d-spheres by finitely many elementary handle additions. According to a result of Walkup, the face vector of any triangulated 4-manifold X with Euler characteristic chi satisfies f(1) >= 5f(0) - 15/2 chi, with equality only for X is an element of K(4). Kuhnel observed that this implies f(0)(f(0) - 11) >= -15 chi, with equality only for 2-neighborly members of K(4). Kuhnel also asked if there is a triangulated 4-manifold with f(0) = 15, chi = -4 (attaining equality in his lower bound). In this paper, guided by Kalai's theorem, we show that indeed there is such a triangulation. It triangulates the connected sum of three copies of the twisted sphere product S-3 (sic) S-1. Because of Kuhnel's inequality, the given triangulation of this manifold is a vertex-minimal triangulation. By a recent result of Effenberger, the triangulation constructed here is tight. Apart from the neighborly 2-manifolds and the infinite family of (2d + 3)-vertex sphere products Sd-1 X S-1 (twisted for d odd), only fourteen tight triangulated manifolds were known so far. The present construction yields a new member of this sporadic family. We also present a self-contained proof of Kalai's result. (C) 2011 Elsevier B.V. All rights reserved.

Velocity distribution function for a dilute granular material in shear flow

The velocity distribution function for the steady shear flow of disks (in two dimensions) and spheres (in three dimensions) in a channel is determined in the limit where the frequency of particle-wall collisions is large compared to particle-particle collisions. An asymptotic analysis is used in the small parameter epsilon, which is naL in two dimensions and na(2)L in three dimensions, where; n is the number density of particles (per unit area in two dimensions and per unit volume in three dimensions), L is the separation of the walls of the channel and a is the particle diameter. The particle-wall collisions are inelastic, and are described by simple relations which involve coefficients of restitution e(t) and e(n) in the tangential and normal directions, and both elastic and inelastic binary collisions between particles are considered. In the absence of binary collisions between particles, it is found that the particle velocities converge to two constant values (u(x), u(y)) = (+/-V, O) after repeated collisions with the wall, where u(x) and u(y) are the velocities tangential and normal to the wall, V = (1 - e(t))V-w/(1 + e(t)), and V-w and -V-w, are the tangential velocities of the walls of the channel. The effect of binary collisions is included using a self-consistent calculation, and the distribution function is determined using the condition that the net collisional flux of particles at any point in velocity space is zero at steady state. Certain approximations are made regarding the velocities of particles undergoing binary collisions :in order to obtain analytical results for the distribution function, and these approximations are justified analytically by showing that the error incurred decreases proportional to epsilon(1/2) in the limit epsilon --> 0. A numerical calculation of the mean square of the difference between the exact flux and the approximate flux confirms that the error decreases proportional to epsilon(1/2) in the limit epsilon --> 0. The moments of the velocity distribution function are evaluated, and it is found that [u(x)(2)] --> V-2, [u(y)(2)] similar to V-2 epsilon and -[u(x)u(y)] similar to V-2 epsilon log(epsilon(-1)) in the limit epsilon --> 0. It is found that the distribution function and the scaling laws for the velocity moments are similar for both two- and three-dimensional systems.

Boundary conditions at a rigid wall for rough granular gases

We derive boundary conditions at a rigid wall for a granular material comprising rough, inelastic particles. Our analysis is confined to the rapid flow, or granular gas, regime in which grains interact by impulsive collisions. We use the Chapman-Enskog expansion in the kinetic theory of dense gases, extended for inelastic and rough particles, to determine the relevant fluxes to the wall. As in previous studies, we assume that the particles are spheres, and that the wall is corrugated by hemispheres rigidly attached to it. Collisions between the particles and the wall hemispheres are characterized by coefficients of restitution and roughness. We derive boundary conditions for the two limiting cases of nearly smooth and nearly perfectly rough spheres, as a hydrodynamic description of granular gases comprising rough spheres is appropriate only in these limits. The results are illustrated by applying the equations of motion and boundary conditions to the problem of plane Couette flow.

Helical structures: The geometry of protein helices and nanotubes

In nature, helical structures arise when identical structural subunits combine sequentially, the orientational and translational relation between each unit and its predecessor remaining constant. A helical structure is thus generated by the repeated action of a screw transformation acting on a subunit. A plane hexagonal lattice wrapped round a cylinder provides a useful starting point for describing the helical conformations of protein molecules, for investigating the geometrical properties of carbon nanotubes, and for certain types of dense packings of equal spheres.

Rayleigh-Benard convection during solidification of an eutectic solution cooled from the top

The interaction between laminar Rayleigh-Benard convection and directional solidification is studied for the case of an eutectic solution kept in a rectangular cavity cooled from the top. Experiments and numerical simulations are carried out using an NH4Cl-H2O solution as the model fluid. The flow is visualized using a sheet of laser light scattered by neutrally buoyant, hollow-glass spheres seeded in the fluid. The numerical modeling is performed using a pressure-based finite-volume method according to the SIMPLER algorithm. The present configuration enables us to visualize flow vortices in the presence of a continuously evolving solid/liquid interface. Clear visualization of the Rayleigh-Benard convective cells and their interaction with the solidification front are obtained. It is observed that the convective cells are characterized by zones of up-flow and down-flow, resulting in the development of a nonplanar interface. Because of the continuous advancement of the solid/liquid interface, the effective liquid height of the cavity keeps decreasing. Once the height of the fluid layer falls below a critical value, the convective cells become weaker and eventually die out, leading to the growth of a planar solidification front. Results of flow visualization and temperature measurement are compared with those from the numerical simulation, and a good agreement is found.

Studies on compressive failure features in syntactic foam material

Syntactic foam made by mechanical mixing of glass hollow spheres in epoxy resin matrix is characterized for compressive properties in the present study. Volume fraction of hollow spheres in the syntactic foam under investigation is kept at 67.8%. Effect of specimen aspect ratio on failure behavior and stress-strain curve of the material is highlighted. Considerable differences are noted in the macroscopic fracture features of the specimen and the stress-strain curve with the variation in specimen aspect ratio, although compressive yield strength values were within a narrow range. Post compression test scanning electron microscopic observations coupled with the macroscopic observations taken during the test helped in explaining the deviation in specimen behavior and in gathering support for the proposed arguments.