Velocity distribution for a dilute vibrated granular material

The velocity distribution for a vibrated granular material is determined in the dilute limit where the frequency of particle collisions with the vibrating surface is large compared to the frequency of binary collisions. The particle motion is driven by the source of energy due to particle collisions with the vibrating surface, and two dissipation mechanisms-inelastic collisions and air drag-are considered. In the latter case, a general form for the drag force is assumed. First, the distribution function for the vertical velocity for a single particle colliding with a vibrating surface is determined in the limit where the dissipation during a collision due to inelasticity or between successive collisions due to drag is small compared to the energy of a particle. In addition, two types of amplitude functions for the velocity of the surface, symmetric and asymmetric about zero velocity, are considered. In all cases, differential equations for the distribution of velocities at the vibrating surface are obtained using a flux balance condition in velocity space, and these are solved to determine the distribution function. It is found that the distribution function is a Gaussian distribution when the dissipation is due to inelastic collisions and the amplitude function is symmetric, and the mean square velocity scales as [[U-2](s)/(1 - e(2))], where [U-2](s) is the mean square velocity of the vibrating surface and e is the coefficient of restitution. The distribution function is very different from a Gaussian when the dissipation is due to air drag and the amplitude function is symmetric, and the mean square velocity scales as ([U-2](s)g/mu(m))(1/(m+2)) when the acceleration due to the fluid drag is -mu(m)u(y)\u(y)\(m-1), where g is the acceleration due to gravity. For an asymmetric amplitude function, the distribution function at the vibrating surface is found to be sharply peaked around [+/-2[U](s)/(1-e)] when the dissipation is due to inelastic collisions, and around +/-[(m +2)[U](s)g/mu(m)](1/(m+1)) when the dissipation is due to fluid drag, where [U](s) is the mean velocity of the surface. The distribution functions are compared with numerical simulations of a particle colliding with a vibrating surface, and excellent agreement is found with no adjustable parameters. The distribution function for a two-dimensional vibrated granular material that includes the first effect of binary collisions is determined for the system with dissipation due to inelastic collisions and the amplitude function for the velocity of the vibrating surface is symmetric in the limit delta(I)=(2nr)/(1 - e)much less than 1. Here, n is the number of particles per unit width and r is the particle radius. In this Limit, an asymptotic analysis is used about the Limit where there are no binary collisions. It is found that the distribution function has a power-law divergence proportional to \u(x)\((c delta l-1)) in the limit u(x)-->0, where u(x) is the horizontal velocity. The constant c and the moments of the distribution function are evaluated from the conservation equation in velocity space. It is found that the mean square velocity in the horizontal direction scales as O(delta(I)T), and the nontrivial third moments of the velocity distribution scale as O(delta(I)epsilon(I)T(3/2)) where epsilon(I) = (1 - e)(1/2). Here, T = [2[U2](s)/(1 - e)] is the mean square velocity of the particles.

Characterization of electrochemically deposited Cu-Ni black coatings

Electrochemically deposited Cu-Ni black coatings on molybdenum substrate from ethylenediaminetetraacetic acid (EDTA) bath solution are shown to exhibit good optical properties (alpha = 0.94, epsilon = 0.09). The deposit is characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM) and X-ray photoelectron spectroscopy (XPS). Cu is present in metallic and +2 oxidation states in the as-prepared Cu-Ni black coating, whereas Ni2+ as well as Ni3+ species are observed in the same coating. Cu and Ni are observed in their metallic state after 10 and 20 min sputtering. X-ray initiated Auger electron spectroscopy (XAES) of Cu and Ni also agrees well with XPS investigations. (C) 2002 Elsevier Science Ltd. All rights reserved.

Lithium borate-strontium bismuth tantalate glass nanocomposite: a novel material for nonlinear optic and ferroelectric applications

Glass nanocomposites in the system (100 - x)Li2B4O7-xSrBi(2)Ta(2)O(9) (0 less than or equal to x less than or equal to 22.5, in molar ratio) were fabricated via a melt quenching technique followed by controlled heat-treatment. The as-quenched samples were confirmed to be glassy and amorphous by differential thermal analysis (DTA) and X-ray powder diffraction (XRD) techniques, respectively. The phase formation and crystallite size of the heat-treated samples (glass nanocomposites) were monitored by XRD and transmission electron microscopy (TEM). The relative permittivities (epsilon(tau)') of the glass nanocomposites for different compositions were found to lie in between that of the parent host glass (Li2B4O7) and strontium bismuth tantalate (SBT) ceramic in the frequency range 100 Hz-40 MHz at 300 K, whereas the dielectric loss (D) of the glass nanocomposite was less than that of both the parent phases. Among the various dielectric models employed to predict the effective relative permittivity of the glass nanocomposite, the one obtained using the Maxwell's model was in good agreement with the experimentally observed value. Impedance analysis was employed to rationalize the electrical behavior of the glasses and glass nanocomposites. The pyroelectric response of the glasses and glass nanocomposites was monitored as a function of temperature and the pyroelectric coefficient for glass and glass nanocomposite (x = 20) at 300 K were 27 muC m(-2) K-1 and 53 muC m(-2) K-1, respectively. The ferroelectric behavior of these glass nanocomposites was established by P vs. E hysteresis loop studies. The remnant polarization (P-r) of the glass nanocomposite increases with increase in SBT content. The coercive field (E-c) and P-r for the glass nanocomposite (x = 20) were 727 V cm(-1) and 0.527 muC cm(-2), respectively. The optical transmission properties of these glass nanocomposites were found to be composition dependent. The refractive index (n = 1.722), optical polarizability (am = 1.266 6 10 23 cm 3) and third-order nonlinear optical susceptibility (x(3) = 3.046 6 10(-21) cm(3)) of the glass nanocomposite (x = 15) were larger than those of the as-quenched glass. Second harmonic generation (SHG) was observed in transparent glass nanocomposites and the d(eff) for the glass nanocomposite (x = 20) was found to be 0.373 pm V-1.

Microstructural, dielectric, pyroelectric and ferroelectric studies on partially grain-oriented SrBi2Ta2O9 ceramics

Partially grain-oriented (48%) ceramics of strontium bismuth tantalate (SrBi2Ta2O9) have been fabricated via conventional sintering. The grain-orientation factor of the ceramics was determined, as a function of both the sintering temperature and duration of sintering using X-ray powder diffraction (XRD) techniques. Variations in microstructural features (from acircular to plate like morphology) as a function of sintering temperature of the pellets were monitored by Scanning Electron Microscopy (SEM). The dielectric constant and loss measurements as functions of both frequency and temperature have been carried out along the directions parallel and perpendicular to the pressing axis. The anisotropy (epsilon(rn)/epsilon(rp)) associated was found to be 2.21. The effective dielectric constant of the samples with varying porosity was predicted using different dielectric mixture formulae. The grain boundary and grain interior contributions to the dielectric properties were rationalized using the impedance spectroscopy. The pyroelectric coefficient for strontium bismuth tantalate ceramic was determined along the parallel and perpendicular directions to the pressing axis and found to be -23 muC/m(2)K and -71 muC/m(2)K, respectively at 300 K. The ferroelectric properties of these partially grain-oriented ceramics are superior in the direction perpendicular to the pressing axis to that in the parallel direction.

Non-Fermi-liquid theory for disordered metals near two dimensions

We consider the Finkelstein action describing a system of spin-polarized or spinless electrons in 2+2epsilon dimensions, in the presence of disorder as well as the Coulomb interactions. We extend the renormalization-group analysis of our previous work and evaluate the metal-insulator transition of the electron gas to second order in an epsilon expansion. We obtain the complete scaling behavior of physical observables like the conductivity and the specific heat with varying frequency, temperature, and/or electron density. We extend the results for the interacting electron gas in 2+2epsilon dimensions to include the quantum critical behavior of the plateau transitions in the quantum Hall regime. Although these transitions have a very different microscopic origin and are controlled by a topological term in the action (theta term), the quantum critical behavior is in many ways the same in both cases. We show that the two independent critical exponents of the quantum Hall plateau transitions, previously denoted as nu and p, control not only the scaling behavior of the conductances sigma(xx) and sigma(xy) at finite temperatures T, but also the non-Fermi-liquid behavior of the specific heat (c(v)proportional toT(p)). To extract the numerical values of nu and p it is necessary to extend the experiments on transport to include the specific heat of the electron gas.

Pressure-induced phase transitions in alpha-ZrMo2O8

We report high-pressure Raman, infrared (IR), and optical-absorption spectra of alpha-ZrMo2O8 (trigonal) up to 38 GPa at room temperature. The spectroscopic studies are consistent with diffraction results that show that alpha-ZrMo2O8 transforms into delta-ZrMo2O8 (monoclinic) at about 1 GPa and the delta phase converts to the epsilon phase (trielinic) at about 2.0 GPa. Optical-absorption measurements give an estimate of the band gap of about 0.6 eV at the lowest pressure. Band-gap changes with pressure are confirmed with visual observations. ZrMo2O8 changes from transparent at 5 GPa to yellow at 10 GPa, red at 18 GPa, and at about 30 GPa it becomes opaque.

Pyroelectric, ferroelectric and optical properties of glass nanocomposite: Lithium borate-bismuth tungstate

Glass nanocomposites in the system (1-x)Li2B4O7-xBi(2)WO(6) (0 less than or equal to x less than or equal to 0.35, in molar ratio) were fabricated by splat quenching technique. The as-quenched samples were X-ray amorphous. Differential Thermal Analyses (DTA) confirmed their glassy nature. The composites on heat-treatment at 720 K yielded monophasic crystalline bismuth tungstate in lithium borate glass matrix. The average size and the spherical nature of the dispersed crystallites were assessed via High Resolution Transmission Electron Microscopy (HRTEM). The dielectric constants (epsilon(r)) of both the as-quenched and post heat-treated composites were found to increase with increase in x (bismuth tungstate content) at all the frequencies (100 Hz-40 MHz) in the temperature range 300 K-870 K. While the dielectric loss (D) decreased with increasing x. The pyroelectric coefficients of the as-quenched (consisting 20 nm sized crystallites) and 720 K heat-treated sample (x = 0.3) were determined as a function of temperature (300 K-873 K) and the values obtained at room temperature were 20 and 60 muC/m(2) K respectively. The as-quenched and heat-treated (720 K) glass nanocomposites exhibited ferroelectric (P Vs E) hysteresis loops. The remnant polarization and coercive field of the heat-treated glass nanocomposite at 300 K were respectively 2.597 muC/cm(2) and 543 V/cm. These glass nanocomposites were birefringent in the 300-873 K temperature range.

Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity

We examine the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two-dimensional (2-D) systems under a plane-strain condition with the principal misfit strain components epsilon(xx)*. and epsilon(yy)*. For systems with cubic elastic moduli, we first show all the shape transitions associated with different values of t = epsilon(yy)*/epsilon(xx)*. We also characterize each of these transitions, by studying its dependence on elastic anisotropy and inhomogeneity. For systems with dilatational misfit (t = 1) and those with pure shear misfit (t = -1), the transition is from an equiaxed shape to an elongated shape, resulting in a break in rotational symmetry. For systems with nondilatational misfit (-1 < t < 1; t not equal 0), the transition involves a break in mirror symmetries normal to the x- and y-axes. The transition is continuous in all cases, except when 0 < t < 1. For systems which allow an invariant line (-1 less than or equal to t < 0), the critical size increases with an increase in the particle stiffness. However, for systems which do not allow an invariant line (0 < t less than or equal to 1), the critical size first decreases, reaches a minimum, and then starts increasing with increasing particle stiffness; moreover, the transition is also forbidden when the particle stiffness is greater than a critical value.

Turbulent near-wake studies behind an infinitely swept wing

The three-dimensional asymmetric turbulent near-Rake behind an infinitely swept wing with GAW(2) airfoil has been investigated at low speeds. The near-wake in the present study is asymmetric because the boundary layers on the top and bottom surfaces of the model develop under different streamwise pressure gradients. Distributions of mean velocity, three turbulent normal stresses, and two important Reynolds shear stresses have been measured using hot-wire anemometry. The profiles of mean velocity and Reynolds shear stress exhibit asymmetry near the trailing edge and seem to have become symmetric within a short distance of 6 trailing edge momentum thicknesses. Results of computation using K-epsilon turbulence model with a simple scheme to predict the near-wake behind the swept wing have also been presented and compared with the experimental data. The agreement of the predicted mean How development with the experiment is fair considering the simplicity of the scheme.

Dielectric anomaly in strontium borate-bismuth vanadate glass nanocomposite

Transparent glass nanocomposites in the pseudo binary system (100 - x) SrB4O7 (SBO)-x Bi2VO5.5 (BiV) (0 less than or equal to n less than or equal to 70) were prepared by the splat quenching technique. The nano-crystallization of bismuth vanadate (BiV) in 50 SBO-50 BiV (in mol%) glass composite has been demonstrated. These were characterized for their structural, thermal and dielectric properties. As-quenched composites under study have been confirmed to be amorphous by X-ray powder diffraction (XRD) studies. The glass transition temperature (T-g) and crystallization temperatures (T-er) were determined using differential thermal analyses (DTA), High resolution transmission electron microscopic (HRTEM) studies carried out on heat-treated samples reveal the presence of spherical nanosize crystallites of Bi2VO5.5 (BiV) dispersed in the glassy matrix of SrB4O7 (SSO). The dielectric constant (epsilon (r)) and the dielectric loss (D) measurements were carried out on the as-quenched and heat-treated glass nanocomposite samples in the frequency range 100 Hz-10 MHz. The as-quenched and the heat-treated at two different temperatures (720 and 820 K) samples exhibited broad dielectric anomalies in the vicinity of the ferroelectric-to-paraelectric transition temperature of the parent BiV ceramics. The Curie-Weiss law was found to be valid at a temperature above the transition temperature, establishing the diffused nature of the transition. (C) 2001 Elsevier Science Ltd. All rights reserved.

A lower bound for the hitting set size for combinatorial rectangles and an application

We prove a lower bound of Omega(1/epsilon (m + log(d - a)) where a = [log(m) (1/4epsilon)] for the hitting set size for combinatorial rectangles of volume at least epsilon in [m](d) space, for epsilon is an element of [m(-(d-2)), 2/9] and d > 2. (C) 2002 Elsevier Science B.V. All rights reserved.

Almost quarter-pinched Kähler metrics and Chern numbers

Given n is an element of Z(+) and epsilon > 0, we prove that there exists delta = delta(epsilon, n) > 0 such that the following holds: If (M(n),g) is a compact Kahler n-manifold whose sectional curvatures K satisfy -1 -delta <= K <= -1/4 and c(I)(M), c(J)(M) are any two Chern numbers of M, then |c(I)(M)/c(J)(M) - c(I)(0)/c(J)(0)| < epsilon, where c(I)(0), c(J)(0) are the corresponding characteristic numbers of a complex hyperbolic space form. It follows that the Mostow-Siu surfaces and the threefolds of Deraux do not admit Kahler metrics with pinching close to 1/4.

Critical properties of the double-exchange ferromagnet Nd(0.6)Pb(0.4)MnO(3)

Results of a study of dc magnetization M(T,H), performed on a Nd(0.6)Pb(0.4)MnO(3) single crystal in the temperature range around T(C) (Curie temperature) which embraces the supposed critical region \epsilon\=\T-T(C)\/T(C)less than or equal to0.05 are reported. The magnetic data analyzed in the critical region using the Kouvel-Fisher method give the values for the T(C)=156.47+/-0.06 K and the critical exponents beta=0.374+/-0.006 (from the temperature dependence of magnetization) and gamma=1.329+/-0.003 (from the temperature dependence of initial susceptibility). The critical isotherm M(T(C),H) gives delta=4.54+/-0.10. Thus the scaling law gamma+beta=deltabeta is fulfilled. The critical exponents obey the single scaling equation of state M(H,epsilon)=epsilon(beta)f(+/-)(H/epsilon(beta+gamma)), where f(+) for T>T(C) and f(-) for T

Modeling of nonreacting and reacting turbulent spray jets using a fully stochastic separated flow approach

Numerical modeling of several turbulent nonreacting and reacting spray jets is carried out using a fully stochastic separated flow (FSSF) approach. As is widely used, the carrier-phase is considered in an Eulerian framework, while the dispersed phase is tracked in a Lagrangian framework following the stochastic separated flow (SSF) model. Various interactions between the two phases are taken into account by means of two-way coupling. Spray evaporation is described using a thermal model with an infinite conductivity in the liquid phase. The gas-phase turbulence terms are closed using the k-epsilon model. A novel mixture fraction based approach is used to stochastically model the fluctuating temperature and composition in the gas phase and these are then used to refine the estimates of the heat and mass transfer rates between the droplets and the surrounding gas-phase. In classical SSF (CSSF) methods, stochastic fluctuations of only the gas-phase velocity are modeled. Successful implementation of the FSSF approach to turbulent nonreacting and reacting spray jets is demonstrated. Results are compared against experimental measurements as well as with predictions using the CSSF approach for both nonreacting and reacting spray jets. The FSSF approach shows little difference from the CSSF predictions for nonreacting spray jets but differences are significant for reacting spray jets. In general, the FSSF approach gives good predictions of the flame length and structure but further improvements in modeling may be needed to improve the accuracy of some details of the Predictions. (C) 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Generalized asymptotic expansions for the wavenumbers in infinite flexible in vacuo orthotropic cylindrical shells

Analytical expressions are found for the wavenumbers and resonance frequencies in flexible, orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders n. The Donnell-Mushtari shell theory is used to model the dynamics of the cylindrical shell. Initially, an in vacuo cylindrical isotropic shell is considered and expressions for all the wavenumbers (bending, near-field bending, longitudinal and torsional) are found. Subsequently, defining a suitable orthotropy parameter epsilon, the problem of wave propagation in an orthotropic shell is posed as a perturbation on the corresponding problem for an isotropic shell. Asymptotic expressions for the wavenumbers in the in vacuo orthotropic shell are then obtained by treating epsilon as an expansion parameter. In both cases (isotropy and orthotropy), a frequency-scaling parameter (eta) and Poisson's ratio (nu) are used to find elegant expansions in the different frequency regimes. The asymptotic expansions are compared with numerical solutions in each of the cases and the match is found to be good. The main contribution of this work lies in the extension of the existing literature by developing closed-form expressions for wavenumbers with arbitrary circumferential orders n in the case of both, isotropic and orthotropic shells. Finally, we present natural frequency expressions in finite shells (isotropic and orthotropic) for the axisymmetric mode and compare them with numerical and ANSYS results. Here also, the comparison is found to be good. (C) 2011 Elsevier Ltd. All rights reserved.