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.

Abstract Characteristic Function

The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel k(S)(z, w) = ( 1 - z(w)over bar)- 1 for |z|, |w| < 1, by means of (1/k(S))( T, T *) = 0, we consider an arbitrary open connected domain Omega in C(n), a kernel k on Omega so that 1/k is a polynomial and a tuple T = (T(1), T(2), ... , T(n)) of commuting bounded operators on a complex separable Hilbert spaceHsuch that (1/k)( T, T *) >= 0. Under some standard assumptions on k, it turns out that whether a characteristic function can be associated with T or not depends not only on T, but also on the kernel k. We give a necessary and sufficient condition. When this condition is satisfied, a functional model can be constructed. Moreover, the characteristic function then is a complete unitary invariant for a suitable class of tuples T.

Cl-35 NQR frequency and spin lattice relaxation time in 3,4-dichlorophenol as a function of pressure and temperature

The pressure dependences of Cl-35 nuclear quadrupole resonance (NQR) frequency, temperature and pressure variation of spin lattice relaxation time (T-1) were investigated in 3,4-dichlorophenol. T-1 was measured in the temperature range 77-300 K. Furthermore, the NQR frequency and T-1 for these compounds were measured as a function of pressure up to 5 kbar at 300 K. The temperature dependence of the average torsional lifetimes of the molecules and the transition probabilities W-1 and W-2 for the Delta m = +/- 1 and Delta m = +/- 2 transitions were also obtained. A nonlinear variation of NQR frequency with pressure has been observed and the pressure coefficients were observed to be positive. A thermodynamic analysis of the data was carried out to determine the constant volume temperature coefficients of the NQR frequency. An attempt is made to compare the torsional frequencies evaluated from NQR data with those obtained by IR spectra. On selecting the appropriate mode from IR spectra, a good agreement with torsional frequency obtained from NQR data is observed. The previously mentioned approach is a good illustration of the supplementary nature of the data from IR studies, in relation to NQR studies of compounds in solid state.

Performance study of high operating temperature HgCdTe mid wave infrared detector through numerical modeling

The design of present generation uncooled Hg1-xCdxTe infrared photon detectors relies on complex heterostructures with a basic unit cell of type (n) under bar (+)/pi/(p) under bar (+). We present an analysis of double barrier (n) under bar (+)/pi/(p) under bar (+) mid wave infrared (x = 0.3) HgCdTe detector for near room temperature operation using numerical computations. The present work proposes an accurate and generalized methodology in terms of the device design, material properties, and operation temperature to study the effects of position dependence of carrier concentration, electrostatic potential, and generation-recombination (g-r) rates on detector performance. Position dependent profiles of electrostatic potential, carrier concentration, and g-r rates were simulated numerically. Performance of detector was studied as function of doping concentration of absorber and contact layers, width of both layers and minority carrier lifetime. Responsivity similar to 0.38 A W-1, noise current similar to 6 x 10(-14) A/Hz(1/2) and D* similar to 3.1 x 10(10)cm Hz(1/2) W-1 at 0.1 V reverse bias have been calculated using optimized values of doping concentration, absorber width and carrier lifetime. The suitability of the method has been illustrated by demonstrating the feasibility of achieving the optimum device performance by carefully selecting the device design and other parameters. (C) 2010 American Institute of Physics. doi:10.1063/1.3463379]

Complete Pick positivity and unitary invariance

The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel k(S) (z, w) = (1 - z (w) over tilde)(-1) for |z|, |w| < 1, by means of (1/k(S))(T,T*) >= 0, we consider an arbitrary open connected domain Omega in C-n, a complete Pick kernel k on Omega and a tuple T = (T-1, ..., T-n) of commuting bounded operators on a complex separable Hilbert space H such that (1/k)(T,T*) >= 0. For a complete Pick kernel the 1/k functional calculus makes sense in a beautiful way. It turns out that the model theory works very well and a characteristic function can be associated with T. Moreover, the characteristic function is then a complete unitary invariant for a suitable class of tuples T.

Expanding universe: thermodynamical aspects from different models

The pivotal point of the paper is to discuss the behavior of temperature, pressure, energy density as a function of volume along with determination of caloric EoS from following two model: w(z)=w (0)+w (1)ln(1+z) & . The time scale of instability for this two models is discussed. In the paper we then generalize our result and arrive at general expression for energy density irrespective of the model. The thermodynamical stability for both of the model and the general case is discussed from this viewpoint. We also arrive at a condition on the limiting behavior of thermodynamic parameter to validate the third law of thermodynamics and interpret the general mathematical expression of integration constant U (0) (what we get while integrating energy conservation equation) physically relating it to number of micro states. The constraint on the allowed values of the parameters of the models is discussed which ascertains stability of universe. The validity of thermodynamical laws within apparent and event horizon is discussed.

Graphene-MoS2 hybrid structures for multifunctional photoresponsive memory devices

Combining the electronic properties of graphene(1,2) and molybdenum disulphide (MoS2)(3-6) in hybrid heterostructures offers the possibility to create devices with various functionalities. Electronic logic and memory devices have already been constructed from graphene-MoS2 hybrids(7,8), but they do not make use of the photosensitivity of MoS2, which arises from its optical-range bandgap(9). Here, we demonstrate that graphene-on-MoS2 binary heterostructures display remarkable dual optoelectronic functionality, including highly sensitive photodetection and gate-tunable persistent photoconductivity. The responsivity of the hybrids was found to be nearly 1 x 10(10) A W-1 at 130 K and 5 x 10(8) A W-1 at room temperature, making them the most sensitive graphene-based photodetectors. When subjected to time-dependent photoillumination, the hybrids could also function as a rewritable optoelectronic switch or memory, where the persistent state shows almost no relaxation or decay within experimental timescales, indicating near-perfect charge retention. These effects can be quantitatively explained by gate-tunable charge exchange between the graphene and MoS2 layers, and may lead to new graphene-based optoelectronic devices that are naturally scalable for large-area applications at room temperature.

Tungsten(0)-carbonyl complexes of naphthylazoimidazoles

The reaction of W(CO)(6) with 1-alkyl-2-(naphthyl-alpha-azo)imidazole (alpha-NaiR) has synthesized [W(CO)(5)(alpha-NaiR-N)] (alpha-NaiR-N refers to the monodentate imidazole-N donor ligand) at room temperature. The structure of[W(CO)(5)(alpha-NaiMe-N)] shows a monodentate imidazole-N coordination of 1-methyl-2-(naphthyl-alpha-azo)imidazole (alpha-NaiMe). The complexes are characterized by elemental, mass and other spectroscopic data (IR, UV-Vis, NMR). On refluxing in THF at 323 K, [W(CO)(5)(alpha-NaiR-N)] undergoes decarbonylation to give [W(CO)(4)(alpha-NaiR-N,N')] (alpha-NaiR-N,N' refers to the imidazole-N(N), azo-N(N') bidentate chelator). Cyclic voltammetry shows metal oxidation (W-0/W-1) and ligand reductions (azo/azo(-), azo(-)/azo(=)). The redox and electronic properties are explained by theoretical calculations using an optimized geometry. DFT computation of [W(CO)(5)(alpha-NaiMe-N)] suggests that the major contribution to the HOMO/HOMO - 1 come from W cl-orbitals and the orbitals of CO. The LUMOs are occupied by alpha-NaiMe functions. The back bonding interaction thus originates from the W(CO)(n) moiety to the LUMO of alpha-NaiR. A TD-DFT calculation has ascribed that HOMO/HOMO - 1 -> LUMO is a mixture of metal-to-ligand and ligand-to-ligand charge transfer underlying the CO -> azoimine contribution. The complexes show emission spectra at room temperature. [W(CO)(4)(alpha-NaiR-N,N')] shows a higher fluorescence quantum yield (phi = 0.05-0.07) than [W(CO)(5)(alpha-NaiR-N)] (phi = 0.01-0.02). (C) 2008 Elsevier Ltd. All rights reserved.

A global convergence criterion for discrete-time multivariable adaptive systems

The paper deals with the basic problem of adjusting a matrix gain in a discrete-time linear multivariable system. The object is to obtain a global convergence criterion, i.e. conditions under which a specified error signal asymptotically approaches zero and other signals in the system remain bounded for arbitrary initial conditions and for any bounded input to the system. It is shown that for a class of up-dating algorithms for the adjustable gain matrix, global convergence is crucially dependent on a transfer matrix G(z) which has a simple block diagram interpretation. When w(z)G(z) is strictly discrete positive real for a scalar w(z) such that w-1(z) is strictly proper with poles and zeros within the unit circle, an augmented error scheme is suggested and is proved to result in global convergence. The solution avoids feeding back a quadratic term as recommended in other schemes for single-input single-output systems.

An avidin-biotin microELISA for rapid measurement of total and allergen-specific human IgE

his paper describes an improved microtiter solid-phase enzyme immunoassay for the determination of total and allergen-specific human IgE. This assay technique is unique in its use of the avidin-biotin interaction to increase sensitivity. The avidin-biotin microtiter enzyme-linked immunosorbant assay (AB-microELISA) was performed in polyvinyl chloride microtiter plates using biotinylated anti-IgE and horseradish peroxidase (HRP)-avidin conjugate. This AB-microELISA technique enabled the quantitation of human serum IgE in the range of 0.1–5 ng/ml (10–500 pg/test) in less than 3 h. Total serum IgE, whether measured by the AB-microELISA or the paper radioimmunosorbant test (PRIST) was similar (correlation coefficient, r = 0.92). Further, the presence or absence of positive skin tests to 7 specific allergens determined in serum donors generally agreed with the presence or absence of allergen-specific IgE in their sera as measured by the AB-microELISA. The quantity of short ragweed allergen-specific IgE as determined by the AB-microELISA agreed with values obtained by the radioimmunosorbant test (RAST) (correlation coefficient, r = 0.89). No significant interference by ragweed-specific IgG (blocking antibody) was observed in the quantitation of allergen-specific IgE. The AB-microELISA is not only rapid and inexpensive, but also more sensitive than other published ELISA procedures and comparable to solid-phase radioimmunoassays in the quantitation of total and allergen-specific IgE.

Optical nonlinearity in lead sulfide microtowers

Lead sulfide (PbS) microtowers on silicon substrates, having the physical properties of bulk PbS, have been synthesized. Optical nonlinearity studies using the open aperture z-scan technique employing 5 ns and 100 fs laser pulses reveal effective two-photon type absorption. For nanosecond excitation the nonlinear absorption coefficients (beta(eff)) are in the order of 10(-11) m W-1, two orders of magnitude less than the values reported for quantum confined PbS nanocrystals. For femtosecond excitation beta(eff) is of the order of 10(-14) m W-1. These results obtained in bulk PbS experimentally confirm the importance of quantum confinement in the enhancement of optical nonlinearities in semiconductor materials.

Aqueous channels within apolar peptide aggregates. Solvated helix of Boc-Aib-Ala-Leu-Aib-Ala-Leu-Aib- -Ala-Leu-Aib-OMe. H2O.CH3OH

Although the peptide Boc-Aibl-Ala2-Leu3- Aib4-Alas Leu'-Aib7-Ala8-Leu9-Aib'0-OMe [with a t-butoxycarbonyl(Boc) blocking group at the amino terminus, a methyl ester (OMe) at the carboxyl terminus, and four a-aminoisobutyric (Aib) residues] has a 3-fold repeat of residues, the helix formed by the peptide backbone is irregular. The carboxyl-terminal half assumes an at-helical form with torsion angles ) and r of approximately -60° and -45°, respectively, whereas the amino-terminal half is distorted by an insertion of a water molecule between the amide nitrogen of Ala5 [N(5)] and the carbonyl oxygen of Ala2 [0(2)]. The water molecule W(1) acts as a bridge by forming hydrogen bonds N(5).W(1) (2.93 A) and W(1)---0(2) (2.86 A). The distortion of the helix exposes the carbonyl oxygens of Aib' and Aib4 to the outside environment, with the consequence that the helix assumes an amphiphilic character despite having all apolar residues. Neighboring helices in the crystal run in antiparallel directions. On one side of a helix there are only hydrophobic contacts with efficient interdigitation of leucine side chains with those from the neighboring helix. On the other side of the helix there are hydrogen bonds between protruding carbonyl oxygens and four water molecules that separate two neighboring helices. Along the helix axis the helices bind head-to-tail with a direct hydrogen bond N(2)-0(9) (3.00 A). Crystals grown from methanol/water solution are in space group P2, with a = 15.778 ± 0.004 A, b = 11.228 ± 0.002 A, c = 18.415 ± 0.003 A, = 102.10 ± 0.02ur and two formula units per cell for C49HON1003 2H2OCH3OH. The overall agreement factorR is 7.5% for 3394 reflections observed with intensities >3a(F), and the resolution is 0.90 A.

An (O)over-bar(m(2)n) randomized algorithm to compute a minimum cycle basis of a directed graph

We consider the problem of computing a minimum cycle basis in a directed graph G. The input to this problem is a directed graph whose arcs have positive weights. In this problem a {- 1, 0, 1} incidence vector is associated with each cycle and the vector space over Q generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of weights of the cycles is minimum is called a minimum cycle basis of G. The current fastest algorithm for computing a minimum cycle basis in a directed graph with m arcs and n vertices runs in O(m(w+1)n) time (where w < 2.376 is the exponent of matrix multiplication). If one allows randomization, then an (O) over tilde (m(3)n) algorithm is known for this problem. In this paper we present a simple (O) over tilde (m(2)n) randomized algorithm for this problem. The problem of computing a minimum cycle basis in an undirected graph has been well-studied. In this problem a {0, 1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of the graph. The fastest known algorithm for computing a minimum cycle basis in an undirected graph runs in O(m(2)n + mn(2) logn) time and our randomized algorithm for directed graphs almost matches this running time.

Tailoring the band gap and transport properties of Cu3BiS3 nanopowders for photodetector applications

We report a facile route to synthesize high quality earth abundant absorber Cu3BiS3, tailoring the band gap with the morphology manipulation and thereby analyzed the secondary phases and their role in the transport property. The sample at 48 hours reaction profile showed good semiconducting behavior, whereas other samples showed mostly a metallic behavior. Band gap was varied from 1.86 eV to 1.42 eV upon controling the reaction profile from 8 hours to 48 hours. The activation energy was calculated to be 0.102 eV. The temperature coefficient of resistance (TCR) was found to be 0.03432 K-1 at 185 K. The IR photodectection properties in terms of photoresponse have been demonstrated. The high internal gain (G = 3.7 x 10(4)), responsivity (R = 3.2 x 10(4) A W-1) for 50 mW cm(-2) at 5 V make Cu3BiS3, an alternative potential absorber in meliorating the technological applications as near IR photodetectors.

On k-stellated and k-stacked spheres

We introduce the class Sigma(k)(d) of k-stellated (combinatorial) spheres of dimension d (0 <= k <= d + 1) and compare and contrast it with the class S-k(d) (0 <= k <= d) of k-stacked homology d-spheres. We have E-1(d) = S-1(d), and Sigma(k)(d) subset of S-k(d) ford >= 2k-1. However, for each k >= 2 there are k-stacked spheres which are not k-stellated. For d <= 2k - 2, the existence of k-stellated spheres which are not k-stacked remains an open question. We also consider the class W-k(d) (and K-k(d)) of simplicial complexes all whose vertex-links belong to Sigma(k)(d - 1) (respectively, S-k(d - 1)). Thus, W-k(d) subset of K-k(d) for d >= 2k, while W-1(d) = K-1(d). Let (K) over bar (k)(d) denote the class of d-dimensional complexes all whose vertex-links are k-stacked balls. We show that for d >= 2k + 2, there is a natural bijection M -> (M) over bar from K-k(d) onto (K) over bar (k)(d + 1) which is the inverse to the boundary map partial derivative: (K) over bar (k)(d + 1) -> (K) over bar (k)(d). Finally, we complement the tightness results of our recent paper, Bagchi and Datta (2013) 5], by showing that, for any field F, an F-orientable (k + 1)-neighbourly member of W-k(2k + 1) is F-tight if and only if it is k-stacked.