Undamped Oscillations of Collisionless Stellar Systems: Spheres,Spheroids and Discs.

The collisionless Boltzmann equation governing self-gravitating systems such as galaxies has recently been shown to admit exact oscillating solutions with planar and spherical symmetry. The relation of the spherically symmetric solutions to the Virial theorem, as well as generalizations to non-uniform spheres, uniform spheroids and discs form the subject of this paper. These models generalize known families of static solutions. The case of the spheroid is worked out in some detail. Quasiperiodic as well as chaotic time variation of the two axes is demonstrated by studying the surface of section for the associated Hamiltonian system with two degrees of freedom. The relation to earlier work and possible implications for the general problem of collisionless relaxation in self gravitating systems are also discussed.

Comparative study on damage identification from lso-Eigen-Value-Change contours and smeared damage model

The paper proposes two methodologies for damage identification from measured natural frequencies of a contiguously damaged reinforced concrete beam, idealised with distributed damage model. The first method identifies damage from Iso-Eigen-Value-Change contours, plotted between pairs of different frequencies. The performance of the method is checked for a wide variation of damage positions and extents. The method is also extended to a discrete structure in the form of a five-storied shear building and the simplicity of the method is demonstrated. The second method is through smeared damage model, where the damage is assumed constant for different segments of the beam and the lengths and centres of these segments are the known inputs. First-order perturbation method is used to derive the relevant expressions. Both these methods are based on distributed damage models and have been checked with experimental program on simply supported reinforced concrete beams, subjected to different stages of symmetric and un-symmetric damages. The results of the experiments are encouraging and show that both the methods can be adopted together in a damage identification scenario.

On the unreasonable effectiveness of Gutzmer's formula

In this article we plan to demonstrate the usefulness of `Gutzmer's formula' in the study of various problems related to the Segal-Bargmann transform. Gutzmer's formula is known in several contexts: compact Lie groups, symmetric spaces of compact and noncompact type, Heisenberg groups and Hermite expansions. We apply Gutzmer's formula to study holomorphic Sobolev spaces, local Peter-Weyl theorems, Paley-Wiener theorems and Poisson semigroups.

Effects of electron correlations in conjugated organic molecules and solids

The discrepancies between the non-interacting models and experimental results for conjugated systems is highlighted in this brief review. The interacting model hamiltonians correctly give the forbidden singlet state below the optical gap in polyenes and also explain both the nonvanishing optical gap in polyacetylenes and the vanishing optical gap in symmetric cyanine dyes. The negative spin densities in polyene radicals is also understood in terms of a correlated picture. The role of electron-electron interactions in other strongly correlated systems, such as polydiacetylene and mixed and segregated stack charge transfer solids, are also briefly discussed.

Solvation of an ion and of a dipole in a dipolar liquid: How different are the dynamics

Theoretical expressions for the time-dependent solvation energy of an ion and of a dipole in a dense dipolar liquid are derived from microscopic considerations. We show that in contradiction to the prediction of the continuum models, the dynamics of these two species are significantly different from each other. Especially, the zero wavevector contribution, which is significant for ions, is totally absent for dipoles. Dipolar solvation may be profoundly influenced by the translational modes of the host solvent.

Effect of Li substitution on dielectric and ferroelectric properties of ZnO thin films grown by pulsed-laser ablation

Li-doped ZnO thin films (Zn1-xLixO, x=0.05-0.15) were grown by pulsed-laser ablation technique. Highly c-axis-oriented films were obtained at a growth temperature of 500 degrees C. Ferroelectricity in Zn1-xLixO was found from the temperature-dependent dielectric constant and from the polarization hysteresis loop. The transition temperature (T-c) varied from 290 to 330 K as the Li concentration increased from 0.05 to 0.15. It was found that the maximum value of the dielectric constant at T-c is a function of Li concentration. A symmetric increase in memory window with the applied gate voltage is observed for the ferroelectric thin films on a p-type Si substrate. A ferroelectric P-E hysteresis loop was observed for all the compositions. The spontaneous polarization (P-s) and coercive field (E-c) of 0.6 mu C/cm(2) and 45 kV/cm were obtained for Zn0.85Li0.15O thin films. These observations reveal that partial replacement of host Zn by Li ions induces a ferroelectric phase in the wurtzite-ZnO semiconductor. The dc transport studies revealed an Ohmic behavior in the lower-voltage region and space-charge-limited conduction prevailed at higher voltages. The optical constants were evaluated from the transmission spectrum and it was found that Li substitution in ZnO enhances the dielectric constant.

Computing a matrix symmetrizer exactly using modified multiple modulus residue arithmetic

A symmetric solution X satisfying the matrix equation XA = AtX is called a symmetrizer of the matrix A. A general algorithm to compute a matrix symmetrizer is obtained. A new multiple-modulus residue arithmetic called floating-point modular arithmetic is described and implemented on the algorithm to compute an error-free matrix symmetrizer.

Influence of crossed electric and quantizing magnetic fields on the Einstein relation in nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestion for experimental determination

An attempt is made to study the Einstein relation for the diffusivity-to-mobility ratio (DMR) under crossed fields' configuration in nonlinear optical materials on the basis of a newly formulated electron dispersion law by incorporating the crystal field in the Hamiltonian and including the anisotropies of the effective electron mass and the spin-orbit splitting constants within the framework of kp formalisms. The corresponding results for III-V, ternary and quaternary compounds form a special case of our generalized analysis. The DMR has also been investigated for II-VI and stressed materials on the basis of various appropriate dispersion relations. We have considered n-CdGeAs2, n-Hg1-xCdxTe, n-In1-xGaxAsyP1-y lattice matched to InP, p-CdS and stressed n-InSb materials as examples. The DMR also increases with increasing electric field and the natures of oscillations are totally band structure dependent with different numerical values. It has been observed that the DMR exhibits oscillatory dependences with inverse quantizing magnetic field and carrier degeneracy due to the Subhnikov-de Haas effect. An experimental method of determining the DMR for degenerate materials in the present case has been suggested. (C) 2010 Elsevier B.V. All rights reserved.

Interaction of metal ions with 6-oxopurine nucleotides. Part 2. X-Ray structures of ternary nickel(II) complexes with 2'-deoxyguanosine 5'-monophosphate or guanosine 5'-monophosphate

The ternary metal nucleotide complexes [Ni(en)1.3(H2O)1.4(H2O)2][Ni(5?-dGMP)2(en)0.7-(H2O)0.6(H2O)2]·7H2O (1) and [Ni(en)2(H2O)2][Ni(5?-GMP)2(H2O)4]·6H2O (2)(en = ethylenediamine, 5?-dGMP = 2?-deoxyguanosine 5?-monophosphate, 5?-GMP = guanosine 5?-monophosphate) have been prepared and their structures analyzed by X-ray diffraction methods. Both compounds crystallise in the space group C2221 with a= 8.810(1), b= 25.090(4), c= 21.084(1)Å, and Z= 4 for (1) and a= 8.730(1), b= 25.691(4), c= 21.313(5)Å, and Z= 4 for (2). The structures were deduced from the analogous CoIII complexes and refined by full-matrix least-squares methods to final R values of 0.087 and 0.131 for 1 211 and 954 reflections for (1) and (2) respectively. An interesting feature of the deoxyribonucleotide complex (1) is that en is not totally labilized from the metal centre on nucleotide co-ordination, as observed in corresponding ribonucleotide complexes. Apart from extensive intra- and inter-molecular hydrogen bonding, the structures are stabilized by significant intracomplex base�base and base�sugar interactions. The nucleotides in both complexes have an anti base, C(2?)-endo sugar pucker, and gauche�gauche conformation about the C(4?)�C(5?) bond.

Outward spherical solidification of a superheated melt with time dependent boundary flux

Short-time analytical solutions of solid and liquid temperatures and freezing front have been obtained for the outward radially symmetric spherical solidification of a superheated melt. Although results are presented here only for time dependent boundary flux, the method of solution can be used for other kinds of boundary conditions also. Later, the analytical solution has been compared with the numerical solution obtained with the help of a finite difference numerical scheme in which the grid points change with the freezing front position. An efficient method of execution of the numerical scheme has been discussed in details. Graphs have been drawn for the total solidification times and temperature distributions in the solid.

On Finding the Natural Number of Topics with Latent Dirichlet Allocation: Some Observations

It is important to identify the ``correct'' number of topics in mechanisms like Latent Dirichlet Allocation(LDA) as they determine the quality of features that are presented as features for classifiers like SVM. In this work we propose a measure to identify the correct number of topics and offer empirical evidence in its favor in terms of classification accuracy and the number of topics that are naturally present in the corpus. We show the merit of the measure by applying it on real-world as well as synthetic data sets(both text and images). In proposing this measure, we view LDA as a matrix factorization mechanism, wherein a given corpus C is split into two matrix factors M-1 and M-2 as given by C-d*w = M1(d*t) x Q(t*w).Where d is the number of documents present in the corpus anti w is the size of the vocabulary. The quality of the split depends on ``t'', the right number of topics chosen. The measure is computed in terms of symmetric KL-Divergence of salient distributions that are derived from these matrix factors. We observe that the divergence values are higher for non-optimal number of topics - this is shown by a `dip' at the right value for `t'.

Approximate multipole coefficients of RF ion traps as functions of aperture size

In this study we present approximate analytical expressions for estimating the variation in multipole expansion coefficients as a function of the size of the apertures in the electrodes in axially symmetric (3D) and two-dimensional (2D) ion trap ion traps. Following the approach adopted in our earlier studies which focused on the role of apertures to fields within the traps, here too, the analytical expression we develop is a sum of two terms, A(n,noAperiure), the multipole expansion coefficient for a trap with no apertures and A(n,dueToAperture), the multipole expansion coefficient contributed by the aperture. A(n,noAperture) has been obtained numerically and A(n,dueToAperture) is obtained from the n th derivative of the potential within the trap. The expressions derived have been tested on two 3D geometries and two 2D geometries. These include the quadrupole ion trap (QIT) and the cylindrical ion trap (CIT) for 3D geometries and the linear ion trap (LIT) and the rectilinear ion trap (RIT) for the 2D geometries. Multipole expansion coefficients A(2) to A(12), estimated by our analytical expressions, were compared with the values obtained numerically (using the boundary element method) for aperture sizes varying up to 50% of the trap dimension. In all the plots presented, it is observed that our analytical expression for the variation of multipole expansion coefficients versus aperture size closely follows the trend of the numerical evaluations for the range of aperture sizes considered. The maximum relative percentage errors, which provide an estimate of the deviation of our values from those obtained numerically for each multipole expansion coefficient, are seen to be largely in the range of 10-15%. The leading multipole expansion coefficient, A(2), however, is seen to be estimated very well by our expressions, with most values being within 1% of the numerically determined values, with larger deviations seen for the QIT and the LIT for large aperture sizes. (C) 2010 Elsevier B.V. All rights reserved.

The structure of ammonium oxalohydroxamate - a monopropellant

Abstract. NHn+.C2H3NzO4, Mr= 137.1, triclinic, Pi, a=3-952(1), b=6.772(1), c=9.993(1)A, a= 98.06 (1), fl= 89.96 (1), ~= 106.96 (1) °. V=253.06 A 3, z = 2, 2(Cu Ka) = 1.5418 A, g =15.29 cm -~, D m = 1.805, D x = 1.798 g cm -3, F(000)= 144, T= 293 K, R = 0.048 for 795 observed reflections. The unit cell contains two independent centrosymmetric molecules, one centred at (0,0,0) and the other at (0.5, 0.0, 0.5). The presence of experimentally determined~N-H groups and the -C=O bond lengths of 1.248 (4) and 1.247 (4)A indicate that the compound exists in the oxamic rather than the oximic form. Only one hydroxyl hydrogen is associated with each molecule. They are located at centres of inversion (0,0.5,0 and 0,0.5,0.5) and are shared between symmetry-related molecules via short symmetric H bonds with O...O=2.454(4), 2.457(4) and all O-H = 1.23 A

Mechanism of interaction of the antileukemic drug cytosine arabinoside with aromatic peptides : role of sugar conformation and peptide backbone

Interaction of the antileukemic drugs, cytosine-arabinoside (Ara-C) and adenosine-arabinoside (Ara-A) and a structural analogue, cytidine, with aromatic dipeptides has been studied by fluorescence and NMR spectroscopy. Ara-C and cytidine bind tryptophanyl and histidyl dipeptides but not tyrosyl dipeptides, while Ara-A does not bind to any of them. Both studies indicate association involving stacking of aromatic moieties. NMR spectra also indicate a protonation of the histidine moiety by Ara-C. In case of cytidine, the chemical shifts observed on binding to His-Phe imply that the backbone protons of the dipeptide participate in the binding. The conformation of the sugar and the base seem to play a very important role in the binding phenomenon as three similar molecules, Ara-C, Ara-A and cytidine bind in totally different ways.

Origin of the plateau in the low-temperature thermal conductivity of silica

Thermal conductivities of glasses at low temperatures show strikingly similar behavior irrespective of their chemical composition. While for T<1 K the thermal conductivity can be understood in the phenomenological tunneling model; the ‘‘universal plateau’’ in the temperature interval 15>T>2 K is totally unexplained. While Rayleigh scattering of phonons by structural disorder should be the natural cause for limiting the mean free path of phonons in this temperature range, it has been concluded before that in glasses a strong enough source of such scattering does not exist. In this study we show by a proper structural analysis in at least one material (namely, silica) that a strong enough source of Rayleigh scattering of phonons in glasses does exist so that the ‘‘universal plateau’’ can be explained without invoking any new mechanism. This may be for the first time that the low-temperature property of a structural glass has been correlated to its structure.