Anomalous behavior of hydrodynamic modes in the two dimensional shear flow of a granular material

The growth rates of the hydrodynamic modes in the homogeneous sheared state of a granular material are determined by solving the Boltzmann equation. The steady velocity distribution is considered to be the product of the Maxwell Boltzmann distribution and a Hermite polynomial expansion in the velocity components; this form is inserted into them Boltzmann equation and solved to obtain the coeificients of the terms in the expansion. The solution is obtained using an expansion in the parameter epsilon =(1 - e)(1/2), and terms correct to epsilon(4) are retained to obtain an approximate solution; the error due to the neglect of higher terms is estimated at about 5% for e = 0.7. A small perturbation is placed on the distribution function in the form of a Hermite polynomial expansion for the velocity variations and a Fourier expansion in the spatial coordinates: this is inserted into the Boltzmann equation and the growth rate of the Fourier modes is determined. It is found that in the hydrodynamic limit, the growth rates of the hydrodynamic modes in the flow direction have unusual characteristics. The growth rate of the momentum diffusion mode is positive, indicating that density variations are unstable in the limit k--> 0, and the growth rate increases proportional to kslash} k kslash}(2/3) in the limit k --> 0 (in contrast to the k(2) increase in elastic systems), where k is the wave vector in the flow direction. The real and imaginary parts of the growth rate corresponding to the propagating also increase proportional to kslash k kslash(2/3) (in contrast to the k(2) and k increase in elastic systems). The energy mode is damped due to inelastic collisions between particles. The scaling of the growth rates of the hydrodynamic modes with the wave vector I in the gradient direction is similar to that in elastic systems. (C) 2000 Elsevier Science B.V. All rights reserved.

Spinning strings and minimal surfaces in AdS(3) with mixed 3-form fluxes

Motivated by the recent proposal for the S-matrix in AdS(3) x S-3 with mixed three form fluxes, we study classical folded string spinning in AdS(3) with both Ramond and Neveu-Schwarz three form fluxes. We solve the equations of motion of these strings and obtain their dispersion relation to the leading order in the Neveu-Schwarz flux b. We show that dispersion relation for the spinning strings with large spin S acquires a term given by -root lambda/2 pi b(2) log(2) S in addition to the usual root lambda/pi log S term where root lambda is proportional to the square of the radius of AdS(3). Using SO(2, 2) transformations and re-parmetrizations we show that these spinning strings can be related to light like Wilson loops in AdS(3) with Neveu-Schwarz flux b. We observe that the logarithmic divergence in the area of the light like Wilson loop is also deformed by precisely the same coefficient of the b(2) log(2) S term in the dispersion relation of the spinning string. This result indicates that the coefficient of b(2) log(2) S has a property similar to the coefficient of the log S term, known as cusp-anomalous dimension, and can possibly be determined to all orders in the coupling lambda using the recent proposal for the S-matrix.

Supersolid and solitonic phases in the one-dimensional extended Bose-Hubbard model

We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.

Cell-dynamical simulation of magnetic hysteresis in the two-dimensional Ising system

We present results from numerical simulations using a ‘‘cell-dynamical system’’ to obtain solutions to the time-dependent Ginzburg-Landau equation for a scalar, two-dimensional (2D), (Φ2)2 model in the presence of a sinusoidal external magnetic field. Our results confirm a recent scaling law proposed by Rao, Krishnamurthy, and Pandit [Phys. Rev. B 42, 856 (1990)], and are also in excellent agreement with recent Monte Carlo simulations of hysteretic behavior of 2D Ising spins by Lo and Pelcovits [Phys. Rev. A 42, 7471 (1990)].

Double Aromaticity in the 3,5-Dehydrophenyl Cation and in Cyclo[6]carbon

The presence of two (4n+2)-electron conjugated systems in perpendicular planes results in considerable aromatic stabilization. Despite having two fewer hydrogens, the 6 pi e-2 sigma e 3,5-dehydrophenyl cation (C6H3+, 1) is 32.7 (CCSD(T)/6-31G**) and 35.2 kcal/mol (RMP4sdtq/6-3iG*//RMP2(fu)/6-31G*) more stable than the phenyl cation (evaluated by an isodesmic reaction involving benzene and m-dehydrobenzene (4)). Cation 1, the global C6H3+ minimum, is 11.7,24.2, 11.8, and 30.4 kcal/mol lower in energy than the 2,6- (11) and 3,4-dehydrophenyl (12) cations as well as the open-chain isomers 13 and 14 (RMP4sdtq/6-31G*//RMP2(fu)/6-31G* + ZPE(RMP2(fu)/6-31G*)). The stability of 1 is increased hyperconjugatively by 2,4,6-trisilyl substitution. The double aromaticity of 1 is indicated by the computed magnetic susceptibility exaltations (IGLO/II//RMP2(fu)/6-31G*) of -5.2, -6.8, -15, and -23.2 relative to 11, 12, 13, and 14, respectively. Thus, 1 fulfills the geometric, energetic, and magnetic criteria of aromaticity. The double aromaticity of the D-6h cyclo[6]carbon is apparent from the same criteria

Enhanced charge and spin currents in the one-dimensional disordered mesoscopic Hubbard ring

We consider a one-dimensional mesoscopic Hubbard ring with and without disorder and compute charge and spin stiffness as a measure of the permanent currents. For finite disorder we identify critical disorder strength beyond which the charge currents in a system with repulsive interactions are larger than those for a free system. The spin currents in the disordered repulsive Hubbard model are enhanced only for small U, where the magnetic state of the system corresponds to a charge-density wave pinned to the impurities. For large U, the state of the system corresponds to localized isolated spins and the spin currents are found to be suppressed. For the attractive Hubbard model we find that the charge currents are always suppressed compared to the free system at all length scales.

A Change in the 3(10)- to alpha-Helical Transition Point in the Heptapeptides Containing Sulfur and Selenium

Crystal structures of three heptapeptides Boc-Ala-Leu-Aib-XXX-Ala-Leu-Aib-OMe (where XXX = methionine in peptide A, selenomethionine in peptide B, and S-benzyl cysteine in peptide C) reveal mixed 3(10)-/alpha-helical conformations with R factors of 6.94, 5.79, and 5.98, respectively. All the structures were solved in the P2(1)2(1)2(1) space group. 3(10)- to a-helical transitions are observed in all of these peptides. The helices begin as a 3(10)-helical segment at the N-terminus and then transit for peptides A and C at residue Aib(3) carbonyl (O(3)), while for peptide B the transition occurs at residue Leu(2) carbonyl oxygen (O(2)). There are water molecules associated in the crystal of each of these peptides and they form different types of hydrogen bonding patterns in each crystal. The observations suggest that 3(10)- to alpha-helical transition is sequence dependent in these short heptapeptide sequences.

Turbulence in the two-dimensional Fourier-truncated Gross-Pitaevskii equation

We undertake a systematic, direct numerical simulation of the twodimensional, Fourier-truncated, Gross-Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of parameters. We find that the time evolution of this system can be classified into four regimes with qualitatively different statistical properties. Firstly, there are transients that depend on the initial conditions. In the second regime, powerlaw scaling regions, in the energy and the occupation-number spectra, appear and start to develop; the exponents of these power laws and the extents of the scaling regions change with time and depend on the initial condition. In the third regime, the spectra drop rapidly for modes with wave numbers k > kc and partial thermalization takes place for modes with k < kc; the self-truncation wave number kc(t) depends on the initial conditions and it grows either as a power of t or as log t. Finally, in the fourth regime, complete thermalization is achieved and, if we account for finite-size effects carefully, correlation functions and spectra are consistent with their nontrivial Berezinskii-Kosterlitz-Thouless forms. Our work is a natural generalization of recent studies of thermalization in the Euler and other hydrodynamical equations; it combines ideas from fluid dynamics and turbulence, on the one hand, and equilibrium and nonequilibrium statistical mechanics on the other.

Compressible 2nd-order boundary-layers for 3-dimensional stagnation point flows with mass-transfer

All the second-order boundary-layer effects have been studied for the steady laminar compressible 3-dimensional stagnation-point flows with variable properties and mass transfer for both saddle and nodal point regions. The governing equations have been solved numerically using an implicit finite-difference scheme. Results for the heat transfer and skin friction have been obtained for several values of the mass-transfer rate, wall temperature, and also for several values of parameters characterizing the nature of stagnation point and variable gas properties. The second-order effects on the heat transfer and skin friction at the wall are found to be significant and at large injection rates, they dominate over the results of the first-order boundary layer, but the effect of large suction is just the opposite. In general, the second-order effects are more pronounced in the saddle-point region than in the nodal-point region. The overall heat-transfer rate for the 3-dimensional flows is found to be more than that of the 2-dimensional flows.

Liquid-Liquid Interphase (Biphasic) as the Reaction Medium in the Assembly of a Hierarchy of Structures of 4,4 `-Azodibenzoic Acid with Zinc and Cadmium

The compounds Zn(C12H8N2)](2)C12N2H8(COO)(2)](2)center dot(C6H12O)center dot(H2O), I, Zn(C12H8N2)]C12N2H8(COO)(2)], II, Cd(C12H8N2)(H2O)]C12N2H8(COO)(2)]center dot(H2O), III, Zn(C10N2H8)]C12N2H8(COO)(2)]center dot 0.5(C10N2H8), IV, Cd(C12N2H8(COO)(2)center dot H2O], V, and Zn-3(mu(2)-O)(mu(3)-O)(3)]C12N2H8(COO)(2)], VI, have been synthesized by using a biphasic approach (I, III, V, VI) or regular hydrothermal method (II, IV). The compounds exhibit one (I and II), two (In), and three dimensionally (IV, V, VI) extended structures. The flexible azodibenzoate ligand gives rise to a 3-fold interpenetration (IV) when the synthesis was carried out using normal hydrothermal methods. The biphasic approach forms structures without any interpenetrations, especially in the three-dimensional structures of V and VI. Formation of Cd2O2 dimers in V and extended M-O(H)-M two-dimensional layers in VI suggests the subtle structural control achieved by the biphasic method. Transformation studies indicate that it is possible to transform I to II. Lewis acid catalytic studies have been performed to evaluate the role of the coordination environment in such reactions. All the compounds have been characterized by a variety of techniques that includes powder X-ray diffraction, infrared, thermogravitric analysis, UV-vis, photoluminescence studies.

A method for stabilizing the cis prolyl peptide bond: influence of an unusual n -> pi* interaction in 1,3-oxazine and 1,3-thiazine containing peptidomimetics

The cis/trans isomer ratios of the Xaa-Pyr (Pyr = pyrrolidine) 3 degrees amide bonds are significantly high (similar to 90% cis) in the novel peptidomimetics where Pyr contains 1,3-oxazine (Oxa) or 1,3-thiazine (Thi) at its 2 position. We find that an unusual n -> pi(i-1)* interaction, selectively stabilizes the cis conformer and the n X n repulsion destabilizes the trans conformer of these molecules. Both these electronic effects oppose the steric effects in the 3 degrees amide bond. The structural requirements for manifestation of these electronic effects are determined. (c) 2012 Elsevier Ltd. All rights reserved.

Analysis of short interproton distances in proline peptides as a guide in the interpretation of nuclear overhauser effects

The conformational dependence of interproton distances in model proline peptides has been investigated in order to facilitate interpretation of the results of Nuclear Overhauser Effect (NOE) studies on such peptides. For this purpose two model systems, namely, Ac-Pro-NHMe and Ac-Pro-X-NHMe have been chosen and used. In the former, short interproton distances detectable in NOE experiments permit a clear distinction between conformations with Pro ψ = -300 (helical region) and those in which ψ is around 1200 (polyproline region). For the latter, the variation of distances between the protons of methyl amide and the Pro ring have been studied by superimposing on the Ramachandran map in the (φ3, ψ3) plane. The results show that β-turns and non-β-turn conformations can be readily distinguished from NOE data and such long range NOEs should be detectable for specific non-β-turn conformations. NOEs involving Cβ and Cγ protons are particularly sensitive to the state of pyrrolidine ring puckering.

Influence of Elastic-Constants on Mode-I Stress-Intensity Factors in 3-Dimensional Crack Problems

Plates with V-through edge notches subjected to pure bending and specimens with rectangular edge-through-notches subjected to combined bending and axial pull were investigated (under live-load and stress-frozen conditions) in a completely nondestructive manner using scattered-light photoelasticity. Stress-intensity factors (SIFs) were evaluated by analysing the singular stress distributions near crack-tips. Improved methods are suggested for the evaluation of SIFs. The thickness-wise variation of SIFs is also obtained in the investigation. The results obtained are compared with the available theoretical solutions.

On a Two-Dimensional Problem in the End-Block Design of Post-Tensioned Prestressed Concrete Beams

Abstract is not available.

Uniqueness of Walkup's 9-vertex 3-dimensional Klein bottle

Via a computer search, Altshuler and Steinberg found that there are 1296+1 combinatorial 3-manifolds on nine vertices, of which only one is non-sphere. This exceptional 3-manifold View the MathML source triangulates the twisted S2-bundle over S1. It was first constructed by Walkup. In this paper, we present a computer-free proof of the uniqueness of this non-sphere combinatorial 3-manifold. As opposed to the computer-generated proof, ours does not require wading through all the 9-vertex 3-spheres. As a preliminary result, we also show that any 9-vertex combinatorial 3-manifold is equivalent by proper bistellar moves to a 9-vertex neighbourly 3-manifold.