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.

Magnetism in MnPSe3: a layered 3d(5) antiferromagnet with unusually large XY anisotropy

The anisotropic magnetic susceptibilities of single crystals of the isostructural layered antiferromagnets, MnPS3 (T-N = 78 K) and MnPSe3 (T-N = 74 K), have been measured as functions of temperature. In both compounds, divalent manganese is present in the high-spin S = 5/2 state. The anisotropies in the susceptibilities of the two are, however, very different; while the susceptibility of MnPS3 is isotropic, that of MnPSe3 shows a large XY anisotropy, unusual for a manganese compound. The anisotropic susceptibilities are described by the zero-field spin Hamiltonian: H = DSiz2 - Sigma J(ij).(S) over right arrow (S) over right arrow(j) with the quadratic single-ion anisotropy term introducing anisotropy in an otherwise isotropic situation. The exchange J and the single-ion zero-field-splitting (ZFS) parameter D were evaluated using the correlated effective-field theory of Lines. For MnPSe3, J/k = -5.29 K and D/k = 26.6 K, while for isotropic MnPS3, J/k = -8.1 K. It is suggested that the large value of the ZFS parameter for MnPSe3 as compared to MnPS3 could be due to the large ligand spin-orbit contribution of the heavier selenium.

Conductance of a photochromic molecular switch with graphene leads

We report a full self-consistent ab initio calculation of the conductance of a diarylethene-based molecular switch with two graphene electrodes. Our results show the contributions of the resonant states of the molecule, of the electrode density of states, and of graphene unique features, such as edge states. The conductivities are found to be significantly different for the two photochromic isomers at zero and finite applied bias. Further we point out the possibility of causing the switching by the application of a large potential difference between the two electrodes.

Effect of strain path change on the evolution of texture and microstructure during rolling of copper and nickel

The effect of strain path change during rolling has been investigated for copper and nickel using X-ray diffraction and electron back scatter diffraction as well as crystal plasticity simulations. Four different strain paths namely: (i) unidirectional rolling; (ii) reverse rolling; (iii) two-step cross rolling and (iv) multi-step cross rolling were employed to decipher the effect of strain path change on the evolution of deformation texture and microstructure. The cross rolled samples showed weaker texture with a prominent Bs {1 1 0}< 1 1 2 > and P(B(ND)) {1 1 0}< 1 1 1 > component in contrast to the unidirectional and reverse rolled samples where strong S {1 2 3}< 6 3 4 > and Cu {1 1 2}< 1 1 1 > components were formed. This was more pronounced for copper samples compared to nickel. The cross rolled samples were characterized by lower anisotropy and Taylor factor as well as less variation in Lankford parameter. Viscoplastic self-consistent simulations indicated that slip activity on higher number of octahedral slip systems can explain the weaker texture as well as reduced anisotropy in the cross rolled samples. (C) 2011 Elsevier B.V. All rights reserved.

Confinement-deconfinement transition and spin correlations in a generalized Kitaev model

We present a spin model, namely, the Kitaev model augmented by a loop term and perturbed by an Ising Hamiltonian, and show that it exhibits both confinement-deconfinement transitions from spin liquid to antiferromagnetic/spin-chain/ferromagnetic phases and topological quantum phase transitions between gapped and gapless spin-liquid phases. We develop a fermionic resonating-valence-bonds (RVB) mean-field theory to chart out the phase diagram of the model and estimate the stability of its spin-liquid phases, which might be relevant for attempts to realize the model in optical lattices and other spin systems. We present an analytical mean-field theory to study the confinement-deconfinement transition for large coefficient of the loop term and show that this transition is first order within such mean-field analysis in this limit. We also conjecture that in some other regimes, the confinement-deconfinement transitions in the model, predicted to be first order within the mean-field theory, may become second order via a defect condensation mechanism. Finally, we present a general classification of the perturbations to the Kitaev model on the basis of their effect on it's spin correlation functions and derive a necessary and sufficient condition, within the regime of validity of perturbation theory, for the spin correlators to exhibit a long-ranged power-law behavior in the presence of such perturbations. Our results reproduce those of Tikhonov et al. [Phys. Rev. Lett. 106, 067203 (2011)] as a special case.

The oxygen potential of the systems Fe+FeCr2O4+ Cr2O3 and Fe+FeV2O4+ V2O3 in the temperature range 750 1600o C

From electromotive force (emf) measurements using solid oxide galvanic cells incorporating ZrOz-CaO and ThOz-YO~.s electrolytes, the chemical potentials of oxygen over the systems Fe + FeCrzO 4 + Cr20 ~ and Fe + FeV204 + V203 were calculated. The values may be represented by the equations: 2Fe(s, I) + Oz(g) + 2Cr2Oa(s) -- 2FeCr204 (s)Akto2 = - 151,400 + 34.7T (• cal= -633,400 + 145.5T(• J (750 to 1536~ A~tO2 = -158,000 + 38.4T(• cal= -661,000 + 160.5T(*1250) J (1536 to 1700~2Fe (s, I) + O2 (g) + 2V203 (s) -- 2FeV204 (s) A/~Oz = - 138,000 + 29.8T(+300) cal= - 577,500 + 124.7T (• J (750 to 1536~A/IO2 = -144,600 + 33.45T(-300) cal = -605,100 + 140.0T(~-1250) J (1536 to 1700~At the oxygen potentials corresponding to Fe + FeCrzO a + Cr203 equilibria, the electronic contribution to the conductivity of ZrO2-CaO electrolyte was found to affect the measured emf. Application of a small 60 cycle A.C. voltage with an amplitude of 50 mv across the cell terminals reduced the time required to attain equilibrium at temperatures between 750 to 9500C by approximately a factor of two. The second law entropy of iron chromite obtained in this study is in good agreement with that calculated from thermal data. The entropies of formation of these spinel phases from the component oxides can be correlated to cation distribution and crystal field theory.

Activities and their relation to cation distribution in NiAl2O4 MgAl2O4 spinel solid solutions

The activity of NiAl2O4 in NiAl2O4MgAl2O4 solid solutions has been measured by using a solid oxide galvanic cell of the type, Pt, Ni + NiAl2O4 + Al2O3(α)/CaOZrO2/Ni + NixMg1−xAl2O4 + Al2O3(α). Pt, in the temperature range 750–1150°C. The activities in the spinel solid solutions show negative deviations from Raoult's law. The cation distribution in the solid solutions has been calculated using site preference energies independent of composition for Ni2+, Mg2+, and Al3+ ions obtained from crystal field theory and measured cation disorder in pure NiAl2O4 and MgAl2O4, and assumi g ideal mixing of cations on the tetrahedral and octahedral positions. The calculated values correctly predict the decrease in the fraction, α, of Ni2+ ions on tetrahedral sites for 1>x>0.25, observed by Porta et al. [J. Solid State Chem.11, 135 (1974)] but do not support their tentative evidence for an increase in α for x < 0.25. The measured excess free energy of mixing can be completely accounted for by using either the calculated or the measured cation distributions. This suggests that the Madelung energy is approximately a linear function of composition in the solid solutions. The composition of NiOMgO solid solutions in equilibrium with NiAl2O4MgAl2O4 solid solutions has been calculated from the results and information available in literature.

Correlations between structure and thermodynamic properties of spinels and their applications in technology

Measurements a/the Gibbs' energy enthalpy and entrupy vffarmation oj chromites, vanadites and alumlnat.:s 0/ F", Ni. Co'. Mn, Zn Mg and Cd, using solid oxide galvanic cells over a ternperature range extending approximately lOOO°C, have shown that the '~'Ilir"!,,, J'JrIl/iJ~ tion 0/ cubic 2-3 oxide spinel phases (MX!O,), from component oxide (MO) with rock-salt and X.Os whir c(1f'l/!ldwn st!'llt'lw,·. call b,' represented by a semi-empirical correlalion, ~S~ = --LiS + L'i,SM +~S~:"d(±O.3) cal.deg-1 mol-1 where /',.SM Is the entropy 0/calian mixing oillhe tetrahedral alld octahedral sites o/the spinel and Sr:~ is tlie enfropy associaf,'d Wifh Ih,' randomization a/the lahn-Telier distortions. A review a/the methods/or evaluating the cation distriblltion lfl spille!s suggeJ{j' l/r,l! Ihe most promising scheme is based Oil octahedral site preference energies from the crystal field theory for the Iral1silioll IIIl'f"! IlIIL';. For I/""-Irallsifioll melal cal ions site preference energies are derived relative /0 thol'lt fLI, [ransilion metal ions from measured high tClllP('ftJi ure Cal iUlI disll iiJuriol1 in spine! phases thar contail! one IransilioJl metal and another non-transition metal carion. For 2-3 srinds compulatiorrs b,IS"J Oil i.!c[J;' Temkin mixing on each catioll subialtice predici JistributionJ that are In fair agreement with X-ray and 1I1'IIIrOll ditTraction, /IIdg""!ic dll.! electrical propcrries, and spectroscopic measurements. In 2-4 spineis mixing vI ions do not foliow strictly ideal slllIistli:al Jaws, Th,' OIl/up) associated with the randomizalion 0/the Jllhn-Teller dislOriioll" appear to be significant, only ill spinels witll 3d'. 3d', 3d' (ifld~UI' iOtls in tetrahedral and 3d' and 3d9 ions in octahedral positions. Application 0/this structural model for predicting the thermodynamic proputies ofspinel solid .,olutiofl5 or,' illustrated. F,lr complex systems additional contributions arising from strain fields, redox equilibria and off-center ions have to be qllalllififti. The entropy correlation for spinels provides a method for evaluating structure tran:.jormafiofl entropies in silllple o.\id.-s, ["founlllion on the relative stabilities ofoxides in different crystallCtructures is USe/III for computer ea/culaliof! a/phase dfugrullls ofIlIrer,',,1 III (N.lll1ie5 by method, similar to thost: used by Kaufman and Bernstein for refractory alloy systems. Examples oftechnoiogical appliCation tnclude the predictioll ofdeoxidation equilibria in Fe-Mn-AI-O s),slelll at 1600°C duj ,'Ulllpltfalion 0/phase relutions in Fe-Ni-Cr-S system,

Transfer matrix modeling of hyperbolic and parabolic ducts with incompressible mean flow

A general differential equation for the propagation of sound in a variable area duct or nozzle carrying incompressible mean flow (of low Mach number) is derived and solved for hyperbolic and parabolic shapes. Expressions for the state variables of acoustic pressure and acoustic mass velocity of the shapes are derived. Self‐consistent expressions for the four‐pole parameters are developed. The conical, exponential, catenoidal, sine, and cosine ducts are shown to be special cases of hyperbolic ducts. Finally, it is shown that if the mean flow in computing the transmission loss of the mufflers involving hyperbolic and parabolic shapes was not neglected, little practical benefit would be derived.

Higher spin quasinormal modes and one-loop determinants in the BTZ black hole

We solve the wave equations of arbitrary integer spin fields in the BTZ black hole background and obtain exact expressions for their quasinormal modes. We show that these quasinormal modes precisely agree with the location of the poles of the corresponding two point function in the dual conformal field theory as predicted by the AdS/CFT correspondence. We then use these quasinormal modes to construct the one-loop determinant of the higher spin field in the thermal BTZ background. This is shown to agree with that obtained from the corresponding heat kernel constructed recently by group theoretic methods.

Texture and Microstructural Evolution in Pearlitic Steel During Triaxial Compression

This article presents the deformation behavior of high-strength pearlitic steel deformed by triaxial compression to achieve ultra-fine ferrite grain size with fragmented cementite. The consequent evolution of microstructure and texture has been studied using scanning electron microscopy, electron back-scatter diffraction, and X-ray diffraction. The synergistic effect of diffusion and deformation leads to the uniform dissolution of cementite at higher temperature. At lower temperature, significant grain refinement of ferrite phase occurs by deformation and exhibits a characteristic deformation texture. In contrast, the high-temperature deformed sample shows a weaker texture with cube component for the ferrite phase, indicating the occurrence of recrystallization. The different mechanisms responsible for the refinement of ferrite as well as the fragmentation of cementite and their interaction with each other have been analyzed. Viscoplastic self-consistent simulation was employed to understand deformation texture in the ferrite phase during triaxial compression.

Quantum corrections to screening at strong coupling

We compute a certain class of corrections to (specific) screening lengths in strongly coupled non-abelian plasmas using the AdS/CFT correspondence. In this holographic framework, these corrections arise from various higher curvature interactions modifying the leading Einstein gravity action. The changes in the screening lengths are perturbative in inverse powers of the `t Hooft coupling or of the number of colors, as can be made precise in the context where the dual gauge theory is superconformal. We also compare the results of these holographic calculations to lattice results for the analogous screening lengths in QCD. In particular, we apply these results within the program of making quantitative comparisons between the strongly coupled quark-gluon plasma and holographic descriptions of conformal field theory. (c) 2012 Elsevier B.V. All rights reserved.

Higher spin fermions in the BTZ black hole

Recently it has been shown that the wave equations of bosonic higher spin fields in the BTZ background can be solved exactly. In this work we extend this analysis to fermionic higher spin fields. We solve the wave equations for arbitrary half-integer spin fields in the BTZ black hole background and obtain exact expressions for their quasinormal modes. These quasinormal modes are shown to agree precisely with the poles of the corresponding two point function in the dual conformal field theory as predicted by the AdS/CFT correspondence. We also obtain an expression for the 1-loop determinant for the Euclidean non-rotating BTZ black hole in terms of the quasinormal modes which agrees with that obtained by integrating the heat kernel found by group theoretic methods.

Evolution of Texture and Microstructure in Commercially Pure Titanium with Change in Strain Path During Rolling

The evolution of microstructure and texture in commercially pure titanium has been studied as a function of strain path during rolling using experimental techniques and viscoplastic self-consistent simulations. Four different strain paths, namely unidirectional rolling, two-step cross rolling, multistep cross rolling, and reverse rolling, have been employed to decipher the effect of strain path change on the evolution of deformation texture and microstructure. The cross-rolled samples show higher hardness with lower microstrain and intragranular misorientation compared to the unidirectional rolled sample as determined from X-ray diffraction and electron backscatter diffraction, respectively. The higher hardness of the cross-rolled samples is attributed to orientation hardening due to the near basal texture. Viscoplastic self-consistent simulations are able to successfully predict the texture evolution of the differently rolled samples. Simulation results indicate the higher contribution of basal slip in the formation of near basal texture and as well as lower intragranular misorientation in the cross-rolled samples.

Simulation of Deformation Texture Evolution During Multi Axial Forging of Interstitial Free Steel

Bulk texture measurement of multi-axial forged body center cubic interstitial free steel performed in this study using x-ray and neutron diffraction indicated the presence of a strong {101}aOE (c) 111 > single texture component. Viscoplastic self-consistent simulations could successfully predict the formation of this texture component by incorporating the complicated strain path followed during this process and assuming the activity of {101}aOE (c) 111 > slip system. In addition, a first-order estimate of mechanical properties in terms of highly anisotropic yield locus and Lankford parameter was also obtained from the simulations.