Cross-correlation-aided transport in stochastically driven accretion flows

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013); Nath et al., Phys. Rev. E 88, 013010 (2013)] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a ``cold'' accretion flow at 3000Kis too ``hot'' in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

A thermodynamic correlation between damage and fracture as applied to concrete fatigue

Fatigue damage in concrete is characterized by the simultaneous presence of micro and macrocracks. The theory of fracture mechanics conveniently handles the propagation of macrocracks, whereas damage mechanics precisely describes the state of microcracking. This paper provides a platform to correlate fracture mechanics and damage mechanics theories through an energy equivalence within a thermodynamic framework by equating the energy dissipated according to each theory. Through this correlation, damage corresponding to a given crack length could be obtained, and alternatively a discrete crack could be transformed into an equivalent damage zone. The results are validated using available experimental data on concrete fatigue including stiffness degradation and acoustic emission. (C) 2015 Elsevier Ltd. All rights reserved.

A thermodynamic correlation between damage and fracture as applied to concrete fatigue

Fatigue damage in concrete is characterized by the simultaneous presence of micro and macrocracics. The theory of fracture mechanics conveniently handles the propagation of macrocracks, whereas damage mechanics precisely describes the state of microcracking. This paper provides a platform to correlate fracture mechanics and damage mechanics theories through an energy equivalence within a thermodynamic framework by equating the energy dissipated according to each theory. Through this correlation, damage corresponding to a given crack length could be obtained, and alternatively a discrete crack could be transformed into an equivalent damage zone. The results are validated using available experimental data on concrete fatigue including stiffness degradation and acoustic emission. (C) 2015 Elsevier Ltd. All rights reserved.

Relationship between entropy and diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by studying diffusion of a point Brownian particle on a model potential energy surface characterized by ruggedness. If we assume that the ruggedness has a Gaussian distribution, then for this model, one can obtain the excess entropy exactly for any dimension. By using the expression for the mean first passage time, we present a statistical mechanical derivation of the well-known and well-tested scaling relation proposed by Rosenfeld between diffusion and excess entropy. In anticipation that Rosenfeld diffusion-entropy scaling (RDES) relation may continue to be valid in higher dimensions (where the mean first passage time approach is not available), we carry out an effective medium approximation (EMA) based analysis of the effective transition rate and hence of the effective diffusion coefficient. We show that the EMA expression can be used to derive the RDES scaling relation for any dimension higher than unity. However, RDES is shown to break down in the presence of spatial correlation among the energy landscape values. (C) 2015 AIP Publishing LLC.

Correlation equations for average deposition rate coefficients of nanoparticles in a cylindrical pore

Nanoparticle deposition behavior observed at the Darcy scale represents an average of the processes occurring at the pore scale. Hence, the effect of various pore-scale parameters on nanoparticle deposition can be understood by studying nanoparticle transport at pore scale and upscaling the results to the Darcy scale. In this work, correlation equations for the deposition rate coefficients of nanoparticles in a cylindrical pore are developed as a function of nine pore-scale parameters: the pore radius, nanoparticle radius, mean flow velocity, solution ionic strength, viscosity, temperature, solution dielectric constant, and nanoparticle and collector surface potentials. Based on dominant processes, the pore space is divided into three different regions, namely, bulk, diffusion, and potential regions. Advection-diffusion equations for nanoparticle transport are prescribed for the bulk and diffusion regions, while the interaction between the diffusion and potential regions is included as a boundary condition. This interaction is modeled as a first-order reversible kinetic adsorption. The expressions for the mass transfer rate coefficients between the diffusion and the potential regions are derived in terms of the interaction energy profile. Among other effects, we account for nanoparticle-collector interaction forces on nanoparticle deposition. The resulting equations are solved numerically for a range of values of pore-scale parameters. The nanoparticle concentration profile obtained for the cylindrical pore is averaged over a moving averaging volume within the pore in order to get the 1-D concentration field. The latter is fitted to the 1-D advection-dispersion equation with an equilibrium or kinetic adsorption model to determine the values of the average deposition rate coefficients. In this study, pore-scale simulations are performed for three values of Peclet number, Pe = 0.05, 5, and 50. We find that under unfavorable conditions, the nanoparticle deposition at pore scale is best described by an equilibrium model at low Peclet numbers (Pe = 0.05) and by a kinetic model at high Peclet numbers (Pe = 50). But, at an intermediate Pe (e.g., near Pe = 5), both equilibrium and kinetic models fit the 1-D concentration field. Correlation equations for the pore-averaged nanoparticle deposition rate coefficients under unfavorable conditions are derived by performing a multiple-linear regression analysis between the estimated deposition rate coefficients for a single pore and various pore-scale parameters. The correlation equations, which follow a power law relation with nine pore-scale parameters, are found to be consistent with the column-scale and pore-scale experimental results, and qualitatively agree with the colloid filtration theory. These equations can be incorporated into pore network models to study the effect of pore-scale parameters on nanoparticle deposition at larger length scales such as Darcy scale.

Evolution of electronic structure with dimensionality in divalent nickelates

We investigate the evolution of electronic structure with dimensionality (d) of Ni-O-Ni connectivity in divalent nickelates, NiO (3-d), La2NiO4, Pr2NiO4 (2-d), Y2BaNiO5 (1-d) and Lu2BaNi5 (0-d), by analyzing the valence band and the Ni 2p core-level photoemission spectra in conjunction with detailed many-body calculations including full multiplet interactions. Experimental results exhibit a reduction in the intensity of correlation-induced satellite features with decreasing dimensionality. The calculations based on the cluster model, but evaluating both Ni 3d and O 2p related photoemission processes on the same footing, provide a consistent description of both valence-band and core-level spectra in terms of various interaction strengths. While the correlation-induced satellite features in NiO is dominated by poorly screened d(8) states as described in the existing literature, we find that the satellite features in the nickelates with lower dimensional Ni-O-Ni connectivity are in fact dominated by the over-screened d(10)L(2) states. It is found that the changing electronic structure with the dimensionality is primarily driven by two factors: (i) a suppression of the nonlocal contribution to screening; and (ii) a systematic decrease of the charge-transfer energy Delta driven by changes in the Madelung potential. [S0163-1829(99)09619-8].

On the measurement of the surface energy budget over a land surface during the summer monsoon

The measurement of surface energy balance over a land surface in an open area in Bangalore is reported. Measurements of all variables needed to calculate the surface energy balance on time scales longer than a week are made. Components of radiative fluxes are measured while sensible and latent heat fluxes are based on the bulk method using measurements made at two levels on a micrometeorological tower of 10 m height. The bulk flux formulation is verified by comparing its fluxes with direct fluxes using sonic anemometer data sampled at 10 Hz. Soil temperature is measured at 4 depths. Data have been continuously collected for over 6 months covering pre-monsoon and monsoon periods during the year 2006. The study first addresses the issue of getting the fluxes accurately. It is shown that water vapour measurements are the most crucial. A bias of 0.25% in relative humidity, which is well above the normal accuracy assumed the manufacturers but achievable in the field using a combination of laboratory calibration and field intercomparisons, results in about 20 W m(-2) change in the latent heat flux on the seasonal time scale. When seen on the seasonal time scale, the net longwave radiation is the largest energy loss term at the experimental site. The seasonal variation in the energy sink term is small compared to that in the energy source term.

Unoccupied electronic states in NiS2-xSex across the metal-insulator transition

We investigate the evolution of the electronic structure across the insulator-metal transition in NiS2-xSex with changing composition, but in the absence of any structural or magnetic changes. A comparison of the inverse photoemission spectra with band-structure calculations establishes the importance of correlation effects in these systems. Systematic changes in the spectral distribution establish the persistence of the upper Hubbard band well into the metallic regime, with the insulator-to-metal transition being driven by a transfer of spectral weight from the Hubbard band to states close to the Fermi energy.

Determination of diffusion parameters and activation energy of diffusion in V3Si phase with A15 crystal structure

Diffusion such is the integrated diffusion coefficient of the phase, the tracer diffusion coefficient of species at different temperatures and the activation energy for diffusion, are determined in V3Si phase with A15 crystal structure. The tracer diffusion coefficient of Si Was found to be negligible compared to the tracer diffusion coefficient of V. The calculated diffusion parameters will help to validate the theoretical analysis of defect structure of the phase, which plays an important role in the superconductivity.

Phase Equilibria in the System $Al_{2}O_{3}-CaO-CoO$ and Gibbs Energy of Formation of $Ca_{3}CoAl_{4}O_{10}$

The floating-zone method with different growth ambiences has been used to selectively obtain hexagonal or orthorhombic DyMnO3 single crystals. The crystals were characterized by x-ray powder diffraction of ground specimens and a structure refinement as well as electron diffraction. We report magnetic susceptibility, magnetization and specific heat studies of this multiferroic compound in both the hexagonal and the orthorhombic structure. The hexagonal DyMnO3 shows magnetic ordering of Mn3+ (S = 2) spins on a triangular Mn lattice at T-N(Mn) = 57 K characterized by a cusp in the specific heat. This transition is not apparent in the magnetic susceptibility due to the frustration on the Mn triangular lattice and the dominating paramagnetic susceptibility of the Dy3+ (S = 9/2) spins. At T-N(Dy) = 3 K, a partial antiferromagnetic order of Dy moments has been observed. In comparison, the magnetic data for orthorhombic DyMnO3 display three transitions. The data broadly agree with results from earlier neutron diffraction experiments, which allows for the following assignment: a transition from an incommensurate antiferromagnetic ordering of Mn3+ spins at T-N(Mn) = 39 K, a lock-in transition at Tlock-in = 16 K and a second antiferromagnetic transition at T-N(Dy) = 5 K due to the ordering of Dy moments. Both the hexagonal and the orthorhombic crystals show magnetic anisotropy and complex magnetic properties due to 4f-4f and 4f-3d couplings.

Effect of spatial dispersion of the dielectric on the binding energy of D- ion in Si and Ge

Using a multivalley effective mass theory, we obtain the binding energy of a D- ion in Si and Ge taking into account the spatial variation of the host dielectric function. We find that on comparison with experimental results the effect of spatial dispersion is important in the estimation of binding energy for the D- formed by As in Si and Ge. The effect is less significant for the case of D- formed by P and Sb donors.

Free Energy Gap Dependence of the Electron-Transfer Rate from the Inverted to the Normal Region

numerical study of the free energy gap (FEG) dependence of the electron-transfer rate in polar solvents is presented. This study is based on the generalized multidimensional hybrid model, which not only includes the solvent polarization and the molecular vibration modes, but also the biphasic polar response of the solvent. The free energy gap dependence is found to be sensitive to several factors, including the solvent relaxation rate, the electronic coupling between the surfaces, the frequency of the high-frequency quantum vibrational mode, and the magnitude of the solvent reorganization energy. It is shown that in some cases solvent relaxation can play an important role even in the Marcus normal regime. The minimal hybrid model involves a large number of parameters, giving rise to a diverse non-Marcus FEG behavior which is often determined collectively by these parameters. The model gives the linear free energy gap dependence of the logarithmic rate over a substantial range of FEG, spanning from the normal to the inverted regime. However, even for favorable values of the relevant parameters, a linear free energy gap dependence of the rate could be obtained only over a range of 5000-6000 cm(-1) (compared to the experimentally observed range of 10000 cm(-1) reported by Benniston et al.). The present work suggests several extensions/generalizations of the hybrid model which might be necessary to fully understand the observed free energy gap dependence.

Free energy landscape of a dense hard-sphere system

The topography of the free energy landscape in phase space of a dense hard-sphere system characterized by a discretized free energy functional of the Ramakishnan-Yussouff form is investigated numerically using a specially devised Monte Carlo procedure. We locate a considerable number of glassy local minima of the free energy and analyze the distributions of the free energy at a minimum and an appropriately defined phase-space "distance" between different minima. We find evidence for the existence of pairs of closely related glassy minima("two-level systems"). We also investigate the way the system makes transitions as it moves from the basin of attraction of a minimum to that of another one after a start under nonequilibrium conditions. This allows us to determine the effective height of free energy barriers that separate a glassy minimum from the others. The dependence of the height of free energy barriers on the density is investigated in detail. The general appearance of the free energy landscape resembles that of a putting green: relatively deep minima separated by a fairly flat structure. We discuss the connection of our results with the Vogel-Fulcher law and relate our observations to other work on the glass transition.

Defect production due to quenching through a multicritical point

We study the generation of defects when a quantum spin system is quenched through a multicritical point by changing a parameter of the Hamiltonian as t/tau, where tau is the characteristic timescale of quenching. We argue that when a quantum system is quenched across a multicritical point, the density of defects (n) in the final state is not necessarily given by the Kibble-Zurek scaling form n similar to 1/tau(d nu)/((z nu+1)), where d is the spatial dimension, and. and z are respectively the correlation length and dynamical exponent associated with the quantum critical point. We propose a generalized scaling form of the defect density given by n similar to 1/(tau d/(2z2)), where the exponent z(2) determines the behavior of the off-diagonal term of the 2 x 2 Landau-Zener matrix at the multicritical point. This scaling is valid not only at a multicritical point but also at an ordinary critical point.

Long range resonance energy transfer from a dye molecule to graphene has (distance)-4 dependence

In our previous report on resonance energy transfer from a dye molecule to graphene [J. Chem. Phys.129, 054703 (2008)], we had derived an expression for the rate of energy transfer from a dye to graphene. An integral in the expression for the rate was evaluated approximately. We found a Yuwaka-type dependence of the rate on the distance. We now present an exact evaluation of the integral involved, leading to very interesting results. For short distances (z < 20 A), the present rate and the previous rate are in good agreement. For larger distances, the rate is found to have a z(-4) dependence on the distance, exactly. Thus we predict that for the case of pyrene on graphene, it is possible to observe fluorescence quenching up to a distance of 300 A. This is in sharp contrast to the traditional fluorescence resonance energy transfer where the quenching is observable only up to 100 A.