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.

Correlation between Discharging Property and Coatings Microstructure during Plasma Electrolytic Oxidation

The voltage-current properties during plasma electrolytic discharge were determined by measuring the current density and cell voltage as functions of processing time and then by mathematical transformation. Correlation between discharge I-V property and the coatings microstructure on aluminum alloy during plasma electrolfic oxidation was determined by comparing the voltage-current properties at different process stages with SEM results of the corresponding coatings. The results show that the uniform passive film corresponds to a I-V property with one critical voltage, and a compound of porous layer and shred ceramic particles corresponds to a I-Vproperty with two critical voltages. The growth regularity of PEO cermet coatings was also studied.

Kinetic theory of normal quantum fluids

Close to equilibrium, a normal Bose or Fermi fluid can be described by an exact kinetic equation whose kernel is nonlocal in space and time. The general expression derived for the kernel is evaluated to second order in the interparticle potential. The result is a wavevector- and frequency-dependent generalization of the linear Uehling-Uhlenbeck kernel with the Born approximation cross section.

The theory is formulated in terms of second-quantized phase space operators whose equilibrium averages are the n-particle Wigner distribution functions. Convenient expressions for the commutators and anticommutators of the phase space operators are obtained. The two-particle equilibrium distribution function is analyzed in terms of momentum-dependent quantum generalizations of the classical pair distribution function h(k) and direct correlation function c(k). The kinetic equation is presented as the equation of motion of a two -particle correlation function, the phase space density-density anticommutator, and is derived by a formal closure of the quantum BBGKY hierarchy. An alternative derivation using a projection operator is also given. It is shown that the method used for approximating the kernel by a second order expansion preserves all the sum rules to the same order, and that the second-order kernel satisfies the appropriate positivity and symmetry conditions.

I. Numerical solution of exact pair equations. II. Numerical solution of first-order pair equations

Part I

Numerical solutions to the S-limit equations for the helium ground state and excited triplet state and the hydride ion ground state are obtained with the second and fourth difference approximations. The results for the ground states are superior to previously reported values. The coupled equations resulting from the partial wave expansion of the exact helium atom wavefunction were solved giving accurate S-, P-, D-, F-, and G-limits. The G-limit is -2.90351 a.u. compared to the exact value of the energy of -2.90372 a.u.

Part II

The pair functions which determine the exact first-order wavefunction for the ground state of the three-electron atom are found with the matrix finite difference method. The second- and third-order energies for the (1s1s)¹S, (1s2s)³S, and (1s2s)¹S states of the two-electron atom are presented along with contour and perspective plots of the pair functions. The total energy for the three-electron atom with a nuclear charge Z is found to be E(Z) = -1.125•Z² +1.022805•Z-0.408138-0.025515•(1/Z)+O(1/Z²)a.u.

Spatial correlation of heat release rate and sound emission from turbulent premixed flames

The two-point spatial correlation of the rate of change of fluctuating heat release rate is central to the sound emission from open turbulent flames, and a few attempts have been made to address this correlation in recent studies. In this paper, the two-point correlation and its role in combustion noise are studied by analysing direct numerical simulation (DNS) data of statistically multi-dimensional turbulent premixed flames. The results suggest that this correlation function depends on the separation distance and direction but, not on the positions inside the flame brush. This correlation can be modelled using a combination of Hermite-Gaussian functions of zero and second order, i.e. functions of the form (1-Ax2)e-Bx2 for constants A and B, to include its possible negative values. The integral correlation volume obtained using this model is about 0.2δL3 with the length scale obtained from its cube root being about 0.6δ L, where δ L is the laminar flame thermal thickness. Both of the values are slightly larger than the values reported in an earlier study because of the anisotropy observed for the correlation. This model together with the turbulence-dependent parameter K, the ratio of the root-mean-square (RMS) value of the rate of change of reaction rate to the mean reaction rate, derived from the DNS data is applied to predict the far-field sound emitted from open flames. The calculated noise levels agree well with recently reported measurements and show a sensitivity to K values. © 2012 The Combustion Institute.

Balance functions from Au+Au, d+Au, and p+p collisions at root s(NN)=200 GeV

Balance functions have been measured for charged-particle pairs, identified charged-pion pairs, and identified charged-kaon pairs in Au + Au, d + Au, and p + p collisions at root s(NN) = 200 GeV at the Relativistic Heavy Ion Collider using the STAR detector. These balance functions are presented in terms of relative pseudorapidity, Delta eta, relative rapidity, Delta y, relative azimuthal angle, Delta phi, and invariant relative momentum, q(inv). For charged-particle pairs, the width of the balance function in terms of Delta eta scales smoothly with the number of participating nucleons, while HIJING and UrQMD model calculations show no dependence on centrality or system size. For charged-particle and charged-pion pairs, the balance functions widths in terms of Delta eta and Delta y are narrower in central Au + Au collisions than in peripheral collisions. The width for central collisions is consistent with thermal blast-wave models where the balancing charges are highly correlated in coordinate space at breakup. This strong correlation might be explained by either delayed hadronization or limited diffusion during the reaction. Furthermore, the narrowing trend is consistent with the lower kinetic temperatures inherent to more central collisions. In contrast, the width of the balance function for charged-kaon pairs in terms of Delta y shows little centrality dependence, which may signal a different production mechanism for kaons. The widths of the balance functions for charged pions and kaons in terms of q(inv) narrow in central collisions compared to peripheral collisions, which may be driven by the change in the kinetic temperature.

Forms and functions of inorganic carbon in the Jiaozhou Bay sediments

Inorganic carbon forms and their influencing factors, mutual transformation and contribution to carbon cycling in the Jiaozhou Bay sediments were discussed. The results show that inorganic carbon in sediments could be divided into five forms: NaCl form, NH3 center dot H2O form, NaOH form, NH2OH center dot HCl form and HCl form. Thereinto, NH2OH center dot HCl form and HCl form account for more than 70% of total inorganic carbon. There was close relationship among every form of inorganic carbon and their correlativity was clearly different with different sedimentary environment except the similar strong positive correlation among NH2OH center dot HCl form, HCl form and total inorganic carbon in all regions of the Jiaozhou Bay. All forms of inorganic carbon were influenced by organic carbon, pH, Eh, Es, nitrogen and phosphorus in sediments, but their influence had different characteristics in different regions. Every farm of inorganic carbon transformed into each other continuously during early diagenesis of sediments and the common phenomenon was that NaCl form, NH3 center dot H2O form, NaOH form and NH2OH center dot HCl form might transform into steady HCl form. NaCl form, NH3 center dot H2O form, NaOH form and NH2OH center dot HCl form could participate in carbon recycle and they are potential carbon source; HCl form may be buried for a long time in sediments, and it may be one of the final resting places of atmospheric CO2. Inorganic carbon which entered into sediments was about 4.98 x 10(10) g in the Jiaozhou Bay every year, in which about 1.47x10(10) g of inorganic carbon might be buried for a long time and about 3.51. x 10(10) g of inorganic carbon might return into seawater and take part in carbon recycling.

Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices

B.M. Brown, M. Marletta, S. Naboko, I. Wood: Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices, J. London Math. Soc., June 2008; 77: 700-718. The full text of this article will be made available in this repository in June 2009 Sponsorship: EPSRC,INTAS

The role of Mittag-Leffler functions in anomalous relaxation

The inertia-corrected Debye model of rotational Brownian motion of polar molecules was generalized by Coffey et al. [Phys. Rev. E, 65, 32 102 (2002)] to describe fractional dynamics and anomalous rotational diffusion. The linear- response theory of the normalized complex susceptibility was given in terms of a Laplace transform and as a function of frequency. The angular-velocity correlation function was parametrized via fractal Mittag-Leffler functions. Here we apply the latter method and complex-contour integral- representation methods to determine the original time-dependent amplitude as an inverse Laplace transform using both analytical and numerical approaches, as appropriate. (C) 2004 Elsevier B.V. All rights reserved.

Modelling the correlation between processing parameters and properties of maraging steels using artificial neural network

An artificial neural network (ANN) model is developed for the analysis and simulation of the correlation between the properties of maraging steels and composition, processing and working conditions. The input parameters of the model consist of alloy composition, processing parameters (including cold deformation degree, ageing temperature, and ageing time), and working temperature. The outputs of the ANN model include property parameters namely: ultimate tensile strength, yield strength, elongation, reduction in area, hardness, notched tensile strength, Charpy impact energy, fracture toughness, and martensitic transformation start temperature. Good performance of the ANN model is achieved. The model can be used to calculate properties of maraging steels as functions of alloy composition, processing parameters, and working condition. The combined influence of Co and Mo on the properties of maraging steels is simulated using the model. The results are in agreement with experimental data. Explanation of the calculated results from the metallurgical point of view is attempted. The model can be used as a guide for further alloy development.

Structure observed in measured electron energy distribution functions in capacitively coupled radio frequency hydrogen plasmas

Electron energy probability functions measured with a passively compensated Langmuir probe in asymmetric capacitively coupled hydrogen and deuterium plasmas exhibit structure. The otherwise relatively continuous distribution appears to have an abrupt peak in electron density near 5 eV. This structure occurs at a higher energy in deuterium than hydrogen and there is a correlation between floating potential and the voltage at which the structure is observed in the second derivative of the I(V) characteristic. While the cause of the structure has yet to be clarified, spectroscopic observations and computer-based hydrogen models indicate that the high energy tail of the distribution is strongly modulated during the radio frequency cycle. The effect of this modulation on plasma properties and probe measurements has yet to be explored. (C) 1999 American Institute of Physics. [S0003-6951(99)00819-0].

Exchange-correlation energy and potential as approximate functionals of occupied and virtual Kohn-Sham orbitals: Application to dissociating H-2

The standard local density approximation and generalized gradient approximations fail to properly describe the dissociation of an electron pair bond, yielding large errors (on the order of 50 kcal/mol) at long bond distances. To remedy this failure, a self-consistent Kohn-Sham (KS) method is proposed with the exchange-correlation (xc) energy and potential depending on both occupied and virtual KS orbitals. The xc energy functional of Buijse and Baerends [Mol. Phys. 100, 401 (2002); Phys. Rev. Lett. 87, 133004 (2001)] is employed, which, based on an ansatz for the xc-hole amplitude, is able to reproduce the important dynamical and nondynamical effects of Coulomb correlation through the efficient use of virtual orbitals. Self-consistent calculations require the corresponding xc potential to be obtained, to which end the optimized effective potential (OEP) method is used within the common energy denominator approximation for the static orbital Green's function. The problem of the asymptotic divergence of the xc potential of the OEP when a finite number of virtual orbitals is used is addressed. The self-consistent calculations reproduce very well the entire H-2 potential curve, describing correctly the gradual buildup of strong left-right correlation in stretched H-2. (C) 2003 American Institute of Physics.

Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study

In this paper, we report a fully ab initio variational Monte Carlo study of the linear and periodic chain of hydrogen atoms, a prototype system providing the simplest example of strong electronic correlation in low dimensions. In particular, we prove that numerical accuracy comparable to that of benchmark density-matrix renormalization-group calculations can be achieved by using a highly correlated Jastrow-antisymmetrized geminal power variational wave function. Furthermore, by using the so-called "modern theory of polarization" and by studying the spin-spin and dimer-dimer correlations functions, we have characterized in detail the crossover between the weakly and strongly correlated regimes of this atomic chain. Our results show that variational Monte Carlo provides an accurate and flexible alternative to highly correlated methods of quantum chemistry which, at variance with these methods, can be also applied to a strongly correlated solid in low dimensions close to a crossover or a phase transition.

Global methylation state at base-pair resolution of the Caulobacter genome throughout the cell cycle.

The Caulobacter DNA methyltransferase CcrM is one of five master cell-cycle regulators. CcrM is transiently present near the end of DNA replication when it rapidly methylates the adenine in hemimethylated GANTC sequences. The timing of transcription of two master regulator genes and two cell division genes is controlled by the methylation state of GANTC sites in their promoters. To explore the global extent of this regulatory mechanism, we determined the methylation state of the entire chromosome at every base pair at five time points in the cell cycle using single-molecule, real-time sequencing. The methylation state of 4,515 GANTC sites, preferentially positioned in intergenic regions, changed progressively from full to hemimethylation as the replication forks advanced. However, 27 GANTC sites remained unmethylated throughout the cell cycle, suggesting that these protected sites could participate in epigenetic regulatory functions. An analysis of the time of activation of every cell-cycle regulatory transcription start site, coupled to both the position of a GANTC site in their promoter regions and the time in the cell cycle when the GANTC site transitions from full to hemimethylation, allowed the identification of 59 genes as candidates for epigenetic regulation. In addition, we identified two previously unidentified N(6)-methyladenine motifs and showed that they maintained a constant methylation state throughout the cell cycle. The cognate methyltransferase was identified for one of these motifs as well as for one of two 5-methylcytosine motifs.

Molecular effects on the cross section for pair production and their importance in the evaluation of the total photonuclear cross section of {^16}O in the {\delta-resonance} region

The screening correction to the coherent pair-production cross section on the oxygen molecule has been calculated using self-consistent relativistic wave functions for the one-center and two-center Coulomb potentials. It is shown that the modification of the wave function due to molecular binding and the interference between contributions from the two atoms have both sizeable effects on the screening correction. The so-obtained coherent pair-production cross section which makes up the largest part of the total atomic cross section was used to evaluate the total nuclear absorption cross section from photon attenuation measurements on liquid oxygen. The result agrees with cross sections for other nuclei if A-scaling is assumed. The molecular effect on the pair cross section amounts to 15 % of the nuclear cross section in the {\delta-resonance} region.