Ordering near the percolation threshold in models of two-dimensional interacting bosons with quenched dilution

Randomly diluted quantum boson and spin models in two dimensions combine the physics of classical percolation with the well-known dimensionality dependence of ordering in quantum lattice models. This combination is rather subtle for models that order in two dimensions but have no true order in one dimension, as the percolation cluster near threshold is a fractal of dimension between 1 and 2: two experimentally relevant examples are the O(2) quantum rotor and the Heisenberg antiferromagnet. We study two analytic descriptions of the O(2) quantum rotor near the percolation threshold. First a spin-wave expansion is shown to predict long-ranged order, but there are statistically rare points on the cluster that violate the standard assumptions of spin-wave theory. A real-space renormalization group (RSRG) approach is then used to understand how these rare points modify ordering of the O(2) rotor. A new class of fixed points of the RSRG equations for disordered one-dimensional bosons is identified and shown to support the existence of long-range order on the percolation backbone in two dimensions. These results are relevant to experiments on bosons in optical lattices and superconducting arrays, and also (qualitatively) for the diluted Heisenberg antiferromagnet La-2(Zn,Mg)(x)Cu1-xO4.

A two-dimensional model for crack closure effect in plates under bending

A two-dimensional model is proposed for taking into account the establishment of contact on the compression side of crack faces in plates under bending. An approximate but simple method is developed for evaluating reduction of stress intensity factor due to such ‘crack closure’. Analysis is first carried out permitting interference of the crack faces. Contact forces are then introduced on the crack faces and their magnitudes determined from the consideration that the interference is just eliminated. The method is based partly on finite element analysis and partly on a continuum analysis using Irwin's solution for point loads on the crack line.

Molecular conformation of alamethicin in dimethylsulfoxide solution A two-dimensional n.m.r. study

The solution conformation of alamethicin, a 20-residue antibiotic peptide, has been investigated using two-dimensional n.m.r. spectroscopy. Complete proton resonance assignments of this peptide have been carried out using COSY, SUPERCOSY, RELAY COSY and NOESY two-dimensional spectroscopies. Observation of a large number of nuclear Overhauser effects between sequential backbone amide protons, between backbone amide protons and CβH protons of preceding residues and extensive intramolecular hydrogen bonding patterns of NH protons has established that this polypeptide is in a largely helical conformation. This result is in conformity with earlier reported solid state X-ray results and a recent n.m.r. study in methanol solution (Esposito et al. (1987) Biochemistry26, 1043-1050) but is at variance with an earlier study which favored an extended conformation for the C-terminal half of alamethicin (Bannerjee et al.

Two-dimensional NMR spectroscopy of connected transitions by linear combination of flip angle dependent cosy: An alternative scheme for E.COSY

An alternative pulse scheme which simplifies and improves the recently proposed P.E.COSY experiment is suggested for the retention of connected or unconnected transitions in a coupled spin system. An important feature of the proposed pulse scheme is the improved phase characteristics of the diagonal peaks. A comparison of various experiments designed for this purpose, namely COSY-45, E.COSY, P.E.COSY and the present scheme (A.E.COSY), is also presented. The suppression of unconnected transitions and the measurement of scalar coupling constants and their relative signs are illustrated from A.E.COSY spectra of 2,3-dibromopropionic acid and 2-(2-thienyl)pyridine.

Unsteady mixed convection over two-dimensional and axisymmetric bodies

The unsteady laminar incompressible mixed convection flow over a two-dimensional body (cylinder) and an axisymmetric body (sphere) has been studied when the buboyancy forces arise from both thermal and mass diffusion and the unsteadiness in the flow field is introduced by the time dependent free stream velocity. The nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The results indicate that for the thermally assisting flow the local skin friction, heat transfer and mass diffusion are enhanced when the buoyancy force from mass diffusion assists the thermal buoyancy force. But this trend is opposite for the thermally opposing flow. The point of zero skin friction moves upstream due to unsteadiness. No singularity is observed at the point of zero skin friction for unsteady flow unlike steady flow. The flow reversal is observed after a certain instant of time. The velocity overshoot occurs for assisting flows.

On the two-dimensional thermoelectric power in quantum wells of non-parabolic materials under magnetic quantization

We present a simplified theoretical formulation of the thermoelectric power (TP) under magnetic quantization in quantum wells (QWs) of nonlinear optical materials on the basis of a newly formulated magneto-dispersion law. We consider the anisotropies in the effective electron masses and the spin-orbit constants within the framework of k.p formalism by incorporating the influence of the crystal field splitting. The corresponding results for III-V materials form a special case of our generalized analysis under certain limiting conditions. The TP in QWs of Bismuth, II-VI, IV-VI and stressed materials has been studied by formulating appropriate electron magneto-dispersion laws. We also address the fact that the TP exhibits composite oscillations with a varying quantizing magnetic field in QWs of n-Cd3As2, n-CdGeAs2, n-InSb, p-CdS, stressed InSb, PbTe and Bismuth. This reflects the combined signatures of magnetic and spatial quantizations of the carriers in such structures. The TP also decreases with increasing electron statistics and under the condition of non-degeneracy, all the results as derived in this paper get transformed into the well-known classical equation of TP and thus confirming the compatibility test. We have also suggested an experimental method of determining the elastic constants in such systems with arbitrary carrier energy spectra from the known value of the TP. (C) 2010 Elsevier Ltd. All rights reserved.

Two-dimensional fuzzy fault tree analysis for chlorine release from a chlor-alkali industry using expert elicitation

The hazards associated with major accident hazard (MAN) industries are fire, explosion and toxic gas releases. Of these, toxic gas release is the worst as it has the potential to cause extensive fatalities. Qualitative and quantitative hazard analyses are essential for the identification and quantification of these hazards related to chemical industries. Fault tree analysis (FTA) is an established technique in hazard identification. This technique has the advantage of being both qualitative and quantitative, if the probabilities and frequencies of the basic events are known. This paper outlines the estimation of the probability of release of chlorine from storage and filling facility of chlor-alkali industry using FTA. An attempt has also been made to arrive at the probability of chlorine release using expert elicitation and proven fuzzy logic technique for Indian conditions. Sensitivity analysis has been done to evaluate the percentage contribution of each basic event that could lead to chlorine release. Two-dimensional fuzzy fault tree analysis (TDFFTA) has been proposed for balancing the hesitation factor involved in expert elicitation. (C) 2010 Elsevier B.V. All rights reserved.

Optimization of two-dimensional NMR by matched accumulation

It is well known that in the time-domain acquisition of NMR data, signal-to-noise (S/N) improves as the square root of the number of transients accumulated. However, the amplitude of the measured signal varies during the time of detection, having a functional form dependent on the coherence detected. Matching the time spent signal averaging to the expected amplitude of the signal observed should also improve the detected signal-to-noise. Following this reasoning, Barna et al. (J Magn. Reson.75, 384, 1987) demonstrated the utility of exponential sampling in one- and two-dimensional NMR, using maximum-entropy methods to analyze the data. It is proposed here that for two-dimensional experiments the exponential sampling be replaced by exponential averaging. The data thus collected can be analyzed by standard fast-Fourier-transform routines. We demonstrate the utility of exponential averaging in 2D NOESY spectra of the protein ubiquitin, in which an enhanced SIN is observed. It is also shown that the method acquires delayed double-quantum-filtered COSY without phase distortion.

Neural network approach for the two-dimensional assignment problem

A neural network approach for solving the two-dimensional assignment problem is proposed. The design of the neural network is discussed and simulation results are presented. The neural network obtains 10-15% lower cost placements on the examples considered, than the adjacent pairwise exchange method.

Analytical solution of the laminar mean flow wave equation in a lined or unlined two-dimensional rectangular duct

The prediction of the sound attenuation in lined ducts with sheared mean flow has been a topic of research for many years. This involves solving the sheared mean flow wave equation, satisfying the relevant boundary condition. As far as the authors' knowledge goes, this has always been done using numerical techniques. Here, an analytical solution is presented for the wave propagation in two-dimensional rectangular lined ducts with laminar mean flow. The effect of laminar mean flow is studied for both the downstream and the upstream wave propagation. The attenuation values predicted for the laminar mean flow case are compared with those for the case of uniform mean flow. Analytical expressions are derived for the transfer matrices.

Integral method for the calculation of incompressible two-dimensional transitional boundary layers

The method proposed here considers the mean flow in the transition zone as a linear combination of the laminar and turbulent boundary layer in proportions determined by the transitional intermittency, the component flows being calculated by approximate integral methods. The intermittency distribution adopted takes into account the possibility of subtransitions within the zone in the presence of strong pressure gradients. A new nondimensional spot formation rate, whose value depends on the pressure gradient, is utilized to estimate the extent of the transition zone. Onset location is determined by a correlation that takes into account freestream turbulence and facility-specific residual disturbances in test data. Extensive comparisons with available experimental results in strong pressure gradients show that the proposed method performs at least as well as differential models, in many cases better, and is always faster.

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)].

Phase diagram of the two-dimensional disordered Hubbard model in the Hartree-Fock approximation

Ground-state properties of the two-dimensional Hubbard model with point-defect disorder are investigated numerically in the Hartree-Fock approximation. The phase diagram in the p(point defect concentration)-delta(deviation from half filling) plane exhibits antiferromagnetic, spin-density-wave, paramagnetic, and spin-glass-like phases. The disorder stabilizes the antiferromagnetic phase relative to the spin-density-wave phase. The presence of U strongly enhances the localization in the antiferromagnetic phase. The spin-density-wave and spin-glass-like phases are weakly localized.