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.

Fractional Hilbert transform extensions and associated analytic signal construction

The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations. (C) 2013 Elsevier B.V. All rights reserved.

Mechanistic Insights into a Non-Classical Diffusion Pathway for the Formation of Hollow Intermetallics: A Route to Multicomponent Hollow Structures

Hollow nanostructures are used for various applications including catalysis, sensing, and drug delivery. Methods based on the Kirkendall effect have been the most successful for obtaining hollow nanostructures of various multicomponent systems. The classical Kirkendall effect relies on the presence of a faster diffusing species in the core; the resultant imbalance in flux results in the formation of hollow structures. Here, an alternate non-Kirkendall mechanism that is operative for the formation of hollow single crystalline particles of intermetallic PtBi is demonstrated. The synthesis method involves sequential reduction of Pt and Bi salts in ethylene glycol under microwave irradiation. Detailed analysis of the reaction at various stages indicates that the formation of the intermetallic PtBi hollow nanoparticles occurs in steps. The mechanistic details are elucidated using control experiments. The use of microwave results in a very rapid synthesis of intermetallics PtBi that exhibits excellent electrocatalytic activity for formic acid oxidation reaction. The method presented can be extended to various multicomponent systems and is independent of the intrinsic diffusivities of the species involved.

Solutions of a system of forced Burgers equation

In this article, we obtain explicit solutions of a system of forced Burgers equation subject to some classes of bounded and compactly supported initial data and also subject to certain unbounded initial data. In a series of papers, Rao and Yadav (2010) 1-3] obtained explicit solutions of a nonhomogeneous Burgers equation in one dimension subject to certain classes of bounded and unbounded initial data. Earlier Kloosterziel (1990) 4] represented the solution of an initial value problem for the heat equation, with initial data in L-2 (R-n, e(vertical bar x vertical bar 2/2)), as a series of self-similar solutions of the heat equation in R-n. Here we express the solutions of certain classes of Cauchy problems for a system of forced Burgers equation in terms of self-similar solutions of some linear partial differential equations. (C) 2013 Elsevier Inc. All rights reserved.

Bivariate frequency analysis of floods using a diffusion based kernel density estimator

Recent focus of flood frequency analysis (FFA) studies has been on development of methods to model joint distributions of variables such as peak flow, volume, and duration that characterize a flood event, as comprehensive knowledge of flood event is often necessary in hydrological applications. Diffusion process based adaptive kernel (D-kernel) is suggested in this paper for this purpose. It is data driven, flexible and unlike most kernel density estimators, always yields a bona fide probability density function. It overcomes shortcomings associated with the use of conventional kernel density estimators in FFA, such as boundary leakage problem and normal reference rule. The potential of the D-kernel is demonstrated by application to synthetic samples of various sizes drawn from known unimodal and bimodal populations, and five typical peak flow records from different parts of the world. It is shown to be effective when compared to conventional Gaussian kernel and the best of seven commonly used copulas (Gumbel-Hougaard, Frank, Clayton, Joe, Normal, Plackett, and Student's T) in estimating joint distribution of peak flow characteristics and extrapolating beyond historical maxima. Selection of optimum number of bins is found to be critical in modeling with D-kernel.

A Diffusion-Based Processor Reallocation Strategy for Tracking Multiple Dynamically Varying Weather Phenomena

Many meteorological phenomena occur at different locations simultaneously. These phenomena vary temporally and spatially. It is essential to track these multiple phenomena for accurate weather prediction. Efficient analysis require high-resolution simulations which can be conducted by introducing finer resolution nested simulations, nests at the locations of these phenomena. Simultaneous tracking of these multiple weather phenomena requires simultaneous execution of the nests on different subsets of the maximum number of processors for the main weather simulation. Dynamic variation in the number of these nests require efficient processor reallocation strategies. In this paper, we have developed strategies for efficient partitioning and repartitioning of the nests among the processors. As a case study, we consider an application of tracking multiple organized cloud clusters in tropical weather systems. We first present a parallel data analysis algorithm to detect such clouds. We have developed a tree-based hierarchical diffusion method which reallocates processors for the nests such that the redistribution cost is less. We achieve this by a novel tree reorganization approach. We show that our approach exhibits up to 25% lower redistribution cost and 53% lesser hop-bytes than the processor reallocation strategy that does not consider the existing processor allocation.

Growth of Phases and Diffusion of Components in the W-Pt System

Growth kinetics, phase boundary compositions, interdiffusion coefficients and the relative mobilities of the components are determined in the W-Pt system. The measured phase boundary compositions for the gamma phase are found to be different from the reported phase diagram. The interdiffusion coefficient and the activation energy decrease in the Pt(W) solid solution with increasing W content. An estimation of the parabolic growth constants and average interdiffusion coefficients in the gamma phase indicates that the diffusion process should be explained based on the estimation of diffusion parameters, which otherwise could lead to a wrong conclusion. The estimation of the relative mobilities of the components in the gamma phase indicates that Pt has a much higher diffusion rate than W. This is explained with the help of the crystal structure and the possible point defects present on different sublattices.

Growth of hafnium and zirconium suicides by reactive diffusion

Diffusion controlled growth of the phases in Hf-Si and Zr-Si systems are studied by bulk diffusion couple technique. Only two phases grow in the interdiffusion zone, although several phases are present in both the systems. The location of the Kirkendall marker plane, detected based on the grain morphology, indicates that disilicides grow by the diffusion of Si. Diffusion of the metal species in these phases is negligible. This indicates that vacancies are present mainly on the Si sublattice. The activation energies for integrated diffusion coefficients in the HfSi2 and ZrSi2 are estimated as 394 +/- 37 and 346 +/- 34 kJ mol(-1), respectively. The same is calculated for the HfSi phase as 485 +/- 42 kJ mol(-1). The activation energies for Si tracer diffusion in the HfSi2 and ZrSi2 phases are estimated as 430 +/- 36 and 348 +/- 34 kJ mol(-1), respectively. (C) 2013 Elsevier B.V. All rights reserved.

Reactive diffusion in the Ti-Si system and the significance of the parabolic growth constant

Solid diffusion couple experiments are conducted to analyse the growth mechanism of the phases and the diffusion mechanism of the components in the Ti-Si system. The calculation of the parabolic growth constants and the integrated diffusion coefficients substantiates that the analysis is intrinsically prone to erroneous conclusions if it is based on just the parabolic growth constants determined for a multiphase interdiffusion zone. The location of the marker plane is detected based on the uniform grain morphology in the TiSi2 phase, which indicates that this phase grows mainly because of Si diffusion. The growth mechanism of the phases and morphological evolution in the interdiffusion zone are explained with the help of imaginary diffusion couples. The activation enthalpies for the integrated diffusion coefficient of TiSi2 and the Si tracer diffusion are calculated as 190 +/- 9 and 197 +/- 8 kJ/mol, respectively. The crystal structure, details on the nearest neighbours of the components, and their relative mobilities indicate that the vacancies are mainly present on the Si sublattice.

Growth of hafnium and zirconium suicides by reactive diffusion

Diffusion controlled growth of the phases in Hf-Si and Zr-Si systems are studied by bulk diffusion couple technique. Only two phases grow in the interdiffusion zone, although several phases are present in both the systems. The location of the Kirkendall marker plane, detected based on the grain morphology, indicates that disilicides grow by the diffusion of Si. Diffusion of the metal species in these phases is negligible. This indicates that vacancies are present mainly on the Si sublattice. The activation energies for integrated diffusion coefficients in the HfSi2 and ZrSi2 are estimated as 394 +/- 37 and 346 +/- 34 kJ mol(-1), respectively. The same is calculated for the HfSi phase as 485 +/- 42 kJ mol(-1). The activation energies for Si tracer diffusion in the HfSi2 and ZrSi2 phases are estimated as 430 +/- 36 and 348 +/- 34 kJ mol(-1), respectively. (C) 2013 Elsevier B.V. All rights reserved.

A Constitutive Equation for Grain Boundary Sliding: An Experimental Approach

Although grain boundary sliding (GBS) has been recognized as an important process during high-temperature deformation in crystalline materials, there is paucity in experimental data for characterizing a constitutive equation for GBS. High-temperature tensile creep experiments were conducted, together with measurements of GBS at different strains, stresses, grain sizes, and temperatures. Experimental data obtained on a Mg AZ31 alloy demonstrate that, for the first time, dynamic recrystallization during creep does not alter the contribution of GBS to creep during high-temperature deformation. The experimentally observed invariance of the sliding contribution with strain was used together with the creep data for developing a constitutive equation for GBS in a manner similar to the standard creep equation. Using this new approach, it is demonstrated that the stress, grain size, and temperature dependence for creep and GBS are identical. This is rationalized by a model based on GBS controlled by dislocations, within grains or near-grain boundaries. (C) The Minerals, Metals & Materials Society and ASM International 2013

Cubic Sieve Congruence of the Discrete Logarithm Problem, and fractional part sequences

The Cubic Sieve Method for solving the Discrete Logarithm Problem in prime fields requires a nontrivial solution to the Cubic Sieve Congruence (CSC) x(3) equivalent to y(2)z (mod p), where p is a given prime number. A nontrivial solution must also satisfy x(3) not equal y(2)z and 1 <= x, y, z < p(alpha), where alpha is a given real number such that 1/3 < alpha <= 1/2. The CSC problem is to find an efficient algorithm to obtain a nontrivial solution to CSC. CSC can be parametrized as x equivalent to v(2)z (mod p) and y equivalent to v(3)z (mod p). In this paper, we give a deterministic polynomial-time (O(ln(3) p) bit-operations) algorithm to determine, for a given v, a nontrivial solution to CSC, if one exists. Previously it took (O) over tilde (p(alpha)) time in the worst case to determine this. We relate the CSC problem to the gap problem of fractional part sequences, where we need to determine the non-negative integers N satisfying the fractional part inequality {theta N} < phi (theta and phi are given real numbers). The correspondence between the CSC problem and the gap problem is that determining the parameter z in the former problem corresponds to determining N in the latter problem. We also show in the alpha = 1/2 case of CSC that for a certain class of primes the CSC problem can be solved deterministically in <(O)over tilde>(p(1/3)) time compared to the previous best of (O) over tilde (p(1/2)). It is empirically observed that about one out of three primes is covered by the above class. (C) 2013 Elsevier B.V. All rights reserved.

Diffusion in an elastic medium: A model for macromolecule transport across the nuclear pore complex

Nuclear pore complexes (NPCs) are very selective filters that sit on the membrane of the nucleus and monitor the transport between the cytoplasm and the nucleoplasm. For the central plug of NPC two models have been suggested in the literature. The first suggests that the plug is a reversible hydrogel while the other suggests that it is a polymer brush. Here we propose a model for the transport of a protein through the plug, which is general enough to cover both the models. The protein stretches the plug and creates a local deformation, which together with the protein, we refer to as the bubble. We start with the free energy for creation of the bubble and consider its motion within the plug. The relevant coordinate is the center of the bubble which executes random walk. We find that for faster relaxation of the gel, the diffusion of the bubble is greater. (C) 2014 Elsevier-B.V. All rights reserved.

Diffusion pattern in MSi2 and M5Si3 silicides in group VB (M = V, Nb, Ta) and VIB (M = Mo, W) refractory metal-silicon systems

Group VB and VIB M-Si systems are considered to show an interesting pattern in the diffusion of components with the change in atomic number in a particular group (M = V, Nb, Ta or M = Mo, W, respectively). Mainly two phases, MSi2 and M5Si3 are considered for this discussion. Except for Ta-silicides, the activation energy for the integrated diffusion of MSi2 is always lower than M5Si3. In both phases, the relative mobilities measured by the ratio of the tracer diffusion coefficients, , decrease with an increasing atomic number in the given group. If determined at the same homologous temperature, the interdiffusion coefficients increase with the atomic number of the refractory metal in the MSi2 phases and decrease in the M5Si3 ones. This behaviour features the basic changes in the defect concentrations on different sublattices with a change in the atomic number of the refractory components.

A fractional order proportional integral controller for path following and trajectory tracking of miniature air vehicles

In this paper, a fractional order proportional-integral controller is developed for a miniature air vehicle for rectilinear path following and trajectory tracking. The controller is implemented by constructing a vector field surrounding the path to be followed, which is then used to generate course commands for the miniature air vehicle. The fractional order proportional-integral controller is simulated using the fundamentals of fractional calculus, and the results for this controller are compared with those obtained for a proportional controller and a proportional integral controller. In order to analyze the performance of the controllers, four performance metrics, namely (maximum) overshoot, control effort, settling time and integral of the timed absolute error cost, have been selected. A comparison of the nominal as well as the robust performances of these controllers indicates that the fractional order proportional-integral controller exhibits the best performance in terms of ITAE while showing comparable performances in all other aspects.