Lipschitz Correspondence between Metric Measure Spaces and Random Distance Matrices

Given a metric space with a Borel probability measure, for each integer N, we obtain a probability distribution on N x N distance matrices by considering the distances between pairs of points in a sample consisting of N points chosen independently from the metric space with respect to the given measure. We show that this gives an asymptotically bi-Lipschitz relation between metric measure spaces and the corresponding distance matrices. This is an effective version of a result of Vershik that metric measure spaces are determined by associated distributions on infinite random matrices.

Formulation of a mathematical approach to regional frequency analysis

Estimation of design quantiles of hydrometeorological variables at critical locations in river basins is necessary for hydrological applications. To arrive at reliable estimates for locations (sites) where no or limited records are available, various regional frequency analysis (RFA) procedures have been developed over the past five decades. The most widely used procedure is based on index-flood approach and L-moments. It assumes that values of scale and shape parameters of frequency distribution are identical across all the sites in a homogeneous region. In real-world scenario, this assumption may not be valid even if a region is statistically homogeneous. To address this issue, a novel mathematical approach is proposed. It involves (i) identification of an appropriate frequency distribution to fit the random variable being analyzed for homogeneous region, (ii) use of a proposed transformation mechanism to map observations of the variable from original space to a dimensionless space where the form of distribution does not change, and variation in values of its parameters is minimal across sites, (iii) construction of a growth curve in the dimensionless space, and (iv) mapping the curve to the original space for the target site by applying inverse transformation to arrive at required quantile(s) for the site. Effectiveness of the proposed approach (PA) in predicting quantiles for ungauged sites is demonstrated through Monte Carlo simulation experiments considering five frequency distributions that are widely used in RFA, and by case study on watersheds in conterminous United States. Results indicate that the PA outperforms methods based on index-flood approach.

EFFICIENT QUANTUM RANDOM NUMBER GENERATION USING QUANTUM INDISTINGUISHABILITY

In this paper, we propose a quantum method for generation of random numbers based on bosonic stimulation. Randomness arises through the path-dependent indeterministic amplification of two competing bosonic modes. We show that the process provides an efficient method for macroscopic extraction of microscopic randomness.

Response of vertically loaded pile in clay: a probabilistic study

This study presents the response of a vertically loaded pile in undrained clay considering spatially distributed undrained shear strength. The probabilistic study is performed considering undrained shear strength as random variable and the analysis is conducted using random field theory. The inherent soil variability is considered as source of variability and the field is modeled as two dimensional non-Gaussian homogeneous random field. Random field is simulated using Cholesky decomposition technique within the finite difference program and Monte Carlo simulation approach is considered for the probabilistic analysis. The influence of variance and spatial correlation of undrained shear strength on the ultimate capacity as summation of ultimate skin friction and end bearing resistance of pile are examined. It is observed that the coefficient of variation and spatial correlation distance are the most important parameters that affect the pile ultimate capacity.

Magnetic field induced delocalization in multi-wall carbon nanotube-polystyrene composite at high fields

In well dispersed multi-wall carbon nanotube-polystyrene composite of 15 wt%, with room temperature conductivity of similar to 5 S/cm and resistivity ratio R-2K/R-200K] of similar to 1.4, the temperature dependence of conductivity follows a power-law behavior. The conductivity increases with magnetic field for a wide range of temperature (2-200 K), and power-law fits to conductivity data show that localization length (xi) increases with magnetic field, resulting in a large negative magnetoresistance (MR). At 50T, the negative MR at 8 K is similar to 13% and it shows a maximum at 90K (similar to 25%). This unusually large negative MR indicates that the field is delocalizing the charge carriers even at higher temperatures, apart from the smaller weak localization contribution at T < 20 K. This field-induced delocalization mechanism of MR can provide insight into the intra and inter tube transport. (C) 2013 Elsevier Ltd. All rights reserved.

A finite element method for the Saint-Venant torsion and bending problems for prismatic beams

In this work, we present a finite element formulation for the Saint-Venant torsion and bending problems for prismatic beams. The torsion problem formulation is based on the warping function, and can handle multiply-connected regions (including thin-walled structures), compound and anisotropic bars. Similarly, the bending formulation, which is based on linearized elasticity theory, can handle multiply-connected domains including thin-walled sections. The torsional rigidity and shear centers can be found as special cases of these formulations. Numerical results are presented to show the good coarse-mesh accuracy of both the formulations for both the displacement and stress fields. The stiffness matrices and load vectors (which are similar to those for a variable body force in a conventional structural mechanics problem) in both formulations involve only domain integrals, which makes them simple to implement and computationally efficient. (C) 2014 Elsevier Ltd. All rights reserved.

EVOLUTION OF DEFORMATION FIELDS IN PLOUGHING OF SAND

This paper reports on an experimental study on the ploughing or orthogonal cutting in sand. Plane strain cutting or ploughing experiments were carried out on model Ottawa sand while being imaged at high resolution. The images obtained were further processed using image analysis and the evolution of the velocity and deformation fields were obtained from these analysis. The deformation fields show the presence of a clear shear zone in which the sand accrues deformation. A net change in the direction of the velocity of the sand is also clearly visible. The effective depth of cut of the sand also increases with continuous cutting as the sand reposes on itself. This deformation mechanics at the incipient stages of cutting is similar to that observed in metal cutting.

Formation and Thermal Stability of Gold-Silica Nanohybrids: Insight into the Mechanism and Morphology by Electron Tomography

Gold-silica hybrids are appealing in different fields of applications like catalysis, sensorics, drug delivery, and biotechnology. In most cases, the morphology and distribution of the heterounits play significant roles in their functional behavior. Methods of synthesizing these hybrids, with variable ordering of the heterounits, are replete; however, a complete characterization in three dimensions could not be achieved yet. A simple route to the synthesis of Au-decorated SiO2 spheres is demonstrated and a study on the 3D ordering of the heterounits by scanning transmission electron microscopy (STEM) tomography is presentedat the final stage, intermediate stages of formation, and after heating the hybrid. The final hybrid evolves from a soft self-assembled structure of Au nanoparticles. The hybrid shows good thermal stability up to 400 degrees C, beyond which the Au particles start migrating inside the SiO2 matrix. This study provides an insight in the formation mechanism and thermal stability of the structures which are crucial factors for designing and applying such hybrids in fields of catalysis and biotechnology. As the method is general, it can be applied to make similar hybrids based on SiO2 by tuning the reaction chemistry as needed.

Assessing GCM Convergence for India Using the Variable Convergence Score

General circulation models (GCMs) use transient climate simulations to predict climate conditions in the future. Coarse-grid resolutions and process uncertainties necessitate the use of downscaling models to simulate precipitation. However, in the downscaling models, with multiple GCMs now available, selecting an atmospheric variable from a particular model which is representative of the ensemble mean becomes an important consideration. The variable convergence score (VCS) provides a simple yet meaningful approach to address this issue, providing a mechanism to evaluate variables against each other with respect to the stability they exhibit in future climate simulations. In this study, VCS methodology is applied to 10 atmospheric variables of particular interest in downscaling precipitation over India and also on a regional basis. The nested bias-correction methodology is used to remove the systematic biases in the GCMs simulations, and a single VCS curve is developed for the entire country. The generated VCS curve is expected to assist in quantifying the variable performance across different GCMs, thus reducing the uncertainty in climate impact-assessment studies. The results indicate higher consistency across GCMs for pressure and temperature, and lower consistency for precipitation and related variables. Regional assessments, while broadly consistent with the overall results, indicate low convergence in atmospheric attributes for the Northeastern parts of India.

A VARIABLE SWITCHING FREQUENCY PWM TECHNIQUE FOR INVERTER-FED INDUCTION MOTOR TO ACHIEVE SPREAD SPECTRUM

Voltage Source Inverter (VSI) fed induction motors are widely used in variable speed applications. For inverters using fixed switching frequency PWM, the output harmonic spectra are located at a few discrete frequencies. The ac motordrives powered by these inverters cause acoustic noise. This paper proposes a new variable switching frequency pwm technique and compares its performance with constant switching frequency pwm technique. It is shown that the proposed technique leads to spread spectra of voltages and currents. Also this technique ensures that no lower order harmonics are present and the current THD is comparable to that of fixed switching frequency PWM and is even better for higher modulation indices.

NON-GLYCINE RESIDUES IN THE DISALLOWED REGIONS OF THE RAMACHANDRAN MAP AND THEIR NEIGHBORHOOD PREFERENCES

The allowed and the ``disallowed'' regions in the celebrated Ramachandran map (phi-psi] map) was elegantly deduced by Ramachandran, Ramakrishnan and Sasisekharan even before the protein crystal structures became available. This powerful map was derived based on rigid geometry of the peptide group and later several investigations on protein crystal structures reported the occurrence of a small fraction of the phi-psi] torsion angles in the disallowed region. The question is what factors make these residues adopt disallowed conformations? Is it driven by the necessity to maintain the overall topology or is it associated with function or is it just that the disallowed conformations are extreme limits of the allowed conformations? Today, with the availability of a large number of high resolution crystal structures, we have revisited this problem. Apart from validating some of the earlier findings such as residue propensities, preferred location in the secondary structure, we have explored their spatial neighborhood preferences using the protein structure network PSN] approach developed in our lab. Finally, the structural and functional implications of the disallowed conformations are examined.

Determination of Internal Structures of Heterogeneous Nanocrystals Using Variable-Energy Photoemission Spectroscopy

This article describes the determination of the internal structure of heterogeneous nanoparticle systems including inverted core-shell (CdS core and CdSe shell) and alloyed (CdSeS) quantum dots using depth-resolved, variable-energy X-ray photoelectron spectroscopy (XPS). A unique feature of this work is the combination of photoelectron spectroscopy performed at lower X-ray energies (400-700 eV), to achieve surface sensitivity, with bulk sensitive measurements at high photon energies (>2000 eV), thereby providing detailed information about the whole nanoparticle structure with a great accuracy. The use of high photon energies furthermore allows us to investigate nanoparticles much larger than those studied thus far. This capability is a consequence of the much-increased mean free path of the photoelectron achieved at high excitation energies. Our results show that the actual structures of the synthesized nanoparticles are considerably different from the nominal, targeted structures, which can be post facto rationalized in terms of the reactivity of different constituents.

Optimal sequential wireless relay placement on a random lattice path

Our work is motivated by impromptu (or ``as-you-go'') deployment of wireless relay nodes along a path, a need that arises in many situations. In this paper, the path is modeled as starting at the origin (where there is the data sink, e.g., the control center), and evolving randomly over a lattice in the positive quadrant. A person walks along the path deploying relay nodes as he goes. At each step, the path can, randomly, either continue in the same direction or take a turn, or come to an end, at which point a data source (e.g., a sensor) has to be placed, that will send packets to the data sink. A decision has to be made at each step whether or not to place a wireless relay node. Assuming that the packet generation rate by the source is very low, and simple link-by-link scheduling, we consider the problem of sequential relay placement so as to minimize the expectation of an end-to-end cost metric (a linear combination of the sum of convex hop costs and the number of relays placed). This impromptu relay placement problem is formulated as a total cost Markov decision process. First, we derive the optimal policy in terms of an optimal placement set and show that this set is characterized by a boundary (with respect to the position of the last placed relay) beyond which it is optimal to place the next relay. Next, based on a simpler one-step-look-ahead characterization of the optimal policy, we propose an algorithm which is proved to converge to the optimal placement set in a finite number of steps and which is faster than value iteration. We show by simulations that the distance threshold based heuristic, usually assumed in the literature, is close to the optimal, provided that the threshold distance is carefully chosen. (C) 2014 Elsevier B.V. All rights reserved.

Maximum mass of stable magnetized highly super-Chandrasekhar white dwarfs: stable solutions with varying magnetic fields

We address the issue of stability of recently proposed significantly super-Chandrasekhar white dwarfs. We present stable solutions of magnetostatic equilibrium models for super-Chandrasekhar white dwarfs pertaining to various magnetic field profiles. This has been obtained by self-consistently including the effects of the magnetic pressure gradient and total magnetic density in a general relativistic framework. We estimate that the maximum stable mass of magnetized white dwarfs could be more than 3 solar mass. This is very useful to explain peculiar, overluminous type Ia supernovae which do not conform to the traditional Chandrasekhar mass-limit.

Fermions in Synthetic Non-Abelian Gauge Fields

Quantum emulation property of the cold atoms has generated a lot of interest in studying systems with synthetic gauge fields. In this article, we describe the physics of two component Fermi gas in the presence of synthetic non-Abelian SU(2) gauge fields. Even for the non-interacting system with the gauge fields, there is an interesting change in the topology of the Fermi surface by tuning only the gauge field strength. When a trapping potential is used in conjunction with the gauge fields, the non-interacting system has the ability to produce novel Hamiltonians and show characteristic change in the density profile of the cloud. Without trap, the gauge fields act as an attractive interaction amplifier and for special kinds of gauge field configurations, there are two-body bound states for any attraction even in three dimensions. For a many body system, the gauge fields can induce a crossover from a weak superfluid to a strong superfluid with transition temperature as high as the Fermi temperature. The superfluid state obtained for a very large gauge field strength is a superfluid of new kind of bosons, called ``rashbons'', the properties of which are independent of its constituent two component fermions and are solely determined by the gauge field strength. We also discuss the collective excitations over the superfluid ground states and the experimental relevance of the physics.