On shock dynamics

This is in continuation of our paper On the propagation of a multi-dimensional shock of arbitrary strength’ published earlier in this journal (Srinivasan and Prasad [9]). We had shown in our paper that Whitham’s shock dynamics, based on intuitive arguments, cannot be relied on for flows other than those involving weak shocks and that too with uniform flow behind the shock. Whitham [12] refers to this as misinterpretation of his approximation and claims that his theory is not only correct but also provides a natural closure of the open system of the equations of Maslov [3]. The main aim of this note is to refute Whitham’s claim with the help of an example and a numerical integration of a problem in gasdynamics.

On the Production of Anorexic Plan Diagrams

A "plan diagram" is a pictorial enumeration of the execution plan choices of a database query optimizer over the relational selectivity space. We have shown recently that, for industrial-strength database engines, these diagrams are often remarkably complex and dense, with a large number of plans covering the space. However, they can often be reduced to much simpler pictures, featuring significantly fewer plans, without materially affecting the query processing quality. Plan reduction has useful implications for the design and usage of query optimizers, including quantifying redundancy in the plan search space, enhancing useability of parametric query optimization, identifying error-resistant and least-expected-cost plans, and minimizing the overheads of multi-plan approaches. We investigate here the plan reduction issue from theoretical, statistical and empirical perspectives. Our analysis shows that optimal plan reduction, w.r.t. minimizing the number of plans, is an NP-hard problem in general, and remains so even for a storage-constrained variant. We then present a greedy reduction algorithm with tight and optimal performance guarantees, whose complexity scales linearly with the number of plans in the diagram for a given resolution. Next, we devise fast estimators for locating the best tradeoff between the reduction in plan cardinality and the impact on query processing quality. Finally, extensive experimentation with a suite of multi-dimensional TPCH-based query templates on industrial-strength optimizers demonstrates that complex plan diagrams easily reduce to "anorexic" (small absolute number of plans) levels incurring only marginal increases in the estimated query processing costs.

Performance Modeling based on Multidimensional Surface Learning for Performance Predictions of Parallel Applications in Non-Dedicated Environments

Modeling the performance behavior of parallel applications to predict the execution times of the applications for larger problem sizes and number of processors has been an active area of research for several years. The existing curve fitting strategies for performance modeling utilize data from experiments that are conducted under uniform loading conditions. Hence the accuracy of these models degrade when the load conditions on the machines and network change. In this paper, we analyze a curve fitting model that attempts to predict execution times for any load conditions that may exist on the systems during application execution. Based on the experiments conducted with the model for a parallel eigenvalue problem, we propose a multi-dimensional curve-fitting model based on rational polynomials for performance predictions of parallel applications in non-dedicated environments. We used the rational polynomial based model to predict execution times for 2 other parallel applications on systems with large load dynamics. In all the cases, the model gave good predictions of execution times with average percentage prediction errors of less than 20%

Influence of planning and governance on the level of urban services

A theoretical framework to analyse the interaction of planning and governance on the extent of outgrowth and level of services is proposed. An indicator framework for quantifying sprawl is also proposed and the same is operationalised for Bangalore. The indicators comprise spatial metrics (derived from temporal satellite remote sensing data) and other metrics obtained from a house-hold survey. The interaction of different indicators with respect to the core city and the outgrowth is determined by multi-dimensional scaling. The analysis reveals the underlying similarities (and dissimilarities) that relate with the different governance structures that prevail here. The paper concludes outlining the challenges in addressing urban sprawl while ensuring adequate level of services that planning and governance have to ensure towards achieving sustainable urbanisation.

An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

Multidimensional data reconstruction for two color fluorescence microscopy

We propose an iterative data reconstruction technique specifically designed for multi-dimensional multi-color fluorescence imaging. Markov random field is employed (for modeling the multi-color image field) in conjunction with the classical maximum likelihood method. It is noted that, ill-posed nature of the inverse problem associated with multi-color fluorescence imaging forces iterative data reconstruction. Reconstruction of three-dimensional (3D) two-color images (obtained from nanobeads and cultured cell samples) show significant reduction in the background noise (improved signal-to-noise ratio) with an impressive overall improvement in the spatial resolution (approximate to 250 nm) of the imaging system. Proposed data reconstruction technique may find immediate application in 3D in vivo and in vitro multi-color fluorescence imaging of biological specimens. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4769058]

Simultaneous acquisition of three NMR spectra in a single experiment for rapid resonance assignments in metabolomics

NMR-based approach to metabolomics typically involves the collection of two-dimensional (2D) heteronuclear correlation spectra for identification and assignment of metabolites. In case of spectral overlap, a 3D spectrum becomes necessary, which is hampered by slow data acquisition for achieving sufficient resolution. We describe here a method to simultaneously acquire three spectra (one 3D and two 2D) in a single data set, which is based on a combination of different fast data acquisition techniques such as G-matrix Fourier transform (GFT) NMR spectroscopy, parallel data acquisition and non-uniform sampling. The following spectra are acquired simultaneously: (1) C-13 multiplicity edited GFT (3,2)D HSQC-TOCSY, (2) 2D H-1- H-1] TOCSY and (3) 2D C-13- H-1] HETCOR. The spectra are obtained at high resolution and provide high-dimensional spectral information for resolving ambiguities. While the GFT spectrum has been shown previously to provide good resolution, the editing of spin systems based on their CH multiplicities further resolves the ambiguities for resonance assignments. The experiment is demonstrated on a mixture of 21 metabolites commonly observed in metabolomics. The spectra were acquired at natural abundance of C-13. This is the first application of a combination of three fast NMR methods for small molecules and opens up new avenues for high-throughput approaches for NMR-based metabolomics.

Organic fluorine involved intramolecular hydrogen bonds in the derivatives of imides: NMR evidence corroborated by DFT based theoretical calculations

The rare occurrence of intramolecular hydrogen bonds (HBs) of the type N-H center dot center dot center dot F-C is detected in the derivatives of imides in a low polarity solvent by using multi-dimensional and multinuclear NMR experiments. The observation of (1h)J(FH), (2h)J(FN), and (2h)J(FF), where the spin magnetization is transmitted through space among the interacting NMR active nuclei, provided strong and unambiguous evidence for the existence of intra-molecular HBs. The variation in the chemical shifts of labile protons depending on physical conditions, such as the solvent dilution and the systematic alteration of temperature confirmed the presence of weak interactions through intramolecular HBs in all the investigated fluorine substituted molecules. The self or cross dimerization of molecules is unequivocally discarded by the analysis of the rates of diffusion obtained using pseudo-two dimensional DOSY experiments. The Density Function Theory (DFT) calculations based on the Quantum Theory of Atoms In Molecules (QTAIM) and Non Covalent Interaction (NCI), are in close agreement with the NMR experimental findings.

ASYMPTOTIC PRESERVING SCHEME FOR A KINETIC MODEL DESCRIBING IN COMPRESSIBLE FLUIDS

The kinetic theory of fluid turbulence modeling developed by Degond and Lemou in 7] is considered for further study, analysis and simulation. Starting with the Boltzmann like equation representation for turbulence modeling, a relaxation type collision term is introduced for isotropic turbulence. In order to describe some important turbulence phenomenology, the relaxation time incorporates a dependency on the turbulent microscopic energy and this makes difficult the construction of efficient numerical methods. To investigate this problem, we focus here on a multi-dimensional prototype model and first propose an appropriate change of frame that makes the numerical study simpler. Then, a numerical strategy to tackle the stiff relaxation source term is introduced in the spirit of Asymptotic Preserving Schemes. Numerical tests are performed in a one-dimensional framework on the basis of the developed strategy to confirm its efficiency.

PLUTO plus : Near-Complete Modeling of Affine Transformations for Parallelism and Locality

Affine transformations have proven to be very powerful for loop restructuring due to their ability to model a very wide range of transformations. A single multi-dimensional affine function can represent a long and complex sequence of simpler transformations. Existing affine transformation frameworks like the Pluto algorithm, that include a cost function for modern multicore architectures where coarse-grained parallelism and locality are crucial, consider only a sub-space of transformations to avoid a combinatorial explosion in finding the transformations. The ensuing practical tradeoffs lead to the exclusion of certain useful transformations, in particular, transformation compositions involving loop reversals and loop skewing by negative factors. In this paper, we propose an approach to address this limitation by modeling a much larger space of affine transformations in conjunction with the Pluto algorithm's cost function. We perform an experimental evaluation of both, the effect on compilation time, and performance of generated codes. The evaluation shows that our new framework, Pluto+, provides no degradation in performance in any of the Polybench benchmarks. For Lattice Boltzmann Method (LBM) codes with periodic boundary conditions, it provides a mean speedup of 1.33x over Pluto. We also show that Pluto+ does not increase compile times significantly. Experimental results on Polybench show that Pluto+ increases overall polyhedral source-to-source optimization time only by 15%. In cases where it improves execution time significantly, it increased polyhedral optimization time only by 2.04x.

Detection of quantum well induced single degenerate-transition-dipoles in ZnO nanorods

Quantifying and characterising atomic defects in nanocrystals is difficult and low-throughput using the existing methods such as high resolution transmission electron microscopy (HRTEM). In this article, using a defocused wide-field optical imaging technique, we demonstrate that a single ultrahigh-piezoelectric ZnO nanorod contains a single defect site. We model the observed dipole-emission patterns from optical imaging with a multi-dimensional dipole and find that the experimentally observed dipole pattern and model-calculated patterns are in excellent agreement. This agreement suggests the presence of vertically oriented degenerate-transition-dipoles in vertically aligned ZnO nanorods. The HRTEM of the ZnO nanorod shows the presence of a stacking fault, which generates a localised quantum well induced degenerate-transition-dipole. Finally, we elucidate that defocused wide-field imaging can be widely used to characterise defects in nanomaterials to answer many difficult questions concerning the performance of low-dimensional devices, such as in energy harvesting, advanced metal-oxide-semiconductor storage, and nanoelectromechanical and nanophotonic devices.

Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains

It is known that all the vector bundles of the title can be obtained by holomorphic induction from representations of a certain parabolic group on finite-dimensional inner product spaces. The representations, and the induced bundles, have composition series with irreducible factors. We write down an equivariant constant coefficient differential operator that intertwines the bundle with the direct sum of its irreducible factors. As an application, we show that in the case of the closed unit ball in C-n all homogeneous n-tuples of Cowen-Douglas operators are similar to direct sums of certain basic n-tuples. (c) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Information theory and one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. It is suggested, for the probability distribution of the transfer matrix of the conductor, the distribution of maximum information-entropy, constrained by the following physical requirements: 1) flux conservation, 2) time-reversal invariance and 3) scaling, with the length of the conductor, of the two lowest cumulants of ζ, where = sh2ζ. The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

Information theory and resistance fluctuations in one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. For the probability distribution of the transfer matrix R of the conductor we propose a distribution of maximum information entropy, constrained by the following physical requirements: (1) flux conservation, (2) time-reversal invariance, and (3) scaling with the length of the conductor of the two lowest cumulants of ω, where R=exp(iω→⋅Jbhat). The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

A transfer matrix approach for evaluation of the response of a multi-layer infinite plate to a two-dimensional pressure excitation

A 6 X 6 transfer matrix is presented to evaluate the response of a multi-layer infinite plate to a given two-dimensional pressure excitation on one of its faces or, alternatively, to evaluate the acoustic pressure distribution excited by the normal velocity components of the radiating surfaces. It is shown that the present transfer matrix is a general case embodying the transfer matrices of normal excitation and one-dimensional pressure excitation due to an oblique incident wave. It is also shown that the present transfer matrix obeys the necessary checks to categorize the physically symmetric multi-layer plate as dynamically symmetric. Expressions are derived to obtain the wave propagation parameters, such as the transmission, absorption and reflection coefficients, in terms of the elements of the transfer matrix presented. Numerical results for transmission loss and reflection coefficients of a two-layer configuration are presented to illustrate the effect of angles of incidence, layer characteristics and ambient media.