On linear series and a conjecture of D. C. Butler

Let C be a smooth irreducible projective curve of genus g and L a line bundle of degree d generated by a linear subspace V of H-0 (L) of dimension n+1. We prove a conjecture of D. C. Butler on the semistability of the kernel of the evaluation map V circle times O-C -> L and obtain new results on the stability of this kernel. The natural context for this problem is the theory of coherent systems on curves and our techniques involve wall crossing formulae in this theory.

Conservation Properties of the Trapezoidal Rule in Linear Time Domain Analysis of Acoustics and Structures

The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and energy in the case of undamped linear elastodynamics problems, and an ``energy-like measure'' in the case of undamped acoustic problems. These conservation properties, thus, provide a rational basis for using this algorithm. In linear elastodynamics problems, variants of the trapezoidal rule that incorporate ``high-frequency'' dissipation are often used, since the higher frequencies, which are not approximated properly by the standard displacement-based approach, often result in unphysical behavior. Instead of modifying the trapezoidal algorithm, we propose using a hybrid finite element framework for constructing the stiffness matrix. Hybrid finite elements, which are based on a two-field variational formulation involving displacement and stresses, are known to approximate the eigenvalues much more accurately than the standard displacement-based approach, thereby either bypassing or reducing the need for high-frequency dissipation. We show this by means of several examples, where we compare the numerical solutions obtained using the displacement-based and hybrid approaches against analytical solutions.

A micropolar peridynamic theory in linear elasticity

A state-based micropolar peridynamic theory for linear elastic solids is proposed. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant material length scale parameters into peridynamics. Non-ordinary type modeling via constitutive correspondence is adopted here to define the micropolar peridynamic material. Along with a general three dimensional model, homogenized one dimensional Timoshenko type beam models for both the proposed micropolar and the standard non-polar peridynamic variants are derived. The efficacy of the proposed models in analyzing continua with length scale effects is established via numerical simulations of a few beam and plane-stress problems. (C) 2015 Elsevier Ltd. All rights reserved.

Optimal Linear Glauber Model

Contrary to the actual nonlinear Glauber model, the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate () in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

Structural and Magnetic Phase Transformations of Hydroxyapatite-Magnetite Composites under Inert and Ambient Sintering Atmospheres

The present work reports the impact of sintering conditions on the phase stability in hydroxyapatite (HA) magnetite (Fe3O4) bulk composites, which were densified using either pressureless sintering in air or by rapid densification via hot pressing in inert atmosphere. In particular, the phase abundances, structural and magnetic properties of the (1-x)HA-xFe(3)O(4) (x = 5, 10, 20, and 40 wt %) composites were quantified by corroborating results obtained from Rietveld refinement of the X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), and Mossbauer spectroscopy. Post heat treatment phase analysis revealed a major retention of Fe3O4 in argon atmosphere, while it was partially/completely oxidized to hematite (alpha-Fe2O3) in air. Mossbauer results suggest the high-temperature diffusion of Fe3+ into hydroxyapatite lattice, leading to the formation of Fe-doped HA. A preferential occupancy of Fe3+ at the Ca(1) and Ca(2) sites under hot-pressing and conventional sintering conditions, respectively, was observed. The lattice expansion in HA from Rietveld analysis correlated well with the amounts of Fe-doped HA determined from the Mossbauer spectra. Furthermore, hydroxyapatite in the monoliths and composites was delineated to exist in the monoclinic (P2(1)/b) structure as against the widely reported hexagonal (P6(3)/m) crystal lattice. The compositional similarity of iron doping in hydroxyapatite to that of tooth enamel and bone presents HA-Fe3O4 composites as potential orthopedic and dental implant materials.

A Polymatroid Approach to Separable Convex Optimization with Linear Ascending Constraints

We revisit a problem studied by Padakandla and Sundaresan SIAM J. Optim., August 2009] on the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation problems in wireless communication settings. It is also a special case of an optimization of a separable convex function over the bases of a specially structured polymatroid. We give an alternative proof of the correctness of the algorithm of Padakandla and Sundaresan. In the process we relax some of their restrictions placed on the objective function.

Composition dependent multiple structural transformations of myoglobin in aqueous ethanol solution: A combined experimental and theoretical study

Experimental studies (circular dichroism and ultra-violet (UV) absorption spectra) and large scale atomistic molecular dynamics simulations (accompanied by order parameter analyses) are combined to establish a number of remarkable (and unforeseen) structural transformations of protein myoglobin in aqueous ethanol mixture at various ethanol concentrations. The following results are particularly striking. (1) Two well-defined structural regimes, one at x(EtOH) similar to 0.05 and the other at x(EtOH) similar to 0.25, characterized by formation of distinct partially folded conformations and separated by a unique partially unfolded intermediate state at x(EtOH) similar to 0.15, are identified. (2) Existence of non-monotonic composition dependence of (i) radius of gyration, (ii) long range contact order, (iii) residue specific solvent accessible surface area of tryptophan, and (iv) circular dichroism spectra and UV-absorption peaks are observed. Interestingly at x(EtOH) similar to 0.15, time averaged value of the contact order parameter of the protein reaches a minimum, implying that this conformational state can be identified as a molten globule state. Multiple structural transformations well known in water-ethanol binary mixture appear to have considerably stronger effects on conformation and dynamics of the protein. We compare the present results with studies in water-dimethyl sulfoxide mixture where also distinct structural transformations are observed along with variation of co-solvent composition. (C) 2015 AIP Publishing LLC.

Alternative Formulation of the Discrete Linear Quadratic Regulator (DLQR)

In this paper, an alternative apriori and aposteriori formulation has been derived for the discrete linear quadratic regulator (DLQR) in a manner analogous to that used in the discrete Kalman filter. It has been shown that the formulation seamlessly fits into the available formulation of the DLQR and the equivalent terms in the existing formulation and the proposed formulation have been identified. Thereafter, the significance of this alternative formulation has been interpreted in terms of the sensitivity of the controller performances to any changes in the states or to changes in the control inputs. The implications of this alternative formulation to adaptive controller tuning have also been discussed.

On the Bounds of Certain Maximal Linear Codes in a Projective Space

The set of all subspaces of F-q(n) is denoted by P-q(n). The subspace distance d(S)(X, Y) = dim(X) + dim(Y)-2dim(X boolean AND Y) defined on P-q(n) turns it into a natural coding space for error correction in random network coding. A subset of P-q(n) is called a code and the subspaces that belong to the code are called codewords. Motivated by classical coding theory, a linear coding structure can be imposed on a subset of P-q(n). Braun et al. conjectured that the largest cardinality of a linear code, that contains F-q(n), is 2(n). In this paper, we prove this conjecture and characterize the maximal linear codes that contain F-q(n).

A fast algorithm for speech polarity detection using long-term linear prediction

Speech polarity detection is a crucial first step in many speech processing techniques. In this paper, an algorithm is proposed that improvises the existing technique using the skewness of the voice source (VS) signal. Here, the integrated linear prediction residual (ILPR) is used as the VS estimate, which is obtained using linear prediction on long-term frames of the low-pass filtered speech signal. This excludes the unvoiced regions from analysis and also reduces the computation. Further, a modified skewness measure is proposed for decision, which also considers the magnitude of the skewness of the ILPR along with its sign. With the detection error rate (DER) as the performance metric, the algorithm is tested on 8 large databases and its performance (DER=0.20%) is found to be comparable to that of the best technique (DER=0.06%) on both clean and noisy speech. Further, the proposed method is found to be ten times faster than the best technique.

An alternative approach to study nonlinear inviscid flow over arbitrary bottom topography

This paper deals with a new approach to study the nonlinear inviscid flow over arbitrary bottom topography. The problem is formulated as a nonlinear boundary value problem which is reduced to a Dirichlet problem using certain transformations. The Dirichlet problem is solved by applying Plemelj-Sokhotski formulae and it is noticed that the solution of the Dirichlet problem depends on the solution of a coupled Fredholm integral equation of the second kind. These integral equations are solved numerically by using a modified method. The free-surface profile which is unknown at the outset is determined. Different kinds of bottom topographies are considered here to study the influence of bottom topography on the free-surface profile. The effects of the Froude number and the arbitrary bottom topography on the free-surface profile are demonstrated in graphical forms for the subcritical flow. Further, the nonlinear results are validated with the results available in the literature and compared with the results obtained by using linear theory. (C) 2015 Elsevier Inc. All rights reserved.

Observation of phase transformations in cement during hydration

We report the phase transformations in Portland cement before and after hydration. The hydration mechanism was studied in detail by using a full Rietveld refinement of the X-ray diffraction (XRD) patterns, Fourier Transformed Infra-Red (FTIR) spectroscopy, Thermogravimetric Analysis (TGA) and Mossbauer spectroscopy at room temperature. From the Rietveld refinement of XRD data, alite, belite, celite, brown-millerite and low quartz phases were detected and quantified as major phases in dry cement powder. After hydration, calcium carbonate, portlandite and ettringite phases were found to form. A large reduction in the amounts of alite and belite phases were observed suggesting the formation of amorphous C-S-H phase and emphasizing the role of alite phase in flash setting of cement, as justified by the XRD and FTIR spectroscopy. Mossbauer spectra of all the unset samples showed quadrupole split doublets corresponding to the brownmillerite phase which remains unchanged even after about one week of hydration, suggesting that brownmillerite did not transform to other phases during initial stage of hydration process. (C) 2015 Elsevier Ltd. All rights reserved.

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.

Fast and slow climate responses to CO2 and solar forcing: A linear multivariate regression model characterizing transient climate change

Climate change in response to a change in external forcing can be understood in terms of fast response to the imposed forcing and slow feedback associated with surface temperature change. Previous studies have investigated the characteristics of fast response and slow feedback for different forcing agents. Here we examine to what extent that fast response and slow feedback derived from time-mean results of climate model simulations can be used to infer total climate change. To achieve this goal, we develop a multivariate regression model of climate change, in which the change in a climate variable is represented by a linear combination of its sensitivity to CO2 forcing, solar forcing, and change in global mean surface temperature. We derive the parameters of the regression model using time-mean results from a set of HadCM3L climate model step-forcing simulations, and then use the regression model to emulate HadCM3L-simulated transient climate change. Our results show that the regression model emulates well HadCM3L-simulated temporal evolution and spatial distribution of climate change, including surface temperature, precipitation, runoff, soil moisture, cloudiness, and radiative fluxes under transient CO2 and/or solar forcing scenarios. Our findings suggest that temporal and spatial patterns of total change for the climate variables considered here can be represented well by the sum of fast response and slow feedback. Furthermore, by using a simple 1-D heat-diffusion climate model, we show that the temporal and spatial characteristics of climate change under transient forcing scenarios can be emulated well using information from step-forcing simulations alone.

Deviated linear cyclic pursuit

This paper analyses deviated linear cyclic pursuit in which an agent pursues its leader with an angle of deviation in both the continuous- and discrete-time domains, while admitting heterogeneous gains and deviations for the agents. Sufficient conditions for the stability of such systems, in both the domains, are presented in this paper along with the derivation of the reachable set, which is a set of points where the agents may converge asymptotically. The stability conditions are derived based on Gershgorin's theorem. Simulations validating the theoretical results presented in this paper are provided.