UNIQUENESS OF SOLUTIONS TO SCHRODINGER EQUATIONS ON H-TYPE GROUPS

This paper deals with the Schrodinger equation i partial derivative(s)u(z, t; s) - Lu(z, t; s) = 0; where L is the sub-Laplacian on the Heisenberg group. Assume that the initial data f satisfies vertical bar f(z, t)vertical bar less than or similar to q(alpha)(z, t), where q(s) is the heat kernel associated to L. If in addition vertical bar u(z, t; s(0))vertical bar less than or similar to q(beta)(z, t), for some s(0) is an element of R \textbackslash {0}, then we prove that u(z, t; s) = 0 for all s is an element of R whenever alpha beta < s(0)(2). This result holds true in the more general context of H-type groups. We also prove an analogous result for the Grushin operator on Rn+1.

Comparative Study of Protein Unfolding in Aqueous Urea and Dimethyl Sulfoxide Solutions: Surface Polarity, Solvent Specificity, and Sequence of Secondary Structure Melting

Elucidation of possible pathways between folded (native) and unfolded states of a protein is a challenging task, as the intermediates are often hard to detect. Here, we alter the solvent environment in a controlled manner by choosing two different cosolvents of water, urea, and dimethyl sulfoxide (DMSO) and study unfolding of four different proteins to understand the respective sequence of melting by computer simulation methods. We indeed find interesting differences in the sequence of melting of alpha helices and beta sheets in these two solvents. For example, in 8 M urea solution, beta-sheet parts of a protein are found to unfold preferentially, followed by the unfolding of alpha helices. In contrast, 8 M DMSO solution unfolds alpha helices first, followed by the separation of beta sheets for the majority of proteins. Sequence of unfolding events in four different alpha/beta proteins and also in chicken villin head piece (HP-36) both in urea and DMSO solutions demonstrate that the unfolding pathways are determined jointly by relative exposure of polar and nonpolar residues of a protein and the mode of molecular action of a solvent on that protein.

Phase transformation, improved ferroelectric and magnetic properties of (1-x) BiFeO3-xPb(Zr0.52Ti0.48)O-3 solid solutions

The authors prepared (1 - x) BiFeO3 - (x)Pb(Zr0.52Ti0.48)O-3 for x <= 0.30 by sol-gel method and investigated the material's structures, magnetic and electrical properties. Detailed Rietveld analysis of X-ray diffraction data revealed that the system retains distorted rhombohedral R3c structure for x <= 0.10 but transforms to monoclinic (Cc) structure for x > 0.10. Disappearance of some Raman modes corresponding to A1 modes and the decrease in the intensities of the remaining A1 modes with increasing x in the Raman spectra, which is a clear indication of structural modification and symmetry changes brought about by PZT doping. Enhanced magnetization with PZT doping content may be attributed to the gradual change and destruction in the spin cycloid structure of BiFeO3. The leakage current density at 3.5 kV/cm was reduced by approximately three orders of magnitude by doping PZT (x = 0.30), compared with BFO ceramics. (C) 2014 AIP Publishing LLC.

Frequency Domain Based Solution for Certain Class of Wave Equations: An exhaustive study of Numerical Solutions

The paper discusses the frequency domain based solution for a certain class of wave equations such as: a second order partial differential equation in one variable with constant and varying coefficients (Cantilever beam) and a coupled second order partial differential equation in two variables with constant and varying coefficients (Timoshenko beam). The exact solution of the Cantilever beam with uniform and varying cross-section and the Timoshenko beam with uniform cross-section is available. However, the exact solution for Timoshenko beam with varying cross-section is not available. Laplace spectral methods are used to solve these problems exactly in frequency domain. The numerical solution in frequency domain is done by discretisation in space by approximating the unknown function using spectral functions like Chebyshev polynomials, Legendre polynomials and also Normal polynomials. Different numerical methods such as Galerkin Method, Petrov- Galerkin method, Method of moments and Collocation method or the Pseudo-spectral method in frequency domain are studied and compared with the available exact solution. An approximate solution is also obtained for the Timoshenko beam with varying cross-section using Laplace Spectral Element Method (LSEM). The group speeds are computed exactly for the Cantilever beam and Timoshenko beam with uniform cross-section and is compared with the group speeds obtained numerically. The shear mode and the bending modes of the Timoshenko beam with uniform cross-section are separated numerically by applying a modulated pulse as the shear force and the corresponding group speeds for varying taper parameter in are obtained numerically by varying the frequency of the input pulse. An approximate expression for calculating group speeds corresponding to the shear mode and the bending mode, and also the cut-off frequency is obtained. Finally, we show that the cut-off frequency disappears for large in, for epsilon > 0 and increases for large in, for epsilon < 0.

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.

Evaluating FuncSION: A software for automated synthesis of design solutions for stimulating ideation during mechanical conceptual design

The goal of the work reported in this paper is to use automated, combinatorial synthesis to generate alternative solutions to be used as stimuli by designers for ideation. FuncSION, a computational synthesis tool that can automatically synthesize solution concepts for mechanical devices by combining building blocks from a library, is used for this purpose. The objectives of FuncSION are to help generate a variety of functional requirements for a given problem and a variety of concepts to fulfill these functions. A distinctive feature of FuncSION is its focus on automated generation of spatial configurations, an aspect rarely addressed by other computational synthesis programs. This paper provides an overview of FuncSION in terms of representation of design problems, representation of building blocks, and rules with which building blocks are combined to generate concepts at three levels of abstraction: topological, spatial, and physical. The paper then provides a detailed account of evaluating FuncSION for its effectiveness in providing stimuli for enhanced ideation.

SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|(n-1)e(beta vertical bar x vertical bar 2)/2, beta >= 0, x is an element of R-n. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.

Modal tailoring and closed-form solutions for rotating non-uniform Euler-Bernoulli beams

In this paper, the free vibration of a rotating Euler-Bernoulli beam is studied using an inverse problem approach. We assume a polynomial mode shape function for a particular mode, which satisfies all the four boundary conditions of a rotating beam, along with the internal nodes. Using this assumed mode shape function, we determine the linear mass and fifth order stiffness variations of the beam which are typical of helicopter blades. Thus, it is found that an infinite number of such beams exist whose fourth order governing differential equation possess a closed form solution for certain polynomial variations of the mass and stiffness, for both cantilever and pinned-free boundary conditions corresponding to hingeless and articulated rotors, respectively. A detailed study is conducted for the first, second and third modes of a rotating cantilever beam and the first and second elastic modes of a rotating pinned-free beam, and on how to pre-select the internal nodes such that the closed-form solutions exist for these cases. The derived results can be used as benchmark solutions for the validation of rotating beam numerical methods and may also guide nodal tailoring. (C) 2014 Elsevier Ltd. All rights reserved.

Recent NMR Methodological Developments for Chiral Analysis in Isotropic Solutions

Chiral auxiliaries are used for NMR spectroscopic study of enantiomers. Often the presence of impurities, severe overlap of peaks, excessive line broadening and complex multiplicity pattern restricts the chiral analysis using 1D H-1 NMR spectrum. There are few approaches to resolve the overlapped peaks. One approach is to use suitable chiral auxiliary, which induces large chemical shift difference between the discriminated peaks (Delta delta(R,S)) and minimize the overlap. Another direction of approach is to design appropriate NMR experiments to circumvent some of these problems, viz, enhancing spectral resolution, unravelling the superimposed spectra of enantiomers, and reduction of spectral complexity. Large number of NMR techniques, such as two dimensional selective F-1 decoupling, RES-TOCSY, multiple quantum detection, frequency selective homodecoupling, band selective homodecoupling, broadband homodecoupling, etc. have been reported for such a purpose. Many of these techniques have aided in chiral analysis for molecules of diverse functionality in the presence of chiral auxiliaries. The present review summarizes the recently reported NMR experimental methodologies, with a special emphasis on the work carried out in authors' laboratory.

Synergistic Effect of Mo plus Cu Codoping on the Photocatalytic Behavior of Metastable TiO2 Solid Solutions

Codoping with Cu and Mo is shown to have a synergistic effect on the photocatalytic activity of TiO2. The enhancement in activity is observed only if the synthesis route results in TiO2 in which (Cu, Mo) codopants are forced into the TiO2 lattice. Using X-ray photoelectron spectroscopy, Cu and Mo are shown to be present in the +2 and +6 oxidation states, respectively. A systematic study of the ternary system shows that TiO2 containing 6 mol % CuO and 1.5 mol % MoO3 is the most active ternary composition. Ab initio calculations show that codoping of TiO2 using (Mo, Cu) introduces levels above the valence band, and below the conduction band, resulting in a significant reduction in the band gap (similar to 0.8 eV). However, codoping also introduces deep defect states, which can have a deleterious impact on photoactivity. This helps rationalize the narrow compositional window over which the enhancement in photocatalytic activity is observed.

Mode coupling theory analysis of electrolyte solutions: Time dependent diffusion, intermediate scattering function, and ion solvation dynamics

A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion diffusion, (ii) intermediate scattering function of the constituent ions, and (iii) ion solvation dynamics in electrolyte solution. Brownian dynamics with implicit water molecules and molecular dynamics method with explicit water are used to check the theoretical predictions. The time dependence of ionic self-diffusion coefficient and the corresponding intermediate scattering function evaluated from our MCT approach show quantitative agreement with early experimental and present Brownian dynamic simulation results. With increasing concentration, the dispersion of electrolyte friction is found to occur at increasingly higher frequency, due to the faster relaxation of the ion atmosphere. The wave number dependence of intermediate scattering function, F(k, t), exhibits markedly different relaxation dynamics at different length scales. At small wave numbers, we find the emergence of a step-like relaxation, indicating the presence of both fast and slow time scales in the system. Such behavior allows an intriguing analogy with temperature dependent relaxation dynamics of supercooled liquids. We find that solvation dynamics of a tagged ion exhibits a power law decay at long times-the decay can also be fitted to a stretched exponential form. The emergence of the power law in solvation dynamics has been tested by carrying out long Brownian dynamics simulations with varying ionic concentrations. The solvation time correlation and ion-ion intermediate scattering function indeed exhibit highly interesting, non-trivial dynamical behavior at intermediate to longer times that require further experimental and theoretical studies. (c) 2015 AIP Publishing LLC.

Ab Initio Molecular Dynamics Simulations of Amino Acids in Aqueous Solutions: Estimating pK(a) Values from Metadynamics Sampling

Changes in the protonation and deprotonation of amino acid residues in proteins play a key role in many biological processes and pathways. Here, we report calculations of the free-energy profile for the protonation deprotonation reaction of the 20 canonical alpha amino acids in aqueous solutions using ab initio Car-Parrinello molecular dynamics simulations coupled with metad-ynamics sampling. We show here that the calculated change in free energy of the dissociation reaction provides estimates of the multiple pK(a) values of the amino acids that are in good agreement with experiment. We use the bond-length-dependent number of the protons coordinated to the hydroxyl oxygen of the carboxylic and the amine groups as the collective variables to explore the free-energy profiles of the Bronsted acid-base chemistry of amino acids in aqueous solutions. We ensure that the amino acid undergoing dissociation is solvated by at least three hydrations shells with all water molecules included in the simulations. The method works equally well for amino acids with neutral, acidic and basic side chains and provides estimates of the multiple pK(a) values with a mean relative error, with respect to experimental results, of 0.2 pK(a) units.

PREDICTION OF TRANSITIONAL AND SEPARATED BOUNDARY LAYERS IN A COMPRESSOR CASCADE

Numerical simulations were performed of experiments from a cascade of stator blades at three low Reynolds numbers representative of flight conditions. Solutions were assessed by comparing blade surface pressures, velocity and turbulence intensity along blade normals at several stations along the suction surface and in the wake. At Re = 210,000 and 380,000 the laminar boundary layer over the suction surface separates and reattaches with significant turbulence fluctuations. A new 3-equation transition model, the k-k(L)-omega model, was used to simulate this flow. Predicted locations of the separation bubble, and profiles of velocity and turbulence fluctuations on blade-normal lines at various stations along the blade were found to be quite close to measurements. Suction surface pressure distributions were not as close at the lower Re. The solution with the standard k-omega SST model showed significant differences in all quantities. At Re = 640,000 transition occurs earlier and it is a turbulent boundary layer that separates near the trailing edge. The solution with the Reynolds stress model was found to be quite close to the experiment in the separated region also, unlike the k-omega SST solution. Three-dimensional computations were performed at Re = 380,000 and 640,000. In both cases there were no significant differences between the midspan solution from 3D computations and the 2D solutions. However, the 3D solutions exhibited flow features observed in the experiments the nearly 2D structure of the flow over most of the span at 380,000 and the spanwise growth of corner vortices from the endwall at 640,000.

Ab Initio MD Simulations of the Bronsted Acidity of Glutathione in Aqueous Solutions: Predicting pK(a) Shifts of the Cysteine Residue

The tripeptide glutathione (GSH) is one of the most abundant peptides and the major repository for nonprotein sulfur in both animal and plant cells. It plays a critical role in intracellular oxidative stress management by the reversible formation of glutathione disulfide with the thiol-disulfide pair acting as a redox buffer. The state of charge of the ionizable groups of GSH can influence the redox couple, and hence the pK(a) value of the cysteine residue of GSH is critical to its functioning. Here we report ab initio Car-Parrinello molecular dynamics simulations of glutathione solvated by 200 water molecules, all of which are considered in the simulation. We show that the free-energy landscape for the protonation-deprotonation reaction of the cysteine residue of GSH computed using metadynamics sampling provides shift in the dissociation constant values as compared with the isolated accurate estimates of the pK(a) and correctly predicts the cysteine amino acid.