On the solution of bivariate population balance equations for aggregation: Pivotwise expansion of solution domain

The solution of a bivariate population balance equation (PBE) for aggregation of particles necessitates a large 2-d domain to be covered. A correspondingly large number of discretized equations for particle populations on pivots (representative sizes for bins) are solved, although at the end only a relatively small number of pivots are found to participate in the evolution process. In the present work, we initiate solution of the governing PBE on a small set of pivots that can represent the initial size distribution. New pivots are added to expand the computational domain in directions in which the evolving size distribution advances. A self-sufficient set of rules is developed to automate the addition of pivots, taken from an underlying X-grid formed by intersection of the lines of constant composition and constant particle mass. In order to test the robustness of the rule-set, simulations carried out with pivotwise expansion of X-grid are compared with those obtained using sufficiently large fixed X-grids for a number of composition independent and composition dependent aggregation kernels and initial conditions. The two techniques lead to identical predictions, with the former requiring only a fraction of the computational effort. The rule-set automatically reduces aggregation of particles of same composition to a 1-d problem. A midway change in the direction of expansion of domain, effected by the addition of particles of different mean composition, is captured correctly by the rule-set. The evolving shape of a computational domain carries with it the signature of the aggregation process, which can be insightful in complex and time dependent aggregation conditions. (c) 2012 Elsevier Ltd. All rights reserved.

Influence of anion on the quadratic nonlinearity and depolarization ratios of scattered second harmonic light from cation-pi complexes

We have investigated quadratic nonlinearity (beta(HRS)) and linear and circular depolarization ratios (D and D', respectively) of a series of 1:1 complexes of tropyliumtetrafluoroborate as a cation and methyl-substituted benzenes as pi-donors by making polarization resolved hyper-Rayleigh scattering measurements in solution. The measured D and D' values are much lower than the values expected from a typical sandwich or a T-shaped geometry of a complex. In the cation-pi complexes studied here, the D value varies from 1.36 to 1.46 and D' from 1.62 to 1.72 depending on the number of methyl substitutions on the benzene ring. In order to probe it further, beta, D and D' were computed using the Zerner intermediate neglect of differential overlap-correction vector self-consistent reaction field technique including single and double configuration interactions in the absence and presence of BF4- anion. In the absence of the anion, the calculated value of D varies from 4.20 to 4.60 and that of D' from 2.45 to 2.72 which disagree with experimental values. However, by arranging three cation-pi BF4- complexes in a trigonal symmetry, the computed values are brought to agreement with experiments. When such an arrangement was not considered, the calculated beta values were lower than the experimental values by more than a factor of two. This unprecedented influence of the otherwise ``unimportant'' anion in solution on the beta value and depolarization ratios of these cation-pi complexes is highlighted and emphasized in this paper. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4716020]

Linearization and Reconstruction of Non-linear Diffuse Optical Tomographic Image

Diffuse optical tomography (DOT) is one of the ways to probe highly scattering media such as tissue using low-energy near infra-red light (NIR) to reconstruct a map of the optical property distribution. The interaction of the photons in biological tissue is a non-linear process and the phton transport through the tissue is modelled using diffusion theory. The inversion problem is often solved through iterative methods based on nonlinear optimization for the minimization of a data-model misfit function. The solution of the non-linear problem can be improved by modeling and optimizing the cost functional. The cost functional is f(x) = x(T)Ax - b(T)x + c and after minimization, the cost functional reduces to Ax = b. The spatial distribution of optical parameter can be obtained by solving the above equation iteratively for x. As the problem is non-linear, ill-posed and ill-conditioned, there will be an error or correction term for x at each iteration. A linearization strategy is proposed for the solution of the nonlinear ill-posed inverse problem by linear combination of system matrix and error in solution. By propagating the error (e) information (obtained from previous iteration) to the minimization function f(x), we can rewrite the minimization function as f(x; e) = (x + e)(T) A(x + e) - b(T)(x + e) + c. The revised cost functional is f(x; e) = f(x) + e(T)Ae. The self guided spatial weighted prior (e(T)Ae) error (e, error in estimating x) information along the principal nodes facilitates a well resolved dominant solution over the region of interest. The local minimization reduces the spreading of inclusion and removes the side lobes, thereby improving the contrast, localization and resolution of reconstructed image which has not been possible with conventional linear and regularization algorithm.

Simple and efficient methods for discrimination of chiral diacids and chiral alpha-methyl amines

The three-component chiral derivatization protocols have been developed for H-1, C-13 and F-19 NMR spectroscopic discrimination of chiral diacids by their coordination and self-assembly with optically active (R)-alpha-methylbenzylamine and 2-formylphenylboronic acid or 3-fluoro-2-formylmethylboronic acid. These protocols yield a mixture of diastereomeric imino-boronate esters which are identified by the well-resolved diastereotopic peaks with significant chemical shift differences ranging up to 0.6 and 2.1 ppm in their corresponding H-1 and F-19 NMR spectra, without any racemization or kinetic resolution, thereby enabling the determination of enantiopurity. A protocol has also been developed for discrimination of chiral alpha-methyl amines, using optically pure trans-1,2-cyclohexanedicarboxylic acid in combination with 2-formylphenylboronic acid or 3-fluoro-2-fluoromethylboronic acid. The proposed strategies have been demonstrated on large number of chiral diacids and chiral alpha-methyl amines.

Strongly magnetized cold degenerate electron gas: Mass-radius relation of the magnetized white dwarf

We consider a relativistic, degenerate electron gas at zero temperature under the influence of a strong, uniform, static magnetic field, neglecting any form of interactions. Since the density of states for the electrons changes due to the presence of the magnetic field (which gives rise to Landau quantization), the corresponding equation of state also gets modified. In order to investigate the effect of very strong magnetic field, we focus only on systems in which a maximum of either one, two, or three Landau level(s) is/are occupied. This is important since, if a very large number of Landau levels are filled, it implies a very low magnetic field strength which yields back Chandrasekhar's celebrated nonmagnetic results. The maximum number of occupied Landau levels is fixed by the correct choice of two parameters, namely, the magnetic field strength and the maximum Fermi energy of the system. We study the equations of state of these one-level, two-level, and three-level systems and compare them by taking three different maximum Fermi energies. We also find the effect of the strong magnetic field on the mass-radius relation of the underlying star composed of the gas stated above. We obtain an exciting result that it is possible to have an electron-degenerate static star, namely, magnetized white dwarfs, with a mass significantly greater than the Chandrasekhar limit in the range 2.3-2.6M(circle dot), provided it has an appropriate magnetic field strength and central density. In fact, recent observations of peculiar type Ia supernovae-SN 2006gz, SN 2007if, SN 2009dc, SN 2003fg-seem to suggest super-Chandrasekhar-mass white dwarfs with masses up to 2.4-2.8M(circle dot) as their most likely progenitors. Interestingly, our results seem to lie within these observational limits.

Rainbow connection number and connected dominating sets

The rainbow connection number of a connected graph is the minimum number of colors needed to color its edges, so that every pair of its vertices is connected by at least one path in which no two edges are colored the same. In this article we show that for every connected graph on n vertices with minimum degree delta, the rainbow connection number is upper bounded by 3n/(delta + 1) + 3. This solves an open problem from Schiermeyer (Combinatorial Algorithms, Springer, Berlin/Hiedelberg, 2009, pp. 432437), improving the previously best known bound of 20n/delta (J Graph Theory 63 (2010), 185191). This bound is tight up to additive factors by a construction mentioned in Caro et al. (Electr J Combin 15(R57) (2008), 1). As an intermediate step we obtain an upper bound of 3n/(delta + 1) - 2 on the size of a connected two-step dominating set in a connected graph of order n and minimum degree d. This bound is tight up to an additive constant of 2. This result may be of independent interest. We also show that for every connected graph G with minimum degree at least 2, the rainbow connection number, rc(G), is upper bounded by Gc(G) + 2, where Gc(G) is the connected domination number of G. Bounds of the form diameter(G)?rc(G)?diameter(G) + c, 1?c?4, for many special graph classes follow as easy corollaries from this result. This includes interval graphs, asteroidal triple-free graphs, circular arc graphs, threshold graphs, and chain graphs all with minimum degree delta at least 2 and connected. We also show that every bridge-less chordal graph G has rc(G)?3.radius(G). In most of these cases, we also demonstrate the tightness of the bounds.

Simultaneous Detection of Two Triplets: A Time-Resolved Resonance Raman Study

Solvents are known to affect the triplet state structure and reactivity. In this paper, we have employed time-resolved resonance Raman (TR3) spectroscopy to understand solvent-induced subtle structural changes in the lowest excited triplet state of thioxanthone. Density functional theory (DFT) combined with the self-consistent reaction field (SCRF) implicit solvation model has been used to calculate the vibrational frequencies in the solvents. Here, we report a unique observation of the coexistence of two triplets, which has been substantiated by the probe wavelength-dependent Raman experiments. The coexistence of two triplets has been further supported by photoreduction experiments carried out at various temperatures.

Mesh Simplification Based on Edge Collapsing Could Improve Computational Efficiency in Near Infrared Optical Tomographic Imaging

The diffusion equation-based modeling of near infrared light propagation in tissue is achieved by using finite-element mesh for imaging real-tissue types, such as breast and brain. The finite-element mesh size (number of nodes) dictates the parameter space in the optical tomographic imaging. Most commonly used finite-element meshing algorithms do not provide the flexibility of distinct nodal spacing in different regions of imaging domain to take the sensitivity of the problem into consideration. This study aims to present a computationally efficient mesh simplification method that can be used as a preprocessing step to iterative image reconstruction, where the finite-element mesh is simplified by using an edge collapsing algorithm to reduce the parameter space at regions where the sensitivity of the problem is relatively low. It is shown, using simulations and experimental phantom data for simple meshes/domains, that a significant reduction in parameter space could be achieved without compromising on the reconstructed image quality. The maximum errors observed by using the simplified meshes were less than 0.27% in the forward problem and 5% for inverse problem.

Expanding universe: thermodynamical aspects from different models

The pivotal point of the paper is to discuss the behavior of temperature, pressure, energy density as a function of volume along with determination of caloric EoS from following two model: w(z)=w (0)+w (1)ln(1+z) & . The time scale of instability for this two models is discussed. In the paper we then generalize our result and arrive at general expression for energy density irrespective of the model. The thermodynamical stability for both of the model and the general case is discussed from this viewpoint. We also arrive at a condition on the limiting behavior of thermodynamic parameter to validate the third law of thermodynamics and interpret the general mathematical expression of integration constant U (0) (what we get while integrating energy conservation equation) physically relating it to number of micro states. The constraint on the allowed values of the parameters of the models is discussed which ascertains stability of universe. The validity of thermodynamical laws within apparent and event horizon is discussed.

Acoustic and optical phonon dynamics from femtosecond time-resolved optical spectroscopy of the superconducting iron pnictide Ca(Fe0.944Co0.056)(2)As-2

We report the temperature evolution of coherently excited acoustic and optical phonon dynamics in the superconducting iron pnictide single crystal Ca(Fe0.944Co0.056)(2)As-2 across the spin density wave transition at T-SDW similar to 85 K and the superconducting transition at T-SC similar to 20 K. The strain pulse propagation model applied to the generation of the acoustic phonons yields the temperature dependence of the optical constants, and longitudinal and transverse sound velocities in the temperature range from 3.1 K to 300 K. The frequency and dephasing times of the phonons show anomalous temperature dependence below T-SC indicating a coupling of these low-energy excitations with the Cooper-pair quasiparticles. A maximum in the amplitude of the acoustic modes at T similar to 170 is seen, attributed to spin fluctuations and strong spin-lattice coupling before T-SDW. Copyright (c) EPLA, 2012

Calculation of Heat of Adsorption of Gases and Refrigerants on Activated Carbons from Direct Measurements Fitted to the Dubinin-Astakhov Equation

The heat of adsorption of methane, ethane, carbon dioxide, R-507a and R-134a on several specimens of microporous activated carbons is derived from experimental adsorption data fitted to the Dubinin-Astakhov equation. These adsorption results are compared with literature data obtained from calorimetric measurements and from the pressure-temperature relation during isosteric heating/cooling. Because the adsorbed phase volume plays an important role, its dependence on temperature and pressure needs to be correctly assessed. In addition, for super-critical gas adsorption, the evaluation of the pseudo-saturation pressure also needs a judicious treatment. Based on the evaluation of carbon dioxide adsorption, it can be seen that sub-critical and super-critical adsorption show different temperature dependences of the isosteric heat of adsorption. The temperature and loading dependence of this property needs to be taken into account while designing practical systems. Some practical implications of these findings are enumerated.

Optimal Linear Codes with a Local-Error-Correction Property

Motivated by applications to distributed storage, Gopalan et al recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such ``local'' parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code.