Homogenization of eigenvalue problems in perforated domains

In this paper, we treat some eigenvalue problems in periodically perforated domains and study the asymptotic behaviour of the eigenvalues and the eigenvectors when the number of holes in the domain increases to infinity Using the method of asymptotic expansion, we give explicit formula for the homogenized coefficients and expansion for eigenvalues and eigenvectors. If we denote by ε the size of each hole in the domain, then we obtain the following aysmptotic expansion for the eigenvalues: Dirichlet: λε = ε−2 λ + λ0 +O (ε), Stekloff: λε = ελ1 +O (ε2), Neumann: λε = λ0 + ελ1 +O (ε2).Using the method of energy, we prove a theorem of convergence in each case considered here. We briefly study correctors in the case of Neumann eigenvalue problem.

A density matrix renormalization group method study of optical properties of porphines and metalloporphines

The symmetrized density matrix renormalization group method is used to study linear and nonlinear optical properties of free base porphine and metalloporphine. Long-range interacting model, namely, Pariser-Parr-Pople model is employed to capture the quantum many-body effect in these systems. The nonlinear optical coefficients are computed within the correction vector method. The computed singlet and triplet low-lying excited state energies and their charge densities are in excellent agreement with experimental as well as many other theoretical results. The rearrangement of the charge density at carbon and nitrogen sites, on excitation, is discussed. From our bond order calculation, we conclude that porphine is well described by the 18-annulenic structure in the ground state and the molecule expands upon excitation. We have modeled the regular metalloporphine by taking an effective electric field due to the metal ion and computed the excitation spectrum. Metalloporphines have D(4h) symmetry and hence have more degenerate excited states. The ground state of metalloporphines shows 20-annulenic structure, as the charge on the metal ion increases. The linear polarizability seems to increase with the charge initially and then saturates. The same trend is observed in third order polarizability coefficients. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3671946]

Growth mechanism of the Nb(X)Si-2 and [Nb(X)](5)Si-3 phases by reactive diffusion in Nb (X = Ti, Mo, or Zr)-Si systems

The effects of Mo, Ti, and Zr on the diffusion and growth of the Nb(X)Si-2 and Nb(X)(5)Si-3 phases in an Nb(X)-Si system are analyzed. The integrated diffusion coefficients are determined from diffusion couple experiments and compared with the data previously calculated in a binary Nb-Si system. The growth rates of both phases are affected by the addition of Mo and Zr, whereas the addition of Ti has no effect. The atomic mechanism of diffusion is also discussed based on the crystal structure and the possible changes in the defect concentrations due to alloying. Finally, the growth mechanism of the phases is discussed on the basis of a physico-chemical approach. (C) 2011 Elsevier Ltd. All rights reserved.

Synthesis and nonlinear optical properties of Lead Telluride nanorods

Lead Telluride (PbTe) nanorods have been uniformly grown on silicon substrates, using the thermal evaporation technique under high vacuum conditions. The structural and morphological studies are done using X-ray diffraction and scanning electron microscopy. Optical nonlinearity studies using the open aperture z-scan employing 5 ns and 100 fs laser pulses reveal a three-photon type absorption. For nanosecond excitation the nonlinear absorption coefficients (gamma) are in the order of 10(-22) m(3) W-2 and for femtosecond excitation it is in the order of 10(-29) m(3) W-2. The role of free carriers and excitons in causing the nonlinearity in both excitation time domains is discussed. Results indicate that PbTe nanorods are good optical limiters with potential device applications. (C) 2011 Elsevier B.V. All rights reserved.

Force measurements on hypersonic waveriders in the IISc hypersonic shock tunnel HST2

The drag and lift coefficients for a viscous optimized Mach 6 conical waverider has been measured using an accelerometer force balance system in the IISc hypersonic shock tunnel. A rubber bush placed in between the waverider model and the steel sting ensures unrestrained motion to the model during shock tunnel testing (500 mu s). Two accelerometers mounted on the model are used to measure the model accelerations in the axial and normal directions. The measured value of lift to drag ratio at zero angle of incidence for the IISc conical waverider with viscous optimized leading edge is 2.149, which compares well with the value reported in the open literature (Anderson et al 1991) for similar class of waveriders designed for a flight Mach number of 6. The details of the experimental study along with illustrative numerical results are discussed in this paper.

Decoupling of diffusion from viscosity: Difference scenario for translational and rotational motions

Recent experiments have indicated a dramatically different viscosity dependence of the translational and the rotational diffusion coefficients in a supercooled liquid as the glass transition temperature is approached from above. While the translational motion seems to be decoupled from the rising viscosity (eta), the rotational motion seems to remain firmly coupled to eta. In order to understand the microscopic origin of this behavior, we have carried nut detailed theoretical calculations of both the quantities by using a self-consistent mode-coupling theory (MCT). it is found that when the size of the solute is same as that of the solvent molecules, the conventional MCT fails to predict the observed decoupling. The solvent inhomogeneity is found to play a decisive role in determining the decoupling. The difference in the viscosity dependence between rotation and translational diffusion coefficient is discussed.

Determinant: Old algorithms, new insights (Extended Abstract)

In this paper we approach the problem of computing the characteristic polynomial of a matrix from the combinatorial viewpoint. We present several combinatorial characterizations of the coefficients of the characteristic polynomial, in terms of walks and closed walks of different kinds in the underlying graph. We develop algorithms based on these characterizations, and show that they tally with well-known algorithms arrived at independently from considerations in linear algebra.

Solution of a class of surface water wave scattering problems involving non-reflecting vertical barriers

A large class of scattering problems of surface water waves by vertical barriers lead to mixed boundary value problems for Laplace equation. Specific attentions are paid, in the present article, to highlight an analytical method to handle this class of problems of surface water wave scattering, when the barriers in question are non-reflecting in nature. A new set of boundary conditions is proposed for such non-reflecting barriers and tile resulting boundary value problems are handled in the linearized theory of water waves. Three basic poblems of scattering by vertical barriers are solved. The present new theory of non-reflecting vertical barriers predict new transmission coefficients and tile solutions of tile mathematical problems turn out to be extremely simple and straight forward as compared to the solution for other types of barriers handled previously.

Interdiffusion in the Fe-Pt System

Diffusion-couple experiments are conducted in the Fe-Pt system. The phase boundary compositions of the phases measured in this study are found to be different than the compositions published previously. In the gamma-FePt solid solution, the interdiffusion coefficient increases with the Pt content up to 25 at. pct Pt. Fe is the faster diffusing species in this phase. The trend in the interdiffusion coefficient is explained with the help of calculated driving force for diffusion. To reduce errors, the average interdiffusion coefficients are calculated in the FePt and FePt3 compounds.

Adsorption of cationic dyes on poly(acrylic acid-co-sodium acrylate-co-acrylamide) superabsorbents

Inverse suspension polymerization was carried out to synthesize poly(acrylic acid-co-sodium acrylate-co-acrylamide) superabsorbent polymers (SAPs) crosslinked with ethylene glycol dimethacrylate (EGDMA). The equilibrium swelling capacities of the SAPs, determined by swelling them in DI water, were found to vary with the acrylamide (AM) content. The SAPs were used to adsorb four cationic dyes (Acriflavine, Auramine-O, Azure-I and Pyronin-Y). The effect of AM content in the SAPs on the adsorption of the cationic dyes was investigated. Different initial concentrations of Azure-I were used with the same amount of the SAP to explore the effect of initial dye concentration on the adsorption. The effect of the adsorbent amount was investigated by taking different amounts of SAP with a fixed initial concentration of Acriflavine. The kinetics of the dye adsorption was modeled by a first order model and the equilibrium amount of the dye adsorbed, adsorption rate coefficients, removal efficiency and partition coefficients were determined. (C) 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Influence of the Methane-Zeolite A Interaction Potential on the Concentration Dependence of Self-diffusivity

Studies on the diffusion of methane in a zeolite structure type LTA (as per IZA nomenclature) have indicated that different types of methane zeolite potentials exist in the literature in which methane is treated within the united-atom model. One set of potentials, referred to as model A, has a methane oxygen diameter of 3.14 angstrom, while another set of potential parameters, model B, employs a larger value of 3.46 angstrom. Fritzsche and co-workers (1993) have shown that these two potentials lead to two distinctly different energetic barriers for the passage of methane through the eight-ring window in the cation-free form of zeolite A. Here, we compute the variation of the self-diffusivity (D) with loading (c) for these two types of potentials and show that this slight variation in the diameter changes the concentration dependence qualitatively: thus, D decreases monotonically with c for model A, while D increases and goes through a maximum before finally decreasing for model B. This effect and the surprising congruence of the diffusion coefficients for both models at high loadings is examined in detail at the molecular level. Simulations for different temperatures reveal the Arrhenius behaviour of the self-diffusion coefficient. The apparent activation energy is found to vary with the loading. We conclude that beside the cage-to-cage jumps, which are essential for the migration of the guest molecules, at high concentrations migration within the cage and guest guest interactions with other molecules become increasingly dominant influences on the diffusion coefficient and make the guest zeolite interaction less important for both model A and model B.

Construction of equivalent circuit of a transformer winding from driving-point impedance function - analytical approach

Analytical solution is presented to convert a given driving-point impedance function (in s-domain) into a physically realisable ladder network with inductive coupling between any two sections and losses considered. The number of sections in the ladder network can vary, but its topology is assumed fixed. A study of the coefficients of the numerator and denominator polynomials of the driving-point impedance function of the ladder network, for increasing number of sections, led to the identification of certain coefficients, which exhibit very special properties. Generalised expressions for these specific coefficients have also been derived. Exploiting their properties, it is demonstrated that the synthesis method essentially turns out to be an exercise of solving a set of linear, simultaneous, algebraic equations, whose solution directly yields the ladder network elements. The proposed solution is novel, simple and guarantees a unique network. Presently, the formulation can synthesise a unique ladder network up to six sections.

A pseudo-time EnKF incorporating shape based reconstruction for diffuse optical tomography

Purpose: The authors aim at developing a pseudo-time, sub-optimal stochastic filtering approach based on a derivative free variant of the ensemble Kalman filter (EnKF) for solving the inverse problem of diffuse optical tomography (DOT) while making use of a shape based reconstruction strategy that enables representing a cross section of an inhomogeneous tumor boundary by a general closed curve. Methods: The optical parameter fields to be recovered are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions) and the EnKF is used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The process and measurement equations in the pseudo-dynamic EnKF (PD-EnKF) presently yield a parsimonious representation of the filter variables, which consist of only the Fourier coefficients and the constant scalar parameter value within the inclusion. Using fictitious, low-intensity Wiener noise processes in suitably constructed ``measurement'' equations, the filter variables are treated as pseudo-stochastic processes so that their recovery within a stochastic filtering framework is made possible. Results: In our numerical simulations, we have considered both elliptical inclusions (two inhomogeneities) and those with more complex shapes (such as an annular ring and a dumbbell) in 2-D objects which are cross-sections of a cylinder with background absorption and (reduced) scattering coefficient chosen as mu(b)(a)=0.01mm(-1) and mu('b)(s)=1.0mm(-1), respectively. We also assume mu(a) = 0.02 mm(-1) within the inhomogeneity (for the single inhomogeneity case) and mu(a) = 0.02 and 0.03 mm(-1) (for the two inhomogeneities case). The reconstruction results by the PD-EnKF are shown to be consistently superior to those through a deterministic and explicitly regularized Gauss-Newton algorithm. We have also estimated the unknown mu(a) from experimentally gathered fluence data and verified the reconstruction by matching the experimental data with the computed one. Conclusions: The PD-EnKF, which exhibits little sensitivity against variations in the fictitiously introduced noise processes, is also proven to be accurate and robust in recovering a spatial map of the absorption coefficient from DOT data. With the help of shape based representation of the inhomogeneities and an appropriate scaling of the CH expansion coefficients representing the boundary, we have been able to recover inhomogeneities representative of the shape of malignancies in medical diagnostic imaging. (C) 2012 American Association of Physicists in Medicine. [DOI: 10.1118/1.3679855]

Evaporation Heat Transfer Coefficient in a Capillary Pumped Loop and Loop Heat Pipe for Different Working Fluids

Capillary pumped loop (CPL) and loop heat pipe (LHP) are passive two-phase heat transport devices. They have been gaining importance as a part of the thermal control system of spacecraft. The evaporation heat transfer coefficient at the tooth-wick interface of an LHP or CPL has a significant impact on the evaporator temperature. It is also the main parameter in sizing of a CPL or LHP. Experimentally determined evaporation heat transfer coefficients from a three-port CPL with tubular axially grooved (TAG) evaporator and a TAG LHP with acetone, R-134A, and ammonia as working fluids are presented in this paper. The influences of working fluid, hydrodynamic blocks in the core, evaporator configuration (LHP or CPL), and adverse elevation (evaporator above condenser) on the heat transfer coefficient are presented.

Interdiffusion and Growth of the Phases in CoNi/Mo and CoNi/W Systems

Deleterious topological-closed-packed (tcp) phases grow in the interdiffusion zone in turbine blades mainly because of the addition of refractory elements such as Mo and W in the Ni- and Co-based superalloys. CoNi/Mo and CoNi/W diffusion couples are prepared to understand the growth mechanism of the phases in the interdiffusion zone. Instead of determining the main and cross-interdiffusion coefficients following the conventional method, we preferred to determine the average effective interdiffusion coefficients of two elements after fixing the composition of one element more or less the same in the interdiffusion zone. These parameters can be directly related to the growth kinetics of the phases and shed light on the atomic mechanism of diffusion. In both systems, the diffusion rate of elements and the phase layer thickness increased because of the addition of Ni in the solid solution phase, probably because of an increase in driving force. On the other hand, the growth rate of the mu phase and the diffusion coefficient of the species decreased because of the addition of Ni. This indicates the change in defect concentration, which assists diffusion. Further, we revisited the previously published Co-Ni-Mo and Co-Ni-W ternary phase diagrams and compared them with the composition range of the phases developed in the interdiffusion zone. Different composition ranges of the tcp phases are found, and corrected phase diagrams are shown. The outcome of this study will help to optimize the concentration of elements in superalloys to control the growth of the tcp phases.