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.

Texture transition in cold-rolled nickel-40 wt.% cobalt alloy

The micromechanical aspects of rolling texture development in Ni-40 wt.% Co alloy during very large reductions (up to epsilon(t) = 3.9) have been studied. The alloy showed a typical Cu-type texture up to a true strain of epsilon(t) = 3; however, the texture undergoes an abrupt transition to Bs-type on further rolling to epsilon(t) approximate to 4. (The Bs-type texture, here, comprises almost equal fractions of Goss and Bs components.) Microstructural observations, at early stages, show that deformation is accommodated entirely by slip, and very little presence of deformation twinning is observed to explain the texture transition. However, at much higher reduction levels, micrographs show a high fraction of Cu-type shear bands. These bands are predominantly found in Cu-oriented grains and the crystallites inside the shear bands are preferentially oriented towards Goss, which could explain the final texture evolution. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The generalized Onsager model for a binary gas mixture

The Onsager model for the secondary flow field in a high-speed rotating cylinder is extended to incorporate the difference in mass of the two species in a binary gas mixture. The base flow is an isothermal solid-body rotation in which there is a balance between the radial pressure gradient and the centrifugal force density for each species. Explicit expressions for the radial variation of the pressure, mass/mole fractions, and from these the radial variation of the viscosity, thermal conductivity and diffusion coefficient, are derived, and these are used in the computation of the secondary flow. For the secondary flow, the mass, momentum and energy equations in axisymmetric coordinates are expanded in an asymptotic series in a parameter epsilon = (Delta m/m(av)), where Delta m is the difference in the molecular masses of the two species, and the average molecular mass m(av) is defined as m(av) = (rho(w1)m(1) + rho(w2)m(2))/rho(w), where rho(w1) and rho(w2) are the mass densities of the two species at the wall, and rho(w) = rho(w1) + rho(w2). The equation for the master potential and the boundary conditions are derived correct to O(epsilon(2)). The leading-order equation for the master potential contains a self-adjoint sixth-order operator in the radial direction, which is different from the generalized Onsager model (Pradhan & Kumaran, J. Fluid Mech., vol. 686, 2011, pp. 109-159), since the species mass difference is included in the computation of the density, viscosity and thermal conductivity in the base state. This is solved, subject to boundary conditions, to obtain the leading approximation for the secondary flow, followed by a solution of the diffusion equation for the leading correction to the species mole fractions. The O(epsilon) and O(epsilon(2)) equations contain inhomogeneous terms that depend on the lower-order solutions, and these are solved in a hierarchical manner to obtain the O(epsilon) and O(epsilon(2)) corrections to the master potential. A similar hierarchical procedure is used for the Carrier-Maslen model for the end-cap secondary flow. The results of the Onsager hierarchy, up to O(epsilon(2)), are compared with the results of direct simulation Monte Carlo simulations for a binary hard-sphere gas mixture for secondary flow due to a wall temperature gradient, inflow/outflow of gas along the axis, as well as mass and momentum sources in the flow. There is excellent agreement between the solutions for the secondary flow correct to O(epsilon(2)) and the simulations, to within 15 %, even at a Reynolds number as low as 100, and length/diameter ratio as low as 2, for a low stratification parameter A of 0.707, and when the secondary flow velocity is as high as 0.2 times the maximum base flow velocity, and the ratio 2 Delta m/(m(1) + m(2)) is as high as 0.5. Here, the Reynolds number Re = rho(w)Omega R-2/mu, the stratification parameter A = root m Omega R-2(2)/(2k(B)T), R and Omega are the cylinder radius and angular velocity, m is the molecular mass, rho(w) is the wall density, mu is the viscosity and T is the temperature. The leading-order solutions do capture the qualitative trends, but are not in quantitative agreement.

New insights into the development of microstructure and deformation texture in nickel-60 wt.% cobalt alloy

The present study investigates the critical role of deformation twinning and Bs-type shear bands in the evolution of deformation texture in a low stacking fault energy Ni-60Co alloy up to very large rolling strain (epsilon(t) approximate to 4). The alloy develops a strong brass-type rolling texture, and its formation is initiated at the early stages of deformation. Extensive twinning is observed at the intermediate stages of deformation, which causes significant texture reorientation towards alpha-fiber. A pseudo-in-situ electron back-scattered diffraction technique adopted to capture orientation changes within individual grains during the early stages suggests that twinning should be subsequently aided by crystallographic slip to attain alpha-fiber (< 1 1 0 >parallel to ND) orientations. Beyond 40% reduction, deformation is dominated by Bs-type shear bands, and the banding coincides with the evolution of < 1 1 1 >parallel to ND components. The volume fraction of shear bands is significant at higher strains, and crystallites within the bands preferentially show < 1 1 0 >parallel to ND components. The absence of the Cu {1 1 2}< 1 1 1 > component in the initial texture, and subsequently during rolling, indicates that, for the evolution of a brass-type texture, the presence of the Cu component is not a necessary condition. The final rolling texture is a synergistic effect of deformation twinning and shear banding. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Diffusion on a rugged energy landscape with spatial correlations

Rugged energy landscapes find wide applications in diverse fields ranging from astrophysics to protein folding. We study the dependence of diffusion coefficient (D) of a Brownian particle on the distribution width (epsilon) of randomness in a Gaussian random landscape by simulations and theoretical analysis. We first show that the elegant expression of Zwanzig Proc. Natl. Acad. Sci. U.S.A. 85, 2029 (1988)] for D(epsilon) can be reproduced exactly by using the Rosenfeld diffusion-entropy scaling relation. Our simulations show that Zwanzig's expression overestimates D in an uncorrelated Gaussian random lattice - differing by almost an order of magnitude at moderately high ruggedness. The disparity originates from the presence of ``three-site traps'' (TST) on the landscape - which are formed by the presence of deep minima flanked by high barriers on either side. Using mean first passage time formalism, we derive a general expression for the effective diffusion coefficient in the presence of TST, that quantitatively reproduces the simulation results and which reduces to Zwanzig's form only in the limit of infinite spatial correlation. We construct a continuous Gaussian field with inherent correlation to establish the effect of spatial correlation on random walk. The presence of TSTs at large ruggedness (epsilon >> k(B)T) gives rise to an apparent breakdown of ergodicity of the type often encountered in glassy liquids. (C) 2014 AIP Publishing LLC.

A constant factor approximation algorithm for boxicity of circular arc graphs

The boxicity (resp. cubicity) of a graph G(V, E) is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes (resp. cubes) in R-k. Equivalently, it is the minimum number of interval graphs (resp. unit interval graphs) on the vertex set V, such that the intersection of their edge sets is E. The problem of computing boxicity (resp. cubicity) is known to be inapproximable, even for restricted graph classes like bipartite, co-bipartite and split graphs, within an O(n(1-epsilon))-factor for any epsilon > 0 in polynomial time, unless NP = ZPP. For any well known graph class of unbounded boxicity, there is no known approximation algorithm that gives n(1-epsilon)-factor approximation algorithm for computing boxicity in polynomial time, for any epsilon > 0. In this paper, we consider the problem of approximating the boxicity (cubicity) of circular arc graphs intersection graphs of arcs of a circle. Circular arc graphs are known to have unbounded boxicity, which could be as large as Omega(n). We give a (2 + 1/k) -factor (resp. (2 + log n]/k)-factor) polynomial time approximation algorithm for computing the boxicity (resp. cubicity) of any circular arc graph, where k >= 1 is the value of the optimum solution. For normal circular arc (NCA) graphs, with an NCA model given, this can be improved to an additive two approximation algorithm. The time complexity of the algorithms to approximately compute the boxicity (resp. cubicity) is O(mn + n(2)) in both these cases, and in O(mn + kn(2)) = O(n(3)) time we also get their corresponding box (resp. cube) representations, where n is the number of vertices of the graph and m is its number of edges. Our additive two approximation algorithm directly works for any proper circular arc graph, since their NCA models can be computed in polynomial time. (C) 2014 Elsevier B.V. All rights reserved.

Perovskite ceramic nanoparticles in polymer composites for augmenting bone tissue regeneration

There is increasing interest in the use of nanoparticles as fillers in polymer matrices to develop biomaterials which mimic the mechanical, chemical and electrical properties of bone tissue for orthopaedic applications. The objective of this study was to prepare poly(epsilon-caprolactone) (PCL) nanocomposites incorporating three different perovskite ceramic nanoparticles, namely, calcium titanate (CT), strontium titanate (ST) and barium titanate (BT). The tensile strength and modulus of the composites increased with the addition of nanoparticles. Scanning electron microscopy indicated that dispersion of the nanoparticles scaled with the density of the ceramics, which in turn played an important role in determining the enhancement in mechanical properties of the composite. Dielectric spectroscopy revealed improved permittivity and reduced losses in the composites when compared to neat PCL. Nanofibrous scaffolds were fabricated via electrospinning. Induction coupled plasma-optical emission spectroscopy indicated the release of small quantities of Ca+2, Sr+2, Ba+2 ions from the scaffolds. Piezo-force microscopy revealed that BT nanoparticles imparted piezoelectric properties to the scaffolds. In vitro studies revealed that all composites support osteoblast proliferation. Expression of osteogenic genes was enhanced on the nanocomposites in the following order: PCL/CT>PCL/ST>PCL/BT>PCL. This study demonstrates that the use of perovskite nanoparticles could be a promising technique to engineer better polymeric scaffolds for bone tissue engineering.

Effect of Sm3+ on dielectric and magnetic properties of Y3Fe5O12 nanoparticles

The Sm3+ doped Y3-xSmxFe5O12 (x = 0-3) nanopowders were prepared using modified sol-gel route. The crystalline structure and morphology was confirmed by X-ray diffraction and atomic force microscopy. The nanopowders were sintered at 950 degrees C/90 min using microwave sintering method. The lattice parameters and density of the samples were increased with an increase of Sm3+ concentration. The room temperature dielectric (epsilon' and epsilon `') and magnetic (mu' and mu `') properties were measured in the frequency range up to 20 GHz. The room temperature magnetization studies were carried out using Vibrating sample magnetometer using filed of 1.5 T. Results of VSM show that the saturation and remnant magnetization of Y3-xSmxFe5O12 (0-3) decreases on increasing the Sm concentration (x). The low values of magnetic (mu' and mu `') properties makes them a good candidates for microwave devices, which can be operated in the high frequency range.

Strategy for Enhancing the Dielectric Constant of Organic Semiconductors Without Sacrificing Charge Carrier Mobility and Solubility

Current organic semiconductors for organic photovoltaics (OPV) have relative dielectric constants (relative permittivities, epsilon(r)) in the range of 2-4. As a consequence, Coulombically bound electron-hole pairs (excitons) are produced upon absorption of light, giving rise to limited power conversion efficiencies. We introduce a strategy to enhance epsilon(r) of well-known donors and acceptors without breaking conjugation, degrading charge carrier mobility or altering the transport gap. The ability of ethylene glycol (EG) repeating units to rapidly reorient their dipoles with the charge redistributions in the environment was proven via density functional theory (DFT) calculations. Fullerene derivatives functionalized with triethylene glycol side chains were studied for the enhancement of epsilon(r) together with poly(p-phenylene vinylene) and diketo-pyrrolopyrrole based polymers functionalized with similar side chains. The polymers showed a doubling of epsilon(r) with respect to their reference polymers in identical backbone. Fullerene derivatives presented enhancements up to 6 compared with phenyl-C-61-butyric acid methyl ester (PCBM) as the reference. Importantly, the applied modifications did not affect the mobility of electrons and holes and provided excellent solubility in common organic solvents.

A Comparison of Machine Learning Techniques for Modeling River Flow Time Series: The Case of Upper Cauvery River Basin

Models of river flow time series are essential in efficient management of a river basin. It helps policy makers in developing efficient water utilization strategies to maximize the utility of scarce water resource. Time series analysis has been used extensively for modeling river flow data. The use of machine learning techniques such as support-vector regression and neural network models is gaining increasing popularity. In this paper we compare the performance of these techniques by applying it to a long-term time-series data of the inflows into the Krishnaraja Sagar reservoir (KRS) from three tributaries of the river Cauvery. In this study flow data over a period of 30 years from three different observation points established in upper Cauvery river sub-basin is analyzed to estimate their contribution to KRS. Specifically, ANN model uses a multi-layer feed forward network trained with a back-propagation algorithm and support vector regression with epsilon intensive-loss function is used. Auto-regressive moving average models are also applied to the same data. The performance of different techniques is compared using performance metrics such as root mean squared error (RMSE), correlation, normalized root mean squared error (NRMSE) and Nash-Sutcliffe Efficiency (NSE).

Strontium eluting graphene hybrid nanoparticles augment osteogenesis in a 3D tissue scaffold

The objective of this work was to prepare hybrid nanoparticles of graphene sheets decorated with strontium metallic nanoparticles and demonstrate their advantages in bone tissue engineering. Strontium-decorated reduced graphene oxide (RGO_Sr) hybrid nanoparticles were synthesized by the facile reduction of graphene oxide and strontium nitrate. X-ray diffraction, transmission electron microscopy, and atomic force microscopy revealed that the hybrid particles were composed of RGO sheets decorated with 200-300 nm metallic strontium particles. Thermal gravimetric analysis further confirmed the composition of the hybrid particles as 22 wt% of strontium. Macroporous tissue scaffolds were prepared by incorporating RGO_Sr particles in poly(epsilon-caprolactone) (PCL). The PCL/RGO_Sr scaffolds were found to elute strontium ions in aqueous medium. Osteoblast proliferation and differentiation was significantly higher in the PCL scaffolds containing the RGO_Sr particles in contrast to neat PCL and PCL/RGO scaffolds. The increased biological activity can be attributed to the release of strontium ions from the hybrid nanoparticles. This study demonstrates that composites prepared using hybrid nanoparticles that elute strontium ions can be used to prepare multifunctional scaffolds with good mechanical and osteoinductive properties. These findings have important implications for designing the next generation of biomaterials for use in tissue regeneration.

Chemical Functionalization of Graphene To Augment Stem Cell Osteogenesis and Inhibit Biofilm Formation on Polymer Composites for Orthopedic Applications

Toward designing the next generation of resorbable biomaterials for orthopedic applications, we studied poly(epsilon-caprolactone) (PCL) composites containing graphene. The role, if any, of the functionalization of graphene on mechanical properties, stem cell response, and biofilm formation was systematically evaluated. PCL composites of graphene oxide (GO), reduced GO (RGO), and amine-functionalized GO (AGO) were prepared at different filler contents (1%, 3%, and 5%). Although the addition of the nanoparticles to PCL markedly increased the storage modulus, this increase was largest for GO followed by AGO and RGO. In vitro cell studies revealed that the AGO and GO particles significantly increased human mesenchymal stem cell proliferation. AGO was most effective in augmenting stem cell osteogenesis leading to mineralization. Bacterial studies revealed that interaction with functionalized GO induced bacterial cell death because of membrane damage, which was further accentuated by amine groups in AGO. As a result, AGO composites were best at inhibiting biofilm formation. The synergistic effect of oxygen containing functional groups and amine groups on AGO imparts the optimal combination of improved modulus, favorable stem cell response, and biofilm inhibition in AGO-reinforced composites desired for orthopedic applications. This work elucidates the importance of chemical functionalization of graphene in polymer composites for biomedical applications.

Cryogenian magmatism and crustal reworking in the Southern Granulite Terrane, India

Understanding Neoproterozoic crustal evolution is fundamental to reconstructing the Gondwana supercontinent, which was assembled at this time. Here we report evidence of Cryogenian crustal reworking in the Madurai Block of the Southern Granulite Terrane of India. The study focuses on a garnet-bearing granite-charnockite suite, where the granite shows in situ dehydration into patches and veins of incipient charnockite along the contact with charnockite. The granite also carries dismembered layers of Mg-Al-rich granulite. Micro-textural evidence for dehydration of granite in the presence of CO2-rich fluids includes the formation of orthopyroxene by the breakdown of biotite, neoblastic zircon growth in the dehydration zone, at around 870 degrees C and 8kbar. The zircon U-Pb ages suggest formation of the granite, charnockite, and incipient charnockite at 836 +/- 73, 831 +/- 31, and 772 +/- 49Ma, respectively. Negative zircon epsilon Hf (t) (-5 to -20) values suggest that these rocks were derived from a reworked Palaeoproterozoic crustal source. Zircon grains in the Mg-Al-rich granulite record a spectrum of ages from ca. 2300 to ca. 500Ma, suggesting multiple provenances ranging from Palaeoproterozoic to mid-Neoproterozoic, with neoblastic zircon growth during high-temperature metamorphism in the Cambrian. We propose that the garnet-bearing granite and charnockite reflect the crustal reworking of aluminous crustal material indicated by the presence of biotite+quartz+aluminosilicate inclusions in the garnet within the granite. This crustal source can be the Mg-Al-rich layers carried by the granite itself, which later experienced high-temperature regional metamorphism at ca. 550Ma. Our model also envisages that the CO2 which dehydrated the garnet-bearing granite generating incipient charnockite was sourced from the proximal massive charnockite through advection. These Cryogenian crustal reworking events are related to prolonged tectonic activities prior to the final assembly of the Gondwana supercontinent.

Pair dispersion of turbulent premixed flame elements

Flame particles are mathematical points comoving with a reacting isoscalar surface in a premixed flame. In this Rapid Communication, we investigate mean square pair separation of flame particles as a function of time from their positions tracked in two sets of direct numerical simulation solutions of H-2-air turbulent premixed flames with detailed chemistry. We find that, despite flame particles and fluid particles being very different concepts, a modified Batchelor's scaling of the form = C-F ( (F)(0) Delta(F)(0))(2/3)t(2) holds for flame particle pair dispersion. The proportionality constant, however, is not universal and depends on the isosurface temperature value on which the flame particles reside. Following this, we attempt to analytically investigate the rationale behind such an observation.

Effect of Ni-Zr codoping on dielectric and magnetic properties of SrFe12O19 via sol-gel route

Nanocrystalline strontium hexaferrites SrFe12-2x (Ni2+-Zr4+)(x)O-19] nanoparticles were successfully synthesized by sal gel process. For densification the powders were sintered at 950 degrees C/4 h. The sintered samples were characterized by X-ray diffraction (XRD), surface area measurement, and field emission scanning electron microscope (FESEM). The lattice parameter a is almost constant but c increased with x upto 0.8 and then decreased. The frequency dependent complex permittivity (epsilon and epsilon `' and permeability (mu' and mu `') and magnetic properties such as saturation magnetization (M-s), coercive field (H-c) were studied. If is observed that saturation magnetization increased gradually from 57.82 emuig to 67.2 emufg as x increased from 0.2 to 0.4 and then decreased from 672 emufg to 31.63 ernufg for x=1.0. In present study, x=0.4 shows high value of M-s 67.2 emu/g. The real part of permittivity (epsilon') remains constant upto a frequency 1 GHz and increases further with an increase of frequency, a resonance and anti resonance peak was observed above 1 GHz for all the samples. In real part of permeability (mu') the relaxation frequency is observed above 1 GHz for all the samples and it is attributed to the domain wall motion. It is well known that the permeability for polycrystalline ferrites can be described as the superposition of two different magnetizing mechanisms: spin rotation and domain wall motion. These low coercive strontium hexaferrites are suitable for magnetic recording applications in hard disks, floppy disks, video tapes, etc. (C) 2015 Elsevier B.V. All rights reserved.