A new beam finite element for the analysis of functionally graded materials

A new beam element is developed to study the thermoelastic behavior of functionally graded beam structures. The element is based on the first-order shear deformation theory and it accounts for varying elastic and thermal properties along its thickness. The exact solution of static part of the governing differential equations is used to construct interpolating polynomials for the element formulation. Consequently, the stiffness matrix has super-convergent property and the element is free of shear locking. Both exponential and power-law variations of material property distribution are used to examine different stress variations. Static, free vibration and wave propagation problems are considered to highlight the behavioral difference of functionally graded material beam with pure metal or pure ceramic beams. (C) 2003 Elsevier Science Ltd. All rights reserved.

Molecular Dynamics of Thermotropic Liquid Crystals: Anomalous relaxation dynamics of calamitic and discotic liquid crystals

Recent optical kerr effect (OKE) studies have demonstrated that orientational relaxation of rod-like nematogens exhibits temporal power law decay at intermediate times not only near the isotropic–nematic (I–N) phase boundary but also in the nematic phase. Such behaviour has drawn an intriguing analogy with supercooled liquids. We have investigated both collective and single-particle orientational dynamics of a family of model system of thermotropic liquid crystals using extensive computer simulations. Several remarkable features of glassy dynamics are on display including non-exponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. Over a temperature range near the I–N phase boundary, the system behaves remarkably like a fragile glass-forming liquid. Using proper scaling, we construct the usual relaxation time versus inverse temperature plot and explicitly demonstrate that one can successfully define a density dependent fragility of liquid crystals. The fragility of liquid crystals shows a temperature and density dependence which is remarkably similar to the fragility of glass forming supercooled liquids. Energy landscape analysis of inherent structures shows that the breakdown of the Arrhenius temperature dependence of relaxation rate occurs at a temperature that marks the onset of the growth of the depth of the potential energy minima explored by the system. A model liquid crystal, consisting of disk-like molecules, has also been investigated in molecular dynamics simulations for orientational relaxation along two isobars starting from the high temperature isotropic phase. The isobars have been so chosen that the phase sequence isotropic (I)–nematic (N)–columnar (C) appears upon cooling along one of them and the sequence isotropic (I)–columnar(C) along the other. While the orientational relaxation in the isotropic phase near the I–N phase transition shows a power law decay at short to intermediate times, such power law relaxation is not observed in the isotropic phase near the I–C phase boundary. The origin of the power law decay in the single-particle second-rank orientational time correlation function (OTCF) is traced to the growth of the orientational pair distribution functions near the I–N phase boundary. As the system settles into the nematic phase, the decay of the single-particle second-rank orientational OTCF follows a pattern that is similar to what is observed with calamitic liquid crystals and supercooled molecular liquids.

LOCAL TWO-DIMENSIONAL PARTICLE-IN-CELL SIMULATIONS OF THE COLLISIONLESS MAGNETOROTATIONAL INSTABILITY

The magnetorotational instability (MRI) is a crucial mechanism of angular momentum transport in a variety of astrophysical accretion disks. In systems accreting at well below the Eddington rate, such as the central black hole in the Milky Way (Sgr A*), the plasma in the disk is essentially collisionless. We present a nonlinear study of the collisionless MRI using first-principles particle-in-cell plasma simulations. We focus on local two-dimensional (axisymmetric) simulations, deferring more realistic three-dimensional simulations to future work. For simulations with net vertical magnetic flux, the MRI continuously amplifies the magnetic field, B, until the Alfven velocity, v(A), is comparable to the speed of light, c (independent of the initial value of v(A)/c). This is consistent with the lack of saturation of MRI channel modes in analogous axisymmetric MHD simulations. The amplification of the magnetic field by the MRI generates a significant pressure anisotropy in the plasma (with the pressure perpendicular to B being larger than the parallel pressure). We find that this pressure anisotropy in turn excites mirror modes and that the volume-averaged pressure anisotropy remains near the threshold for mirror mode excitation. Particle energization is due to both reconnection and viscous heating associated with the pressure anisotropy. Reconnection produces a distinctive power-law component in the energy distribution function of the particles, indicating the likelihood of non-thermal ion and electron acceleration in collisionless accretion disks. This has important implications for interpreting the observed emission-from the radio to the gamma-rays-of systems such as Sgr A*.

q-Gaussian based Smoothed Functional Algorithms for Stochastic Optimization

The q-Gaussian distribution results from maximizing certain generalizations of Shannon entropy under some constraints. The importance of q-Gaussian distributions stems from the fact that they exhibit power-law behavior, and also generalize Gaussian distributions. In this paper, we propose a Smoothed Functional (SF) scheme for gradient estimation using q-Gaussian distribution, and also propose an algorithm for optimization based on the above scheme. Convergence results of the algorithm are presented. Performance of the proposed algorithm is shown by simulation results on a queuing model.

A general geomorphological recession flow model for river basins

Recession flows in a basin are controlled by the temporal evolution of its active drainage network (ADN). The geomorphological recession flow model (GRFM) assumes that both the rate of flow generation per unit ADN length (q) and the speed at which ADN heads move downstream (c) remain constant during a recession event. Thereby, it connects the power law exponent of -dQ/dt versus Q (discharge at the outlet at time t) curve, , with the structure of the drainage network, a fixed entity. In this study, we first reformulate the GRFM for Horton-Strahler networks and show that the geomorphic ((g)) is equal to D/(D-1), where D is the fractal dimension of the drainage network. We then propose a more general recession flow model by expressing both q and c as functions of Horton-Strahler stream order. We show that it is possible to have = (g) for a recession event even when q and c do not remain constant. The modified GRFM suggests that is controlled by the spatial distribution of subsurface storage within the basin. By analyzing streamflow data from 39 U.S. Geological Survey basins, we show that is having a power law relationship with recession curve peak, which indicates that the spatial distribution of subsurface storage varies across recession events. Key Points The GRFM is reformulated for Horton-Strahler networks. The GRFM is modified by allowing its parameters to vary along streams. Sub-surface storage distribution controls recession flow characteristics.

Dense shallow granular flows

Simplified equations are derived for a granular flow in the `dense' limit where the volume fraction is close to that for dynamical arrest, and the `shallow' limit where the stream-wise length for flow development (L) is large compared with the cross-stream height (h). The mass and diameter of the particles are set equal to 1 in the analysis without loss of generality. In the dense limit, the equations are simplified by taking advantage of the power-law divergence of the pair distribution function chi proportional to (phi(ad) - phi)(-alpha), and a faster divergence of the derivativ rho(d chi/d rho) similar to (d chi/d phi), where rho and phi are the density and volume fraction, and phi(ad) is the volume fraction for arrested dynamics. When the height h is much larger than the conduction length, the energy equation reduces to an algebraic balance between the rates of production and dissipation of energy, and the stress is proportional to the square of the strain rate (Bagnold law). In the shallow limit, the stress reduces to a simplified Bagnold stress, where all components of the stress are proportional to (partial derivative u(x)/partial derivative y)(2), which is the cross-stream (y) derivative of the stream-wise (x) velocity. In the simplified equations for dense shallow flows, the inertial terms are neglected in the y momentum equation in the shallow limit because the are O(h/L) smaller than the divergence of the stress. The resulting model contains two equations, a mass conservation equations which reduces to a solenoidal condition on the velocity in the incompressible limit, and a stream-wise momentum equation which contains just one parameter B which is a combination of the Bagnold coefficients and their derivatives with respect to volume fraction. The leading-order dense shallow flow equations, as well as the first correction due to density variations, are analysed for two representative flows. The first is the development from a plug flow to a fully developed Bagnold profile for the flow down an inclined plane. The analysis shows that the flow development length is ((rho) over barh(3)/B) , where (rho) over bar is the mean density, and this length is numerically estimated from previous simulation results. The second example is the development of the boundary layer at the base of the flow when a plug flow (with a slip condition at the base) encounters a rough base, in the limit where the momentum boundary layer thickness is small compared with the flow height. Analytical solutions can be found only when the stream-wise velocity far from the surface varies as x(F), where x is the stream-wise distance from the start of the rough base and F is an exponent. The boundary layer thickness increases as (l(2)x)(1/3) for all values of F, where the length scale l = root 2B/(rho) over bar. The analysis reveals important differences between granular flows and the flows of Newtonian fluids. The Reynolds number (ratio of inertial and viscous terms) turns out to depend only on the layer height and Bagnold coefficients, and is independent of the flow velocity, because both the inertial terms in the conservation equations and the divergence of the stress depend on the square of the velocity/velocity gradients. The compressibility number (ratio of the variation in volume fraction and mean volume fraction) is independent of the flow velocity and layer height, and depends only on the volume fraction and Bagnold coefficients.

Finite size scaling in crossover among different random matrix ensembles in microscopic lattice models

Using numerical diagonalization we study the crossover among different random matrix ensembles (Poissonian, Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE) and Gaussian symplectic ensemble (GSE)) realized in two different microscopic models. The specific diagnostic tool used to study the crossovers is the level spacing distribution. The first model is a one-dimensional lattice model of interacting hard-core bosons (or equivalently spin 1/2 objects) and the other a higher dimensional model of non-interacting particles with disorder and spin-orbit coupling. We find that the perturbation causing the crossover among the different ensembles scales to zero with system size as a power law with an exponent that depends on the ensembles between which the crossover takes place. This exponent is independent of microscopic details of the perturbation. We also find that the crossover from the Poissonian ensemble to the other three is dominated by the Poissonian to GOE crossover which introduces level repulsion while the crossover from GOE to GUE or GOE to GSE associated with symmetry breaking introduces a subdominant contribution. We also conjecture that the exponent is dependent on whether the system contains interactions among the elementary degrees of freedom or not and is independent of the dimensionality of the system.

Low frequency modulation of jets in quasigeostrophic turbulence

Quasigeostrophic turbulence on a beta-plane with a finite deformation radius is studied numerically, with particular emphasis on frequency and combined wavenumber-frequency domain analyses. Under suitable conditions, simulations with small-scale random forcing and large-scale drag exhibit a spontaneous formation of multiple zonal jets. The first hint of wave-like features is seen in the distribution of kinetic energy as a function of frequency; specifically, for progressively larger deformation scales, there are systematic departures in the form of isolated peaks (at progressively higher frequencies) from a power-law scaling. Concomitantly, there is an inverse flux of kinetic energy in frequency space which extends to lower frequencies for smaller deformation scales. The identification of these peaks as Rossby waves is made possible by examining the energy spectrum in frequency-zonal wavenumber and frequency-meridional wavenumber diagrams. In fact, the modified Rhines scale turns out to be a useful measure of the dominant meridional wavenumber of the modulating Rossby waves; once this is fixed, apart from a spectral peak at the origin (the steady jet), almost all the energy is contained in westward propagating disturbances that follow the theoretical Rossby dispersion relation. Quite consistently, noting that the zonal scale of the modulating waves is restricted to the first few wavenumbers, the energy spectrum is almost entirely contained within the corresponding Rossby dispersion curves on a frequency-meridional wavenumber diagram. Cases when jets do not form are also considered; once again, there is a hint of Rossby wave activity, though the spectral peaks are quite muted. Further, the kinetic energy scaling in frequency domain follows a -5/3 power-law and is distributed much more broadly in frequency-wavenumber diagrams. (C) 2015 AIP Publishing LLC.

Minimization Problems Based on Relative alpha-Entropy I: Forward Projection

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative alpha-entropies (denoted I-alpha), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative alpha-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative alpha-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Renyi or Tsallis entropy principle. The minimizing probability distribution (termed forward I-alpha-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse I-alpha-projection is studied.

Homogeneous isotropic superfluid turbulence in two dimensions: Inverse and forward cascades in the Hall-Vinen-Bekharevich-Khalatnikov model

We present the first direct-numerical-simulation study of the statistical properties of two-dimensional superfluid turbulence in the simplified, Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both normalfluid and superfluid energy spectra can exhibit two power-law regimes, the first associated with an inverse cascade of energy and the second with the forward cascade of enstrophy. We quantify the mutual-friction-induced alignment of normal and superfluid velocities by obtaining probability distribution functions of the angle between them and the ratio of their moduli.

Transport properties of solution processed Cu2SnS3/AZnO heterostructure for low cost photovoltaics

Cu2SnS3 thin films were deposited by a facile sot-gel technique followed by annealing. The annealed films were structurally characterized by grazing incidence X-ray diffraction (GIXRD) and transmission electron microscopy (TEM). The crystal structure was found to be tetragonal with crystallite sizes of 2.4-3 nm. Texture coefficient calculations from the GIXRD revealed the preferential orientation of the film along the (112) plane. The morphological investigations of the films were carried out using field emission scanning electron microscopy (FESEM) and the composition using electron dispersive spectroscopy (EDS). The temperature dependent current, voltage characteristics of the Cu2SnS3/AZnO heterostructure were studied. The log I-log V plot exhibited three regions of different slopes showing linear ohmic behavior and non-linear behavior following the power law. The temperature dependent current voltage characteristics revealed the variation in ideality factor and barrier height with temperature. The Richardson constant was calculated and its deviation from the theoretical value revealed the inhomogeneity of the barrier heights. Transport characteristics were modeled using the thermionic emission model. The Gaussian distribution of barrier heights was applied and from the modified Richardson plot the value of the Richardson constant was found to be 47.18 A cm(-2) K-2. (c) 2015 Elsevier B.V. All rights reserved.

Anomalous lifetime statistics of ligand-receptor binding in a tethered polymer system

In this paper, motivated by observations of non-exponential decay times in the stochastic binding and release of ligand-receptor systems, exemplified by the work of Rogers et al on optically trapped DNA-coated colloids (Rogers et al 2013 Soft Matter 9 6412), we explore the general problem of polymer-mediated surface adhesion using a simplified model of the phenomenon in which a single polymer molecule, fixed at one end, binds through a ligand at its opposite end to a flat surface a fixed distance L away and uniformly covered with receptor sites. Working within the Wilemski-Fixman approximation to diffusion-controlled reactions, we show that for a flexible Gaussian chain, the predicted distribution of times f(t) for which the ligand and receptor are bound is given, for times much shorter than the longest relaxation time of the polymer, by a power law of the form t(-1/4). We also show when the effects of chain stiffness are incorporated into this model (approximately), the structure of f(t) is altered to t(-1/2). These results broadly mirror the experimental trends in the work cited above.

Structure and Dynamics of Octamethylcyclotetrasiloxane Confined between Mica Surfaces

Using a molecular model for octamethylcydotetrasiloxane (OMCTS), molecular dynamics simulations are carried out to probe the phase state of OMCTS confined between two mica surfaces in equilibrium With a reservoir. Molecular dynamics simulations are carried out for elevations ranging from 5 to 35 K above the melting point for the OMCTS model used in this study. The Helmholtz free energy is, computed for a specific confinement using the :two-phase thermodynamic (2PT) method. Analysis of the in-plane pair correlation functions did not reveal signatures of freezing even under an extreme confinement of two layers. OMCTS is found to orient with a wide distribution of orientations with respect to the mica surface, with a distinct preference for the surface parallel configuration in the contact layers. The self-intermediate scattering function is found to decay with increasing relaxation times as the surface separation is decreased, and the two-step relaxation in the scattering function, a signature of glassy dynamics, distinctly evolves as the temperature is lowered. However, even at 5 K above the melting point, we did not observe a freezing transition and the self-intermediate scattering functions relax within 200 ps for the seven-layered confined system. The self diffusivity and relaxation times obtained from the Kohlrausch-Williams-Watts stretched exponential fits to the late alpha-relaxation exhibit power law scalings with the packing fraction as predicted by mode coupling theory. A distinct discontinuity in the Helmholtz free energy, potential energy, and a sharp change in the local bond order parameter, Q(4), was observed at 230 K for a five-layered system upon cooling, indicative of a first-order transition. A freezing point depression of about 30 K was observed for this five-layered confined system, and at the lower temperatures, contact layers were found to be disordered with long-range order present only in the inner layers. These dynamical signatures indicate that confined OMCTS undergoes a slowdown akin to a fluid approaching a glass transition upon increasing confinement, and freezing under confinement would require substantial subcooling below the bulk melting point of OMCTS.

Fractals and Scaling in Fracture Induced by Microcrack Coalescence

A numerical model is proposed to simulate fracture induced by the coalescence of numerous microcracks, in which the condition for coalescence between two randomly nucleated microcracks is determined in terms of a load-sharing principle. The results of the simulation show that, as the number density of nucleated microcracks increases, stochastic coalescence first occurs followed by a small fluctuation, and finally a newly nucleated microcrack triggers a cascade coalescence of microcracks resulting in catastrophic failure. The fracture profiles exhibit self-affine fractal characteristics with a universal roughness exponent, but the critical damage threshold is sensitive to details of the model. The spatiotemporal distribution of nucleated microcracks in the vicinity of critical failure follows a power-law behaviour, which implies that the microcrack system may evolve to a critical state.

Avalanche behavior and statistical properties in a microcrack coalescence process

Fracture owing to the coalescence of numerous microcracks can be described by a simple statistical model, where a coalescence event stochastically occurs as the number density of nucleated microcracks increases. Both numerical simulation and statistical analysis reveal that a microcrack coalescence process may display avalanche behavior and that the final failure is catastrophic. The cumulative distribution of coalescence events in the vicinity of critical fracture follows a power law and the fracture profile has self-affine fractal characteristic. Some macromechanical quantities may be traced back and extracted from the mesoscopic process based on the statistical analysis of coalescence events.