Vorticity moments in four numerical simulations of the 3D Navier-Stokes equations

The issue of intermittency in numerical solutions of the 3D Navier-Stokes equations on a periodic box 0, L](3) is addressed through four sets of numerical simulations that calculate a new set of variables defined by D-m(t) = (pi(-1)(0) Omega(m))(alpha m) for 1 <= m <= infinity where alpha(m) = 2m/(4m - 3) and Omega(m)(t)](2m) = L-3 integral(v) vertical bar omega vertical bar(2m) dV with pi(0) = vL(-2). All four simulations unexpectedly show that the D-m are ordered for m = 1,..., 9 such that Dm+1 < D-m. Moreover, the D-m squeeze together such that Dm+1/D-m NE arrow 1 as m increases. The values of D-1 lie far above the values of the rest of the D-m, giving rise to a suggestion that a depletion of nonlinearity is occurring which could be the cause of Navier-Stokes regularity. The first simulation is of very anisotropic decaying turbulence; the second and third are of decaying isotropic turbulence from random initial conditions and forced isotropic turbulence at fixed Grashof number respectively; the fourth is of very-high-Reynolds-number forced, stationary, isotropic turbulence at up to resolutions of 4096(3).

Taming of large diameter triaxial setup

Triaxial tests are essential to estimate the shear strength properties of the soil or rock. Normally triaxial tests are carried out on samples of 38 mm diameter and 76 mm height. Granular materials, predominantly used in base/sub-base construction of pavements or in railways have size range of 60-75 mm. Determination of shear strength parameters of those materials can be made possible only through triaxial tests on large diameter samples. This paper describes a large diameter cyclic triaxial testing facility set up in the Geotechnical Engineering lab of Indian Institute of Science. This setup consists of 100 kN capacity dynamic loading frame, which facilitates testing of samples of up to 300 mm diameter and 600 mm height. The loading ram can be actuated up to a maximum frequency of 10 Hz, with maximum amplitude of 100 mm. The setup is capable of carrying out static as well as dynamic triaxial tests under isotropic, anisotropic conditions with a maximum confining pressure of 1 MPa. Working with this setup is a difficult task because of the size of the sample. In this paper, a detailed discussion on the various problems encountered during the initial testing using the equipment, the ideas and solutions adopted to solve them are presented. Pilot experiments on granular sub-base material of 53 mm down size are also presented.

On Uniform Approximate Solutions in Bending of Symmetric Laminated Plates

A layer-wise theory with the analysis of face ply independent of lamination is used in the bending of symmetric laminates with anisotropic plies. More realistic and practical edge conditions as in Kirchhoff's theory are considered. An iterative procedure based on point-wise equilibrium equations is adapted. The necessity of a solution of an auxiliary problem in the interior plies is explained and used in the generation of proper sequence of two dimensional problems. Displacements are expanded in terms of polynomials in thickness coordinate such that continuity of transverse stresses across interfaces is assured. Solution of a fourth order system of a supplementary problem in the face ply is necessary to ensure the continuity of in-plane displacements across interfaces and to rectify inadequacies of these polynomial expansions in the interior distribution of approximate solutions. Vertical deflection does not play any role in obtaining all six stress components and two in-plane displacements. In overcoming lacuna in Kirchhoff's theory, widely used first order shear deformation theory and other sixth and higher order theories based on energy principles at laminate level in smeared laminate theories and at ply level in layer-wise theories are not useful in the generation of a proper sequence of 2-D problems converging to 3-D problems. Relevance of present analysis is demonstrated through solutions in a simple text book problem of simply supported square plate under doubly sinusoidal load.

Influence of Spatial Variation of Hydraulic Conductivity of Municipal Solid Waste on Performance of Bioreactor Landfill

The current study analyzes the leachate distribution in the Orchard Hills Landfill, Davis Junction, Illinois, using a two-phase flow model to assess the influence of variability in hydraulic conductivity on the effectiveness of the existing leachate recirculation system and its operations through reliability analysis. Numerical modeling, using finite-difference code, is performed with due consideration to the spatial variation of hydraulic conductivity of the municipal solid waste (MSW). The inhomogeneous and anisotropic waste condition is assumed because it is a more realistic representation of the MSW. For the reliability analysis, the landfill is divided into 10 MSW layers with different mean values of vertical and horizontal hydraulic conductivities (decreasing from top to bottom), and the parametric study is performed by taking the coefficients of variation (COVs) as 50, 100, 150, and 200%. Monte Carlo simulations are performed to obtain statistical information (mean and COV) of output parameters of the (1) wetted area of the MSW, (2) maximum induced pore pressure, and (3) leachate outflow. The results of the reliability analysis are used to determine the influence of hydraulic conductivity on the effectiveness of the leachate recirculation and are discussed in the light of a deterministic approach. The study is useful in understanding the efficiency of the leachate recirculation system. (C) 2013 American Society of Civil Engineers.

Floquet generation of Majorana end modes and topological invariants

We show how Majorana end modes can be generated in a one-dimensional system by varying some of the parameters in the Hamiltonian periodically in time. The specific model we consider is a chain containing spinless electrons with a nearest-neighbor hopping amplitude, a p-wave superconducting term, and a chemical potential; this is equivalent to a spin-1/2 chain with anisotropic XY couplings between nearest neighbors and a magnetic field applied in the (z) over cap direction. We show that varying the chemical potential (or magnetic field) periodically in time can produce Majorana modes at the ends of a long chain. We discuss two kinds of periodic driving, periodic delta-function kicks, and a simple harmonic variation with time. We discuss some distinctive features of the end modes such as the inverse participation ratio of their wave functions and their Floquet eigenvalues which are always equal to +/- 1 for time-reversal-symmetric systems. For the case of periodic delta-function kicks, we use the effective Hamiltonian of a system with periodic boundary conditions to define two topological invariants. The first invariant is a well-known winding number, while the second invariant has not appeared in the literature before. The second invariant is more powerful in that it always correctly predicts the numbers of end modes with Floquet eigenvalues equal to + 1 and -1, while the first invariant does not. We find that the number of end modes can become very large as the driving frequency decreases. We show that periodic delta-function kicks in the hopping and superconducting terms can also produce end modes. Finally, we study the effect of electron-phonon interactions (which are relevant at finite temperatures) and a random noise in the chemical potential on the Majorana modes.

Solid-solid collapse transition in a two dimensional model molecular system

Solid-solid collapse transition in open framework structures is ubiquitous in nature. The real difficulty in understanding detailed microscopic aspects of such transitions in molecular systems arises from the interplay between different energy and length scales involved in molecular systems, often mediated through a solvent. In this work we employ Monte-Carlo simulation to study the collapse transition in a model molecular system interacting via both isotropic as well as anisotropic interactions having different length and energy scales. The model we use is known as Mercedes-Benz (MB), which, for a specific set of parameters, sustains two solid phases: honeycomb and oblique. In order to study the temperature induced collapse transition, we start with a metastable honeycomb solid and induce transition by increasing temperature. High density oblique solid so formed has two characteristic length scales corresponding to isotropic and anisotropic parts of interaction potential. Contrary to the common belief and classical nucleation theory, interestingly, we find linear strip-like nucleating clusters having significantly different order and average coordination number than the bulk stable phase. In the early stage of growth, the cluster grows as a linear strip, followed by branched and ring-like strips. The geometry of growing cluster is a consequence of the delicate balance between two types of interactions, which enables the dominance of stabilizing energy over destabilizing surface energy. The nucleus of stable oblique phase is wetted by intermediate order particles, which minimizes the surface free energy. In the case of pressure induced transition at low temperature the collapsed state is a disordered solid. The disordered solid phase has diverse local quasi-stable structures along with oblique-solid like domains. (C) 2013 AIP Publishing LLC.

ENDOR studies of hydrogen bonding of the AsO44- centre in x-ray irradiated KH2AsO4

We here report what we believe to be an important method for studying hydrogen bonding in systems containing a paramagnetic centre. The technique of electron-nuclear double resonance ( ENDOR) has been applied to study the hydrogen-bond network around the AsO44-. centre in X-ray irradiated KH2AsO4. ENDOR transitions from several sets of hydrogen nuclei surrounding the centre were observed at 4.2 degrees K and the spectra for two sets of neighbouring nuclei are identified. The angular dependences for these spectra are fitted with a spin-Hamiltonian to obtain the isotropic and anisotropic magnetic hyperfine constants. The results are discussed in terms of the available spectroscopic and crystallographic data on KH2AsO4 and the order-disorder model of ferroelectrictricity in this class of crystals.

Non-Destructive Evaluation of Defects and Damage in Composite Materials and Structures

The mechanical behaviour of composite materials differs from that of conventional structural materials owing to their heterogeneous and anisotropic nature. Different types of defects and anomalies get induced in these materials during the fabrication process. Further, during their service life, the components made of composite materials develop different types of damage. The performance and life of such components is governed by the combined effect of all these defects and damage. While porosity, voids, inclusions etc., are some defects those can get induced during the fabrication of composites, matrix cracks, interface debonds, delaminations and fiber breakage are major types of service induced damage which are of concern. During the service life of components made of composites, one type of damage can grow and initiate another type of damage. For example, matrix cracks can gradually grow to the interface and initiate debonds. Interface debonds in a particular plane can lead to delaminations. Consequently, the combined effect of different types of distributed damage causes the failure of the component. A set of non-destructive evaluation (NDE) methods is well established for testing conventional metallic materials. Some of them can also be utilized for composite materials as they are, and in some cases with a little different approach or modification. Ultrasonics, Radiography, Thermography, Fiber Optics, Acoustic Emision Techniques etc., to name a few. Detection, evaluation and characterization of different types of defects and damage encountered in composite materials and structures using different NDE tools is discussed briefly in this paper.

A finite element method for the Saint-Venant torsion and bending problems for prismatic beams

In this work, we present a finite element formulation for the Saint-Venant torsion and bending problems for prismatic beams. The torsion problem formulation is based on the warping function, and can handle multiply-connected regions (including thin-walled structures), compound and anisotropic bars. Similarly, the bending formulation, which is based on linearized elasticity theory, can handle multiply-connected domains including thin-walled sections. The torsional rigidity and shear centers can be found as special cases of these formulations. Numerical results are presented to show the good coarse-mesh accuracy of both the formulations for both the displacement and stress fields. The stiffness matrices and load vectors (which are similar to those for a variable body force in a conventional structural mechanics problem) in both formulations involve only domain integrals, which makes them simple to implement and computationally efficient. (C) 2014 Elsevier Ltd. All rights reserved.

Nonequilibrium noise in electrophoresis: The microion wind

A colloid supported against gravitational settling by means of an imposed electric field behaves, on average, as if it is at equilibrium in a confining potential T. M. Squires, J. Fluid Mech. 443, 403 (2001)]. We show, however, that the effective Langevin equation for the colloid contains a nonequilibrium noise source, proportional to the field, arising from the thermal motion of dissolved ions. The position fluctuations of the colloid show strong, experimentally testable signatures of nonequilibrium behavior, including a highly anisotropic, frequency-dependent ``effective temperature'' obtained from the fluctuation-dissipation ratio.

Thermal conduction and multiphase gas in cluster cores

We examine the role of thermal conduction and magnetic fields in cores of galaxy clusters through global simulations of the intracluster medium (ICM). In particular, we study the influence of thermal conduction, both isotropic and anisotropic, on the condensation of multiphase gas in cluster cores. Previous hydrodynamic simulations have shown that cold gas condenses out of the hot ICM in thermal balance only when the ratio of the cooling time (t(cool)) and the free-fall time (t(ff)) is less than approximate to 10. Since thermal conduction is significant in the ICM and it suppresses local cooling at small scales, it is imperative to include thermal conduction in such studies. We find that anisotropic (along local magnetic field lines) thermal conduction does not influence the condensation criterion for a general magnetic geometry, even if thermal conductivity is large. However, with isotropic thermal conduction cold gas condenses only if conduction is suppressed (by a factor less than or similar to 0.3) with respect to the Spitzer value.

Constraining gravity using entanglement in AdS/CFT

We investigate constraints imposed by entanglement on gravity in the context of holography. First, by demanding that relative entropy is positive and using the Ryu-Takayanagi entropy functional, we find certain constraints at a nonlinear level for the dual gravity. Second, by considering Gauss-Bonnet gravity, we show that for a class of small perturbations around the vacuum state, the positivity of the two point function of the field theory stress tensor guarantees the positivity of the relative entropy. Further, if we impose that the entangling surface closes off smoothly in the bulk interior, we find restrictions on the coupling constant in Gauss-Bonnet gravity. We also give an example of an anisotropic excited state in an unstable phase with broken conformal invariance which leads to a negative relative entropy.

Wave propagation analysis in laminated composite plates with transverse cracks using the wavelet spectral finite element method

This paper presents a newly developed wavelet spectral finite element (WFSE) model to analyze wave propagation in anisotropic composite laminate with a transverse surface crack penetrating part-through the thickness. The WSFE formulation of the composite laminate, which is based on the first-order shear deformation theory, produces accurate and computationally efficient results for high frequency wave motion. Transverse crack is modeled in wavenumber-frequency domain by introducing bending flexibility of the plate along crack edge. Results for tone burst and impulse excitations show excellent agreement with conventional finite element analysis in Abaqus (R). Problems with multiple cracks are modeled by assembling a number of spectral elements with cracks in frequency-wavenumber domain. Results show partial reflection of the excited wave due to crack at time instances consistent with crack locations. (C) 2014 Elsevier B.V. All rights reserved.

Unzipping Carbon Nanotubes at High Impact

The way nanostructures behave and mechanically respond to high impact collision is a topic of intrigue. For anisotropic nanostructures, such as carbon nanotubes, this response will be complicated based on the impact geometry. Here we report the result of hypervelocity impact of nanotubes against solid targets and show that impact produces a large number of defects in the nanotubes, as well as rapid atom evaporation, leading to their unzipping along the nanotube axis. Fully atomistic reactive molecular dynamics simulations are used to gain further insights of the pathways and deformation and fracture mechanisms of nanotubes under high energy mechanical impact. Carbon nanotubes have been unzipped into graphene nanoribbons before using chemical treatments but here the instability of nanotubes against formation, fracture, and unzipping is revealed purely through mechanical impact. defect

Fabrication and characterization of gold coated hollow silicon microneedle array for drug delivery

In this paper, we present the fabrication and characterization of Ti and Au coated hollow silicon microneedles for transdermal drug delivery applications. The hollow silicon microneedles are fabricated using isotropic etching followed by anisotropic etching to obtain a tapered tip. Silicon microneedle of 300 mu m in height, with 130 mu m outer diameter and 110 mu m inner diameter at the tip followed by 80 mu m inner diameter and 160 mu m outer diameter at the base have been fabricated. In order to improve the biocompatibility of microneedles, the fabricated microneedles were coated with Ti (500 nm) by sputtering technique followed by gold coating using electroplating. A breaking force of 225 N was obtained for the fabricated microneedles, which is 10 times higher than the skin resistive force. Hence, fabricated microneedles can easily be inserted inside the skin without breakage. The fluid flow through the microneedles was studied for different inlet pressures. A minimum inlet pressure of 0.66 kPa was required to achieve a flow rate of 50 mu l in 2 s with de-ionized water as a fluid medium. (C) 2014 Elsevier B.V. All rights reserved.