Porous Three Dimensional Arrays of Plasmonic Nanoparticles

Plasmonic interactions in a well-defined array of metallic nanoparticles can lead to interesting optical effects, such as local electric field enhancement and shifts in the extinction spectra, which are of interest in diverse technological applications, including those pertaining to biochemical sensing and photonic circuitry. Here, we report on a single-step wafer scale fabrication of a three-dimensional array of metallic nanoparticles whose sizes and separations can be easily controlled to be anywhere between fifty to a few hundred nanometers, allowing the optical response of the system to be tailored with great control in the visible region of the spectrum. The substrates, apart from having a large surface area, are inherently porous and therefore suitable for optical sensing applications, such as surface enhanced Raman scattering, containing a high density of spots with enhanced local electric fields arising from plasmonic couplings.

A model of coupled thermal, mechanical, and electrostatic field effects in III-N thin film heterostructures

A one-dimensional coupled multi-physics based model has been developed to accurately compute the effects of electrostatic, mechanical, and thermal field interactions on the electronic energy band structure in group III-nitrides thin film heterostructures. Earlier models reported in published literature assumes electro-mechanical field with uniform temperature thus neglecting self-heating. Also, the effects of diffused interface on the energy band structure were not studied. We include these effects in a self-consistent manner wherein the transport equation is introduced along with the electro-mechanical models, and the lattice structural variation as observed in experiments are introduced at the interface. Due to these effects, the electrostatic potential distribution in the heterostructure is altered. The electron and hole ground state energies decrease by 5% and 9%, respectively, at a relative temperature of 700 K, when compared with the results obtained from the previously reported electro-mechanical model assuming constant and uniform temperature distribution. A diffused interface decreases the ground state energy of electrons and holes by about 11% and 9%, respectively, at a relative temperature of 700 K when compared with the predictions based on uniform temperature based electro-mechanical model. (C) 2013 AIP Publishing LLC.

Majorana fermions in superconducting wires: Effects of long-range hopping, broken time-reversal symmetry, and potential landscapes

We present a comprehensive study of two of the most experimentally relevant extensions of Kitaev's spinless model of a one-dimensional p-wave superconductor: those involving (i) longer-range hopping and superconductivity and (ii) inhomogeneous potentials. We commence with a pedagogical review of the spinless model and, as a means of characterizing topological phases exhibited by the systems studied here, we introduce bulk topological invariants as well as those derived from an explicit consideration of boundary modes. In time-reversal symmetric systems, we find that the longer range hopping leads to topological phases characterized by multiple Majorana modes. In particular, we investigate a spin model that respects a duality and maps to a fermionic model with multiple Majorana modes; we highlight the connection between these topological phases and the broken symmetry phases in the original spin model. In the presence of time-reversal symmetry breaking terms, we show that the topological phase diagram is characterized by an extended gapless regime. For the case of inhomogeneous potentials, we explore phase diagrams of periodic, quasiperiodic, and disordered systems. We present a detailed mapping between normal state localization properties of such systems and the topological phases of the corresponding superconducting systems. This powerful tool allows us to leverage the analyses of Hofstadter's butterfly and the vast literature on Anderson localization to the question of Majorana modes in superconducting quasiperiodic and disordered systems, respectively. We briefly touch upon the synergistic effects that can be expected in cases where long-range hopping and disorder are both present.

Turbulence in the two-dimensional Fourier-truncated Gross-Pitaevskii equation

We undertake a systematic, direct numerical simulation of the twodimensional, Fourier-truncated, Gross-Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of parameters. We find that the time evolution of this system can be classified into four regimes with qualitatively different statistical properties. Firstly, there are transients that depend on the initial conditions. In the second regime, powerlaw scaling regions, in the energy and the occupation-number spectra, appear and start to develop; the exponents of these power laws and the extents of the scaling regions change with time and depend on the initial condition. In the third regime, the spectra drop rapidly for modes with wave numbers k > kc and partial thermalization takes place for modes with k < kc; the self-truncation wave number kc(t) depends on the initial conditions and it grows either as a power of t or as log t. Finally, in the fourth regime, complete thermalization is achieved and, if we account for finite-size effects carefully, correlation functions and spectra are consistent with their nontrivial Berezinskii-Kosterlitz-Thouless forms. Our work is a natural generalization of recent studies of thermalization in the Euler and other hydrodynamical equations; it combines ideas from fluid dynamics and turbulence, on the one hand, and equilibrium and nonequilibrium statistical mechanics on the other.

Effects of initial height on the steady-state persistence probability of linear growth models

The effects of the initial height on the temporal persistence probability of steady-state height fluctuations in up-down symmetric linear models of surface growth are investigated. We study the (1 + 1)-dimensional Family model and the (1 + 1)-and (2 + 1)-dimensional larger curvature (LC) model. Both the Family and LC models have up-down symmetry, so the positive and negative persistence probabilities in the steady state, averaged over all values of the initial height h(0), are equal to each other. However, these two probabilities are not equal if one considers a fixed nonzero value of h(0). Plots of the positive persistence probability for negative initial height versus time exhibit power-law behavior if the magnitude of the initial height is larger than the interface width at saturation. By symmetry, the negative persistence probability for positive initial height also exhibits the same behavior. The persistence exponent that describes this power-law decay decreases as the magnitude of the initial height is increased. The dependence of the persistence probability on the initial height, the system size, and the discrete sampling time is found to exhibit scaling behavior.

Hypersonic interference heating on flat plate with short three-dimensional protuberances

Experiments were conducted to measure the heat flux in the vicinity of a three-dimensional protuberance placed on a flat plate facing a hypersonic flow at zero angle of attack. The effects of flow enthalpy and height of the protuberance on the interference heating in its vicinity were studied. Evidence of disturbed flow with highly three-dimensional characteristics and heightened vorticity was observed near the protrusion. A parametric study by changing the deflection angle of the protuberance was also made. Correlations exist in the open literature for enthalpy values lower than 2  MJ/kg. This effort has yielded a new correlation that is valid for enthalpies up to 6  MJ/kg. The Z-type schlieren technique was used to visualize the flow features qualitatively for one of the flow conditions studied.

Three-Dimensional Study of Natural Convection in a Horizontal Channel With Discrete Heaters on One of Its Vertical Walls

Three-dimensional natural convection in a horizontal channel with an array of discrete flush-mounted heaters on one of its vertical walls is numerically studied. Effects of thermal conductivities of substrate and heaters and convection on outer sides of the channel walls on heat transfer are examined. The substrate affects heat transfer in a wider range of thermal conductivities than do the heaters. At lower heater thermal conductivities a higher heat portion is transferred by direct convection from the heaters to the adjacent coolant. However, higher substrate conductivity is associated with higher heat portion transferred through the substrate. The innermost heater column is found to become the hottest heater column due to the lower coolant accessibility. The heat transfer in the channel is strongly influenced by convection on the outer sides of the channel walls. Correlations are presented for dimensionless temperature maximum and average Nusselt number.

Cavitation in brittle metallic glasses - Effects of stress state and distributed weak zones

Experimental studies and atomistic simulations have shown that brittle metallic glasses fail by a cavitation mechanism whose origin has been traced to the presence of intrinsic atomic density fluctuations which give rise to weak zones with reduced yield strength. It has been shown recently through continuum analysis that the presence of these zones can lower the cavitation stress considerably under equibiaxial loading. The objective of the present work is to study the effect of the applied stress state on the cavitation behavior of such a heterogeneous plastic solid with distributed weak zones. To this end, 2D plane strain finite element simulations are performed by subjecting a unit cell containing a weak zone to different (biaxiality) stress ratios. The volume fraction and yield strength of the weak zone are varied over a wide range. The results show that unlike in a homogeneous plastic solid, the cavitation stress of the heterogeneous aggregate does not reduce appreciably as the stress ratio decreases from unity when the yield strength of the weak zone is low. It is found that a non-dimensional parameter characterizing the stress state prevailing in the weak zone and its yield properties uniquely control the cavitation stress. The nature of cavitation bifurcation may change from unstable bifurcation to the left at sufficiently low stress ratio to one involving snap cavitation at high stress ratio. (C) 2014 Elsevier Ltd. All rights reserved.

Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation

We carry out an extensive numerical study of the dynamics of spiral waves of electrical activation, in the presence of periodic deformation (PD) in two-dimensional simulation domains, in the biophysically realistic mathematical models of human ventricular tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNPO4 model). We first consider simulations in cable-type domains, in which we calculate the conduction velocity theta and the wavelength lambda of a plane wave; we show that PD leads to a periodic, spatial modulation of theta and a temporally periodic modulation of lambda; both these modulations depend on the amplitude and frequency of the PD. We then examine three types of initial conditions for both TP06 and TNNPO4 models and show that the imposition of PD leads to a rich variety of spatiotemporal patterns in the transmembrane potential including states with a single rotating spiral (RS) wave, a spiral-turbulence (ST) state with a single meandering spiral, an ST state with multiple broken spirals, and a state SA in which all spirals are absorbed at the boundaries of our simulation domain. We find, for both TP06 and TNNPO4 models, that spiral-wave dynamics depends sensitively on the amplitude and frequency of PD and the initial condition. We examine how these different types of spiral-wave states can be eliminated in the presence of PD by the application of low-amplitude pulses by square- and rectangular-mesh suppression techniques. We suggest specific experiments that can test the results of our simulations.

Dielectric elastomers: Asymptotically-correct three-dimensional displacement field

Asymptotically-accurate dimensional reduction from three to two dimensions and recovery of 3-D displacement field of non-prestretched dielectric hyperelastic membranes are carried out using the Variational Asymptotic Method (VAM) with moderate strains and very small ratio of the membrane thickness to its shortest wavelength of the deformation along the plate reference surface chosen as the small parameters for asymptotic expansion. Present work incorporates large deformations (displacements and rotations), material nonlinearity (hyperelasticity), and electrical effects. It begins with 3-D nonlinear electroelastic energy and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a 2-D nonlinear plate analysis. Major contribution of this paper is a comprehensive nonlinear through-the-thickness analysis which provides a 2-D energy asymptotically equivalent of the 3-D energy, a 2-D constitutive relation between the 2-D generalized strain and stress tensors for the plate analysis and a set of recovery relations to express the 3-D displacement field. Analytical expressions are derived for warping functions and stiffness coefficients. This is the first attempt to integrate an analytical work on asymptotically-accurate nonlinear electro-elastic constitutive relation for compressible dielectric hyperelastic model with a generalized finite element analysis of plates to provide 3-D displacement fields using VAM. A unified software package `VAMNLM' (Variational Asymptotic Method applied to Non-Linear Material models) was developed to carry out 1-D non-linear analysis (analytical), 2-D non-linear finite element analysis and 3-D recovery analysis. The applicability of the current theory is demonstrated through an actuation test case, for which distribution of 3-D displacements are provided. (C) 2014 Elsevier Ltd. All rights reserved.

Turbulent states and their transitions in mathematical models for ventricular tissue: The effects of random interstitial fibroblasts

We study the dynamical behaviors of two types of spiral-and scroll-wave turbulence states, respectively, in two-dimensional (2D) and three-dimensional (3D) mathematical models, of human, ventricular, myocyte cells that are attached to randomly distributed interstitial fibroblasts; these turbulence states are promoted by (a) the steep slope of the action-potential-duration-restitution (APDR) plot or (b) early afterdepolarizations (EADs). Our single-cell study shows that (1) the myocyte-fibroblast (MF) coupling G(j) and (2) the number N-f of fibroblasts in an MF unit lower the steepness of the APDR slope and eliminate the EAD behaviors of myocytes; we explore the pacing dependence of such EAD suppression. In our 2D simulations, we observe that a spiral-turbulence (ST) state evolves into a state with a single, rotating spiral (RS) if either (a) G(j) is large or (b) the maximum possible number of fibroblasts per myocyte N-f(max) is large. We also observe that the minimum value of G(j), for the transition from the ST to the RS state, decreases as N-f(max) increases. We find that, for the steep-APDR-induced ST state, once the MF coupling suppresses ST, the rotation period of a spiral in the RS state increases as (1) G(j) increases, with fixed N-f(max), and (2) N-f(max) increases, with fixed G(j). We obtain the boundary between ST and RS stability regions in the N-f(max)-G(j) plane. In particular, for low values of N-f(max), the value of G(j), at the ST-RS boundary, depends on the realization of the randomly distributed fibroblasts; this dependence decreases as N-f(max) increases. Our 3D studies show a similar transition from scroll-wave turbulence to a single, rotating, scroll-wave state because of the MF coupling. We examine the experimental implications of our study and propose that the suppression (a) of the steep slope of the APDR or (b) EADs can eliminate spiral-and scroll-wave turbulence in heterogeneous cardiac tissue, which has randomly distributed fibroblasts.

NON-DIMENSIONAL KINETOELASTOSTATIC MAPS FOR COMPLIANT MECHANISMS

How do we assess the capability of a compliant mechanism of given topology and shape? The kinetoelastostatic maps proposed in this paper help answer this question. These maps are drawn in 2D using two non-dimensional quantities, one capturing the nonlinear static response and the other the geometry, material, and applied forces. Geometrically nonlinear finite element analysis is used to create the maps for compliant mechanisms consisting of slender beams. In addition to the topology and shape, the overall proportions and the proportions of the cross-sections of the beam segments are kept fixed for a map. The finite region of the map is parameterized using a non-dimensional quantity defined as the slenderness ratio. The shape and size of the map and the parameterized curves inside it indicate the complete kinetoelastostatic capability of the corresponding compliant mechanism of given topology, shape, and fixed proportions. Static responses considered in this paper include input/output displacement, geometric amplification, mechanical advantage, maximum stress, etc. The maps can be used to compare mechanisms, to choose a suitable mechanism for an application, or re-design as may be needed. The usefulness of the non-dimensional maps is presented with multiple applications of different variety. Non-dimensional portrayal of snap-through mechanisms is one such example. The effect of the shape of the cross-section of the beam segments and the role of different segments in the mechanism as well as extension to 3D compliant mechanisms, the cases of multiple inputs and outputs, and moment loads are also explained. The effects of disproportionate changes on the maps are also analyzed.

Macroporous three-dimensional graphene oxide foams for dye adsorption and antibacterial applications

Several reports illustrate the wide range applicability of graphene oxide (GO) in water remediation. However, a few layers of graphene oxide tend to aggregate under saline conditions thereby reducing its activity. The effects of aggregation can be minimized by having a random arrangement of GO layers in a three dimensional architecture. The current study emphasizes the potential benefits of highly porous, ultralight graphene oxide foams in environmental applications. These foams were prepared by a facile and cost effective lyophilization technique. The 3D architecture allowed the direct use of these foams in the removal of aqueous pollutants without any pretreatment such as ultrasonication. Due to its macroporous nature, the foams exhibited excellent adsorption abilities towards carcinogenic dyes such as rhodamine B (RB), malachite green (MG) and acriflavine (AF) with respective sorption capacities of 446, 321 and 228 mg g(-1) of foam. These foams were also further investigated for antibacterial activities against E. coli bacteria in aqueous and nutrient growth media. The random arrangement of GO layers in the porous foam architecture allowed it to exhibit excellent antibacterial activity even under physiological conditions by following the classical wrapping-perturbation mechanism. These results demonstrate the vast scope of GO foam in water remediation for both dye removal and antibacterial activity.

Effects of 'sinking in' and 'piling up' on estimating the contact area under load in indentation

The phenomena of the 'piling up' and 'sinking-in' of surface profiles in conical indentation in elastic-plastic solids with work hardening are studied using dimensional and finite-element analysis. The degree of sinking in and piling up is shown to depend on the ratio of the initial yield strength Y to Young's modulus E and on the work-hardening exponent n. The widely used procedure proposed by Oliver and Pharr for estimating contact depth is then evaluated systematically. By comparing the contact depth obtained directly from finite-element calculations with that obtained from the initial unloading slope using the Oliver-Pharr procedure, the applicability of the procedure is discussed.

An Analytical Solution for Three-Dimensional Diffraction of Plane P-Waves by a Hemispherical Alluvial Valley with Saturated Soil Deposits

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot's dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot's dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.