Nonlinear gravity-wave interactions in stratified turbulence

To investigate the dynamics of gravity waves in stratified Boussinesq flows, a model is derived that consists of all three-gravity-wave-mode interactions (the GGG model), excluding interactions involving the vortical mode. The GGG model is a natural extension of weak turbulence theory that accounts for exact three-gravity-wave resonances. The model is examined numerically by means of random, large-scale, high-frequency forcing. An immediate observation is a robust growth of the so-called vertically sheared horizontal flow (VSHF). In addition, there is a forward transfer of energy and equilibration of the nonzero-frequency (sometimes called ``fast'') gravity-wave modes. These results show that gravity-wave-mode interactions by themselves are capable of systematic interscale energy transfer in a stratified fluid. Comparing numerical simulations of the GGG model and the full Boussinesq system, for the range of Froude numbers (Fr) considered (0.05 a parts per thousand currency sign Fr a parts per thousand currency sign 1), in both systems the VSHF is hardest to resolve. When adequately resolved, VSHF growth is more vigorous in the GGG model. Furthermore, a VSHF is observed to form in milder stratification scenarios in the GGG model than the full Boussinesq system. Finally, fully three-dimensional nonzero-frequency gravity-wave modes equilibrate in both systems and their scaling with vertical wavenumber follows similar power-laws. The slopes of the power-laws obtained depend on Fr and approach -2 (from above) at Fr = 0.05, which is the strongest stratification that can be properly resolved with our computational resources.

Crack stability in edge-notched clamped beam specimens: modeling and experiments

Stability of a fracture toughness testing geometry is important to determine the crack trajectory and R-curve behavior of the specimen. Few configurations provide for inherent geometric stability, especially when the specimen being tested is brittle. We propose a new geometrical construction called the single edge notched clamped bend specimen (SENCB), a modified form of three point bending, yielding stable cracking under load control. It is shown to be particularly suitable for small-scale structures which cannot be made free-standing, (e.g., thin films, coatings). The SENCB is elastically clamped at the two ends to its parent material. A notch is inserted at the bottom center and loaded in bending, to fracture. Numerical simulations are carried out through extended finite element method to derive the geometrical factor f(a/W) and for different beam dimensions. Experimental corroborations of the FEM results are carried out on both micro-scale and macro-scale brittle specimens. A plot of vs a/W, is shown to rise initially and fall off, beyond a critical a/W ratio. The difference between conventional SENB and SENCB is highlighted in terms of and FEM simulated stress contours across the beam cross-section. The `s of bulk NiAl and Si determined experimentally are shown to match closely with literature values. Crack stability and R-curve effect is demonstrated in a PtNiAl bond coat sample and compared with predicted crack trajectories from the simulations. The stability of SENCB is shown for a critical range of a/W ratios, proving that it can be used to get controlled crack growth even in brittle samples under load control.

Shear-imposed falling film

The study of a film falling down an inclined plane is revisited in the presence of imposed shear stress. Earlier studies regarding this topic (Smith, J. Fluid Mech., vol. 217, 1990, pp. 469-485; Wei, Phys. Fluids, vol. 17, 2005a, 012103), developed on the basis of a low Reynolds number, are extended up to moderate values of the Reynolds number. The mechanism of the primary instability is provided under the framework of a two-wave structure, which is normally a combination of kinematic and dynamic waves. In general, the primary instability appears when the kinematic wave speed exceeds the speed of dynamic waves. An equality criterion between their speeds yields the neutral stability condition. Similarly, it is revealed that the nonlinear travelling wave solutions also depend on the kinematic and dynamic wave speeds, and an equality criterion between the speeds leads to an analytical expression for the speed of a family of travelling waves as a function of the Froude number. This new analytical result is compared with numerical prediction, and an excellent agreement is achieved. Direct numerical simulations of the low-dimensional model have been performed in order to analyse the spatiotemporal behaviour of nonlinear waves by applying a constant shear stress in the upstream and downstream directions. It is noticed that the presence of imposed shear stress in the upstream (downstream) direction makes the evolution of spatially growing waves weaker (stronger).

In a hot bubble: why does superbubble feedback work, but isolated supernovae do not?

Using idealized one-dimensional Eulerian hydrodynamic simulations, we contrast the behaviour of isolated supernovae with the superbubbles driven by multiple, collocated supernovae. Continuous energy injection via successive supernovae exploding within the hot/dilute bubble maintains a strong termination shock. This strong shock keeps the superbubble over-pressured and drives the outer shock well after it becomes radiative. Isolated supernovae, in contrast, with no further energy injection, become radiative quite early (less than or similar to 0.1Myr, tens of pc), and stall at scales less than or similar to 100 pc. We show that isolated supernovae lose almost all of their mechanical energy by 1 Myr, but superbubbles can retain up to similar to 40 per cent of the input energy in the form of mechanical energy over the lifetime of the star cluster (a few tens of Myr). These conclusions hold even in the presence of realistic magnetic fields and thermal conduction. We also compare various methods for implementing supernova feedback in numerical simulations. For various feedback prescriptions, we derive the spatial scale below which the energy needs to be deposited in order for it to couple to the interstellar medium. We show that a steady thermal wind within the superbubble appears only for a large number (greater than or similar to 10(4)) of supernovae. For smaller clusters, we expect multiple internal shocks instead of a smooth, dense thermalized wind.

The ballistic resistance of thin aluminium plates with varying degrees of fixity along the circumference

The ballistic performance of thin aluminium targets and influence thereon of different circumferential fixity conditions were studied both experimentally and by finite element simulations. A pressure gun was employed to carry out the experiments while the numerical simulations were performed on ABAQUS/Explicit finite element code using Johnson-Cook elasto-viscoplastic material model. 1 mm thick 1100-H12 aluminium plates of free span diameter 255 mm were normally impacted by 19 mm diameter ogive and blunt nosed projectiles. The boundary conditions of the plate were varied by varying the region of fixity along its circumference as 100%, 75%, 50% and 25% in experiments and the numerical simulations. Further, simulations were carried out to compare the response of the plates with 50% and 75% continuous fixity with those with two and three symmetrical intermittent regions of 25% fixity respectively. The variation in the boundary condition has been found to have insignificant influence on the failure mode of the target however; it significantly affected the mechanics of target deformation and its energy absorption capacity. The ballistic limit increased with decrease in the region of fixity. It decreased for intermittent fixity in comparison with equivalent continuous fixity. And, it has been found to be higher for the impact with projectile having blunt nose in comparison with the one having ogive nose. (C) 2014 Elsevier Ltd. All rights reserved.

Secondary instability as a possible mechanism for clear-air turbulence: a case study

Many theories and mechanisms have been proposed to explain the phenomenon of clear-air turbulence (CAT), and some of them have been successful in predicting light, moderate and, in some cases, severe turbulence. It is only recently that skill in the forecasting of the severe form of CAT, which could lead to injuries to passengers and damage to aircraft, has improved. Recent observations and simulations suggest that some severe to extreme turbulence could be caused by horizontal vortex tubes resulting from secondary instabilities of regions of high shear in the atmosphere. We have conducted direct numerical simulations to understand the scale relationship between primary structures (larger-scale structures related to one of the causes mentioned above) and secondary structures (smaller-sized, shear structures of the size of aircraft). From shear layer simulations, we find that the ratio of sizes of primary and secondary vortices is of the right order to generate aircraft-scale vortex tubes from typical atmospheric shear layers. We have also conducted simulations with a mesoscale atmospheric model, to understand possible causes of turbulence experienced by a flight off the west coast of India. Our simulations show the occurrence of primary flow structures related to synoptic conditions around the time of the incident. The evidence presented for this mechanism also has implications for possible methods of detection and avoidance of severe CAT.

Long range emission enhancement and anisotropy in coupled quantum dots induced by aligned gold nanoantenna

Quantum dot arrays have been projected as the material of choice for next generation displays and photodetectors. Extensive ongoing research aims at improving optical and electrical efficiencies of such devices. We report experimental results on non-local long range emission intensity enhancement and anisotropy in quantum dot assemblies induced by isolated and partially aligned gold nanoantennas. Spatially resolved photoluminescence clearly demonstrate that the effect is maximum, when the longitudinal surface plasmon resonance of the nanoantenna is resonant with the emission maxima of the quantum dots. We estimated the decay length of this enhancement to be similar to 2.6 mu m, which is considerably larger than the range of near field interaction of metal nanoantenna. Numerical simulations qualitatively capture the near field behavior of the nanorods but fail to match the experimentally observed non-local effects. We have suggested how strong interactions of quantum dots in the close packed assemblies, mediated by the nanoantennas, could lead to such observed behavior. (C) 2014 AIP Publishing LLC.

Transition from dissipative to conservative dynamics in equations of hydrodynamics

We show, by using direct numerical simulations and theory, how, by increasing the order of dissipativity (alpha) in equations of hydrodynamics, there is a transition from a dissipative to a conservative system. This remarkable result, already conjectured for the asymptotic case alpha -> infinity U. Frisch et al., Phys. Rev. Lett. 101, 144501 (2008)], is now shown to be true for any large, but finite, value of alpha greater than a crossover value alpha(crossover). We thus provide a self-consistent picture of how dissipative systems, under certain conditions, start behaving like conservative systems and hence elucidate the subtle connection between equilibrium statistical mechanics and out-of-equilibrium turbulent flows.

Newton-based stochastic optimization using q-Gaussian smoothed functional algorithms

We present the first q-Gaussian smoothed functional (SF) estimator of the Hessian and the first Newton-based stochastic optimization algorithm that estimates both the Hessian and the gradient of the objective function using q-Gaussian perturbations. Our algorithm requires only two system simulations (regardless of the parameter dimension) and estimates both the gradient and the Hessian at each update epoch using these. We also present a proof of convergence of the proposed algorithm. In a related recent work (Ghoshdastidar, Dukkipati, & Bhatnagar, 2014), we presented gradient SF algorithms based on the q-Gaussian perturbations. Our work extends prior work on SF algorithms by generalizing the class of perturbation distributions as most distributions reported in the literature for which SF algorithms are known to work turn out to be special cases of the q-Gaussian distribution. Besides studying the convergence properties of our algorithm analytically, we also show the results of numerical simulations on a model of a queuing network, that illustrate the significance of the proposed method. In particular, we observe that our algorithm performs better in most cases, over a wide range of q-values, in comparison to Newton SF algorithms with the Gaussian and Cauchy perturbations, as well as the gradient q-Gaussian SF algorithms. (C) 2014 Elsevier Ltd. All rights reserved.

An Eigen Approach to Transmit Beamforming in Wireless Networks With Single Antenna Receivers

In this paper, we propose an eigen framework for transmit beamforming for single-hop and dual-hop network models with single antenna receivers. In cases where number of receivers is not more than three, the proposed Eigen approach is vastly superior in terms of ease of implementation and computational complexity compared with the existing convex-relaxation-based approaches. The essential premise is that the precoding problems can be posed as equivalent optimization problems of searching for an optimal vector in the joint numerical range of Hermitian matrices. We show that the latter problem has two convex approximations: the first one is a semi-definite program that yields a lower bound on the solution, and the second one is a linear matrix inequality that yields an upper bound on the solution. We study the performance of the proposed and existing techniques using numerical simulations.

Life of flame particles embedded in premixed flames interacting with near isotropic turbulence

Flame particles are surface points that always remain embedded on, by comoving with a given iso-scalar surface within a flame. Tracking flame particles allow us to study the fate of propagating surface locations uniquely identified throughout their evolution with time. In this work, using Direct Numerical Simulations we study the finite lifetime of such flame particles residing on iso-temperature surfaces of statistically planar H-2-air flames interacting with near-isotropic turbulence. We find that individual flame particles as well as their ensemble, experience progressively increasing tangential straining rate (K-t) and increasing negative curvature (kappa) near the end of their lifetime to finally get annihilated. By studying two different turbulent flow conditions, flame particle tracking shows that such tendency of local flame surfaces to be strained and cusped towards pinch-off from the main surface is a rather generic feature, independent of initial conditions, locations and ambient turbulence intensity levels. The evolution of the alignments between the flame surface normals and the principal components of the local straining rates are also tracked. We find that the surface normals initially aligned with the most extensive principal strain rate components, rotate near the end of flame particles' lifetime to enable preferential alignment between the surface tangent and the most extensive principal strain rate component. This could explain the persistently increasing tangential strain rate, sharp negative curvature formation and eventual detachment. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

The cold mode: a phenomenological model for the evolution of density perturbations in the intracluster medium

Cool cluster cores are in global thermal equilibrium but are locally thermally unstable. We study a non-linear phenomenological model for the evolution of density perturbations in the intracluster medium (ICM) due to local thermal instability and gravity. We have analysed and extended a model for the evolution of an overdense blob in the ICM. We find two regimes in which the overdense blobs can cool to thermally stable low temperatures. One for large t(cool)/t(ff) (t(cool) is the cooling time and t(ff) is the free-fall time), where a large initial overdensity is required for thermal runaway to occur; this is the regime which was previously analysed in detail. We discover a second regime for t(cool)/t(ff) less than or similar to 1 (in agreement with Cartesian simulations of local thermal instability in an external gravitational field), where runaway cooling happens for arbitrarily small amplitudes. Numerical simulations have shown that cold gas condenses out more easily in a spherical geometry. We extend the analysis to include geometrical compression in weakly stratified atmospheres such as the ICM. With a single parameter, analogous to the mixing length, we are able to reproduce the results from numerical simulations; namely, small density perturbations lead to the condensation of extended cold filaments only if t(cool)/t(ff) less than or similar to 10.

Fracture in metallic glasses: mechanics and mechanisms

Significant progress in understanding the mechanical behavior of metallic glasses (MGs) was made over the past decade, particularly on mechanisms of plastic deformation. However, recent research thrust has been on exploring the mechanics and physics of fracture. MGs can be very brittle with K-Ic values similar to silicate glasses and ceramics or very tough with K-Ic akin to high toughness crystalline metals. Even the tough MGs can become brittle with structural relaxation following annealing at temperatures close to glass transition temperature (T-g). Detailed experimental studies coupled with complementary numerical simulations of the recent past have provided insights on the micromechanisms of failure as well as nature of crack tip fields, and established the governing fracture criteria for ductile and brittle glasses. In this paper, the above advances are reviewed and outstanding issues in the context of fracture of amorphous alloys that need to be resolved are identified.

A micropolar peridynamic theory in linear elasticity

A state-based micropolar peridynamic theory for linear elastic solids is proposed. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant material length scale parameters into peridynamics. Non-ordinary type modeling via constitutive correspondence is adopted here to define the micropolar peridynamic material. Along with a general three dimensional model, homogenized one dimensional Timoshenko type beam models for both the proposed micropolar and the standard non-polar peridynamic variants are derived. The efficacy of the proposed models in analyzing continua with length scale effects is established via numerical simulations of a few beam and plane-stress problems. (C) 2015 Elsevier Ltd. All rights reserved.

Secondary breakup of a drop at moderate Weber numbers

We present volume of fluid based numerical simulations of secondary breakup of a drop with high density ratio (approx. 1000) and also perform experiments by injecting monodisperse water droplets in a continuous jet of air and capture the breakup regimes, namely, bag formation, bag-stamen, multibag and shear breakup, observed in the moderate Weber number range (20-120). We observe an interesting transition regime between bag and shear breakup for We = 80, in both simulations as well as experiments, where the formation of multiple lobes, is observed, instead of a single bag, which are connected to each other via thicker rim-like threads that hold them. We show that the transition from bag to shear breakup occurs owing to the rim dynamics which shows retraction under capillary forces at We = 80, whereas the rim is sheared away with flow at We = 120 thus resulting in a backward facing bag. The drop characteristics and timescales obtained in simulations are in good agreement with experiments. The drop size distribution after the breakup shows bimodal nature for the single-bag breakup mode and a unimodal nature following lognormal distribution for higher Weber numbers.