Instabilities induced by variation of Brunt-Vaisala frequency in compressible stratified shear flows

The stability characteristics of a Helmholtz velocity profile in a stably stratified, compressible fluid in the presence of a lower rigid boundary are studied. A jump in the Brunt-Vaisala frequency at a level different from the shear zone is introduced and the variation of the Brunt-Vaisala frequency with respect to the vertical coordinate in the middle layer of the three-layered model is considered. An analytic solution in each of the layers is obtained, and the dispersion relation is solved numerically for parameters relevant to the model. The effect of shear in the lowermost layer of the three-layered model for a Boussinesq fluid is discussed. The results are compared with the earlier studies of Lindzen and Rosenthal, and Sachdev and Satya Narayanan. In the present model, new unstable modes with larger growth rates are obtained and the most unstable gravity wave modes are found to agree closely with the observed ones at various heights. Physics of Fluids is copyrighted by The American Institute of Physics.

Estimation of peak ground acceleration and spectral acceleration for South India with local site effects: probabilistic approach

In this work an attempt has been made to evaluate the seismic hazard of South India (8.0 degrees N-20 degrees N; 72 degrees E-88 degrees E) based on the probabilistic seismic hazard analysis (PSHA). The earthquake data obtained from different sources were declustered to remove the dependent events. A total of 598 earthquakes of moment magnitude 4 and above were obtained from the study area after declustering, and were considered for further hazard analysis. The seismotectonic map of the study area was prepared by considering the faults, lineaments and the shear zones in the study area which are associated with earthquakes of magnitude 4 and above. For assessing theseismic hazard, the study area was divided into small grids of size 0.1 degrees x0.1 degrees, and the hazard parameters were calculated at the centre of each of these grid cells by considering all the seismic sources with in a radius of 300 km. Rock level peak horizontal acceleration (PHA) and spectral acceleration (SA) values at 1 corresponding to 10% and 2% probability of exceedance in 50 years have been calculated for all the grid points. The contour maps showing the spatial variation of these values are presented here. Uniform hazard response spectrum (UHRS) at rock level for 5% damping and 10% and 2% probability of exceedance in 50 years were also developed for all the grid points. The peak ground acceleration (PGA) at surface level was calculated for the entire South India for four different site classes. These values can be used to find the PGA values at any site in South India based on site class at that location. Thus, this method can be viewed as a simplified method to evaluate the PGA values at any site in the study area.

Size dependence and dispersion behavior of the first hyperpolarizability of copper nanoparticles

We have probed the size dependency of the first hyperpolarizability (b) of copper nanoparticles by hyper-Rayleigh scattering (HRS). Our results indicate that second harmonic generation (SHG) originates predominantly at the surface of the nanoparticles as long as the size (d) remains small compared to the wavelength (k). However, volume contribution to the SH response due to the retardation effect becomes important when particle size grows beyond the `small particle limit'. There is a significant dispersion in the b values of copper nanoparticles owing tothe presence of the strong surface plasmon resonance (SPR) band.

A Monte Carlo study of crystal structure transformations

The Metropolis algorithm has been generalized to allow for the variation of shape and size of the MC cell. A calculation using different potentials illustrates how the generalized method can be used for the study of crystal structure transformations. A restricted MC integration in the nine dimensional space of the cell components also leads to the stable structure for the Lennard-Jones potential.

Effects of Isothermal and Adiabatic Thermal Loadings on Size and Strain Rate Dependence of Copper Nanowire

In the present paper, the size and strain rate effects on ultra-thin < 100 >/{100} Cu nanowires at an initial temperature of 10 K have been discussed. Extensive molecular dynamics (MD) simulations have been performed using Embedded atom method (EAM) to investigate the structural behaviours and properties under high strain rate. Velocity-Verlet algorithm has been used to solve the equation of motions. Two different thermal loading cases have been considered: (i) Isothermal loading, in which Nose-Hoover thermostat is used to maintain the constant system temperature, and (ii) Adiabatic loading, i.e., without any thermostat. Five different wire cross-sections were considered ranging from 0.723 x 0.723 nm(2) to 2.169 x 2.169 nm(2) The strain rates used in the present study were 1 x 10(9) s(-1), 1 x 10(8) s(-1), and 1 x 10(7) s(-1). The effect of strain rate on the mechanical properties of copper nanowires was analysed, which shows that elastic properties are independent of thermal loading for a given strain rate and cross-sectional dimension of nanowire. It showed a decreasing yield stress and yield strain with decreasing strain rate for a given cross- section. Also, a decreasing yield stress and increasing yield strain were observed for a given strain rate with increasing cross-sectional area. Elastic modulus was found to be similar to 100 GPa, which was independent of processing temperature, strain rate, and size for a given initial temperature. Reorientation of < 100 >/{100} square cross-sectional copper nanowire into a series of stable ultra-thin Pentagon copper nanobridge structures with dia of similar to 1 nm at 10 K was observed under high strain rate tensile loading. The effect of isothermal and adiabatic loading on the formation of such pentagonal nanobridge structure has been discussed.

Size optimization of a cantilever beam under deformation-dependent loads with application to wheat stalks

In this paper, we consider the optimization of the cross-section profile of a cantilever beam under deformation-dependent loads. Such loads are encountered in plants and trees, cereal crop plants such as wheat and corn in particular. The wind loads acting on the grain-bearing spike of a wheat stalk vary with the orientation of the spike as the stalk bends; this bending and the ensuing change in orientation depend on the deformation of the plant under the same load.The uprooting of the wheat stalks under wind loads is an unresolved problem in genetically modified dwarf wheat stalks. Although it was thought that the dwarf varieties would acquire increased resistance to uprooting, it was found that the dwarf wheat plants selectively decreased the Young's modulus in order to be compliant. The motivation of this study is to investigate why wheat plants prefer compliant stems. We analyze this by seeking an optimal shape of the wheat plant's stem, which is modeled as a cantilever beam, by taking the large deflection of the stem into account with the help of co-rotational finite element beam modeling. The criteria considered here include minimum moment at the fixed ground support, adequate stiffness and strength, and the volume of material. The result reported here is an example of flexibility, rather than stiffness, leading to increased strength.

Size effect on the lattice parameter of KCl during mechanical milling

The size effect on the lattice parameter of ionic KCl nanocrystals was studied systematically during mechanical milling of Pure KCl powder under vacuum. The results suggest anomalous lattice expansion, with the lattice parameter increasing from 6.278 angstrom at d = 6 mu m to 6.30307 angstrom at d = 85 mn. The defects generated during ball milling of KCl and surface stress are deemed to be responsible for this lattice parameter expansion. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Texture strengthening in warm-rolled cadmium-1% silver alloy

The variation in the tensile properties at 77 K and 300 K in warm-rolled (300 K) Cd-1% Ag alloy with deformation has been studied in longitudinal as well as transverse specimens. The low-temperature yield strength increases with warm rolling without much loss in ductility. The strength at 300 K, however, decreases with heavy warm deformation. From microstructural studies and X-ray investigations, it was observed that changes in grain size and texture occur during warm rolling. Both these changes are found to be important in deciding the tensile properties. The longitudinal and transverse strengths at 77 K vary linearly with l-frac12, where l is the average grain diameter, and thus they obey the Hall-Petch relation. The Hall-Petch slope, k, is lower in specimens with favourable lcub1013rcub texture while the intercept σo is higher when the lcub0002rcub texture is less favourable.