Normal mode sound propagation in an ocean with random narrow-band surface waves

Normal mode sound propagation in an isovelocity ocean with random narrow-band surface waves is considered, assuming the root-mean-square wave height to be small compared to the acoustic wavelength. Nonresonant interaction among the normal modes is studied straightforward perturbation technique. The more interesting case of resonant interaction is investigated using the method of multiple scales to obtain a pair of stochastic coupled amplitude equations which are solved using the Peano-Baker expansion technique. Equations for the spatial evolution of the first and second moments of the mode amplitudes are also derived and solved. It is shown that, irrespective of the initial conditions, the mean values of the mode amplitudes tend to zero asymptotically with increasing range, the mean-square amplitudes tend towards a state of equipartition of energy, and the total energy of the modes is conserved.

Random sequential multilayer deposition of different‐sized k mers on a one dimensional infinite substrate

Kinetics of random sequential, irreversible multilayer deposition of macromolecules of two different sizes on a one dimensional infinite lattice is analyzed at the mean field level. A formal solution for the corresponding rate equation is obtained. The Jamming limits and the distribution of gaps of exact sizes are discussed. In the absence of screening, the jamming limits are shown to be the same for all the layers. A detailed analysis for the components differing by one monomer unit is presented. The small and large time behaviors and the dependence of the individual jamming limits of the k mers and (k−1) mers on k and the rate parameters are analyzed.

Spectral approach for the soliton and periodic solutions of the nonlinear wave equation

A spectral method that obtains the soliton and periodic solutions to the nonlinear wave equation is presented. The results show that the nonlinear group velocity is a function of the frequency shift as well as of the soliton power. When the frequency shift is a function of time, a solution in terms of the Jacobian elliptic function is obtained. This solution is periodic in nature, and, to generate such an optical pulse train, one must simultaneously amplitude- and frequency-modulate the optical carrier. Finally, we extend the method to include the effect of self-steepening.

Adaptive Keeper Design for Dynamic Logic Circuits Using Rate Sensing Technique

The increasing variability in device leakage has made the design of keepers for wide OR structures a challenging task. The conventional feedback keepers (CONV) can no longer improve the performance of wide dynamic gates for the future technologies. In this paper, we propose an adaptive keeper technique called rate sensing keeper (RSK) that enables faster switching and tracks the variation across different process corners. It can switch upto 1.9x faster (for 20 legs) than CONV and can scale upto 32 legs as against 20 legs for CONV in a 130-nm 1.2-V process. The delay tracking is within 8% across the different process corners. We demonstrate the circuit operation of RSK using a 32 x 8 register file implemented in an industrial 130-nm 1.2-V CMOS process. The performance of individual dynamic logic gates are also evaluated on chip for various keeper techniques. We show that the RSK technique gives superior performance compared to the other alternatives such as Conditional Keeper (CKP) and current mirror-based keeper (LCR).

Influence of Substrate Temperature and Deposition Rate on Structural and Mechanical Properties of Shape Memory NiTi Films

NiTi thin films deposited by DC magnetron sputtering of an alloy (Ni/Ti:45/55) target at different deposition rates and substrate temperatures were analyzed for their structure and mechanical properties. The crystalline structure, phase-transformation and mechanical response were characterized by X-ray diffraction (XRD), Differential Scanning Calorimetry (DSC) and Nano-indentation techniques, respectively. The films were deposited on silicon substrates maintained at temperatures in the range 300 to 500 degrees C and post-annealed at 600 degrees C for four hours to ensure film crystallinity. Films deposited at 300 degrees C and annealed for 600 degrees C have exhibited crystalline behavior with Austenite phase as the prominent phase. Deposition onto substrates held at higher deposition temperatures (400 and 500 degrees C) resulted in the co-existence of Austenite phase along with Martensite phase. The increase in deposition rates corresponding to increase in cathode current from 250 to 350 mA has also resulted in the appearance of Martensite phase as well as improvement in crystallinity. XRD analysis revealed that the crystalline film structure is strongly influenced by process parameters such as substrate temperature and deposition rate. DSC results indicate that the film deposited at 300 degrees C had its crystallization temperature at 445 degrees C in the first thermal cycle, which is further confirmed by stress temperature response. In the second thermal cycle the Austenite and Martensite transitions were observed at 75 and 60 degrees C respectively. However, the films deposited at 500 degrees C had the Austenite and Martensite transitions at 73 and 58 degrees C, respectively. Elastic modulus and hardness values increased from 93 to 145 GPa and 7.2 to 12.6 GPa, respectively, with increase in deposition rates. These results are explained on the basis of change in film composition and crystallization. (C) 2010 Published by Elsevier Ltd

Strong nonlocalization induced by small scale parameter on terahertz flexural wave dispersion characteristics of a monolayer graphene

This paper presents the strong nonlocal scale effect on the flexural wave propagation in a monolayer graphene sheet. The graphene is modeled as an isotropic plate of one atom thick. Nonlocal governing equation of motion is derived and wave propagation analysis is performed using spectral analysis. The present analysis shows that the flexural wave dispersion in graphene obtained by local and nonlocal elasticity theories is quite different. The nonlocal elasticity calculation shows that the wavenumber escapes to infinite at certain frequency and the corresponding wave velocity tends to zero at that frequency indicating localization and stationary behavior. This behavior is captured in the spectrum and dispersion curves. The cut-off frequency of flexural wave not only depend on the axial wavenumber but also on the nonlocal scaling parameter. The effect of axial wavenumber on the wave behavior in graphene is also discussed in the present manuscript. (C) 2010 Elsevier B.V. All rights reserved.

Mass transfer and shear rate in baffled surface aerator

The scale up or scale down of the process variables in a surface aerator requires information about the shear rate prevailing in the system. In fact, the performance of surface aerator depends upon the shear rate. Shear rate affects the mass transfer operation needed by the surface aerator. Theoretical analysis of shear rate suggests a nonlinear behavior with rotational speed of the impeller, which has been shown in the present work. Present work also shows that in a geometrically similar system of baffled surface aerator, shear rate can be used as a governing parameter for scaling up or down the mass transfer phenomena.

A bicharacteristic formulation of the ideal MHD equations

On a characteristic surface Omega of a hyperbolic system of first-order equations in multi-dimensions (x, t), there exits a compatibility condition which is in the form of a transport equation along a bicharacteristic on Omega. This result can be interpreted also as a transport equation along rays of the wavefront Omega(t) in x-space associated with Omega. For a system of quasi-linear equations, the ray equations (which has two distinct parts) and the transport equation form a coupled system of underdetermined equations. As an example of this bicharacteristic formulation, we consider two-dimensional unsteady flow of an ideal magnetohydrodynamics gas with a plane aligned magnetic field. For any mode of propagation in this two-dimensional flow, there are three ray equations: two for the spatial coordinates x and y and one for the ray diffraction. In spite of little longer calculations, the final four equations (three ray equations and one transport equation) for the fast magneto-acoustic wave are simple and elegant and cannot be derived in these simple forms by use of a computer program like REDUCE.

Constitutive modeling of ice in the high strain rate regime

The objective of the present work is to propose a constitutive model for ice by considering the influence of important parameters such as strain rate dependence and pressure sensitivity on the response of the material. In this regard, the constitutive model proposed by Carney et al. (2006) is considered as a starting basis and subsequently modified to incorporate the effect of brittle cracking within a continuum damage mechanics framework. The damage is taken to occur in the form of distributed cracking within the material during impact which is consistent with experimental observations. At the point of failure, the material is assumed to be fluid-like with deviatoric stress almost dropping down to zero. The constitutive model is implemented in a general purpose finite element code using an explicit formulation. Several single element tests under uniaxial tension and compression, as well as biaxial loading are conducted in order to understand the performance of the model. Few large size simulations are also performed to understand the capability of the model to predict brittle damage evolution in un-notched and notched three point bend specimens. The proposed model predicts lower strength under tensile loading as compared to compressive loading which is in tune with experimental observations. Further the model also asserts the strain rate dependency of the strength behavior under both compressive as well as tensile loading, which also corroborates well with experimental results. (C) 2010 Elsevier Ltd. All rights reserved.

A formula for the solution of general Abel integral equation

A new formula for the solution of the general Abel Integral equation is derived, and an important special case is checked with the known result.

Grinding abrasive wear and associated particle size effect

The type of abrasion that the grinding medium experiences inside a ball mill is classified as high stress or grinding abrasion, because the stress levels at the surface of the medium exceed the yield stress of the metal when hard abrasives are crushed. During dry grinding of ores the medium undergoes not only abrasion but also erosion and impact. As all three mechanisms of wear occur simultaneously, it is difficult to follow the individual components of wear. However, it is possible to show that the overall kinetics of wear follows a simple power law of the type w = at(b), where w is the weight loss of the grinding medium for a specified grinding time t and a and b are constants. Experimental data, obtained from dry grinding of quartz for a wide range of times using AISI 52100 steel balls having various microstructures in a laboratory scale batch mill, are fitted to the proposed equation and the wear rate w is calculated from the first derivative of the equation. The mean particle sizes of the quartz charge DBAR corresponding to 50 and 80% retained size are determined by mechanical sieving of the ground product after a grinding time t and thus the relationship between wear rate and particle size of the abrasive is established. It is found that w increases rapidly with DBAR up to some critical size and then increases at a much lower rate.

Transverse plane wave analysis of short elliptical chamber mufflers: An analytical approach

Short elliptical chamber mufflers are used often in the modern day automotive exhaust systems. The acoustic analysis of such short chamber mufflers is facilitated by considering a transverse plane wave propagation model along the major axis up to the low frequency limit. The one dimensional differential equation governing the transverse plane wave propagation in such short chambers is solved using the segmentation approaches which are inherently numerical schemes, wherein the transfer matrix relating the upstream state variables to the downstream variables is obtained. Analytical solution of the transverse plane wave model used to analyze such short chambers has not been reported in the literature so far. This present work is thus an attempt to fill up this lacuna, whereby Frobenius solution of the differential equation governing the transverse plane wave propagation is obtained. By taking a sufficient number of terms of the infinite series, an approximate analytical solution so obtained shows good convergence up to about 1300 Hz and also covers most of the range of muffler dimensions used in practice. The transmission loss (TL) performance of the muffler configurations computed by this analytical approach agrees excellently with that computed by the Matrizant approach used earlier by the authors, thereby offering a faster and more elegant alternate method to analyze short elliptical muffler configurations. (C) 2010 Elsevier Ltd. All rights reserved.

On Computation of Minimum Distance of Linear Block Codes Above 1/2 Rate Coding

The minimum distance of linear block codes is one of the important parameter that indicates the error performance of the code. When the code rate is less than 1/2, efficient algorithms are available for finding minimum distance using the concept of information sets. When the code rate is greater than 1/2, only one information set is available and efficiency suffers. In this paper, we investigate and propose a novel algorithm to find the minimum distance of linear block codes with the code rate greater than 1/2. We propose to reverse the roles of information set and parity set to get virtually another information set to improve the efficiency. This method is 67.7 times faster than the minimum distance algorithm implemented in MAGMA Computational Algebra System for a (80, 45) linear block code.