Computer modeling of pulsed CO2 lasers for lidar applications

The experimental results will enable a comparison of the numerical code output with experimental data. This will ensure verification of the validity of the code. The measurements were made on a modified commercial CO2 laser. Results are listed as following. (1) The pulse shape and energy dependence on gas pressure were measured. (2) The intrapulse frequency chirp due to plasma and laser induced medium perturbation effects were determined. A simple numerical model showed quantitative agreement with these measurements. The pulse to pulse frequency stability was also determined. (3) The dependence was measured of the laser transverse mode stability on cavity length. A simple analysis of this dependence in terms of changes to the equivalent fresnel number and the cavity magnification was performed. (4) An analysis was made of the discharge pulse shape which enabled the low efficiency of the laser to be explained in terms of poor coupling of the electrical energy into the vibrational levels. And (5) the existing laser resonator code was changed to allow it to run on the Cray XMP under the new operating system

Underwater Sound Scattering Model of the Topographic Features of the Sea Floor

A description of the sea floor with respect to underwater acoustic transmission giving rise to reflection and scattering is studied. The plane wave reflection coefficients and scattering coefficients are estimated from the topographic features of the floor and the physical properties of the sediments. A bottom loss model for an area off west coast of India is presented

Nonlinear Absorption, Scattering and Optical Limiting Studies of CdS Nanoparticles

The nonlinear optical absorption, scattering and optical limiting properties of CdS nanoparticles dispersed in dimethylformamide (DMF) are investigated. The nanoparticles are synthesized using the standard chemical synthesis method with thioglycerol as the capping agent. The investigations are carried out at 532 nm in the ns regime. Strong two-photon absorption and nonlinear scattering are found to be responsible for good optical limiting characteristics in these nanoparticles

Development of a Geometric Model Retrieval System: A design exemplar case study

This paper presents a case study examining design exemplar technology implemented as a search and retrieval tool for tyre mould inserts. Limitations of using the geometric-based exemplar approach, such as tediousness of authoring exemplars and time complexity, are identified and addressed through a new parametric-based exemplar approach. Here, the maxima and minima are calculated based upon the specifications of the query mould insert. The design exemplar is demonstrated to be useful primarily in prototyping query mechanisms. Ultimately, customer requirements necessitated implementing the parametric approach as a dedicated software package grounded on the exemplar-based prototyped query mechanism

Numerical Simulation of Supersonic Combustion with Parallel Injection of Hydrogen Fuel

Thermochemical exploration of mixing and combustion of parallel hydrogen injection into supersonic vitiated air stream in a divergent duct is presented. Three-dimensional Navier Stokes equations along with twoequation turbulence models and Eddy dissipation concept (EDC)-based combustion models are solved using commercial CFD software. Chemical reaction for H2-air system is modelled by two different simple chemical kinetic schemes namely; infinitely fast rate kinetics as well as the single-step finite rate kinetics. Grid convergence of the solution is demonstrated and a grid convergence index-based error estimate has been provided. Insight into the mixing and combustion of high-speed turbulent reacting flow is obtained through the analysis of various thermochemical variables. Very good comparisons are obtained for the exit profiles for various fluid dynamical and chemical variables for the mixing case. For reacting case, the comparison between the experimental and the numerical values are reasonable. Parametric studies were carried out to study the effect of different turbulence models and turbulent Schmidt numbers. It is seen that Wilcox k-w turbulence model performed better than the other two-equation turbulence models in its class. Strong dependence of flow behaviour on turbulent Schmidt number was observed. The results indicate that simple chemical kinetics is adequate to describe the H2-air reaction in the scramjet combustor.Defence Science Journal, 2010, 60(5), pp.465-475, DOI:http://dx.doi.org/10.14429/dsj.60.5

Conversion of Dynamic High Pressures from Air to Water for a Spherical TNT Charge

A numerical method has been applied to convert the dynamic high pressures from air-to-water for a spherical TNT charge. Standard equation of scaling law in air for TNT has been utilised to make the necessary conversions. The investigations have been made by taking into consideration the ambient pressure values for the two media. The calculations have been performed under the scaled distances to get better results. Experimental measurements using indigenous blast pressure gauge have been undertaken by detonating spherical charges of TNT under the same scaled distances in water to check the correctness of results and direct application of this method. A fairly close agreement between the theoretically computed and the experimental values of the dynamic high pressures shows the practical utility of this approach in that it enables an estimate of the experimental shock wave pressures, without conducting underwater experiments

Representations of integers by certain positive definite binary quadratic forms

We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n=x^2+Ny^2 for a squarefree integer N.Comment: 8 pages, submitte

Characterizing Intrinsic Compositionality in Transformers with Tree Projections

When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems like human languages? There is an apparent tension between compositional accounts of human language understanding, which are based on a restricted bottom-up computational process, and the enormous success of neural models like transformers, which can route information arbitrarily between different parts of their input. One possibility is that these models, while extremely flexible in principle, in practice learn to interpret language hierarchically, ultimately building sentence representations close to those predictable by a bottom-up, tree-structured model. To evaluate this possibility, we describe an unsupervised and parameter-free method to \emph{functionally project} the behavior of any transformer into the space of tree-structured networks. Given an input sentence, we produce a binary tree that approximates the transformer's representation-building process and a score that captures how "tree-like" the transformer's behavior is on the input. While calculation of this score does not require training any additional models, it provably upper-bounds the fit between a transformer and any tree-structured approximation. Using this method, we show that transformers for three different tasks become more tree-like over the course of training, in some cases unsupervisedly recovering the same trees as supervised parsers. These trees, in turn, are predictive of model behavior, with more tree-like models generalizing better on tests of compositional generalization.Comment: Fixed title and metadat