426 resultados para Ritz Method


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The finite-difference form of the basic conservation equations in laminar film boiling have been solved by the false-transient method. By a judicious choice of the coordinate system the vapour-liquid interface is fitted to the grid system. Central differencing is used for diffusion terms, upwind differencing for convection terms, and explicit differencing for transient terms. Since an explicit method is used the time step used in the false-transient method is constrained by numerical instability. In the present problem the limits on the time step are imposed by conditions in the vapour region. On the other hand the rate of convergence of finite-difference equations is dependent on the conditions in the liquid region. The rate of convergence was accelerated by using the over-relaxation technique in the liquid region. The results obtained compare well with previous work and experimental data available in the literature.

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It is shown that a method based on the principle of analytic continuation can be used to solve a set of infinite simultaneous equations encountered in solving for the electric field of a periodic electrode structure.

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The transmission-line or the impedance-tube method for the measurement of the acoustic impedance of any termination involves a search for various minima and maxima of pressure. For this purpose, arrangement has to be made for the microphone to travel along the length of the impedance tube, and this complicates the design of the tube considerably. The present paper discusses a method which consists in evaluating the tube attenuation factor at any convenient frequency by making use of measured SPL's at two (or more) fixed locations with a rigid termination, calculating the tube attenuation factor and wave number at the required frequency of interest with or without mean flow (as applicable), and finally evaluating the impedance of the given termination by measuring and using SPL's at three (or more) fixed locations. Thus, the required impedance tube is considerably smaller in length, simpler in design, easier to manufacture, cheaper in cost and more convenient to use. The design of the tube is also discussed. Incidentally, it is also possible to evaluate the impedance at any low frequency without having to use a larger impedance tube.

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A simple method for preparing bulk quantities of tRNA from chick embryo has been developed. In this method chick embryos were homogenized in a buffer of pH 4.5, followed by deproteinization with phenol. The aqueous layer was allowed to separate under gravity. The resulting aqueous layer, after two more phenol treatments, was directly passed through a DEAE-cellulose column and the tRNA eluted therefrom with 1 Image NaCl. The tRNA prepared by this method was as active as the one prepared at neutral pH.

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A new, rapid, simple, and sensitive colorimetric method for the estimation of resorcinol in microgram amounts is described.

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A method for separation of stresses in two and three-dimensional photo elasticity using the harmonisation ofjrst stress invariant along a straight section is deve- ,dped. For two-dimensions, the equations of equilibrium are reformulated in terms ojsum and difference of normal stresses and relations are obtained which can be used for harmonisation of the first invariant of stress along a straight section. A similar procedure is adopted for three-dimensions by making use of the Beltrmi-MicheN equations. The new relations are used in finite d~yerencefo rm to evaluate the sum of normal stresses along straight sections in a three-dimensional body. The method requires photoelastic data along the section as well ~rra djacent sections. This method could be used as an alternative to the shear d@erence method for separation of stresses in photoelasticity. 7he accuracy and reliability of the method is ver$ed by applying the method to problems whose solutions are known.

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Downscaling to station-scale hydrologic variables from large-scale atmospheric variables simulated by general circulation models (GCMs) is usually necessary to assess the hydrologic impact of climate change. This work presents CRF-downscaling, a new probabilistic downscaling method that represents the daily precipitation sequence as a conditional random field (CRF). The conditional distribution of the precipitation sequence at a site, given the daily atmospheric (large-scale) variable sequence, is modeled as a linear chain CRF. CRFs do not make assumptions on independence of observations, which gives them flexibility in using high-dimensional feature vectors. Maximum likelihood parameter estimation for the model is performed using limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization. Maximum a posteriori estimation is used to determine the most likely precipitation sequence for a given set of atmospheric input variables using the Viterbi algorithm. Direct classification of dry/wet days as well as precipitation amount is achieved within a single modeling framework. The model is used to project the future cumulative distribution function of precipitation. Uncertainty in precipitation prediction is addressed through a modified Viterbi algorithm that predicts the n most likely sequences. The model is applied for downscaling monsoon (June-September) daily precipitation at eight sites in the Mahanadi basin in Orissa, India, using the MIROC3.2 medium-resolution GCM. The predicted distributions at all sites show an increase in the number of wet days, and also an increase in wet day precipitation amounts. A comparison of current and future predicted probability density functions for daily precipitation shows a change in shape of the density function with decreasing probability of lower precipitation and increasing probability of higher precipitation.

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A one-step synthesis of Ga2O3 nanorods by heating molten gallium in ambient air at high temperatures is presented. The high-temperature synthesis creates oxygen vacancies and incorporates nitrogen from the environment. The oxygen vacancy in Ga2O3 is responsible for the emission in the blue-green region, while nitrogen in Ga2O3 is responsible for red emission.

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The effect of the method of preparation and pretreatment on catalyst texture was investigated in the case of alumina, silica-alumina, 10 × molecular sieve and thoria catalysts. All the catalysts were characterised with respect to their specific surface area, surface acidity, pore size distribution and pore volume. The above properties were found to reflect the textural changes that might have been undergone by the catalyst surface as a result of the method of preparation and pretreatment. The method of preparation was found to influence markedly the acidity of the surface and to a lesser extent the surface area and pore size distribution. Acid-treatment was found to increase selectively the acidity of the catalyst while heat-treatment was found to decrease proportionally the acidity as well as surface area of the catalyst.

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Relative band strengths of diatomic molecules for which the product of Franck-Condon factor and r-centroid is approximately equal to 1 for (0,0) band can be determined by a simple method which will be in good agreement with the smoothed array of experimental values.

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A simple protoplast isolation protocol that was designed to recover totipotent plant protoplasts with relative ease has been described. The key elements of the protocol are, tissue digestion at slightly elevated temperatures and use of protoplast-releasing enzymes that are stable and efficient at higher temperatures. Besides enzymes, the protoplast isolation cocktail consisted of an osmoticum (mannitol or MgSO4), and a protectant (CaCl2 2H2O), all dissolved in distilled water. The protocol has ensured reproducibility, higher yields and is gentle on protoplasts as the protoplasts obtained were amenable to cell wall regeneration and cell division. Plant regeneration was demonstrated forNicotiana tabacum cv. Thompson from protoplasts isolated by this method. Wall regeneration and cell division were obtained in other species. The merits of the protocol are, simple and easy-to-handle procedure, non-requirement of preconditioning of donor plant and explants, incubation without agitation, satisfactory yields, culturability of the protoplasts isolated and applicability of the protocol to a large number of species including mucilage-containing plants.

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We describe the solution combustion synthesis and characterization of La1-xKxMnO3 (0.0 <= x <= 0.25) perovskite phases, which is a low temperature initiated, rapid route to prepare metal oxides. As-synthesized compounds are amorphous in nature; crystallinity was observed on heating at 800 degrees C for 5 min. Structural parameters were determined by the Rietveld refinement method using powder XRD data. Parent LaMnO3 compound crystallizes in the orthorhombic structure (space group Pbnm, No. 62). Potassium substituted compounds were crystallized with rhombohedral symmetry (space group R-3c, No. 167). The ratio of the Mn3+/Mn4+ was determined by the iodometric titration. The Fourier transform infrared spectrum (FTIR) shows two absorption bands for Mn-O stretching vibration (v, mode), Mn-O-Mn deformation vibration (v(b) mode) around 600 cm(-1) and 400 cm(-1) for the compositions, x = 0.0, 0.05 and 0-10. Four-probe electrical resistivity measurements reveal a composition controlled metal to insulator transition (TM-1), the maximum TM-1 was observed for the composition La0.85K0.15MnO3 at 287 K. Room temperature vibrating sample magnetometer data indicate that for the composition up to x = 0-10, the compounds are paramagnetic whereas composition with x = 0.15, 0.20 and 0.25 show magnetic moments of 27, 29 and 30 emu/g, respectively.

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A new 8-node serendipity quadrilateral plate bending element (MQP8) based on the Mindlin-Reissner theory for the analysis of thin and moderately thick plate bending problems using Integrated Force Method is presented in this paper. The performance of this new element (MQP8) is studied for accuracy and convergence by analyzing many standard benchmark plate bending problems. This new element MQP8 performs excellent in both thin and moderately thick plate bending situations. And also this element is free from spurious/zero energy modes and free from shear locking problem.

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The subspace intersection method (SIM) provides unbiased bearing estimates of multiple acoustic sources in a range-independent shallow ocean using a one-dimensional search without prior knowledge of source ranges and depths. The original formulation of this method is based on deployment of a horizontal linear array of hydrophones which measure acoustic pressure. In this paper, we extend SIM to an array of acoustic vector sensors which measure pressure as well as all components of particle velocity. Use of vector sensors reduces the minimum number of sensors required by a factor of 4, and also eliminates the constraint that the intersensor spacing should not exceed half wavelength. The additional information provided by the vector sensors leads to performance enhancement in the form of lower estimation error and higher resolution.

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A fully implicit integration method for stochastic differential equations with significant multiplicative noise and stiffness in both the drift and diffusion coefficients has been constructed, analyzed and illustrated with numerical examples in this work. The method has strong order 1.0 consistency and has user-selectable parameters that allow the user to expand the stability region of the method to cover almost the entire drift-diffusion stability plane. The large stability region enables the method to take computationally efficient time steps. A system of chemical Langevin equations simulated with the method illustrates its computational efficiency.