Derivation of the solution of certain singular integral equations

It is shown that the a;P?lication of the Poincare-Bertrand fcm~ulaw hen made in a suitable manner produces the s~lutiano f certain singular integral equations very quickly, thc method of arriving at which, otherwise, is too complicaled. Two singular integral equations are considered. One of these quaiions is with a Cauchy-tyge kcrnel arid the other is an equalion which appears in the a a w guide theory and the theory of dishcations. Adifferent approach i? alw made here to solve the singular integralquation> of the waveguide theor? ind this i ~ v o l v eth~e use of the inversion formula of the Cauchy-type singular integral equahn and dudion to a system of TIilberl problems for two unknowns which can be dwupled wry easily to obi& tbe closed form solutim of the irilegral equatlou at band. The methods of the prescnt paper avoid all the complicaled approaches of solving the singular integral equaticn of the waveguide theory knowr todate.

On the non-existence of hydrodynamic solution of surface plasmons at the bimetallic interface

It is shown that for an abrupt bimetallic interface a hydrodynamic solution for interface plasmons does not exist. It appears that this result is valid irrespective of the choice of of the additional boundary condition, thereby suggesting a careful look at the use of usual hydrodynamic equations for a bimetallic interface.

Perturbation of critical solution temperatures by impurity doping

An expression is developed for the variation of the critical solution temperature of a binary liquid system when a third component (dopant) is added, using an extension of the regular solution theory. The model can be used for UCST, LCST and for closed loop systems and has the correct features in the limiting cases.

In-situ measurements of concentration and temperature during transient solidification of aqueous solution of ammonium chloride using laser interferometry

The variation in temperature and concentration plays a crucial role in predicting the final microstructure during solidification of a binary alloy. Most of the experimental techniques used to measure concentration and temperature are intrusive in nature and affect the flow field. In this paper, the main focus is laid on in-situ, non-intrusive, transient measurement of concentration and temperature during the solidification of a binary mixture of aqueous ammonium chloride solution (a metal-analog system) in a top cooled cavity using laser based Mach-Zehnder Interferometric technique. It was found from the interferogram, that the angular deviation of fringe pattern and the total number of fringes exhibit significant sensitivity to refractive index and hence are functions of the local temperature and concentration of the NH4Cl solution inside the cavity. Using the fringe characteristics, calibration curves were established for the range of temperature and concentration levels expected during the solidification process. In the actual solidification experiment, two hypoeutectic solutions (5% and 15% NH4Cl) were chosen. The calibration curves were used to determine the temperature and concentration of the solution inside the cavity during solidification of 5% and 15% NH4Cl solution at different instants of time. The measurement was carried out at a fixed point in the cavity, and the concentration variation with time was recorded as the solid-liquid interface approached the measurement point. The measurement exhibited distinct zones of concentration distribution caused by solute rejection and Rayleigh Benard convection. Further studies involving flow visualization with laser scattering confirmed the Rayleigh Benard convection. Computational modeling was also performed, which corroborated the experimental findings. (C) 2011 Elsevier Ltd. All rights reserved.

Approximate solution of u'=-A2u using a relation between exp(-tA2) and exp(itA)

Let A be a positive definite operator in a Hilbert space and consider the initial value problem for u(t) = -A(2)u. Using a representation of the semigroup exp(-A(2)t) in terms of the group exp(iAt) we express u in terms of the solution of the standard heat equation w(t) = W-yy, with initial values v solving the initial value problem for v(y) = iAv. This representation is used to construct a method for approximating u in terms of approximations of v. In the case that A is a 2(nd) order elliptic operator the method is combined with finite elements in the spatial variable and then reduces the solution of the 4(th) order equation for u to that of the 2(nd) order equation for v, followed by the solution of the heat equation in one space variable.

Solution conformations of penta and heptapeptides containing repetitive α-aminoisobutyryl-Image -alanyl and α -aminoisobutyryl-Image -valyl sequences

The presence of folded solution conformations in the peptides Boc-Ala-(Aib-Ala)2-OMe, Boc-Val-(Aib-Val) 2-OMe, Boc-Ala-(Aib-Ala)3-OMe and Boc-Val-(Aib-Val)3-OMe has been established by 270MHz 1H NMR. Intramolecularly H-bonded NH groups have been identified using temperature and solvent dependence of NH chemical shifts and paramagnetic radical induced broadening of NH resonances. Both pentapeptides adopt 310 helical conformations possessing 3 intramolecular H-bonds in CDCl3 and (CD3)2SO. The heptapeptides favour helical structures with 5 H-bonds in CDCl3. In (CD3)2SO only 4 H-bonds are readily detected.

Solution of a generalized Korteweg—de Vries equation

The solitary-wavelike solution of the generalized Korteweg-de Vries equation with mixed nonlinearity is obtained. Two asymptotic cases of the solution have been discussed and solitary wave solutions have been derived. ©1974 American Institute of Physics.

Solution of a generalized Korteweg-de Vries equation

The solitary-wavelike solution of the generalized Korteweg-de Vries equation with mixed nonlinearity is obtained. Two asymptotic cases of the solution have been discussed and solitary wave solutions have been derived.

A Convenient Route for the Synthesis of Complex Metal Oxides Employing Solid-Solution Precursors

Synthesis of complex metal oxides by the thermal decomposition of solid-solution precursors (formed by isomorphous compounds of component metals) has been investigated since the method enables mixing of cations on an atomic scale and drastically reduces diffusion distances to a few angstroms. Several interesting oxides such as Ca2Fe03,5C, aCoz04,C a2C0205a, nd Ca,FeCo05 have been prepared by this technique starting from carbonate solid solutions of the type Ca,-,Fe,C03, Cal-,Co,C03, and Ca,-,,M,M'yC03 (M, M' = Mn, Fe, Co). The method has been extended to oxalate solid-solution precursors, and the possibility of making use of other kinds of precursor solid solutions is indicated.

Approximate solution for the redistribution of impurities during second oxidation

The impurity profile for the second oxidation, used in MOST fabrication, has been obtained by Margalit et al. [1]. The disadvantage of this technique is that the accuracy of their solution is directly dependent on the computer time. In this article, an analytical solution is presented using the approximation of linearizing the second oxidation procedure.

X-Pro peptides: Synthesis and solution conformation of benzyloxycarbonyl-(Aib-Pro)4methyl ester. Evidence for a novel helical structure

The synthesis of the octapeptide, benzyloxycarbonyl-(-aminoisobutyryl-L-prolyl)4-methyl ester [Z-(Aib-Pro)4-OMe] and an analysis of its solution conformation is reported. The octapeptide is shown to possess three strong intramolecular hydrogen bonds on the basis of studies of the solvent and temperature dependence of NH chemical shifts and rates of hydrogen-deuterium exchange. 13C studies are consistent with a structure involving only trans Aib-Pro bonds, while ir experiments support a hydrogen-bonded conformation. The Aib 3, 5, and 7 NH groups are shown to participate in hydrogen bonding. A 310 helical conformation compatible with the spectroscopic data is suggested. The proposed conformation consists of three type III -turns with Aib and Pro at the corners and stabilized by 4 1 intramolecular hydrogen bonds.

Solution of MDPS using simulation-based value iteration

This article proposes a three-timescale simulation based algorithm for solution of infinite horizon Markov Decision Processes (MDPs). We assume a finite state space and discounted cost criterion and adopt the value iteration approach. An approximation of the Dynamic Programming operator T is applied to the value function iterates. This 'approximate' operator is implemented using three timescales, the slowest of which updates the value function iterates. On the middle timescale we perform a gradient search over the feasible action set of each state using Simultaneous Perturbation Stochastic Approximation (SPSA) gradient estimates, thus finding the minimizing action in T. On the fastest timescale, the 'critic' estimates, over which the gradient search is performed, are obtained. A sketch of convergence explaining the dynamics of the algorithm using associated ODEs is also presented. Numerical experiments on rate based flow control on a bottleneck node using a continuous-time queueing model are performed using the proposed algorithm. The results obtained are verified against classical value iteration where the feasible set is suitably discretized. Over such a discretized setting, a variant of the algorithm of [12] is compared and the proposed algorithm is found to converge faster.

Effect of boundary condition description on convergence of solution in a boundary-value problem

It is well known that the numerical accuracy of a series solution to a boundary-value problem by the direct method depends on the technique of approximate satisfaction of the boundary conditions and on the stage of truncation of the series. On the other hand, it does not appear to be generally recognized that, when the boundary conditions can be described in alternative equivalent forms, the convergence of the solution is significantly affected by the actual form in which they are stated. The importance of the last aspect is studied for three different techniques of computing the deflections of simply supported regular polygonal plates under uniform pressure. It is also shown that it is sometimes possible to modify the technique of analysis to make the accuracy independent of the description of the boundary conditions.

Comparative study of different formulations and solution methods for two phase flow in saturated porous media

Six models (Simulators) are formulated and developed with all possible combinations of pressure and saturation of the phases as primary variables. A comparative study between six simulators with two numerical methods, conventional simultaneous and modified sequential methods are carried out. The results of the numerical models are compared with the laboratory experimental results to study the accuracy of the model especially in heterogeneous porous media. From the study it is observed that the simulator using pressure and saturation of the wetting fluid (PW, SW formulation) is the best among the models tested. Many simulators with nonwetting phase as one of the primary variables did not converge when used along with simultaneous method. Based on simulator 1 (PW, SW formulation), a comparison of different solution methods such as simultaneous method, modified sequential and adaptive solution modified sequential method are carried out on 4 test problems including heterogeneous and randomly heterogeneous problems. It is found that the modified sequential and adaptive solution modified sequential methods could save the memory by half and as also the CPU time required by these methods is very less when compared with that using simultaneous method. It is also found that the simulator with PNW and PW as the primary variable which had problem of convergence using the simultaneous method, converged using both the modified sequential method and also using adaptive solution modified sequential method. The present study indicates that pressure and saturation formulation along with adaptive solution modified sequential method is the best among the different simulators and methods tested.

On the solution of the equation ut+unux+H(x, t, u)=0

We consider the equation u(t) + u(n)u(x) + H(x, t, u) = 0 and derive a transformation relating it to u(t) + u(n)u(x) = 0. Special cases of the equation appearing in applications are discussed. Initial value problems and asymptotic behaviour of the solution are studied.