A collocation method for solving singular integro-differential equations

This paper describes a collocation method for numerically solving Cauchy-type linear singular integro-differential equations. The numerical method is based on the transformation of the integro-differential equation into an integral equation, and then applying a collocation method to solve the latter. The collocation points are chosen as the Chebyshev nodes. Uniform convergence of the resulting method is then discussed. Numerical examples are presented and solved by the numerical techniques.

A singular integro-differential equation model for dryout in LMFBR boiler tubes

A 2D steady model for the annular two-phase flow of water and steam in the steam-generating boiler pipes of a liquid metal fast breeder reactor is proposed The model is based on thin-layer lubrication theory and thin aerofoil theory. The exchange of mass between the vapour core and the liquid film due to evaporation of the liquid film is accounted for using some simple thermodynamics models, and the resultant change of phase is modelled by proposing a suitable Stefan problem Appropriate boundary conditions for the now are discussed The resulting non-lineal singular integro-differential equation for the shape of the liquid film free surface is solved both asymptotically and numerically (using some regularization techniques) Predictions for the length to the dryout point from the entry of the annular regime are made The influence of both the traction tau provided by the fast-flowing vapour core on the liquid layer and the mass transfer parameter eta on the dryout length is investigated

A METHOD FOR THE STUDY OF ACCRETION DISK EMISSION IN CATACLYSMIC VARIABLES. I. THE MODEL

We have developed a spectrum synthesis method for modeling the ultraviolet (UV) emission from the accretion disk from cataclysmic variables (CVs). The disk is separated into concentric rings, with an internal structure from the Wade & Hubeny disk-atmosphere models. For each ring, a wind atmosphere is calculated in the comoving frame with a vertical velocity structure obtained from a solution of the Euler equation. Using simple assumptions, regarding rotation and the wind streamlines, these one-dimensional models are combined into a single 2.5-dimensional model for which we compute synthetic spectra. We find that the resulting line and continuum behavior as a function of the orbital inclination is consistent with the observations, and verify that the accretion rate affects the wind temperature, leading to corresponding trends in the intensity of UV lines. In general, we also find that the primary mass has a strong effect on the P Cygni absorption profiles, the synthetic emission line profiles are strongly sensitive to the wind temperature structure, and an increase in the mass-loss rate enhances the resonance line intensities. Synthetic spectra were compared with UV data for two high orbital inclination nova-like CVs-RW Tri and V347 Pup. We needed to include disk regions with arbitrary enhanced mass loss to reproduce reasonably well widths and line profiles. This fact and a lack of flux in some high ionization lines may be the signature of the presence of density-enhanced regions in the wind, or alternatively, may result from inadequacies in some of our simplifying assumptions.

Monotone positive solutions for a fourth order equation with nonlinear boundary conditions

This work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions. The results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions. Numerical simulations are also presented. (C) 2009 Elsevier Ltd. All rights reserved.

Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows

This work deals with the development of a numerical technique for simulating three-dimensional viscoelastic free surface flows using the PTT (Phan-Thien-Tanner) nonlinear constitutive equation. In particular, we are interested in flows possessing moving free surfaces. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are considered. The PTT equation is solved by a high order method, which requires the calculation of the extra-stress tensor on the mesh contours. To validate the numerical technique developed in this work flow predictions for fully developed pipe flow are compared with an analytic solution from the literature. Then, results of complex free surface flows using the FIT equation such as the transient extrudate swell problem and a jet flowing onto a rigid plate are presented. An investigation of the effects of the parameters epsilon and xi on the extrudate swell and jet buckling problems is reported. (C) 2010 Elsevier B.V. All rights reserved.

A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

ENO adaptive method for solving one-dimensional conservation laws

In this work an efficient third order non-linear finite difference scheme for solving adaptively hyperbolic systems of one-dimensional conservation laws is developed. The method is based oil applying to the solution of the differential equation an interpolating wavelet transform at each time step, generating a multilevel representation for the solution, which is thresholded and a sparse point representation is generated. The numerical fluxes obtained by a Lax-Friedrichs flux splitting are evaluated oil the sparse grid by an essentially non-oscillatory (ENO) approximation, which chooses the locally smoothest stencil among all the possibilities for each point of the sparse grid. The time evolution of the differential operator is done on this sparse representation by a total variation diminishing (TVD) Runge-Kutta method. Four classical examples of initial value problems for the Euler equations of gas dynamics are accurately solved and their sparse solutions are analyzed with respect to the threshold parameters, confirming the efficiency of the wavelet transform as an adaptive grid generation technique. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

On the Hamilton-Jacobi equation in the framework of generalized functions

In this work we study, in the framework of Colombeau`s generalized functions, the Hamilton-Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions. (C) 2011 Elsevier Inc. All rights reserved.

Integral group ring of the Suzuki sporadic simple group

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm the Kimmerle`s conjecture on prime graphs.

CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS

In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u subset of Z(U(ZC(p,q))) and by applying our results, we prove that u generates a subgroup of finite index.

Development of a sequential injection-square wave voltammetry method for determination of paraquat in water samples employing the hanging mercury drop electrode

This work describes the development and optimization of a sequential injection method to automate the determination of paraquat by square-wave voltammetry employing a hanging mercury drop electrode. Automation by sequential injection enhanced the sampling throughput, improving the sensitivity and precision of the measurements as a consequence of the highly reproducible and efficient conditions of mass transport of the analyte toward the electrode surface. For instance, 212 analyses can be made per hour if the sample/standard solution is prepared off-line and the sequential injection system is used just to inject the solution towards the flow cell. In-line sample conditioning reduces the sampling frequency to 44 h(-1). Experiments were performed in 0.10 M NaCl, which was the carrier solution, using a frequency of 200 Hz, a pulse height of 25 mV, a potential step of 2 mV, and a flow rate of 100 mu L s(-1). For a concentration range between 0.010 and 0.25 mg L(-1), the current (i(p), mu A) read at the potential corresponding to the peak maximum fitted the following linear equation with the paraquat concentration (mg L(-1)): ip = (-20.5 +/- 0.3) Cparaquat -(0.02 +/- 0.03). The limits of detection and quantification were 2.0 and 7.0 mu g L(-1), respectively. The accuracy of the method was evaluated by recovery studies using spiked water samples that were also analyzed by molecular absorption spectrophotometry after reduction of paraquat with sodium dithionite in an alkaline medium. No evidence of statistically significant differences between the two methods was observed at the 95% confidence level.

Calculating Flash Point Numbers from Molecular Structure: An Improved Method for Predicting the Flash Points of Acyclic Alkanes

We report a novel method for calculating flash points of acyclic alkanes from flash point numbers, N(FP), which can be calculated from experimental or calculated boiling point numbers (Y(BP)) with the equation N(FP) = 1.020Y(BP) - 1.083 Flash points (FP) are then determined from the relationship FP(K) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901 For it data set of 102 linear and branched alkanes, the correlation of literature and predicted flash points has R(2) = 0.985 and an average absolute deviation of 3.38 K. N(FP) values can also be estimated directly from molecular structure to produce an even closer correspondence of literature and predicted FP values. Furthermore, N(FP) values provide a new method to evaluate the reliability of literature flash point data.

Simple Method to Evaluate and to Predict Flash Points of Organic Compounds

Flash points (T(FP)) of organic compounds are calculated from their flash point numbers, N(FP), with the relationship T(FP) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901. In turn, the N(FP) values can be predicted from boiling point numbers (Y(BP)) and functional group counts with the equation N(FP) = 0.974Y(BP) + Sigma(i)n(i)G(i) + 0.095 where G(i) is a functional group-specific contribution to the value of N(FP) and n(i) is the number of such functional groups in the structure. For a data set consisting of 1000 diverse organic compounds, the average absolute deviation between reported and predicted flash points was less than 2.5 K.