A generic framework for time-stepping partial differential equations (PDEs): general linear methods,object-oriented implementation and application to fluid problems

Time-stepping algorithms and their implementations are a critical component within the solution of time-dependent partial differential equations (PDEs). In this article, we present a generic framework – both in terms of algorithms and implementations – that allows an almost seamless switch between various explicit, implicit and implicit–explicit (IMEX) time-stepping methods. We put particular emphasis on how to incorporate time-dependent boundary conditions, an issue that goes beyond classical ODE theory but which plays an important role in the time-stepping of the PDEs arising in computational fluid dynamics. Our algorithm is based upon J.C. Butcher's unifying concept of general linear methods that we have extended to accommodate the family of IMEX schemes that are often used in engineering practice. In the article, we discuss design considerations and present an object-oriented implementation. Finally, we illustrate the use of the framework by applications to a model problem as well as to more complex fluid problems.     

Design considerations for tunnel diode non-linear transmission lines

A tunnel diode non-linear transmission line has been investigated for second and third harmonic generation purposes. Design criteria are given and performance predictions have been obtained simulating the single diode behavior by means of a polynomial expression. An optimization of the non-linear transmission line as a harmonic generator has been obtained as a function of the number of diodes, their separation distances and the bias voltage.     

There Are Not Too Many Magic Configurations

A finite planar point set P is called a magic configuration if there is an assignment of positive weights to the points of P such that, for every line l determined by P, the sum of the weights of all points of P on l equals 1. We prove a conjecture of Murty from 1971 and show that if a set of n points P is a magic configuration, then P is in general position, or P contains n−1 collinear points, or P is a special configuration of 7 points. The research by Rom Pinchasi was supported by a Grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development.     

Geometric properties of the self-adjoint Sturm-Liouville problems

In this paper, geometric properties of the self-adjoint Sturm-Liouville problems are investigated. It is proved that for linear self-adjoint Sturm-Liouville problems, the eigenfunctions correspond exactly to the projections of the curvature lines on the energy functional surface with an appropriate metric and that the eigenvalues correspond exactly to the principal curvatures (at the origin) of the same energy functional surface.     

A review of optically pumped far-infrared laser lines from methanol isotopes

The technique of optical pumping in polar molecules is the most efficient for Far-Infrared (FIR) laser generation, providing also a versatile and powerful tool for molecular spectroscopy in this spectral region. Methanol (CH₃OH) and its isotopic varieties are the best media for optically pumped FIR laser, with over thousand lines observed, and the most widely used for investigations and applications. In this sense, it is important organize and make available catalogues of FIR laser lines as complete as possible. Since the last critical reviews of 1984 [1] on methanol and its isotopic varieties [2,3,4], over hundred papers have been published dealing with hundreds of new FIR laser lines. In 1992 a review of FIR laser lines from CH₃OH was presented [5]. In this communication we extend this work to the other methanol isotopes, namely CH₃OD, CD₃OH, CD₃OD,¹³CH₃OH,¹³CD₃OH,¹³CD₃OD, CH₃ ¹⁸OH, CH₂DOH, CHD₂OH and CH₂DOD.Work supported by FAPESP, CNPq, FAEP-Brasil, and CNR-Italia     

13CH3OH and13CD3OH optically pumped fir laser: New large offset emission and optoacoustic spectroscopy

27 new, large offset, FIR laser lines from¹³CH₃OH and one from¹³CD₃OH have been discovered by pumping with a high tunability waveguide CW CO₂ laser. Optoacoustic measurements of isotopic methyl alcohol have also been performed and the pump offsets of the new and of previously known lines have been measured and checked. Frequency tunability by Stark effect has been observed for 6 strong lines. Some assignments are discussed.     

Intensity measurements of H2O lines in the spectral region 8000-9350 cm

This paper presents new measurements of H₂¹⁶O lines performed on spectra recorded with the GSMA Fourier Transform Spectrometer (FTS). Our experimental conditions allow one to obtain new line intensity measurements from 10⁻²⁵ to 10⁻²¹ cm/molec at 296 K and self-broadening coefficients in the spectral range centered at 8800 cm⁻¹. In the HITRAN database, data reported for this region is taken from the work of Mandin et al. (1988) [8] and [9] and several articles pointed out problems on the line intensities. We present in this paper some intensity comparisons, first with the HITRAN database, and then with the recent article of Tolchenov and Tennyson (2005) [3]. We finish by a comparison on self-broadening coefficients.     

Corrections to statistical modeling of spectra for plasmas at moderate or low temperatures

For plasmas in LTE at moderate or low temperatures (1–50 eV), the statistical approach for calculating emission or absorption spectra may become inaccurate and need improvement to account for the Boltzmann factor in the population of the levels. In this work, corrections to the transition rates are computed by using the moments of emission or absorption zones, which represent the set of levels within a configuration that provide the dominant part of the emissivity (or opacity). Partition functions are also improved by using high-order moments of level energy distributions. Corrections to the statistical models are derived in a non-relativistic framework as a function of these moments, which can be deduced from already published formulas. Numerical comparisons of detailed line-by-line and statistical calculations are presented that clearly illustrate the importance of correcting the models at low temperatures. Thus, these corrections are of great interest for applications such as Warm Dense Matter, LTE photo-absorption experiments where the targets are heated to ∼T_e = 20 eV and astrophysical plasmas.     

Infinite Systems of Quasilinear Differential Difference Inequalities and Applications

The article deals with the initial boundary value problem for an infinite system of first order quasilinear functional differential equations. A comparison result concerning infinite systems of differential difference inequalities is proved. A function satisfying such inequalities is estimated by a solution of a suitable Cauchy problem for an ordinary functional differential system. The comparison result is used in an existence theorem and in the investigation of the stability of the numerical method of lines for the original problem. A theorem on the error estimate of the method is given. The infinite system of first order functional differential equations contains, as particular cases, equations with a deviated argument and integral differential equations of the Volterra type.     

Separation of systems based on uranium hexafluoride and some of halogen fluorides

The purpose of this paper is to present the results of the comprehensive study of the phase equilibriums liquid-solid and liquid-vapour in binary and ternary systems, formed by uranium hexafluoride, bromine trifluoride and iodine pentafluoride.Investigation of the phase equilibriums in condensed systems is done by methods of differential thermoanalysis and visual polythermal analysis. All systems belong to simple eutectics; formation of the compounds is not detected. For all systems under investigation diagrams of the phase equilibrium liquid-solid are plotted.Phase equilibriums liquid-vapour in studied systems were studied by statistical method. All systems are non-aseotropic. The article presents diagrams of the phase equilibrium liquid-vapour in binary systems, pressure of the saturated vapour dependences on liquid composition, surface of the boiling liquid and lines of the constant content of uranium hexafluoride and iodine pentafluoride in vapour phase of the ternary system UF₆-BrF₃-IF₅.