Time-stepping algorithms for semidiscretized linear parabolic PDEs based on rational approximants with distinct real poles

Time dependent problems in Partial Differential Equations (PDEs) are often solved by the Method Of Lines (MOL). For linear parabolic PDEs, the exact solution of the resulting system of first order Ordinary Differential Equations (ODEs) satisfies a recurrence relation involving the matrix exponential function. In this paper, we consider the development of a fourth order rational approximant to the matrix exponential function possessing real and distinct poles which, consequently, readily admits a partial fraction expansion, thereby allowing the distribution of the work in solving the corresponding linear algebraic systems in essentially Backward Euler-like solves on concurrent processors. The resulting parallel algorithm possesses appropriate stability properties, and is implemented on various parabolic PDEs from the literature including the forced heat equation and the advection-diffusion equation.Dedicated to Professor J. Crank on the occasion of his 80th birthday     

Pressure effects on 2p5 3p - 2p5 3d transitions in neon

The collisional broadening and shift of four spectral lines of neon (747.2, 748.8, 753.5, 754.4 nm) arising from 2p⁵ 3p - 2p⁵ 3d transitions, emitted from a low-pressure glow discharge in pure neon and neon-helium mixtures have been measured using a Fabry-Perot interferometer. The values of pressure broadening and shift coefficients are determined and analyzed in terms of the impact theory.     

Pressure dependence of the spectral lines of a high power, high pressure atomic fluorine laser pumped by a charge transfer from He2

Various transitions of a pressure tunable atomic fluorine laser have been observed over a rather wide spectral range, 634.8–755.2 nm, by exciting the atmospheric pressure of helium containing 0.2% F₂ in a preionized Blumlein discharge device with a charging voltage of 10–15 kV. The intensity of two quartet transitions, 739.9 and 755.2 nm, increases with pressure, whereas that of the other quartet and doublet lines, 634.8, 641.4, 712.8 and 731.1 nm, decreases with increasing atmospheric fill-pressure. The pumping mechanisms at high pressures appear to be different from those at relatively low pressures.     

Assignments of optically pumped CD3OH laser lines

Six FIR laser lines from CD₃OH pumped by the 10R(36) and the 10R(18) CO₂ laser lines are assigned to specific rotational energy levels in the excited C–0 stretch state. It is found that their upper laser levels are shifted by a Fermi resonance between the C–0 stretch vibration and the third and forth harmonics of the torsional mode. The Fermi resonance shifts are +0.332 cm^–1 and +2.251 cm^–1 for the upper laser levels pumped by the 10R(36) and the 10R(18) CO₂ laser lines, respectively. Calculated frequencies of the pump and the laser transitions agree with those of the pump CO₂ laser lines and the observed FIR laser lines within estimated accuracy.     

order and disorder lines in systems with competing interactions: II. The IRF model

Systems with competing interactions can be often exactly solved on a restricted subspace of the parameter space, called an order or disorder trajectory. A simple method introduced within the transfer matrix formalism allows for the calculation of the free energy and spin-spin correlation functions along the order and disorder lines of the Ising model with all possible interactions around a face of the square lattice (IRF model). The general eight-vertex model is thoroughly examined and shows full analogy with the quantum spin chain results of the previous paper.On leave from and address after September 1, 1982: Institute for Theoretical Physics, Eötvös University, 1088 Budapest, Puskin U. 5–7, Hungary.     

Stark Broadening of F III Lines in Laboratory and Stellar Plasma

Using a semiclassical approach, we have considered electron-, proton-, and ionized helium-impact line widths and shifts for the F III 2p^{3 4}S^o-3s ⁴P resonant line. Moreover, for 10 F III multiplets where the full semiclassical perturbation approach is not applicable in an adequate way due to the lack of reliable atomic data, electron-impact line widths have been calculated within the modified semiempirical approach. Results are obtained as a function of temperature for perturber density of 10¹⁷ cm⁻³. The theoretical data obtained have been used to consider the influence of Stark broadening for A-type star atmosphere conditions. __________ Published in Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 3, pp. 412–415, May–June, 2005.     

Are the Elements Elementary? Nineteenth-Century Chemical and Spectroscopical Answers

We analyze the role and influence of a tradition of research linked to the concept of primary matter in nineteenth-century studies on the nature of the elements.The suggestion of William Prout (1785-1850) in 1816 that the atomic weights of pure chemical elements are whole numbers and multiples of the atomic weight of hydrogen, taken as unity, was met with serious confutations,which in turn prompted several attempts to save Prouts hypothesis.We discuss these attempts in detail and the objections raised against them, for instance by Dmitry Ivanovich Mendeleev (1834-1907). We pay particular attention to the use of spectroscopy as a method for proving the existence of elementary forms of matter inside atoms. Leaders in this field of research were two English scientists, the astrophysicist Norman Lockyer (1836-1920) and the chemist William Crookes (1832- 1919). Both of their approaches involved the idea of primary matter. However, while Crookess approach proved to be incorrect, Lockyers ideas survived for several years and supported the discovery of the electron by J.J.Thomson (1856-1940).     

Wavelet bases in

Some years ago, compactly supported divergence-free wavelets were constructed which also gave rise to a stable (biorthogonal) wavelet splitting of . These bases have successfully been used both in the analysis and numerical treatment of the Stokes and Navier-Stokes equations. In this paper, we construct stable wavelet bases for the stream function spaces . Moreover, -free vector wavelets are constructed and analysed. The relationship between and are expressed in terms of these wavelets. We obtain discrete (orthogonal) Hodge decompositions.

Our construction works independently of the space dimension, but in terms of general assumptions on the underlying wavelet systems in that are used as building blocks. We give concrete examples of such bases for tensor product and certain more general domains . As an application, we obtain wavelet multilevel preconditioners in and .

     

Simulation optimization of buffer allocations in production lines with unreliable machines

We use a recent simulationbased optimization method, sample path optimization, to find optimal buffer allocations in tandem production lines where machines are subject to random breakdowns and repairs, and the product is fluidtype. We explore some of the functional properties of throughput of such systems and exploit these properties to prove the almost sure convergence of our optimization technique, under a regularity condition on the steady state. Utilizing a generalized semiMarkov process (GSMP) representation of the system, we derive recursive expressions to compute onesided directional derivatives of throughput, from a single simulation run. Finally, we give computational results for lines with up to 50 machines. We also compare results for smaller lines with the results from a more conventional method, stochastic approximation, whenever applicable. In these numerical studies, our method performed quite well on problems that are considered difficult by current computational standards.     

强外加电场与大调制度下光折变动力学光栅形成研究

强外加电场与大调制度在光折变效应的研究中已经得到了广泛应用。采用PDECOL算法,严格求解光折变带输运方程,得到外加电场时不同调制度下光折变晶体中随时间变化的空间电荷场、载流子浓度,并讨论了外加电场对它们的影响。通过将物质方程与耦合波方程联立数值求解,可得到光折变光栅形成过程中两波耦合增益系数以及光束条纹相位的变化。模拟结果表明,在强外加电场作用下,两束记录光之间的光强与相位耦合都得到了增强,而原有的解析式忽视了强外加电场与大调制度对空间电荷场相位耦合的影响,此时不再适用。同时发现折射率光栅与记录光束条纹均发生弯曲,并不再保持平行。