Optical waveguides in porous silicon pre-patterned by localised nitrogen implantation.

FIPOS technology forms islands of silicon isolated from a silicon substrate by (oxidised) porous silicon. The larger refractive index of the silicon islands suggests their use as optical waveguides. Sets of these silicon islands have been fabricated and the anticipated waveguiding has been observed at wavelengths of 1.15 and 1.3 μm in the silicon islands. However, the dominant waveguiding in these FIPOS structures is observed in the porous silicon between the silicon islands, close to the sample surface. A simple dynamic model of the anodisation process has been developed to explain the origin of this unexpected waveguiding.     

Production and location on a network under demand uncertainty

The Hakimi theorem is fundamental in location theory. It says that the set of nodes and market-places necessarily contains a profit-maximizing location when the transportation costs are concave in distance. The purpose of this letter is to discuss the validity of this theorem in the context of a two-stage stochastic model of the location of a firm on a network. In the first stage, the firm chooses its location and production level before knowing the exact demands. In the second stage, it observes the realization of the random variables representing the demands and decides upon the distribution of its production. It is shown that the Hakimi theorem still holds in this model when the firm is risk-neutral. On the other hand, in the case of a risk-averse firm, it ceases to be true in that all the points of the network must be considered to obtain an optimal location.     

The excitation energy spectrum of liquid He II based on theU-matrix theory

Summary In this paper, we apply theU-matrix theory to derive an explicit expression for the excitation energy spectrum of liquid⁴He. Using a model for the effective chemical potential for⁴He, we are able to produce an excitation spectrum which is very close to the observed one. The inverse of the effective mass,i.e. 1/m ^*, is obtained as a function of momentumk. The ratio between the effective mass and the mass of helium atom atk=2.0 ?⁻¹,i.e. near the roton depth, is found to bem ^*(k=2.0 ?⁻¹)/m _He=0.18298, while the ratio atk=1.0 ?⁻¹ ism ^*(k=1.0 ?⁻¹)/m _He=−0.17103. The theoretical result of the excitation spectrum is consistent with observational data.

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Riassunto In questo lavoro si applica la teoria della matriceU per dedurre un'espressione esplicita per lo spettro d'energia di eccitazione dell'⁴He liquido. Usando un modello per il potenziale chimico efficace per l'⁴He si è in grado di produrre uno spettro di eccitazione molto simile a quello osservato. L'inverso della massa efficace, cioè 1/m ^*, è ottenuto in funzione del momentok. Si trova che il rapporto tra massa efficace e la massa dell'atomo di elio ak=2.0 ?⁻¹, cioè vicino alla profondità del rotore, èm ^* (k=2.0 ?⁻¹)/m _He= =0.18298, mentre quello ak=1.0 ?⁻¹ èm ^* (k=1.0 ?⁻¹)/m _he=−0.17103. Il risultato teorico dello spettro di eccitazione è coerente con i dati sperimentali.

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Резюме В этой статье мы применяем теориюU-матрицы для вывода явного выражения для энергетического спектра возбуждений Зидкого⁴He. Используя модель для эффективного химического потенциала для⁴He, мы воспроизводим спектр возбуждений который оказывается очень близким к зкспериментально наблюдаемому. Вычисляется обратная величина эффективной массы, т.е. 1/m ^*, как функция импульсаk. Получено отношение эффективной массы к массе атома гелия приk=2.0 ?⁻¹, которое составляетm ^* (k=2.0 ?⁻¹)/m _He=0.18298, тогда как это отношение приk=1.0 ?⁻¹ равноm ^* (k=1.0 ?⁻¹)/m _He=−0.17103. Теоретический результат для спектра возбужений согласуется с имеющимися экспериментальными данными.

     

Existence of invariant manifolds for stochastic equations in infinite dimension

We provide a Frobenius type existence result for finite-dimensional invariant submanifolds for stochastic equations in infinite dimension, in the spirit of Da Prato and Zabczyk (Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, UK, 1992). We recapture and make use of the convenient calculus on Fréchet spaces, as developed by Kriegl and Michor (The Convenient Setting for Global Analysis, Surveys and Monographs, Vol. 53, Amer. Math. Soc., Providence, RI, 1997). Our main result is a weak version of the Frobenius theorem on Fréchet spaces. As an application, we characterize all finite-dimensional realizations for a stochastic equation which describes the evolution of the term structure of interest rates.     

Max-min matching problems with multiple assignments

In job assignment and matching problems, we may sometimes need to assign several jobs to one processor or several processors to one job with some limit on the number of permissible assignments. Some examples include the assignment of courses to faculty, consultants to projects, etc. In terms of objectives, we may wish to maximize profits or minimize costs, or maximize the minimal value (max-min criterion) of an attribute such as the performance rating of a processor in the matching, or combine the two goals into one composite objective function entailing time-cost tradeoffs. The regular bipartite matching algorithms cannot solve the matching problem, when upper and lower bounds are imposed on the number of assignments. In this paper, we present a method, referred to as the node-splitting method, that transforms the given problem into an assignment problem solvable by the Hungarian method.     

Cost Efficient Lie Group Integrators in the RKMK Class

In this work a systematic procedure is implemented in order to minimise the computational cost of the Runge—Kutta—Munthe-Kaas (RKMK) class of Lie-group solvers. The process consists of the application of a linear transformation to the stages of the method and the analysis of a graded free Lie algebra to reduce the number of commutators involved. We consider here RKMK integration methods up to order seven based on some of the most popular Runge—Kutta schemes.This revised version was published online in October 2005 with corrections to the Cover Date.     

A formula for the error of finite sinc-interpolation over a finite interval

Sinc-interpolation is a very efficient infinitely differentiable approximation scheme from equidistant data on the infinite line. It, however, requires that the interpolated function decreases rapidly or is periodic. We give an error formula for the case where neither of these conditions is satisfied. In celebration of Leonhard Euler’s 300th birthday. Work partly supported by the Swiss National Science Foundation under grant Nr 200020-103662/1.     

Propagation of shape-preserving optical pulses in inhomogeneously broadened multi-level systems

We study stable propagation of multiple shape-preserving optical pulses in an inhomogeneously broadened multi-level atomic medium. By analytically solving the Maxwell-Schr?dinger equations governing the evolution of N coupled optical fields and atomic amplitudes we show that N pulsed optical waves coupling to (N+1)-levels can be automatically matched with the same soliton waveform and identical yet very slow propagation velocity. Several sets of coupled soliton solutions for two different (N+1)-level models are given and their stability is studied by using a numerical simulation.     

A theoretical investigation on Pt3Sn(1 0 2) surface alloy and CO-Pt3Sn(1 0 2) system

The adsorption properties of CO on experimentally verified stepped Pt₃Sn(1 0 2) surface were investigated using quantum mechanical calculations. The two possible terminations of Pt₃Sn(1 0 2) were generated and on these terminations all types of possible adsorption sites were determined. The adsorption energies and geometries of the CO molecule for all those sites were calculated. The most favorable sites for adsorption were determined as the short bridge site on the terrace of pure-Pt row of the mixed-atom-ending termination, atop site at the step-edge of the pure row of pure-Pt-ending termination and atop site at the step-edge of the pure-Pt row of the mixed-atom-ending termination. The results were compared with those for similar sites on the flat Pt₃Sn(1 1 0) surface considering the fact that Pt₃Sn(1 0 2) has terraces with (1 1 0) orientation. The LDOS analysis of bare sites clearly shows that there are significant differences between the electronic properties of Pt atoms at stepped Pt₃Sn(1 0 2) surface and the electronic properties of Pt atoms at flat (1 1 0) surface, which leads to changes in the CO bonding energies of these Pt atoms. Adsorption on Pt₃Sn(1 0 2) surface is in general stronger compared to that on Pt₃Sn(1 1 0) surface. The difference in adsorption strength of similar sites on these two surface terminations is a result of stepped structure of Pt₃Sn(1 0 2). The local density of states (LDOS) of the adsorbent Pt and C of adsorbed CO was utilized. The LDOS of the surface metal atoms with CO-adsorbed atop and of their bare state were compared to see the effect of CO chemisorption on the electron density distribution of the corresponding Pt atom. The downward shift in energy peak in the LDOS curves as well as changes in the electron densities of the corresponding energy levels indicate the orbital mixing between CO molecular orbitals and metal d-states. The present study showed that the adsorption strength of the sites has a direct relation with their LDOS profiles.