Cavity identification in linear elasticity and thermoelasticity

The aim of this paper is an analysis of geometric inverse problems in linear elasticity and thermoelasticity related to the identification of cavities in two and three spatial dimensions. The overdetermined boundary data used for the reconstruction are the displacement and temperature on a part of the boundary. We derive identifiability results and directional stability estimates, the latter using the concept of shape derivatives, whose form is known in elasticity and newly derived for thermoelasticity. For numerical reconstructions we use a least‐squares formulation and a geometric gradient descent based on the associated shape derivatives. The directional stability estimates guarantee the stability of the gradient descent approach, so that an iterative regularization is obtained. This iterative scheme is then regularized by a level set approach allowing the reconstruction of multiply connected shapes. Copyright © 2007 John Wiley & Sons, Ltd.     

Dual-wavelength laser emission from an organic microcavity with terahertz beating

We report on the dynamics of laser emission from an anisotropic organic microcavity filled with the guest-host composite of tris-(8-hydroxy quinoline) aluminium (Alq₃) and 4-(dicyanomethylene)-2-methyl-6-(p-dimethylaminostyryl)-4H-pyran (DCM). In a single microcavity, a linesplitting of 0.18 THz between two perpendicularly polarized laser modes is observed. We ascribe this effect to an optical anisotropy in the distributed Bragg reflectors surrounding the organic layer. The temporal behavior of the electromagnetic field is studied by an up-conversion technique and shows an optical beating of 0.18 THz. Two modeling approaches are used to gain insight in the temporal evolution and phase behavior of the two modes. Both point towards the presence of a phase-coupling mechanism in this system. PACS 42.55.Sa     

Mean Waiting Time Approximations in the G/G/1 Queue

It is known that correlations in an arrival stream offered to a single-server queue profoundly affect mean waiting times as compared to a corresponding renewal stream offered to the same server. Nonetheless, this paper uses appropriately constructed GI/G/1 models to create viable approximations for queues with correlated arrivals. The constructed renewal arrival process, called PMRS (Peakedness Matched Renewal Stream), preserves the peakedness of the original stream and its arrival rate; furthermore, the squared coefficient of variation of the constructed PMRS equals the index of dispersion of the original stream. Accordingly, the GI/G/1 approximation is termed PMRQ (Peakedness Matched Renewal Queue). To test the efficacy of the PMRQ approximation, we employed a simple variant of the TES⁺ process as the autocorrelated arrival stream, and simulated the corresponding TES ⁺/G/1 queue for several service distributions and traffic intensities. Extensive experimentation showed that the proposed PMRQ approximations produced mean waiting times that compared favorably with simulation results of the original systems. Markov-modulated Poisson process (MMPP) is also discussed as a special case.     

Photon correlation spectra of poly(phenylmethyl siloxane) under high pressures

We report polarized photon correlation measurements of bulk poly(phenylmethyl siloxane) (PPMS) with a molecular weight of about 2500 at different pressures from 1 to 1750 bar and temperatures between 269 and 308 K. In the Frequency range accessible by present-day digital correlators, the time correlation function can measure a slow q²-dependent diffusional process due to local concentration fluctuations and a fast α-mode structural relaxation process. The mean characteristic times of the two processes approach each other at low temperatures and high pressures, in contrast to the behavior of the α- and β-relaxation times. We should be cautious in relating the mean characteristic times for the structural relaxation process obtained by different experimental techniques, such as Brillouin scattering and photon correlation spectroscopy, because of the differnces in the probe emphasis and the extremely broad frequency distribution of such relaxation processes.     

Glass transition,crystallization, and morphology relationships in miscible poly(aryl ether ketones) and poly(ether imide) blends

The relationships among glass transition, crystallization, melting, and crystal morphology of poly(aryl ether ketone) (PAEK)/poly(other imide) (PEI) blends was studied by thermal, optical and small-angle x-ray scattering (SAXS) methods. Two types of PAEK were chosen for this work: poly(aryl ether ether ketone), PEEK, and poly(aryl ether ketone ketone), PEKK, which have distinctly different crystallization rates. Both PAEKs show complete miscibility with PEI in the amorphous phase. As PAEK crystallizes, the noncrystallizable PEI component is rejected from the crystalline region, resulting in a broad amorphous population, which was indicated by the broadening and the increase of T_g over that of the purely amorphous mixture. The presence of the PEI component significantly decreases the bulk crystallization and crystal growth rate of PAEK, but the equilibrium melting temperature and crystal surface free energies are not affected. The morphology of the PEI segregation was investigated by SAXS measurements. The results indicated that the inter(lamellar-bundle) PEI trapping morphology was dominant in the PEEK/PEI blends under rapid crystallization conditions, whereas the interspherulitic morphology was dominant in the slow crystallizing PEKK/PEI blends. These morphologies were qualitatively explained by the expression δ=D/G, where G was the crystal growth rate and D was the mutual diffusion coefficient. © 1993 John Wiley & Sons, Inc.     

A Classification of Fully Residually Free Groups of Rank Three or Less

A groupGisfully residually freeprovided to every finite setS ⊂ G\{1} of non-trivial elements ofGthere is a free groupF_Sand an epimorphismh_S:G → F_Ssuch thath_S(g) ≠ 1 for allg ∈ S. Ifnis a positive integer, then a groupGisn-freeprovided every subgroup ofGgenerated bynor fewer distinct elements is free. Our main result shows that a fully residually free group of rank at most 3 is either abelian, free, or a free rank one extension of centralizers of a rank two free group. To prove this we prove that every 2-free, fully residually free group is actually 3-free. There are fully residually free groups which are not 2-free and there are 3-free, fully residually free groups which are not 4-free.     

Equivalence of Two Approaches to Integrable Hierarchies of KdV type

The equivalence between the approaches of Drinfeld-Sokolov and Feigin-Frenkel to the mKdV and KdV hierarchies is established. A new derivation of the mKdV equations in the zero curvature form is given. Connection with the Baker-Akhiezer function and the tau-function is also discussed. Received: Received: 1 July 1996 / Accepted: 21 October 1996     

Solvent dynamics following charge transfer at the liquid-liquid interface

The dynamics of solvent reorganization following charge transfer at the interface between two immiscible liquids, one polar and the other non-polar are investigated by molecular dynamics. Both charge separation and charge recombination processes in two different orientations at the surface are considered and are compared with the same processes in the bulk polar solvent. The relaxation at the surface is significantly slower than in the bulk, in contrast to predictions of continuum models. The linear response approximation works reasonably well in the bulk but fails at the interface. The Langevin model is in poor agreement with the exact equilibrium correlations, especially at short time, but can qualitatively account for the overall rate.     

A nonlinear bilevel model for analysis of electric utility demand-side planning issues

An application of bilevel programming in the electric utility industry is presented. The model is nonlinear and is used to analyze various economic issues that affect electric utility planning. The electric utility at the upper level of the model seeks to minimize costs or maximize benefits while controlling electric rates and subsidizing energy conservation programs. Customers at the lower level attempt to maximize their net benefit by consuming electricity and investing in conservation. This model considers factors such as free riders and the rebound effect which affect the net benefits of utility resource plans but are ignored by most planning models. The model's solutions shed light on utility issues including whether there can be a practical difference between various objectives, including minimizing cost (least cost planning) and maximizing net social welfare (value based planning).