Model validation and model structure determination

This paper gives a tutorial overview of basic approaches for model validation and model structure determination.Work partially supported by the Swedish Research Council for Engineering Sciences under contract 98-654.     

Reliability Potential Of Epoxy Based Encapsulants For Automotive Applications

Automotive under-the-hood electronics often have to withstand temperatures up to 175 °C in combination with harsh environment conditions. This paper gives an overview about the reliability potential of epoxy based encapsulants for automotive applications. Therefore the resistance of epoxy molding compound against typical automotive fluids at temperature of use is analyzed. Six epoxy molding compounds available on the market, showing high temperature automotive potential have been carefully selected to undergo a media resistance testing. For this purpose a dedicated mold tool has been designed and manufactured to prepare these encapsulants for material testing. Thermo-mechanical, mechanical and thermal properties had been determined in initial state directly after molding and after storage in aggressive fluids typical for automotive applications as e.g. gas oil, automatic transmission fluid (ATF), brake fluid or accumulator acid at the respective temperature of use.     

April in Paris: signs of artificial life along the Seine

What if every public space and surface were transformed into an interactive experience - capturing our movements, gestures, sounds and actions and using these to produce new sounds, images, text and actions? Bus stops could come alive and talk back, advertisements could look back at you and talk to you and public park robotic devices could play games with you. Will public places eventually become our social barometer as well as director? Will billboards display the populace's discourse? The author look at some special streets in France where the city is literally alive with art and explores what it might mean for us to live in a world of artistic interactivity.     

Performance of coherent data transmission in frequency-selectiveRayleigh fading channels

The error probability of digital transmission through a frequency-selective channel with random multipath fading due to uncorrelated scatterers is calculated. The error probability is averaged with respect to the randomly varying delays, with a given delay power spectrum. Two coherent receivers, suboptimum without any knowledge of the channel and optimum with perfectly known channel, are compared. The results are applied to continuous-phase-modulation (CPM) signals     

Banach spaces of distributions having two module structures

After a discussion of a space of test functions and the corresponding space of distributions, a family of Banach spaces (B, ∥ ∥_B) in standard situation is described. These are spaces of distributions having a pointwise module structure and also a module structure with respect to convolution. The main results concern relations between the different spaces associated to B established by means of well-known methods from the theory of Banach modules, among them B₀ and $\text{B}\text{?}$, the closure of the test functions in B and the weak relative completion of B, respectively. The latter is shown to be always a dual Banach space. The main diagram, given in Theorem 4.7, gives full information concerning inclusions between these spaces, showing also a complete symmetry. A great number of corresponding formulas is established. How they can be applied is indicated by selected examples, in particular by certain Segal algebras and the A_p-algebras of Herz. Various further applications are to be given elsewhere.     

Fabrication and Characterization of Two‐Photon Polymerized Features in Colloidal Crystals

The fabrication and characterization of two‐photon polymerized features written within and outside of colloidal crystals is presented. Two‐photon polymerization (TPP) response diagrams are introduced and developed to map the polymerization and damage thresholds for features written via modulated beam rastering. The use of tris[4‐(7‐benzothiazol‐2‐yl‐9,9‐diethylfluoren‐2‐yl)phenyl]amine (AF‐350) as an initiator for TPP is demonstrated for the first time and TPP response diagrams illustrate the polymerization window. These diagrams also demonstrate that the polymerization behavior within and outside of colloidal crystals is similar and electron microscopy reveals nearly identical resolution. Fluorescence confocal microscopy further enables visualization of non‐self‐supporting, three‐dimensional TPP features within self‐assembled photonic crystals. Finally, microspot spectroscopy is collected from a two‐photon feature written within a colloidal crystal and this is compared with simulation.     

Molecular flow and wall collision age distributions

The use of storage cells has become a standard technique for internal gas targets in conjunction with high energy storage rings. In case of spin-polarized hydrogen and deuterium gas targets the interaction of the injected atoms with the walls of the storage cell can lead to depolarization and recombination. Thus the number of wall collisions of the atoms in the target gas is important for modeling the processes of spin relaxation and recombination. It is shown in this article that the diffusion process of rarefied gases in long tubes or storage cells can be described with the help of the one-dimensional diffusion equation. Mathematical methods are presented that allow one to calculate collision age distributions (CAD) and their moments analytically. These methods provide a better understanding of the different aspects of diffusion than Monte Carlo calculations. Additionally it is shown that measurements of the atomic density or polarization of a gas sample taken from the center of the tube allow one to determine the possible range of the corresponding density weighted average values along the tube. The calculations are applied to the storage cell geometry of the HERMES internal polarized hydrogen and deuterium gas target. Received 9 July 2001 and Received in final form 18 September 2001     

Particle production at high energies in the Cardy pomeron model

Particle production at very high energies inhh, hA andAB collisions is studied in the framework of the pomeron model with a strong self-interaction proposed by Cardy. It is shown that the interaction between pomerons substancially damps the production rate one nuclei, the multiplicities forhA collisions becomingA-independent.     

Bivariate Free Knot Splines

We consider the least squares approximation of gridded 2D data by tensor product splines with free knots. The smoothing functional to be minimized—a generalization of the univariate Schoenberg functional—is chosen in such a way that the solution of the bivariate problem separates into the solution of a sequence of univariate problems in case of fixed knots. The resulting optimization problem is a constrained separable least squares problem with tensor product structure. Based on some ideas developed by the authors for the univariate case, an efficient method for solving the specially structured 2D problem is proposed, analyzed and tested on hand of some examples from the literature.