Iterative Algorithms for Multiscale State Estimation, Part 2: Numerical Investigations

Usually, direct methods are employed for the solution of linear systems arising in the context of optimization. However, motivated by the potential of multiscale refinement schemes for large problems of dynamic state estimation, we investigate in this paper the application of iterative solvers based on the concepts developed in Ref. 1. Specifically, we explore the effect of different system reductions for various Krylov-space iteration methods as well as three concepts of preconditioning. The first one is the normalization of states and outputs, which also favors error analysis. Next, diagonal scale-dependent preconditioners are compared; they all bound the condition numbers independently of the refinement scale, but exhibit significant quantitative differences. Finally, the effect of the regularization parameter on condition numbers and iteration numbers is analyzed. It turns out that a so-called simplified Uzawa scheme with Jacobi preconditioning and suitable regularization parameter is most efficient. The experiments also reveal that further improvements are necessary.     

Classical Heisenberg ferromagnets with defects

A ferromagnet (dimensionality d) containing defects (of dimensionality d′) is treated by the phenomenological Landau theory. It is shown that for d′<d?1 no change of the critical exponent of the local magnetization near the defect occurs, in contrast to the case of the local magnetization near a surface (d′=d?1). The case of point defects (d′=0) in classical Heisenberg ferromagnets with nearest neighbor interactions is treated both by the mean field approximation and the Monte-Carlo method with effective field boundary conditions. We obtain rough agreement between these two approaches—two special cases are considered in detail: (a) interaction with, the defect being zero, (b) anti-ferromagnetic interactions across the defect (which is a crude model of superexchange). It is pointed out that it is a reasonable approximation to express the deviation of the local magnetization from the bulk value near the defect in terms of the spin pair correlation functions of the undisturbed system.     

Monte Carlo modelling of the polymer glass transition

We are proposing a lattice model with chemical input for the computer modelling of the polymer glass transition. The chemical input information is obtained by a coarse graining procedure applied to a microscopic model with full chemical detail. We use this information on Bisphenol-A-Polycarbonate to predict it's Vogel-Fulcher temperature out of a dynamic Monte Carlo Simulation. The microscopic structure of the lattice model is that of a genuine amorphous material, and the structural relaxation obeys the time temperature superposition.     

Monte Carlo simulation of a three-dimensional spin glass

Similarly to two dimensions, the Edwards-Anderson model of (Ising) spins with a Gaussian nearest-neighbor exchange-force distribution gives near $\text{T}{}_{\mathrm{<mtext>c</mtext>}}\text{≈1.5}\text{ΔJ}\text{k}{}_{\mathrm{<mtext>B</mtext>}}$ a cusp in the susceptibility, a peak in the specific heat, and a continuous vanishing of the “order parameter”.     

Focused tandem shock waves in water and their potential application in cancer treatment

The generator of two focused successive (tandem) shock waves (FTSW) in water produced by underwater multichannel electrical discharges at two composite electrodes, with a time delay between the first and second shock waves of 10  $\upmu $ s, was developed. It produces, at the focus, a strong shock wave with a peak positive pressure of up to 80 MPa, followed by a tensile wave with a peak negative pressure of up to $-80$  MPa, thus generating at the focus a large amount of cavitation. Biological effects of FTSW were demonstrated in vitro on hemolysis of erythrocytes and cell viability of human acute lymphoblastic leukemia cells as well as on tumor growth delay ex vivo and in vivo experiments performed with B16 melanoma, T-lymphoma, and R5-28 sarcoma cell lines. It was demonstrated in vivo that FTSW can enhance antitumor effects of chemotherapeutic drugs, such as cisplatin, most likely due to increased permeability of the membrane of cancer cells induced by FTSW. Synergetic cytotoxicity of FTSW with sonosensitive porphyrin-based drug Photosan on tumor growth was observed, possibly due to the cavitation-induced sonodynamic effect of FTSW.     

Biaxial ordering of terminal diene groups in lipid membranes: an infrared linear dichroism study

The molecular order within the hydrophobic core of membranes of the diene lipid di-tetradecadienoylphosphatidylcholine was studied by means of infrared spectroscopy on multibilayer assemblies which orient macroscopically on the surface of an attenuated total reflection crystal. The relative humidity and temperature were used as variable parameters to demonstrate that there were profound differences in the melting transition of lipids possessing predominantly cis and trans diene groups. The cis isomer undergoes the phase transition at a vapor pressure which is increased by 0.15 GPa when compared with that of the trans isomer. The methylene wagging band progression gives no indication of differences between the acyl chain conformation of the cis and trans forms in the gel state. The frequencies of a number of absorption bands of the diene groups reveal that these moieties are predominantly in the s-trans conformation to accommodate a favorable packing within the bilayer. The linear dichroism of selected in-plane and out-of-plane vibrations of the diene groups gives indications of the biaxial ordering of these moieties. We present the basic equations for the quantitative analysis of IR dichroism data of lamellar structures in terms of transverse and longitudinal molecular order parameters. It turns out that the planes of the rigid diene groups orient preferentially in a perpendicular direction with respect to the bilayer surface and parallel to each other forming in this way a layer of well-aligned diene groups in the bilayer center. This finding is confirmed by the results of X-ray measurements. We suggest that the partial interdigitation of the diene groups of the sn-1 acyl chains promotes the formation of the inverse H_II phase and/or enables the formation of covalent bonds between both the monolayers upon polymerization of diene lipids.     

Thin-Film Zinc/Manganese Dioxide Electrodes

Summary.  Thin-film electrodes allow the manufacturing of flat batteries of variable design. Their electric performance is better than that of customary cells because of a larger contact area between anode and cathode and better utilization of the electrochemically active materials. Bipolar thin-film electrodes for the rechargeable alkaline zinc/manganese dioxide system were assembled using graphite-filled plastics (high-density polyethylene and polyisobutylene). In a different approach, extremely thin electrodes were obtained using 25 μm thick foils made of non-conductive micro-porous polypropylene. The electroactive materials were electrolytically deposited into the pores of the previously metallized foil, providing the required conductive connection through the plastic matrix by themselves. Cycle behavior, cumulated capacities, and energies of batteries with up to two bipolar units were measured. At this early stage of development, batteries based on graphite-filled polymer foils showed better results with regard to storage capacity per unit area and to cycle life. Prototypes based on micro-porous polypropylene suffered from the relatively small fraction of pore volume available for the deposition of active material (about 38%) and from current collector corrosion. Received May 30, 2000. Accepted December 18, 2000