Approximate Conditions and Passage to the Limit in Sobolev Spaces over Thin and Composite Structures

Approximate properties of variable measures compose a base of the two-scale convergence method with respect to a variable measure, which is used in averaging on periodic thin and composite structures. The paper gives a survey of methods for verifying approximate properties. The main focus is on studying composite measures, which have been little studied. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 16, Partial Differential Equations, 2004.     

Schottky metal library for ZNO-based UV photodiode fabricated by the combinatorial ion beam-assisted deposition

A binary alloy Schottky barrier diode on zinc oxide (ZnO) was developed using the combinatorial ion beam-assisted deposition system. The compositional fraction of the binary alloy was continuously varied using the composition-spread technique, to control the Schottky barrier height. After metal deposition, patterned Schottky diodes were fabricated on a ZnO single-crystal substrate. Pt-Ru alloy was selected from the work function viewpoint. Our experiments showed that the compositional fraction of the Schottky binary alloys changed continuously as designed and the Schottky barrier heights measured by current-voltage (I-V) measurements increased with increasing Pt content. Maximum barrier height difference for ZnO was 137 meV. Using ion beam deposition in parallel with the combinatorial system showed that the Schottky barrier heights for ZnO can be controlled by binary metal alloying.     

On the S-procedure and Some Variants

We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.The many suggestions and detailed corrections of an anonymous referee are gratefully acknowledged.     

Controlled structure and density of “living” polystyrene brushes on flat silica surfaces

Thin layers of polystyrene were grown from surface-grafted nitroxide initiators via controlled “living” free radical polymerization. The “reactive” Langmuir-Blodgett deposition method allowed an effective control of the initiator layer density leading to PS brushes with different and high grafting density and stretching. The influence of the grafting density on the layer structure was studied. Comparison with theoretical predictions for monodispersed brushes in bad solvent was discussed. The thickness was found to vary linearly with molecular weight and the density dependence was shown using wetting measurements. Special features of controlled radical nitroxide polymerization from a surface were discussed. A direct comparison of the molecular weight and polydispersity between surface and bulk polymers was made by de-grafting the brushes into a toluene/HF solution. Finally, some evidence of a “surface Fischer” effect was shown from re-initiated layers. Received 20 December 2001     

Magnetooptical investigation of the micromagnetic structure and magnetization processes in Co69Fe4Si12B15 amorphous microwires

Magnetooptical investigation of the micromagnetic structure of Co₆₉Fe₄Si₁₂B₁₅ amorphous microwires 10–50 μm in diameter is carried out. The existence of domains with transverse circumferential magnetization is experimentally demonstrated in the near-surface region of microwires. The dependence of the width of circular domains on the length and diameter of wires is obtained. It is shown that the near-surface micromagnetic structure of amorphous wires is changed under a stretch-induced stress. It is proved that the magnetization reversal of microwires in a longitudinal magnetic field occurs due to the rotation of local magnetization vectors in circular domains.     

A Successful Implementation of Locating Passive Cooling Facilities: The Case of Northern Thailand

This paper reports the actual implementation of a location-allocation study, which is one aspect of the overall Passive Cooling (Thailand) Project conducted in Northern Thailand since 1985. The goal has been to generate decision supports for ‘optimal’ placements of cooling facilities and the assignment of sites to these facilities as part of the post-harvest handling-chain operation of agricultural products. The basic questions addressed in this work are the issues of how many facilities to set up and where to locate them for maximum utility. Our selected approach is to use discrete location-allocation modelling, as, among other reasons, the problem at hand has a most natural network setting. Direct methods as well as efficient heuristics are examined, and sample numerical results are reported as illustrations of the continual implementation.     

Winding Numbers and Average Frequencies in Phase Oscillator Networks

We study networks of coupled phase oscillators and show that network architecture can force relations between average frequencies of the oscillators. The main tool of our analysis is the coupled cell theory developed by Stewart, Golubitsky, Pivato, and Torok, which provides precise relations between network architecture and the corresponding class of ODEs in R^M and gives conditions for the flow-invariance of certain polydiagonal subspaces for all coupled systems with a given network architecture. The theory generalizes the notion of fixed-point subspaces for subgroups of network symmetries and directly extends to networks of coupled phase oscillators. For systems of coupled phase oscillators (but not generally for ODEs in R^M, where M ≥ 2), invariant polydiagonal subsets of codimension one arise naturally and strongly restrict the network dynamics. We say that two oscillators i and j coevolve if the polydiagonal θ_i = θ_j is flow-invariant, and show that the average frequencies of these oscillators must be equal. Given a network architecture, it is shown that coupled cell theory provides a direct way of testing how coevolving oscillators form collections with closely related dynamics. We give a generalization of these results to synchronous clusters of phase oscillators using quotient networks, and discuss implications for networks of spiking cells and those connected through buffers that implement coupling dynamics.     

Electronic spectra of cationic forms of meso-tetrapropylporphin in a nanoporous silicate gel matrix

We have studied the fluorescence and fluorescence excitation spectra at 300 K, 77 K, and 4.2 K for silicate gel matrices colored with meso-tetrapropylporphin by impregnation of the matrix with a solution of the pigment. Comparison of the data obtained with the absorption spectra in acidified solutions and analysis of the low-temperature fine-structure vibronic spectra, and also taking into account data obtained earlier for octaethylporphin in a xerogel showed formation of two cationic forms of meso-tetrapropylporphin in the gel matrix: the short-wavelength form has a dicationic structure, while the long-wavelength form has a monocationic structure. We have traced out the correlations of the vibrational structure in the spectra of the dicationic form with data for the porphin dication, and we have drawn a number of conclusions concerning the normal vibrational modes that are active in the vibronic fluorescence and absorption spectra of the studied cationic forms. Using the AM1 semiempirical quantum chemical method, we optimized the geometry of the mesotetrapropylporphin dication: the most stable of the possible conformers is the dication structure with saddleshaped macrocycle nonplanarity. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 4, pp. 453–461, July–August, 2006.     

Flat Information Geometries in Black Hole Thermodynamics

The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein–Maxwell equations. The picture of state space that we obtain makes some properties such as the occurence of divergent specific heats transparent.Supported by VR.