Abstract:
We study development of singularities for the spherically symmetric Yang-Mills equations in $d+1$ dimensional Minkowski spacetime for $d=4$ (the critical dimension) and $d=5$ (the lowest supercritical dimension). Using combined numerical and analytical methods we show in both cases that generic solutions starting with sufficiently large initial data blow up in finite time. The mechanism of singularity formation depends on the dimension: in $d=5$ the blowup is exactly self-similar while in $d=4$ the blowup is only approximately self-similar and can be viewed as the adiabatic shrinking of the marginally stable static solution. The threshold for blowup and the connection with critical phenomena in the gravitational collapse (which motivated this research) are also briefly discussed.

Abstract:
We study numerically the Cauchy problem for equivariant wave maps from 3+1 Minkowski spacetime into the 3-sphere. On the basis of numerical evidence combined with stability analysis of self-similar solutions we formulate two conjectures. The first conjecture states that singularities which are produced in the evolution of sufficiently large initial data are approached in a universal manner given by the profile of a stable self-similar solution. The second conjecture states that the codimension-one stable manifold of a self-similar solution with exactly one instability determines the threshold of singularity formation for a large class of initial data. Our results can be considered as a toy-model for some aspects of the critical behavior in formation of black holes.

Abstract:
Given discrete degrees of freedom (spins) on a graph interacting via an energy function, what can be said about the energy local minima and associated inherent structures? Using the lid algorithm in the context of a spin glass energy function, we investigate the properties of the energy landscape for a variety of graph topologies. First, we find that the multiplicity Ns of the inherent structures generically has a lognormal distribution. In addition, the large volume limit of ln/ differs from unity, except for the Sherrington-Kirkpatrick model. Second, we find simple scaling laws for the growth of the height of the energy barrier between the two degenerate ground states and the size of the associated valleys. For finite connectivity models, changing the topology of the underlying graph does not modify qualitatively the energy landscape, but at the quantitative level the models can differ substantially.

Abstract:
We consider the vacuum gravitational collapse for cohomogeneity-two solutions of the nine dimensional Einstein equations. Using combined numerical and analytical methods we give evidence that within this model the Schwarzschild-Tangherlini black hole is asymptotically stable. In addition, we briefly discuss the critical behavior at the threshold of black hole formation.

Abstract:
The article shows the results of investigations of the mechanical properties conducted on austenitic ductile iron with an addi-tion of 23-24% Ni. The examined mechanical properties included: tensile strength (Rm), proof stress (Rp0,2), elongation (A5) and reduction of area (Z) at reduced and low temperatures.

Abstract:
In the study an algorithm based on a lattice gas model is proposed as a tool for enhancing quality of lowresolution images of binary structures. Analyzed low-resolution gray-level images are replaced with binary images, in which pixel size is decreased. The intensity in the pixels of these new images is determined by corresponding gray-level intensities in the original low-resolution images. Then the white phase pixels in the binary images are assumed to be particles interacting with one another, interacting with properly defined external field and allowed to diffuse. The evolution is driven towards a state with maximal energy by Metropolis algorithm. This state is used to estimate the imaged object. The performance of the proposed algorithm and local and global thresholding methods are compared.

Abstract:
Purpose: The aim of this paper was to investigate the effect of wood filler additions on the microstructure, fractographic features and cracking mechanism of low density polyethylene (LPDE).Design/methodology/approach: For the tests, waste polyethylene from industrial and common films and Lignocel CB 120 wood fibers have been used. Three types of compositions (composites) with 10, 20 and 30% of wood flour have been prepared for the tests. To evaluate the role of used filler conducted it’s quantitative analysis by linear method. Parameters like volume fraction of the filler, the number particles of wood flour per surface area and mean wood fiber diameter, were determinated.Findings: The results of microscopic observations of the etched sections and fractures obtained at room temperature and at liquid nitrogen temperature indicate good matching between the filler particles and the structure of basic polymer, due mainly to bonding of the individual lamellae in spherulites. The reinforced polymer reveals a cracking micromechanism which is called crazing.Research limitations/implications: The further research are required to solve the problem of the filler contrast.Practical implications: From practical point of view, this research can be used to project composites (wood flour – polyethylene).Originality/value: Originality of this work is the fact that stereological measurements shown usefulness this method to estimate filler’s influence of forming microstructure and properties of the investigated composite.

Abstract:
We demonstrate that magnetic multilayer nanopillars can be efficiently protected from oxidation by coating with silicon. Both the protected and the oxidized nanopillars exhibit an increase of reversal current at cryogenic temperatures. However the magnetic excitation onset current increases only in the oxidized samples. We show that oxidized nanopillars exhibit anomalous switching statistics at low temperature, providing a simple test for the quality of magnetic nanodevices.