On theK-property of some planar hyperbolic billiards

TheK-property is demonstrated for a class of planar billiards satisfying Wojtkowski's principles. Their boundary may consist of convex-scattering, concave and linear pieces. Earlier Wojtkowski showed that these billards had non-zero Lyapunov exponents.     

Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.     

Damage and fracture evaluation of granular composite materials by digital image correlation method

This paper presents the applications of digital image correlation technique to the mesoscopic damage and fracture study of some granular based composite materials including steelfiber reinforced concrete, sandstone and crystal-polymer composite. The deformation fields of the composite materials resulted from stress localization were obtained by the correlation computation of the surface images with loading steps and thus the related damage prediction and fracture parameters were evaluated. The correlation searching could be performed either directly based on the gray levels of the digital images or from the wavelet transform (WT) coefficients of the transform spectrum. The latter was developed by the authors and showed higher resolution and sensitivity to the singularity detection. Because the displacement components came from the rough surfaces of the composite materials without any coats of gratings or fringes of optical interferometry, both surface profiles and the deformation fields of the composites were visualized which was helpful to compare each other to analyze the damage of those heterogeneous materials. The project supported by the National Natural Science Foundation of China (10125211 and 10072002), the Scientific Committee of Yunnan Province for the Program of Steel Fiber Reinforced Concrete, and the Institute of Chemical Materials, CAEP at Mianyang     

Accuracy of the chemical data evaluated from one-atom-at-a-time experiments

Studies of chemistry of the transactinoid elements, which are available only as single atoms, by gas (thermo)chromatographic techniques can provide the adsorption enthalpies of the atoms or molecules. These values serve the ultimate goal—to characterize bulk volatility of the species in terms like sublimation enthalpies. The paper attempts an in-depth discussion of the statistical significance of the adsorption enthalpies derived in such experiments. Usually, the counting statistics are very poor and one faces nonstandard problems in evaluating the confidence intervals for the values of parameters. Here, a most efficient way seems to be the Bayesian approach, realized, when necessary, by Monte Carlo simulations of the counting results. Necessarily, the adsorption enthalpy is not evaluated based on the second law of thermodynamics but through accepting an a priori value of the adsorption entropy. More additional assumptions about the mechanisms and parameters involved are needed. This may produce systematic errors in the quantitative conclusions; the analysis of some recent works with elements 106 and 108 corroborates this concern. Despite such problems, it is possible to reveal qualitative differences in the adsorption behavior of a transactinoid and its expected known congeners as well as to use chemistry for an independent assignment of the atomic numbers of transactinoid nuclides.     

Vertical migration of 85Sr, 137Cs and 131I in various arable and undisturbed soils

The vertical migration of ⁸⁵Sr, ¹³⁷Cs and ¹³¹I in some arable and undisturbed single-contaminated soils was studied by gamma-spectrometry measurements under lysimetric laboratory conditions during irrigation of the soil profiles with wet atmospheric precipitation for about one year, except ¹³¹I. A new simple exponential compartment (box) model was derived, which makes it possible to calculate the migration rate constants and migration rates in the individual soil layers (vertical sections) as well as the total vertical migration rate constants and total vertical migration rates of radionuclides in the bulk soil horizon. The relaxation times of radionuclides in respective soil horizons can also be evaluated.     

Aluminum(III) complexes containing O,O chelating ligand

The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH₂)₂C₆H₃OH (LH) revealed compounds L₃Al ( 1 ) and L₂AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe₂ ( 3 ), rather 2 together with Me₃Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, ¹H and ¹³C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph₃SnOH, giving LSnPh₃ ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy and ¹H, ¹¹⁹Sn HMBC experiments. The system 2 and B(C₆F₅)₃ in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd.     

Cyclic deformation of aluminium and its alloys

The formation of slip bands is the main mechanism of cyclic deformation in pure Al. Their density, orientation and heights in polycrystalline Al were investigated during cycling. Types, sizes and densities of precipitates are responsible for the mode of cyclic deformation in AlCu4 pure alloy. In technical Al alloys intermetallic phases have detrimental effects on deformation homogeneity and largely govern the fatigue mechanism of the material and especially microcrack initiation.     

Searching for optimal configurations by simulated tunneling

Optimization theory deals with algorithms finding the lowest cost (energy) configuration in a minimal number of steps. When the cost function has many local minima, the deterministic algorithms become easily trapped in suboptimal solutions. The simulated annealing method tries to overcome this difficulty by introducting thermal noise in the problem. Here we explore the possibility of implementing search procedures analogous to the quantum tunneling effect. The suggested dynamics is a guided diffusion process of an interactingpopulation of configurations. Different dynamical aspects of the search process are formulated first in a simple one-dimensional tight-binding model with a hierarchical potential. The new algorithm is then applied to the Traveling Salesman Problem. It is demonstrated that the use of interacting, evolving populations of tours representing our wave packet leads to systematic improvements and possibly, to the optimal tour. In addition, the structure of the cost function landscape for a given instance becomes locally accessible. The performance of the algorithm and its implications for parallel computing and genetic programming are briefly discussed.