Diffraction microstrain in nanocrystalline solids under load - heterogeneous medium approach

This is an account of the computation of X-ray microstrain in a polycrystal with anisotropic elasticity under uniaxial external load. The results have been published in the article "Microstrain in nanocrystalline solids under load by virtual diffraction", at Europhysics Letters 89, 66002 (2010). The present information was submitted to Europhysics Letters as part of the manuscript package, and was available to the reviewers who recommended the paper for publication.Comment: Supporting online material for J. Markmann, D. Bachurin, L.-H. Shao, P. Gumbsch, J. Weissm\"uller, Microstrain in nanocrystalline solids under load by virtual diffraction, Europhys. Lett. 89, 66002 (2010

Perfect retroreflectors and billiard dynamics

We construct semi infinite billiard domains which reverse the direction of most incoming particles. We prove that almost all particles will leave the open billiard domain after a finite number of reflections. Moreover, with high probability the exit velocity is exactly opposite to the entrance velocity, and the particle's exit point is arbitrarily close to its initial position. The method is based on asymptotic analysis of statistics of entrance times to a small interval for irrational circle rotations. The rescaled entrance times have a limiting distribution in the limit when the length of the interval vanishes. The proof of the main results follows from the study of related limiting distributions and their regularity properties. © 2011 AIMSciences

Ab initio study of hydrogen behavior in titanium beryllides

An interest in titanium beryllides as candidate materials for advanced neutron multiplier for the Helium Cooled Pebble Bed breeding blanket of European DEMO fusion reactor is related to their lower tritium retention, lower swelling and higher oxidation resistance in comparison with pure beryllium. The latter was initially suggested as neutron multiplier in the International Thermonuclear Experimental Reactor (ITER) and for the above reasons has a number of limitations compared to beryllides. One of the most important questions is how much weaker tritium, which is formed as a result of the interaction of high-energy neutrons with the pebbles is bound in titanium beryllides in contrast to pure beryllium. Such an interaction awakes formation of helium bubbles and degradation of the material properties. One of the main promising methods for studying the behavior of hydrogen in titanium beryllides is first-principles modeling technique based on density functional theory. The present work is devoted to ab initio study of hydrogen (isotope effects were neglected and hydrogen was considered instead of tritium) behavior in three titanium beryllides (Be2Ti, Be17Ti2, Be12Ti). All of them have different crystal structure and contain a different number of crystallographically non-equivalent interstitial hydrogensites. Both the hydrogen solution energy in defect-free lattice and binding energy with a vacancy are important characteristics in terms of tritium dissolution, retention and release. Static ab initio calculations demonstrate that hydrogen solution energy in all interstitial non-equivalent sites is noticeably lower as compared with pure beryllium suggesting an easier dissolution of hydrogen atoms in titanium beryllides. Computation of binding energy of single hydrogen atom with all non-equivalent monovacancies reveals that hydrogen might be trapped by a vacancy without being inside it. The obtained results sheds light on the understanding of earlier tritium release in different titanium beryllides during thermo-desorption experiments and expand our knowledge of their properties

Ergodic directions for billiards in a strip with periodically located obstacles

We study the size of the set of ergodic directions for the directional billiard flows on the infinite band $\R\times [0,h]$ with periodically placed linear barriers of length $0<\lambda<h$. We prove that the set of ergodic directions is always uncountable. Moreover, if $\lambda/h\in(0,1)$ is rational the Hausdorff dimension of the set of ergodic directions is greater than 1/2. In both cases (rational and irrational) we construct explicitly some sets of ergodic directions.Comment: The article is complementary to arXiv:1109.458

Effect of impurities on microstructural evolution under irradiation in beryllium

Impurities are known to affect mechanical properties of beryllium, but their effect on development of irradiation induced microstructure is still unknown. In this contribution we are making further attempt to reveal behavior of impurities in neutron irradiated beryllium pebbles by using both analytical transmission electron microscope (TEM) and first principles computer simulations. TEM studies have revealed Al-Fe-Be precipitates, complex multiple phase precipitates, homogeneous segregations of elements to grain boundaries as well as abundant precipitation along dislocations. All precipitates are richly decorated with helium bubbles which are smaller in size than typical bubbles inside grains. Precipitate-free and helium-bubble-free zones were observed along grain boundaries. Using density functional theory approach, we have calculated interaction of typical solutes found in beryllium, namely, Al, Fe, Cr, Mg and Si with vacancies, interstitials and free surfaces which can simulate a surface of helium bubbles. Interesting correlation has been revealed: an impurity which has attractive binding with a vacancy has also positive affinity to free surface. In particular, Al, Mg and Si are strongly bound with vacancies and also attracted by the free surfaces. This result is supported by the EDX measurements, (see Fig. above) which reveal decoration of He bubbles with Al, Si and Mg, while Fe is homogeneously distributed. Those impurities which repulse vacancies are attracted by self-interstitials, however, no correlation with the formation volume of respective substitutional atoms was found in this case

Optimization in the Natural Sciences: 30th Euro Mini-Conference, EmC-ONS 2014, Aveiro, Portugal, February 5-9, 2014: revised selected papers

This book constitutes the refereed proceedings of the 30th Euro Mini-Conference, EmC-ONS 2014, held in Aveiro, Portugal, in February 2014. The 13 revised full papers presented were carefully reviewed and selected from 70 submissions. The papers are organized in topical sections on dynamical systems; optimization and applications; modeling and statistical techniques for data analysis

Mathematical retroreflectors

Retroreflectors are optical devices that reverse the direction of incident beams of light. Here we present a collection of billiard type retroreflectors consisting of four objects; three of them are asymptotically perfect retroreflectors, and the fourth one is a retroreflector which is very close to perfect. Three objects of the collection have recently been discovered and published or submitted for publication. The fourth object - notched angle - is a new one; a proof of its retroreflectivity is given.Comment: 32 pages, 19 figure

Key factors of ion induced nanopatterning

We have reported the dependence of projectile mass, chemical reactivity and effect of molecular beams on the ion induced nano structure formation, when 8 keV He1+, N1+, O1+, Ar1+ atomic ions and 16 keV N21+ and O21+ molecular ions are bombarded on the Si(100) surface at an incidence angle of 60^{\circ}. Atomic force microscopy (AFM) measurement shows that the initiation and growth of ripple structures are determined not only by the collision cascades but also by the chemical reactivity and molecular state of the projectiles. This experimental investigation explores the necessary requirements for ion induced controlled nanopatterning

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of R^d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called `quenched random Lorentz tube'. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.Comment: Final version for J. Stat. Phys., 18 pages, 4 figure