The diameter of a random subgraph of the hypercube

In this paper we present an estimation for the diameter of random subgraph of a hypercube. In the article by A. V. Kostochka (Random Struct Algorithms 4 (1993) 215–229) the authors obtained lower and upper bound for the diameter. According to their work, the inequalities n + m_p ≤ D(G_n) ≤ n + m_p + 8 almost surely hold as n → ∞, where n is dimension of the hypercube and m_p depends only on sampling probabilities. It is not clear from their work, whether the values of the diameter are really distributed on these 9 values, or whether the inequality can be sharpened. In this paper we introduce several new ideas, using which we are able to obtain an exact result: D(G_n) = n + m_p (almost surely). © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

Dynamic Data-Driven Genetic Algorithm for forest fire spread prediction

This work represents the first step towards a Dynamic Data-Driven Application System (DDDAS) for wildland fire prediction. Our main efforts are focused on taking advantage of the computing power provided by High Performance Computing systems and to propose computational data-driven steering strategies to overcome input data uncertainty. In doing so, prediction quality can be enhanced significantly. On the other hand, these proposals reduce the execution time of the overall prediction process in order to be of use during real-time crisis. In particular, this work describes a Dynamic Data-Driven Genetic Algorithm (DDDGA) used as steering strategy to automatically adjust highly dynamic input data values of forest fire simulators taking into account the underlying propagation model and real fire behaviour.     

Molecular polymeric matter, Weissenberg, Astbury and the pleasure of being wrong

The career of Karl Weissenberg began with X-ray structure studies of biopolymers. His background in scattering theory clearly affected his later approach to the measurements and modelling of the rheology of complex fluids. We show how the combination of scattering and rheology now informs molecular theories of the flow of entangled polymer melts. Very recently, the concepts generated by linear rheology have themselves contributed to the study of dynamics in biopolymers via single molecule experiments.     

Evaluation of self-consistent polycrystal plasticity models for magnesium alloy AZ31B sheet

Various self-consistent polycrystal plasticity models for hexagonal close packed (HCP) polycrystals are evaluated by studying the deformation behavior of magnesium alloy AZ31B sheet under different uniaxial strain paths. In all employed polycrystal plasticity models both slip and twinning contribute to plastic deformation. The material parameters for the various models are fitted to experimental uniaxial tension and compression along the rolling direction (RD) and then used to predict uniaxial tension and compression along the traverse direction (TD) and uniaxial compression in the normal direction (ND). An assessment of the predictive capability of the polycrystal plasticity models is made based on comparisons of the predicted and experimental stress responses and R values. It is found that, among the models examined, the self-consistent models with grain interaction stiffness halfway between those of the limiting Secant (stiff) and Tangent (compliant) approximations give the best results. Among the available options, the Affine self-consistent scheme results in the best overall performance. Furthermore, it is demonstrated that the R values under uniaxial tension and compression within the sheet plane show a strong dependence on imposed strain. This suggests that developing anisotropic yield functions using measured R values must account for the strain dependence.     

A Thermodynamically Consistent Theory of the Ferro/Paramagnetic Transition

We propose a continuum theory describing the evolution of magnetization and temperature in a rigid magnetic body. The theory is based on a microforce balance, an energy balance, and an entropy imbalance. We advance the choice of a class of constitutive equations, consistent with the entropy imbalance, that appear appropriate to describe the phase transition taking place in a ferromagnet at the Curie point. By combining these constitutive equations with the balance laws, we formulate an initial-boundary value problem for the magnetization and temperature fields, and we prove existence of weak solutions.     

Some examples of 5 and 7 descent for elliptic curves over Q

We perform descent calculations for the families of elliptic curves over Q with a rational point of order n = 5 or 7. These calculations give an estimate for the Mordell-Weil rank which we relate to the parity conjecture. We exhibit explicit elements of the Tate-Shafarevich group of order 5 and 7, and show that the 5-torsion of the Tate-Shafarevich group of an elliptic curve over Q may become arbitrarily large. Received October 6, 2000 / final version received November 14, 2000?Published online February 15, 2001     

Studies on the Anode/Electrolyte Interfacein Lithium Ion Batteries

Summary.  Rechargeable lithium ion cells operate at voltages of 3.5–4.5 V, which is far beyond the thermodynamic stability window of the battery electrolyte. Strong electrolyte reduction and anode corrosion has to be anticipated, leading to irreversible loss of electroactive material and electrolyte and thus strongly deteriorating cell performance. To minimize these reactions, anode and electrolyte components have to be combined that induce the electrolyte reduction products to form an effectively protecting film at the anode/electrolyte interface, which hinders further electrolyte decomposition reactions, but acts as membrane for the lithium cations, i.e. behaving as a solid electrolyte interphase (SEI). This paper focuses on important aspects of the SEI. By using key examples, the effects of film forming electrolyte additives and the change of the active anode material from carbons to lithium storage alloys are highlighted. Received May 30, 2000. Accepted June 14, 2000     

Hydraulics of Peat Filters Treating Septic Tank Effluent

Peat is an alternative filter medium for the treatment of various waste streams including septic tank effluent. The water holding capacity and adsorption capacity of peat make it a favorable filter medium over sand or gravel which are commonly used as the filter medium for the drainage field of septic systems. This paper presents the results of a field study to evaluate the hydraulics of a peat filter used to treat the septic tank effluent from a public school west of Ottawa, Canada. An experimental box was placed within the filter during its construction to provide access to the vertical profile of the peat layer. The filter is periodically pulsed with septic tank effluent, which is distributed over the top of the filter and flows vertically through the peat. The filter was instrumented with tensiometers and transducers to monitor the pore water pressures in response to a pulse of septic tank effluent. An in-depth study of the hydraulics of the system was completed. The soil moisture retention curve and the hydraulic conductivity as a function of density were determined in laboratory experiments. A one-dimensional unsaturated flow model was used to predict the pressure response due to a pulse. A comparison of the field and model results illustrates the impact of the density variations, and the corresponding hydraulic conductivity variations, on the model predictions. The compaction of the peat is an important design consideration for the filter since it directly impacts the flow characteristics and the hydraulic retention time within the filter.     

A parallel Krylov-Schur implementation for large Hermitian and non-Hermitian eigenproblems

This work presents a new implementation of a Krylov-Schur eigensolver in SLEPc (Scalable Library for Eigenvalue Problem Computations), a software library for the solution of large, sparse eigenvalue problems on parallel computers. Some parallel performance results are given, showing better scalability compared to ARPACK. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The nido–osmaboranes [2,2,2-(CO)(PPh3)2-nido-2-OsB5H9] and [6,6,6-(CO)(PPh3)2-nido-6-OsB9H13]

The structural characterization of the osmahexaborane 2-carbonyl-2,2-bis­(tri­phenyl­phosphine)-nido-2-osmahexaborane(9), [Os(B₅H₉)(C₁₈H₁₅P)₂(CO)], (I), a metallaborane analogue of B₆H₁₀, confirms the structure proposed from NMR spectroscopy. The structure of the osmadecaborane 6-carbonyl-6,6-bis­(tri­phenyl­phosphine)-nido-6-osmadecaborane(13), [Os(B₉H₁₃)(C₁₈H₁₅P)₂(CO)], (IV), is similarly confirmed. The short basal B—B distance of 1.652 (8) Å in (I), not bridged by an H atom, mirrors that in the parent hexaborane(10) [1.626 (4) Å].