Unbounded Orbits for Semicircular Outer Billiard

We show that the outer billiard around a semicircle has an open ball escaping to infinity. Submitted: April 19, 2008.; Accepted: January 11, 2009.     

A Novel One-Pot Synthesis Ofesters Byexchange Reactions between Carbonates and Anhydrides

A new method for the synthesis of esters by exchange reaction between anhydrides and carbonates, without any solvent, in the presence of Ti or Sn based catalyst is presented.     

Large-Eddy Simulations of cavitation in a square surface cavity

We report on the development and application of a multiphase approach to the prediction of cavitation induced by high-speed flow over and within a square surface cavity. The approach entails employing a full cavitation model in conjunction with Large-Eddy Simulations in order to capture the initiation and development of bubble formations in turbulent-flow conditions. The incipient formation of the bubble cloud, and the flow processes of vortex shedding and shear-layer oscillations are tracked using the Volume of Fluid method. The validity of the computational approach was assessed by comparisons with experiments on cavitating flow over a hydrofoil. Application to the case of flow over and within a two-dimensional square cavity with cavitation clearly reveal the presence of traveling cavitation at the corner of the cavity trailing edge, and vortex cavitation within the cavity. It is shown that the collapse of cavitation bubbles results in an impact frequency that is higher than the frequency of the shear-layer oscillations. This implies that structural damage due to cavitation is likely to be most severe at the corner formed at the intersection of the cavity’s trailing edge and the flat surface upstream of it.     

Deformation induced martensite transformation in a cold-worked forming process of austenitic stainless steel

Within the last years the goal of industrial manufacturing processes – such as tube forming – has shifted towards an optimization of technological as well as mechanical properties of the manufactured structures. For example, during the forming procedure of sheets made of austenitic stainless steel X5CrNi18-10, the content of strain-induced martensite needs to be controlled. In order to achieve optimal structural properties of the manufactured tube with respect to very high-cycle fatigue (VHCF), a martensite ratio of approximately 25% needs to be obtained [1]. On the basis of experimental investigations this contribution deals with the numerical simulation of the tube-forming process with special consideration of the martensite ratio c as a function of temperature and deformation field. For this purpose we extend an existing martensite model on polyaxial states of stress and compare experimental results and numerical simulations for the modified model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mixing in the Absence of the Shrinking Target Property

Using reparametrizations of linear flows, we show that thereexist area-preserving real analytic maps of the three-dimensionaltorus that are ‘mixing of all orders’ and do notenjoy the monotone shrinking target property. Prior to that,we give a short proof of a result of Kurzweil from 1955: namely,that a translation T of the torus T^d has the monotone shrinkingtarget property if and only if the vector is badly approximable(that is, of constant type). 2000 Mathematics Subject Classification37E45, 37A25, 11J13. 2000 Mathematics Subject Classification37E45, 37A25, 11J13.     

On a Lie-theoretic approach to generalized doubly stochastic matrices and applications

In this article, we study generalized doubly stochastic matrices using the theory of Lie groups and Lie algebras. Applications to the inverse eigenvalue problem for symmetric doubly stochastic matrices are presented.     

Topologically mixing and minimal but not ergodic, analytic transformation onT 5

We give an example of an analytic transformation onT ⁵ that conserves the Haar measure, that is minimal and topologically mixing, but is not ergodic.     

Polycatenar oligophenylene liquid crystals

We report the synthesis of oligophenylene polycatenar liquid crystals incorporating 1,4-disubstituted phenyl rings joined by a direct carbon carbon bond and some pyrimidine analogues. The nature of the linkages does appear to affect the mesomorphism significantly. The ratio of the aromatic core to the aliphatic chains is varied systematically by changing the number of 1,4-disubstituted phenyl rings and the length of the aliphatic chains. This strongly influences the transition temperatures of the mesophases. Some of the compounds are columnar over an extended temperature range of more than 200°C with melting points below room temperature. We suggest that a combination of the poor overlap of the conjugated electron system of the molecular cores making up the columnar structure and the high concentration of aliphatic chains leads to a low charge-carrier mobility.     

Quasistatic Thermoviscoelastic Frictional Contact Problem with Damped Response

We analyze a problem which describes the frictional contact between a thermoviscoelastic body and a rigid foundation. The process is assumed to be quasistatic and the contact is modeled by a general normal damped response condition with friction law and heat exchange. Then we present a variational formulation of the problem, which is set in an abstract form as a system of evolution equations for the displacements and temperature. We establish the existence and uniqueness of the weak solution, using general results on evolution equations with monotone operators and fixed point arguments. Finally, we study the continuous dependence of the solution with respect to the initial data and contact conditions.