Parallel efficiency of a boundary integral equation method for nonlinear water waves

We describe the application of domain decomposition on a boundary integral method for the study of nonlinear surface waves on water in a test case for which the domain decomposition approach is an important tool to reduce the computational effort. An important aspect is the determination of the optimum number of domains for a given parallel architecture. Previous work on hetero- geneous clusters of workstations is extended to (dedicated) parallel platforms. For these systems a better indication of the parallel performance of the domain decomposition method is obtained because of the absence of varying speed of the processing elements

How to Specify and How to Prove Correctness of Secure Routing Protocols for MANET

Secure routing protocols for mobile ad hoc networks have been developed recently, yet, it has been unclear what are the properties they achieve, as a formal analysis of these protocols is mostly lacking. In this paper, we are concerned with this problem, how to specify and how to prove the correctness of a secure routing protocol. We provide a definition of what a protocol is expected to achieve independently of its functionality, as well as communication and adversary models. This way, we enable formal reasoning on the correctness of secure routing protocols. We demonstrate this by analyzing two protocols from the literature

Low Momentum Classical Mechanics with Effective Quantum Potentials

A recently introduced effective quantum potential theory is studied in a low momentum region of phase space. This low momentum approximation is used to show that the new effective quantum potential induces a space-dependent mass and a smoothed potential both of them constructed from the classical potential. The exact solution of the approximated theory in one spatial dimension is found. The concept of effective transmission and reflection coefficients for effective quantum potentials is proposed and discussed in comparison with an analogous quantum statistical mixture problem. The results are applied to the case of a square barrier.Comment: 4 figure

Testing conformal mapping with kitchen aluminum foil

We report an experimental verification of conformal mapping with kitchen aluminum foil. This experiment can be reproduced in any laboratory by undergraduate students and it is therefore an ideal experiment to introduce the concept of conformal mapping. The original problem was the distribution of the electric potential in a very long plate. The correct theoretical prediction was recently derived by A. Czarnecki (Can. J. Phys. 92, 1297 (2014))

Galactic consequences of clustered star formation

If all stars form in clusters and both the stars and the clusters follow a power law distribution which favours the creation of low mass objects, then the numerous low mass clusters will be deficient in high mass stars. Therefore, the mass function of stars, integrated over the whole galaxy (the Integrated Galactic Initial Mass Function, IGIMF) will be steeper at the high mass end than the underlying IMF of the stars. We show how the steepness of the IGIMF depends on the sampling method and on the assumptions made for the star cluster mass function. We also investigate the O-star content, integrated photometry and chemical enrichment of galaxies that result from several IGIMFs, as compared to more standard IMFs.Comment: 4 pages, 2 figures, to appear in online version of Proceedings of IAU S266, a two page version will appear in the Proceedings of IAU S26

Frobenius theorem and invariants for Hamiltonian systems

We apply Frobenius integrability theorem in the search of invariants for one-dimensional Hamiltonian systems with a time-dependent potential. We obtain several classes of potential functions for which Frobenius theorem assures the existence of a two-dimensional foliation to which the motion is constrained. In particular, we derive a new infinite class of potentials for which the motion is assurately restricted to a two-dimensional foliation. In some cases, Frobenius theorem allows the explicit construction of an associated invariant. It is proven the inverse result that, if an invariant is known, then it always can be furnished by Frobenius theorem