The lowest crossing in 2D critical percolation

We study the following problem for critical site percolation on the triangular lattice. Let A and B be sites on a horizontal line e separated by distance n. Consider, in the half-plane above e, the lowest occupied crossing R from the half-line left of A to the half-line right of B. We show that the probability that R has a site at distance smaller than m from AB is of order (log (n/m))^{-1}, uniformly in 1 <= m < n/2. Much of our analysis can be carried out for other two-dimensional lattices as well.Comment: 16 pages, Latex, 2 eps figures, special macros: percmac.tex. Submitted to Annals of Probabilit

Coarse graining of slow variables in dynamic simulations of soft matter

A new Brownian dynamics model is presented to describe the coarse grain dynamics of particles with long-lived memory. Instead of solving a set of generalized Langevin equations we introduce a set of variables describing the slowly fluctuating thermodynamic state of the ignored degrees of freedom. These variables give rise to additional transient forces on the simulated particles, whose interpretation provides a new way of thinking about memory effects in soft-matter physics. We illustrate the proposed method by simulating shear thinning of synthetic resins.\u

Rock-Paper-Scissors; A New and Elegant Proof

I provide an elegant proof identifying the unique mixed Nash equilibrium of the Rock-Paper-Scissors game. The proof is based on intuition rather than elimination of cases. It shows that for any mixed strategy other than the one that puts equal probability on each of a player’s actions, it holds that this strategy is not a best response to any mixed strategy that is a best response to it.

Spectral Types of Field and Cluster O-Stars

The recent catalog of spectral types of Galactic O-type stars by Mai'z-Apella'niz et al. has been used to study the differences between the frequencies of various subtypes of O-type stars in the field, in OB associations and among runaway stars. At a high level of statistical significance the data show that O-stars in clusters and associations have earlier types (and hence presumably larger masses and/or younger ages) than those that are situated in the general field. Furthermore it is found that the distribution of spectral subtypes among runaway O-stars is indistinguishable from that among field stars, and differs significantly from that of the O-type stars that are situated in clusters and associations. The difference is in the sense that runaway O-stars, on average, have later subtypes than do those that are still located in clusters and associations.Comment: To be published in the October 2004 issue of the Astronomical Journal Included Figure 1, page

Efficient implicit simulation for incremental forming

Single Point Incremental Forming (SPIF) is a displacement controlled process performed on a CNC machine. A clamped blank is deformed by the movement of a small sized tool that follows a prescribed tool path. An extensive overview of the process has been given in [1]. The tool size plays a crucial role in the SPIF process. The small radius of the forming tool concentrates the strain at the zone of deformation in the sheet under the forming tool. The tool has to travel a lengthy forming path all over the blank to introduce the deformation. Numerically, this requires performing thousands of load increments on a relatively fine FE model resulting in enormous computing time. A typical computing time for implicit simulation of a small academic test is measured in by days. The focus of this paper is to efficiently use the implicit time integration method in order to reduce the required computing time for incremental forming implicit simulation drastically

A Closer Look at Jamnitzer's Polyhedra

The Renaissance artist Wentzel Jamnitzer designed series of intriguing polyhedra in perspective in his book “Perspectiva Corporum Regularium”. In this paper we investigate the possible principles of the construction of the polyhedra and create 3D computer models of them. Comparing those to the originals, we get an idea of how successful he was in drawing the complex structures by imagination. Furthermore, we analyse Jamnitzer's use of linear perspective, an important key in creating such drawings

Fully equipped half bridge building block for fast prototyping of switching power converters

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TACOP: A Cognitive Agent for a Naval Training Simulation Environment

The full version of this paper appeared in: Doesburg, W. A. van, Heuvelink, A., and Broek, E. L. van den (2005). TACOP: A cognitive agent for a naval training simulation environment. In M. Pechoucek, D. Steiner, and S. Thompson (Eds.), Proceedings of the Industry Track of the Fourth International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS-05), p.34-41. July 25-29, Utrecht, The Netherlands