Boundary conditions for coupled quasilinear wave equations with application to isolated systems

We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] \times \Sigma$, where $\Sigma$ is a compact manifold with smooth boundaries $\partial\Sigma$. By using an appropriate reduction to a first order symmetric hyperbolic system with maximal dissipative boundary conditions, well posedness of such problems is established for a large class of boundary conditions on $\partial\Sigma$. We show that our class of boundary conditions is sufficiently general to allow for a well posed formulation for different wave problems in the presence of constraints and artificial, nonreflecting boundaries, including Maxwell's equations in the Lorentz gauge and Einstein's gravitational equations in harmonic coordinates. Our results should also be useful for obtaining stable finite-difference discretizations for such problems.Comment: 22 pages, no figure

Self-balancing beam permits safe, easy load handling under overhang

The use of a self-balancing I-beam with a counterweight and motor simplifies moving heavy loads that are inaccessible for cranes. The beam cannot be overloaded, as the counterweight will not balance the load, and thus acts as an automatic safety device

Phase transition and percolation in Gibbsian particle models

We discuss the interrelation between phase transitions in interacting lattice or continuum models, and the existence of infinite clusters in suitable random-graph models. In particular, we describe a random-geometric approach to the phase transition in the continuum Ising model of two species of particles with soft or hard interspecies repulsion. We comment also on the related area-interaction process and on perfect simulation.Comment: Survey article, 25 page

Safety yoke would protect construction workers from falling

Simple dismountable yoke protects construction workers on narrow steel I beams at high levels. The yoke engages the upper flat of the I beam and slides freely along it to permit freedom of movement to the worker while limiting his ability to fall by a harness attached to the yoke

Optimal prediction and the Klein-Gordon equation

The method of optimal prediction is applied to calculate the future means of solutions to the Klein-Gordon equation. It is shown that in an appropriate probability space, the difference between the average of all solutions that satisfy certain constraints at time t=0, and the average computed by an approximate method, is small with high probability.Comment: 18 page