Timothy D. Andersen

Cross-layer interference-aware routing for wireless multi-hop networks

In this paper we address the problem of interference-aware routing that tightly couples the design of the lower three layers of the ISO Open Systems Interconnection (OSI) protocol stack. This is primarily motivated by the observation that shortest path routing could potentially lead to degrading the single-hop throughput which constitutes an upper bound on the end-to-end multi-hop throughput. We introduce the concept of set-based routing in an attempt to incorporate interference into the routing decision as well as reduce the problem complexity. Towards this objective, we propose a novel algorithm that takes routing, scheduling and power control decisions for a set of interference-coupled transmitters. Furthermore, we discuss set coordination schemes for combating inter-set interference. Finally, we conduct a simulation study that shows considerable throughput improvement over a reference system that uses minimum hop routing and collision-free scheduling.

Negative specific heat in a quasi-2D generalized vorticity model

Negative specific heat is a dramatic phenomenon where processes decrease in temperature when adding energy. It has been observed in gravo-thermal collapse of globular clusters. We now report finding this phenomenon in bundles of nearly parallel, periodic, single-sign generalized vortex filaments in the electron magnetohydrodynamic model for the unbounded plane under strong magnetic confinement. We derive the specific heat using a steepest-descent method and a mean-field property. Our derivations show that as temperature increases, the overall size of the system increases exponentially and the energy drops. The implication of negative specific heat is a runaway reaction, resulting in a collapsing inner core surrounded by an expanding halo of filaments.

Introduction to vortex filaments in equilibrium

Introduction.- Vortex Filaments and Where to Find Them.- Statistical Mechanics.- Parallel Filaments.- Curved Filaments.- Quantum Fluids.- Plasmas.- Computational Methods.- Quasi 2-D Monte Carlo in Deep Ocean Convection.- Conclusion.

A length-scale formula for confined quasi-two-dimensional plasmas

Typically a magnetohydrodynamical model for neutral plasmas must take into account both the ionic and the electron fluids and their interaction. However, at short time scales, the ionic fluid appears to be stationary compared to the electron fluid. On these scales, we need consider only the electron motion and associated field dynamics, and a single fluid model called the electron magnetohydrodynamical model which treats the ionic fluid as a uniform neutralizing background applies. Using Maxwells equations, the vorticity of the electron fluid and the magnetic field can be combined to give a generalized vorticity field, and one can show that Eulers equations govern its behavior. When the vorticity is concentrated into slender, periodic, and nearly parallel (but slightly three-dimensional) filaments, one can also show that Eulers equations simplify into a Hamiltonian system and treat the system in statistical equilibrium, where the filaments act as interacting particles. In this paper, we show that, under a mean-field approximation, as the number of filaments becomes infinite (with appropriate scaling to keep the vorticity constant) and given that angular momentum is conserved, the statistical length scale, R, of this system in the Gibbs canonical ensemble follows an explicit formula, which we derive. This formula shows how the most critical statistic of an electron plasma of this type, its size, varies with angular momentum, kinetic energy, and filament elasticity (a measure of the interior structure of each filament) and in particular it shows how three-dimensional effects cause significant increases in the system size from a perfectly parallel, two-dimensional, one-component Coulomb gas.

Explicit mean-field radius for nearly parallel vortex filaments in statistical equilibrium with applications to deep ocean convection

Deep ocean convection, under appropriate conditions, gives rise to quasi-2D vortex structures with axes parallel to the rotational axis. These vortex structures appear in axisymmetric arrays that have a characteristic radius or size. This size is dependent, not only on competition between vortex interaction and conservation of angular momentum, but on 3D effects that 2D point vortex models leave out. In this article, we propose a hypothesis that as 3D variations become more significant in these arrays, the process of interaction/angular momentum competition gives way to entropy/angular momentum competition and that this shift results in a reversal of the trend of the radius to decrease with increasing kinetic energy. We derive an explicit, closed-form, mean-field expression for the radius using a quasi-2D model for filaments with a local induction approximation (LIA). We validate the formula with Monte Carlo simulations. Both confirm that there is a reversal in the 2D point vortex contraction trend. We conclude that the proposed shift in competition does happen and that this simple LIA model is sufficient to show it.