We present here a simple analytical model for self-oscillations in nano-electro-mechanical systems. We show that a field emission self-oscillator can be described by a lumped electrical circuit and that this approach is generalizable to other electromechanical oscillator devices. The analytical model is supported by dynamical simulations where the electrostatic parameters are obtained by finite element computations.

In the present paper we are concerned with developing more realistic dynamic models of route choice and departure time decisions of transportation network users than have been proposed in the literature heretofore. We briefly review one class of models that is a dynamic generalization of the static Wardropian user equilibrium, the so-called Boston traffic equilibrium. In contrast, we then propose a new class of models that is also a dynamic generalization of the static Wardropian user equilibrium. In particular, we show for the first time that there is a variational inequality formulation of dynamic user equilibrium with simultaneous route choice and departure time decisions which, when appropriate regularity conditions hold, preserves the first in, first out queue discipline.

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In this paper we present tatonnement models for calculating static Wardropian user equilibria on congested networks with fully general demand and cost structures. We present both a qualitative analysis of stability and numerical studies which show that such an approach provides a reliable means for determining static user equilibria. We also describe circumstances for which these models depict day-to-day adjustments from one realizable disequilibrium state to another and how these adjustment processes differ depending on the “quality” of the information being provided by (abstract) traveler information systems. Specifically, we demonstrate that such dynamic adjustment processes settle down to equilibria both when information is complete and when it is incomplete.

In this paper we present results from a new two-dimensional numerical relativity code used to study the interaction of gravitational waves with a black hole. The initial data correspond to a single black hole superimposed with time-symmetric gravitational waves (Brill waves). A gaugeinvariant method is presented for extracting the gravitational waves from the numerically generated spacetime. We show that the interaction between the gravitational wave and the black hole excites the quasinormal modes of the black hole. An extensive comparison of these results is made to blackhole perturbation theory. For low-amplitude initial gravitational waves, we find excellent agreement between the theoretically predicted t = 2 and t = 4 wave forms and the wave forms generated by the code. Additionally, a code test is performed wherein the propagation of the wave on the black-hole background is compared to the evolution predicted by perturbation theory. PACS number(s): 04.30.+~,95.3O.S1,97.60.Lf I. I N T R O D U C T I O N 45 3544

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The dynamics of apparent and event horizons of various black hole spacetimes, including those containing distorted, rotating and colliding black holes, are studied. We have developed a powerful and efficient new method for locating the event horizon, making possible the study of both types of horizons in numerical relativity. We show that both the event and apparent horizons, in all dynamical black hole spacetimes studied, oscillate with the quasinormal frequency.Comment: 4 pages, 94-