Given a network with a continuum of users at some origins, suppose that the users wish to reach specific destinations, but that they are not indifferent to the time needed to reach their destination. They may have several possibilities (of routes or deparure time), but their choices modify the travel times on the network. Hence, each user faces the following problem: given a pattern of travel t...

The paper develops a stochastic dynamic model of economic equilibrium with locally interacting agents. The main focus of the study is on the modeling of market interactions – those arising in connection with commodity exchange and regulated by price mechanisms. The mathematical framework is a control theory for random vector fields on directed graphs. The graphs involved serve to describe the s...

The biological functions of many proteins are crucially coupled to protonation equilibria, for instance, in the enzymatic reactions of serine proteases and carbonic anhydrase, and in integral membrane proton pumps such as bacteriorhodopsin, cytochrome c oxidase (COX), and FOF1-ATP synthase. [8] Proton-transfer (PT) reactions are also crucial in many other areas of chemistry, such as membrane pe...

We study equilibrium properties of discrete-time, infinite-horizon smooth economies whose equilibria can be represented as a sequence of interrelated equations, and provide sufficient conditions to guarantee existence, (generic) determinacy and (generic) robustness of equilibria. Our approach exploits the sequential nature of a dynamic economy. An equilibrium is represented by a sequence of end...

We investigate a model for contact angle motion of quasi-static capillary drops resting on a horizontal plane. We prove global in time existence and long time behavior (convergence to equilibrium) in a class of star-shaped initial data for which we show that topological changes of drops can be ruled out for all times. Our result applies to any drop which is initially star-shaped with respect to...

Recent experiments have convincingly demonstrated the existence of surface nanobubbles on submerged hydrophobic surfaces. However, classical theory dictates that small gaseous bubbles quickly dissolve because their large Laplace pressure causes a diffusive outflux of gas. Here we suggest that the bubbles are stabilized by a continuous influx of gas near the contact line, due to the gas attracti...

We study optimal bank regulation in an economy with aggregate uncertainty. Bank liabilities are used as “money” and hence earn lower returns than equity. In laissez faire equilibrium, banks maximize market value, trading off the funding advantage of debt against the risk of costly default. The capital structure is not socially optimal because external costs of distress are not internalized by t...

1. A dogfish from which all six ampullae have been removed maintains its equilibrium; the righting reactions occur promptly; compensatory movements of the eyes occur in response to rotations in all planes except the horizontal; the compensatory position of the eyes is retained if the animal is held in an abnormal position. Both the static and dynamic functions of equilibrium continue, therefore...