Mesoscopic superconductors in the London limit: equilibrium properties and metastability

We present a study of the behaviour of metastable vortex states in mesoscopic superconductors. Our analysis relies on the London limit within which it is possible to derive closed analytical expressions for the magnetic field and the Gibbs free energy. We consider in particular the situation where the vortices are symmetrically distributed along a closed ring. There, we obtain expressions for the confining Bean-Livingston barrier and for the magnetization which turns out to be paramagnetic away from thermodynamic equilibrium. At low temperature, the barrier is high enough for this regime to be observable. We propose also a local description of both thermodynamic and metastable states based on elementary topological considerations; we find structural phase transitions of vortex patterns between these metastable states and we calculate the corresponding critical fields.Comment: 24 pages, 20 figure

On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games

This paper provides a dual characterization of the limit set of perfect public equilibrium payoffs in stochastic games (in particular, repeated games) as the discount factor tends to one. As a first corollary, the folk theorems of Fudenberg, Levine and Maskin (1994), Kandori and Matsushima (1998) and Hörner, Sugaya, Takahashi and Vieille (2011) obtain. As a second corollary, in the context of repeated games, it follows that this limit set of payoffs is a polytope (a bounded polyhedron) when attention is restricted to equilibria in pure strategies. We provide a two-player game in which this limit set is not a polytope when mixed strategies are considered.Stochastic games, Repeated games, Folk theorem

Sleeper end resistance of ballasted railway tracks

This paper describes model tests used to investigate how ballast shoulder width and height contribute to a railway sleeper’s resistance to lateral movement for a range of shoulder widths and heights. Deflection and resistance were measured and photographs taken during the tests.The photographs were analyzed using a digital image correlation technique to identify the zones of ballast surface disturbance, which demonstrated that a bulbed failure volume was mobilized at the ultimate limit state. An idealized three-dimensional failure mechanism is proposed, and resistances are calculated using the limit equilibrium approach. The calculation provides a reliable estimate of the measured resistance. The work identifies the optimum shoulder width and height. The calculations are extended to demonstrate that when a number of sleepers are moved simultaneously, the sleeper end resistance may be one-third less per sleeper than that indicated in tests on an isolated sleeper. Image analysis and limit equilibrium calculations show that this is caused by overlapping of mobilized failure volumes from adjacent sleepers

One-dimensional Bargaining with Markov Recognition Probabilities

We study a process of bargaining over social outcomes represented by points in theunit interval. The identity of the proposer is determined by a general Markov process and the acceptance of a proposal requires the approval of it by all the players. We show that for every value of the discount factor below one the subgame perfect equilibrium in stationary strategies is essentially unique and equal to what we call the bargaining equilibrium. We provide a general characterization of the bargaining equilibrium. We consider next the asymptotic behavior of the equilibrium proposals when the discount factor approaches one. We give a complete characterization of the limit of the equilibrium proposals. We show that the limit equilibrium proposals of all the players are the same if the proposer selection process satisfies an irreducibility condition, or more generally, has a unique absorbing set. In general, the limit equilibrium proposals depend on the partition of the set of players in absorbing sets and transient states of the proposer selection process. We fully characterize the limit equilibrium proposals as the unique generalized fixed point of a particular function.This function depends in a simple way on the stationary distribution related to the proposer selection process. We compare the proposal selected according to our bargaining model to the one corresponding to the median voter theorem.microeconomics ;

Nash and Limit Equilibria of Games with a Continuum of Players

We show that a strategy is a Nash equilibrium in a game with a continuum of players if and only if there exists a sequence of finite games such that its restriction is an "n-equilibria, with "n converging to zero. In our characterization, the sequence of finite games approaches the continuum game in the sense that the set of players and the distribution of characteristics and actions in the finite games converge to those of the continuum game. These results render approximate equilibria of large finite economies as an alternative way of obtaining strategic insignificance. Also, they suggest defining a refinement of Nash equilibria for games with a continuum of agents as limit points of equilibria of finite games. This allows us to discard those Nash equilibria that are artifacts of the continuum model, making limit equilibrium a natural equilibrium concept for games with a continuum of players.Nash equilibrium, limit equilibrium, noncooperative games, continuum of players

Nash and Limit Equilibria of Games with a Continuum of Players

We show that a strategy is a Nash equilibrium in a game with a continuum of players if and only if there exists a sequence of finite games such that its restriction is an $\varepsilon_n$-equilibria, with $\varepsilon_n$ converging to zero. In our characterization, the sequence of finite games approaches the continuum game in the sense that the set of players and the distribution of characteristics and actions in the finite games converge to those of the continuum game. These results render approximate equilibria of large finite economies as an alternative way of obtaining strategic insignificance. Also, they suggest defining a refinement of Nash equilibria for games with a continuum of agents as limit points of equilibria of finite games. This allows us to discard those Nash equilibria that are artifacts of the continuum model, making limit equilibrium a natural equilibrium concept for games with a continuum of players.Nash equilibrium, limit equilibrium, games with a continuum of players

The Folk theorem and bertrand competition

We examine if the folk theorem of perfect competition holds under Bertrand competition (when firms supply all demand), both when entry is exogenous, as well as when it is free. Inter alia, we also characterize the limit equilibrium sets.Bertrand oligopoly, folk theorem, limit properties, exogenous entry, free entry

The limit equilibrium method of slope stability analysis

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