Propagating speeds of bistable transition fronts in spatially periodic media

This paper is concerned with the propagating speeds of transition fronts in $R^N$ for spatially periodic bistable reaction-diffusion equations. The notion of transition fronts generalizes the standard notions of traveling fronts. Under the a priori assumption that there exist pulsating fronts for every direction $e$ with nonzero speeds, we show some continuity and differentiability properties of the front speeds and profiles with respect to the direction $e$. Finally, we prove that the propagating speed of any transition front is larger than the infimum of speeds of pulsating fronts and less than the supremum of speeds of pulsating fronts.Comment: Some modifications are made. Some notions are cited from arXiv:1302.4817. Some auxiliary lemmas are cited from arXiv:1408.072

postbid market interaction and auction choice

We study the influence of product market competition on the first-price sealed auction and the English ascending auction with independent cost types. Bidders, valuing the license basing on the information released in the first stage license bidding game and the possible game they will play in the product market, care about not only whether they can win and thus how much to bid, but also the information released in the auction when they win. As in the English ascending auction, all bidders are able to constantly adjust their belief about their potential rival’s cost distribution, and the higher the bid goes, the lower the potential rival’s cost, the lower the expected gain from winning a license, thus bidders will keep downgrade the value of license and bid more conservatively and the government will generate lower expected revenue from the English auction than in first-price sealed auction. In particular, if the government uses the English ascending auction while the Bertrand price-cutting game being played in the product market, then all bidders except the two lowest cost type bidder will quit the bidding game sequentially and the expected revenue will be close to zero. Furthermore, as the Bertrand competition is more intensive than the Cournot competition, the government’s expected revenue is lower when the product market game played as a Bertrand gameAuction, Oligopoly

Dynamics of the Thermohaline Circulation under Wind forcing

The ocean thermohaline circulation, also called meridional overturning circulation, is caused by water density contrasts. This circulation has large capacity of carrying heat around the globe and it thus affects the energy budget and further affects the climate. We consider a thermohaline circulation model in the meridional plane under external wind forcing. We show that, when there is no wind forcing, the stream function and the density fluctuation (under appropriate metrics) tend to zero exponentially fast as time goes to infinity. With rapidly oscillating wind forcing, we obtain an averaging principle for the thermohaline circulation model. This averaging principle provides convergence results and comparison estimates between the original thermohaline circulation and the averaged thermohaline circulation, where the wind forcing is replaced by its time average. This establishes the validity for using the averaged thermohaline circulation model for numerical simulations at long time scales

Characterising plastic collapse of pipe bend structures

Two recently proposed design by analysis criteria of plastic collapse based on plastic work concepts, the plastic work (PW) criterion and the plastic work curvature (PWC) criterion, are applied to a strain hardening pipe bend arrangement subject to combined pressure and in-plane moment loading. Calculated plastic pressure-moment interaction surfaces are compared with limit surfaces, large deformation analysis instability surfaces and plastic load surfaces given by the ASME Twice Elastic Slope criterion and the tangent intersection criterion. The results show that both large deformation theory and material strain hardening have a significant effect on the elastic-plastic response and calculated static strength of the component. The PW criterion is relatively simple to apply in practice and gives plastic load values similar to the tangent intersection criterion. The PWC criterion is more subjective to apply in practice but it allows the designer to follow the development of the gross plastic deformation mechanism in more detail. The PWC criterion indicates a more significant strain hardening strength enhancement effect than the other criteria considered, leading to a higher calculated plastic load

A Stochastic Generalized Ginzburg-Landau Equation Driven by Jump Noise

This paper is concerned with the stochastic generalized Ginzburg-Landau equation driven by a multiplicative noise of jump type. By a prior estimate, weak convergence and monotonicity technique, we prove the existence and uniqueness of the solution of an initial-boundary value problem with homogeneous Dirichlet boundary condition. However, for the generalized Ginzburg-Landau equation, such a locally monotonic condition of the nonlinear term can not be satisfied in a straight way. For this, we utilize the characteristic structure of nonlinear term and refined analysis to overcome this gap