Bistable pulsating fronts for reaction-diffusion equations in a periodic habitat

International audienceThis paper is concerned with the existence and qualitative properties of pulsating fronts for spatially periodic reaction-diffusion equations with bistable nonlinearities. We focus especially on the influence of the spatial period and, under various assumptions on the reaction terms and by using different types of arguments, we show several existence results when the spatial period is small or large. We also establish some properties of the set of periods for which there exist non-stationary fronts. Furthermore, we prove the existence of stationary fronts or non-stationary partial fronts at any period which is on the boundary of this set. Lastly, we characterize the sign of the front speeds and we show the global exponential stability of the non-stationary fronts for various classes of initial conditions

Transition fronts for periodic bistable reaction-diffusion equations

International audienceThis paper is concerned with the existence and qualitative properties of transition fronts for spatially periodic reaction-diffusion equations with bistable nonlinearities. The notion of transition fronts connecting two stable steady states generalizes the standard notion of pulsating fronts. In this paper, we prove that the time-global solutions in the class of transition fronts share some common features. In particular, we establish a uniform estimate for the mean speed of transition fronts, independently of the spatial scale. Under the a priori existence of a pulsating front with nonzero speed or under a more general condition guaranteeing the existence of such a pulsating front, we show that transition fronts are reduced to pulsating fronts, and thus are unique up to shift in time. On the other hand, when the spatial period is large, we also obtain the existence of a new type of transition fronts which are not pulsating fronts. This example, which is the first one in periodic media, shows that even in periodic media, the notion of generalized transition fronts is needed to describe the set of solutions connecting two stable steady states

An Optimization Approach for Pricing of Sherpa Target Redemption Notes

Based on the one-factor CIR interest rate model, the pricing of Sherpa Target Redemption Notes (STARN) with early-excise features is investigated in this paper. Firstly, the characteristics of Sherpa target redemption notes were described and the partial differential equation was proposed. Secondly, both non-arbitrage jump conditions on the coupon date and early-excise policy on the redemption date were provided; furthermore, the boundary conditions of partial differential equations were also discussed. Thirdly, a numerical method for solving the partial differential equation was obtained based on the control volume in the theory of finite volume by making use of the upwind weighting scheme to avoid the numerical oscillation phenomenon. Finally, the sensitivity of the model parameters was analyzed. The results show that the STARN value decreases rapidly with the increase in short-term interest rates, furthermore, when short-term interest rates reached a turning point the rate of decline slowed. As volatility increases, the value of the Notes is increased; increasingly as the proportion redeemed is large, STARN value increases

Contact stiffness of bolted joint with different material combination in machine tools

Bolted joint is a commonly used complex flexible interface in machine tools. The stiffness influential factors-based dynamic model provides a high accuracy modeling method of bolted joints in machine tools. The key of wide application of this method is the database of the stiffness matrices of bolted joints under different conditions. This paper mainly concerns the contact stiffness of bolted joints with different material combination in machine tools and tries to establish the relationship of them. Using the stiffness influential factors-based dynamic modeling method, the contact stiffness of bolted joint is expressed as the stiffness matrix of the connection finite element. After impact modal tests were carried on the specimens, stiffness matrices of bolted joints with different material combinations are identified from the frequency response functions. The ratio of the stiffness matrices validates the effectiveness of the conclusion that the contact stiffness of bolted joints with different material combination is proportional to the corresponding equivalent elastic modulus deduced from Hertz contact theory. The reliable proportional relationship provides a great convenience to the wide application of the stiffness influential factors-based dynamic modeling method of bolted joint