A stochastic jump and deterministic dynamics model of impact failure evolution with rate effect

Motivated by the observation of the rate effect on material failure, a model of nonlinear and nonlocal evolution is developed, that includes both stochastic and dynamic effects. In phase space a transitional region prevails, which distinguishes the failure behavior from a globally stable one to that of catastrophic. Several probability functions are found to characterize the distinctive features of evolution due to different degrees of nucleation, growth and coalescence rates. The results may provide a better understanding of material failure.

Effects of stochastic extension in ideal microcrack system

The effects of stochastic extension on the statistical evolution of the ideal microcrack system are discussed. First, a general theoretical formulation and an expression for the transition probability of extension process are presented, then the features of evolution in stochastic model are demonstrated by several numerical results and compared with that in deterministic model.

Evolution and propagation of density waves on galactic disk .2. An approximation of the thin transition layer

In this part of the present work, a simplified model—the thin transition layer theory is proposed. The comparison of this model with the G-L sheet model is made.

Endogenous fisheries management in a stochastic model: Why do fishery agencies use TAC

The aim of this paper is to explain under which circumstances using TACs as instrument to manage a fishery along with fishing periods may be interesting from a regulatory point of view. In order to do this, the deterministic analysis of Homans and Wilen (1997)and Anderson (2000) is extended to a stochastic scenario where the resource cannot be measured accurately. The resulting endogenous stochastic model is numerically solved for finding the optimal control rules in the Iberian sardine stock. Three relevant conclusions can be highligted from simulations. First, the higher the uncertainty about the state of the stock is, the lower the probability of closing the fishery is. Second, the use of TACs as management instrument in fisheries already regulated with fishing periods leads to: i) An increase of the optimal season length and harvests, especially for medium and high number of licences, ii) An improvement of the biological and economic variables when the size of the fleet is large; and iii) Eliminate the extinction risk for the resource. And third, the regulator would rather select the number of licences and do not restrict the season length.