The directed-polymer?directed-percolation transition
We study the relation between the directed polymer and the directed percolation models, for the case of a disordered energy landscape where the energies are taken from bimodal distribution. We find that at the critical concentration of the directed percolation, the directed polymer undergoes a transition from the directed polymer universality class to the directed percolation universality class. We also find that directed percolation clusters affect the characteristics of the directed polymer below the critical concentration.
Transition for Optimal Paths in Bimodal Directed Polymers
The problem for optimal paths in bimodal directed polymers is studied. It is shown that the distribution of the thermal average position of the endpoints of the optimal paths is discontinuous below the threshold p<pc. The origin is that there is a finite possibility that only one endpoint takes the global minimum energy for p<pc. Our results suggest that the percolation threshold for directed percolation is also the critical point of the transition for the possibility that the optimal paths converge to one endpoint.
Numerical Simulation of Induction Heating Process of Continuous Casting Slab
Compared with traditional blazing furnace, the Continuous Casting-Direct Rolling is an advanced manufacturing steel technology, which can reduce energy waste, decrease pollution and enhance efficiency. The characteristics of steels during induction heating are complex, the change of material properties with temperature makes exact analysis methods very difficult to implement. Therefore, a powerful computer aided numerical tool (i.e., finite difference analysis) is selected to numerically model the induction heating process in this paper. The mathematic model coupling with electromagnetic field and thermal field was established, and it was solved by finite difference method (FDM), thus the slab temperature distribution and its variation with time were obtained, and the characteristics in whole induction heating process were studied. To validate the program feasible, the results were evaluated and compared with experiment results, which showed that the simulation results are reliable and effective. The skin effect in heating process from the two results was studied and demonstrated, the temperature change caused by different parameters such as the induced power intensity and the corner radian were also presented, which indicate that the slab temperature can be heated uniformly through adjusting these parameters, thus the continuous casting slab can meet the rolling requirement.