L. Shapiro has presented and solved a problem of a class of random walks with absorbing points on plane lattice points .[1]He divided the all lattice points on line y=x(x>0) into two classes by modulo 2, and select...L. Shapiro has presented and solved a problem of a class of random walks with absorbing points on plane lattice points .[1]He divided the all lattice points on line y=x(x>0) into two classes by modulo 2, and selected one of the two classes to be the set of absorbing points. In this paper,we generalize the Shapiro problem:divide the all lattice points on line y = x(x>0) into k classes by modulo k,and select one class or more classes of the k classes to be the set of absorbing points. We solve the generalized problem by using the residue method and give an application of it to probability theory.展开更多
This paper introduces two kinds of methods with high accuracy for fi-nite element probability computing method,by which the function value on one or afew nodes can be calculated without forming the total stiffness mat...This paper introduces two kinds of methods with high accuracy for fi-nite element probability computing method,by which the function value on one or afew nodes can be calculated without forming the total stiffness matrix.展开更多
In this article,the random walking method is used to solve the steady linear convection-diffusion equation(CDE)with disc boundary condition.The integral solution corresponding to the random walking method is deduced a...In this article,the random walking method is used to solve the steady linear convection-diffusion equation(CDE)with disc boundary condition.The integral solution corresponding to the random walking method is deduced and the relationship between the diffusion coefficient of CDE and the intensity of the random diffusion motion is obtained.The random number generator for arbitrary axisymmetric disc boundary is deduced through the polynomial fitting and inverse transform sampling method.The proposed method is tested through two numerical cases.The results show that the random walking method can solve the steady linear CDE effectively.The influence of the parameters on the results is also studied.It is found that the error of the solution can be decreased by increasing the particle releasing rate and the total walking time.展开更多
The flow and seawater exchange rates have been predicted using a two-dimensional numerical model and a Lagrangian method for a semi-enclosed shallow bay where reclaiming and dredging works are scheduled. The wind effe...The flow and seawater exchange rates have been predicted using a two-dimensional numerical model and a Lagrangian method for a semi-enclosed shallow bay where reclaiming and dredging works are scheduled. The wind effect on the flow and material transport has been emphasized, and a thirty-year mean value of wind has been considered in the numerical simulation. As a whole, even after the reclaiming and dredging are conducted, the flow pattern looks similar to the original state. However, velocity variations up to 20% to 100% appear in the vicinity of the construction area. In the case of summcr wind forcing, the seawater exchange rate increases from 71.6% to 82.9% after the reclaiming and dredging, as indicated by a particle-tracking method. On the contrary, in the case of winter wind forcing, thc seawater cxchange rate appears to be 97.2% under natural conditions but decrcases slightly to 93.2% aftcr the rcclaiming and dredging. Thus, the wind forcing plays an important role in controlling the seawater exchangc rates. The seawater cxchange rate is further improved by 15% if the dredging is simultaneously carried out with the reclaiming. This suggests that the dredging can be an effective means to mitigate the variation of flow.展开更多
文摘L. Shapiro has presented and solved a problem of a class of random walks with absorbing points on plane lattice points .[1]He divided the all lattice points on line y=x(x>0) into two classes by modulo 2, and selected one of the two classes to be the set of absorbing points. In this paper,we generalize the Shapiro problem:divide the all lattice points on line y = x(x>0) into k classes by modulo k,and select one class or more classes of the k classes to be the set of absorbing points. We solve the generalized problem by using the residue method and give an application of it to probability theory.
基金the National Natural Scinence Foundation of China
文摘This paper introduces two kinds of methods with high accuracy for fi-nite element probability computing method,by which the function value on one or afew nodes can be calculated without forming the total stiffness matrix.
基金supported by the International Scientific and Technological Cooperation Program of China(Grant No.2011DFG13020)the China Postdoctoral Science Foundation(Grant No.2013M530043)the National Hi-Tech Research and Development Program of China("863"Project)(Grant No.2007AA05Z426)
文摘In this article,the random walking method is used to solve the steady linear convection-diffusion equation(CDE)with disc boundary condition.The integral solution corresponding to the random walking method is deduced and the relationship between the diffusion coefficient of CDE and the intensity of the random diffusion motion is obtained.The random number generator for arbitrary axisymmetric disc boundary is deduced through the polynomial fitting and inverse transform sampling method.The proposed method is tested through two numerical cases.The results show that the random walking method can solve the steady linear CDE effectively.The influence of the parameters on the results is also studied.It is found that the error of the solution can be decreased by increasing the particle releasing rate and the total walking time.
文摘The flow and seawater exchange rates have been predicted using a two-dimensional numerical model and a Lagrangian method for a semi-enclosed shallow bay where reclaiming and dredging works are scheduled. The wind effect on the flow and material transport has been emphasized, and a thirty-year mean value of wind has been considered in the numerical simulation. As a whole, even after the reclaiming and dredging are conducted, the flow pattern looks similar to the original state. However, velocity variations up to 20% to 100% appear in the vicinity of the construction area. In the case of summcr wind forcing, the seawater exchange rate increases from 71.6% to 82.9% after the reclaiming and dredging, as indicated by a particle-tracking method. On the contrary, in the case of winter wind forcing, thc seawater cxchange rate appears to be 97.2% under natural conditions but decrcases slightly to 93.2% aftcr the rcclaiming and dredging. Thus, the wind forcing plays an important role in controlling the seawater exchangc rates. The seawater cxchange rate is further improved by 15% if the dredging is simultaneously carried out with the reclaiming. This suggests that the dredging can be an effective means to mitigate the variation of flow.
