Numerical Solutions of Stochastic Differential Equations

In this dissertation, we consider the problem of simulation of stochastic differential equations driven by Brownian motions or the general Levy processes. There are two types of convergence for a numerical solution of a stochastic differential equation, the strong convergence and the weak convergence. We first introduce the strong convergence of the tamed Euler-Maruyama scheme under non-globally Lipschitz conditions, which allow the polynomial growth for the drift and diffusion coefficients. Then we prove a new weak convergence theorem given that the drift and diffusion coefficients of the stochastic differential equation are only twice continuously differentiable with bounded derivatives up to order 2 and the test function are third order continuously differentiable with all of its derivatives up to order 3 satisfying a polynomial growth condition. We also introduce the multilevel Monte Carlo method, which is efficient in reducing the total computational complexity of computing the expectation of a functional of the solution of a stochastic differential equation. This method combines the three sides of the simulation of stochastic differential equations: the strong convergence, the weak convergence and the Monte Carlo method. At last, a recent progress of the strong convergence of the numerical solutions of stochastic differential equations driven by Levy processes under non-globally Lipschitz conditions is also presented

The Development and Application of Crop Evaluation System Based on GRA

Ever since it was proposed, grey system theory has attracted the attention of scientific researchers and scholars. And it also has been widely used in many fields and solved a large number of practical problems in production, life, and scientific research. With the development and popularization of computer science and network technology, this traditional mathematical model can be applied more simply and efficiently to solve practical problems. Firstly, this paper, to implement steps of grey relational analysis, has made the exclusive analysis and has made the simple introduction to grey relational analysis characteristics. Then, based on grey relational theory and ASP.NET technology, the crop evaluation system is developed. Lastly, by using Excel and the crop evaluation system, the paper carries out a comprehensive evaluation about eight features of Fuji apple, which is from nine different producing areas, respectively. The experiment results show that the crop evaluation system is effective and could greatly improve the work efficiency of the researcher and expand the application scope

Effect of AFM nanoindentation loading rate on the characterization of mechanical properties of vascular endothelial cell

Vascular endothelial cells form a barrier that blocks the delivery of drugs entering into brain tissue for central nervous system disease treatment. The mechanical responses of vascular endothelial cells play a key role in the progress of drugs passing through the blood–brain barrier. Although nanoindentation experiment by using AFM (Atomic Force Microscopy) has been widely used to investigate the mechanical properties of cells, the particular mechanism that determines the mechanical response of vascular endothelial cells is still poorly understood. In order to overcome this limitation, nanoindentation experiments were performed at different loading rates during the ramp stage to investigate the loading rate effect on the characterization of the mechanical properties of bEnd.3 cells (mouse brain endothelial cell line). Inverse finite element analysis was implemented to determine the mechanical properties of bEnd.3 cells. The loading rate effect appears to be more significant in short-term peak force than that in long-term force. A higher loading rate results in a larger value of elastic modulus of bEnd.3 cells, while some mechanical parameters show ambiguous regulation to the variation of indentation rate. This study provides new insights into the mechanical responses of vascular endothelial cells, which is important for a deeper understanding of the cell mechanobiological mechanism in the blood–brain barrier

Geometric optimization of a hinge-barge wave energy converter

Based on a small prototype of the McCabe wave pump device, this paper studies the optimal size of an interconnected pontoon system, where the power take-off systems attached to each barge are equipped with optimal linear passive dampers. To this end, an optimization procedure is developed, where the objective is to maximize the extracted energy of the device under given sea states. A multi-DOF mathematical model is presented to describe the device motion, and associated hydrodynamic parameters are computed using a boundary element model tool, based on linear potential flow theory. Numerical results, under regular and irregular waves, are presented. Simulation results show that the optimal dimension of the device, under given sea states, can be found using the developed methodology. In addition, it is found that the three-body hinge-barge device tends to perform like a two-body system under optimal control conditions. This indicates that a two-barge control system may be a better design solution in those situations, considering the high cost of power take-off systems

[1,1′-Bis(diphenyl­phosphan­yl)ferrocene-κ2 P,P′]dichloridocadmium(II) dichloro­methane disolvate

In the title complex, [CdFe(C17H14P)2Cl2]·2CH2Cl2, the CdII atom has a distorted tetra­hedral coordination geometry by two chloride anions and two P atoms of 1,1′-bis­(diphenyl­phosphan­yl)ferrocene. In the crystal, complex mol­ecules are linked into a three-dimensional network by C—H⋯Cl hydrogen bonds involving the dichloro­methane solvent mol­ecules