Xuhao Li

A higher order non-polynomial spline method for fractional sub-diffusion problems

In this paper we shall develop a numerical scheme for a fractional sub-diffusion problem using parametric quintic spline. The solvability, convergence and stability of the scheme will be established and it is shown that the convergence order is higher than some earlier work done. We also present some numerical examples to illustrate the efficiency of the numerical scheme as well as to compare with other methods. A high order numerical scheme for fractional sub-diffusion problems is proposed.The solvability, stability and convergence are established rigorously.Theoretical spatial convergence order is improved.Simulation performance is better than previous methods.

Observer based adaptive control for optical manipulation of cell

In this paper, an observer based adaptive control method is proposed for optical manipulation of cell. The dynamics of the robotic manipulator of the laser source is introduced in the optical tweezers system, so that a closed-loop control method is formulated and solved, and a backstepping approach is used to derive a control input for the manipulator. The interaction between the cell dynamics and the manipulator dynamics leads to a fourth-order overall dynamics, and hence a nonlinear observer is constructed to avoid the use of high-order derivatives of the positions in the control input. Stability of the closed-loop system is analyzed by using Lyapunov-like analysis. Simulation results are presented to illustrate the performance of the proposed control methods.

High order approximation to new generalized Caputo fractional derivatives and its applications

In this paper, we shall develop a generalized L1 − 2 formula for new generalized fractional Caputo derivatives. It is theoretically shown that this new approximation achieves O(τ3−α) (τ is the step size) which improves earlier work done to date. Also, numerical tests and an application are presented to demonstrate the efficiency and accuracy of the proposed method.In this paper, we shall develop a generalized L1 − 2 formula for new generalized fractional Caputo derivatives. It is theoretically shown that this new approximation achieves O(τ3−α) (τ is the step size) which improves earlier work done to date. Also, numerical tests and an application are presented to demonstrate the efficiency and accuracy of the proposed method.

A non-polynomial numerical scheme for fourth-order fractional diffusion-wave model

Abstract In this paper, we tackle the numerical treatment of a fourth-order fractional diffusion-wave problem. By using parametric quintic spline in the spatial dimension and an approximation of Caputo derivatives at half-points, we propose a numerical scheme and rigorously prove its solvability, convergence and stability in maximum norm. It is shown that the theoretical convergence order improves those of earlier work. To confirm, simulation is carried out to demonstrate the numerical efficiency of the proposed scheme as well as the better performance over other methods.

Nonpolynomial numerical scheme for fourth-order fractional sub-diffusion equations

We shall develop a high order numerical scheme for a fourth-order fractional sub-diffusion problem. Theoretical results will be established in maximum norm and it is shown that the convergence order is higher than some earlier work done. Numerical experiments will be carried out to demonstrate the efficiency of the proposed scheme as well as to compare with other methods.

A new implicit numerical scheme for fractional sub-diffusion equation

In this paper we shall develop a numerical scheme for a fractional sub-diffusion problem using parametric quintic spline. The solvability, convergence and stability of the scheme will be established and it is shown that the convergence order is higher than some earlier work done. We also present two numerical examples to illustrate the effectiveness of the numerical scheme.

Multi-cellular aggregation using optical traps

Multi-cellular aggregation is a fundamental phenomenon observed in many biological processes. Investigating cells aggregation helps us to have better understanding of many biological processes. Moreover, it is useful in finding cure for the diseases caused by cells aggregation. In this paper, we present a control methodology to obtain multi-cellular aggregation by using multiple optical trapping. The proposed method is also useful for study of multiple cell fusion which is an important cellular process. Experimental results are presented to show the effectiveness of the proposed method in achieving multi-cellular aggregation.