Turing Patterns in a Reaction-Diffusion System

We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel-Epstein model. Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations.     

Moving Finite Element Simulations for Reaction-Diffusion Systems

This work is concerned with the numerical simulations for two reaction-diffusion systems, i.e., the Brusselator model and the Gray-Scott model. The numerical algorithm is based upon a moving finite element method which helps to resolve large solution gradients. High quality meshes are obtained for both the spot replication and the moving wave along boundaries by using proper monitor functions. Unlike [33], this work finds out the importance of the boundary grid redistribution which is particularly important for a class of problems for the Brusselator model. Several ways for verifying the quality of the numerical solutions are also proposed, which may be of important use for comparisons.     

Spiral and Antispiral Waves in Reaction-Diffusion Systems

Spiral waves are ubiquitous phenomena in nonlinear chemical, physical, and biological systems. But antispiral waves are infrequent to date. The transition between spiral and antispiral waves has been rarely explored. We have analyzed the extended Brusselator model and the extended Oregonator model by linear stability analysis. We have demonstrated that it is possible and plausible to realize the transition between them by control of diffusion coefficient of inactivator from theoretical analysis and numerical simulations.     

Spiral and Antispiral Waves in Reaction-Diffusion Systems

Spiral waves are ubiquitous phenomena in nonlinear chemical, physical, and biological systems. But antispiral waves are infrequent to date. The transition between spiral and antispiral waves has been rarely explored. We have analyzed the extended Brusselator model and the extended Oregonator model by linear stability analysis. We have demonstrated that it is possible and plausible to realize the transition between them by control of diffusion coefficient of inactivator from theoretical analysis and numerical simulations.     

On the Steady State Correlation Functions of Open Interacting Systems

We address the existence of steady state Green-Keldysh correlation functions of interacting fermions in mesoscopic systems for both the partitioning and partition-free scenarios. Under some spectral assumptions on the non-interacting model and for sufficiently small interaction strength, we show that the system evolves to a NESS which does not depend on the profile of the time-dependent coupling strength/bias. For the partitioned setting we also show that the steady state is independent of the initial state of the inner sample. Closed formulae for the NESS two-point correlation functions (Green-Keldysh functions), in the form of a convergent expansion, are derived. In the partitioning approach, we show that the 0^th order term in the interaction strength of the charge current leads to the Landauer-Büttiker formula, while the 1^st order correction contains the mean-field (Hartree–Fock) results.     

Highly Efficient Transfer of Quantum State and Robust Generation of Entanglement State Around Exceptional Lines

Exceptional points (EPs) are non-Hermitian degeneracies or branch points where eigenvalues and their corresponding eigenvectors coalesce. Due to the complex non-trivial topology of Riemann surfaces associated with non-Hermitian Hamiltonians, the dynamical encirclement or proximity of EPs in parameter space has been shown to lead to topological mode conversions and some novel physical phenomena. In fact, degeneracies can also form continuous line geometries, which are called exceptional lines (ELs). The problem is whether the state transfer around the ELs can show different characteristics from the EPs, which is less explored. Here, novel properties of quantum state transfer around the ELs based on a quantum walk platform are explored. It is found that the evolutionary state around the ELs is independent of the initial state and evolution direction, and the transfer of quantum state is more efficient than the case around the EPs. Furthermore, based on such a property, an entangled state generation insensitive to the incident state is realized experimentally. The work opens up a new way for the application of non-Hermitian physics in the field of quantum information.     

Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain Disturbances

In this paper, a robust trajectory tracking control method with state constraints and uncertain disturbances on the ground of adaptive dynamic programming (ADP) is proposed for nonlinear systems. Firstly, the augmented system consists of the tracking error and the reference trajectory, and the tracking control problems with uncertain disturbances is described as the problem of robust control adjustment. In addition, considering the nominal system of the augmented system, the guaranteed cost tracking control problem is transformed into the optimal control problem by using the discount coefficient in the nominal system. A new safe Hamilton–Jacobi–Bellman (HJB) equation is proposed by combining the cost function with the control barrier function (CBF), so that the behavior of violating the safety regulations for the system states will be punished. In order to solve the new safe HJB equation, a critic neural network (NN) is used to approximate the solution of the safe HJB equation. According to the Lyapunov stability theory, in the case of state constraints and uncertain disturbances, the system states and the parameters of the critic neural network are guaranteed to be uniformly ultimately bounded (UUB). At the end of this paper, the feasibility of the proposed method is verified by a simulation example.     

Sign-invariant and Explicit Solutions of Nonlinear Reaction-Diffusion Systems

Using the sign-invariant theory, we study the nonlinear reaction-diffusion systems. We also obtain some new explicit solutions to the nonlinear resulting systems.     

Robust Controller Design for Multi-Input Multi-Output Systems Using Coefficient Diagram Method

The coupling between variables in the multi-input multi-output (MIMO) systems brings difficulties to the design of the controller. Aiming at this problem, this paper combines the particle swarm optimization (PSO) with the coefficient diagram method (CDM) and proposes a robust controller design strategy for the MIMO systems. The decoupling problem is transformed into a compensator parameter optimization problem, and PSO optimizes the compensator parameters to reduce the coupling effect in the MIMO systems. For the MIMO system with measurement noise, the effectiveness of CDM in processing measurement noise is analyzed. This paper gives the control design steps of the MIMO systems. Finally, simulation experiments of four typical MIMO systems demonstrate the effectiveness of the proposed method.     

稳态法导热系数测量的误差分析及改进方案

稳态法测量导热系数实验影响测量结果的因素有很多,总结、分析及恰当处理引起误差的主要因素,对测量原理的完善、新型装置的设计以及测量数据的处理具有重要的指导作用.     

Influence of Coulomb Interactions on Dissipative Structures in Reaction-Diffusion Systems

Reaction-Diffusion-Systems with charged particles are considered. Conditions for the appearance of dissipative structures because of disturbances of an uniform initial stationary state in continuous and simple compartment systems are derived. As an example the appearance of a dissipative structure is demonstrated in a simple capacitor model. Based on this effect nonequilibrium electrical cells could be developed.     

Efficient Computational Schemes of the Conjugate Gradient Method for Solving Linear Systems

The technique of the initial guess calculation for the conjugate gradient method is proposed. Computational schemes of the linear system solution with symmetrical positive definite matrices are constructed on its basis. Their efficient modifications for systems with five-diagonal matrices are proposed. The investigation of the developed methods using the problem of two-dimensional numerical simulation of bipolar transistors has been carried out. Experimental evidence of the proposed method's efficiency has been obtained.     

The Steady State Fluctuation Relation for the Dissipation Function

We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities. The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been considered previously, and show how they are described in the context of this work.     

稳态平板法测导热系数精度的研究

从稳态平板法测导热系数的原理出发,通过对推导过程的近似处理进行有效的修正,得到更为准确的导热系数表达式,并且对数据处理进行了讨论,显示了利用origin软件的数值拟合功能,能够有效的提高散热速率的测量,从而提高了导热系数结果的精度。     

Efficient Scheme for Greenberger-Horne-Zeilinger State and Cluster State with Trapped Ions

We propose a scheme to generate the Greenberger-Horne-Zeilinger （GHZ） states and the cluster states of many trapped ions. In the scheme, the ion is illuminated by a single laser tuned to the first lower vibrational sideband. The scheme only requires resonant interactions. Thus the scheme is very simple and the quantum dynamics operation can be realized at a high speed, which is important in view of decoherence.     

Efficient and Robust Design for Absorbing Boundary Conditions in Atomistic Computations

We propose an efficient and robust way to design absorbing boundary conditions in atomistic computations. An optimal discrete boundary condition is obtained by minimizing a functional of a reflection coefficient integral over a range of wave numbers. The minimization is performed with respect to a set of wave numbers, at which transparent absorption is reached. Compared with the optimization with respect to the boundary condition coefficients suggested by E and Huang [Phys. Rev. Lett. 87 （2001） 133501], we reduce considerably the number of independent variables and the computing cost. We further demonstrate with numerical examples that both the optimization and the wave absorption are more robust in the proposed design.     

一种鲁棒的目标跟踪方法

针对传统特征光流场跟踪方法中由于误差积累和错误匹配而导致的特征点丢失问题,基于一种新的Harris-SIFT特征点表示方法,提出基于预测帧与关键帧的算法框架,实现了光流场运动估计与局部特征识别相结合的目标跟踪方法.预测帧利用塔式分解和递归算法计算特征点的光流场运动矢量,使用运动矢量直方图获取目标的运动矢量,并剔除误匹配点;当特征点数量小于5个时,关键帧使用Harris-SIFT特征点进行局部特征匹配,利用仿射模型对目标精确定位及姿态修正.实验结果表明,本方法对视频序列中的纹理特征目标跟踪的鲁棒性较好,在背景复杂、目标遮挡或暂时丢失情况下,仍可以继续完成目标的可靠跟踪.     

一种鲁棒的目标跟踪方法

针对传统特征光流场跟踪方法中由于误差积累和错误匹配而导致的特征点丢失问题,基于一种新的Harris-SIFT特征点表示方法,提出基于预测帧与关键帧的算法框架,实现了光流场运动估计与局部特征识别相结合的目标跟踪方法.预测帧利用塔式分解和递归算法计算特征点的光流场运动矢量,使用运动矢量直方图获取目标的运动矢量,并剔除误匹配点;当特征点数量小于5个时,关键帧使用Harris-SIFT特征点进行局部特征匹配,利用仿射模型对目标精确定位及姿态修正.实验结果表明,本方法对视频序列中的纹理特征目标跟踪的鲁棒性较好,在背景复杂、目标遮挡或暂时丢失情况下,仍可以继续完成目标的可靠跟踪.     

Fluctuation-Induced First-Order Transition in a Nonequilibrium Steady State

We present the first example of a phase transition in a nonequilibrium steady state that can be argued analytically to be first order. The system of interest is a two-species reaction-diffusion problem whose control parameter is the total density . Mean-field theory predicts a second-order transition between two stationary states at a critical density = _c. We develop a phenomenological picture that instead predicts a first-order transition below the upper critical dimension d _c=4. This picture is confirmed by hysteresis found in numerical simulations, and by the study of a renormalization-group improved equation of state. The latter approach is inspired by the Coleman–Weinberg mechanism in QED.