耦合双稳映象格子模型的时空混沌控制

变量反馈技术实现了耦合双稳映象格子模型的时空混沌控制.数值实验结果表明,利用不同的反馈技术和不同的反馈强度,可以将双稳映象系统的混沌及耦合双稳映象格子模型的时空混沌控制到不动点或周期轨道.变量反馈控制法除了局域双稳映象系统的定态点外,不需要先获取耦合双稳映象格子时空系统的动力学信息,它对抑制耦合双稳映象系统中的湍流具有一定的指导作用.     

耦合映象格子中时空混沌的控制

采用相同的相空间压缩方法,有效地控制了均匀及非均匀耦合映象格子中的时空混沌.数值模拟结果表明,在一定的相空间压缩参数区域内,控制时空混沌到均匀稳定状态时,控制结果与控制参数之间存在确定的函数关系.利用这个控制方程,选择不同的相空间压缩参数控制耦合映象格子中的时空混沌,获得了各种所需要的稳定斑图 关键词： 时空混沌 耦合映象格子     

单向耦合映象格子的时空混沌同步

以耦合映象格子为对象,研究了时空混沌系统的同步问题. 基于Lyapunov稳定性定理,通过恰当地选择驱动函数,实现了两个单向耦合映象格子的完全同步. 仿真模拟验证了这种同步方法的有效性. 讨论了控制参量对同步速率的影响. 仿真模拟还表明,在存在系统偏差并受到噪声影响的情况下,仍然可以实现两系统的同步,这种同步方法具有一定的抗干扰能力. 关键词： 时空混沌 同步 耦合映象格子     

Controlling Spatiotemporal Chaos in Coupled Map Lattices to Periodic Orbits

Two methods are presented for controlling spatiotemporal chaotic motion in coupled map lattices to a kind of periodic orbit where the dynamical variables of all lattice sites are equal and act periodically as time evolves. Stability analysis of the periodic orbits is presented. We prove that especially the second controlling method can stabilize all the periodic orbits we concern. Basin of attraction and noise problem are discussed.     

Controlling Spatiotemporal Chaos in Coupled Map Lattices to Periodic Orbits

Two methods are presented for controlling spatiotemporal chaotic motion in coupled map lattices to a kind of periodic orbit where the dynamicM variables of all lattice sites are equM and act periodically as time evolves. Stability analysis of the periodic orbits is presented. We prove that especially the second controlling method can stabilize all the periodic orbits we concern. Basin of attraction and noise problem are discussed.     

Improvement of Renormalization Group for Barenblatt Equation

We construct a Hartree-Fock (self-consistent)-like algorithm with renormalization group (RG) approach to calculate the anomalous dimension in a nonlinear diffusion equation. We find that our result improves the original RG work because we include the effect of Heaviside function.     

基于可变参数双向耦合映像系统的时空混沌Hash函数设计

在分析单向与双向耦合映像格子系统的初值与参数敏感性的基础上，提出了一种基于可变参数双向耦合映像系统的时空混沌单向Hash函数构造方案.该方案以耦合映像系统的部分初态作为密钥，在迭代过程中, 通过上一次的迭代值和线性变换后的不同位置的明文消息比特动态确定双向耦合映像系统模型参数，将明文消息多格点并行注入时空混沌轨迹中；取迭代序列中最后一轮迭代结果的适当空间项，线性映射为Hash值要求的128 bit值.由于耦合映像系统的双向扩散机理与混乱作用，迭代过程具有极强的不可逆性及初值与参数敏感性，Hash结果的每位都与明文及密钥有着敏感、复杂的非线性强耦合关系.仿真实验与分析结果表明，该算法达到了Hash函数的各项性能要求，安全性好，执行效率高. 关键词： Hash函数 时空混沌 耦合映像格子     

A Cryptographic Scheme Based on Spatiotemporal Chaos of Coupled Map Lattices

We propose a cryptographic scheme based on spatiotemporal chaos of coupled map lattices (CML) ,which is based on one-time pad. The structure of the cryptosystem determines that the progress in decryption implies the progress in exploring the dynamical behavior of spatiotemporal chaos in CML. A part of the initial condition of CML is used as a secret key, and the recovery of the secret key by exhaustive search is impossible due to the sensitivity to the initial condition in spatiotemporal chaos system. Specially the software implementation of the scheme is easy.     

The Fixed Point of a Generalization of the Renormalization Group Maps for Self-Avoiding Paths on Gaskets

Let W(x,y) = ax ³+ bx ⁴+ f ₅ x ⁵+ f ₆ x ⁶+ (3 ax ²)² y+ g ₅ x ⁵ y + h ₃ x ³ y ² + h ₄ x ⁴ y ² + n ₃ x ³ y ³+a ₂₄ x ² y ⁴+a ₀₅ y ⁵+a ₁₅ xy ⁵+a ₀₆ y ⁶, and X = , , where the coefficients are non-negative constants, with a > 0, such that X ²(x,x ²)−Y(x,x ²) is a polynomial of x with non-negative coefficients. Examples of the 2 dimensional map Φ: (x,y)↦ (X(x,y),Y(x,y)) satisfying the conditions are the renormalization group (RG) maps (modulo change of variables) for the restricted self-avoiding paths on the 3 and 4 dimensional pre-gaskets. We prove that there exists a unique fixed point (x _f ,y _f ) of Φ in the invariant set . 2000 Mathematics Subject Classification Numbers: 82B28; 60G99; 81T17; 82C41.     

Improvement of Renormalization Group for Barenblatt Equation

We construct a Hartree-Fock (seff-consistent)-like algorithm with renormalization group (RG) approach to calculate the anomalous dimension in a nonlinear diffusion equation. We find that our result improves the original RG work because we include the effect of Heaviside function.     

The Renormalization Group Treatment of the Hubbard Model

The article presents the renormalization group treatment to the Hubbard model. To begin with, the bosonization of Hubbard model Hamiltonian is performed. We have obtained the sine-Gordon Hamiltonian. We have further approximated this Hamiltonian by the Hamiltonian of ⁴-theory. Then we utilized Wilson's results of the renormalization group method and obtained the recursion formula for the Hubbard model. Having solved these formulas we have obtained the critical indices for the Hubbard model.     

预测反馈法控制双向闭环时空混沌系统的理论及实验

预测反馈控制方法可以用于控制时空混沌系统,该方法是在耦合映象格子中的每个格点处加入局部预测反馈控制器.本文以双向环形Henon耦合映象格子为例,在理论上给出了将系统控制到不稳定不动点的充分条件,并通过数值计算及电路仿真实验证实该方法的有效性.     

Renormalization Group Study of Ising Transition in Double-Frequency sine-Gordon Model

We utilize the renormalization group (RG) technique to analyze the Ising critical behavior in the doublefrequency sine-Gordon model. The one-loop RG equations obtained show unambiguously that there exist two Isingcritical points besides the trivial Gaussian fixed point. The topology of the RG flows is obtained as well.     

Block Renormalization Group Approach for Correlation Functions of Interacting Fermions

Inspired by a decomposition of the lattice Laplacian operator into massive terms (coming from the use of the block renormalization group transformation for bosonic systems), we establish a telescopic decomposition of the Dirac operator into massive terms, with a property named orthogonality between scales. Making a change of Grassmann variables and writing the initial fields in terms of the eigenfunctions of the operators related to this decomposition, we propose a multiscale structure for the generating function of interacting fermions. Due to the orthogonality property we obtain simple formulas, establishing a trivial link between the correlation functions and the effective potential theories. In particular, for the infrared analysis of some asymptotically free models, the two point correlation function is written as a dominant term (decaying at large distances as the free propagator) plus a correction with faster decay, and the study of both terms is straightforward once the effective potential theory is controlled.     

Renormalization Group Study of Ising Transition in Double－Frequency sine－Gordon Model

We utilize the renormallzation group (RG) technique to analyze the Ising critical behavior in the double frequency Sine-Gordon model. The one-loop RG equations obtained show unambiguously that there exist two Ising critical points besides the trivial Gaussian fixed point. The topology of the RG flows is obtained as well.     

The Renormalization Group and Optimization of Entropy

We illustrate the possible connection that exists between the extremal properties of entropy expressions and the renormalization group (RG) approach when applied to systems with scaling symmetry. We consider three examples: (1) Gaussian fixed-point criticality in a fluid or in the capillary-wave model of an interface; (2) Lévy-like random walks with self-similar cluster formation; and (3) long-ranged bond percolation. In all cases we find a decreasing entropy function that becomes minimum under an appropriate constraint at the fixed point. We use an equivalence between random-walk distributions and order-parameter pair correlations in a simple fluid or magnet to study how the dimensional anomaly at criticality relates to walks with long-tailed distributions.     

Renormalization Group Approach to Multiscale Modelling in Materials Science

Dendritic growth, and the formation of material microstructure in general, necessarily involves a wide range of length scales from the atomic up to sample dimensions. The phase field approach of Langer, enhanced by optimal asymptotic methods and adaptive mesh refinement, copes with this range of scales, and provides an effective way to move phase boundaries. However, it fails to preserve memory of the underlying crystallographic anisotropy, and thus is ill-suited for problems involving defects or elasticity. The phase field crystal (PFC) equation—a conserving analogue of the Swift-Hohenberg equation—is a phase field equation with periodic solutions that represent the atomic density. It can natively model elasticity, the formation of solid phases, and accurately reproduces the nonequilibrium dynamics of phase transitions in real materials. However, the PFC models matter at the atomic scale, rendering it unsuitable for coping with the range of length scales in problems of serious interest. Here, we show that a computationally-efficient multiscale approach to the PFC can be developed systematically by using the renormalization group or equivalent techniques to derive appropriate coarse-grained coupled phase and amplitude equations, which are suitable for solution by adaptive mesh refinement algorithms. PACS numbers: 81.16.Rf, 05.10.Cc, 61.72.Cc, 81.15.Aa     

Exact Renormalization Group for the Brazovskii Model of Striped Patterns

We consider the coarse graining of the generalized Brazovskii free energy functional for striped patterns. The technique developed by Shankar for the Fermi liquids is combined with the irreducible version of the exact renormalization group to calculate the recursion relations for interaction vertices. We perform the one-loop calculations from this method taking the eight-point vertex into account.     

Synchronization of Spatiotemporal Chaos in Coupled Complex Ginzburg-Landau Oscillators

Synchronization of spatiotemporal distributed system is investigated by considering the model of 1D dif-fusively coupled complex Ginzburg-Landau oscillators. An itinerant approach is suggested to randomly move turbulentsignal injections in the space of spatiotemporal chaos. Our numerical simulations show that perfect turbulence synchro-nization can be achieved with properly selected itinerant time and coupling intensity.