随机相位扰动抑制激发介质中漂移的螺旋波

研究了一类二维变量描述的激发系统中漂移螺旋波的抑制问题.通过在整个系统中局部注入带随机相位的电信号，如在系统256×256格点的边界或中心区域中选取4×4或者5×5格点区域施加一个带随机相位的外部激励电信号，在系统内部产生一个持续的靶波信号，实现靶波对螺旋波的动态竞争.数值计算表明：该方法对于Barkley模型中螺旋波有很强的抑制作用，与简单的局部周期信号驱动比较，具有暂态过程比较短的特点，而且对于时空噪声具有一定的抗干扰性.在一定的噪声范围内，即使系统出现不均匀性，也可以观测到靶波，新出现的靶波对螺旋波有抑制作用. 关键词： 螺旋波 靶波 Barkley模型 随机相位     

Ultraweak Continuity of σ-derivations on von Neumann Algebras

Let σ be a surjective ultraweakly continuous ∗-linear mapping and d be a σ-derivation on a von Neumann algebra . We show that there are a surjective ultraweakly continuous ∗-homomorphism and a Σ-derivation such that D is ultraweakly continuous if and only if so is d. We use this fact to show that the σ-derivation d is automatically ultraweakly continuous. We also prove the converse in the sense that if σ is a linear mapping and d is an ultraweakly continuous ∗-σ-derivation on , then there is an ultraweakly continuous linear mapping such that d is a ∗-Σ-derivation.      

Suppression of Spiral Waves and Spatiotemporal Chaos Under Local Self-adaptive Coupling Interactions

In this paper, a close-loop feedback control is imposed locally on the Fitzhugh-Nagumo (FHN) system to suppress the stable spirals and spatiotemporal chaos according to the principle of self-adaptive coupling interaction. The simulation results show that an expanding target wave is stimulated by the spiral waves under dynamic control period when a local area of 5×5 grids is controlled, or the spiral tip is driven to the board of the system. It is also found that the spatiotemporal chaos can be suppressed to get a stable homogeneous state within 50 time units as two local grids are controlled mutually. The mechanism of the scheme is briefly discussed.     

Unbounded derivations commuting with compact group actions

Let be a closed * derivation in aC* algebra which commutes with an ergodic action of a compact group on . Then generates aC* dynamics of . Similar results are obtained for non-ergodic actions on abelianC* algebras and on the algebra of compact operators.Research supported by N.S.F.     

SBV Regularity for Genuinely Nonlinear, Strictly Hyperbolic Systems of Conservation Laws in one Space Dimension

We prove that if t ? u(t) ? BV(\mathbbR){t \mapsto u(t) \in BV(\mathbb{R})} is the entropy solution to a N × N strictly hyperbolic system of conservation laws with genuinely nonlinear characteristic fields     

On the Davey–Stewartson and Ishimori Systems

We study the initial value problem for the two-dimensional nonlinear nonlocal Schrödinger equations i u_t + u = N(v), (t, x, y) R³, u(0, x, y) = u₀(x, y), (x, y) R² (A), where the Laplacian = ² _x + ² _y, the solution u is a complex valued function, the nonlinear term N = N₁ + N₂ consists of the local nonlinear part N₁(v) which is cubic with respect to the vector v=(u,u_x,u_y,\overline{u},\overline{u}_{x},\overline{u}_{y}) in the neighborhood of the origin, and the nonlocal nonlinear part N₂(v) =(v, ^{– 1} _x K_x(v)) + (v, ^{– 1} _y K_y(v)), where (, ) denotes the inner product, and the vectors K_x (C⁴(C⁶; C))⁶ and K_y (C⁴(C⁶; C))⁶ are quadratic with respect to the vector v in the neighborhood of the origin. We assume that the components K⁽²⁾ _x = K⁽⁴⁾ _x 0, K⁽³⁾ _y = K⁽⁶⁾ _y 0. In particular, Equation (A) includes two physical examples appearing in fluid dynamics. The elliptic–hyperbolic Davey–Stewartson system can be reduced to Equation (A) with , and all the rest components of the vectors K_x and K_y are equal to zero. The elliptic–hyperbolic Ishimori system is involved in Equation (A), when , and . Our purpose in this paper is to prove the local existence in time of small solutions to the Cauchy problem (A) in the usual Sobolev space, and the global-in-time existence of small solutions to the Cauchy problem (A) in the weighted Sobolev space under some conditions on the complex conjugate structure of the nonlinear terms, namely if N(eⁱ v) = eⁱ N(v) for all R.     

The CPT Group of the Dirac Field

Using the standard representation of the Dirac equation, we show that, up to signs, there exist only two sets of consistent solutions for the matrices of charge conjugation (C), parity (P), and time reversal (T), which give the transformation of fields , and , where and . These sets are given by , , and , , . Then , and two successive applications of the parity transformation to fermion fields necessarily amount to a 2 rotation. Each of these sets generates a non abelian group of 16 elements, respectively, and , which are non isomorphic subgroups of the Dirac algebra, which, being a Clifford algebra, gives a geometric nature to the generators, in particular to charge conjugation. It turns out that and , where is the dihedral group of eight elements, the group of symmetries of the square, and 16E is a non trivial extension of by , isomorphic to a semidirect product of these groups; S₆ and S₈ are the symmetric groups of six and eight elements. The matrices are also given in the Weyl representation, suitable for taking the massless limit, and in the Majorana representation, describing self-conjugate fields. Instead, the quantum operators C, P and T, acting on the Hilbert space, generate a unique group , which we call the CPT group of the Dirac field. This group, however, is compatible only with the second of the above two matrix solutions, namely with , which is then called the matrix CPT group. It turns out that , where is the dicyclic group of 8 elements and S₁₀ is the symmetric group of 10 elements. Since , the quaternion group, and , the 0-sphere, then .     

Hyperfine structure and isotope shift study in singly ionized lead

Hyperfine structure and isotope shifts in five optical transitions: 424.5 nm ( – ), 537.2 nm ( – ), 554.5 nm ( – ), 560.9 nm ( – ) and 666.0 nm ( – ) of Pb  II have been measured. As a light source the discharge tube was used. The hyperfine structure measurements were performed using metallic isotope ²⁰⁷Pb. For isotope shifts measurements natural lead was used. The high resolution spectral apparatus consisted of a silver coated Fabry-Perot etalon and a grating spectrograph combined with a CCD camera used as a detector. In the analysis of the spectra a computer simulation technique was used. The hyperfine structure observations yielded the splitting constants A for seven levels of Pb II. The isotope shift studies enabled to separate the mass and the field shifts and to determine values of changes of the mean square nuclear charge radii.     

用同步复极化终止心脏中的螺旋波和时空混沌

为了模拟电击除颤导致动作电位持续时间缩短, 在Luo-Rudy相I心脏模型中引入了同步复极化. 研究了同步复极化对螺旋波和时空混沌动力学的影响. 数值结果表明: 在控制周期比较小的情况下, 同步复极化可以有效消除螺旋波和时空混沌, 在有一些控制参数下, 同步复极化只能消除螺旋波, 或者只能消除时空混沌. 当螺旋波不被控制时, 观察到螺旋波转变为长周期和长波长的螺旋波或破碎成时空混沌的现象. 并对控制机制进行了分析. 关键词： 螺旋波 时空混沌 同步复极化 控制     

Accelerated expansion from braneworld models with variable vacuum energy

We study the acceleration of the universe as a consequence of the time evolution of the vacuum energy in cosmological models based in braneworld theories in 5D. A variable vacuum energy may appear if the size of the extra dimension changes during the evolution of the universe. In this scenario the acceleration of the universe is related not only to the variation of the cosmological term, but also to the time evolution of G and, possibly, to the variation of other fundamental constants as well. This is because the expansion rate of the extra dimensionappears in different contexts, notably in expressions concerning the variation of rest mass and electric charge. We concentrate our attention on spatially-flat, homogeneous and isotropic, brane-universes where the matter density decreases as an inverse power of the scale factor, similar (but at different rate) to the power law in FRW-universes of general relativity. We show that these braneworld cosmologies are consistent with the observed accelerating universe and other observational requirements. In particular, G becomes constant and asymptotically in time. Another important feature is that the models contain no adjustable parameters. All the quantities, even the five-dimensional ones, can be evaluated by means of measurements in 4D. We provide precise constrains on the cosmological parameters and demonstrate that the effective equation of state of the universe can, in principle, be determined by measurements of the deceleration parameter alone. We give an explicit expression relating the density parameters , and the deceleration parameter q. These results constitute concrete predictions that may help in observations for an experimental/observational test of the model.     

Destruction of Spiral Wave Using External Electric Field Modulated by Logistic Map

Evolution of spiral wave generated from the excitable media within the Barkley model is investigated. The external gradient electric field modulated by the logistic map is imposed on the media （along x- and y-axis）. Drift and break up of spiral wave are observed when the amplitude of the electric field is modulated by the chaotic signal from the logistic map, and the whole system could become homogeneous finally and the relevant results are compared when the gradient electric field is modulated by the Lorenz or Rossler chaotic signal.     

非连续反馈控制激发介质中的螺旋波

采用非连续反馈方法来控制Fitz-Hugh-Nagumo方程描述的激发介质中的螺旋波. 在控制过程中,对于系统各个格点快变量的幅值进行观测并和设定的阈值进行比较,当采样格点的快变量的值大于这个阈值时,则对系统进行直接小幅度的负反馈. 研究发现：在对系统所有格点快变量幅值观测时选择比较小的阈值则更容易将系统的螺旋波消除掉并使系统达到稳定均匀态. 在比较大的阈值下,系统的螺旋波则变得稀疏,也可以导致螺旋波的破裂. 在任意选择单个格点的快变量观测下,比较小的反馈强度仍然可以消除螺旋波,系统也达到稳定均匀态. 当 关键词： 螺旋波 Fitz-Hugh-Nagumo方程 反馈控制     

二维单原子斐波那契类准晶电子能谱特性研究

利用单电子、紧束缚、最近邻座模型,在重整化群的基础上,用分解-消元法分析了二维单原子斐波那契类准晶FC(n)的电子能谱分裂规律,数值计算了其电子能谱值,发现在一级近似下,该类二维准晶格中全部都只存在n×n,n×(n+1),(n+1)×(n+1)等三种原子簇分子,相应的能谱按Y_m-n-l方式分裂,得出了其电子能谱的能级数目通式,发现描述其能级数目的参量存在所谓的“斐波那契类数集合”,并且确定了该集合的前11个整数的稳定值,找出了有关斐波那契类数集合的经验公式.分析结果与数值计算值相符 关键词： 斐波那契类 准晶 电子能谱 重整化群     

用运动控制器来终止心律失常

采用Luo-Rudy相Ⅰ心脏模型对通过局部电击使细胞复极化来消除心脏中的螺旋波和时空混沌进行数值模拟。提出利用控制器局部电击螺旋波波头周围的心肌细胞来抑制螺旋波的旋转,使螺旋波漂移出边界,进而控制螺旋波和时空混沌。数值模拟表明：适当选择控制的格点数和膜电位控制阈值,螺旋波和时空混沌都可以被抑制。最少的控制格点数为9个,最短的单螺旋波控制时间小于150 ms,最短的时空混沌控制时间小于500 ms。     

Evolution of spiral wave and pattern formation in a vortical polarized electric field

In this paper, the evolution of the pattern transition induced by the vortical electric field （VEF） is investigated. Firstly, a scheme is suggested to generate the VEF by changing the spatial magnetic field. Secondly, the VEF is imposed on the whole medium, and the evolutions of the spiral wave and the spatiotemporal chaos are investigated by using the numerical simulation. The result confirms that the drift and the breakup of the spiral wave and the new net-like pattern are observed when different polarized fields are imposed on the whole medium respectively. Finally, the pattern transition induced by the polarized field is discussed theoretically.     

Three Attractive Osculating Walkers and a Polymer Collapse Transition

Consider n interacting lock-step walkers in one dimension which start at the points {0,2,4,...,2(n?1)} and at each tick of a clock move unit distance to the left or right with the constraint that if two walkers land on the same site their next steps must be in the opposite direction so that crossing is avoided. When two walkers visit and then leave the same site an osculation is said to take place. The space-time paths of these walkers may be taken to represent the configurations of n fully directed polymer chains of length t embedded on a directed square lattice. If a weight λ is associated with each of the i osculations the partition function is $Z_t^{(n)} (\lambda ) = \sum\nolimits_{i = 0}^{\left\lfloor {\tfrac{{(n - 1)t}}{2}} \right\rfloor } {z_{t,i}^{(n)} } \lambda ^i $ where z ⁽ⁿ⁾ _t,i is the number of t-step configurations having i osculations. When λ=0 the partition function is asymptotically equal to the number of vicious walker star configurations for which an explicit formula is known. The asymptotics of such configurations was discussed by Fisher in his Boltzmann medal lecture. Also for n=2 the partition function for arbitrary λ is easily obtained by Fisher's necklace method. For n>2 and λ≠0 the only exact result so far is that of Guttmann and Vöge who obtained the generating function $G^{(n)} (\lambda ,u) \equiv \sum\nolimits_{t = 0}^\infty {Z_t^{(n)} (\lambda )u^t } $ for λ=1 and n=3. The main result of this paper is to extend their result to arbitrary λ. By fitting computer generated data it is conjectured that Z ⁽³⁾ _t (λ) satisfies a third order inhomogeneous difference equation with constant coefficients which is used to obtain $$G^{(n)} (\lambda ,u) = \frac{{(\lambda - 3)(\lambda + 2) - \lambda (12 - 5\lambda + \lambda ^2 )u - 2\lambda ^3 u^2 + 2(\lambda - 4)(\lambda ^2 u^2 - 1){\text{ }}c(2u)}}{{(\lambda - 2 - \lambda ^2 u)(\lambda - 1 - 4\lambda u - 4\lambda ^2 u^2 )}}$$ where $c(u) = \tfrac{{1 - \sqrt {1 - 4u} }}{{2u}}$ , the generating function for Catalan numbers. The nature of the collapse transition which occurs at λ=4 is discussed and extensions to higher values of n are considered. It is argued that the position of the collapse transition is independent of n.     

A Space–Time Integral Estimate For A Large Data Semi-linear Wave Equation on the Schwarzschild Manifold

We consider the wave equation with in . The wave equation on a spherically symmetric manifold with a single closed geodesic surface or on the exterior of the Schwarzschild manifold can be reduced to this form. Using a smoothed Morawetz estimate which does not require a spherical harmonic decomposition, we show that there is decay in for initial data in the energy class, even if the initial data is large. This requires certain conditions on the potentials V, V _L and f. We show that a key condition on the weight in the smoothed Morawetz estimate can be reduced to an ODE condition, which is verified numerically.      

On the existence of asymptotically flat initial data sets for space-times containing manifolds with ends

A 3-manifoldM is said to have ends if the complement of a compact set inM is the finite disjoint union of sets diffeomorphic to the exterior of a sphere in ³. This paper gives a necessary and sufficient condition for when an asymptotically flat initial data set ( ) onM is determined by a set of freely specifiable York data.This research was partially supported by the National Science Foundation grant No. 7901801.     

一类非线性方程的compacton解及其移动compacton解

研究一类非线性方程,即广义Camassa-Holm方程C(n):ut+kux+β1u\{xxt\}+β2u\{n+1\}x+β3uxun\{xx\}+β4uun\{xxx\}=0.通过四种拟设得到丰富的精确解，特别是当k≠0时得到了com pacton解,当k=0时得到了移动compacton解.最后利用线 性化的方法得到了其他形式的广义Camassa-Holm方程的compacton解. 关键词： 广义Camassa-Holm方程 compacton解 移动compacton解     

Bianchi VI cosmological models representing perfect fluid and radiation with electric-type free gravitational fields

A homogeneous Bianchi type VI_h cosmological model filled with perfect fluid, null electromagnetic field and streaming neutrinos is obtained for which the free gravitational field is of the electric type. The barotropic equation of statep = (–1) is imposed in the particular case of Bianchi VI₀ string models. Various physical and kinematical properties of the models are discussed.