一个强、弱耗散功能可分隔系统中的特征激变

报道一个由保守映象和耗散映象不连续、不可逆地分段描述的系统，以及在其中发生的一例特征激变.激变的独特之处在于逃逸孔洞.由映象的不连续、不可逆性而导致相平面中出现一个胖分形迭代禁区网，它使得一个混沌吸引子突然失稳而发生激变后出现的两个周期吸引子的吸引域边界成为点滴状.仅仅在每个周期点邻近存在这样的一个作为逃逸孔洞的、受到强耗散性支配和禁区边界限制的规则边界吸引域. 关键词： 激变 保守映象 耗散映象 逃逸孔洞     

两参量平面上双重激变尖点研究

应用广义胞映射图论(GCMD)方法,研究两参量正弦强迫振子的双重激变现象,确定了两参量平面上的双重激变尖点,在这个尖点上两条边界激变曲线和两条内部激变曲线相汇交,四种不同的激变重合.物理上,在这样一个尖点附近的参量扰动(噪声)导致动力学行为戏剧性变化. 关键词： 全局分析 广义胞映射 双重激变尖点 混沌鞍     

一类新的边界激变现象:混沌的边界激变

混沌吸引子的激变是一类普遍现象.借助于广义胞映射图论(generalized cell mapping digraph)方法发现了嵌入在分形吸引域边界内的混沌鞍,这个混沌鞍由于碰撞混沌吸引子导致混沌吸引子完全突然消失,是一类新的边界激变现象,称为混沌的边界激变.可以证明混沌的边界激变是由于混沌吸引子与分形吸引域边界上的混沌鞍相碰撞产生的,在这种情况下,当系统参数通过激变临界值时,混沌吸引子连同它的吸引域突然消失,同时这个混沌鞍也突然增大 关键词： 广义胞映射 有向图 激变 混沌鞍     

常微分方程系统中内部激变现象的研究

应用广义胞映射图论方法研究常微分方程系统的激变.揭示了边界激变是由于混沌吸引子与 在其吸引域边界上的周期鞍碰撞产生的,在这种情况下,当系统参数通过激变临界值时,混 沌吸引子连同它的吸引域突然消失,在相空间原混沌吸引子的位置上留下了一个混沌鞍.研 究混沌吸引子大小(尺寸和形状)的突然变化,即内部激变.发现这种混沌吸引子大小的突然 变化是由于混沌吸引子与在其吸引域内部的混沌鞍碰撞产生的,这个混沌鞍是相空间非吸引 的不变集,代表内部激变后混沌吸引子新增的一部分.同时研究了这个混沌鞍的形成与演化. 给出了对永久自循环胞集和瞬态自循环胞集进行局部细化的方法. 关键词： 广义胞映射 有向图 激变 混沌鞍     

两个周期激励下Duffing-van der Pol系统的混沌瞬态和广义激变

运用广义胞映射图方法研究两个周期激励作用下Duffing-van der Pol系统的全局特性.发现了系统的混沌瞬态以及两种不同形式的瞬态边界激变, 揭示了吸引域和边界不连续变化的原因. 瞬态边界激变是由吸引域内部或边界上的混沌鞍和分形边界上周期鞍的稳定流形碰撞产生.第一种瞬态边界激变导致吸引域突然变小, 吸引域边界突然变大; 第二种瞬态边界激变使两个不同的吸引域边界合并成一体.此外, 在瞬态合并激变中两个混沌鞍发生合并, 最后系统的混沌瞬态在内部激变中消失. 这些广义激变现象对混沌瞬态的研究具有重要意义. 关键词： 广义胞映射图方法 Duffing-van der Pol 混沌瞬态 广义激变     

一类含非黏滞阻尼的Duffing单边碰撞系统的激变研究

以一类含非黏滞阻尼的Duffing单边碰撞系统为研究对象, 运用复合胞坐标系方法, 分析了该系统的全局分岔特性. 对于非黏滞阻尼模型而言, 它与物体运动速度的时间历程相关, 能更真实地反映出结构材料的能量耗散现象. 研究发现, 随着阻尼系数、松弛参数及恢复系数的变化, 系统发生两类激变现象: 一种是混沌吸引子与其吸引域内的混沌鞍发生碰撞而产生的内部激变, 另一种是混沌吸引子与吸引域边界上的周期鞍(混沌鞍)发生碰撞而产生的常规边界激变(混沌边界激变), 这两类激变都使得混沌吸引子的形状发生突然改变. 关键词： 非黏滞阻尼 Duffing碰撞振动系统 激变 复合胞坐标系方法     

Duffing单边碰撞系统的混沌鞍合并激变

以典型的Duffing单边碰撞系统为研究对象,对系统中的混沌鞍进行了细致的分析.研究表明,系统的混沌鞍同样存在合并激变,合并激变是由连接两个混沌鞍的周期鞍的稳定流形与不稳定流形相切所诱发,相切使得边界上的混沌鞍与内部的混沌鞍发生碰撞而突然合并为一个较大的边界混沌鞍.混沌鞍的合并激变行为最终会诱导混沌吸引子的合并激变发生. 关键词： Duffing碰撞系统 混沌鞍 周期鞍 稳定与不稳定流形     

一类分段光滑映象中有新特征的激变

讨论了描述一类电子张弛振子的分段光滑映象中的两种不连续性导致激变的特性.一种激变发生的机理是一个混沌吸引子吸引域内的不稳定周期轨道与映象的不连续区碰撞;而另一种激变的机理是一个混沌吸引子与两个映象的不连续区构成的“映孔”碰撞.发现第一种激变的平均层流相长度的标度律为〈τ〉∝^-1.8,层流相长度分布的标度律为P(τ)=1〈τ〉·exp-τ〈τ〉,而第二种激变的标度律分别为〈τ〉∝exp(k^-1/2)和P(τ)=1〈τ〉exp-τ〈τ〉. 关键词：     

动力学不连续性所导致的奇异排斥子

借助一类具有“映孔”的分段线性一维映象，阐明“映孔导致激发”是“不连续性导致奇异排斥子”出现的结果．此奇异排斥子使得叠代轨道经过映孔逃出原混沌吸引子，从而造成混沌吸引子的突然扩张．证明了叠代轨道在原吸引子中的寿命反比于逃逸速率，并解析地得到了平均寿命随控制参量的变化关系     

耦合不连续系统同步转换过程中的多吸引子共存

本文研究了耦合不连续系统的同步转换过程中的动力学行为, 发现由混沌非同步到混沌同步的转换过程中特殊的多吸引子共存现象. 通过计算耦合不连续系统的同步序参量和最大李雅普诺夫指数随耦合强度的变化, 发现了较复杂的同步转换过程: 临界耦合强度之后出现周期非同步态(周期性窗口); 分析了系统周期态的迭代轨道,发现其具有两类不同的迭代轨道: 对称周期轨道和非对称周期轨道, 这两类周期吸引子和同步吸引子同时存在, 系统表现出对初值敏感的多吸引子共存现象. 分析表明, 耦合不连续系统中的周期轨道是由于局部动力学的不连续特性和耦合动力学相互作用的结果. 最后, 对耦合不连续系统的同步转换过程进行了详细的分析, 结果表明其同步呈现出较复杂的转换过程.     

Dynamics of a Peierls system in a light field

Equations describing the temporal dynamics of the order parameter ξ(t) of a metal-semiconductor phase transition and the density n(t) of electron-hole pairs in a Peierls system in a light field are obtained on the basis of the Lagrange equation for the phonon mode and the Liouville equation for the density matrix of the electronic subsystem. The equations obtained are analyzed for a stationary state (with adiabatically slow variation of the light intensity I) and for a transient process near the initial and final states of dynamic equilibrium (with the light field switched on abruptly). It is shown that for adiabatically slow growth of the intensity I up to a certain critical value I _c the band gap of the electronic spectrum decreases but the semiconductor phase of the Peierls system remains stable. For I>I _c the stationary semiconductor state (ξ≠0) becomes unstable. When the light is switched on abruptly, the deviation of the system parameters from the initial values is described by an exponential law with a characteristic reciprocal of the rise time of the process linearly dependent on the irradiation intensity I. As a new position of equilibrium is approached, three qualitatively different regimes of behavior of the order parameter ξ and density n are possible. For low intensities I(I< I ₁) a purely relaxational aperiodic process occurs. For intermediate intensities I(I ₁<I<I _c) damped oscillations of ξ and n are observed near a new stationary semiconductor state with a smaller band gap. For I>I _c the stationary semiconductor state with ξ≠0 is absent. The experimental data on the irradiation of a vanadium dioxide film with a powerful laser pulse is interpreted on the basis of the theory developed. Zh. éksp. Teor. Fiz. 116, 2154–2175 (December 1999)     

Giant thermodynamical optical effect near ferroelastic phase transition point in Cs3Bi2I9 layered crystal

For the first time we have found a new giant thermodynamical optical effect near the ferroelastic phase transition point in Cs₃Bi₂I₉ layered crystal. The effect is appeared as periodical oscillations in time of the reflection coefficient. This phenomenon is caused by the small temperature deviations in thermodynamical system the appearance of which in the reflection spectra is strongly amplified in the ferroelastic phase transition point. The optical oscillations are explained on the base of a model that takes into account the temperature dependence of the refractive index through the order parameter (spontaneous strain) of the crystal.     

Beam wander of J 0- and I 0-Bessel Gaussian beams propagating in turbulent atmosphere

Root mean square (rms) beam wander of J ₀-Bessel Gaussian and I ₀-Bessel Gaussian beams, normalized by the rms beam wander of the fundamental Gaussian beam, is evaluated in atmospheric turbulence. Our formulation is based on the first and the second statistical moments obtained from the Rytov series. It is found that after propagating in atmospheric turbulence, the collimated J ₀-Bessel Gaussian and the I ₀-Bessel Gaussian beams have smaller rms beam wander than that of the Gaussian beam, regardless of the choice of Bessel width parameter. However, the extent of such an advantage depends on the chosen width parameter, Gaussian source size, propagation distance and the wavelength. Focusing at finite distances of the considered beams causes the rms beam wander to decrease sharply at the propagation distances equal to the focusing parameter.     

Development of the Meissner state instability in an ordered 3D Josephson medium

A new approach based on analysis of continuous configurational modification in the direction of a decrease in the Gibbs potential is proposed for computing the penetration of an external magnetic field in an ordered 3D Josephson medium. The configuration to which the Meissner state passes when the external field slightly exceeds the Meissner stability threshold is determined. This configuration contains a periodic sequence of linear vortices with centers lying in an alternating cell, parallel to the boundary, and located at a certain distance from it. A further increase in the field reveals that the 3D medium behaves like a long periodically modulated Josephson junction. However, the critical value I _C of the pinning parameter for a 3D medium, which lies in the interval 0.7–0.8, is lower than the analogous value I _C = 0.9716 for a long junction. The values of H _max for I < I _C , as well as the steepness of the decrease in the magnetic field at the boundary for I > I _C , are higher in the 3D medium than in a long junction. For very large values of I, the field penetrates the boundary region not as a 2D lattice of linear vortices, but as a 1D lattice of plane vortices, which are mathematically equivalent to the vortices in a long junction.     

Symmetry dependence of rms Charge Radii

The nucleon number dependence of rms charge radii is often approximated by some simple formula containing the mass number only, R(A)=r(A)A^1/3, where r(A) is a slowly varying function of A. However, for nuclei off the stability line, the mass number A=N + Z is not enough to characterise the dependence of the R(Z, N) radius surface on the nucleon numbers Z and N. In the present work, an additional term has been included, depending on the symmetry parameter I=(N ? Z)/A. Several parametrisations were tried, using weighted least-squares procedures for the fit to a present-day data base. The best fit (with χ²/ń=17) was found for R(A, I)=r(A)A^1/3 + b_I/(I ? I_stab), where I_stab=(N_stab ? Z_stab)/A is the value of the symmetry parameter of the stable isobar with mass number A, and b_I=?0.83 fm. The formula R(A, I)=[r(A) + a_I(I ? I_stab)]A^1/3 is only slightly inferior to the previous one, moreover, it is supported by simple model calculations; here a_I=?0.20 fm (χ²/ń=20). The difficulty in determining the right parametrisation is caused by the fact that the surface R_exp(A, I) is not smooth: there are strong shell and deformation effects. To avoid the distorting effect of these deviations on the parameter values, more than half of the original data had to be omitted.     

Pinning of pancake vortices in a three-dimensional Josephson medium and structure of the vortex lattice in the “critical” state

A system of pancake vortices formed near the boundary of a sample in a monotonically increasing external magnetic field is calculated with allowance for pinning due to the cellular structure of the medium for various values of the pinning parameter I, which is proportional to the critical current of the junction and the cell diameter. The shortest distance from the outermost vortex to the nearest neighbor is proportional to I ⁻¹¹. It is shown that the pinning parameter has a critical value I _c separating two regimes with different types of critical states. For I<I _c the external magnetic field has a threshold value H _t(I), above which the field immediately penetrates the interior of the junction to an infinite distance. For I>I _c the magnetic field decays linearly from the boundary into the interior of the junction. The value obtained in the study, I _c=3.369, differs from the value of 0.9716 postulated by other authors. The dependence of the slope of the magnetic field profile near the boundary on I is determined. It is shown that the slope is independent of I in intervals 2πk<I<2πk+π. Fiz. Tverd. Tela (St. Petersburg) 39, 1958–1963 (November 1997)     

Penetration of magnetic field into a long periodically modulated Josephson contact

A new approach to magnetic field profiling inside a Josephson contact is suggested. Its essence consists in analyzing continuous variation of a current configuration leading to a decrease in the Gibbs potential. With this approach, one can find a configuration into which the Meissner state turns when an external field slightly exceeds the upper boundary of the Meissner regime and trace the evolution of this configuration with increasing field. Calculations show that there exists critical value I _c of the pinning parameter in the range 0.95–1.00. This critical value separates two possible conditions of magnetic field penetration into the contact. At I > I _c, a near-boundary current configuration completely compensating for the external field inside the contact arises irrespective of the external field strength. At I < I _c, such a situation is observed only until the external field strength exceeds certain value H _max. Higher fields penetrate into the contact indefinitely deep. In nearboundary configurations, the magnetic field drops with increasing depth almost linearly. Its slope k has rational values, which remain constant within finite intervals of I. As I goes beyond a given interval, k rises stepwise and takes on another rational value. When an external magnetic field is switched on adiabatically, configurations with a maximal growth rate of the magnetic field are observed.     

Temperature dependence of the intensity of phonon-free luminescence lines of Rb3UO2F5 crystals in the 4.2–40 K range

We have investigated the behavior of the intensity of phonon-free lines appearing in the luminescence spectra of Rb₃UO₂F₅ crystals in the 4.2–40 K range due to a pure electron transition and its vibrational recurrences with the frequency of fully symmetrical stretching vibrations of the uranyl ion. It is shown that the temperature dependence of the total integrated intensity of these phonon-free lines, I_Σ, can be described using a model of configuration coordinates of an impurity center with one local vibration. An empirical expression has been obtained for the dependence I_Σ = I_Σ(T) in the form of the product I_Σ(T) = I₀(T)S_Σ(T), where the first factor describes the temperature dependence of the integrated intensity of the pure electron transition line and the second can be approximated by an exponential function of the Stokes parameter. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 1, pp. 129–131, January–February, 2000.     

Anomalous dependence of the critical current of 45° grain boundaries in YBa2Cu3O7−x on an applied magnetic field

Grain boundaries grown by the biepitaxial technique do not show Fraunhofer-type critical current I _c vs. magnetic field H _a dependences, which are a hallmark of standard Josephson junctions. To clarify the reason for this unusual behavior, we have fabricated asymmetric 45° grain boundaries using the bicrystal technique and analyzed their I _c (H _a) characteristics. These characteristics crisply show a number of remarkable features, which suggest that due to the particular orientation of these junctions, their I _c (H _a) dependence is intrinsically non-Fraunhofer. Conventional models, relying on standard tunneling and a superconducting order parameter with s-wave symmetry, do not account for the I _c (H _a) characteristics observed.     

An efficient model for laser surface hardening of hypo-eutectoid steels

This paper presents a model able to predict the austenization of hypo-eutectoid steels during very fast heat cycle such as laser hardening. Laser surface hardening is a process highly suitable for hypo-eutectoid carbon steels with carbon content below 0.6% or for low alloy steels where the critical cooling rate is reached by means of the thermal inertia of the bulk. As proposed by many authors, the severe heat cycle occurring in laser hardening leads to the pearlite to austenite microstructures transformation happening to a temperature much higher than the eutectoid temperature A_c1 and, afterwards, all the austenite predicted during the heating phase become martensite during quenching. Anyway, all these models usually generate a predicted hardness profile into the material depth with an on-off behavior or very complicated and time consumed software simulators. In this paper, a new austenization model for fast heating processes based on the austenite transformation time parameter I_p→a is proposed. By means of the I_p→a parameter it is possible to predict the typical hardness transition from the treated surface to the base material. At the same time, this new austenization model also reduces the calculation time. I_p→a was determined by experimental tests and it was postulated to be constant for low-medium carbon steels. Several experimental examples are proposed to validate the assumptions and to show the accuracy of the model.