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111.
LI De-Sheng LUO Cheng-Xin 《理论物理通讯》2006,46(8)
In this paper, we improve the method for deriving Jacobi elliptic function solutions of nonlinear evolution equations given in Ref. [12] and apply it to the integrable higher-order Broer-Kaup system in (2 1)-dimensional spaces.Some new elliptic function solutions are obtained. 相似文献
112.
Physically unacceptable chaotic numerical solutions of nonlinear circuits and systems are discussed in this paper. First, as an introduction, a simple example of a wrong choice of a numerical solver to deal with a second-order linear ordinary differential equation is presented. Then, the main result follows with the analysis of an ill-designed numerical approach to solve and analyze a particular nonlinear memristive circuit. The obtained trajectory of the numerical solution is unphysical (not acceptable), as it violates the presence of an invariant plane in the continuous systems. Such a poor outcome is then turned around, as we look at the unphysical numerical solution as a source of strong chaotic sequences. The 0–1 test for chaos and bifurcation diagrams are applied to prove that the unacceptable (from the continuous system point of view) numerical solutions are, in fact, useful chaotic sequences with possible applications in cryptography and the secure transmission of data. 相似文献
113.
Jianmei Liu Hong Wang Zhi Ma Qianheng Duan Yangyang Fei Xiangdong Meng 《Entropy (Basel, Switzerland)》2022,24(7)
In this paper, we consider the optimization of the quantum circuit for discrete logarithm of binary elliptic curves under a constrained connectivity, focusing on the resource expenditure and the optimal design for quantum operations such as the addition, binary shift, multiplication, squaring, inversion, and division included in the point addition on binary elliptic curves. Based on the space-efficient quantum Karatsuba multiplication, the number of CNOTs in the circuits of inversion and division has been reduced with the help of the Steiner tree problem reduction. The optimized size of the CNOTs is related to the minimum degree of the connected graph. 相似文献
114.
In this paper, we present a fully Lagrangian method based on the radial basis function (RBF) finite difference (FD) method for solving convection–diffusion partial differential equations (PDEs) on evolving surfaces. Surface differential operators are discretized by the tangent plane approach using Gaussian RBFs augmented with two-dimensional (2D) polynomials. The main advantage of our method is the simplicity of calculating differentiation weights. Additionally, we couple the method with anisotropic RBFs (ARBFs) to obtain more accurate numerical solutions for the anisotropic growth of surfaces. In the ARBF interpolation, the Euclidean distance is replaced with a suitable metric that matches the anisotropic surface geometry. Therefore, it will lead to a good result on the aspects of stability and accuracy of the RBF-FD method for this type of problem. The performance of this method is shown for various convection–diffusion equations on evolving surfaces, which include the anisotropic growth of surfaces and growth coupled with the solutions of PDEs. 相似文献
115.
The Pauli master equation describes the statistical equilibration of a closed quantum system. Simplifying and generalizing an approach developed in two previous papers, we present a derivation of that equation using concepts developed in quantum chaos and random-matrix theory. We assume that the system consists of subsystems with strong internal mixing. We can then model the system as an ensemble of random matrices. Equilibration results from averaging over the ensemble. The direction of the arrow of time is determined by an (ever-so-small) coupling to the outside world. The master equation holds for sufficiently large times if the average level densities in all subsystems are sufficiently smooth. These conditions are quantified in the text, and leading-order correction terms are given. 相似文献
116.
提出了采用高阶常微分方程模型代替传统时序分析中所用的ARMA模型来实现一维时间序列的建模和预报.设计的将遗传程序设计与遗传算法相嵌套的动态演化建模算法,用遗传程序设计优化模型结构,以遗传算法优化模型参数,边收集数据边建模边预报,首次成功地实现了时间序列实时预报的程序自动化.两个时间序列的应用实例表明采用此算法可获得较好的实时预报效果. 相似文献
117.
118.
以基于准位相匹配和频与差频级联二阶非线性[X^(2):X^(2)]基础上的全光开关的理论分析作指导,进行了周期极化铌酸锂晶体(PPLN)和退火质子交换光波导(APE)的实验制备,利用所研制的PPLN-APE器件,以自行研制的工作波长为1.54μm的被动调Q掺钴铝酸镁激光器作为控制光源,以工作波长为1.5μm的连续二极管激光器为信号光源进行了级联二阶非线性全光开关实验。当控制光峰值功率为3kw,信号光功率为1mW时,实现13%的开关效率,分析了进一步提高全光开关性能的途径。 相似文献
119.
Pierre Beaujean Lionel Sanguinet Vincent Rodriguez Frdric Castet Benoît Champagne 《Molecules (Basel, Switzerland)》2022,27(9)
This contribution employs quantum chemistry methods to describe the variations of the second nonlinear optical responses of molecular switches based on benzazolo-oxazolidine (BOX) units, connected by π-linkers, along their successive opening/closing. Under the fully closed forms, all of them display negligible first hyperpolarizability (β) values. When one BOX is opened, which is sketched as C→O, a push–pull π-conjugated segment is formed, having the potential to enhance β and to set the depolarization ratio (DR) to its one-dimensional-like value (DR = 5). This is observed when only one BOX is open, either for the monoBOX species (C→O) or for the diBOX (CC→CO) and triBOX (CCC→CCO) compounds, i.e., when the remaining BOXs stay closed. The next BOX openings have much different effects. For the diBOXs, the second opening (CO→OO) is associated with a decrease of β, and this decrease is tuned by controlling the conformation of the π-linker, i.e., the centrosymmetry of the whole compound because β vanishes in centrosymmetric compounds. For the triBOXs, the second opening gives rise to a Λ-shape compound, with a negligible change of β, but a decrease of the DR whereas, along the third opening, β remains similar and the DR decreases to the typical value of octupolar systems (DR = 1.5). 相似文献
120.