An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps

The Lyapunov exponent is primarily used to quantify the chaos of a dynamical system. However, it is difficult to compute the Lyapunov exponent of dynamical systems from a time series. The entropic chaos degree is a criterion for quantifying chaos in dynamical systems through information dynamics, which is directly computable for any time series. However, it requires higher values than the Lyapunov exponent for any chaotic map. Therefore, the improved entropic chaos degree for a one-dimensional chaotic map under typical chaotic conditions was introduced to reduce the difference between the Lyapunov exponent and the entropic chaos degree. Moreover, the improved entropic chaos degree was extended for a multidimensional chaotic map. Recently, the author has shown that the extended entropic chaos degree takes the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. However, the author has assumed a value of infinity for some numbers, especially the number of mapping points. Nevertheless, in actual numerical computations, these numbers are treated as finite. This study proposes an improved calculation formula of the extended entropic chaos degree to obtain appropriate numerical computation results for two-dimensional chaotic maps.     

TEM investigation of the formation mechanism of deformation twins in Fe–Mn–Si–Al TWIP steels

The microstructure of a Fe–Mn–Si–Al twinning-induced plasticity (TWIP) steel exhibiting remarkable work hardening rate under uniaxial tensile deformation was investigated using transmission electron microscopy to uncover the mechanism(s) controlling the nucleation and growth of the mechanically induced twins. The results show that the stair-rod cross-slip deviation mechanism is necessary for the formation of the twins, while large extrinsic stacking faults homogenously distributed within the grains could act as preferential sources for the activation of the deviation process. The influence of such features on the thickness and strength of the twins and the resulting mechanical behaviour is discussed and compared to similar works recently performed on Fe–Mn–C TWIP steels.     

G波段500 W带状注扩展互作用速调管设计研究

针对太赫兹频段实现高功率面临物理机制上的难题,设计了一个G波段带状注速调管,展示了基于非相对论带状电子注和扩展互作用技术所能达到的功率水平以及影响性能的物理因素。文中设计基于电压24.5 kV、电流0.6 A,1 mm×0.15 mm的椭圆电子注,以及与之相匹配的互作用系统,即横向过尺寸哑铃型多间隙谐振腔,可以实现高功率和高增益。三维PIC仿真结果显示,在考虑实际腔体损耗的情况下,能够获得超过500 W的功率,电子效率和增益分别达到3.65%和38.2 dB。研究发现,输出功率和效率的提升很大程度上受到多间隙腔模式稳定性以及电路欧姆损耗的制约;输出腔的欧姆损耗对输出功率影响尤为显著,工程设计需要特别考虑。本文的研究为高频段带状注扩展互作用器件的研发打下了良好的基础。     

Soliton molecules and the CRE method in the extended mKdV equation

The soliton molecules of the(1+1)-dimensional extended modified Korteweg–de Vries(mKdV)system are obtained by a new resonance condition, which is called velocity resonance. One soliton molecule and interaction between a soliton molecule and one-soliton are displayed by selecting suitable parameters. The soliton molecules including the bright and bright soliton, the dark and bright soliton, and the dark and dark soliton are exhibited in figures 1–3, respectively.Meanwhile, the nonlocal symmetry of the extended mKdV equation is derived by the truncated Painlevé method. The consistent Riccati expansion(CRE) method is applied to the extended mKdV equation. It demonstrates that the extended mKdV equation is a CRE solvable system. A nonauto-B?cklund theorem and interaction between one-soliton and cnoidal waves are generated by the CRE method.     

Pansystems studies in stability,bifurcation and chaos

This paper divides fixed subsets into three kinds, mainly discusses the existence of II-type fixed subset, connects the investigations infixed subsets with the studies in non-linear problems, such as stability, bifurcation, chaos, etc., and proposes a kind of discrete simulation to Liapunov stability and his second method.     

The attractor—basin portrait of a cellular automaton

Local space-time structures, such as domains and the intervening dislocations, dominate a wide class of cellular automaton (CA) behavior. For such spatially-extended dynamics regular domains, vicinities, and attractors are introduced as organizing principles to identify the discretized analogs of attractors, basins, and separatrices: structures used in classifying dissipative continuous-state dynamical systems. We describe the attractor-basin portrait of nonlinear elementary CA rule 18, whose global dynamics is largely determined by a single regular attracting domain. The latter's basin is analyzed in terms of subbasin and portal structures associated with particle annihilation. The conclusion is that the computational complexity of such CA is more apparent than real. Transducer machines are constructed that automatically identify domain and dislocation structures in space-time, count the number of dislocations in a spatial pattern, and implement an isomorphism between rule 18 and rule 90. We use a transducer to trace dislocation trajectories, and confirm that in rule 18, isolated dislocation trajectories, as well as a dislocation gas, agree extremely well with the classical model of annihilating diffusive particles. The CA efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space-time.     

Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrdinger equation with variable coefficients

In this paper, the extended symmetry transformation of (3+1)-dimensional (3D) generalized nonlinear Schrdinger (NLS) equations with variable coefficients is investigated by using the extended symmetry approach and symbolic computation. Then based on the extended symmetry, some 3D variable coefficient NLS equations are reduced to other variable coefficient NLS equations or the constant coefficient 3D NLS equation. By using these symmetry transformations, abundant exact solutions of some 3D NLS equations with distributed dispersion, nonlinearity, and gain or loss are obtained from the constant coefficient 3D NLS equation.     

Boiti-Leon-Pempinelli系统的新变量分离解及其方形孤子和分形孤子

利用拓展的Riccati方程映射法，得到了(2+1)维Boiti-Leon-Pempinelli系统新的变量分离 解．根据得到的分离变量解，构造出该系统新型的孤子结构——方孤子和分形孤子． 关键词： Boiti-Leon-Pempinelli系统 拓展Riccati映射 方形孤子 分形孤子     

Deformed C λ-Extended Heisenberg Algebra in Noncommutative Phase-Space

We construct a deformed C _λ-extended Heisenberg algebra in two-dimensional space using noncommuting coordinates which close an algebra depends on statistical parameter characterizing exotic particles. The obtained symmetry is nothing but an exotic particles algebra interpolating between bosonic and deformed fermionic algebras. PACS numbers: 03.65.Fd, 02.40.Gh, 05.30.Pr     

推广x重新标度模型的重标度参数经验公式

给出了推广x重新标度模型的重标度参数经验公式,其中建立了重标度参数与原子核的平均结合能之间的联系,由该公式可以得出A≥12的所有核的重标度参数值,利用这些参数值可以计算有关核过程并做出预言.