Period doubling effects in the oscillations of persistent currents in discretized Aharonov–Bohm rings

One shows that the oscillations with respect to the magnetic flux in the one-dimensional discretized Aharonov–Bohm rings are sensitive with respect to the parity of the number of electrons N_e. Resorting to basic flux intervals of unit length indicates that the period of such oscillations is given by the flux quantum Φ₀=hc/e and by 2Φ₀ if N_e is odd and even, respectively. Accordingly, one deals with a period doubling effect when passing from odd N_e-values to even ones, which may be useful in the design of further nanodevices. Interaction free limits of the Drude weight are also discussed.     

Characteristics of terahertz slow-wave system with two-dimensional photonic band-gap structure

A terahertz slow-wave system model consists of a photonic crystal with two-dimensional band-gap structure and a slow-wave plate as its periodic unit. The electromagnetic field in the slow-wave system has been numerically simulated. The dispersion relation and the coupled impedance of the backward wave mode in the system have been calculated for a variety of geometric settings. The results indicate that this model would be a promising candidate for the slow-wave system with single stable backward wave mode.     

The period function for quadratic integrable systems with cubic orbits

This paper is concerned with the monotonicity of the period function for families of quadratic systems with centers whose orbits lie on cubic planar curves. It is proved that each such system has a period function with at most one critical point.     

On the period function of x″+f(x)x′+g(x)=0

We study the period function T of a center O of the title's equation. A sufficient condition for the monotonicity of T, or for the isochronicity of O, is given. Such a condition is also necessary, when f and g are odd and analytic. In this case a characterization of isochronous centers is given. Some classes of plane systems equivalent to such equation are considered, including some Kukles’ systems.     

代数曲线上的Hadamard定理

本文在紧Riemann曲面上引入了拟距离函数和圆环域的概念,并给出了这种圆环域上的Hadamard定理.     

θ方法解滞时微分方程的动力学性质

本文研究求解滞时微分方程的θ-方法数值解的渐近性和方程真实解的关系。首先，我们把数值方法看成以步长为参数的动力系统，考察非线性滞时微分方程θ-方法的数值稳定性。并且证明了A－稳定的θ-方法是NP－稳定的。其次我们证明了θ-方法没有伪不动点，还研究了伪周期2解的存在性。最后我们给出一个例子说明了滞时微分方程θ-方法产生的伪周期2解是不稳定的。     

具有有界位势的Lagrange系统的周期解

本文考虑Lagrange系统 d/dt ?/?(q,q)-?/?q(q,q)=0 (?)这儿?(q,ξ)=1/2 wum form i,j=1 to n a_(ij)(q)eξξ-V(q),q∈R~n,ξ∈R~n 。假设位势函数V有界,并且lim V(q)/|q|~2 =δ>0,V(q)=V(-q),则系统(?)具有一个以适当大的正数T为周期的非平凡解。     

小当量地下爆炸的质点速度模型

在第四纪砂砾层中进行了系列公斤至百公斤级的地下封闭爆炸,研究了小当量化学爆炸地震波传播规律。在近场,地震波持时很短,水平振幅强于垂向振幅。质点速度随当量呈现指数增加,水平向指数为1.09,垂直向指数为0.77,质点速度随距离呈现指数衰减,水平向和垂直向指数分别为2.07与1.57。Sadauskas模型、显函模型和双极模型都能定量描述小当量地下爆炸地震波质点速度变化,但他们之间的反演精度存在差异,双极模型的残差最小。换言之,采用双极模型反演的数据更接近实际。     

On the Planck scale and properties of matter

Invariant and long-lived physical properties and structures of matter are modeled by intrinsic rotations in three and four degrees of freedom. The rotations are quantized starting from the Planck scale by using a nonlinear 1/r potential and period doubling—a common property of nonlinear dynamical systems. The absolute values given by the scale-independent model fit closely with observations in a wide range of scales. A comparison is made between the values calculated from the model and the properties of the basic elementary particles, particle processes, planetary systems, and other physical phenomena. The model also shows that the perceived forces can be divided into two categories: (1) force is always attractive, like in gravitation and (2) force is attractive or repulsive, like in electrostatics. An erratum to this article can be found at