Explicit exact periodic wave solutions and their limit forms for a long waves-short waves model

A long waves-short waves model is studied by using the approach of dynamical systems. The sufficient conditions to guarantee the existence of solitary wave, kink and anti-kink waves, and periodic wave in different regions of the parametric space are given. All possible explicit exact parametric representations of above traveling waves are presented. When the energy of Hamiltonian system corresponding to this model varies, we also show the convergence of the periodic wave solutions, such as the periodic wave solutions converge to the solitary wave solutions, kink and anti-kink wave solutions, and periodic wave solutions, respectively.     

稳态力输出的实验与理论研究(英文)

对低频共振情况下激光引擎的基本特性与其理论预测值做了比较,并研究了实现这些技术的重要步骤,认为基于不同学科与工业组织之间的合作,不久的将来会实现利用累计势能来驱动微型汽车。     

Lie Symmetrical Hojman Conserved Quantity of Relativistic Mechanical System

In this paper, we study the Lie symmetrical Hojman conserved quantity of a relativistic mechanical system under general infinitesimal transformations of groups in which the time parameter is variable. The determining equation of Lie symmetry of the system is established. The theorem of the Lie symmetrical Hojman conserved quantity of the system is presented. The above results are generalization to Hojman's conclusions, in which the time parameter is not variable and the system is non-relativistic. An example is given to illustrate the application of the results in the last.     

de Sitter空间S1m+1中具有平行Blaschke张量的正则类空超曲面

本文引入两个以de Sitter空间为模型的非齐性坐标来覆盖共形空间Q₁^m+1.利用球面S^m+1中超曲面的Möbius几何的方法,本文研究了Q₁^m+1中正则类空超曲面的共形几何.作为其结果,本文对所有具有平行Blaschke张量的正则类空超曲面进行了完全分类.     

The Willmore functional and the containment problem in R4

Let ∑ be a convex hypersurface in the Euclidean space R4 with mean curvature H. We obtain a geometric lower bound for the Willmore functional f∑ H2dσ. This bound is an invariant involving the area of ∑, the volume and Minkowski quermassintegrals of the convex body that ∑bounds. We also obtain a sufficient condition for a convex body to contain another in the Euclidean space R4.     

洛仑兹破缺标量场的霍金隧穿辐射

把洛仑兹破缺的标量场方程推广到弯曲时空中,并通过Aether-like项对标量场方程进行修正,该项所产生的效应也会影响到黑洞时空视界附近处的物理效应.接着,进一步在半经典近似下得到了修正的Hamilton-Jacobi方程,然后用这一修正的Hamilton-Jacobi方程研究了史瓦西黑洞的隧穿辐射特征,并讨论了洛仑兹破缺对黑洞霍金辐射和黑洞熵的影响.结果表明,u~α=δ_t~αu~t,δ_r~αu~r形式的Aether-like项的效应可能使黑洞温度增加,而黑洞熵降低.该工作可以帮助我们更深刻地理解弯曲时空中的洛仑兹破缺效应的物理性质.     

Interaction of Love waves with coupled cavity modes in a 2D holey phononic crystal

The interaction of Love waves with square array of pillars deposited on a cavity defined in a 2D holey phononic crystal is numerically investigated using Finite Element Method. First, the existence of SH surface modes is demonstrated separately for phononic crystals that consist of square arrayed holes, or rectangular arrayed Ni pillars, respectively in, or on, a SiO₂ film deposited on a ST-cut quartz substrate. The coupling between SH modes and torsional mode in pillars induces a transmission dip that occurs at a frequency located in the range of the band-gap of the holey phononic crystal. Second, a cavity is constructed by removing lines of holes in the holey phononic crystal and results in a transmission peak that matches the dip. The optimal geometrical parameters enable us to create a coupling of the cavity mode and the localized pillar mode by introducing lines of pillars into the cavity, which significantly improved the efficiency of the cavity without increasing the crystal size. The obtained results will pave the way to implement advanced designs of high-performance electroacoustic sensors based on coupling modes in phononic crystals.     

Optical emission behaviors of C,Al, Ti,Fe, Cu,Mo, Ag,Ta, and W wire explosions in gaseous media

Electrical explosion of wires (EEW) is a promising method for nanopowders preparation and insensitive explosives ignition. Plasma radiation plays a key role in the ignition process while little attention has been paid on this phenomenon before. This letter introduces optical emission behaviors of electrical explosions for nine materials in air, Helium, and Argon with the SWE-2 platform. Experimental results indicated that the light intensity for non-refractory metals decayed rapidly after the discharge ended. In contrast, for refractory metals, the emission continued to increase and lasted for a long period after the discharge ceased. As for spectra, the emission consisted of line and continuous spectra. With the atomic number increased, the density of lines grew rapidly, leading to a “continuous” appearance.     

Phenomenological model of chain-branching premixed flames

In this work, we introduce a global kinetic model that includes fuel, oxygen, products and two radical species involved in the reversible chain-branching, chain-propagation and chain-termination reactions. The model naturally extends the Zeldovich–Liñán and Zeldovich–Barenblatt–Dold models and can be used to describe both premixed and diffusion flames. Here it is applied to the problem of the deflagration wave propagation in the hydrocarbon fuel/air mixture with arbitrary equivalence ratio under the simplifying thermal-diffusive approximation. The conservation equations are solved numerically in order to obtain the velocity and structure of the combustion wave. It is demonstrated that the peak values of the adiabatic flame temperature and deflagration velocity are shifted towards the rich mixture composition if the reverse reactions of product decomposition are taken into account. The dependence of the flame speed and temperature on parameters of the system is analysed. The prospects of further investigation are discussed.     

Fifth-Order Alice-Bob Systems and Their Abundant Periodic and Solitary Wave Solutions*

The study on the nonlocal systems is one of the hot topics in nonlinear science. In this paper, the well-known fifth-order integrable systems including the Sawada-Kotera (SK) equation, the Kaup-Kupershmidt (KK) equation and the fifth-order Koterweg-de Vrise (FOKdV) equation are extended to a generalized two-place nonlocal form, the generalised fifth-order Alice-Bob system. The Lax integrability of two sets of Alice-Bob systems for all the SK, KK and FOKdV type systems are explicitly given via matrix Lax pairs. The $\hat{P}\hat{T}$ symmetry breaking and symmetry invariant periodic and solitary waves for one set of nonlocal SK, KK and FOKdV system are investigated via a special travelling wave solution ansatz.