Global well-posedness and scattering for a nonlinear Klein–Gordon system in low dimensions

This article investigates the global well-posedness and the scattering for a nonlinear Klein–Gordon system in spatial dimensions 1 and 2. We establish a Morawetz estimate for this system which is similar to the Morawetz estimate established by Nakanishi [K. Nakanishi, Energy scattering for nonlinear Klein–Gordon and Schrödinger equations in spatial dimensions 1 and 2, J. Funct. Anal. 169(1), pp. 201–225], combining this Morawetz estimate with the induction on energy argument developed by Bourgain [J. Bourgain, Global well-posedness of defocusing 3D critical NLS in the radial case, J. Am. Math. Soc. 12 (1999), pp. 145–171], the bound of a certain space-time norm and scattering result are obtained.     

自成像局域空心光束产生的新方法及粒子俘获

本文提出了产生自成像局域空心光束(self-imaged bottle beams)的一种光学元件------液体轴棱锥.从衍射理论结合几何光学对经过轴棱锥后的光场进行了分析, 得出注入液体折射率小于轴棱锥材料折射率时可产生自成像局域空心光束.并通过软件MathCAD模拟, 得到一个完整周期光束的变换过程和局域空心光束的演变过程.研究发现液体轴棱锥产生的自成像局域 空心光束具有周期及相干长度可调的特点.分析了如何利用自成像局域空心光束对粒子进行俘获, 讨论了用自成像局域空心光束进行多层面粒子俘获的优势.     

圆顶轴棱锥产生多个局域空心光束

首次提出圆顶轴棱锥这一新型光学元件.由衍射理论分析了平面波通过圆顶轴棱锥后的光场强度分布,用软件对光强分布进行仿真.结果表明,平行光通过圆顶轴棱锥后可以形成多个局域空心光束(bottle beam),由于球面波能量在焦点附近高度集中,所得的bottle beam在焦点附近强度极大.通过仿真对比得知用圆顶轴棱锥产生的bottlebeam的暗域周围光强远大于用两束Bessel光束干涉所得,大幅度提高了bottle beam囚禁粒子的效率.通过比较这两种方法产生的bottle beam对粒子囚禁的散射力,证实了圆顶轴棱锥产生bottle beam在粒子囚禁方面更具优势.     

Electrophoresis of Bottle‐Brush Polyelectrolytes in an Attractive Nanochannel

A molecular dynamics study of the electrophoresis of bottle‐brush polyelectrolytes (BPEs) through nanochannels is reported. The BPE molecules consist of a neutral backbone with charged side chains. For strong attractive interactions between the BPE and the wall, the BPE is being trapped on the channel surface. A stretching–shrinking migration of the BPE in a channel of radius 6σ is observed at relatively strong electric fields. The stretching–shrinking transition is periodic for intermediate electric fields but not for stronger electric fields. The BPE also shows a transverse migration toward the wall at weak electric fields, while toward the center with further enhancing the electric field. For a channel with larger radius 12σ, the BPE does not migrate in the stretching–shrinking manner.

     

Remarks on gravitational interaction in Kaluza–Klein models

In these remarks, we clarify the problematic aspects of gravitational interaction in a weak-field limit of Kaluza–Klein models. We explain why some models meet the classical gravitational tests, while others do not. We show that variation of the total volume of the internal spaces generates the fifth force. This is the main reason of the problem. It happens for all considered models (linear with respect to the scalar curvature and nonlinear f(R)$f(R)$, with toroidal and spherical compactifications). We explicitly single out the contribution of the fifth force to nonrelativistic gravitational potentials. In the case of models with toroidal compactification, we demonstrate how tension (with and without effects of nonlinearity) of the gravitating source can fix the total volume of the internal space, resulting in the vanishing fifth force and consequently in agreement with the observations. It takes place for latent solitons, black strings and black branes. We also demonstrate a particular example where non-vanishing variations of the internal space volume do not contradict the gravitational experiments. In the case of spherical compactification, the fifth force is replaced by the Yukawa interaction for models with the stabilized internal space. For large Yukawa masses, the effect of this interaction is negligibly small, and considered models satisfy the gravitational tests at the same level of accuracy as general relativity.     

Applications of the first integral method to nonlinear evolution equations

<正>In this paper,we establish travelling wave solutions for some nonlinear evolution equations.The first integral method is used to construct the travelling wave solutions of the modified Benjamin-Bona-Mahony and the coupled Klein-Gordon equations.The obtained results include periodic and solitary wave solutions.The first integral method presents a wider applicability to handling nonlinear wave equations.     

Generalized Klein–Gordon field equations with octonion space-time (OST) algebra

The concept of space-time representation is redefined using the octonion space-time (OST) algebra. In this study, describing the properties of octonions and their possible connection with Euclidean space-times, the internal and external space-time events are represented within the OST algebra. Keeping in mind the octonionic dual-Euclidean space-times, we express the homogeneous field equations which leads to the symmetrical nature of internal and external space-times. We derive the generalized Proca–Maxwell equations for massive-dyons in the case of the OST algebra. Accordingly, we have obtained a new set of octonionic Klein–Gordon potential (KGP) and Klein–Gordon field (KGF) equations for massive dyons from the generalized Proca–Maxwell equations. This formalism demonstrates that the octonionic KGP and KGF equations can be expressed in a single equation and it is equivalent to energy-momentum relation for dyons. As such, we have made an attempt to write the conservation of Noetherian current from the octonionic Klein–Gordon equations.     

Conformational Aspects and Intramolecular Phase Separation of Alternating Copolymacromonomers: A Computer Simulation Study

Summary: Using the bond fluctuation model (BFM), simulations have been performed on molecular bottle brushes with two chemically different types of side chains. In the first part of this work, rigidity of the backbone is imposed. The influence of solvent quality and side chain length on the intramolecular phase separation of side chain material, leading to Janus cylinders, has been investigated and compared to theoretical predictions. In the second part of this work, the restriction of rigidity for the backbone is relaxed. In a poor solvent, the side chain material collapses into a globular state. Several globules containing each one type of side chain material are connected together by backbone material. When imposing different solvent conditions for both types of side chains, a bending of the backbone is found as predicted by theory and observed in very recent experiments.

Comparison between typical snapshots in θ solvent. The side chain length is 25 beads. Dark and light coloured side chains repel each other.