Symmetry groups of mathematical physics

Recent work on Lie’s method of extended groups to obtain symmetry groups and invariants of differential equations of mathematical physics is surveyed. As an essentially new contribution one-parameter Lie groups admitted by three-dimensional harmonic oscillator, three-dimensional wave equation, Klein-Gordon equation, two-component Weyl’s equation for neutrino and four-component Dirac equation for Fermions are obtained.     

Nodal sets in mathematical physics

We describe the main lines of mathematical research dealing with nodal sets of eigenfunctions since the days of Chladni. We present the material in a form hopefully suited to a nonspecialized but mathematically educated audience.     

Old mathematical errors in statistical physics

In this paper, we discuss the following questions of quantum statistics: (1) the absence of Bose condensate in ideal Bose gas in the two-dimensional and one-dimensional case; (2) the concentration of the Bose condensate in an ideal Bose gas at the lowest level of the spectrum of the Schrödinger operator. In classical statistics, we discuss the discrepancy between the notion of Boltzman-Maxwell ideal gas with the notion of saturated vapor. The appearance of clusters requires the complete revision of the Clayperon equation as an equation depending on the number of degrees of freedom. For the new ideal gas and the ideal virtual liquid, we describe the phase transition of the first kind by specifying the concept of negative pressure for ideal virtual liquids.     

数学物理方法教学内容改革的探索

在比较数学物理方法课程不同内容体系的基础上．探索了一种适合于应用物理专业的新内容体系,经过教学实践的试点,取得了预期的效果．     

未确知数学方法处理物理实验数据

介绍未确知数学方法，并用未确知数学方法分析处理物理实验数据，与传统的数据处理方法比较，未确知数学方法不必对数据作任何假设，因此更合理，也更符合实际。     

数学物理方程中的通解问题

通过例证说明,通解法对于偏微分方程而言,其适用范围要比通常认为的大.并表明,只要适当变通,行波法就可用于有界情况.     

相干彩虹的形成机制

用一束白光激光聚焦照射液体(水、丙酮、无水乙醇、汽水等)或固体(冰、有色玻璃、塑料、彩色蜡等),出现了多级的彩色干涉环,即相干彩虹.高强度白光局部地加热了液体(固体),改变了它的密度(以及折射性质),从而导致光程差的出现,不同波长的光都发生干渉,形成了彩色的干涉环.有色玻璃在反射模式下也出现了相干彩虹,此时的干涉完全来自于玻璃表面轮廓的变化,并且无参数拟合的结果定量地符合观测到的干涉图案.     

Soliton-type solutions for two models in mathematical physics

In this paper, the generalised Klein-Gordon and Kadomtsov–Petviashvili Benjamin–Bona–Mahony equations with power law nonlinearity are investigated. Our study is based on reducing the form of both equations to a first-order ordinary differential equation having the travelling wave solutions. Subsequently, soliton-type solutions such as compacton and solitary pattern solutions are obtained analytically. Additionally, the peaked soliton has been derived where it exists under a specific restrictions. In addition to the soliton solutions, the mathematical method which is exploited in this work also creates a few amount of travelling wave solutions.     

“图解”数学物理方法的教学实践

《数学物理方法》虽然是数学课,但是它是介绍在物理中应用的数学.物理课程多媒体教学的经验启发我们,合理地选择《数学物理方法》课程中有物理背景的内容,恰当地使用可视化以展现数学公式的物理图像,就能提高教学效果,对一些随时间演变的方程,还可以用动画来表现.我们用两种方法实现可视化,一是用解析解作图,另一个是通过数值求解方程,再将数值计算结果作图.本文介绍我们在《数学物理方法》课开展可视化教学的实践.     

"图解"数学物理方法的教学实践

《数学物理方法》虽然是数学课，但是它是介绍在物理中应用的数学．物理课程多媒体教学的经验启发我们，合理地选择《数学物理方法》课程中有物理背景的内容，恰当地使用可视化以展现数学公式的物理图像，就能提高教学效果，对一些随时间演变的方程，还可以用动画来表现．我们用两种方法实现可视化，一是用解析解作图，另一个是通过数值求解方程，再将数值计算结果作图．本文介绍我们在《数学物理方法》课开展可视化教学的实践．     

应用未确知数学理论评价物理实验室的优劣

应用未确知数学的理论与方法,给出了一种较科学的物理实验室评价方法,该方法能够全面、客观和准确地反映被评实验室的优劣,可广泛用于各类评价工作.     

关于数学物理方法课程的若干问答(续2)

26如果偏微分方程具有一定的对称性(不变性),它的解是否一定具有同样的对称性(不变性)?不一定!例如,二维拉普拉斯方程具有平移不变性、反射不变性以及旋转不变性,但是它的解x或y就不具有这些不变性.同样,x2-y2也是二维拉普拉斯方程的解,但是它也不具有平移不变性和旋转     

On a new mathematical framework for fundamental theoretical physics

It is shown by means of general principles and specific examples that, contrary to a long-standing misconception, the modern mathematical physics of compressible fluid dynamics provides a generally consistent and efficient language for describing many seemingly fundamental physical phenomena. It is shown to be appropriate for describing electric and gravitational force fields, the quantized structure of charged elementary particles, the speed of light propagation, relativistic phenomena, the inertia of matter, the expansion of the universe, and the physical nature of time. New avenues and opportunities for fundamental theoretical research are thereby illuminated.     

Zero-degree focusing of channeled ions and crystal rainbows

We analyze here theoretically the connection between the effect of zero-degree focusing of channeled ions and the crystal rainbow effect. The calculations were performed for Ne¹⁰⁺ ions and a 〈100〉 Si thin crystal. The ion energy was 60 MeV and the crystal thickness was varied between 630 and 750 atomic layers. These conditions correspond to the neighborhood of the first maximum of the zero-degree yield of the channeled ions. The obtained results show that the effect of zero-degree focusing is influenced strongly by the crystal rainbow effect.