First integrals of the axisymmetric shape equation of lipid membranes

The shape equation of lipid membranes is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation(ODE) by Zheng and Liu(Phys. Rev.E 48 2856(1993)). Here we try to further reduce this second-order ODE to a first-order ODE. First, we invert the usual process of variational calculus, that is, we construct a Lagrangian for which the ODE is the corresponding Euler–Lagrange equation. Then, we seek symmetries of this Lagrangian according to the Noether theorem. Under a certain restriction on Lie groups of the shape equation, we find that the first integral only exists when the shape equation is identical to the Willmore equation, in which case the symmetry leading to the first integral is scale invariance. We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor.     

Exploring fundamental laws of classical mechanics via predicting the orbits of planets based on neural networks

Neural networks have provided powerful approaches to solve various scientific problems. Many of them are even difficult for human experts who are good at accessing the physical laws from experimental data. We investigate whether neural networks can assist us in exploring the fundamental laws of classical mechanics from data of planetary motion. Firstly, we predict the orbits of planets in the geocentric system using the gate recurrent unit, one of the common neural networks. We find that the precision of the prediction is obviously improved when the information of the Sun is included in the training set. This result implies that the Sun is particularly important in the geocentric system without any prior knowledge, which inspires us to gain Copernicus' heliocentric theory. Secondly, we turn to the heliocentric system and make successfully mutual predictions between the position and velocity of planets. We hold that the successful prediction is due to the existence of enough conserved quantities (such as conservations of mechanical energy and angular momentum) in the system. Our research provides a new way to explore the existence of conserved quantities in mechanics system based on neural networks.     

Challenges in the theoretical investigations of lipid membrane configurations

We report some key results in the theoretical investigations of configurations of lipid membranes and present several challenges in this field,which involve(i)the exact solutions to the shape equation of lipid vesicles,(ii)the exact solutions to the governing equations of open lipid membranes,(iii)the neck condition of two-phase vesicles in the budding state,(iv) the nonlocal theory of membrane elasticity,and(v)the relationship between the symmetry and the magnitude of the free energy.     

Recent advance on the efficiency at maximum power of heat engines

This review reports several key advances on the theoretical investigations of efficiency at maximum power of heat engines in the past five years. The analytical results of efficiency at maximum power for the Curzon-Ahlborn heat engine, the stochastic heat engine constructed from a Brownian particle, and Feynman's ratchet as a heat engine are presented. It is found that: the efficiency at maximum power exhibits universal behavior at small relative temperature differences; the lower and the upper bounds might exist under quite general conditions; and the problem of efficiency at maximum power comes down to seeking for the minimum irreversible entropy production in each finite-time isothermal process for a given time.     

Bounds of Efficiency at Maximum Power for Normal-, Sub- and Super-Dissipative Carnot-Like Heat Engines

The Carnot-like heat engines are classified into three types (normal-, sub- and, super-dissipative) according to relations between the minimum irreversible entropy production in the "isothermal" processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between η C /2 and η C /(2 η C ), η C /2 and η C , 0 and η C /(2 η C ), respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Lett. 98 (2012) 40001] although the dissipative engines and the irreversible ones are inequivalent to each other.     

小系统的非平衡统计力学与随机热力学

热力学是一个古老的课题,古典热力学以宏观的具有大粒子数的系统为研究对象,自17世纪以来,科学家们构建了热力学的完备公理化体系。将热力学推广至小系统是近三十年来的研究前沿。文章介绍小系统的非平衡统计力学以及小系统的随机热力学。作为研究案例,利用时间依赖的谐振子势场控制单个粒子来构造随机热机的类卡诺循环,并发现该热机最大功率对应的效率等于1-Tc/Th,其中Tc和Th分别对应于低温热库和高温热库的温度。     

彭桓武先生与青年研究生

在考入中国科学院理论物理研究所做研究生之前,我们就从各种渠道得知,彭桓武先生早年是清华大学物理系的“四杰”之一,研究生毕业不久,即远涉重洋赴英国爱丁堡拜师马克斯·玻恩从事固体物理研究,之后受薛定谔之聘两次前往都柏林高等研究院,与海特勒合作从事介子物理研究,还与玻恩合作研究量子场论,取得当时国际知名的研究成果.1947年回国后,转向核物理和核工程,带出一批又红又专的研究生,并带领他们开展我国反应堆和核武器理论设计工作,为我国“两弹一星”研制做出巨大的历史性贡献,是我们心目中功劳大、学问大的大师.彭先生为了祖国的核事…     

Challenges in theoretical investigations of configurations of lipid membranes

We report some key results in the theoretical investigations of configurations of lipid membranes and present several challenges in this field, which involve (i) the exact solutions to the shape equation of lipid vesicles, (ii) the exact solutions to the governing equations of open lipid membranes, (iii) the neck condition of two-phase vesicles in the budding state, (iv) the nonlocal theory of membrane elasticity, and (v) the relationship between the symmetry and the magnitude of the free energy.     

等温捷径的理论和实验

温度是热力学中核心的物理量,也是我们日常生活中最常接触的物理量之一。简单来说,温度是我们对物体冷热程度的度量①。如果我们进一步追溯温度的定义和测量过程,就会接触到另一个我们熟知的重要概念——热平衡。考虑一个如图1(a)所示的带有活塞的气缸,气缸内部封闭一定量的理想气体。我们假设气缸具有导热性,理想气体可以通过气缸与外界环境交换热量。