Degrees of Freedom of a Time Series

We give a formal proof that if f is a smooth dynamics on a d-dimensional smooth manifold and is an ergodic and exact dimensional measure with Hausdorff dimension dim >d–1, then the number d of degrees of freedom of the dynamics can be recovered from the observation of an orbit. We implement, with this purpose, an algorithm based on the analysis of the microstructure of . We show how a correct estimation of d permits the computation of the Liapunov spectrum with a high accuracy avoiding the issue of the spurious exponents.     

Dirac粒子的正-反粒子自由度和正-反粒子量子数

对Dirac粒子引进了正 反粒子自由度和相应的内部τ空间的算子,把γ矩阵分解成自旋σ算子和正 反粒子τ算子;Dirac方程的解出现了正 反粒子量子数;正 反粒子变换是Dirac粒子的哈密顿量的反对称变换,Dirac粒子负能态能量的负值来自正 反粒子量子数的负值;γ矩阵这种分解是处理物理相互作用的需要. he particle-antiparticle degrees of freedom and the corresponding intrinsic space are introduced to study the dynamical symmetry of the Dirac particle. As a result, the particle-antiparticle quantum number appears naturally and the Dirac particle has five quantum numbers instead of four. An anti-symmetry of the Dirac Hamiltonian and a dual symmetry of its eigen functions are explored. The operator of the Dirac equation in central potentials is found to be the analog of the helicity operator of ...     

Magnetized Stiff Fluid Cylindrically Symmetric Universe with Two Degrees of Freedom in General Relativity

A magnetized stiff fluid cylindrically symmetric universe with two degrees of freedom for perfect fluid distribution, is investigated. The magnetic field is due to an electric current produced along x-axis. The distribution consists of an electrically neutral perfect fluid with an infinite electrical conductivity. The behaviour of the model in presence and absence of magnetic field is discussed. The other physical aspects of the model related to the observations are also discussed.     

六自由度电磁探测的快速数值算法

提出一种六自由度电磁探测的快速数值算法,对500 mm×500 mm×500 mm范围内的空间磁场进行数值仿真,并与电流环近似算法和严格算法进行比较,归一化计算时间比为10⁶:70:1,结果表明该算法可行可靠.最后讨论怎样有效地克服螺线管线圈的有限长效应引起的偏差,从而进一步提高探测系统的探测精度及稳定性.     

Operat orized Bogoliubov Transformat ion and Seniority Mixing in Collective States of Nuclei

The operatorized Bogoliubov transformation (OBT) to deal with the seniority mixing problem in the cojlective states composed of S and D nucleon pairs is introduced. The spurious components of such states due to seniority mixing are disdussed and evaluated by using OBT.     

Structure of D Pair in Collective States of Nuclei

As a successive work a modified D pair independent of the S pair treated in our previous papers is introduced to avoid the seniority mixing problem. The structure amplitudes of this D pair and S pair are determined simultaneously and self-consistently by iteration.     

Structure of D Pair in Collective States of Nuclei

As a successive work a modified D pair independent of the S pair treated in our previous papers is introduced to avoid the seniority mixing problem. The structure amplitudes of this D pair and S pair are determined simultaneously and self-consistently by iteration,     

Reply to “Comment on ‘Contextuality within quantum mechanics manifested in subensemble mean values’ [Phys. Lett. A 373 (2009) 3430]” [Phys. Lett. A 374 (2010) 1397]

In this reply, we point out that the claim by De Zela (2010) [2] is unjustified because the setup he discusses is not equivalent to the setup analysed in our paper (Pan and Home (2009) [1]). Hence his subsequent argument claiming the reproducibility of our demonstrated quantum effect of path-spin contextuality by the Kochen-Specker realist model is not relevant.     

On a reconsideration of classical nucleation theory

A correct account of the collective motion of a cluster does not require the Lothe-Pound correction; furthermore, this correction is shown to contradict the laws of thermodynamics.     

Relational Evolution of the Degrees of Freedom of Generally Covariant Quantum Theories

We study the classical and quantum dynamics of generally covariant theories with vanishing Hamiltonian and with a finite number of degrees of freedom. In particular, the geometric meaning of the full solution of the relational evolution of the degrees of freedom is displayed, which means the determination of the total number of evolving constants of motion required. Also a method to find evolving constants is proposed. The generalized Heisenberg picture needs M time variables, as opposed to the Heisenberg picture of standard quantum mechanics where one time variable t is enough. As an application, we study the parametrized harmonic oscillator and the SL(2, R) model with one physical degree of freedom that mimics the constraint structure of general relativity where a Schrödinger equation emerges in its quantum dynamics.     

用不确定度评价测量结果中的有效自由度的作用

论述了有效自由度的计算方法及有效自由度量值在分析测量结果中的应用。     

The Effective Degree of Freedom of Low Energy QCD

The adiabatic effective baryon-baryou interactions and dibaryon candidates are studied systematically with three constituent quark models based on different effective degrees of freedom:Glozman-Riska-Brown Goldstone boson exchange model based on constituent quark and Goldstone boson coupling;Fujiwara model based on constituent quark gluon coupling and Nijmegen one-boson exchange;QDCSM based on constituent quark and gluon coupling with quark delocalization and color screening.We find that the three models predicted the similar effective baryon-baryon interactions for roughly two thirds among the 64 states consisted of octet and decuplet baryons.The differences among three models and their separate characteristics are also studied.     

Real space renormalization group theory of the percolation model

A cluster expansion renormalization group method in real space is-developed to determine the critical properties of the percolation model. In contrast to previous renormalization group approaches, this method considers the cluster size distribution (free energy) rather than the site or bond probability distribution (coupling constants) and satisfies the basic renormalization group requirement of free energy conservation. In the construction of the renormalization group transformation, new couplings are generated which alter the topological structure of the clusters and which must be introduced in the original system. Predicted values of the critical exponents appear to converge to presumed exact values as higher orders in the expansion are considered. The method can in principle be extended to different lattice structures, as well as to different dimensions of space.This paper is dedicated to Prof. Philippe Choquard.     

两自由度轨摆实验的理论计算和数值分析

用两个自由度微振动理论,导出了轨摆的运动微分方程和两个固有圆频率,给出了微分方程解的一般形式;并通过计算机画图,讨论了两个自由度均以同一圆频率作简谐振动的特殊情况．     

Elimination of Fast Chaotic Degrees of Freedom: On the Accuracy of the Born Approximation

We apply standard projection operator techniques known from nonequilibrium statistical mechanics to eliminate fast chaotic degrees of freedom in a low-dimensional dynamical system. Through the usual perturbative approach we end up in second order with a stochastic system where the fast chaotic degrees of freedom are modelled by Gaussian white noise. The accuracy of the perturbation expansion is analysed in detail by the discussion of an exactly solvable model.     

双自由度海浪发电实验机

通过对海浪的研究,设计出一种二维的海浪发电装置,并使用经典波浪模型对装置的发电效率进行计算以及探索如何提高发电效率.此装置可用于研究浮子结构对发电效率的影响,并可作为实验教学仪器供学生探索研究,弥补了海浪发电教学环节的空白,对提高教学质量和激发学生创新能力有着重要的意义.     

Second Law of Thermodynamics for Macroscopic Mechanics Coupled to Thermodynamic Degrees of Freedom

Starting from and only using classical Hamiltonian dynamics, we prove the maximum work principle in a system where macroscopic dynamical degrees of freedom are intrinsically coupled to microscopic degrees of freedom. Unlike in many of the standard and recent works on the second law, the macroscopic dynamics is not governed by an external action but undergoes the back reaction of the microscopic degrees of freedom. Our theorems cover such physical situations as impact between macroscopic bodies, thermodynamic machines, and molecular motors. Our work identifies and quantifies the physical limitations on the applicability of the second law for small systems.