Lie symmetries and conserved quantities of non—holonomic mechanical systems with unilateral Vacco constraints

In this paper,we study the Lie symmetries and the conserved quantities of non-holonomic mechanical systems with unilateral Vacco constraints.we give the conditions and the form of conserved quantities due to the Lie symmetries of the systems,and present the inverse problem of the above proble,i.e.finding the corresponding Lie symmetry transformation according to a given integral of the system.Finally,we give an example to illustrate the application of the results.     

Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems

This paper concentrates on studying the Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems. Based on the infinitesimal transformation, we establish the Lie symmetric determining equations and restrictive equations and give three definitions of Lie symmetries before the structure equations and conserved quantities of the Lie symmetries are obtained. Then we make a study of the inverse problems. Finally, an example is presented for illustrating the results.     

Lie symmetry and Mei continuum conservation law of system＊

Lie symmetry and Mei conservation law of continuum Lagrange system are studied in this paper. The equation of motion of continuum system is established by using variational principle of continuous coordinates. The invariance of the equation of motion under an infinitesimal transformation group is determined to be Lie-symmetric. The condition of obtaining Mei conservation theorem from Lie symmetry is also presented. An example is discussed for applications of the results.     

Form invariance and Lie symmetry of equations of non—holonomic systems

In this paper,we study the relation between the form invariance and Lie symmetry of non-holonomic systems.Firstly,we give the definitions and criteria of the form invariance and Lie symmetry in the systems.Next,their relation is deduced.We show that the structure equation and conserved quantity of the form invariance and Lie symmetry of non-holonomic systems have the same form.Finally,we give an example to illustrate the application of the result.     

Aharonov—Anandan phase gate in sub Hilbert space of a coupling flux qubits system

We study two flux qubits with a parameter coupling scenario. Under the rotating wave approximation, we truncate the 4-dimension Hilbert space of a coupling flux qubits system to a 2-dimension subspace spanned by two dressed states |01> and |10>. In this subspace, we illustrate how to generate an Aharnov--Anandan phase, based on which, we can construct a NOT gate (as effective as a C-NOT gate) in this coupling flux qubits system. Finally, the fidelity of the NOT gate is also calculated in the presence of the simulated classical noise.     

Mei symmetry and Mei conserved quantity of Nielsen equations for a non-holonomic system of Chetaev’s type with variable mass

Mei symmetry and Mei conserved quantity of Nielsenequations for a non-holonomic, non-conservative system of Chetaev'stype with variable mass are studied. The differential equations ofmotion of the Nielsen equation for the system, the definition andcriterion of Mei symmetry, and the condition and the form of Meiconserved quantity deduced directly by Mei symmetry for the systemare obtained. An example is given to illustrate the application ofthe results.     

Influence of composition and direct current on phase formation in solid-liquid alloys of a Bi—Cd system

The article discusses the influence of composition and direct current on the phase state of Bi-Cd alloys in a liquid-solid state. It is shown that solid inclusions are displaced to electrodes by current j = 5 × 10⁵ A/m², depending on the effective charge of these inclusions. Bi is displaced to the positive electrode, while Cd is displaced to the negative electrode.     

“Symmetrical” phase and collective excitations in the proton system of ice

A model of the ice proton system taking into account quantum-mechanical tunneling of protons along hydrogen bonds has been formulated and investigated. When the tunneling amplitude is small the quantum ground state of the proton system is degenerate, like the classical ground state. At higher tunneling amplitudes, however, a transition to a nondegenerate state with a symmetrical distribution of protons on hydrogen bonds (a symmetrical phase of ice) is possible. Collective excitations of protons in the nonsymmetrical phase have been considered, and an equation that determines their spectrum has been derived. Zh. éksp. Teor. Fiz. 115, 2207–2213 (June 1999)     

NMR in Laves phase alloy system GdPt x —analysis of nonstoichiometry in intermetallic compounds

NMR is applied to ferromagnetic Laves phase compounds Gd_1–x A _x Pt₂ (A=Sc, La) and GdPt _x (2x3). The different hyperfine field contributions are analyzed. Neighbour contributions to the Gd hyperfine field and strength of ferromagnetic coupling are compared. It is found that there is a strong predominance of the nearest neighbour contribution (92%) to the Pt hyperfine field. We show that the Pt NMR allows to derive the deviation in occupation number of Gd atoms on Gd sites in nonstoichiometric compounds with about 4% accuracy.Now with Dürrwächter K. G., Pforzheim     

Ab initio study on the ground states,phase stability,and mechanical properties of the Au–Pt system

For the equilibrium immiscible Au–Pt system, ground states are studied based on the results of the cluster expansion method combined with ab initio calculations. The obtained results show that there is no stable phase for the Au–Pt system at 0 K. The further obtained enthalpies of formation for hypothetical crystalline L1₂, D0₁₉, D0₃ structured Au₃Pt and AuPt₃, as well as L1₀ structured AuPt compounds also have positive values. Moreover, elastic constants are predicted from ab initio for the first time for the metastable L1₂ Au₃Pt, AuPt₃ and L1₀ AuPt compound. Finally, there is an imaginary phonon appearing in the obtained phonon spectra, implying an internal instability of the positions of the nuclear coordinates of the L1₂Au₃Pt compound.     

相空间中力学系统的Lie-Mei对称性

研究了相空间中力学系统的一种新对称性——Lie-Mei对称性及其守恒量. 提出这种新对称性的定义, 给出了系统Lie-Mei对称性的判据, 得到了系统Lie-Mei对称性导致的广义Hojman守恒量和Mei守恒量. 举例说明了结果的应用.关键词：相空间力学系统Lie-Mei对称性守恒量     

New Type of Conserved Quantities of Lie Symmetry for Nonholonomic Mechanical Systems in Phase Space

The new types of conserved quantities, which are directly induced by Lie symmetry of nonholonomie mechanical systems in phase space, are studied. Firstly, the criterion of the weak Lie symmetry and the strong Lie symmetry are given. Secondly, the conditions of existence of the new type of conserved quantities induced by the weak Lie symmetry and the strong Lie symmetry directly are obtained, and their form is presented. Finaily, an Appell-Hamel example is discussed to further illustrate the applications of the results.     

A New Type of Conserved Quantity Deduced from Mei Symmetry for Relativistic Mechanical System in Phase Space

In this paper, a new type of conserved quantity indirectly deduced from the Mei symmetry for relativistic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The condition for existence and the form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.     

相空间中离散完整系统的Noether对称性和Mei对称性

研究相空间中离散完整系统的Noether对称性、Mei对称性及其导致的守恒量.利用差分离散变分方法,给出相空间中离散完整系统的差分离散变分原理,建立系统的离散正则方程和能量演化方程;给出系统Noether对称性和Mei对称性的判定条件,得到系统离散形式的Noether守恒量和Mei守恒量及其存在的条件.举例说明结果的应用.关键词：相空间离散完整系统对称性守恒量