Symplectic reduction of holonomic open-chain multi-body systems with constant momentum

This paper presents a two-step symplectic geometric approach to the reduction of Hamilton’s equation for open-chain, multi-body systems with multi-degree-of-freedom holonomic joints and constant momentum. First, symplectic reduction theorem is revisited for Hamiltonian systems on cotangent bundles. Then, we recall the notion of displacement subgroups, which is the class of multi-degree-of-freedom joints considered in this paper. We briefly study the kinematics of open-chain multi-body systems consisting of such joints. And, we show that the relative configuration manifold corresponding to the first joint is indeed a symmetry group for an open-chain multi-body system with multi-degree-of-freedom holonomic joints. Subsequently using symplectic reduction theorem at a non-zero momentum, we express Hamilton’s equation of such a system in the symplectic reduced manifold, which is identified by the cotangent bundle of a quotient manifold. The kinetic energy metric of multi-body systems is further studied, and some sufficient conditions are introduced, under which the kinetic energy metric is invariant under the action of a subgroup of the configuration manifold. As a result, the symplectic reduction procedure for open-chain, multi-body systems is extended to a two-step reduction process for the dynamical equations of such systems. Finally, we explicitly derive the reduced dynamical equations in the local coordinates for an example of a six-degree-of-freedom manipulator mounted on a spacecraft, to demonstrate the results of this paper.     

Dynamics of the normal–superconductor phase transition and the puzzle of the Meissner effect

The analysis of Pippard (1950) for the growth of the normal phase into the superconducting phase in the presence of a magnetic field H>H_c$H>H_c$ is applied in reverse to the case H<H_c$H<H_c$ (H_c=$H_c=$ critical magnetic field). We carry out the analysis both for a planar and a cylindrical geometry. As the superconducting phase grows into the normal phase, a supercurrent is generated at the superconductor–normal phase boundary that flows in direction opposite to the Faraday electric field resulting from the moving phase boundary. This supercurrent motion is in direction opposite to what is dictated by the Lorentz force on the current carriers, and in addition requires that mechanical momentum of opposite sign be transferred to the system as a whole to ensure momentum conservation. In the cylindrical geometry case, a macroscopic torque of unknown origin acts on the body as a whole as the magnetic field is expelled. We argue that the conventional BCS-London theory of superconductivity cannot explain these facts, and that as a consequence the Meissner effect remains unexplained within the conventional theory of superconductivity. We propose that the Meissner effect can only be understood by assuming that there is motion of charge in direction perpendicular to the normal–superconductor phase boundary and point out that the unconventional theory of hole superconductivity describes this physics.     

The dynamic properties of the two-level entangled atom in an optical field

The interaction of an optical field and one of the entangled atoms is analyzed in detail in this paper. Furthermore, the dynamic properties of the two-level entangled atom are manifested. The properties of the action are dependent on the initial state of the atom. After detecting the atom out of the field, we can obtain the state of the other atom moving in the field. It is shown that the state of the atom out of the field influences the dynamic properties of the atom in the field.     

Parameters choosing for a time-of-flight momentum mapping system with truncated cone-shaped head

Based on the operating principle, we analyzed the restrictive interrelationship of the key parameters of the COLTRIMS (cold target recoil ion momentum spectroscopy)-type time-of-flight (TOF) momentum mapping system with truncated cone-shaped head. The analysis demonstrated how to appropriately choose and even optimize these parameters, the axial uniform magnetic field B, the relative position of the differential aperture relative to the electrons source sc and the aperture radius rc for the given energy range to be detected. The conclusion also showed that the cone-shaped head can be optimized by making a compromise between the relative position of the differential aperture relative to the electrons source sc and the differential pumping effect according to the actual acceptance angle. The presented example gave a good demonstration for the conclusion.     

从头计算研究超共轭效应对2-氯乙醇电子波函数的影响

运用从头算的B3LYP和MP2方法研究了2-氯乙醇分子五种构象的电子结构．在自然键轨道理论分析的基础上讨论了存在的分子内氢键和超共轭作用对构象稳定性的影响,结果说明后者是构象稳定性的主要因素．结合电子动量谱学研究了这种超共轭作用对最外价壳层轨道(HOMO)的电子波函数的影响,演示了动量空间HOMO波函数的不同．     

Laser assisted bound-free transition of a polaron bound to an impurity center

The scattering of a bound Frohlich large polaron in the presence of a coulomb impurity center as well as a linearly polarized laser field is studied. The differential (DCS) as well as the momentum transfer cross sections (MTCS) and the conductivity depend remarkably on the electron–phonon coupling (_αP${\alpha }_P$) and the strength of the coulomb impurity (β$\beta$). The strongly bound polaron is found to be reluctant to contribute to the conductivity which is justified physically. The curves for MTCS and conductivity verses _αP${\alpha }_P$ and β$\beta$ appear to be complementary, indicating the possibility of controlling the mobility and thereby conductivity by varying one of the parameters. This behavior indicates the possibility of optimizing the composition of optoelectronic materials where laser is the dominant source of excitation.     

Tetraplectic structures, tri-momentum maps, and quaternionic flag manifolds

The purpose of this note is to define tri-momentum maps for certain manifolds with an Sp(1)ⁿ-action. We exhibit many interesting examples of such spaces using quaternions. We show how these maps can be used to reduce such manifolds to ones with fewer symmetries. The images of such maps for quaternionic flag manifolds, which are defined using the Dieudonné determinant, resemble the polytopes from the complex case.     

低温液体流动沸腾数值计算中的动量模拟

采用双流体模型计算了液氮在垂直管内的过冷流动沸腾过程,着重考察了相间动量传输模型对数值预测结果准确性的影响。研究表明,相间非曳力,尤其是壁面润湿力对于数值预测的准确性有着决定性的作用。此外,正确地估计沸腾系统中气泡的平均直径对于两相流传输特性的准确预测也有着十分重要的作用。     

Nonlinear Stability of Riemann Ellipsoids with Symmetric Configurations

Using modern differential geometric methods, we study the relative equilibria for Dirichlet’s model of a self-gravitating fluid mass having at least two equal axes. We show that the only relative equilibria of this type correspond to Riemann ellipsoids for which the angular velocity and vorticity are parallel to the same principal axis of the body configuration. The two solutions found are MacLaurin and transversal spheroids. The singular reduced energy-momentum method developed in Rodríguez-Olmos (Nonlinearity 19(4):853–877, 2006) is applied to study their nonlinear stability and instability. We found that the transversal spheroids are nonlinearly stable for all eccentricities while for the MacLaurin spheroids, we recover the classical results. Comparisons with other existing results and methods in the literature are also made.      

An Analytical Study of Boundary Layer Flows on a Continuous Stretching Surface

In this paper the momentum and heat transfer characteristics for a self-similarity boundary layer on exponentially stretching surface modeled by a system of nonlinear differential equations is studied. The system is solved using the Homotopy Analysis Method (HAM), which yields an analytic solution in the form of a rapidly convergent infinite series with easily computable terms. Homotopy analysis method contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region of solution series. By suitable choice of the auxiliary parameter ℏ, reasonable solutions for large modulus can be obtained.