On Generalized Non-holonomic Systems

Generalized non-holonomic mechanical systems are analyzed from a geometric point of view. The existence and uniqueness of solutions, D’Alembert principle, Gauss principle of minimal constraint, the non-holonomic momentum and Gibbs–Appell equations for such systems are studied in an invariant Lagrangian framework.      

Symmetry of Lagrangians of nonholonomic systems

In this Letter, a new symmetry of nonholonomic systems is put forward. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which the symmetry can lead to a conserved quantity is presented. Finally, two examples are shown to illustrate the application of the results.     

Multisymplectic Structures and Discretizations for One-way Wave Equations

Multisymplectic structures for one-way wave equations are presented in this letter. Based on the multisymplectic formulation, we obtain the corresponding multisymplectic discretizations. The structure-preserving property of a finite difference scheme for the first-order one-way wave equation is proved. Implications and applications of this result are explored.      

Is the Hamiltonian geometrical criterion for chaos always reliable?

It is found that the application of a newly developed geometrical criterion, in which negative eigenvalues of the associated matrix determined by the dynamical curvature of a conformal metric for a Hamiltonian system are used to identify the onset of local instability or chaos, is somewhat problematic in some circumstances. In fact, this criterion is neither necessary nor sufficient for the prediction of instability of orbits on a same energy hypersurface because it is not in good agreement with information on unstable or chaotic behavior given by the maximal Lyapunov exponent in general.     

Closed Geodesics and Billiards on Quadrics Related to Elliptic KdV Solutions

We consider algebraic geometrical properties of the integrable billiard on a quadric Q with elastic impacts along another quadric confocal to Q. These properties are in sharp contrast with those of the ellipsoidal Birkhoff billiards in ⁿ . Namely, generic complex invariant manifolds are not Abelian varieties, and the billiard map is no more algebraic. A Poncelet-like theorem for such system is known. We give explicit sufficient conditions both for closed geodesics and periodic billiard orbits on Q and discuss their relation with the elliptic KdV solutions and elliptic Calogero system.     

An invariant formula for a star product with separation of variables

We give an invariant formula for a star product with separation of variables on a pseudo-Kähler manifold.     

Equilibrium theory in 2D Riemann manifold for heterogeneous biomembranes with arbitrary variational modes

Based on the first and second gradient operators and their integral theorems in 2D Riemann manifold, the equilibrium differential equations and geometrically constraint equations for heterogeneous biomembranes with arbitrary variation modes are developed. Through the combination of these equations, the equilibrium theory for heterogeneous biomembranes is established in 2D Riemann manifold. From the equilibrium theory, various interesting information is revealed: Different from homogeneous biomembranes, heterogeneous one posses new equations within the membrane’s tangential planes, i.e. the in-plane equilibrium differential equations, the in-plane boundary conditions and the in-plane geometrically constraint equations. Different from the equilibrium theory in Euclidean space, the one in 2D Riemann manifold displays strict constraints between the physical coefficients and characteristic geometric parameters of biomembranes.     

Difference schrödinger operators with linear and exponential discrete spectra

Using the factorization method, we construct finite-difference Schrödinger operators (Jacobi matrices) whose discrete spectra are composed from independent arithmetic, or geometric series. Such systems originate from the periodic, orq-periodic closure of a chain of corresponding Darboux transformations. The Charlier, Krawtchouk, Meixner orthogonal polynomials, theirq-analogs, and some other classical polynomials appear as the simplest examples forN = 1 andN = 2 (N is the period of closure). A natural generalization involves discrete versions of the Painlevé transcendents.On leave of absence from the Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia.     

A frame bundle generalization of multisymplectic momentum mappings

We construct momentum mappings for covariant Hamiltonian field theories using a generalization of symplectic geometry to the bundle L_VY of vertically adapted linear frames over the bundle of field configurations Y. Field momentum observables are vector-valued momentum mappings generated from automorphisms of Y, using the (n + k)-symplectic geometry of L_VY. These momentum observables on L_VY generalize those in covariant multisymplectic geometry and produce conserved field quantities along flows. Three examples illustrate the utility of these momentum mappings: orthogonal symmetry of a Kaluza-Klein theory generates the conservation of field angular momentum, affine reparametrization symmetry in time-evolution mechanics produces a version of the parallel axis theorem of rotational dynamics, and time reparametrization symmetry in time-evolution mechanics gives us an improvement upon a parallel transport law.     

Integral invariants of the Buttin bracket

We study the densities (most general objects which may be integrated over supersurfaces in superspace), invariant with respect to supercanonical transformations which do not change the Buttin bracket. The only such nontrivial object is, in a definite sense, the odd semidensity explicitly constructed here.     

Goldfish Geodesics and Hamiltonian Reduction of Matrix Dynamics

We describe the Hamiltonian reduction of a time-dependent real-symmetric N×N matrix system to free vector dynamics, and also provide a geodesic interpretation of Ruijsenaars–Schneider systems. The simplest of the latter, the goldfish equation, is found to represent a flat-space geodesic in curvilinear coordinates.      

Effects of Zn substitution on the magnetic and transport properties of La0.6Sr0.4Mn1−yZnyO3−δ (0≤y≤0.3)

Phase-singular solid solutions of La_0.6Sr_0.4Mn_1−yZn_yO_3−δ(0≤y≤0.3) [LSMZO] perovskite of rhombohedral symmetry (space group: ) with y up to 30 at.% could be synthesized notwithstanding the differences in ionic radii of Mn_{V I}³⁺ (i.r.=0.645 Å) and Zn_{V I}²⁺ (i.r.=0.74 Å). The LSMZO≤02 compositions are ferromagnetic metallic (FMM) at room temperature whereas LSMZO-02-08 are ferromagnetic insulators (FMI) and LSMZO>08 are paramagnetic insulators (PMI). Total obliteration of the FM transition is unique to Zn-doping at leading to PMI even at low temperatures, measured up to 8 K (presently). The FM to PM transition (T_c) and the peak (T_p) in resistivity-temperature curves decreases with the Zn-content. The charge-transport in p-type LSMZO is predictable by variable range hopping (VRH), which changes to nearest-neighbor hopping of small polarons (NNHP) at T>T_p. Non-stoichiometry (0.005≤δ≤0.21) evaluated chemically from redox titrations indicated the prevalence of excess oxygen vacancy rather than charge compensatively predictable values which, in turn, indicates the diminishing Mn⁴⁺ content in LSMZO. The ’s act as electron donors in p-LSMZO and this increases the resistivity (ρ_RT) associated with the shift in T_c to low temperatures. Increased ρ_RT on annealing in low is a clear evidence on the role of in LSMZO.     

First-principles study on the effect of the interstitial oxygen ion on the spectral properties of PWO crystal and the origin of the green luminescence band

The electronic structures and absorption spectra of PWO crystals containing interstitial oxygen ions have been calculated using density functional theory code CASTEP with lattice structure optimized. It is shown by calculation that: (1) the interstitial oxygen ion in the perfect PWO crystal doesn’t bring any obvious absorption in the visible region; (2) the green emission of lead tungstate origin is closely related to the interstitial oxygen ion, and probably originates from the center of “ WO₄+O_i”.