Effect of channel connection on flow and salinity distribution of Danshuei River estuary

Numerical models are often used to evaluate the potential impact of human alteration of natural water bodies and to help the design the alternation to mitigate its impacts. A vertical (laterally integrated) two-dimensional hydrodynamic model was expanded to include the capability of simulating river loops as well as tributaries. The model was performed and applied to the Danshuei River estuarine system in northern Taiwan which consists of three major tributaries: the Tahan Stream, Hsintien Stream, Keelung River, and one river loop under the Chung-Hsin Bridge. The expanded model was reverified with observational field data of 2000. The verified model was then used to hindcast the river hydrodynamic conditions with a loop connection between the Danshuei River and Keelung River, which existed prior to 1965. It was found that the configuration of river loop connection has significant impacts on the residual transport along the connecting channel and the salinities in the connected river branches. The results show that the model may provide an ideal tool for management decision.     

Special polynomials in free framed Lie algebra

A framed Lie algebra is an algebra with two operations which is a Lie algebra with respect to one of these operations. A basic example is a Lie algebra of vector fields on a manifold with connection where the covariant derivative serves as an additional operation. In a free framed Lie algebra, we distinguish a set of special polynomials that geometrically correspond to invariantly defined tensors. A necessary condition of being special is derived, and we presume that this condition is also sufficient. Translated from Algebra i Logika, Vol. 47, No. 5, pp. 571–583, September–October, 2008.     

Schur-Weyl duality and the heat kernel measure on the unitary group

We investigate a relation between the Brownian motion on the unitary group and the most natural random walk on the symmetric group, based on Schur-Weyl duality. We use this relation to establish a convergent power series expansion for the expectation of a product of traces of powers of a random unitary matrix under the heat kernel measure. This expectation turns out to be the generating series of certain paths in the Cayley graph of the symmetric group. Using our expansion, we recover asymptotic results of Xu, Biane and Voiculescu. We give an interpretation of our main expansion in terms of random ramified coverings of a disk.     

Synchronization of N different coupled chaotic systems with ring and chain connections

Synchronization of N different coupled chaotic systems with ring and chain Lorenz system, and the R(o)ssler system are used as examples in verifying effectiveness of the method. Based on the Lyapunov stability theory, the form of the controller is designed and the area of the coupling coefficients is determined. Simulations indicate that global synchronization of the N different chaotic systems can be realized by choosing appropriate coupling coefficients by using the controller.     

An Explicit Formula for a Strong Connection

An explicit formula for a strong connection form in a principal extension by a coseparable coalgebra is given.      

Vrănceanu connections and foliations with bundle-like metrics

We show that the Vrănceanu connection which was initially introduced on non-holonomic manifolds can be used to study the geometry of foliated manifolds. We prove that a foliation is totally geodesic with bundle-like metric if and only if this connection is a metric one. We introduce the notion of a foliated Riemannian manifold of constant transversal Vrănceanu curvature and the notion of a transversal Einstein foliated Riemannian manifold. The geometry of these two classes of manifolds is studied and the relationship between them is determined.     

Some geometric properties of quantum phases and calculation of phase formulas

An introduction to several geometrical ideas which are of use to quantum mechanics is presented. The Aharonov‐Anandan phase is introduced and without reference to any dynamical equation, this phase is formulated by defining an appropriate connection on a specific fiber bundle. The holonomy element gives the phase. By introducing another connection, the Pancharatnam phase formula is derived following a different procedure. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACETIME (Ⅰ)

By the theory of Modern Geometry, the mechanical principle and advanced calculus, the dynamics in Newtonian-Galilean spacetime is generalized to Newtonian-Riemannian Spacetime, and the dynamics in N-R spacetime is established. Being divided it into some parts. This paper is one of them. The others are to be continued. CLC number: 0313.1 Document code: A     

Higher order Hessian structures on manifolds

In this paper we define nth order Hessian structures on manifolds and study them. In particular, whenn = 3, we make a detailed study and establish a one-to-one correspondence betweenthird-order Hessian structures and acertain class of connections on the second-order tangent bundle of a manifold. Further, we show that a connection on the tangent bundle of a manifold induces a connection on the second-order tangent bundle. Also we define second-order geodesics of special second-order connection which gives a geometric characterization of symmetric third-order Hessian structures.     

Brownian motion of a polymer-bound colloidal particle

A simple model of Brownian motion of a colloidal particle attached to the flat surface by a polymer thread is presented. The model results are discussed in terms of the measurability of the elastic properties of a linear polymer chain in the dispersion medium by observation of the motion of a colloidal particle connected to a fixed point by the polymer. Received: 11 November 1998 Accepted: 9 December 1998