22 research outputs found
Independent Eigenstates of Angular Momentum in a Quantum N-body System
The global rotational degrees of freedom in the Schr\"{o}dinger equation for
an -body system are completely separated from the internal ones. After
removing the motion of center of mass, we find a complete set of
independent base functions with the angular momentum . These are
homogeneous polynomials in the components of the coordinate vectors and the
solutions of the Laplace equation, where the Euler angles do not appear
explicitly. Any function with given angular momentum and given parity in the
system can be expanded with respect to the base functions, where the
coefficients are the functions of the internal variables. With the right choice
of the base functions and the internal variables, we explicitly establish the
equations for those functions. Only (3N-6) internal variables are involved both
in the functions and in the equations. The permutation symmetry of the wave
functions for identical particles is discussed.Comment: 24 pages, no figure, one Table, RevTex, Will be published in Phys.
Rev. A 64, 0421xx (Oct. 2001
A Quantum-mechanical Approach for Constrained Macromolecular Chains
Many approaches to three-dimensional constrained macromolecular chains at
thermal equilibrium, at about room temperatures, are based upon constrained
Classical Hamiltonian Dynamics (cCHDa). Quantum-mechanical approaches (QMa)
have also been treated by different researchers for decades. QMa address a
fundamental issue (constraints versus the uncertainty principle) and are
versatile: they also yield classical descriptions (which may not coincide with
those from cCHDa, although they may agree for certain relevant quantities).
Open issues include whether QMa have enough practical consequences which differ
from and/or improve those from cCHDa. We shall treat cCHDa briefly and deal
with QMa, by outlining old approaches and focusing on recent ones.Comment: Expands review published in The European Physical Journal (Special
Topics) Vol. 200, pp. 225-258 (2011
A Physical-Geometric Approach to Model Thin Dynamical Structures in CAD Systems
The efficient accurate modeling of thin, approximately one-dimensional structures, like cables, fibers, threads, tubes, wires, etc. in CAD systems is a complicated task since the dynamical behavior has to be computed at interactive frame rates to enable a productive workflow. Traditional physical methods often have the deficiency that the solution process is expensive and heavily dependent on minor details of the underlying geometry and the configuration of the applied numerical solver. In contrast, pure geometrical methods are not able to handle all occurring effects in an accurate way.
To overcome this shortcomings, we present a novel and general hybrid physical-geometric approach: the structureâs dynamics is handled in a physically accurate way based on the special Cosserat theory of rods capable of capturing effects like bending, twisting, shearing, and extension deformations, while collisions are resolved using a fast geometric sweep strategy which is robust under different numerical and geometric resolutions.
As a result, fast editable high quality tubes can easily be designed including their dynamical behavior
High-order discontinuous Galerkin solution of unsteady flows by using an advanced implicit method
The aim of this paper is to investigate and evaluate a multi-stage and multi-step method that is an evolution of the more common Backward Differentiation Formulae (BDF). This new class of formulae, called Two Implicit Advanced Step-point (TIAS), has been applied to a high-order Discontinuous Galerkin (DG) discretization of the Navier-Stokes equations, coupling the high temporal accuracy gained by the TIAS scheme with the high space accuracy of the DG method. The performance of the DG-TIAS scheme has been evaluated by means of two test cases: an inviscid isentropic convecting vortex and a laminar vortex shedding behind a circular cylinder. The advantages of the high-order time discretization are illustrated comparing the sixth-order accurate TIAS scheme with the second-order accurate BDF scheme using the same spatial discretization