4,040 research outputs found
Completely integrable systems: a generalization
We present a slight generalization of the notion of completely integrable
systems to get them being integrable by quadratures. We use this generalization
to integrate dynamical systems on double Lie groups.Comment: Latex, 15 page
The Structure of Conserved Charges in Open Spin Chains
We study the local conserved charges in integrable spin chains of the XYZ
type with nontrivial boundary conditions. The general structure of these
charges consists of a bulk part, whose density is identical to that of a
periodic chain, and a boundary part. In contrast with the periodic case, only
charges corresponding to interactions of even number of spins exist for the
open chain. Hence, there are half as many charges in the open case as in the
closed case. For the open spin-1/2 XY chain, we derive the explicit expressions
of all the charges. For the open spin-1/2 XXX chain, several lowest order
charges are presented and a general method of obtaining the boundary terms is
indicated. In contrast with the closed case, the XXX charges cannot be
described in terms of a Catalan tree pattern.Comment: 22 pages, harvmac.tex (minor clarifications and reference corrections
added
Jacobi-Nijenhuis algebroids and their modular classes
Jacobi-Nijenhuis algebroids are defined as a natural generalization of
Poisson-Nijenhuis algebroids, in the case where there exists a Nijenhuis
operator on a Jacobi algebroid which is compatible with it. We study modular
classes of Jacobi and Jacobi-Nijenhuis algebroids
On quasi-Jacobi and Jacobi-quasi bialgebroids
We study quasi-Jacobi and Jacobi-quasi bialgebroids and their relationships
with twisted Jacobi and quasi Jacobi manifolds. We show that we can construct
quasi-Lie bialgebroids from quasi-Jacobi bialgebroids, and conversely, and also
that the structures induced on their base manifolds are related via a quasi
Poissonization
Poisson-Jacobi reduction of homogeneous tensors
The notion of homogeneous tensors is discussed. We show that there is a
one-to-one correspondence between multivector fields on a manifold ,
homogeneous with respect to a vector field on , and first-order
polydifferential operators on a closed submanifold of codimension 1 such
that is transversal to . This correspondence relates the
Schouten-Nijenhuis bracket of multivector fields on to the Schouten-Jacobi
bracket of first-order polydifferential operators on and generalizes the
Poissonization of Jacobi manifolds. Actually, it can be viewed as a
super-Poissonization. This procedure of passing from a homogeneous multivector
field to a first-order polydifferential operator can be also understood as a
sort of reduction; in the standard case -- a half of a Poisson reduction. A
dual version of the above correspondence yields in particular the
correspondence between -homogeneous symplectic structures on and
contact structures on .Comment: 19 pages, minor corrections, final version to appear in J. Phys. A:
Math. Ge
Hubbard Models as Fusion Products of Free Fermions
A class of recently introduced su(n) `free-fermion' models has recently been
used to construct generalized Hubbard models. I derive an algebra defining the
`free-fermion' models and give new classes of solutions. I then introduce a
conjugation matrix and give a new and simple proof of the corresponding
decorated Yang-Baxter equation. This provides the algebraic tools required to
couple in an integrable way two copies of free-fermion models. Complete
integrability of the resulting Hubbard-like models is shown by exhibiting their
L and R matrices. Local symmetries of the models are discussed. The
diagonalization of the free-fermion models is carried out using the algebraic
Bethe Ansatz.Comment: 14 pages, LaTeX. Minor modification
A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
This paper presents a geometric description of Lagrangian and Hamiltonian
systems on Lie affgebroids subject to affine nonholonomic constraints. We
define the notion of nonholonomically constrained system, and characterize
regularity conditions that guarantee that the dynamics of the system can be
obtained as a suitable projection of the unconstrained dynamics. It is shown
that one can define an almost aff-Poisson bracket on the constraint AV-bundle,
which plays a prominent role in the description of nonholonomic dynamics.
Moreover, these developments give a general description of nonholonomic systems
and the unified treatment permits to study nonholonomic systems after or before
reduction in the same framework. Also, it is not necessary to distinguish
between linear or affine constraints and the methods are valid for explicitly
time-dependent systems.Comment: 50 page
Influence of Machining Parameters on Heat Generation during Milling of Aluminum Alloys
Thin-walled components, i.e. fuselage frames of airplanes, are prone to an unstable process behavior during milling. Therefore, tools with a chamfer between the cutting edge and the flank face are often used for such machining tasks. During milling, the chamfered area comes into contact with the just cut surface. This contact leads to process damping forces and the induced heat into the workpiece in this contact zone is increased. Furthermore, the amount of induced heat depends on the process parameters. At certain spots on the machined surface this may lead to a local overheating, which can reduce stiffness significantly. When this occurs during milling of a thin-walled component, the component is often regarded as reject. In this paper, the influence of chamfers and process parameters on the induced heat into the workpiece is investigated experimentally. In addition, a simulation which predict the temperature in the workpiece in dependence of the process parameters is presented.Ministry of Economics, Labour and Transport of Lower Saxony/ZW3-80134969DFG/DE 447/90-
Marketing National Parks for Sustainable Tourism: Bridging the Conservation Human Usage Divide Through Track/ Trail Based Interpretation
- …