12 research outputs found
A note on isoparametric polynomials
We show that any homogeneous polynomial solution of |\nabla
F(x)|^2=m^2|x|^(2m-2), m>1, is either a radially symmetric polynomial F(x)=\pm
|x|^m (for even m's) or it is a composition of a Chebychev polynomial and a
Cartan-M\"unzner polynomial.Comment: 6 page
A Study of the Antiferromagnetic Phase in the Hubbard Model by means of the Composite Operator Method
We have investigated the antiferromagnetic phase of the 2D, the 3D and the
extended Hubbard models on a bipartite cubic lattice by means of the Composite
Operator Method within a two-pole approximation. This approach yields a fully
self-consistent treatment of the antiferromagnetic state that respects the
symmetry properties of both the model and the algebra. The complete phase
diagram, as regards the antiferromagnetic and the paramagnetic phases, has been
drawn. We firstly reported, within a pole approximation, three kinds of
transitions at half-filling: Mott-Hubbard, Mott-Heisenberg and Heisenberg. We
have also found a metal-insulator transition, driven by doping, within the
antiferromagnetic phase. This latter is restricted to a very small region near
half filling and has, in contrast to what has been found by similar approaches,
a finite critical Coulomb interaction as lower bound at half filling. Finally,
it is worth noting that our antiferromagnetic gap has two independent
components: one due to the antiferromagnetic correlations and another coming
from the Mott-Hubbard mechanism.Comment: 20 pages, 37 figures, RevTeX, submitted to Phys. Rev.
The Hubbard model within the equations of motion approach
The Hubbard model has a special role in Condensed Matter Theory as it is
considered as the simplest Hamiltonian model one can write in order to describe
anomalous physical properties of some class of real materials. Unfortunately,
this model is not exactly solved except for some limits and therefore one
should resort to analytical methods, like the Equations of Motion Approach, or
to numerical techniques in order to attain a description of its relevant
features in the whole range of physical parameters (interaction, filling and
temperature). In this manuscript, the Composite Operator Method, which exploits
the above mentioned analytical technique, is presented and systematically
applied in order to get information about the behavior of all relevant
properties of the model (local, thermodynamic, single- and two- particle ones)
in comparison with many other analytical techniques, the above cited known
limits and numerical simulations. Within this approach, the Hubbard model is
shown to be also capable to describe some anomalous behaviors of the cuprate
superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference
Micro-EDM of Carbon Fibre-Reinforced Plastics
AbstractDue to the inhomogeneous material structure, micromachining of fibre reinforced plastics places high requirements on machining processes. Using the hole drilling machining of carbon fibre reinforced plastics as an example, experiments on electro discharge machinability were carried out by means of solid carbide electrodes. Basing on the variation of technological process parameters, the tests were conducted with regard to both workpiece-related and tool-related parameters.The results accentuate the complexity of the influencing parameters affecting surface quality and thermal damage of the mater ial as well as tool wear. However, evidence of a low damage production of small drill holes could be provided