7,224 research outputs found
Moving frames for cotangent bundles
Cartan's moving frames method is a standard tool in riemannian geometry. We
set up the machinery for applying moving frames to cotangent bundles and its
sub-bundles defined by non-holonomic constraints.Comment: 13 pages, to appear in Rep. Math. Phy
Singularities of affine equidistants: projections and contacts
Using standard methods for studying singularities of projections and of
contacts, we classify the stable singularities of affine -equidistants
of -dimensional closed submanifolds of , for ,
whenever is a pair of nice dimensions.Comment: 18 pages, v2 (minimal changes) agrees with version to appear in
Journal of Singularitie
The role of the Berry Phase in Dynamical Jahn-Teller Systems
The presence/absence of a Berry phase depends on the topology of the manifold
of dynamical Jahn-Teller potential minima. We describe in detail the relation
between these topological properties and the way the lowest two adiabatic
potential surfaces get locally degenerate. We illustrate our arguments through
spherical generalizations of the linear T x h and H x h cases, relevant for the
physics of fullerene ions. Our analysis allows us to classify all the spherical
Jahn-Teller systems with respect to the Berry phase. Its absence can, but does
not necessarily, lead to a nondegenerate ground state.Comment: revtex 7 pages, 2 eps figures include
Levy-Nearest-Neighbors Bak-Sneppen Model
We study a random neighbor version of the Bak-Sneppen model, where "nearest
neighbors" are chosen according to a probability distribution decaying as a
power-law of the distance from the active site, P(x) \sim |x-x_{ac
}|^{-\omega}. All the exponents characterizing the self-organized critical
state of this model depend on the exponent \omega. As \omega tends to 1 we
recover the usual random nearest neighbor version of the model. The pattern of
results obtained for a range of values of \omega is also compatible with the
results of simulations of the original BS model in high dimensions. Moreover,
our results suggest a critical dimension d_c=6 for the Bak-Sneppen model, in
contrast with previous claims.Comment: To appear on Phys. Rev. E, Rapid Communication
Gel Electrophoresis of DNA Knots in Weak and Strong Electric Fields
Gel electrophoresis allows to separate knotted DNA (nicked circular) of equal
length according to the knot type. At low electric fields, complex knots being
more compact, drift faster than simpler knots. Recent experiments have shown
that the drift velocity dependence on the knot type is inverted when changing
from low to high electric fields. We present a computer simulation on a lattice
of a closed, knotted, charged DNA chain drifting in an external electric field
in a topologically restricted medium. Using a simple Monte Carlo algorithm, the
dependence of the electrophoretic migration of the DNA molecules on the type of
knot and on the electric field intensity was investigated. The results are in
qualitative agreement with electrophoretic experiments done under conditions of
low and high electric fields: especially the inversion of the behavior from low
to high electric field could be reproduced. The knot topology imposes on the
problem the constrain of self-avoidance, which is the final cause of the
observed behavior in strong electric field.Comment: 17 pages, 5 figure
On Weyl Quantization from geometric Quantization
A. Weinstein has conjectured a nice looking formula for a deformed product of
functions on a hermitian symmetric space of non-compact type. We derive such a
formula for symmetric symplectic spaces using ideas from geometric quantization
and prequantization of symplectic groupoids. We compute the result explicitly
for the natural 2-dimensional symplectic manifolds: the euclidean plane, the
sphere and the hyperbolic plane. For the euclidean plane we obtain the well
known Moyal-Weyl product. The other cases show that Weinstein's original idea
should be interpreted with care. We conclude with comments on the status of our
result.Comment: 11 pages. (v2: corrected a couple of typos
Semiclassical Evolution of Dissipative Markovian Systems
A semiclassical approximation for an evolving density operator, driven by a
"closed" hamiltonian operator and "open" markovian Lindblad operators, is
obtained. The theory is based on the chord function, i.e. the Fourier transform
of the Wigner function. It reduces to an exact solution of the Lindblad master
equation if the hamiltonian operator is a quadratic function and the Lindblad
operators are linear functions of positions and momenta.
Initially, the semiclassical formulae for the case of hermitian Lindblad
operators are reinterpreted in terms of a (real) double phase space, generated
by an appropriate classical double Hamiltonian. An extra "open" term is added
to the double Hamiltonian by the non-hermitian part of the Lindblad operators
in the general case of dissipative markovian evolution. The particular case of
generic hamiltonian operators, but linear dissipative Lindblad operators, is
studied in more detail. A Liouville-type equivariance still holds for the
corresponding classical evolution in double phase, but the centre subspace,
which supports the Wigner function, is compressed, along with expansion of its
conjugate subspace, which supports the chord function.
Decoherence narrows the relevant region of double phase space to the
neighborhood of a caustic for both the Wigner function and the chord function.
This difficulty is avoided by a propagator in a mixed representation, so that a
further "small-chord" approximation leads to a simple generalization of the
quadratic theory for evolving Wigner functions.Comment: 33 pages - accepted to J. Phys.
Critical exponents of the anisotropic Bak-Sneppen model
We analyze the behavior of spatially anisotropic Bak-Sneppen model. We
demonstrate that a nontrivial relation between critical exponents tau and
mu=d/D, recently derived for the isotropic Bak-Sneppen model, holds for its
anisotropic version as well. For one-dimensional anisotropic Bak-Sneppen model
we derive a novel exact equation for the distribution of avalanche spatial
sizes, and extract the value gamma=2 for one of the critical exponents of the
model. Other critical exponents are then determined from previously known
exponent relations. Our results are in excellent agreement with Monte Carlo
simulations of the model as well as with direct numerical integration of the
new equation.Comment: 8 pages, three figures included with psfig, some rewriting, + extra
figure and table of exponent
Potencial econômico de algumas palmeiras nativas da Amazônia.
Apresenta-se aqui um breve relato sobre os esforços já conseguidos com a pesquisa em recursos genéticos com algumas espécies de palmeiras de grande utilidade na Amazônia, com excelente potencial econômico e possibilidade de valor agregado
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