937 research outputs found
An analysis of the XOR dynamic problem generator based on the dynamical system
This is the post-print version of the article - Copyright @ 2010 Springer-VerlagIn this paper, we use the exact model (or dynamical system approach) to describe the standard evolutionary algorithm (EA) as a discrete dynamical system for dynamic optimization problems (DOPs). Based on this dynamical system model, we analyse the properties of the XOR DOP Generator, which has been widely used by researchers to create DOPs from any binary encoded problem. DOPs generated by this generator are described as DOPs with permutation, where the fitness vector is changed according to a permutation matrix. Some properties of DOPs with permutation are analyzed, which allows explaining some behaviors observed in experimental results. The analysis of the properties of problems created by the XOR DOP Generator is important to understand the results obtained in experiments with this generator and to analyze the similarity of such problems to real world DOPs.This work was supported by Brazil FAPESP under Grant 04/04289-6 and by UK EPSRC under Grant EP/E060722/2
The Dynamics of a Rigid Body in Potential Flow with Circulation
We consider the motion of a two-dimensional body of arbitrary shape in a
planar irrotational, incompressible fluid with a given amount of circulation
around the body. We derive the equations of motion for this system by
performing symplectic reduction with respect to the group of volume-preserving
diffeomorphisms and obtain the relevant Poisson structures after a further
Poisson reduction with respect to the group of translations and rotations. In
this way, we recover the equations of motion given for this system by Chaplygin
and Lamb, and we give a geometric interpretation for the Kutta-Zhukowski force
as a curvature-related effect. In addition, we show that the motion of a rigid
body with circulation can be understood as a geodesic flow on a central
extension of the special Euclidian group SE(2), and we relate the cocycle in
the description of this central extension to a certain curvature tensor.Comment: 28 pages, 2 figures; v2: typos correcte
Generalized Euler-Poincar\'e equations on Lie groups and homogeneous spaces, orbit invariants and applications
We develop the necessary tools, including a notion of logarithmic derivative
for curves in homogeneous spaces, for deriving a general class of equations
including Euler-Poincar\'e equations on Lie groups and homogeneous spaces.
Orbit invariants play an important role in this context and we use these
invariants to prove global existence and uniqueness results for a class of PDE.
This class includes Euler-Poincar\'e equations that have not yet been
considered in the literature as well as integrable equations like Camassa-Holm,
Degasperis-Procesi, CH and DP equations, and the geodesic equations
with respect to right invariant Sobolev metrics on the group of diffeomorphisms
of the circle
Meson Exchange Currents in (e,e'p) recoil polarization observables
A study of the effects of meson-exchange currents and isobar configurations
in reactions is presented. We use a distorted wave
impulse approximation (DWIA) model where final-state interactions are treated
through a phenomenological optical potential. The model includes relativistic
corrections in the kinematics and in the electromagnetic one- and two-body
currents. The full set of polarized response functions is analyzed, as well as
the transferred polarization asymmetry. Results are presented for proton
knock-out from closed-shell nuclei, for moderate to high momentum transfer.Comment: 44 pages, 18 figures. Added physical arguments explaining the
dominance of OB over MEC, and a summary of differences with previous MEC
calculations. To be published in PR
Resummation Methods at Finite Temperature: The Tadpole Way
We examine several resummation methods for computing higher order corrections
to the finite temperature effective potential, in the context of a scalar
theory. We show by explicit calculation to four loops that dressing
the propagator, not the vertex, of the one-loop tadpole correctly counts
``daisy'' and ``super-daisy'' diagrams.Comment: 18 pages, LaTeX, CALT-68-1858, HUTP-93-A011, EFI-93-2
Next-to-next-to-leading-order Δ expansion for a Fermi gas at infinite scattering length
We extend previous work on applying the expansion to universal properties of a cold, dilute Fermi gas in the unitary regime of infinite scattering length. We compute the ratio Ο=Ό/F of chemical potential to ideal gas Fermi energy to next-to-next-to-leading-order (NNLO) in =4-d, where d is the number of spatial dimensions. We also explore the nature of corrections from the order after NNLO
Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
This paper studies the construction of geometric integrators for nonholonomic
systems. We derive the nonholonomic discrete Euler-Lagrange equations in a
setting which permits to deduce geometric integrators for continuous
nonholonomic systems (reduced or not). The formalism is given in terms of Lie
groupoids, specifying a discrete Lagrangian and a constraint submanifold on it.
Additionally, it is necessary to fix a vector subbundle of the Lie algebroid
associated to the Lie groupoid. We also discuss the existence of nonholonomic
evolution operators in terms of the discrete nonholonomic Legendre
transformations and in terms of adequate decompositions of the prolongation of
the Lie groupoid. The characterization of the reversibility of the evolution
operator and the discrete nonholonomic momentum equation are also considered.
Finally, we illustrate with several classical examples the wide range of
application of the theory (the discrete nonholonomic constrained particle, the
Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a
rotating table and the two wheeled planar mobile robot).Comment: 45 page
Calculations of parity nonconserving s-d transitions in Cs, Fr, Ba II, and Ra II
We have performed ab initio mixed-states and sum-over-states calculations of
parity nonconserving (PNC) electric dipole (E1) transition amplitudes between
s-d electron states of Cs, Fr, Ba II, and Ra II. For the lower states of these
atoms we have also calculated energies, E1 transition amplitudes, and
lifetimes. We have shown that PNC E1 transition amplitudes between s-d states
can be calculated to high accuracy. Contrary to the Cs 6s-7s transition, in
these transitions there are no strong cancelations between different terms in
the sum-over-states approach. In fact, there is one dominating term which
deviates from the sum by less than 20%. This term corresponds to an s-p_{1/2}
weak matrix element, which can be calculated to better than 1%, and a
p_{1/2}-d_{3/2} E1 transition amplitude, which can be measured. Also, the s-d
amplitudes are about four times larger than the corresponding s-s transitions.
We have shown that by using a hybrid mixed-states/sum-over-states approach the
accuracy of the calculations of PNC s-d amplitudes could compete with that of
Cs 6s-7s if p_{1/2}-d_{3/2} E1 amplitudes are measured to high accuracy.Comment: 15 pages, 8 figures, submitted to Phys. Rev.
Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size
We construct affinization of the algebra of ``complex size''
matrices, that contains the algebras for integral values of the
parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra
results in the quadratic Gelfand--Dickey structure on the
Poisson--Lie group of all pseudodifferential operators of fractional order.
This construction is extended to the simultaneous deformation of orthogonal and
simplectic algebras that produces self-adjoint operators, and it has a
counterpart for the Toda lattices with fractional number of particles.Comment: 29 pages, no figure
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