24,028 research outputs found
Study of a model for the distribution of wealth
An equation for the evolution of the distribution of wealth in a population
of economic agents making binary transactions with a constant total amount of
"money" has recently been proposed by one of us (RLR). This equation takes the
form of an iterated nonlinear map of the distribution of wealth. The
equilibrium distribution is known and takes a rather simple form. If this
distribution is such that, at some time, the higher momenta of the distribution
exist, one can find exactly their law of evolution. A seemingly simple
extension of the laws of exchange yields also explicit iteration formulae for
the higher momenta, but with a major difference with the original iteration
because high order momenta grow indefinitely. This provides a quantitative
model where the spreading of wealth, namely the difference between the rich and
the poor, tends to increase with time.Comment: 12 pages, 2 figure
One-dimensional relativistic dissipative system with constant force and its quantization
For a relativistic particle under a constant force and a linear velocity
dissipation force, a constant of motion is found. Problems are shown for
getting the Hamiltoninan of this system. Thus, the quantization of this system
is carried out through the constant of motion and using the quantization of the
velocity variable. The dissipative relativistic quantum bouncer is outlined
within this quantization approach.Comment: 11 pages, no figure
Lattice calculations on the spectrum of Dirac and Dirac-K\"ahler operators
We present a matrix technique to obtain the spectrum and the analytical index
of some elliptic operators defined on compact Riemannian manifolds. The method
uses matrix representations of the derivative which yield exact values for the
derivative of a trigonometric polynomial. These matrices can be used to find
the exact spectrum of an elliptic operator in particular cases and in general,
to give insight into the properties of the solution of the spectral problem. As
examples, the analytical index and the eigenvalues of the Dirac operator on the
torus and on the sphere are obtained and as an application of this technique,
the spectrum of the Dirac-Kahler operator on the sphere is explored.Comment: 11 page
Nonlinear Interaction of Transversal Modes in a CO2 Laser
We show the possibility of achieving experimentally a Takens-Bogdanov
bifurcation for the nonlinear interaction of two transverse modes ()
in a laser. The system has a basic O(2) symmetry which is perturbed by
some symmetry-breaking effects that still preserve the symmetry. The
pattern dynamics near this codimension two bifurcation under such symmetries is
described. This dynamics changes drastically when the laser properties are
modified.Comment: 16 pages, 0 figure
Velocity quantization approach of the one-dimensional dissipative harmonic oscillator
Given a constant of motion for the one-dimensional harmonic oscillator with
linear dissipation in the velocity, the problem to get the Hamiltonian for this
system is pointed out, and the quantization up to second order in the
perturbation approach is used to determine the modification on the eigenvalues
when dissipation is taken into consideration. This quantization is realized
using the constant of motion instead of the Hamiltonian.Comment: 10 pages, 2 figure
Radiative two-pion decay of the tau lepton
We consider the bremsstrahlung and model-dependent contributions to the
radiative decay in the context of a
meson dominance model. We focus on several observables related to this decay,
including the branching ratio and the photon and di-pion spectra. Particular
attention is paid to the sensitivity of different observables upon the effects
of model-dependent contributions and of the magnetic dipole moment of the
vector meson. Important numerical differences are found with
respect to results obtained in the framework of chiral perturbation theory.Comment: 14 pages, 8 figures, submitted for publicatio
On algebraic classification of quasi-exactly solvable matrix models
We suggest a generalization of the Lie algebraic approach for constructing
quasi-exactly solvable one-dimensional Schroedinger equations which is due to
Shifman and Turbiner in order to include into consideration matrix models. This
generalization is based on representations of Lie algebras by first-order
matrix differential operators. We have classified inequivalent representations
of the Lie algebras of the dimension up to three by first-order matrix
differential operators in one variable. Next we describe invariant
finite-dimensional subspaces of the representation spaces of the one-,
two-dimensional Lie algebras and of the algebra sl(2,R). These results enable
constructing multi-parameter families of first- and second-order quasi-exactly
solvable models. In particular, we have obtained two classes of quasi-exactly
solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge
Spatially resolved kinematics of the central regions of M83: hidden mass signatures and the role of supernovae
The barred grand-design spiral M83 (NGC 5236) is one of the most studied
galaxies given its proximity, orientation, and particular complexity.
Nonetheless, many aspects of the central regions remain controversial conveying
our limited understanding of the inner gas and stellar kinematics, and
ultimately of the nucleus evolution.
In this work, we present AO VLT-SINFONI data of its central ~235x140 pc with
an unprecedented spatial resolution of ~0.2 arcsec, corresponding to ~4 pc. We
have focused our study on the distribution and kinematics of the stars and the
ionised and molecular gas by studying in detail the Pa_alpha and Br_gamma
emission, the H_2 1-0S(1) line at 2.122 micron and the [FeII] line at 1.644
micron, together with the CO absorption bands at 2.293 micron and 2.323 micron.
Our results reveal a complex situation where the gas and stellar kinematics are
totally unrelated. Supernova explosions play an important role in shaping the
gas kinematics, dominated by shocks and inflows at scales of tens of parsecs
that make them unsuitable to derive general dynamical properties.
We propose that the location of the nucleus of M83 is unlikely to be related
to the off-centre 'optical nucleus'. The study of the stellar kinematics
reveals that the optical nucleus is a gravitationally bound massive star
cluster with M_dyn = (1.1 \pm 0.4)x10^7 M_sun, formed by a past starburst. The
kinematic and photometric analysis of the cluster yield that the stellar
content of the cluster is well described by an intermediate age population of
log T(yr) = 8.0\pm0.4, with a mass of M \simeq (7.8\pm2.4)x10^6 M_sun.Comment: 14 pages, 10 figures, accepted for publication in Ap
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