10,752 research outputs found
Computer simulations of an impurity in a granular gas under planar Couette flow
We present in this work results from numerical solutions, obtained by means
of the direct simulation Monte Carlo (DSMC) method, of the Boltzmann and
Boltzmann--Lorentz equations for an impurity immersed in a granular gas under
planar Couette flow. The DSMC results are compared with the exact solution of a
recent kinetic model for the same problem. The results confirm that, in steady
states and over a wide range of parameter values, the state of the impurity is
enslaved to that of the host gas: it follows the same flow velocity profile,
its concentration (relative to that of the granular gas) is constant in the
bulk region, and the impurity/gas temperature ratio is also constant. We
determine also the rheological properties and nonlinear hydrodynamic transport
coefficients for the impurity, finding a good semi-quantitative agreement
between the DSMC results and the theoretical predictions.Comment: 23 pages, 11 figures; v2: minor change
Spatial dispersion in Casimir forces: A brief review
We present the basic principles of non-local optics in connection with the
calculation of the Casimir force between half-spaces and thin films.
At currently accessible distances , non-local corrections amount to about
half a percent, but they increase roughly as 1/L at smaller separations. Self
consistent models lead to corrections with the opposite sign as models with
abrupt surfaces.Comment: Proceedings of QFEXT05, Barcelona, Sept. 5-9, 200
Non-affine geometrization can lead to nonphysical instabilities
Geometrization of dynamics consists of representing trajectories by geodesics
on a configuration space with a suitably defined metric. Previously, efforts
were made to show that the analysis of dynamical stability can also be carried
out within geometrical frameworks, by measuring the broadening rate of a bundle
of geodesics. Two known formalisms are via Jacobi and Eisenhart metrics. We
find that this geometrical analysis measures the actual stability when the
length of any geodesic is proportional to the corresponding time interval. We
prove that the Jacobi metric is not always an appropriate parametrization by
showing that it predicts chaotic behavior for a system of harmonic oscillators.
Furthermore, we show, by explicit calculation, that the correspondence between
dynamical- and geometrical-spread is ill-defined for the Jacobi metric. We find
that the Eisenhart dynamics corresponds to the actual tangent dynamics and is
therefore an appropriate geometrization scheme.Comment: Featured on the Cover of the Journal. 9 pages, 6 figures:
http://iopscience.iop.org/1751-8121/48/7/07510
Ultrafast non-linear optical signal from a single quantum dot: exciton and biexciton effects
We present results on both the intensity and phase-dynamics of the transient
non-linear optical response of a single quantum dot (SQD).
The time evolution of the Four Wave Mixing (FWM) signal on a subpicosecond
time scale is dominated by biexciton effects. In particular, for the
cross-polarized excitation case a biexciton bound state is found. In this
latter case, mean-field results are shown to give a poor description of the
non-linear optical signal at small times. By properly treating exciton-exciton
effects in a SQD, coherent oscillations in the FWM signal are clearly
demonstrated. These oscillations, with a period corresponding to the inverse of
the biexciton binding energy, are correlated with the phase dynamics of the
system's polarization giving clear signatures of non-Markovian effects in the
ultrafast regime.Comment: 10 pages, 3 figure
Riccati-parameter solutions of nonlinear second-order ODEs
It has been proven by Rosu and Cornejo-Perez in 2005 that for some nonlinear
second-order ODEs it is a very simple task to find one particular solution once
the nonlinear equation is factorized with the use of two first-order
differential operators. Here, it is shown that an interesting class of
parametric solutions is easy to obtain if the proposed factorization has a
particular form, which happily turns out to be the case in many problems of
physical interest. The method that we exemplify with a few explicitly solved
cases consists in using the general solution of the Riccati equation, which
contributes with one parameter to this class of parametric solutions. For these
nonlinear cases, the Riccati parameter serves as a `growth' parameter from the
trivial null solution up to the particular solution found through the
factorization procedureComment: 5 pages, 3 figures, change of title and more tex
Non perturbative renormalization in coordinate space
We present an exploratory study of a gauge-invariant non-perturbative
renormalization technique. The renormalization conditions are imposed on
correlation functions of composite operators in coordinate space on the
lattice. Numerical results for bilinears obtained with overlap and
O(a)-improved Wilson fermions are presented. The measurement of the quark
condensate is also discussed.Comment: Lattice2003(improve), 3 page
A one-sided Prime Ideal Principle for noncommutative rings
Completely prime right ideals are introduced as a one-sided generalization of
the concept of a prime ideal in a commutative ring. Some of their basic
properties are investigated, pointing out both similarities and differences
between these right ideals and their commutative counterparts. We prove the
Completely Prime Ideal Principle, a theorem stating that right ideals that are
maximal in a specific sense must be completely prime. We offer a number of
applications of the Completely Prime Ideal Principle arising from many diverse
concepts in rings and modules. These applications show how completely prime
right ideals control the one-sided structure of a ring, and they recover
earlier theorems stating that certain noncommutative rings are domains (namely,
proper right PCI rings and rings with the right restricted minimum condition
that are not right artinian). In order to provide a deeper understanding of the
set of completely prime right ideals in a general ring, we study the special
subset of comonoform right ideals.Comment: 38 page
Geometrical resonance in spatiotemporal systems
We generalize the concept of geometrical resonance to perturbed sine-Gordon,
Nonlinear Schrödinger and Complex Ginzburg-Landau equations. Using this
theory we can control different dynamical patterns. For instance, we can
stabilize breathers and oscillatory patterns of large amplitudes successfully
avoiding chaos. On the other hand, this method can be used to suppress
spatiotemporal chaos and turbulence in systems where these phenomena are
already present. This method can be generalized to even more general
spatiotemporal systems.Comment: 2 .epl files. Accepted for publication in Europhysics Letter
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