11,375 research outputs found
A Hamiltonian functional for the linearized Einstein vacuum field equations
By considering the Einstein vacuum field equations linearized about the
Minkowski metric, the evolution equations for the gauge-invariant quantities
characterizing the gravitational field are written in a Hamiltonian form by
using a conserved functional as Hamiltonian; this Hamiltonian is not the analog
of the energy of the field. A Poisson bracket between functionals of the field,
compatible with the constraints satisfied by the field variables, is obtained.
The generator of spatial translations associated with such bracket is also
obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie
Diffusive transport and self-consistent dynamics in coupled maps
The study of diffusion in Hamiltonian systems has been a problem of interest
for a number of years.
In this paper we explore the influence of self-consistency on the diffusion
properties of systems described by coupled symplectic maps. Self-consistency,
i.e. the back-influence of the transported quantity on the velocity field of
the driving flow, despite of its critical importance, is usually overlooked in
the description of realistic systems, for example in plasma physics. We propose
a class of self-consistent models consisting of an ensemble of maps globally
coupled through a mean field. Depending on the kind of coupling, two different
general types of self-consistent maps are considered: maps coupled to the field
only through the phase, and fully coupled maps, i.e. through the phase and the
amplitude of the external field. The analogies and differences of the diffusion
properties of these two kinds of maps are discussed in detail.Comment: 13 pages, 14 figure
Clustering transition in a system of particles self-consistently driven by a shear flow
We introduce a simple model of active transport for an ensemble of particles
driven by an external shear flow. Active refers to the fact that the flow of
the particles is modified by the distribution of particles itself. The model
consists in that the effective velocity of every particle is given by the
average of the external flow velocities felt by the particles located at a
distance less than a typical radius, . Numerical analysis reveals the
existence of a transition to clustering depending on the parameters of the
external flow and on . A continuum description in terms of the number
density of particles is derived, and a linear stability analysis of the density
equation is performed in order to characterize the transitions observed in the
model of interacting particles.Comment: 11 pages, 2 figures. To appear in PR
Finite Larmor radius effects on non-diffusive tracer transport in a zonal flow
Finite Larmor radius (FLR) effects on non-diffusive transport in a
prototypical zonal flow with drift waves are studied in the context of a
simplified chaotic transport model. The model consists of a superposition of
drift waves of the linearized Hasegawa-Mima equation and a zonal shear flow
perpendicular to the density gradient. High frequency FLR effects are
incorporated by gyroaveraging the ExB velocity. Transport in the direction of
the density gradient is negligible and we therefore focus on transport parallel
to the zonal flows. A prescribed asymmetry produces strongly asymmetric non-
Gaussian PDFs of particle displacements, with L\'evy flights in one direction
but not the other. For zero Larmor radius, a transition is observed in the
scaling of the second moment of particle displacements. However, FLR effects
seem to eliminate this transition. The PDFs of trapping and flight events show
clear evidence of algebraic scaling with decay exponents depending on the value
of the Larmor radii. The shape and spatio-temporal self-similar anomalous
scaling of the PDFs of particle displacements are reproduced accurately with a
neutral, asymmetric effective fractional diffusion model.Comment: 14 pages, 13 figures, submitted to Physics of Plasma
Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty
We analyze the quantum dynamics of the non-relativistic two-dimensional
isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken
as toy model to analyze some of the various quantum theories that can be built
from the application of Dirac's quantization rule to the various symplectic
structures recently reported for this classical system. It is pointed out that
that these quantum theories are inequivalent in the sense that the mean values
for the operators (observables) associated with the same physical classical
observable do not agree with each other. The inequivalence does not arise from
ambiguities in the ordering of operators but from the fact of having several
symplectic structures defined with respect to the same set of coordinates. It
is also shown that the uncertainty relations between the fundamental
observables depend on the particular quantum theory chosen. It is important to
emphasize that these (somehow paradoxical) results emerge from the combination
of two paradigms: Dirac's quantization rule and the usual Copenhagen
interpretation of quantum mechanics.Comment: 8 pages, LaTex file, no figures. Accepted for publication in Phys.
Rev.
Debye Potentials for Maxwell and Dirac Fields from a Generalisation of the Killing-Yano Equation
By using conformal Killing-Yano tensors, and their generalisations, we obtain
scalar potentials for both the source-free Maxwell and massless Dirac
equations. For each of these equations we construct, from conformal
Killing-Yano tensors, symmetry operators that map any solution to another.Comment: 35 pages, plain Te
Experimental and computational study of conductivity of multilayer graphene in polypropylene nanocomposites
[EN] We study the electric conductivity of compounds formed by multilayer graphene in polypropylene. Our study makes a comparative analysis between the experimental and computational results. To obtain an experimental measurement of the electronic properties, we deposited multilayer graphene (MLG) nanoparticles over a polypropylene matrix. The deposition was made over several stages, in which we added to the polymer matrix different percentages of MLG nanoparticles using the melt compounding technique, and we studied the conductivities of the nanocomposites by means of electrochemical impedance spectroscopy (EIS). The second part consists of computational calculations, in which we studied the electronic properties of a graphene sheet under a polypropylene molecule with different slabs in the monomer. In both analyses, there is a strong percolation phenomenon with a percolation threshold of around 18% of the MLG nanoparticles. Before the percolation threshold, the charge carriers are constrained in the polypropylene molecule, making the system an insulating material and creating p-type doping. After the percolation threshold, the charge carriers are constrained in the graphene, making the system a conductor material and creating n-type doping with conductivity values of around 20 S m(-1). This phenomenon is a consequence of a change in the mechanism of charge transfer in the interface between the polypropylene molecule and graphene sheet. To describe the charge transfer mechanism, it is necessary to consider the quantum effect. The incorporation of the quantum effects and the percolation phenomenon make it possible for the theoretical conductivity to be close to the conductivity measured experimentally.This research has been supported by the ENE/2015-69203-R project, granted by the Ministerio de Economia y Competitividad (MINECO), Spain. Also, the authors are grateful to UNAM-DGAPA-PAPIIT projects IG 100618 y IG 114818, DGTIC-UNAM for access to the Miztli-UNAM supercomputer LANCAD-UNAM-DGTIC-055, and UNAM-DGAPA for the Postdoctoral grant for Roxana M. del Castillo.Del Castillo, RM.; Del Castillo, LF.; Calles, AG.; Compañ Moreno, V. (2018). Experimental and computational study of conductivity of multilayer graphene in polypropylene nanocomposites. Journal of Materials Chemistry C. 6:7232-7241. https://doi.org/10.1039/c8tc01135dS723272416H. G. Karian , Handbook of polypropylene and polypropylene composites , RheTec, Inc. , Whitmore Lake, Michigan , 2nd edn, 2003 , https://books.google.es/books?hl=es&lr=&id=C0nzeNPUpoIC&oi=fnd&pg=PP1&dq=Handbook+of+polypropylene+and+polypropylene+composites&ots=LYqYBYg45n&sig=3gtYXigr8_O8CUJeefBCtGI7QXA#v=onepage&q=Handbook%20of%20polypropylene%20and%20polypropylene%20composites&f=falseRath, T., & Li, Y. (2011). Nanocomposites based on polystyrene-b-poly(ethylene-r-butylene)-b-polystyrene and exfoliated graphite nanoplates: Effect of nanoplatelet loading on morphology and mechanical properties. Composites Part A: Applied Science and Manufacturing, 42(12), 1995-2002. doi:10.1016/j.compositesa.2011.09.002Kim, M.-S., Yan, J., Kang, K.-M., Joo, K.-H., Kang, Y.-J., & Ahn, S.-H. (2013). Soundproofing ability and mechanical properties of polypropylene/exfoliated graphite nanoplatelet/carbon nanotube (PP/xGnP/CNT) composite. International Journal of Precision Engineering and Manufacturing, 14(6), 1087-1092. doi:10.1007/s12541-013-0146-3Zhang, K., Yu, H.-O., Shi, Y.-D., Chen, Y.-F., Zeng, J.-B., Guo, J., … Wang, M. (2017). Morphological regulation improved electrical conductivity and electromagnetic interference shielding in poly(l-lactide)/poly(ε-caprolactone)/carbon nanotube nanocomposites via constructing stereocomplex crystallites. 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