62,440 research outputs found
Thermodynamic Formalism for Topological Markov Chains on Borel Standard Spaces
We develop a Thermodynamic Formalism for bounded continuous potentials
defined on the sequence space , where is a general
Borel standard space. In particular, we introduce meaningful concepts of
entropy and pressure for shifts acting on and obtain the existence of
equilibrium states as additive probability measures for any bounded continuous
potential. Furthermore, we establish convexity and other structural properties
of the set of equilibrium states, prove a version of the
Perron-Frobenius-Ruelle theorem under additional assumptions on the regularity
of the potential and show that the Yosida-Hewitt decomposition of these
equilibrium states do not have a purely additive part.
We then apply our results to the construction of invariant measures of
time-homogeneous Markov chains taking values on a general Borel standard space
and obtain exponential asymptotic stability for a class of Markov operators. We
also construct conformal measures for an infinite collection of interacting
random paths which are associated to a potential depending on infinitely many
coordinates. Under an additional differentiability hypothesis, we show how this
process is related after a proper scaling limit to a certain infinite
dimensional diffusion.Comment: Accepted for publication in Discrete and Continuous Dynamical
Systems. 23 page
The Jacobi identity for Dirac-like brackets
For redundant second-class constraints the Dirac brackets cannot be defined
and new brackets must be introduced. We prove here that the Jacobi identity for
the new brackets must hold on the surface of the second-class constraints. In
order to illustrate our proof we work out explicitly the cases of a fractional
spin particle in 2+1 dimensions and the original Brink-Schwarz massless
superparticle in D=10 dimensions in a Lorentz covariant constraints separation.Comment: 14 pages, Latex. Final version to be published in Int. J. Mod. Phys.
Electron-scale shear instabilities: magnetic field generation and particle acceleration in astrophysical jets
Strong shear flow regions found in astrophysical jets are shown to be
important dissipation regions, where the shear flow kinetic energy is converted
into electric and magnetic field energy via shear instabilities. The emergence
of these self-consistent fields make shear flows significant sites for
radiation emission and particle acceleration. We focus on electron-scale
instabilities, namely the collisionless, unmagnetized Kelvin-Helmholtz
instability (KHI) and a large-scale dc magnetic field generation mechanism on
the electron scales. We show that these processes are important candidates to
generate magnetic fields in the presence of strong velocity shears, which may
naturally originate in energetic matter outburst of active galactic nuclei and
gamma-ray bursters. We show that the KHI is robust to density jumps between
shearing flows, thus operating in various scenarios with different density
contrasts. Multidimensional particle-in-cell (PIC) simulations of the KHI,
performed with OSIRIS, reveal the emergence of a strong and large-scale dc
magnetic field component, which is not captured by the standard linear fluid
theory. This dc component arises from kinetic effects associated with the
thermal expansion of electrons of one flow into the other across the shear
layer, whilst ions remain unperturbed due to their inertia. The electron
expansion forms dc current sheets, which induce a dc magnetic field. Our
results indicate that most of the electromagnetic energy developed in the KHI
is stored in the dc component, reaching values of equipartition on the order of
in the electron time-scale, and persists longer than the proton
time-scale. Particle scattering/acceleration in the self generated fields of
these shear flow instabilities is also analyzed
Transverse electron-scale instability in relativistic shear flows
Electron-scale surface waves are shown to be unstable in the transverse plane
of a shear flow in an initially unmagnetized plasma, unlike in the
(magneto)hydrodynamics case. It is found that these unstable modes have a
higher growth rate than the closely related electron-scale Kelvin-Helmholtz
instability in relativistic shears. Multidimensional particle-in-cell
simulations verify the analytic results and further reveal the emergence of
mushroom-like electron density structures in the nonlinear phase of the
instability, similar to those observed in the Rayleigh Taylor instability
despite the great disparity in scales and different underlying physics.
Macroscopic () fields are shown to be generated by these
microscopic shear instabilities, which are relevant for particle acceleration,
radiation emission and to seed MHD processes at long time-scales
Mortalidade de lagartas de primeiro instar do curuquerê alimentado com folhas de algodoeiro tratadas com extrato de sisal.
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