27,299 research outputs found
Field Theory Entropy, the -theorem and the Renormalization Group
We consider entropy and relative entropy in Field theory and establish
relevant monotonicity properties with respect to the couplings. The relative
entropy in a field theory with a hierarchy of renormalization group fixed
points ranks the fixed points, the lowest relative entropy being assigned to
the highest multicritical point. We argue that as a consequence of a
generalized theorem Wilsonian RG flows induce an increase in entropy and
propose the relative entropy as the natural quantity which increases from one
fixed point to another in more than two dimensions.Comment: 25 pages, plain TeX (macros included), 6 ps figures. Addition in
title. Entropy of cutoff Gaussian model modified in section 4 to avoid a
divergence. Therefore, last figure modified. Other minor changes to improve
readability. Version to appear in Phys. Rev.
Electrification in granular gases leads to constrained fractal growth
The empirical observation of aggregation of dielectric particles under the
influence of electrostatic forces lies at the origin of the theory of
electricity. The growth of clusters formed of small grains underpins a range of
phenomena from the early stages of planetesimal formation to aerosols. However,
the collective effects of Coulomb forces on the nonequilibrium dynamics and
aggregation process in a granular gas -- a model representative of the above
physical processes -- have so far evaded theoretical scrutiny. Here, we
establish a hydrodynamic description of aggregating granular gases that
exchange charges upon collisions and interact via the long-ranged Coulomb
forces. We analytically derive the governing equations for the evolution of
granular temperature, charge variance, and number density for homogeneous and
quasi-monodisperse aggregation. We find that, once the aggregates are formed,
the system obeys a physical constraint of nearly constant dimensionless ratio
of characteristic electrostatic to kinetic energy . This
constraint on the collective evolution of charged clusters is confirmed both by
the theory and the detailed molecular dynamics simulations. The inhomogeneous
aggregation of monomers and clusters in their mutual electrostatic field
proceeds in a fractal manner. Our theoretical framework is extendable to more
precise charge exchange mechanism, a current focus of extensive
experimentation. Furthermore, it illustrates the collective role of long-ranged
interactions in dissipative gases and can lead to novel designing principles in
particulate systems
Non-Sobolev modelling of radiation pressure driven flows in Active Galactic Nuclei
We present a new general scheme for calculating the structure and dynamics of
radiation pressure driven, photoionized flows. The new method goes one step
beyond the Sobolev approximation. It involves a numerical solution of the
radiative transfer in absorption lines including the effects of differential
expansion and line interactions such as line locking and blanketing. We also
present a new scheme for calculating the radiation pressure due to trapped line
photons in finite, differentially expanding flows. We compare our results for
the radiation pressure force with those obtained using the Sobolev
approximation and show the limitations of the latter. In particular, we
demonstrate that the Sobolev method gives a poor approximation near
discontinuity surfaces and its neglect of line blanketing can lead to erroneous
results in high velocity flows. We combine the newly calculated radiation
pressure force with self-consistent photoionization and thermal calculations to
study the dynamics and spectral features of broad absorption line flows and
highly ionized gas flows in AGN. A comparison with Sobolev-type calculations
shows that the latter over estimates the flow's terminal velocity and,
conversely, under estimates its opacity. We also show that line locking on
broad emission lines can have a significant effect on the dynamics and spectral
features of AGN flows.Comment: 12 pages, 14 figures; includes an erratum on page 12 which corrects
an erroneous reference to the work of Elitzur & Ferland (1986
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