248,325 research outputs found
Non-axisymmetric relativistic Bondi-Hoyle accretion onto a Schwarzschild black hole
We present the results of an exhaustive numerical study of fully relativistic
non-axisymmetric Bondi-Hoyle accretion onto a moving Schwarzschild black hole.
We have solved the equations of general relativistic hydrodynamics with a
high-resolution shock-capturing numerical scheme based on a linearized Riemann
solver. The numerical code was previously used to study axisymmetric flow
configurations past a Schwarzschild hole. We have analyzed and discussed the
flow morphology for a sample of asymptotically high Mach number models. The
results of this work reveal that initially asymptotic uniform flows always
accrete onto the hole in a stationary way which closely resembles the previous
axisymmetric patterns. This is in contrast with some Newtonian numerical
studies where violent flip-flop instabilities were found. As discussed in the
text, the reason can be found in the initial conditions used in the
relativistic regime, as they can not exactly duplicate the previous Newtonian
setups where the instability appeared. The dependence of the final solution
with the inner boundary condition as well as with the grid resolution has also
been studied. Finally, we have computed the accretion rates of mass and linear
and angular momentum.Comment: 21 pages, 13 figures, Latex, MNRAS (in press
Marginal AMP Chain Graphs
We present a new family of models that is based on graphs that may have
undirected, directed and bidirected edges. We name these new models marginal
AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP
chain graph under marginalization of some of its nodes. However, MAMP chain
graphs do not only subsume AMP chain graphs but also multivariate regression
chain graphs. We describe global and pairwise Markov properties for MAMP chain
graphs and prove their equivalence for compositional graphoids. We also
characterize when two MAMP chain graphs are Markov equivalent.
For Gaussian probability distributions, we also show that every MAMP chain
graph is Markov equivalent to some directed and acyclic graph with
deterministic nodes under marginalization and conditioning on some of its
nodes. This is important because it implies that the independence model
represented by a MAMP chain graph can be accounted for by some data generating
process that is partially observed and has selection bias. Finally, we modify
MAMP chain graphs so that they are closed under marginalization for Gaussian
probability distributions. This is a desirable feature because it guarantees
parsimonious models under marginalization.Comment: Changes from v1 to v2: Discussion section got extended. Changes from
v2 to v3: New Sections 3 and 5. Changes from v3 to v4: Example 4 added to
discussion section. Changes from v4 to v5: None. Changes from v5 to v6: Some
minor and major errors have been corrected. The latter include the
definitions of descending route and pairwise separation base, and the proofs
of Theorems 5 and
Non-Abelian gauge potentials in graphene bilayers
We study the effect of spatial modulations in the interlayer hopping of
graphene bilayers, such as those that arise upon shearing or twisting. We show
that their single-particle physics, characterized by charge accumulation and
recurrent formation of zero-energy bands as the pattern period L increases, is
governed by a non-Abelian gauge potential arising in the low-energy electronic
theory due to the coupling between layers. We show that such gauge-type
couplings give rise to a potential that, for certain discrete values of L,
spatially confines states at zero energy in particular regions of the Moir\'e
patterns. We also draw the connection between the recurrence of the flat
zero-energy bands and the non-Abelian character of the potential.Comment: 5 pages, 3 figures, published versio
n-ary algebras: a review with applications
This paper reviews the properties and applications of certain n-ary
generalizations of Lie algebras in a self-contained and unified way. These
generalizations are algebraic structures in which the two entries Lie bracket
has been replaced by a bracket with n entries. Each type of n-ary bracket
satisfies a specific characteristic identity which plays the r\^ole of the
Jacobi identity for Lie algebras. Particular attention will be paid to
generalized Lie algebras, which are defined by even multibrackets obtained by
antisymmetrizing the associative products of its n components and that satisfy
the generalized Jacobi identity (GJI), and to Filippov (or n-Lie) algebras,
which are defined by fully antisymmetric n-brackets that satisfy the Filippov
identity (FI). Three-Lie algebras have surfaced recently in multi-brane theory
in the context of the Bagger-Lambert-Gustavsson model. Because of this,
Filippov algebras will be discussed at length, including the cohomology
complexes that govern their central extensions and their deformations
(Whitehead's lemma extends to all semisimple n-Lie algebras). When the
skewsymmetry of the n-Lie algebra is relaxed, one is led the n-Leibniz
algebras. These will be discussed as well, since they underlie the
cohomological properties of n-Lie algebras.
The standard Poisson structure may also be extended to the n-ary case. We
shall review here the even generalized Poisson structures, whose GJI reproduces
the pattern of the generalized Lie algebras, and the Nambu-Poisson structures,
which satisfy the FI and determine Filippov algebras. Finally, the recent work
of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be
briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra
structure and on why the A_4 model may be formulated in terms of an ordinary
Lie algebra, and on its Nambu bracket generalization.Comment: Invited topical review for JPA Math.Theor. v2: minor changes,
references added. 120 pages, 318 reference
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