420 research outputs found
Explaining the elongated shape of 'Oumuamua by the Eikonal abrasion model
The photometry of the minor body with extrasolar origin (1I/2017 U1)
'Oumuamua revealed an unprecedented shape: Meech et al. (2017) reported a shape
elongation b/a close to 1/10, which calls for theoretical explanation. Here we
show that the abrasion of a primordial asteroid by a huge number of tiny
particles ultimately leads to such elongated shape. The model (called the
Eikonal equation) predicting this outcome was already suggested in Domokos et
al. (2009) to play an important role in the evolution of asteroid shapes.Comment: Accepted by the Research Notes of the AA
Baryon Number-Induced Chern-Simons Couplings of Vector and Axial-Vector Mesons in Holographic QCD
We show that holographic models of QCD predict the presence of a Chern-Simons
coupling between vector and axial-vector mesons at finite baryon density. In
the AdS/CFT dictionary, the coefficient of this coupling is proportional to the
baryon number density, and is fixed uniquely in the five-dimensional
holographic dual by anomalies in the flavor currents. For the lightest mesons,
the coupling mixes transverse and polarization states. At
sufficiently large baryon number densities, it produces an instability, which
causes the and mesons to condense in a state breaking both
rotational and translational invariance.Comment: 4 page
Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds
We find sharp bounds for the norm inequality on a Pseudo-hermitian manifold,
where the L^2 norm of all second derivatives of the function involving
horizontal derivatives is controlled by the L^2 norm of the sub-Laplacian.
Perturbation allows us to get a-priori bounds for solutions to sub-elliptic PDE
in non-divergence form with bounded measurable coefficients. The method of
proof is through a Bochner technique. The Heisenberg group is seen to be en
extremal manifold for our inequality in the class of manifolds whose Ricci
curvature is non-negative.Comment: 13 page
A topological classification of convex bodies
The shape of homogeneous, generic, smooth convex bodies as described by the
Euclidean distance with nondegenerate critical points, measured from the center
of mass represents a rather restricted class M_C of Morse-Smale functions on
S^2. Here we show that even M_C exhibits the complexity known for general
Morse-Smale functions on S^2 by exhausting all combinatorial possibilities:
every 2-colored quadrangulation of the sphere is isomorphic to a suitably
represented Morse-Smale complex associated with a function in M_C (and vice
versa). We prove our claim by an inductive algorithm, starting from the path
graph P_2 and generating convex bodies corresponding to quadrangulations with
increasing number of vertices by performing each combinatorially possible
vertex splitting by a convexity-preserving local manipulation of the surface.
Since convex bodies carrying Morse-Smale complexes isomorphic to P_2 exist,
this algorithm not only proves our claim but also generalizes the known
classification scheme in [36]. Our expansion algorithm is essentially the dual
procedure to the algorithm presented by Edelsbrunner et al. in [21], producing
a hierarchy of increasingly coarse Morse-Smale complexes. We point out
applications to pebble shapes.Comment: 25 pages, 10 figure
Formation of sharp edges and planar areas of asteroids by polyhedral abrasion
While the number of asteroids with known shapes has drastically increased
over the past few years, little is known on the the time-evolution of shapes
and the underlying physical processes. Here we propose an averaged abrasion
model based on micro-collisons, accounting for asteroids not necessarily
evolving toward regular spheroids, rather (depending on the fall-back rate of
ejecta) following an alternative path, thus confirming photometry-derived
features, e.g. existence of large, relatively flat areas separated by edges. We
show that our model is realistic, since the bulk of the collisions falls into
this category.Comment: 17 pages, 3 figures, accepted by Astrophysical Journa
Lepton pairs from thermal mesons
We study the net dielectron production rates from an ensemble of thermal
mesons, using an effective Lagrangian to model their interaction. The coupling
between the electromagnetic and the hadronic sectors is done through the vector
meson dominance approach. For the first time, a complete set of light mesons is
considered. We include contributions from decays of the type
V~(PS)~~PS~(V)~+~, where V is a vector meson and PS is a
pseudoscalar, as well as those from binary reactions PS~+~PS, V~+~V, and
V~+~PS~. Direct decays of the type V~
are included and shown to be important. We find that the dielectron invariant
mass spectrum naturally divides in distinct regions: in the low mass domain the
decays from vector and pseudoscalar mesons form the dominant contribution. The
pion--pion annihilation and direct decays then pick up and form the leading
signal in an invariant mass region that includes the complex
and extends up to the . Above invariant mass ~1~GeV other
two-body reactions take over as the prominent mechanisms for lepton pair
generation. These facts will have quantitative bearing on the eventual
identification of the quark--gluon plasma.Comment: In ReVTeX 3.0, 9 figs. available from above email address. McGill
93/8, TPI-MINN-93/19-
On the equilibria of finely discretized curves and surfaces
Our goal is to identify the type and number of static equilibrium points of
solids arising from fine, equidistant -discretrizations of smooth, convex
surfaces. We assume uniform gravity and a frictionless, horizontal, planar
support. We show that as approaches infinity these numbers fluctuate around
specific values which we call the imaginary equilibrium indices associated with
the approximated smooth surface. We derive simple formulae for these numbers in
terms of the principal curvatures and the radial distances of the equilibrium
points of the solid from its center of gravity. Our results are illustrated on
a discretized ellipsoid and match well the observations on natural pebble
surfaces.Comment: 21 pages, 2 figure
Quantum Deformations of Space-Time Symmetries with Mass-Like Deformation Parameter
The difficulties with the measurability of classical space-time distances are
considered. We outline the framework of quantum deformations of D=4 space-time
symmetries with dimensionfull deformation parameter, and present some recent
results.Comment: 4 pages, LaTeX, uses file stwol.sty, to be published in the
Proceedings of XXXII International Rochester Conference in High Energy
Physics (Warsaw, 24.07-31.07 1996
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