6,562 research outputs found
Mathematics of random growing interfaces
We establish a thermodynamic limit and Gaussian fluctuations for the height
and surface width of the random interface formed by the deposition of particles
on surfaces. The results hold for the standard ballistic deposition model as
well as the surface relaxation model in the off-lattice setting. The results
are proved with the aid of general limit theorems for stabilizing functionals
of marked Poisson point processes.Comment: 12 page
Growing Perfect Decagonal Quasicrystals by Local Rules
A local growth algorithm for a decagonal quasicrystal is presented. We show
that a perfect Penrose tiling (PPT) layer can be grown on a decapod tiling
layer by a three dimensional (3D) local rule growth. Once a PPT layer begins to
form on the upper layer, successive 2D PPT layers can be added on top resulting
in a perfect decagonal quasicrystalline structure in bulk with a point defect
only on the bottom surface layer. Our growth rule shows that an ideal
quasicrystal structure can be constructed by a local growth algorithm in 3D,
contrary to the necessity of non-local information for a 2D PPT growth.Comment: 4pages, 2figure
Radiating black hole solutions in Einstein-Gauss-Bonnet gravity
In this paper, we find some new exact solutions to the Einstein-Gauss-Bonnet
equations. First, we prove a theorem which allows us to find a large family of
solutions to the Einstein-Gauss-Bonnet gravity in -dimensions. This family
of solutions represents dynamic black holes and contains, as particular cases,
not only the recently found Vaidya-Einstein-Gauss-Bonnet black hole, but also
other physical solutions that we think are new, such as, the Gauss-Bonnet
versions of the Bonnor-Vaidya(de Sitter/anti-de Sitter) solution, a global
monopole and the Husain black holes. We also present a more general version of
this theorem in which less restrictive conditions on the energy-momentum tensor
are imposed. As an application of this theorem, we present the exact solution
describing a black hole radiating a charged null fluid in a Born-Infeld
nonlinear electrodynamics
One loop superstring effective actions and N=8 supergravity
In a previous article we have shown the existence of a new independent R^4
term, at one loop, in the type IIA and heterotic effective actions, after
reduction to four dimensions, besides the usual square of the Bel-Robinson
tensor. It had been shown that such a term could not be directly
supersymmetrized, but we showed that was possible after coupling to a scalar
chiral multiplet. In this article we study the extended (N=8)
supersymmetrization of this term, where no other coupling can be taken. We show
that such supersymmetrization cannot be achieved at the linearized level. This
is in conflict with the theory one gets after toroidal compactification of type
II superstrings being N=8 supersymmetric. We interpret this result in face of
the recent claim that perturbative supergravity cannot be decoupled from string
theory in d>=4, and N=8, d=4 supergravity is in the swampland.Comment: 28 pages, no figure
Strict inequalities of critical values in continuum percolation
We consider the supercritical finite-range random connection model where the
points of a homogeneous planar Poisson process are connected with
probability for a given . Performing percolation on the resulting
graph, we show that the critical probabilities for site and bond percolation
satisfy the strict inequality . We also show
that reducing the connection function strictly increases the critical
Poisson intensity. Finally, we deduce that performing a spreading
transformation on (thereby allowing connections over greater distances but
with lower probabilities, leaving average degrees unchanged) {\em strictly}
reduces the critical Poisson intensity. This is of practical relevance,
indicating that in many real networks it is in principle possible to exploit
the presence of spread-out, long range connections, to achieve connectivity at
a strictly lower density value.Comment: 38 pages, 8 figure
On a thermodynamically consistent modification of the Becker-Doering equations
Recently, Dreyer and Duderstadt have proposed a modification of the
Becker--Doering cluster equations which now have a nonconvex Lyapunov function.
We start with existence and uniqueness results for the modified equations. Next
we derive an explicit criterion for the existence of equilibrium states and
solve the minimization problem for the Lyapunov function. Finally, we discuss
the long time behavior in the case that equilibrium solutions do exist
Information Equation of State
Landauer's principle is applied to information in the universe. Once stars
began forming, the increasing proportion of matter at high stellar temperatures
compensated for the expanding universe to provide a near constant information
energy density. The information equation of state was close to the dark energy
value, w = -1, for a wide range of redshifts, 10> z >0.8, over one half of
cosmic time. A reasonable universe information bit content of only 10^87 bits
is sufficient for information energy to account for all dark energy. A time
varying equation of state with a direct link between dark energy and matter,
and linked to star formation in particular, is clearly relevant to the cosmic
coincidence problem.In answering the "Why now?" question we wonder "What next?"
as we expect the information equation of state to tend towards w = 0 in the
future.Comment: 10 pages, 2 figure
Degree Correlations in Random Geometric Graphs
Spatially embedded networks are important in several disciplines. The
prototypical spatial net- work we assume is the Random Geometric Graph of which
many properties are known. Here we present new results for the two-point degree
correlation function in terms of the clustering coefficient of the graphs for
two-dimensional space in particular, with extensions to arbitrary finite
dimension
Spacetime structure of static solutions in Gauss-Bonnet gravity: charged case
We have studied spacetime structures of static solutions in the
-dimensional Einstein-Gauss-Bonnet-Maxwell- system. Especially we
focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet
coefficient is non-negative and in
order to define the relevant vacuum state. Solutions have the
-dimensional Euclidean sub-manifold whose curvature is , or -1.
In Gauss-Bonnet gravity, solutions are classified into plus and minus branches.
In the plus branch all solutions have the same asymptotic structure as those in
general relativity with a negative cosmological constant. The charge affects a
central region of the spacetime. A branch singularity appears at the finite
radius for any mass parameter. There the Kretschmann invariant
behaves as , which is much milder than divergent behavior of
the central singularity in general relativity . Some charged
black hole solutions have no inner horizon in Gauss-Bonnet gravity. Although
there is a maximum mass for black hole solutions in the plus branch for
in the neutral case, no such maximum exists in the charged case. The solutions
in the plus branch with and have an "inner" black hole, and
inner and the "outer" black hole horizons. Considering the evolution of black
holes, we briefly discuss a classical discontinuous transition from one black
hole spacetime to another.Comment: 20 pages, 10 figure
Asymptotic behavior of the generalized Becker-D\"oring equations for general initial data
We prove the following asymptotic behavior for solutions to the generalized
Becker-D\"oring system for general initial data: under a detailed balance
assumption and in situations where density is conserved in time, there is a
critical density such that solutions with an initial density converge strongly to the equilibrium with density , and
solutions with initial density converge (in a weak sense) to
the equilibrium with density . This extends the previous knowledge that
this behavior happens under more restrictive conditions on the initial data.
The main tool is a new estimate on the tail of solutions with density below the
critical density
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