71,437 research outputs found
Discontinuous Transition in a Boundary Driven Contact Process
The contact process is a stochastic process which exhibits a continuous,
absorbing-state phase transition in the Directed Percolation (DP) universality
class. In this work, we consider a contact process with a bias in conjunction
with an active wall. This model exhibits waves of activity emanating from the
active wall and, when the system is supercritical, propagating indefinitely as
travelling (Fisher) waves. In the subcritical phase the activity is localised
near the wall. We study the phase transition numerically and show that certain
properties of the system, notably the wave velocity, are discontinuous across
the transition. Using a modified Fisher equation to model the system we
elucidate the mechanism by which the the discontinuity arises. Furthermore we
establish relations between properties of the travelling wave and DP critical
exponents.Comment: 14 pages, 9 figure
Cohomological characterization of vector bundles on multiprojective spaces
We show that Horrock's criterion for the splitting of vector bundles on
\PP^n can be extended to vector bundles on multiprojective spaces and to
smooth projective varieties with the weak CM property (see Definition 3.11). As
a main tool we use the theory of -blocks and Beilinson's type spectral
sequences. Cohomological characterizations of vector bundles are also showed
Gauge Field Emergence from Kalb-Ramond Localization
A new mechanism, valid for any smooth version of the Randall-Sundrum model,
of getting localized massless vector field on the brane is described here. This
is obtained by dimensional reduction of a five dimension massive two form, or
Kalb-Ramond field, giving a Kalb-Ramond and an emergent vector field in four
dimensions. A geometrical coupling with the Ricci scalar is proposed and the
coupling constant is fixed such that the components of the fields are
localized. The solution is obtained by decomposing the fields in transversal
and longitudinal parts and showing that this give decoupled equations of motion
for the transverse vector and KR fields in four dimensions. We also prove some
identities satisfied by the transverse components of the fields. With this is
possible to fix the coupling constant in a way that a localized zero mode for
both components on the brane is obtained. Then, all the above results are
generalized to the massive form field. It is also shown that in general an
effective and forms can not be localized on the brane and we have
to sort one of them to localize. Therefore, we can not have a vector and a
scalar field localized by dimensional reduction of the five dimensional vector
field. In fact we find the expression which determines what forms
will give rise to both fields localized. For , as expected, this is valid
only for the KR field.Comment: Improved version. Some factors corrected and definitions added. The
main results continue vali
New Analytical Solutions for Bosonic Field Trapping in Thick Branes
New analytical solutions for gravity, scalar and vector field localization in
Randall-Sundrum(RS) models are found. A smooth version of the warp factor with
an associated function inside the walls () is
defined, leading to an associated equation and physical constraints on the
continuity and smoothness of the background resulting in a new space of
analytical solutions. We solve this associated equation analytically for the
parabolic and P\"oschl-Teller potentials and analyze the spectrum of resonances
for these fields. By using the boundary conditions we are able to show that,
for any of these solutions, the density probability for finding a massive mode
in the membrane has a universal behavior for small values of mass given by
. As a
consequence, the form of the leading order correction, for example, to the
Newton's law is general and does not depend on the potential used. At the end
we also discuss why complications arises when we try to use the method to find
analytical solutions to the fermion case.Comment: 11 pages, 4 figures; v2: extended version; references and section
added; title, conclusions and abstract change
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