34,918 research outputs found
Self-dual Hopfions
We construct static and time-dependent exact soliton solutions with
non-trivial Hopf topological charge for a field theory in 3+1 dimensions with
the target space being the two dimensional sphere S**2. The model considered is
a reduction of the so-called extended Skyrme-Faddeev theory by the removal of
the quadratic term in derivatives of the fields. The solutions are constructed
using an ansatz based on the conformal and target space symmetries. The
solutions are said self-dual because they solve first order differential
equations which together with some conditions on the coupling constants, imply
the second order equations of motion. The solutions belong to a sub-sector of
the theory with an infinite number of local conserved currents. The equation
for the profile function of the ansatz corresponds to the Bogomolny equation
for the sine-Gordon model.Comment: plain latex, no figures, 23 page
A remark on the asymptotic form of BPS multi-dyon solutions and their conserved charges
We evaluate the gauge invariant, dynamically conserved charges, recently
obtained from the integral form of the Yang-Mills equations, for the BPS
multi-dyon solutions of a Yang-Mills-Higgs theory associated to any compact
semi-simple gauge group G. Those charges are shown to correspond to the
eigenvalues of the next-to-leading term of the asymptotic form of the Higgs
field at spatial infinity, and so coinciding with the usual topological charges
of those solutions. Such results show that many of the topological charges
considered in the literature are in fact dynamical charges, which conservation
follows from the global properties of classical Yang-Mills theories encoded
into their integral dynamical equations. The conservation of those charges can
not be obtained from the differential form of Yang-Mills equations.Comment: Version to be published in JHEP, Journal of High Energy Physics (19
pages, no figures, some examples added
Integrable theories and loop spaces: fundamentals, applications and new developments
We review our proposal to generalize the standard two-dimensional flatness
construction of Lax-Zakharov-Shabat to relativistic field theories in d+1
dimensions. The fundamentals from the theory of connections on loop spaces are
presented and clarified. These ideas are exposed using mathematical tools
familiar to physicists. We exhibit recent and new results that relate the
locality of the loop space curvature to the diffeomorphism invariance of the
loop space holonomy. These result are used to show that the holonomy is abelian
if the holonomy is diffeomorphism invariant.
These results justify in part and set the limitations of the local
implementations of the approach which has been worked out in the last decade.
We highlight very interesting applications like the construction and the
solution of an integrable four dimensional field theory with Hopf solitons, and
new integrability conditions which generalize BPS equations to systems such as
Skyrme theories. Applications of these ideas leading to new constructions are
implemented in theories that admit volume preserving diffeomorphisms of the
target space as symmetries. Applications to physically relevant systems like
Yang Mills theories are summarized. We also discuss other possibilities that
have not yet been explored.Comment: 64 pages, 8 figure
A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity
We consider a one dimensional transport model with nonlocal velocity given by
the Hilbert transform and develop a global well-posedness theory of probability
measure solutions. Both the viscous and non-viscous cases are analyzed. Both in
original and in self-similar variables, we express the corresponding equations
as gradient flows with respect to a free energy functional including a singular
logarithmic interaction potential. Existence, uniqueness, self-similar
asymptotic behavior and inviscid limit of solutions are obtained in the space
of probability measures with finite second
moments, without any smallness condition. Our results are based on the abstract
gradient flow theory developed in \cite{Ambrosio}. An important byproduct of
our results is that there is a unique, up to invariance and translations,
global in time self-similar solution with initial data in
, which was already obtained in
\textrm{\cite{Deslippe,Biler-Karch}} by different methods. Moreover, this
self-similar solution attracts all the dynamics in self-similar variables. The
crucial monotonicity property of the transport between measures in one
dimension allows to show that the singular logarithmic potential energy is
displacement convex. We also extend the results to gradient flow equations with
negative power-law locally integrable interaction potentials
Mean-field analysis of the majority-vote model broken-ergodicity steady state
We study analytically a variant of the one-dimensional majority-vote model in
which the individual retains its opinion in case there is a tie among the
neighbors' opinions. The individuals are fixed in the sites of a ring of size
and can interact with their nearest neighbors only. The interesting feature
of this model is that it exhibits an infinity of spatially heterogeneous
absorbing configurations for whose statistical properties we
probe analytically using a mean-field framework based on the decomposition of
the -site joint probability distribution into the -contiguous-site joint
distributions, the so-called -site approximation. To describe the
broken-ergodicity steady state of the model we solve analytically the
mean-field dynamic equations for arbitrary time in the cases n=3 and 4. The
asymptotic limit reveals the mapping between the statistical
properties of the random initial configurations and those of the final
absorbing configurations. For the pair approximation () we derive that
mapping using a trick that avoids solving the full dynamics. Most remarkably,
we find that the predictions of the 4-site approximation reduce to those of the
3-site in the case of expectations involving three contiguous sites. In
addition, those expectations fit the Monte Carlo data perfectly and so we
conjecture that they are in fact the exact expectations for the one-dimensional
majority-vote model
Crystallization, data collection and data processing of maltose-binding protein (MalE) from the phytopathogen Xanthomonas axonopodis pv. citri
Maltose-binding protein is the periplasmic component of the ABC transporter
responsible for the uptake of maltose/maltodextrins. The Xanthomonas axonopodis
pv. citri maltose-binding protein MalE has been crystallized at 293 Kusing
the hanging-drop vapour-diffusion method. The crystal belonged to the
primitive hexagonal space group P6_122, with unit-cell parameters a = 123.59,
b = 123.59, c = 304.20 Å, and contained two molecules in the asymetric unit. It
diffracted to 2.24 Å resolution
The structures underlying soliton solutions in integrable hierarchies
We point out that a common feature of integrable hierarchies presenting
soliton solutions is the existence of some special ``vacuum solutions'' such
that the Lax operators evaluated on them, lie in some abelian subalgebra of the
associated Kac-Moody algebra. The soliton solutions are constructed out of
those ``vacuum solitons'' by the dressing transformation procedure.Comment: Talk given at the I Latin American Symposium on High Energy Physics,
I SILAFAE, Merida, Mexico, November/96, 5 pages, LaTeX, needs aipproc.tex,
aipproc.sty, aipproc.cls, available from
ftp://ftp.aip.org/ems/tex/macros/proceedings/6x9
On the large-scale angular distribution of short-Gamma ray bursts
We investigate the large-scale angular distribution of the short-Gamma ray
bursts (SGRBs) from BATSE experiment, using a new coordinates-free method. The
analyses performed take into account the angular correlations induced by the
non-uniform sky exposure during the experiment, and the uncertainty in the
measured angular coordinates. Comparising the large-scale angular correlations
from the data with those expected from simulations using the exposure function
we find similar features. Additionally, confronting the large-angle
correlations computed from the data with those obtained from simulated maps
produced under the assumption of statistical isotropy we found that they are
incompatible at 95% confidence level. However, such differences are restricted
to the angular scales 36o - 45o, which are likely to be due to the non-uniform
sky exposure. This result strongly suggests that the set of SGRBs from BATSE
are intrinsically isotropic. Moreover, we also investigated a possible
large-angle correlation of these data with the supergalactic plane. No evidence
for such large-scale anisotropy was found.Comment: Accepted for publication in The Astrophysical Journal, 6 pages, 3
figure
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