27,695 research outputs found
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
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
Molecular dynamics simulations of ballistic annihilation
Using event-driven molecular dynamics we study one- and two-dimensional
ballistic annihilation. We estimate exponents and that describe
the long-time decay of the number of particles () and of
their typical velocity (). To a good accuracy our results
confirm the scaling relation . In the two-dimensional case our
results are in a good agreement with those obtained from the Boltzmann kinetic
theory.Comment: 4 pages; some changes; Physical Review E (in press
Aggregation in a mixture of Brownian and ballistic wandering particles
In this paper, we analyze the scaling properties of a model that has as
limiting cases the diffusion-limited aggregation (DLA) and the ballistic
aggregation (BA) models. This model allows us to control the radial and angular
scaling of the patterns, as well as, their gap distributions. The particles
added to the cluster can follow either ballistic trajectories, with probability
, or random ones, with probability . The patterns were
characterized through several quantities, including those related to the radial
and angular scaling. The fractal dimension as a function of
continuously increases from (DLA dimensionality) for
to (BA dimensionality) for . However, the
lacunarity and the active zone width exhibt a distinct behavior: they are
convex functions of with a maximum at . Through the
analysis of the angular correlation function, we found that the difference
between the radial and angular exponents decreases continuously with increasing
and rapidly vanishes for , in agreement with recent
results concerning the asymptotic scaling of DLA clusters.Comment: 7 pages, 6 figures. accepted for publication on PR
Activated sludge monitoring of a wastewater treatment plant using image analysis and partial least squares
The wastewater treatment plant activated sludge is a complex ecosystem mainly of
bacteria and protozoa. Bacteria agglomerate as settleable robust aggregates leading
to low organic matter and turbidity final effluents. However, when the operating
conditions are not perfect some malfunctions may occur leading to bulking
problems. Classical methods to survey the bacteria aggregation and contents
resided on manual counting which are, rather tiring, imprecise and time-consuming
urging the development of faster automated image analysis methods. Therefore, the
prime objective of this work resided on surveying the activated sludge filamentous
bacteria and aggregates contents and morphology, and establish relationships
between the biomass and some operating parameters by multivariable statistical
techniques.
One of the main conclusions of this work resided on the determination of a
filamentous, rather than a zoogleal, bulking problem in the course of this survey.
This conclusion could be withdrawn by the strong resemblance between the sludge
volume index and the filaments/aggregates contents ratio behaviour throughout the
experiment time and by the high filamentous bacteria/suspended solids ratio (above
10000 mm/mg) which clearly indicates the existence of a filamentous bulking
problem. Furthermore, an in-depth statistical analysis revealed that the filamentous
bacteria/suspended solids ratio parameter may be used, at some extent, to monitor
the SVI behaviour in a wastewater treatment plant aeration tank, whereas the
suspended solids could be satisfactory monitored by the total aggregates area
parameter.
However, these results refer only to a wastewater treatment plant experiencing a
bulking phenomenon and further studies should be developed in normal plants
Evaluating matrix elements relevant to some Lorenz violating operators
Carlson, Carone and Lebed have derived the Feynman rules for a consistent
formulation of noncommutative QCD. The results they obtained were used to
constrain the noncommutativity parameter in Lorentz violating noncommutative
field theories. However, their constraint depended upon an estimate of the
matrix element of the quark level operator (gamma.p - m) in a nucleon. In this
paper we calculate the matrix element of (gamma.p - m), using a variety of
confinement potential models. Our results are within an order of magnitude
agreement with the estimate made by Carlson et al. The constraints placed on
the noncommutativity parameter were very strong, and are still quite severe
even if weakened by an order of magnitude.Comment: 4 pages, 3 figures, RevTex, minor change
Activated sludge monitoring of a wastewater treatment plant using image analysis and partial least squares regression
The biomass present in awastewater treatment plantwas surveyed and their morphological properties related with operating parameters such
as the total suspended solids (TSS) and sludge volume index (SVI). For that purpose image analysis was used to provide the morphological
data subsequently treated by partial least squares regression (PLS) multivariable statistical technique. The results denoted the existence of a
severe bulking problem of non-zoogleal nature and the PLS analysis revealed a strong relationship between the TSS and the total aggregates
area as well as a close correlation between the filamentous bacteria per suspended solids ratio and the SVI.Fundação para a Ciência e a Tecnologia (FCT) – PRAXIS XXI/BD/20325/99
- …