889 research outputs found
Einstein-Cartan theory as a theory of defects in space-time
The Einstein-Cartan theory of gravitation and the classical theory of defects
in an elastic medium are presented and compared. The former is an extension of
general relativity and refers to four-dimensional space-time, while we
introduce the latter as a description of the equilibrium state of a
three-dimensional continuum. Despite these important differences, an analogy is
built on their common geometrical foundations, and it is shown that a
space-time with curvature and torsion can be considered as a state of a
four-dimensional continuum containing defects. This formal analogy is useful
for illustrating the geometrical concept of torsion by applying it to concrete
physical problems. Moreover, the presentation of these theories using a common
geometrical basis allows a deeper understanding of their foundations.Comment: 18 pages, 7 EPS figures, RevTeX4, to appear in the American Journal
of Physics, revised version with typos correcte
Scaling in a continuous time model for biological aging
In this paper we consider a generalization to the asexual version of the
Penna model for biological aging, where we take a continuous time limit. The
genotype associated to each individual is an interval of real numbers over
which Dirac --functions are defined, representing genetically
programmed diseases to be switched on at defined ages of the individual life.
We discuss two different continuous limits for the evolution equation and two
different mutation protocols, to be implemented during reproduction. Exact
stationary solutions are obtained and scaling properties are discussed.Comment: 10 pages, 6 figure
Von-Neumann's and related scaling laws in Rock-Paper-Scissors type models
We introduce a family of Rock-Paper-Scissors type models with symmetry
( is the number of species) and we show that it has a very rich structure
with many completely different phases. We study realizations which lead to the
formation of domains, where individuals of one or more species coexist,
separated by interfaces whose (average) dynamics is curvature driven. This type
of behavior, which might be relevant for the development of biological
complexity, leads to an interface network evolution and pattern formation
similar to the ones of several other nonlinear systems in condensed matter and
cosmology.Comment: 5 pages, 6 figures, published versio
A symplectic realization of the Volterra lattice
We examine the multiple Hamiltonian structure and construct a symplectic
realization of the Volterra model. We rediscover the hierarchy of invariants,
Poisson brackets and master symmetries via the use of a recursion operator. The
rational Volterra bracket is obtained using a negative recursion operator.Comment: 8 page
Urban Blasting Vibrations: Case Histories of Vibration Monitoring in New York City
This paper summarizes the monitoring experienced gained from several urban rock blasting projects in New York City and one just beyond the city limits. The majority of the experience was gained on the new South Ferry Terminal Structural Box project that included a new subway terminal station and section of tunnel on the number 1-line subway located in Battery Park in Lower Manhattan. The paper will review lessons learned and the limitations of using “off-the-shelf” seismographs for near-field blast monitoring. We allege that standard and widely available seismograph equipment is not generally utilized to its fullest potential, and that alternative forms of monitoring are often overlooked in favor of criteria based on peak particle velocity alone. The new South Ferry Terminal tunnel and station comprised a 1,300 ft long excavation varying in width from 25 to 60 ft and 20 to 50 ft in depth. The excavation necessitated blasting adjacent to and underneath existing subway lines at several locations. A separate project currently underway and at a site located north of New York City, is also mentioned due to its wider variation of blast parameters relative to the more typical “urban” blast projects of New York City
Spontaneous emergence of spatial patterns ina a predator-prey model
We present studies for an individual based model of three interacting
populations whose individuals are mobile in a 2D-lattice. We focus on the
pattern formation in the spatial distributions of the populations. Also
relevant is the relationship between pattern formation and features of the
populations' time series. Our model displays travelling waves solutions,
clustering and uniform distributions, all related to the parameters values. We
also observed that the regeneration rate, the parameter associated to the
primary level of trophic chain, the plants, regulated the presence of
predators, as well as the type of spatial configuration.Comment: 17 pages and 15 figure
Synchronization and Stability in Noisy Population Dynamics
We study the stability and synchronization of predator-prey populations
subjected to noise. The system is described by patches of local populations
coupled by migration and predation over a neighborhood. When a single patch is
considered, random perturbations tend to destabilize the populations, leading
to extinction. If the number of patches is small, stabilization in the presence
of noise is maintained at the expense of synchronization. As the number of
patches increases, both the stability and the synchrony among patches increase.
However, a residual asynchrony, large compared with the noise amplitude, seems
to persist even in the limit of infinite number of patches. Therefore, the
mechanism of stabilization by asynchrony recently proposed by R. Abta et. al.,
combining noise, diffusion and nonlinearities, seems to be more general than
first proposed.Comment: 3 pages, 3 figures. To appear in Phys. Rev.
Phase transition in a spatial Lotka-Volterra model
Spatial evolution is investigated in a simulated system of nine competing and
mutating bacterium strains, which mimics the biochemical war among bacteria
capable of producing two different bacteriocins (toxins) at most. Random
sequential dynamics on a square lattice is governed by very symmetrical
transition rules for neighborhood invasion of sensitive strains by killers,
killers by resistants, and resistants by by sensitives. The community of the
nine possible toxicity/resistance types undergoes a critical phase transition
as the uniform transmutation rates between the types decreases below a critical
value above which all the nine types of strain coexist with equal
frequencies. Passing the critical mutation rate from above, the system
collapses into one of the three topologically identical states, each consisting
of three strain types. Of the three final states each accrues with equal
probability and all three maintain themselves in a self-organizing polydomain
structure via cyclic invasions. Our Monte Carlo simulations support that this
symmetry breaking transition belongs to the universality class of the
three-state Potts model.Comment: 4 page
Nonlocal Electrodynamics of Rotating Systems
The nonlocal electrodynamics of uniformly rotating systems is presented and
its predictions are discussed. In this case, due to paucity of experimental
data, the nonlocal theory cannot be directly confronted with observation at
present. The approach adopted here is therefore based on the correspondence
principle: the nonrelativistic quantum physics of electrons in circular
"orbits" is studied. The helicity dependence of the photoeffect from the
circular states of atomic hydrogen is explored as well as the resonant
absorption of a photon by an electron in a circular "orbit" about a uniform
magnetic field. Qualitative agreement of the predictions of the classical
nonlocal electrodynamics with quantum-mechanical results is demonstrated in the
correspondence regime.Comment: 23 pages, no figures, submitted for publicatio
First and second order optimality conditions for optimal control problems of state constrained integral equations
This paper deals with optimal control problems of integral equations, with
initial-final and running state constraints. The order of a running state
constraint is defined in the setting of integral dynamics, and we work here
with constraints of arbitrary high orders. First and second-order necessary
conditions of optimality are obtained, as well as second-order sufficient
conditions
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