1,024 research outputs found
A STRAINED SPACE-TIME TO EXPLAIN THE LARGE SCALEPROPERTIES OF THE UNIVERSE
Space-time can be treated as a four-dimensional material continuum. The corresponding generally curved manifold can be thought of as having been obtained, by continuous deformation, from a four-dimensional Euclidean manifold. In a three-dimensional ordinary situation such a deformation process would lead to strain in the manifold. Strain in turn may be read as half the di®erence between the actual metric tensor and the Euclidean metric tensor of the initial unstrained manifold. On the other side we know that an ordinary material would react to the attempt to introduce strain giving rise to internal stresses and one would have correspondingly a deformation energy term. Assuming the conditions of linear elasticity hold, the deformation energy is easily written in terms of the strain tensor. The Einstein-Hilbert action is generalized to include the new deformation energy term. The new action for space-time has been applied to a Friedmann-Lemaitre- Robertson-Walker universe filled with dust and radiation. The accelerated expansion is recovered, then the theory has been put through four cosmological tests: primordial isotopic abundances from Big Bang Nucleosynthesis; Acoustic Scale of the CMB; Large Scale Structure formation; luminosity/redshift relation for type Ia supernovae. The result is satisfying and has allowed to evaluate the parameters of the theor
Generalized Tomonaga-Schwinger equation from the Hadamard formula
A generalized Tomonaga--Schwinger equation, holding on the entire boundary of
a {\em finite} spacetime region, has recently been considered as a tool for
studying particle scattering amplitudes in background-independent quantum field
theory. The equation has been derived using lattice techniques under
assumptions on the existence of the continuum limit. Here I show that in the
context of continuous euclidean field theory the equation can be directly
derived from the functional integral formalism, using a technique based on
Hadamard's formula for the variation of the propagator.Comment: 11 pages, no figure
Vector field theories in cosmology
Recently proposed theories based on the cosmic presence of a vectorial field
are compared and contrasted. In particular the so called Einstein aether theory
is discussed in parallel with a recent proposal of a strained space-time theory
(Cosmic Defect theory). We show that the latter fits reasonably well the cosmic
observed data with only one, or at most two, adjustable parameters, whilst
other vector theories use much more. The Newtonian limits are also compared.
Finally we show that the CD theory may be considered as a special case of the
aether theories, corresponding to a more compact and consistent paradigm.Comment: 19 pages, 1 figure, to appear on Phys. Rev.
Synchronization of Chaotic Oscillators due to Common Delay Time Modulation
We have found a synchronization behavior between two identical chaotic
systems^M when their delay times are modulated by a common irregular signal. ^M
This phenomenon is demonstrated both in two identical chaotic maps whose
delay times are driven by a common^M chaotic or random signal and in two
identical chaotic oscillators whose delay times are driven by^M a signal of
another chaotic oscillator. We analyze the phenomenon by using^M the Lyapunov
exponents and discuss it in relation with generalized synchronization.^MComment: 5 pages, 4 figures (to be published in PRE
Influence of local carrying capacity restrictions on stochastic predator-prey models
We study a stochastic lattice predator-prey system by means of Monte Carlo
simulations that do not impose any restrictions on the number of particles per
site, and discuss the similarities and differences of our results with those
obtained for site-restricted model variants. In accord with the classic
Lotka-Volterra mean-field description, both species always coexist in two
dimensions. Yet competing activity fronts generate complex, correlated
spatio-temporal structures. As a consequence, finite systems display transient
erratic population oscillations with characteristic frequencies that are
renormalized by fluctuations. For large reaction rates, when the processes are
rendered more local, these oscillations are suppressed. In contrast with
site-restricted predator-prey model, we observe species coexistence also in one
dimension. In addition, we report results on the steady-state prey age
distribution.Comment: Latex, IOP style, 17 pages, 9 figures included, related movies
available at http://www.phys.vt.edu/~tauber/PredatorPrey/movies
Extinction in Lotka-Volterra model
Competitive birth-death processes often exhibit an oscillatory behavior. We
investigate a particular case where the oscillation cycles are marginally
stable on the mean-field level. An iconic example of such a system is the
Lotka-Volterra model of predator-prey competition. Fluctuation effects due to
discreteness of the populations destroy the mean-field stability and eventually
drive the system toward extinction of one or both species. We show that the
corresponding extinction time scales as a certain power-law of the population
sizes. This behavior should be contrasted with the extinction of models stable
in the mean-field approximation. In the latter case the extinction time scales
exponentially with size.Comment: 11 pages, 17 figure
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
Competition Among Companies: Coexistence and Extinction
We study a spatially homogeneous model of a market where several agents or
companies compete for a wealth resource. In analogy with ecological systems the
simplest case of such models shows a kind of "competitive exclusion" principle.
However, the inclusion of terms corresponding for instance to "company
efficiency" or to (ecological) "intracompetition" shows that, if the associated
parameter overcome certain threshold values, the meaning of "strong" and "weak"
companies should be redefined. Also, by adequately adjusting such a parameter,
a company can induce the "extinction" of one or more of its competitors.Comment: 5 pages, 3 figures include
On Foundation of the Generalized Nambu Mechanics
We outline the basic principles of canonical formalism for the Nambu
mechanics---a generalization of Hamiltonian mechanics proposed by Yoichiro
Nambu in 1973. It is based on the notion of Nambu bracket which generalizes the
Poisson bracket to the multiple operation of higher order on
classical observables and is described by Hambu-Hamilton equations of motion
given by Hamiltonians. We introduce the fundamental identity for the
Nambu bracket which replaces Jacobi identity as a consistency condition for the
dynamics. We show that Nambu structure of given order defines a family of
subordinated structures of lower order, including the Poisson structure,
satisfying certain matching conditions. We introduce analogs of action from and
principle of the least action for the Nambu mechanics and show how dynamics of
loops (-dimensional objects) naturally appears in this formalism. We
discuss several approaches to the quantization problem and present explicit
representation of Nambu-Heisenberg commutation relation for case. We
emphasize the role higher order algebraic operations and mathematical
structures related with them play in passing from Hamilton's to Nambu's
dynamical picture.Comment: 27 page
Fluctuations and Correlations in Lattice Models for Predator-Prey Interaction
Including spatial structure and stochastic noise invalidates the classical
Lotka-Volterra picture of stable regular population cycles emerging in models
for predator-prey interactions. Growth-limiting terms for the prey induce a
continuous extinction threshold for the predator population whose critical
properties are in the directed percolation universality class. Here, we discuss
the robustness of this scenario by considering an ecologically inspired
stochastic lattice predator-prey model variant where the predation process
includes next-nearest-neighbor interactions. We find that the corresponding
stochastic model reproduces the above scenario in dimensions 1< d \leq 4, in
contrast with mean-field theory which predicts a first-order phase transition.
However, the mean-field features are recovered upon allowing for
nearest-neighbor particle exchange processes, provided these are sufficiently
fast.Comment: 5 pages, 4 figures, 2-column revtex4 format. Emphasis on the lattice
predator-prey model with next-nearest-neighbor interaction (Rapid
Communication in PRE
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