152,516 research outputs found
Identification of criticality in neuronal avalanches: I. A theoretical investigation of the non-driven case
In this paper, we study a simple model of a purely excitatory neural network that, by construction, operates at a critical point. This model allows us to consider various markers of criticality and illustrate how they should perform in a finite-size system. By calculating the exact distribution of avalanche sizes, we are able to show that, over a limited range of avalanche sizes which we precisely identify, the distribution has scale free properties but is not a power law. This suggests that it would be inappropriate to dismiss a system as not being critical purely based on an inability to rigorously fit a power law distribution as has been recently advocated. In assessing whether a system, especially a finite-size one, is critical it is thus important to consider other possible markers. We illustrate
one of these by showing the divergence of susceptibility as the critical point of the system is approached. Finally, we provide evidence that power laws may underlie other observables of the system that may be more amenable to robust experimental assessment
Approximation of the potential in scalar field dark energy models
We study the nature of potentials in scalar field based models for dark
energy - with both canonical and noncanonical kinetic terms. We calculate
numerically, and using an analytic approximation around ,
potentials for models with constant equation-of-state parameter, . We
find that for a wide range of models with canonical and noncanonical kinetic
terms there is a simple approximation for the potential that holds when the
scale factor is in the range . We discuss how this
form of the potential can also be used to represent models with non-constant
and, hence, how it could be used in reconstruction from cosmological
data.Comment: 17 pages, 6 figures. Accepted by Phys. Rev.
Approximated Lax Pairs for the Reduced Order Integration of Nonlinear Evolution Equations
A reduced-order model algorithm, called ALP, is proposed to solve nonlinear
evolution partial differential equations. It is based on approximations of
generalized Lax pairs. Contrary to other reduced-order methods, like Proper
Orthogonal Decomposition, the basis on which the solution is searched for
evolves in time according to a dynamics specific to the problem. It is
therefore well-suited to solving problems with progressive front or wave
propagation. Another difference with other reduced-order methods is that it is
not based on an off-line / on-line strategy. Numerical examples are shown for
the linear advection, KdV and FKPP equations, in one and two dimensions
Reduced-Order Modeling based on Approximated Lax Pairs
A reduced-order model algorithm, based on approximations of Lax pairs, is
proposed to solve nonlinear evolution partial differential equations. Contrary
to other reduced-order methods, like Proper Orthogonal Decomposition, the space
where the solution is searched for evolves according to a dynamics specific to
the problem. It is therefore well-suited to solving problems with progressive
waves or front propagation. Numerical examples are shown for the KdV and FKPP
(nonlinear reaction diffusion) equations, in one and two dimensions
Continuous variable entanglement dynamics in structured reservoirs
We address the evolution of entanglement in bimodal continuous variable
quantum systems interacting with two independent structured reservoirs. We
derive an analytic expression for the entanglement of formation without
performing the Markov and the secular approximations and study in details the
entanglement dynamics for various types of structured reservoirs and for
different reservoir temperatures, assuming the two modes initially excited in a
twin-beam state. Our analytic solution allows us to identify three dynamical
regimes characterized by different behaviors of the entanglement: the
entanglement sudden death, the non-Markovian revival and the non-secular
revival regimes. Remarkably, we find that, contrarily to the Markovian case,
the short-time system-reservoir correlations in some cases destroy quickly the
initial entanglement even at zero temperature.Comment: 12 pages, 8 figure
Continuous approximations of a class of piece-wise continuous systems
In this paper we provide a rigorous mathematical foundation for continuous
approximations of a class of systems with piece-wise continuous functions. By
using techniques from the theory of differential inclusions, the underlying
piece-wise functions can be locally or globally approximated. The approximation
results can be used to model piece-wise continuous-time dynamical systems of
integer or fractional-order. In this way, by overcoming the lack of numerical
methods for diffrential equations of fractional-order with discontinuous
right-hand side, unattainable procedures for systems modeled by this kind of
equations, such as chaos control, synchronization, anticontrol and many others,
can be easily implemented. Several examples are presented and three comparative
applications are studied.Comment: IJBC, accepted (examples revised
ROAM: a Radial-basis-function Optimization Approximation Method for diagnosing the three-dimensional coronal magnetic field
The Coronal Multichannel Polarimeter (CoMP) routinely performs coronal
polarimetric measurements using the Fe XIII 10747 and 10798 lines,
which are sensitive to the coronal magnetic field. However, inverting such
polarimetric measurements into magnetic field data is a difficult task because
the corona is optically thin at these wavelengths and the observed signal is
therefore the integrated emission of all the plasma along the line of sight. To
overcome this difficulty, we take on a new approach that combines a
parameterized 3D magnetic field model with forward modeling of the polarization
signal. For that purpose, we develop a new, fast and efficient, optimization
method for model-data fitting: the Radial-basis-functions Optimization
Approximation Method (ROAM). Model-data fitting is achieved by optimizing a
user-specified log-likelihood function that quantifies the differences between
the observed polarization signal and its synthetic/predicted analogue. Speed
and efficiency are obtained by combining sparse evaluation of the magnetic
model with radial-basis-function (RBF) decomposition of the log-likelihood
function. The RBF decomposition provides an analytical expression for the
log-likelihood function that is used to inexpensively estimate the set of
parameter values optimizing it. We test and validate ROAM on a synthetic test
bed of a coronal magnetic flux rope and show that it performs well with a
significantly sparse sample of the parameter space. We conclude that our
optimization method is well-suited for fast and efficient model-data fitting
and can be exploited for converting coronal polarimetric measurements, such as
the ones provided by CoMP, into coronal magnetic field data.Comment: 23 pages, 12 figures, accepted in Frontiers in Astronomy and Space
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