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## ‣ Self-organization in leaky threshold systems: The influence of near-mean field dynamics and its implications for earthquakes, neurobiology, and forecasting

Fonte: National Academy of Sciences
Publicador: National Academy of Sciences

Tipo: Artigo de Revista Científica

Publicado em 19/02/2002
Português

Relevância na Pesquisa

59.08005%

Threshold systems are known to be some of the most important nonlinear self-organizing systems in nature, including networks of earthquake faults, neural networks, superconductors and semiconductors, and the World Wide Web, as well as political, social, and ecological systems. All of these systems have dynamics that are strongly correlated in space and time, and all typically display a multiplicity of spatial and temporal scales. Here we discuss the physics of self-organization in earthquake threshold systems at two distinct scales: (i) The “microscopic” laboratory scale, in which consideration of results from simulations leads to dynamical equations that can be used to derive the results obtained from sliding friction experiments, and (ii) the “macroscopic” earthquake fault-system scale, in which the physics of strongly correlated earthquake fault systems can be understood by using time-dependent state vectors defined in a Hilbert space of eigenstates, similar in many respects to the mathematics of quantum mechanics. In all of these systems, long-range interactions induce the existence of locally ergodic dynamics. The existence of dissipative effects leads to the appearance of a “leaky threshold” dynamics, equivalent to a new scaling field that controls the size of nucleation events relative to the size of background fluctuations. At the macroscopic earthquake fault-system scale...

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## ‣ Dynamics of fully coupled rotators with unimodal and bimodal frequency distribution

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/08/2015
Português

Relevância na Pesquisa

58.754043%

#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Statistical Mechanics#Nonlinear Sciences - Chaotic Dynamics

We analyze the synchronization transition of a globally coupled network of N
phase oscillators with inertia (rotators) whose natural frequencies are
unimodally or bimodally distributed. In the unimodal case, the system exhibits
a discontinuous hysteretic transition from an incoherent to a partially
synchronized (PS) state. For sufficiently large inertia, the system reveals the
coexistence of a PS state and of a standing wave (SW) solution. In the bimodal
case, the hysteretic synchronization transition involves several states.
Namely, the system becomes coherent passing through traveling waves (TWs), SWs
and finally arriving to a PS regime. The transition to the PS state from the SW
occurs always at the same coupling, independently of the system size, while its
value increases linearly with the inertia. On the other hand the critical
coupling required to observe TWs and SWs increases with N suggesting that in
the thermodynamic limit the transition from incoherence to PS will occur
without any intermediate states. Finally a linear stability analysis reveals
that the system is hysteretic not only at the level of macroscopic indicators,
but also microscopically as verified by measuring the maximal Lyapunov
exponent.; Comment: 22 pages...

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## ‣ A comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

59.22721%

#Nonlinear Sciences - Cellular Automata and Lattice Gases#Condensed Matter - Statistical Mechanics#Physics - Physics and Society

Using a stochastic cellular automaton model for urban traffic flow, we study
and compare Macroscopic Fundamental Diagrams (MFDs) of arterial road networks
governed by different types of adaptive traffic signal systems, under various
boundary conditions. In particular, we simulate realistic signal systems that
include signal linking and adaptive cycle times, and compare their performance
against a highly adaptive system of self-organizing traffic signals which is
designed to uniformly distribute the network density. We find that for networks
with time-independent boundary conditions, well-defined stationary MFDs are
observed, whose shape depends on the particular signal system used, and also on
the level of heterogeneity in the system. We find that the spatial
heterogeneity of both density and flow provide important indicators of network
performance. We also study networks with time-dependent boundary conditions,
containing morning and afternoon peaks. In this case, intricate hysteresis
loops are observed in the MFDs which are strongly correlated with the density
heterogeneity. Our results show that the MFD of the self-organizing traffic
signals lies above the MFD for the realistic systems, suggesting that by
adaptively homogenizing the network density...

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## ‣ Programmable reaction-diffusion fronts

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/07/2014
Português

Relevância na Pesquisa

48.71328%

#Nonlinear Sciences - Pattern Formation and Solitons#Physics - Biological Physics#Physics - Chemical Physics

Morphogenesis is central to biology but remains largely unexplored in
chemistry. Reaction-diffusion (RD) mechanisms are, however, essential to
understand how shape emerges in the living world. While numerical methods
confirm the incredible potential of RD mechanisms to generate patterns, their
experimental implementation, despite great efforts, has yet to surpass the
paradigm of stationary Turing patterns achieved 25 years ago. The principal
reason for our difficulty to synthesize arbitrary concentration patterns from
scratch is the lack of fully programmable reaction-diffusion systems. To solve
this problem we introduce here a DNA-based system where kinetics and diffusion
can be individually tuned. We demonstrate the capability to precisely control
reaction-diffusion properties with an autocatalytic network that propagates in
a one-dimensional reactor with uniform velocity, typically 100 {\mu}m min-1.
The diffusion coefficient of the propagating species can be reduced up to a
factor 2.7 using a species-specific strategy relying on self-assembled
hydrodynamic drags. Our approach is modular as we illustrate by designing three
alternative front generating systems, two of which can pass through each other
with little interaction. Importantly...

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## ‣ Route to extreme events in excitable systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/08/2014
Português

Relevância na Pesquisa

48.582925%

Systems of FitzHugh-Nagumo units with different coupling topologies are
capable of self-generating and -terminating strong deviations from their
regular dynamics that can be regarded as extreme events due to their rareness
and recurrent occurrence. Here we demonstrate the crucial role of an interior
crisis in the emergence of extreme events. In parameter space we identify this
interior crisis as the organizing center of the dynamics by employing concepts
of mixed-mode oscillations and of leaking chaotic systems. We find that extreme
events occur in certain regions in parameter space, and we show the robustness
of this phenomenon with respect to the system size.

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