8,487 research outputs found
A moment-equation-copula-closure method for nonlinear vibrational systems subjected to correlated noise
We develop a moment equation closure minimization method for the inexpensive
approximation of the steady state statistical structure of nonlinear systems
whose potential functions have bimodal shapes and which are subjected to
correlated excitations. Our approach relies on the derivation of moment
equations that describe the dynamics governing the two-time statistics. These
are combined with a non-Gaussian pdf representation for the joint
response-excitation statistics that has i) single time statistical structure
consistent with the analytical solutions of the Fokker-Planck equation, and ii)
two-time statistical structure with Gaussian characteristics. Through the
adopted pdf representation, we derive a closure scheme which we formulate in
terms of a consistency condition involving the second order statistics of the
response, the closure constraint. A similar condition, the dynamics constraint,
is also derived directly through the moment equations. These two constraints
are formulated as a low-dimensional minimization problem with respect to
unknown parameters of the representation, the minimization of which imposes an
interplay between the dynamics and the adopted closure. The new method allows
for the semi-analytical representation of the two-time, non-Gaussian structure
of the solution as well as the joint statistical structure of the
response-excitation over different time instants. We demonstrate its
effectiveness through the application on bistable nonlinear
single-degree-of-freedom energy harvesters with mechanical and electromagnetic
damping, and we show that the results compare favorably with direct Monte-Carlo
Simulations
Markov Chain Methods For Analyzing Complex Transport Networks
We have developed a steady state theory of complex transport networks used to
model the flow of commodity, information, viruses, opinions, or traffic. Our
approach is based on the use of the Markov chains defined on the graph
representations of transport networks allowing for the effective network
design, network performance evaluation, embedding, partitioning, and network
fault tolerance analysis. Random walks embed graphs into Euclidean space in
which distances and angles acquire a clear statistical interpretation. Being
defined on the dual graph representations of transport networks random walks
describe the equilibrium configurations of not random commodity flows on
primary graphs. This theory unifies many network concepts into one framework
and can also be elegantly extended to describe networks represented by directed
graphs and multiple interacting networks.Comment: 26 pages, 4 figure
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
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