4,425 research outputs found
On noise-induced synchronization and consensus of nonlinear network systems under input disturbances
This paper is concerned with the study of synchronization and consensus
phenomena in complex networks of diffusively-coupled nodes subject to external
disturbances. Specifically, we make use of stochastic Lyapunov functions to
provide conditions for synchronization and consensus for networks of nonlinear,
diffusively coupled nodes, where noise diffusion is not just additive but it
depends on the nodes' state. The sufficient condition we provide, wich links
together network topology, coupling strength and noise diffusion, offers two
interesting interpretations. First, as suggested by {\em intuition}, in order
for a network to achieve synchronization/consensus, its nodes need to be
sufficiently well connected together. The second implication might seem,
instead, counter-intuitive: if noise diffusion is {\em properly} designed, then
it can drive an unsynchronized network towards synchronization/consensus.
Motivated by our current research in Smart Cities and Internet of Things, we
illustrate the effectiveness of our approach by showing how our results can be
used to control certain collective decision processes.Comment: Preprint submitted to SIAM SICON. arXiv admin note: text overlap with
arXiv:1602.0646
Nearly K\"ahler six-manifolds with two-torus symmetry
We consider nearly K\"ahler 6-manifolds with effective 2-torus symmetry. The
multi-moment map for the -action becomes an eigenfunction of the Laplace
operator. At regular values, we prove the -action is necessarily free on
the level sets and determines the geometry of three-dimensional quotients. An
inverse construction is given locally producing nearly K\"ahler six-manifolds
from three-dimensional data. This is illustrated for structures on the
Heisenberg group.Comment: 13 page
A Finite Difference Ghost-Cell Multigrid Approach for Poisson Equation with Mixed Boundary Conditions in Arbitrary Domain
In this paper we present a multigrid approach to solve the Poisson equation
in arbitrary domain (identified by a level set function) and mixed boundary
conditions. The discretization is based on finite difference scheme and
ghost-cell method. This multigrid strategy can be applied also to more general
problems where a non-eliminated boundary condition approach is used. Arbitrary
domain make the definition of the restriction operator for boundary conditions
hard to find. A suitable restriction operator is provided in this work,
together with a proper treatment of the boundary smoothing, in order to avoid
degradation of the convergence factor of the multigrid due to boundary effects.
Several numerical tests confirm the good convergence property of the new
method
On noise-induced synchronization and consensus
In this paper, we present new results for the synchronization and consensus
of networks described by Ito stochastic differential equations. From the
methodological viewpoint, our results are based on the use of stochastic
Lyapunov functions. This approach allowed us to consider networks where nodes
dynamics can be nonlinear and non-autonomous and where noise is not just
additive but rather its diffusion can be nonlinear and depend on the network
state. We first present a sufficient condition on the coupling strength and
topology ensuring that a network synchronizes (fulfills consensus) despite
noise. Then, we show that noise can be useful, and present a result showing how
to design noise so that it induces synchronization/consensus. Motivated by our
current research in Smart Cities and Internet of Things, we also illustrate the
effectiveness of our approach by showing how our results can be used to
analyze/control the onset of synchronization in noisy networks and to study
collective decision processes.Comment: Keywords: Ito differential equations, Synchronization, Complex
network
Explicit rationality of some cubic fourfolds
Recent results of Hassett, Kuznetsov and others pointed out countably many
divisors in the open subset of
parametrizing
all cubic 4-folds and lead to the conjecture that the cubics corresponding to
these divisors should be precisely the rational ones. Rationality has been
proved by Fano for the first divisor and in [arXiv:1707.00999] for the
divisors and . In this note we describe explicit birational
maps from a general cubic fourfold in , in and in to
, providing concrete geometric realizations of the more abstract
constructions in [arXiv:1707.00999].Comment: Shortened versio
Congruences of 5-secant conics and the rationality of some admissible cubic fourfolds
The works of Hassett and Kuznetsov identify countably many divisors in
the open subset of
parametrizing
all cubic 4-folds and conjecture that the cubics corresponding to these
divisors are precisely the rational ones. Rationality has been known
classically for the first family . We use congruences of 5-secant
conics to prove rationality for the first three of the families ,
corresponding to in Hassett's notation.Comment: We added more details, improving the presentation, and modified some
discursive parts. Theorem 1 has been restated in a weaker form with a
hypothesis always satisfied in our application
Implicit-Explicit Runge-Kutta schemes for hyperbolic systems with stiff relaxation and applications
In this paper we give an overview of Implicit-Explicit Runge-Kutta schemes
applied to hyperbolic systems with stiff relaxation. In particular, we focus on
some recent results on the uniform accuracy for hyperbolic systems with stiff
relaxation [6], and hyperbolic system with diffusive relaxation [7, 5, 4]. In
the latter case, we present an original application to a model problem arising
in Extended Thermodynamics.Comment: 19 page
A New Class of Conservative Large Time Step Methods for the BGK Models of the Boltzmann Equation
This work is aimed to develop a new class of methods for the BGK model of the
Boltzmann equation. This technique allows to get high order of accuracy both in
space and time, theoretically without CFL stability limitation. It's based on a
Lagrangian formulation of the problem: information is stored on a fixed grid in
space and velocity, and the equation is integrated along the characteristics.
The source term is treated implicitly by using a DIRK (Diagonally Implicit
Runge Kutta) scheme in order to avoid the time step restriction due to the
stiff relaxation. In particular some L-stable schemes are tested by smooth and
Riemann problems, both in rarefied and fully fluid regimes. Numerical results
show good accuracy and efficiency of the method
Sensitivity and safety of fully probabilistic control
In this paper we present a sensitivity analysis for the so-called fully
probabilistic control scheme. This scheme attempts to control a system modeled
via a probability density function (pdf) and does so by computing a
probabilistic control policy that is optimal in the Kullback-Leibler sense.
Situations where a system of interest is modeled via a pdf naturally arise in
the context of neural networks, reinforcement learning and data-driven
iterative control. After presenting the sensitivity analysis, we focus on
characterizing the convergence region of the closed loop system and introduce a
safety analysis for the scheme. The results are illustrated via simulations.
This is the preliminary version of the paper entitled "On robust stability of
fully probabilistic control with respect to data-driven model uncertainties"
that will be presented at the 2019 European Control Conference.Comment: accepted for presentation at the 2019 European Control Conference
(ECC 2019
A High Order Multi-Dimensional Characteristic Tracing Strategy for the Vlasov-Poisson System
In this paper, we consider a finite difference grid-based semi-Lagrangian
approach in solving the Vlasov-Poisson (VP) system. Many of existing methods
are based on dimensional splitting, which decouples the problem into solving
linear advection problems, see {\em Cheng and Knorr, Journal of Computational
Physics, 22(1976)}. However, such splitting is subject to the splitting error.
If we consider multi-dimensional problems without splitting, difficulty arises
in tracing characteristics with high order accuracy. Specifically, the
evolution of characteristics is subject to the electric field which is
determined globally from the distribution of particle densities via the
Poisson's equation. In this paper, we propose a novel strategy of tracing
characteristics high order in time via a two-stage multi-derivative
prediction-correction approach and by using moment equations of the VP system.
With the foot of characteristics being accurately located, we proposed to use
weighted essentially non-oscillatory (WENO) interpolation to recover function
values between grid points, therefore to update solutions at the next time
level. The proposed algorithm does not have time step restriction as Eulerian
approach and enjoys high order spatial and temporal accuracy. However, such
finite difference algorithm does not enjoy mass conservation; we discuss one
possible way of resolving such issue and its potential challenge in numerical
stability. The performance of the proposed schemes are numerically demonstrated
via classical test problems such as Landau damping and two stream
instabilities
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