17,383 research outputs found
Well-posedness for a coagulation multiple-fragmentation equation
We consider a coagulation multiple-fragmentation equation, which describes
the concentration of particles of mass at the
instant in a model where fragmentation and coalescence phenomena
occur. We study the existence and uniqueness of measured-valued solutions to
this equation for homogeneous-like kernels of homogeneity parameter and bounded fragmentation kernels, although a possibly infinite
total fragmentation rate, in particular an infinite number of fragments, is
considered. This work relies on the use of a Wasserstein-type distance, which
has shown to be particularly well-adapted to coalescence phenomena. It was
introduced in previous works on coagulation and coalescence
Stochastic Coalescence Multi-Fragmentation Processes
We study infinite systems of particles which undergo coalescence and
fragmentation, in a manner determined solely by their masses. A pair of
particles having masses and coalesces at a given rate . A
particle of mass fragments into a collection of particles of masses
at rate . We assume
that the kernels and satisfy H\"older regularity conditions with
indices and respectively. We show
existence of such infinite particle systems as strong Markov processes taking
values in , the set of ordered sequences
such that \sum\_{i \ge 1} m\_i^{\lambda} \textless{} \infty. We show that
these processes possess the Feller property. This work relies on the use of a
Wasserstein-type distance, which has proved to be particularly well-adapted to
coalescence phenomena.Comment: arXiv admin note: substantial text overlap with arXiv:1301.193
The Most Exigent Eigenvalue: Guaranteeing Consensus under an Unknown Communication Topology and Time Delays
This document aims to answer the question of what is the minimum delay value
that guarantees convergence to consensus for a group of second order agents
operating under different protocols, provided that the communication topology
is connected but unknown. That is, for all the possible communication
topologies, which value of the delay guarantees stability? To answer this
question we revisit the concept of most exigent eigenvalue, applying it to two
different consensus protocols for agents driven by second order dynamics. We
show how the delay margin depends on the structure of the consensus protocol
and the communication topology, and arrive to a boundary that guarantees
consensus for any connected communication topology. The switching topologies
case is also studied. It is shown that for one protocol the stability of the
individual topologies is sufficient to guarantee consensus in the switching
case, whereas for the other one it is not
Smoluchowski's equation: rate of convergence of the Marcus-Lushnikov process
We derive a satisfying rate of convergence of the Marcus-Lushnikov process
toward the solution to Smoluchowski's coagulation equation. Our result applies
to a class of homogeneous-like coagulation kernels with homogeneity degree
ranging in . It relies on the use of a Wasserstein-type distance,
which has shown to be particularly well-adapted to coalescence phenomena.Comment: 34 Page
Some Special Cases in the Stability Analysis of Multi-Dimensional Time-Delay Systems Using The Matrix Lambert W function
This paper revisits a recently developed methodology based on the matrix
Lambert W function for the stability analysis of linear time invariant, time
delay systems. By studying a particular, yet common, second order system, we
show that in general there is no one to one correspondence between the branches
of the matrix Lambert W function and the characteristic roots of the system.
Furthermore, it is shown that under mild conditions only two branches suffice
to find the complete spectrum of the system, and that the principal branch can
be used to find several roots, and not the dominant root only, as stated in
previous works. The results are first presented analytically, and then verified
by numerical experiments
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