29,529 research outputs found
A unified view on bipartite species-reaction and interaction graphs for chemical reaction networks
The Jacobian matrix of a dynamic system and its principal minors play a
prominent role in the study of qualitative dynamics and bifurcation analysis.
When interpreting the Jacobian as an adjacency matrix of an interaction graph,
its principal minors correspond to sets of disjoint cycles in this graph and
conditions for various dynamic behaviors can be inferred from its cycle
structure. For chemical reaction systems, more fine-grained analyses are
possible by studying a bipartite species-reaction graph. Several results on
injectivity, multistationarity, and bifurcations of a chemical reaction system
have been derived by using various definitions of such bipartite graph. Here,
we present a new definition of the species-reaction graph that more directly
connects the cycle structure with determinant expansion terms, principal
minors, and the coefficients of the characteristic polynomial and encompasses
previous graph constructions as special cases. This graph has a direct relation
to the interaction graph, and properties of cycles and sub-graphs can be
translated in both directions. A simple equivalence relation enables to
decompose determinant expansions more directly and allows simpler and more
direct proofs of previous results.Comment: 27 pages. submitted to J. Math. Bio
Partial norms and the convergence of general products of matrices
Motivated by the theory of inhomogeneous Markov chains, we determine a
sufficient condition for the convergence to 0 of a general product formed from
a sequence of real or complex matrices. When the matrices have a common
invariant subspace , we give a sufficient condition for the convergence to 0
on of a general product. Our result is applied to obtain a condition for
the weak ergodicity of an inhomogeneous Markov chain. We compare various types
of contractions which may be defined for a single matrix, such as
paracontraction, --contraction, and --contraction, where is an
invariant subspace of the matrix
Control of Towing Kites for Seagoing Vessels
In this paper we present the basic features of the flight control of the
SkySails towing kite system. After introduction of coordinate definitions and
basic system dynamics we introduce a novel model used for controller design and
justify its main dynamics with results from system identification based on
numerous sea trials. We then present the controller design which we
successfully use for operational flights for several years. Finally we explain
the generation of dynamical flight patterns.Comment: 12 pages, 18 figures; submitted to IEEE Trans. on Control Systems
Technology; revision: Fig. 15 corrected, minor text change
Stability of the decagonal quasicrystal in the Lennard-Jones-Gauss system
Although quasicrystals have been studied for 25 years, there are many open
questions concerning their stability: What is the role of phason fluctuations?
Do quasicrystals transform into periodic crystals at low temperature? If yes,
by what mechanisms? We address these questions here for a simple
two-dimensional model system, a monatomic decagonal quasicrystal, which is
stabilized by the Lennard-Jones-Gauss potential in thermodynamic equilibrium.
It is known to transform to the approximant Xi, when cooled below a critical
temperature. We show that the decagonal phase is an entropically stabilized
random tiling. By determining the average particle energy for a series of
approximants, it is found that the approximant Xi is the one with lowest
potential energy.Comment: 7 pages, 2 figures, Proceedings of Quasicrystals - The Silver Jubile
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