58 research outputs found
A graph-theoretic condition for irreducibility of a set of cone preserving matrices
Given a closed, convex and pointed cone K in R^n , we present a result which infers K-irreducibility of sets of K-quasipositive matrices from strong connectedness of certain bipartite digraphs. The matrix-sets are defined via products, and the main result is relevant to applications in biology and chemistry. Several examples are presented
Directed transport of two interacting particles in a washboard potential
We study the conservative and deterministic dynamics of two nonlinearly
interacting particles evolving in a one-dimensional spatially periodic
washboard potential. A weak tilt of the washboard potential is applied biasing
one direction for particle transport. However, the tilt vanishes asymptotically
in the direction of bias. Moreover, the total energy content is not enough for
both particles to be able to escape simultaneously from an initial potential
well; to achieve transport the coupled particles need to interact
cooperatively. For low coupling strength the two particles remain trapped
inside the starting potential well permanently. For increased coupling strength
there exists a regime in which one of the particles transfers the majority of
its energy to the other one, as a consequence of which the latter escapes from
the potential well and the bond between them breaks. Finally, for suitably
large couplings, coordinated energy exchange between the particles allows them
to achieve escapes -- one particle followed by the other -- from consecutive
potential wells resulting in directed collective motion. The key mechanism of
transport rectification is based on the asymptotically vanishing tilt causing a
symmetry breaking of the non-chaotic fraction of the dynamics in the mixed
phase space. That is, after a chaotic transient, only at one of the boundaries
of the chaotic layer do resonance islands appear. The settling of trajectories
in the ballistic channels associated with transporting islands provides
long-range directed transport dynamics of the escaping dimer
Nonlinear response of a linear chain to weak driving
We study the escape of a chain of coupled units over the barrier of a
metastable potential. It is demonstrated that a very weak external driving
field with suitably chosen frequency suffices to accomplish speedy escape. The
latter requires the passage through a transition state the formation of which
is triggered by permanent feeding of energy from a phonon background into humps
of localised energy and elastic interaction of the arising breather solutions.
In fact, cooperativity between the units of the chain entailing coordinated
energy transfer is shown to be crucial for enhancing the rate of escape in an
extremely effective and low-energy cost way where the effect of entropic
localisation and breather coalescence conspire
Emergence of continual directed flow in Hamiltonian systems
We propose a minimal model for the emergence of a directed flow in autonomous
Hamiltonian systems. It is shown that internal breaking of the spatio-temporal
symmetries, via localised initial conditions, that are unbiased with respect to
the transporting degree of freedom, and transient chaos conspire to form the
physical mechanism for the occurrence of a current. Most importantly, after
passage through the transient chaos, trajectories perform solely regular
transporting motion so that the resulting current is of continual ballistic
nature. This has to be distinguished from the features of transport reported
previously for driven Hamiltonian systems with mixed phase space where
transport is determined by intermittent behaviour exhibiting power-law decay
statistics of the duration of regular ballistic periods
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