924 research outputs found
Metastability of solitary roll wave solutions of the St. Venant equations with viscosity
We study by a combination of numerical and analytical Evans function
techniques the stability of solitary wave solutions of the St. Venant equations
for viscous shallow-water flow down an incline, and related models. Our main
result is to exhibit examples of metastable solitary waves for the St. Venant
equations, with stable point spectrum indicating coherence of the wave profile
but unstable essential spectrum indicating oscillatory convective instabilities
shed in its wake. We propose a mechanism based on ``dynamic spectrum'' of the
wave profile, by which a wave train of solitary pulses can stabilize each other
by de-amplification of convective instabilities as they pass through successive
waves. We present numerical time evolution studies supporting these
conclusions, which bear also on the possibility of stable periodic solutions
close to the homoclinic. For the closely related viscous Jin-Xin model, by
contrast, for which the essential spectrum is stable, we show using the
stability index of Gardner--Zumbrun that solitary wave pulses are always
exponentially unstable, possessing point spectra with positive real part.Comment: 42 pages, 9 figure
Dynamical independence: discovering emergent macroscopic processes in complex dynamical systems
We introduce a notion of emergence for coarse-grained macroscopic variables
associated with highly-multivariate microscopic dynamical processes, in the
context of a coupled dynamical environment. Dynamical independence instantiates
the intuition of an emergent macroscopic process as one possessing the
characteristics of a dynamical system "in its own right", with its own
dynamical laws distinct from those of the underlying microscopic dynamics. We
quantify (departure from) dynamical independence by a transformation-invariant
Shannon information-based measure of dynamical dependence. We emphasise the
data-driven discovery of dynamically-independent macroscopic variables, and
introduce the idea of a multiscale "emergence portrait" for complex systems. We
show how dynamical dependence may be computed explicitly for linear systems via
state-space modelling, in both time and frequency domains, facilitating
discovery of emergent phenomena at all spatiotemporal scales. We discuss
application of the state-space operationalisation to inference of the emergence
portrait for neural systems from neurophysiological time-series data. We also
examine dynamical independence for discrete- and continuous-time deterministic
dynamics, with potential application to Hamiltonian mechanics and classical
complex systems such as flocking and cellular automata.Comment: 38 pages, 7 figure
The Pivotal Role of Causality in Local Quantum Physics
In this article an attempt is made to present very recent conceptual and
computational developments in QFT as new manifestations of old and well
establihed physical principles. The vehicle for converting the
quantum-algebraic aspects of local quantum physics into more classical
geometric structures is the modular theory of Tomita. As the above named
laureate to whom I have dedicated has shown together with his collaborator for
the first time in sufficient generality, its use in physics goes through
Einstein causality. This line of research recently gained momentum when it was
realized that it is not only of structural and conceptual innovative power (see
section 4), but also promises to be a new computational road into
nonperturbative QFT (section 5) which, picturesquely speaking, enters the
subject on the extreme opposite (noncommutative) side.Comment: This is a updated version which has been submitted to Journal of
Physics A, tcilatex 62 pages. Adress: Institut fuer Theoretische Physik
FU-Berlin, Arnimallee 14, 14195 Berlin presently CBPF, Rua Dr. Xavier Sigaud
150, 22290-180 Rio de Janeiro, Brazi
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