105 research outputs found
Local Causal States and Discrete Coherent Structures
Coherent structures form spontaneously in nonlinear spatiotemporal systems
and are found at all spatial scales in natural phenomena from laboratory
hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary
climate dynamics. Phenomenologically, they appear as key components that
organize the macroscopic behaviors in such systems. Despite a century of
effort, they have eluded rigorous analysis and empirical prediction, with
progress being made only recently. As a step in this, we present a formal
theory of coherent structures in fully-discrete dynamical field theories. It
builds on the notion of structure introduced by computational mechanics,
generalizing it to a local spatiotemporal setting. The analysis' main tool
employs the \localstates, which are used to uncover a system's hidden
spatiotemporal symmetries and which identify coherent structures as
spatially-localized deviations from those symmetries. The approach is
behavior-driven in the sense that it does not rely on directly analyzing
spatiotemporal equations of motion, rather it considers only the spatiotemporal
fields a system generates. As such, it offers an unsupervised approach to
discover and describe coherent structures. We illustrate the approach by
analyzing coherent structures generated by elementary cellular automata,
comparing the results with an earlier, dynamic-invariant-set approach that
decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht
Fractal Stability Border in Plane Couette Flow
We study the dynamics of localised perturbations in plane Couette flow with
periodic lateral boundary conditions. For small Reynolds number and small
amplitude of the initial state the perturbation decays on a viscous time scale
. For Reynolds number larger than about 200, chaotic transients
appear with life times longer than the viscous one. Depending on the type of
the perturbation isolated initial conditions with infinite life time appear for
Reynolds numbers larger than about 270--320. In this third regime, the life
time as a function of Reynolds number and amplitude is fractal. These results
suggest that in the transition region the turbulent dynamics is characterised
by a chaotic repeller rather than an attractor.Comment: 4 pages, Latex, 4 eps-figures, submitted to Phys. Rev. Le
Complex temporal patterns in molecular dynamics:a direct measure of the phase-space exploration by the trajectory at macroscopic time scales
Computer simulated trajectories of bulk water molecules form complex spatiotemporal structures at the picosecond time scale. This intrinsic complexity, which underlies the formation of molecular structures at longer time scales, has been quantified using a measure of statistical complexity. The method estimates the information contained in the molecular trajectory by detecting and quantifying temporal patterns present in the simulated data (velocity time series). Two types of temporal patterns are found. The first, defined by the short-time correlations corresponding to the velocity autocorrelation decay times (â‰0.1â€ps), remains asymptotically stable for time intervals longer than several tens of nanoseconds. The second is caused by previously unknown longer-time correlations (found at longer than the nanoseconds time scales) leading to a value of statistical complexity that slowly increases with time. A direct measure based on the notion of statistical complexity that describes how the trajectory explores the phase space and independent from the particular molecular signal used as the observed time series is introduced
Degeneracy: a link between evolvability, robustness and complexity in biological systems
A full accounting of biological robustness remains elusive; both in terms of the mechanisms by which robustness is achieved and the forces that have caused robustness to grow over evolutionary time. Although its importance to topics such as ecosystem services and resilience is well recognized, the broader relationship between robustness and evolution is only starting to be fully appreciated. A renewed interest in this relationship has been prompted by evidence that mutational robustness can play a positive role in the discovery of adaptive innovations (evolvability) and evidence of an intimate relationship between robustness and complexity in biology.
This paper offers a new perspective on the mechanics of evolution and the origins of complexity, robustness, and evolvability. Here we explore the hypothesis that degeneracy, a partial overlap in the functioning of multi-functional components, plays a central role in the evolution and robustness of complex forms. In support of this hypothesis, we present evidence that degeneracy is a fundamental source of robustness, it is intimately tied to multi-scaled complexity, and it establishes conditions that are necessary for system evolvability
Parameter estimation in spatially extended systems: The Karhunen-Loeve and Galerkin multiple shooting approach
Parameter estimation for spatiotemporal dynamics for coupled map lattices and
continuous time domain systems is shown using a combination of multiple
shooting, Karhunen-Loeve decomposition and Galerkin's projection methodologies.
The resulting advantages in estimating parameters have been studied and
discussed for chaotic and turbulent dynamics using small amounts of data from
subsystems, availability of only scalar and noisy time series data, effects of
space-time parameter variations, and in the presence of multiple time-scales.Comment: 11 pages, 5 figures, 4 Tables Corresponding Author - V. Ravi Kumar,
e-mail address: [email protected]
Multibaryons as Symmetric Multiskyrmions
We study non-adiabatic corrections to multibaryon systems within the bound
state approach to the SU(3) Skyrme model. We use approximate ansatze for the
static background fields based on rational maps which have the same symmetries
of the exact solutions. To determine the explicit form of the collective
Hamiltonians and wave functions we only make use of these symmetries. Thus, the
expressions obtained are also valid in the exact case. On the other hand, the
inertia parameters and hyperfine splitting constants we calculate do depend on
the detailed form of the ansatze and are, therefore, approximate. Using these
values we compute the low lying spectra of multibaryons with B <= 9 and
strangeness 0, -1 and -B. Finally, we show that the non-adiabatic corrections
do not affect the stability of the tetralambda and heptalambda found in a
previous work.Comment: 17 pages, RevTeX, no figure
Skyrmion-anti-Skyrmion Annihilation with Omega Mesons
We study numerically the annihilation of an omega-stabilized Skyrmion and an
anti-Skyrmion in three spatial dimensions. To our knowledge this is a first
successful simulation of Skyrmion-anti-Skyrmion annihilation which follows
through to the point where the energy is carried by outgoing meson waves.
We encounter instabilities similar to those encountered is earlier
calculations, but in our case these are not fatal and we are able to simulate
through this process with a global energy loss of less than 8%, and to identify
robust features of the final radiation pattern. The system passes through a
singular configuration at the time of half-annihilation. This is followed by
the onset of fast oscillations which are superimposed on the smoother process
which leads to the appearence of outgoing spherical waves.
We investigate the two prominent features of this process, the proliferation
of small, fast oscillations, and the singular intermediate configuration. We
find that our equations of motion allow for a regime in which the amplitude of
certain small perturbations increases exponentially. This regime is similar but
not identical to the situation pointed out earlier regarding the original
Skyrme model. We argue that the singularity may be seen as the result of a
pinch effect similar to that encountered in plasmas.Comment: 26 pages, 15 figure
Differences in Preferences Towards the Environment: The Impact of a Gender, Age and Parental Effect
The paper investigates empirically the differences in preferences towards protection of the environment. Using seven different dependent variables to focus on the impact of age, gender and children we use a large micro data set covering data from 33 Western and Eastern European countries. The results indicate that women have both a stronger preference towards the environment and a stronger willingness to contribute. Moreover, we observe the tendency of a negative correlation between age and environmental preferences. However, a positive effect is visible once we focus on the impact of age on social norms (environmental morale). Finally, we were not able to observe that having children is positively correlated with a stronger preference towards the environment
- …