264 research outputs found
Trace formulas for stochastic evolution operators: Smooth conjugation method
The trace formula for the evolution operator associated with nonlinear
stochastic flows with weak additive noise is cast in the path integral
formalism. We integrate over the neighborhood of a given saddlepoint exactly by
means of a smooth conjugacy, a locally analytic nonlinear change of field
variables. The perturbative corrections are transfered to the corresponding
Jacobian, which we expand in terms of the conjugating function, rather than the
action used in defining the path integral. The new perturbative expansion which
follows by a recursive evaluation of derivatives appears more compact than the
standard Feynman diagram perturbation theory. The result is a stochastic analog
of the Gutzwiller trace formula with the ``hbar'' corrections computed an order
higher than what has so far been attainable in stochastic and
quantum-mechanical applications.Comment: 16 pages, 1 figure, New techniques and results for a problem we
considered in chao-dyn/980703
Beyond the periodic orbit theory
The global constraints on chaotic dynamics induced by the analyticity of
smooth flows are used to dispense with individual periodic orbits and derive
infinite families of exact sum rules for several simple dynamical systems. The
associated Fredholm determinants are of particularly simple polynomial form.
The theory developed suggests an alternative to the conventional periodic orbit
theory approach to determining eigenspectra of transfer operators.Comment: 29 pages Latex2
High Macroalgal Cover and Low Coral Recruitment Undermines the Potential Resilience of the World's Southernmost Coral Reef Assemblages
Coral reefs are under increasing pressure from anthropogenic and climate-induced stressors. The ability of reefs to reassemble and regenerate after disturbances (i.e., resilience) is largely dependent on the capacity of herbivores to prevent macroalgal expansion, and the replenishment of coral populations through larval recruitment. Currently there is a paucity of this information for higher latitude, subtropical reefs. To assess the potential resilience of the benthic reef assemblages of Lord Howe Island (31°32′S, 159°04′E), the worlds' southernmost coral reef, we quantified the benthic composition, densities of juvenile corals (as a proxy for coral recruitment), and herbivorous fish communities. Despite some variation among habitats and sites, benthic communities were dominated by live scleractinian corals (mean cover 37.4%) and fleshy macroalgae (20.9%). Live coral cover was higher than in most other subtropical reefs and directly comparable to lower latitude tropical reefs. Juvenile coral densities (0.8 ind.m−2), however, were 5–200 times lower than those reported for tropical reefs. Overall, macroalgal cover was negatively related to the cover of live coral and the density of juvenile corals, but displayed no relationship with herbivorous fish biomass. The biomass of herbivorous fishes was relatively low (204 kg.ha−1), and in marked contrast to tropical reefs was dominated by macroalgal browsing species (84.1%) with relatively few grazing species. Despite their extremely low biomass, grazing fishes were positively related to both the density of juvenile corals and the cover of bare substrata, suggesting that they may enhance the recruitment of corals through the provision of suitable settlement sites. Although Lord Howe Islands' reefs are currently coral-dominated, the high macroalgal cover, coupled with limited coral recruitment and low coral growth rates suggest these reefs may be extremely susceptible to future disturbances
Participatory research in complex marine conservation settings: A review of recent trends and lessons for the future
The conservation of marine ecosystems and species is inherently complex, plagued by social, political, economic and ecological uncertainty. Navigating these challenges to sustain marine systems requires the understanding, consideration and uptake of multiple knowledge systems within decision-making processes. Participatory research approaches, such as knowledge co-production, are advocated given their potential to generate knowledge with those who are most affected by the issue at hand and, based on that knowledge, develop and implement meaningful conservation practices collaboratively. In doing so participatory research is positioned to make marine research more democratic and impactful, and as such, has been a field of growing research enquiry. The aim of this study, therefore, is to synthesise (via a systematic scoping review) the existing literature to generate guidance that can help researchers and practitioners plan and apply participatory research approaches in a complex marine context. Results from systematically identifying and analyzing 337 articles show that the implementation of participatory research approaches are most common in the global north. Participatory research approaches most frequently included representatives from government, industry and civil society (e.g. community groups), while indigenous groups and communities were rarely included. A diversity of participatory research approaches have been used in relation to marine conservation in different settings and at various stages of the participatory process, each with their own challenges and benefits, that can lead to either positive outcomes for actors (e.g. social learning) or negative outcomes (e.g. disempowerment). We draw on our findings to provide guidance for improving the implementation of participatory research approaches in marine conservation such as taking the time to understand context before commencing participatory research approaches, and ensuring transparency with all actors throughout the process. We highlight key implications for researcher and practitioners implementing participatory research approaches including the importance of a diversity of approaches and methods to ensure access, supporting two way communication, addressing power imbalances, and the need to recognise, report on and address pre-existing barriers. Many of these require greater investment in terms of money or personnel, and new funding models are needed with a focus on longevity and sustainability
Continued-fraction expansion of eigenvalues of generalized evolution operators in terms of periodic orbits
A new expansion scheme to evaluate the eigenvalues of the generalized
evolution operator (Frobenius-Perron operator) relevant to the
fluctuation spectrum and poles of the order- power spectrum is proposed. The
``partition function'' is computed in terms of unstable periodic orbits and
then used in a finite pole approximation of the continued fraction expansion
for the evolution operator. A solvable example is presented and the approximate
and exact results are compared; good agreement is found.Comment: CYCLER Paper 93mar00
Weak noise approach to the logistic map
Using a nonperturbative weak noise approach we investigate the interference
of noise and chaos in simple 1D maps. We replace the noise-driven 1D map by an
area-preserving 2D map modelling the Poincare sections of a conserved dynamical
system with unbounded energy manifolds. We analyze the properties of the 2D map
and draw conclusions concerning the interference of noise on the nonlinear time
evolution. We apply this technique to the standard period-doubling sequence in
the logistic map. From the 2D area-preserving analogue we, in addition to the
usual period-doubling sequence, obtain a series of period doubled cycles which
are elliptic in nature. These cycles are spinning off the real axis at
parameters values corresponding to the standard period doubling events.Comment: 22 pages in revtex and 8 figures in ep
Changes in mangrove cover and exposure to coastal hazards in Kenya
Mangroves are effective carbon sinks, support coastal fisheries and provide wood and non-wood resources to coastal communities. They are threatened by natural and hu-man-induced stresses including over-exploitation, conversion pressures, pollution and climate change. Understanding changes in this important ecosystem is essential to inform the sus-tainable management of mangroves and assess the implications related to the loss of ecosystem services. This study used global remote sensing mangrove forest data to quantify changes in mangrove cover in Kenya between 2010 and 2016 and applied the InVEST coastal vulnerability model to assess the implications concerning the provision of natural coastal protection services in Kenya. Results indicate that the annual rates of mangrove cover loss in Kenya were 0.15% between 2010 and 2016. Currently, 16% of the Kenyan coastline is at higher levels of exposure to coastal hazards but this could increase to 41% if coastal ecosystems (mangroves, corals and seagrasses) are lost. The study further identified that higher rates of mangrove loss are observed in areas at higher risk of exposure in the southern and northern counties of Kwale and Lamu, where monitoring and management efforts should be prioritised
Electron localization by a magnetic vortex
We study the problem of an electron in two dimensions in the presence of a
magnetic vortex with a step-like profile. Dependending on the values of the
effective mass and gyromagnetic factor of the electron, it may be trapped by
the vortex. The bound state spectrum is obtained numerically, and some limiting
cases are treated analytically.Comment: 8 pages, latex, 4 figure
Non-integrability of the mixmaster universe
We comment on an analysis by Contopoulos et al. which demonstrates that the
governing six-dimensional Einstein equations for the mixmaster space-time
metric pass the ARS or reduced Painlev\'{e} test. We note that this is the case
irrespective of the value, , of the generating Hamiltonian which is a
constant of motion. For we find numerous closed orbits with two
unstable eigenvalues strongly indicating that there cannot exist two additional
first integrals apart from the Hamiltonian and thus that the system, at least
for this case, is very likely not integrable. In addition, we present numerical
evidence that the average Lyapunov exponent nevertheless vanishes. The model is
thus a very interesting example of a Hamiltonian dynamical system, which is
likely non-integrable yet passes the reduced Painlev\'{e} test.Comment: 11 pages LaTeX in J.Phys.A style (ioplppt.sty) + 6 PostScript figures
compressed and uuencoded with uufiles. Revised version to appear in J Phys.
Fractal Weyl laws for chaotic open systems
We present a result relating the density of quantum resonances for an open
chaotic system to the fractal dimension of the associated classical repeller.
The result is supported by numerical computation of the resonances of the
system of n disks on a plane. The result generalizes the Weyl law for the
density of states of a closed system to chaotic open systems.Comment: revtex4, 4 pages, 3 figure
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