178 research outputs found
Metastability in Interacting Nonlinear Stochastic Differential Equations II: Large-N Behaviour
We consider the dynamics of a periodic chain of N coupled overdamped
particles under the influence of noise, in the limit of large N. Each particle
is subjected to a bistable local potential, to a linear coupling with its
nearest neighbours, and to an independent source of white noise. For strong
coupling (of the order N^2), the system synchronises, in the sense that all
oscillators assume almost the same position in their respective local potential
most of the time. In a previous paper, we showed that the transition from
strong to weak coupling involves a sequence of symmetry-breaking bifurcations
of the system's stationary configurations, and analysed in particular the
behaviour for coupling intensities slightly below the synchronisation
threshold, for arbitrary N. Here we describe the behaviour for any positive
coupling intensity \gamma of order N^2, provided the particle number N is
sufficiently large (as a function of \gamma/N^2). In particular, we determine
the transition time between synchronised states, as well as the shape of the
"critical droplet", to leading order in 1/N. Our techniques involve the control
of the exact number of periodic orbits of a near-integrable twist map, allowing
us to give a detailed description of the system's potential landscape, in which
the metastable behaviour is encoded
Universality of residence-time distributions in non-adiabatic stochastic resonance
We present mathematically rigorous expressions for the residence-time and
first-passage-time distributions of a periodically forced Brownian particle in
a bistable potential. For a broad range of forcing frequencies and amplitudes,
the distributions are close to periodically modulated exponential ones.
Remarkably, the periodic modulations are governed by universal functions,
depending on a single parameter related to the forcing period. The behaviour of
the distributions and their moments is analysed, in particular in the low- and
high-frequency limits.Comment: 8 pages, 1 figure New version includes distinction between
first-passage-time and residence-time distribution
Empirical Model Development for Predicting Shock Response on Composite Materials Subjected to Pyroshock Loading: Appendices
The NASA Engineering and Safety Center (NESC) received a request to develop an analysis model based on both frequency response and wave propagation analyses for predicting shock response spectrum (SRS) on composite materials subjected to pyroshock loading. The model would account for near-field environment (approx. 9 inches from the source) dominated by direct wave propagation, mid-field environment (approx. 2 feet from the source) characterized by wave propagation and structural resonances, and far-field environment dominated by lower frequency bending waves in the structure. This document contains appendices to the Volume I report
Empirical Model Development for Predicting Shock Response on Composite Materials Subjected to Pyroshock Loading
The NASA Engineering and Safety Center (NESC) received a request to develop an analysis model based on both frequency response and wave propagation analyses for predicting shock response spectrum (SRS) on composite materials subjected to pyroshock loading. The model would account for near-field environment (approx. 9 inches from the source) dominated by direct wave propagation, mid-field environment (approx. 2 feet from the source) characterized by wave propagation and structural resonances, and far-field environment dominated by lower frequency bending waves in the structure. This report documents the outcome of the assessment
Empirical Model Development for Predicting Shock Response on Composite Materials Subjected to Pyroshock Loading
The NASA Engineering and Safety Center (NESC) received a request to develop an analysis model based on both frequency response and wave propagation analyses for predicting shock response spectrum (SRS) on composite materials subjected to pyroshock loading. The model would account for near-field environment (~9 inches from the source) dominated by direct wave propagation, mid-field environment (approximately 2 feet from the source) characterized by wave propagation and structural resonances, and far-field environment dominated by lower frequency bending waves in the structure. This document contains appendices to the Volume I report
Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems
We introduce a new method, allowing to describe slowly time-dependent
Langevin equations through the behaviour of individual paths. This approach
yields considerably more information than the computation of the probability
density. The main idea is to show that for sufficiently small noise intensity
and slow time dependence, the vast majority of paths remain in small space-time
sets, typically in the neighbourhood of potential wells. The size of these sets
often has a power-law dependence on the small parameters, with universal
exponents. The overall probability of exceptional paths is exponentially small,
with an exponent also showing power-law behaviour. The results cover time spans
up to the maximal Kramers time of the system. We apply our method to three
phenomena characteristic for bistable systems: stochastic resonance, dynamical
hysteresis and bifurcation delay, where it yields precise bounds on transition
probabilities, and the distribution of hysteresis areas and first-exit times.
We also discuss the effect of coloured noise.Comment: 37 pages, 11 figure
Extensive release of methane from Arctic seabed west of Svalbard during summer 2014 does not influence the atmosphere
© 2016. American Geophysical Union. All Rights Reserved. We find that summer methane (CH4) release from seabed sediments west of Svalbard substantially increases CH4 concentrations in the ocean but has limited influence on the atmospheric CH4 levels. Our conclusion stems from complementary measurements at the seafloor, in the ocean, and in the atmosphere from land-based, ship and aircraft platforms during a summer campaign in 2014. We detected high concentrations of dissolved CH4 in the ocean above the seafloor with a sharp decrease above the pycnocline. Model approaches taking potential CH4 emissions from both dissolved and bubble-released CH4 from a larger region into account reveal a maximum flux compatible with the observed atmospheric CH4 mixing ratios of 2.4-3.8 nmol m-2 s-1. This is too low to have an impact on the atmospheric summer CH4 budget in the year 2014. Long-term ocean observatories may shed light on the complex variations of Arctic CH4 cycles throughout the year.The project MOCA- Methane Emissions from the Arctic OCean to the Atmosphere: Present and Future Climate Effects is funded by the Research Council of Norway, grant no.225814 CAGE – Centre for Arctic Gas Hydrate, Environment and Climate research work was supported by the Research Council of Norway through its Centres of Excellence funding scheme grant no. 223259. Nordic Center of Excellence eSTICC (eScience Tool for Investigating Climate Change in northern high latitudes) funded by Nordforsk, grant no. 57001
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