47,085 research outputs found
Nonlinearity and Multifractality of Climate Change in the Past 420,000 Years
Evidence of past climate variations are stored in ice and indicate
glacial-interglacial cycles characterized by three dominant time periods of
20kyr, 40kyr, and 100kyr. We study the scaling properties of temperature proxy
records of four ice cores from Antarctica and Greenland. These series are
long-range correlated in the time scales of 1-100kyr. We show that these series
are nonlinear as expressed by volatility correlations and a broad multifractal
spectrum. We present a stochastic model that captures the scaling and the
nonlinear properties observed in the data.Comment: 4 revtex pages, 4 figures, 1 tabl
Identification of quasi-optimal regions in the design space using surrogate modeling
The use of Surrogate Based Optimization (SBO) is widely spread in engineering design to find optimal performance characteristics of expensive simulations (forward analysis: from input to optimal output). However, often the practitioner knows a priori the desired performance and is interested in finding the associated input parameters (reverse analysis: from desired output to input). A popular method to solve such reverse (inverse) problems is to minimize the error between the simulated performance and the desired goal. However, there might be multiple quasi-optimal solutions to the problem. In this paper, the authors propose a novel method to efficiently solve inverse problems and to sample Quasi-Optimal Regions (QORs) in the input (design) space more densely. The development of this technique, based on the probability of improvement criterion and kriging models, is driven by a real-life problem from bio-mechanics, i.e., determining the elasticity of the (rabbit) tympanic membrane, a membrane that converts acoustic sound wave into vibrations of the middle ear ossicular bones
Self-tuning to the Hopf bifurcation in fluctuating systems
The problem of self-tuning a system to the Hopf bifurcation in the presence
of noise and periodic external forcing is discussed. We find that the response
of the system has a non-monotonic dependence on the noise-strength, and
displays an amplified response which is more pronounced for weaker signals. The
observed effect is to be distinguished from stochastic resonance. For the
feedback we have studied, the unforced self-tuned Hopf oscillator in the
presence of fluctuations exhibits sharp peaks in its spectrum. The implications
of our general results are briefly discussed in the context of sound detection
by the inner ear.Comment: 37 pages, 7 figures (8 figure files
Chaotic Dynamics Enhance the Sensitivity of Inner Ear Hair Cells
Hair cells of the auditory and vestibular systems are capable of detecting
sounds that induce sub-nanometer vibrations of the hair bundle, below the
stochastic noise levels of the surrounding fluid. Hair bundles of certain
species are also known to oscillate without external stimulation, indicating
the presence of an underlying active mechanism. We propose that chaotic
dynamics enhance the sensitivity and temporal resolution of the hair bundle
response, and provide experimental and theoretical evidence for this effect. By
varying the viscosity and ionic composition of the surrounding fluid, we are
able to modulate the degree of chaos observed in the hair bundle dynamics in
vitro. We consistently find that the hair bundle is most sensitive to a
stimulus of small amplitude when it is poised in the weakly chaotic regime.
Further, we show that the response time to a force step decreases with
increasing levels of chaos. These results agree well with our numerical
simulations of a chaotic Hopf oscillator and suggest that chaos may be
responsible for the sensitivity and temporal resolution of hair cells
Dimension reduction for systems with slow relaxation
We develop reduced, stochastic models for high dimensional, dissipative
dynamical systems that relax very slowly to equilibrium and can encode long
term memory. We present a variety of empirical and first principles approaches
for model reduction, and build a mathematical framework for analyzing the
reduced models. We introduce the notions of universal and asymptotic filters to
characterize `optimal' model reductions for sloppy linear models. We illustrate
our methods by applying them to the practically important problem of modeling
evaporation in oil spills.Comment: 48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanof
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