Crucifix, M. and J. Rougier, 2009, «On the use of simple
dynamical systems for climate predictions: A Bayesian prediction of the next glacial inception», Published in Eur.
«The idea behind using
dynamical systems for computation is to build a machine such that its dynamics — which has to do with the structure of the machine or the structure of the math — will lead it to the answer based on feeding it the question,» said Rothganger, a computer scientist.
Except in perturbative contexts (such as the neighbourhood of a fixed point or invariant torus), the long - time evolution of
a dynamical system for deterministic data is still largely only controllable by the classical tools of exact solutions, conservation laws and monotonicity formulae; a discovery of a new and effective tool for this purpose would be a major breakthrough.
Not exact matches
Thus, non-deterministic (or non-predictable) outcomes must occur
for all
dynamical systems if they are examined at a sufficiently refined scale of computational analysis.8
Mirzakhani got the Fields Medal
for Mathematics in 2014
for her work on complex geometry and
dynamical systems.
Future observations and studies into the
dynamical lifetimes of non-resonant planet - crossing orbits in the far regions of the outer solar
system could help to further test the case
for the existence and whereabouts of a ninth planet, Malhotra and her co-authors write.
«Markov partitioning is transforming a continuous trajectory of a
dynamical system stored in variables of high resolution into something discrete that can be stored in a finite set of variables with finite resolution,
for instance, an alphabet,» said Nicolás Rubido of the Universidad de la República.
Employing
dynamical systems theory, the authors map out a strategy
for modeling the trajectories of various SWEITs through their evolution.
Rubido pointed out that this new approach offers no advantage over some of the existing methods
for very simple cases, but said it could be especially useful
for analyzing high - dimension
dynamical systems, which quickly overwhelm existing computing power.
Lead author Dr Chris Bakal, leader of the
Dynamical Cell
Systems Team at The Institute of Cancer Research, London, said: «The endoplasmic reticulum is the factory of our cells, creating the proteins and lipids needed
for our cells to grow and proliferate.
«This camera has the potential to greatly enhance our understanding of very fast biological interactions and chemical processes that will allow us to build better models of complex,
dynamical systems such as cellular respiration, or to help doctors better deliver and monitor light - based therapies,» says Richard Conroy, Ph.D., program director
for Optical Imaging at NIBIB.
Nature Communications published the finding — a practical algorithm
for inferring laws of nature from time - series data of
dynamical systems.
The vibratory states of a
dynamical (chaotic)
system could to date only be visualized with methods requiring several graphs that are hard to interpret
for non-mathematicians.
Avila won
for work in the theory of
dynamical systems.
The findings are believed to be very general, but the investigation should clearly be extended also to other model
systems to further support the view of coinciding structural and
dynamical inhomogeneities being responsible
for glass formation.
The 2015 TWAS - Lenovo Science Prize was awarded to Artur Avila,
for his outstanding contributions to several areas of
dynamical systems, especially to the spectral theory of one - frequency Schrödinger operators.
The chance to study an actual ejection of a star from a multiple
system can provide a critical test
for the
dynamical theories.
The paper, titled «
Dynamical Considerations
for Life in Multihabitable Planetary
Systems» has been accepted
for publication in the Astrophysical Journal.
Results, which were published in the June 1 issue of PLoS Computational Biology, have implications
for how evolutionary pressures can improve the function of receptor
systems by selectively optimizing a few fundamental
dynamical parameters.
In an attempt to understand and feel the mathematical concept of strange attractors in
dynamical systems, she jumbles her recent obsession
for doughnuts, fortune - tellers, hemorrhoids, and things detected in the world».
Rockel, B., C.L. Castro, R.A. Pielke Sr., H. von Storch, and G. Leoncini, 2008:
Dynamical downscaling: Assessment of model
system dependent retained and added variability
for two different regional climate models.
Feedbacks are not what gives rise to chaos, but
for some
dynamical systems they can.
At present there is less theoretical basis
for a first principles development of the
dynamical behaviour of the terrestrial
system.
(The original article has a great deal of interesting discussion under it,
for those with the stomach
for talk of strange attractors,
dynamical systems, and stochastic processes.)
We have used the Grid ENabled Integrated Earth
system modelling (GENIE) framework to undertake a systematic search
for bi-stability of the ocean thermohaline circulation (THC)
for different surface grids and resolutions of 3 - D ocean (GOLDSTEIN) under a 3 - D
dynamical atmosphere model (IGCM).
The IMA (Institute
for Mathematics and its Applications) has a 2013 Thematic Year on Infinite Dimensional and Stochastic
Dynamical Systems and their Applications with a workshop on Atmospheres and Oceans.
The fact is as soon as there is any external perturbation of a chaotic
system not accounted
for in the
dynamical equations, you have bumped the
system from one path in phase space to another.
There are no «perturbations» inside a chaotic
system — a solution of the
dynamical equations is what it is and all the «perturbations» are already accounted
for.
One of the strongest opponents I know of this appropriation of climate models is the preeminent expert in numerical analysis and
dynamical systems, Chris Essex, who himself worked on climate models
for years.
More broadly, variations in the attenuation of visible radiation in the upper ocean, which directly relates to changes in ZSD, alter local heating and, consequently, have an effect on the thermal and fluid
dynamical processes
for the ocean - atmosphere
system.
«We first state the main problem of the statistical analysis of stochastic
dynamical systems as we understand it: based on a statistical analysis of these
systems, to reveal their common features that are realized with probability one, i.e.,
for almost every realization of the relevant
dynamical system.
James McWilliams, of the Department of Atmospheric and Oceanic Sciences at the University of California Los Angeles, says that «sensitive dependence and structural instability are humbling twin properties
for chaotic
dynamical systems, indicating limits about which kinds of questions are theoretically answerable.»
Lorenz type chaos is a phenomenon that is true only
for simple
systems of few dominating variables, which follow their
dynamical equations with high precision without significant stochastic disruptions.
A
dynamical climate model driven hydrologic prediction
system for the Fraser River, Canada.
This is an incredibly vague statement; but part of the difficulty with this problem, which also exists in one form or another in many other famous problems (e.g. Riemann hypothesis,, P = NP, twin prime and Goldbach conjectures, normality of digits of Pi, Collatz conjecture, etc.) is that we expect any sufficiently complex (but deterministic)
dynamical system to behave «chaotically» or «pseudorandomly», but we still have very few tools
for actually making this intuition precise, especially if one is considering deterministic initial data rather than generic data.
The model is not quite state - of - the - art, in that it does not solve the full Stokes equation but a simpler form of the
dynamical system that is appropriate
for ice shelves and ice streams.
The journal
Dynamical Systems is one of publications
for this field, covering such exciting topics as «Periodic Orbits of Oval Billiards on Surfaces of Constant Curvature».
For a complex
dynamical system we have the possibility that dissipative processes are strong enough to maintain long term stability and to remove the possibility major state shifts.
As James McWilliams said — «Sensitive dependence and structural instability are humbling twin properties
for chaotic
dynamical systems, indicating limits about which kinds of questions are theoretically answerable.
Aires, F., and W.B. Rossow, 2003: Inferring instantaneous, multivariate and nonlinear sensitivities
for the analysis of feedback processes in a
dynamical system: The Lorenz model case study.
Sensitive dependence and structural instability are humbling twin properties
for chaotic
dynamical systems, indicating limits about which kinds of questions are theoretically answerable.
It appears to me, caveat as above, that AGW has created a lifeless
system in thinking in this «energy balance» much as it has done with CO2 with its destruction of the
dynamical system which is all life by thinking of plants merely as «carbon sinks», somewhere merely to store CO2; from which the used to be known fact that CO2 was food
for all living carbon life forms is practically unknown and now at the absurd reasoning from not knowing it, that it can defy gravity and stay removed and out of reach from the carbon life forms which evolved from its property of being available at ground level.
Obtained the Oozy Technical Achievement Honor
for the involvement of nonlinear
dynamical system analysis