Early organization
of the nonlinear right brain and development of a predisposition to psychiatric disorders.
Within a biopsychosocial frame, we argue, that development is resulting
of a nonlinear combination of various
Journal
of Nonlinear Dynamics in Psychology and Life Sciences, 16, 331 - 352.
An existence theorem for weak solution
of a nonlinear dam problem, Applicable Anal.
Obtained the Oozy Technical Achievement Honor for the involvement
of nonlinear dynamical system analysis
The time scale of variability of the patterns is longer than the decorrelation time scale of the stochastic forcing, because of the temporal integration of the forcing by the equations of motion limited by the effects
of nonlinear dynamics and friction.
My earlier research has concerned, among others things, the use and the reliability of LES, the application
of nonlinear time series analysis on flow fields, and the inclusion of marine organic aerosol sources in global climate models.
The data show a lag of one component relative to another, which is another indication
of NONLINEAR DYNAMICS.
Of course Jims observations about the potential buildup
of nonlinear effects from the state of the ground (soil moisture, vegetaion, snow / ice cover etc.), is still valid.
The Greenland and Antarctic ice sheets have much larger masses and consequently much longer time constants, but there is already observational evidence
of nonlinear response.
Simple models are very different, and are more like an effective sensitivity and may well lack
some of the nonlinear dynamics / regional processes that occur in the real world and, in a more limited way, in the complex models.
This is why, I think, projections
of nonlinear melting are not allowed in the IPCC reports.
Similarly, if they allowed the nose
of the nonlinear camel under the tent, pretty soon they have a whole camel in their laps.
Earth's history provides evidence
of nonlinear switches in state or modes of variability of components of the climate system (6 ⇓ ⇓ ⇓ — 10).
By applying methods
of nonlinear dynamics, the solar activity cycle is studied using solar activity proxies that have been reaching into the past for over 9300 years.
Nor is there much understanding
of the nonlinear equations at the core of climate models — and why that curtails climate prediction.
The complexity of the system is expressed by several parameters
of nonlinear dynamics, such as embedding dimension or false nearest neighbors, and the method of delay coordinates is applied to the time series.
Biophysical Mechanisms and Feedbacks
of Nonlinear Feedbacks, Thresholds, and Hysteresis Trees that make up the main canopy, or emerge above it, access moisture
I hope to live long enough to read presentations of systems
of nonlinear dynamic systems that are complete enough, tested enough, and accurate enough to make reasonably dependable predictions at least decades ahead.
This is a property of the broad class
of nonlinear, complex, dynamic systems.
The issue of feedbacks is raised but trying to understand feedbacks in climate without a framework
of a nonlinear / nonequilibrium dynamic system is like trying to understand chemistry without the periodic table.
In other words, there's no indication
of a nonlinear system exhibiting jump resonance as an intrinsic response characteristic.
«On the trend, detrending, and variability
of nonlinear and nonstationary time series.»
Joshua, why can't you grasp the notion
of nonlinear systems?
The S from the IPCC comes from a definition that assumes we know the future of the full behavior
of the nonlinear system and can let the 2xCO2 effect run to completion (or absent that ideal value, can approximate it using models and possibly also using various simplified assumptions and calculations to speed how long it takes to calculate the value).
Any change in a model can produce divergent solutions that are not predictable beforehand — it is the nature
of the nonlinear Navier - Stokes equations.
Optimum Niño3.4 breakpoints are positive (> +0.4 °C) in the majority
of the nonlinear models, confirming that ENSO / precipitation relationships differs between La Niña / neutral and El Niño winters.
Our atmosphere - ocean model shows that the freshwater spurs amplifying feedbacks that would accelerate ice shelf and ice sheet mass loss, thus providing support for our assumption
of a nonlinear ice sheet response.
Two types
of nonlinear model — both one - sided GEV regressions where linear relationships are allowed to differ above / below a Niño3.4 index threshold — are considered.
Given the collective paleoclimatological evidence from the Paleogene, and a little knowledge
of nonlinear dynamical systems, it seems strange to think that anyone who understands these matters would think their heuristics and experience would continue to apply in a world which is no longer as stable as it once was.
Possible manifestation
of nonlinear effects when solar activity affects climate changes, M. G. Ogurtsov et al., 02/2010, Geomagnetism and Aeronomy, Volume 50, Number 1, pp. 15 - 20
Each of the members of the ensemble is a non-unique solution of a set
of nonlinear equations.
Any change in a model can produce divergent solutions that are not predictable beforehand — it is the nature
of the nonlinear Navier - Stokes equations — this extends to the range of uncertainty in climate data and to the number and breadth of couplings.
For that, we require that A˜mOrt should be higher than the sum
of the nonlinear terms in the original nonlinear barotropic vorticity equation on a sphere (see, e.g., ref.
This suggests that Amazon forest loss offsets the cooling effect imposed by wNA forest loss and is evidence
of a nonlinear geographic response due to forest loss in the two locations.
Here we show that climate oscillations over the past four million years can be explained by a single mechanism: the synchronization
of nonlinear internal climate oscillations and the 413,000 - year eccentricity cycle.»
Actually, Jeff Weiss comes from the community
of nonlinear geosciences, which does look at climate problems and issues related to the circulation of the oceans and atmosphere.
(Note: the combination of natural internal variability plus solar variability remains a plausible explanation for most of the 20th century variability; the issue
of nonlinear interactions between forcings and responses has not been convincingly explored.)
Given the range of possible outcomes
of nonlinear processes in individual models — the usefulness of this is a matter of perspective.
Let S+T be S distorted by the addition
of some nonlinear signal T. Detrending S+T by T gives back S, which admits the original orthogonal decomposition.
3) The removal
of any nonlinear trend destroys the orthogonality of decomposition.
«Synchronization is a fundamental nonlinear phenomenon and one basic mechanism of self - organization in complex systems 14, and synchronization
of nonlinear oscillators to external forcing (see Supplementary Information) is commonly encountered in physics, chemistry, biology, engineering and climatology 13 — 17.
Ah — the wonders
of nonlinear responses in the planetary system.
[20] Some internal soliton packets are the result
of the nonlinear evolution of the internal tide.
Such chaotic behaviour may limit the predictability
of nonlinear dynamical systems.»
To understand why requires a little knowledge
of nonlinear dynamics and complexity science.
This revolution has brought new understanding
of nonlinear dynamics, complex systems, chaos theory, catastrophe theory.
Finite precision computer realizations
of nonlinear models give unrealistic solutions because of deterministic chaos, a direct consequence of round - off error growth in iterative numerical computations.»
«The great revolution
of nonlinear dynamics over recent decades has provided a wealth of information about the bifurcations that can destabilise a slowly evolving system like the Earth's climate.
This revolution has brought new understanding
of nonlinear dynamics, complex systems, ch...