Abortive responses and rapid chattering between modes are common problems in
nonlinear systems with not quite enough oomph, the reason why old fluorescent lights flicker.
(3) Now, if we enlarge the system further to include the deep ocean, we have
a nonlinear system with a component that has response times on the order of a millennium.
However, this apparent impulsive behavior explicitly highlights the fact that humanity is poking a complex,
nonlinear system with GHG forcing — and that there are no guarantees to how the climate may respond.
And just to be clear on this «In simple English, knock
an nonlinear system with hysteresis hard enough, it may not return back to its original stability point.
Not exact matches
Spin
systems are
nonlinear and difficult to work
with, Li said, while spring
systems, or harmonic oscillators, are linear and easier to work
with.
Therefore, the results achieved in this study have shown that
nonlinear effects in graphene nano - mechanical resonators reveal a hybridization effect at high energies that, if controlled, could open up new possibilities to manipulate vibrational states, engineer hybrid states
with mechanical modes at completely different frequencies, and to study the collective motion of highly tunable
systems.
Now, a team of scientists has streamlined the problem by combining ocean wave data
with a healthy dose of
nonlinear dynamics of the wave
system.
People have a tendency to approach the body [a
nonlinear system]
with a linear mentality i.e — If I do X, I'll get Y; If I eat X calories, in Y weeks I'll have Z amounts of fat loss.
Is there a chunk of the climate - change - radar - screen (concerned
with nonlinear systems and their interconnections and coupled responses) missing?
• Lack of formal model verification & validation, which is the norm for engineering and regulatory science • Circularity in arguments validating climate models against observations, owing to tuning & prescribed boundary conditions • Concerns about fundamental lack of predictability in a complex
nonlinear system characterized by spatio - temporal chaos
with changing boundary conditions • Concerns about the epistemology of models of open, complex
systems
Didier Sornette identified extremes in a number of dynamic
nonlinear systems — «associated
with what can be called equivalently a phase transition, a bifurcation, a catastrophe (in the sense of Rene Thom) or a tipping point» — as dragon - kings.
``... we should recognise that we are dealing
with a coupled
nonlinear chaotic
system, and therefore that the long - term prediction of future climate states is not possible.»
Each component is part of a complex and
nonlinear mechanism that in concert acts in ways consistent
with the behaviour of a broad class of deterministically chaotic
systems.
One part of the difficulty is that the Earth is a highly multivariate and chaotic driven / open
system with complex
nonlinear coupling between all of its many drivers, and
with anything but a regular surface.
If one tried to actually write «the» partial differential equation for the global climate
system, it would be a set of coupled Navier - Stokes equations
with unbelievably nasty
nonlinear coupling terms — if one can actually include the physics of the water and carbon cycles in the N - S equations at all.
In the paper he said: «However, in the Earth — ocean — atmosphere
system,
nonlinear oscillations and excitation of the [Chandler Wobble] occur primarily at combinational frequencies of the Chandler frequency (
with periods of 2.4, 3.6, 4.8, and 6.0 years), rather than at the principal resonant frequency.»
Experience
with solution algorithms, data assimilation methods and tools, coupling of components and processes,
nonlinear and linear solvers, limiters, and / or other numerical issues common
with complex codes within earth
system models of varying complexity
If «[t] he inconvenient truth remains,» according to Philip Stott, that «climate is the most complex, coupled,
nonlinear, chaotic
system known,» then like flipping a coin, It will not matter if we devise a mathematical model to combine the data of the last 100 flips
with a dataset reflecting the 100 flips before that — even if you consider want to consider how many tails you got on the previous 1,000 flips — the odds for the next flip still will be 50 - 50.
The model output is evidence of the result of the many processes working together, much as the Pythagorean theorem provides evidence about the hypoteneuses of a large set imperfectly studied right triangles; or long term simulations of the planetary movements based on Newton's laws provide evidence that the orbits are chaotic rather than periodic; or simulations provide evidence that high - dimensional
nonlinear dissipative
systems are never in equilibrium or steady state even
with constant input.
As a card carrying member of the climate is acomplex fairly simple
nonlinear system, I sleep
with one eye open and watch every available monitoring
system for... of all things... lol... 60 - year cycles, especially the negative 1/2»cause I'm pretty much convinced there ain't gonna be one.
Recent global climate change is also likely to affect large - scale atmospheric circulation patterns,
with strong
nonlinear feedbacks between thermodynamic and dynamic components of the climate
system (10, 11).
In a
system such as the climate, we can never include enough variables to describe the actual
system on all relevant length scales (e.g. the butterfly effect — MICROSCOPIC perturbations grow exponentially in time to drive the
system to completely different states over macroscopic time) so the best that we can often do is model it as a complex
nonlinear set of ordinary differential equations
with stochastic noise terms — a generalized Langevin equation or generalized Master equation, as it were — and average behaviors over what one hopes is a spanning set of butterfly - wing perturbations to assess whether or not the resulting
system trajectories fill the available phase space uniformly or perhaps are restricted or constrained in some way.
«WG1.said «we should recognize that we are dealing
with a coupled
nonlinear chaotic
system, and therefore that the long - term prediction of future climate states is not possible.
Did you know that the exact same real world
system can be modeled
with the exact same feedback as either linear or
nonlinear by choice of flow variables?
The complete set forms a non-Markovian
nonlinear, coupled integrodifferential
system with timescales stretching from minutes to millions of years.
I, like you, am very skeptical of any attempt to remove some particular «natural signal» from a coupled
nonlinear chaotic
system with gazillions of feedbacks known and unknown and (mostly) transient, fluctuations that happened to nucleate at some particular point and grow.
The timing of interglacials indicates that the
system is a periodically forced
nonlinear oscillator,
with the dominant forcing being obliquity.
Can one describe the climate
system as a (weakly) periodically forced
nonlinear oscillator, in terms of the interaction of its internal
nonlinear dynamics
with external periodic forcing?
Although the Earth
system does seem to share behaviours
with these
nonlinear sets of equations — is this merely coincidental?
The cornerstone is the theory of random dynamical
systems, which allows us to probe the detailed geometric structure of the random attractors associated
with nonlinear, stochastically perturbed
systems.
In 2007, WG1.said «we should recognize that we are dealing
with a coupled
nonlinear chaotic
system, and therefore that the long - term prediction of future climate states is not possible.»
It is my opinion, based on my familiarity
with nonlinear dynamical
systems and
with the physics driving these mechanisms, that temperature increases of this magnitude will not stabilize at these levels as the feedbacks kick in.
phil said: «It is beyond any doubt that a large dissipative open
system with obvious chaotic dynamics such as the climate, is subject to internally driven
nonlinear oscillations over a wide range of time scales.»
The
system could well be a «weakly forced
nonlinear oscillator» in which a range of external forcings (solar, tidal, Milankovich etc.) interact
with the
systems own
nonlinear oscillations and resonances to yield the end result of an almost intractably complex climate
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