Sentences with phrase «in nonlinear systems»

On Universality of Transition to Chaos Scenario in Nonlinear Systems of Ordinary Differential Equations of Shilnikov's Type

The fact though, is that «averages» in a nonlinear systems are close to useless and RH is nothing more than an average.

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.

While in Tampere, he did research in nonlinear systems, image recognition and classification, image correspondence, computational learning theory, multiscale and spectral methods, and statistical signal processing.

In a nonlinear system, the decay rate must be determined by measurement.

Though, as these are statistics about largely linear questions in a nonlinear system, that approach is of somewhat dubious merit.

Not exact matches

And his book suggests that scientists should address the obvious metaphysical implications of twentieth - century physics: e.g., Einstein and quantum mechanics and the more recent developments in the field of chaos theory and nonlinear systems.

We hope that our work will further spark interest in studying and manipulating nonlinear optical effects in novel nanoscale systems using unconventional excitation beams.»

This relation of the Schrödinger equation to classical waves is already revealed in the way that a variant called the nonlinear Schrödinger equation is commonly used to describe other classical wave systems — for example in optics and even in ocean waves, where it provides a mathematical picture of unusually large and robust «rogue waves.»

The new system now demonstrated will soon allow further experiments on phase transitions in classical systems and in the quantum universe as well as tests in the field of nonlinear physics (e.g. solitons) to be performed in a well - controlled comparative system.

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.

Many natural phenomena, like changing weather patterns, are nonlinear in nature — as are human - made systems, like financial markets.

«To predict the effects this type of deforestation has on the relationship between rain forest and the savanna — and on the local and global climate — it's necessary to understand how the transitional forest evolves in time and reacts to disturbances,» explained Yannick De Decker, associate professor at the Center for Nonlinear Phenomena and Complex Systems, as well as the Nonlinear Physical Chemistry Unit at ULB.

Today, scientists around the world, including those at the Potsdam Institute for Climate Impact Research that Schellnhuber founded in 1992, are successfully investigating the nonlinear dynamics of the complex climate system, and religious leaders like Pope Francis - whose green Encyclical Schellnhuber had the honor to present to the world in 2015 - joined in the call for avoiding dangerous climate change.

Heebner was cited for his «numerous innovations, achievements and technical leadership in high - energy laser systems and integrated optics including nonlinear optical microresonators and ultrafast light deflectors.»

«The intriguing interactions among the materials» micromechanical properties and various nonlinearities may provide new scientific opportunities to emulate the symbiotic interactions in biological systems,» Ed Habtour, PhD, an ARL researcher who specializes in nonlinear structural dynamics, said in a statement.

Heebner was cited for his «numerous innovations, achievements and technical leadership in high - energy laser systems and integrated optics including nonlinear...

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.

You see, the human body is a nonlinear system and things like the calories in versus calories out model — a linear system — at best, give us only a guide of how things will go.

Capitalism is a complex, dynamic, adaptive and nonlinear system because it has elements or agents that interact in large numbers together forming one or more structures that arise from interactions between such agents.

The economy, and most industries are nonlinear dynamic systems, which means there will be cyclical behavior, and that behavior will be more volatile the greater the level of fixed commitments in the system that must be satisfied.

Nassim Taleb thinks in the same way, including the nonlinear impact of systems level interactions.

• 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

Nature is a nonlinear dynamic system, you are starring on the selected, smoothed linear Mauna Loa data in a 50 years time window at 4 km altitude.

In climate — nothing is certain but that the system is multiply coupled and nonlinear.

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.

«A dynamical system such as the climate system, governed by nonlinear deterministic equations (see Nonlinearity), may exhibit erratic or chaotic behaviour in the sense that very small changes in the initial state of the system in time lead to large and apparently unpredictable changes in its temporal evolution.

Ah — the wonders of nonlinear responses in the planetary system.

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.

«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.

In the context of a coupled, nonlinear system — the system is sensitive to small changes in power iIn the context of a coupled, nonlinear system — the system is sensitive to small changes in power iin power inin.

Similarly, contraction theory can be systematically and simply extended to address classical questions in hybrid nonlinear systems.

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.&raquIn 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.&raquin 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.»

In principle climate is a coupled, nonlinear, chaotic system — but how recurrent (technically ergodic)-- are these patterns?

They provide exact necessary and sufficient conditions for these characteristics for all linear systems and some nonlinear systems... Now I am merely trying to acquaint climate change scientists, physicists, lawyers and politicians promoting such things as Kyoto Protocols that chemical process control system engineering has a useful voice, weak as it is, in climate control engineering....

This spread results because the model equations provide a deterministic set of results that each can be different since the climate is a chaotic nonlinear system both in the model, and even more so in the real world.

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.

He may have in mind that sort of integration or NONlinear systems that indeed can create harmonics and subharmonics.

In this paper, af - ter a brief tutorial on the basics of climate nonlinearity, we provide a number of illustrative examples and highlight key mechanisms that give rise to nonlinear behavior, address scale and methodological issues, suggest a robust alternative to prediction that is based on using integrated assessments within the framework of vulnerability studies and, lastly, recommend a number of research priorities and the establishment of education programs in Earth Systems SciencIn this paper, af - ter a brief tutorial on the basics of climate nonlinearity, we provide a number of illustrative examples and highlight key mechanisms that give rise to nonlinear behavior, address scale and methodological issues, suggest a robust alternative to prediction that is based on using integrated assessments within the framework of vulnerability studies and, lastly, recommend a number of research priorities and the establishment of education programs in Earth Systems Sciencin Earth Systems Science.

Complex nonlinear multivariate systems often exhibit «strange attractors» — local fixed points in a set of coupled nonlinear ordinary differential equations — that function as foci for Poincare cycles in the multivariate phase space.

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 waIn 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 wain 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 wain some way.

In the long term, forward, process - based models of proxy formation are needed for explicitly representing multivariate, nonlinear, and potentially nonstationary relationships between the proxy and climate systems [Evans et al., 2013].

For it was Lovelock's Gaia Hypothesis which first popularised the idea that the biosphere is a massively complex nonlinear system that works to regulate many different subsystems towards a relatively narrow envelope of values necessary for the continuity of life on the planet through a tangle of negative feedbacks, in much the same way the human body maintains constant internal conditions necessary for life.

That the most complex nonlinear system on the planet has a built - in runaway feedback mechanism based on the common and important molecules of H2O and CO2.

To quote again from Rial et al 2004 — it «is imperative that the Earth's climate system research community embraces this nonlinear paradigm if we are to move forward in the assessment of the human influence on climate.»

Let me try to summarize the state of affairs before I speculate a little, based on what I know from somewhat analogous nonlinear systems seen in biophysics and neurobiology that also flip.

IMO, the standard 1D energy balance model of the Earth's climate system will provide little in the way of further insights; rather we need to bring additional physics and theory (e.g. entropy and the 2nd law) into the simple models, and explore the complexity of coupled nonlinear climate system characterized by spatiotemporal chaos.

«The Earth's climate system is highly nonlinear: inputs and outputs are not proportional, change is often episodic and abrupt, rather than slow and gradual,... It is imperative that the Earth's climate system research community embraces this nonlinear paradigm if we are to move forward in the assessment of the human influence on climate..»

«The Earth's climate system is highly nonlinear: inputs and outputs are not proportional, change is often episodic and abrupt, rather than slow and gradual, and multiple equilibria are the norm... there is a relatively poor understanding of the different types of nonlinearities, how they manifest under various conditions, and whether they reflect a climate system driven by astronomical forcings, by internal feedbacks, or by a combination of both... [We] suggest a robust alternative to prediction that is based on using integrated assessments within the framework of vulnerability studies... It is imperative that the Earth's climate system research community embraces this nonlinear paradigm if we are to move forward in the assessment of the human influence on climate.»