scholarly journals Climate change in mechanical systems: the snapshot view of parallel dynamical evolutions

2021 ◽  
Author(s):  
Dániel Jánosi ◽  
György Károlyi ◽  
Tamás Tél
Keyword(s):  
Climate Change ◽  
Initial Conditions ◽  
Mechanical Systems ◽  
Quantitative Measure ◽  
Pairwise Distance ◽  
Dissipative Systems ◽  
Class Iii ◽  
Kam Tori ◽  
Bistable Systems ◽  
Low Dimensional

AbstractWe argue that typical mechanical systems subjected to a monotonous parameter drift whose timescale is comparable to that of the internal dynamics can be considered to undergo their own climate change. Because of their chaotic dynamics, there are many permitted states at any instant, and their time dependence can be followed—in analogy with the real climate—by monitoring parallel dynamical evolutions originating from different initial conditions. To this end an ensemble view is needed, enabling one to compute ensemble averages characterizing the instantaneous state of the system. We illustrate this on the examples of (i) driven dissipative and (ii) Hamiltonian systems and of (iii) non-driven dissipative ones. We show that in order to find the most transparent view, attention should be paid to the choice of the initial ensemble. While the choice of this ensemble is arbitrary in the case of driven dissipative systems (i), in the Hamiltonian case (ii) either KAM tori or chaotic seas should be taken, and in the third class (iii) the best choice is the KAM tori of the dissipation-free limit. In all cases, the time evolution of the chosen ensemble on snapshots illustrates nicely the geometrical changes occurring in the phase space, including the strengthening, weakening or disappearance of chaos. Furthermore, we show that a Smale horseshoe (a chaotic saddle) that is changing in time is present in all cases. Its disappearance is a geometrical sign of the vanishing of chaos. The so-called ensemble-averaged pairwise distance is found to provide an easily accessible quantitative measure for the strength of chaos in the ensemble. Its slope can be considered as an instantaneous Lyapunov exponent whose zero value signals the vanishing of chaos. Paradigmatic low-dimensional bistable systems are used as illustrative examples whose driving in (i, ii) is chosen to decay in time in order to maintain an analogy with case (iii) where the total energy decreases all the time.

scholarly journals Climate Change in Mechanical Systems: The Snapshot View of Parallel Dynamical Evolutions

2021 ◽  
Author(s):  
Daniel Janosi ◽  
Gyorgy Karolyi ◽  
Tamas Tel
Keyword(s):  
Climate Change ◽  
Initial Conditions ◽  
Mechanical Systems ◽  
Quantitative Measure ◽  
Pairwise Distance ◽  
Dissipative Systems ◽  
Class Iii ◽  
Kam Tori ◽  
Bistable Systems ◽  
Low Dimensional

Abstract We argue that typical mechanical systems subjected to a monotonous parameter drift whose time scale is comparable to that of the internal dynamics can be considered to undergo their own climate change. Because of their chaotic dynamics, there are many permitted states at any instant, and their time dependence can be followed - in analogy with the real climate - by monitoring parallel dynamical evolutions originating from different initial conditions. To this end an ensemble view is needed, enabling one to compute ensemble averages characterizing the instantaneous state of the system. We illustrate this on the examples of (i) driven dissipative and (ii) Hamiltonian systems and of (iii) non-driven dissipative ones. We show that in order to find the most transparent view, attention should be paid to the choice of the initial ensemble. While the choice of this ensemble is arbitrary in the case of driven dissipative systems (i), in the Hamiltonian case (ii) either KAM tori or chaotic seas should be taken, and in the third class (iii) the best choice is the KAM tori of the dissipation-free limit. In all cases, the time evolution of the chosen ensemble on snapshots illustrates nicely the geometrical changes occurring in the phase space, including the strengthening, weakening or disappearance of chaos. Furthermore, we show that a Smale horseshoe (a chaotic saddle) that is changing in time is present in all cases. Its disappearance is a geometrical sign of the vanishing of chaos. The so-called ensemble-averaged pairwise distance is found to provide an easily accessible quantitative measure for the strength of chaos in the ensemble. Its slope can be considered as an instantaneous Lyapunov exponent whose zero value signals the vanishing of chaos. Paradigmatic low-dimensional bistable systems are used as illustrative examples whose driving in (i, ii) is chosen to decay in time in order to maintain an analogy with case (iii) where the total energy decreases all the time.

Numerical Analysis of Conservative Maps: A Possible Foundation of Nonextensive Phenomena

2004 ◽  
Author(s):  
Fulvio Baldovin
Keyword(s):  
Statistical Mechanics ◽  
High Energy Physics ◽  
Financial Analysis ◽  
Initial Conditions ◽  
Research Area ◽  
Distribution Functions ◽  
Point Of View ◽  
Dissipative Systems ◽  
Definition Of ◽  
Low Dimensional

We discuss the sensitivity to initial conditions and the entropy production of low-dimensional conservative maps, focusing on situations where the phase space presents complex (fractal-like) structures. We analyze numerically the standard map as a specific example and we observe a scenario that presents appealing analogies with anomalies detected in long-range Hamiltonian systems. We see how the Tsallis nonextensive formalism handles this situation both from a dynamical and from a statistical mechanics point of view…. In recent years, the Tsallis extension of the Boltzmann-Gibbs (BG) statistical mechanics [9, 26], usually referred to as nonextensive (NE) statistical mechanics, has become an intense and exciting research area (see, e.g., Tsallis [25]). The q-exponential distribution functions that emerge as a consequence of the NE formalism have been applied to an impressive variety of problems, ranging from turbulence, to high-energy physics, epilepsy, protein folding, and financial analysis. Yet, the foundation of this formalism, as well as the definition of its area of applicability, is still not completely understood, and it stands as a present challenge in the affirmation of the whole proposal. An intensive effort is currently being made to investigate this point, precisely in trying to understand: (1) which mechanisms lead to a crisis of the BG formalism; and (2) in these cases, does the NE formalism provide a "way out" to some of the problems? A possible approach to these questions comes from the study of the underlying dynamics that gives the basis for a statistical mechanic treatment of the system. This idea is not new. Einstein, in his critical remark about the validity of the Boltzmann principle [10], was one of the first to call attention to the relevance of a dynamical foundation of statistical mechanics. Another fundamental contribution is Krylov's seminal work [14] on the mixing properties of dynamical systems. In one-dimensional (dissipative) systems, intensive effort has been made to analyze the properties of the systems at the edge of chaos, i.e., at the critical poin that marks the transition between chaoticity and regularity [6, 8, 16, 19, 18, 23, 27].

scholarly journals “Fuzzy Band Gaps”: A Physically Motivated Indicator of Bloch Wave Evanescence in Phononic Systems

Crystals ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 66
Author(s):  
Connor D. Pierce ◽  
Kathryn H. Matlack
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Quantitative Measure ◽  
Bloch Wave ◽  
Phononic Crystals ◽  
Wave Transmission ◽  
Band Gaps ◽  
Dissipative Systems ◽  
Frequency Range ◽  
Wave Modes

Phononic crystals (PCs) have been widely reported to exhibit band gaps, which for non-dissipative systems are well defined from the dispersion relation as a frequency range in which no propagating (i.e., non-decaying) wave modes exist. However, the notion of a band gap is less clear in dissipative systems, as all wave modes exhibit attenuation. Various measures have been proposed to quantify the “evanescence” of frequency ranges and/or wave propagation directions, but these measures are not based on measurable physical quantities. Furthermore, in finite systems created by truncating a PC, wave propagation is strongly attenuated but not completely forbidden, and a quantitative measure that predicts wave transmission in a finite PC from the infinite dispersion relation is elusive. In this paper, we propose an “evanescence indicator” for PCs with 1D periodicity that relates the decay component of the Bloch wavevector to the transmitted wave amplitude through a finite PC. When plotted over a frequency range of interest, this indicator reveals frequency regions of strongly attenuated wave propagation, which are dubbed “fuzzy band gaps” due to the smooth (rather than abrupt) transition between evanescent and propagating wave characteristics. The indicator is capable of identifying polarized fuzzy band gaps, including fuzzy band gaps which exists with respect to “hybrid” polarizations which consist of multiple simultaneous polarizations. We validate the indicator using simulations and experiments of wave transmission through highly viscoelastic and finite phononic crystals.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

Low-dimensional HfS2 as SO2 adsorbent and gas sensor: Effect of water and sulfur vacancies

2021 ◽  
Author(s):  
Amina Bouheddadj ◽  
Tarik Ouahrani ◽  
Gbèdodé Wilfried KANNHOUNON ◽  
Boufatah Reda ◽  
Sumeya Bedrane ◽  
...  
Keyword(s):  
Climate Change ◽  
Density Functional Theory ◽  
Dft Calculations ◽  
Gas Sensor ◽  
First Principles ◽  
Density Functional ◽  
Two Dimensional ◽  
Functional Theory ◽  
Sensor Effect ◽  
Low Dimensional

First-principles based on density functional theory (DFT) calculations were performed to investigate the interaction of two-dimensional (2D) HfS2 with SO2, a harmful gas with implications for climate change. In particular,...

scholarly journals New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries

2020 ◽  
Vol 17 (06) ◽  
pp. 2050090 ◽  
Author(s):  
Jordi Gaset ◽  
Xavier Gràcia ◽  
Miguel C. Muñoz-Lecanda ◽  
Xavier Rivas ◽  
Narciso Román-Roy
Keyword(s):  
Dynamical Systems ◽  
Mechanical Systems ◽  
Dissipative Systems ◽  
Conserved Quantities ◽  
Dynamical Equations ◽  
Lagrangian Formulations ◽  
New Form

We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian formalisms, studying their equivalence. We define several kinds of symmetries for contact dynamical systems, as well as the notion of dissipation laws, prove a dissipation theorem and give a way to construct conserved quantities. Some well-known examples of dissipative systems are discussed.

Climate and Environmental Crises

2020 ◽  
Author(s):  
Victor Galaz
Keyword(s):  
Climate Change ◽  
Food Insecurity ◽  
Carbon Dioxide Emissions ◽  
Heat Waves ◽  
Initial Conditions ◽  
Marine Species ◽  
Climate System ◽  
Weather Extremes ◽  
Intergovernmental Panel ◽  
Climate Crisis

Climate change is increasingly being framed as a “climate crisis.” Such a crisis could be viewed both to unfold in the climate system, as well as to be induced by it in diverse areas of society. Following from current understandings of modern crises, it is clear that climate change indeed can be defined as a “crisis.” As the Intergovernmental Panel on Climate Change 1.5oC special report elaborates, the repercussions of a warming planet include increased food insecurity, increased frequency and intensity of severe droughts, extreme heat waves, the loss of coral reef ecosystems and associated marine species, and more. It is also important to note that a range of possible climate-induced crises (through, e.g., possible increased food insecurity and weather extremes) will not be distributed evenly, but will instead disproportionally affect already vulnerable social groups, communities, and countries in detrimental ways. The multifaceted dimensions of climate change allow for multiple interpretations and framings of “climate crisis,” thereby forcing us to acknowledge the deeply contextual nature of what is understood as a “crisis.” Climate change and its associated crises display a number of challenging properties that stem from its connections to basically all sectors in society, its propensity to induce and in itself embed nonlinear changes such as “tipping points” and cascading shocks, and its unique and challenging long-term temporal dimensions. The latter pose particularly difficult decision-making and institutional challenges because initial conditions (in this case, carbon dioxide emissions) do not result in immediate or proportional responses (say, global temperature anomalies), but instead play out through feedbacks among the climate system, oceans, the cryosphere, and changes in forest biomes, with some considerable delays in time. Additional challenges emerge from the fact that early warnings of pending so-called “catastrophic shifts” face numerous obstacles, and that early responses are undermined by a lack of knowledge, complex causality, and severe coordination challenges.

Periodic orbits analysis for the Zhou system via variational approach

2019 ◽  
Vol 33 (19) ◽  
pp. 1950212 ◽  
Author(s):  
Chengwei Dong ◽  
Lian Jia
Keyword(s):  
Fixed Points ◽  
Periodic Orbits ◽  
Symbolic Dynamics ◽  
Variational Approach ◽  
Topological Classification ◽  
Dissipative Systems ◽  
Systematic Calculation ◽  
Low Dimensional ◽  
General Method

We proposed a general method for the systematic calculation of unstable cycles in the Zhou system. The variational approach is employed for the cycle search, and we establish interesting symbolic dynamics successfully based on the orbits circuiting property with respect to different fixed points. Upon the defined symbolic rule, cycles with topological length up to five are sought and ordered. Further, upon parameter changes, the homotopy evolution of certain selected cycles are investigated. The topological classification methodology could be widely utilized in other low-dimensional dissipative systems.

Efficient Numerical Shadowing Global Error Estimation for High Dimensional Dissipative Systems

2004 ◽  
Vol 4 (2) ◽  
Author(s):  
Jon Collis ◽  
Erik S. Van Vleck
Keyword(s):  
Error Estimation ◽  
Initial Conditions ◽  
Efficient Estimation ◽  
Global Error ◽  
Dissipative Systems ◽  
High Dimensional ◽  
Initial Value ◽  
Small Perturbations ◽  
One Step ◽  
Global Error Estimation

AbstractShadowing is a means of characterizing global errors in the numerical solution of initial value differential equations by allowing for small perturbations in the initial conditions. The method presented in this paper provides a technique for efficient estimation of the shadowing global error for systems that have a large number of exponentially decaying modes. The method is formulated for one-step methods and is applied to the spatial discretization of some dissipative PDEs.

CHAOTIC ANALYSIS OF A TIME SERIES COMPOSED OF SEISMIC EVENTS RECORDED IN JAPAN

1994 ◽  
Vol 04 (01) ◽  
pp. 87-98 ◽  
Author(s):  
G.P. PAVLOS ◽  
L. KARAKATSANIS ◽  
J.B. LATOUSSAKIS ◽  
D. DIALETIS ◽  
G. PAPAIOANNOU
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Initial Conditions ◽  
Low Frequency ◽  
Underlying Mechanism ◽  
Largest Lyapunov Exponent ◽  
Seismic Events ◽  
Earthquake Dynamics ◽  
The Largest Lyapunov Exponent ◽  
Low Dimensional

A chaotic analysis approach was applied to an earthquake time series recorded in the Japanese area in order to test the assumption that the earthquake process could be the manifestation of a chaotic low dimensional process. For the study of the seismicity we have used a time series consisting of time differences between two consecutive seismic events with magnitudes greater than 2.6. The results of our study show that the underlying mechanism, as expressed by the time series, can be described by low dimensional chaotic dynamics. The power spectrum of the time series shows a power law profile with two slopes, α=1.4 in the low frequency and α=0.05 in the high frequency regions, while the slopes of the correlation integrals show an apparent plateau at the scaling region, which saturates at the value D≈3.2. The largest Lyapunov exponent was found to be ≈0.9. The positive value of the largest Lyapunov exponent reveals strong sensitivity to initial conditions of the supposed earthquake dynamics.

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