On the critical equilibrium of the spiral spring pendulum

2009 ◽  
Vol 466 (2114) ◽  
pp. 407-421 ◽  
Author(s):  
P. Coullet ◽  
J.-M. Gilli ◽  
G. Rousseaux
Keyword(s):  
Nonlinear Oscillator ◽  
Inverted Pendulum ◽  
Physical Systems ◽  
Supercritical Bifurcation ◽  
Euler Elastica ◽  
Critical Equilibrium ◽  
Spiral Spring ◽  
Joseph Larmor ◽  
Angular Amplitude ◽  
First Time

Physical systems such as an inverted pendulum driven by a spiral spring, an unbalanced Euler elastica with a travelling mass, a heavy body with a parabolic section and an Ising ferromagnet are very different. However, they all behave in the same manner close to the critical regime for which nonlinearities are prominent. We demonstrate experimentally, for the first time, an old prediction by Joseph Larmor, which states that a nonlinear oscillator close to its supercritical bifurcation oscillates with a period inversely proportional to its angular amplitude. We perform our experiments with a Holweck–Lejay-like pendulum which was used to measure the gravity field during the twentieth century.

scholarly journals Compositional cyber-physical epidemiology of COVID-19

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Jin Woo Ro ◽  
Nathan Allen ◽  
Weiwei Ai ◽  
Debi Prasad ◽  
Partha S. Roop
Keyword(s):  
New Zealand ◽  
Government Policy ◽  
Cyber Physical Systems ◽  
Published Data ◽  
Disease Dynamics ◽  
Physical Systems ◽  
The Government ◽  
The Impact ◽  
First Time ◽  
New Framework

Abstract The COVID-19 pandemic has posed significant challenges globally. Countries have adopted different strategies with varying degrees of success. Epidemiologists are studying the impact of government actions using scenario analysis. However, the interactions between the government policy and the disease dynamics are not formally captured. We, for the first time, formally study the interaction between the disease dynamics, which is modelled as a physical process, and the government policy, which is modelled as the adjoining controller. Our approach enables compositionality, where either the plant or the controller could be replaced by an alternative model. Our work is inspired by the engineering approach for the design of Cyber-Physical Systems. Consequently, we term the new framework Compositional Cyber-Physical Epidemiology. We created different classes of controllers and applied these to control the disease in New Zealand and Italy. Our controllers closely follow government decisions based on their published data. We not only reproduce the pandemic progression faithfully in New Zealand and Italy but also show the tradeoffs produced by differing control actions.

COMPLEX DYNAMICS IN COUPLED NONLINEAR ELEMENT SYSTEMS

1991 ◽  
Vol 05 (08) ◽  
pp. 1179-1214 ◽  
Author(s):  
KENJU OTSUKA
Keyword(s):  
Nonlinear Oscillator ◽  
Complex Dynamics ◽  
Landau Equation ◽  
Computer Experiments ◽  
Time Dependent ◽  
Chain Model ◽  
Ginzburg Landau ◽  
Physical Systems ◽  
Local Attractors ◽  
Discrete Complex

This paper reviews complex dynamics which arise through the interaction of simple nonlinear elements without chaotic response, including self-induced switching among local attractors (chaotic itinerancy) and related phenomena. Several realistic physical systems consisting of coupled nonlinear elements are considered on the basis of computer experiments: coupled nonlinear oscillator (e.g., discrete complex time-dependent Ginzburg-Landau equation) systems, coupled laser arrays, and a coupled multistable optical chain model.

scholarly journals Compositional Cyber-Physical Epidemiology of COVID-19

2020 ◽  
Author(s):  
Jin Woo Ro ◽  
Nathan Allen ◽  
Weiwei Ai ◽  
Debi Prasad ◽  
Partha S. Roop
Keyword(s):  
New Zealand ◽  
Government Policy ◽  
Cyber Physical Systems ◽  
Published Data ◽  
Disease Dynamics ◽  
Physical Systems ◽  
The Government ◽  
The Impact ◽  
First Time ◽  
New Framework

AbstractCOVID-19 pandemic has posed significant challenges globally. Countries have adopted different strategies with varying degrees of success. Epidemiologists are studying the impact of government actions using scenario analysis. However, the interactions between the government policy and the disease dynamics are not formally captured.We, for the first time, formally study the interaction between the disease dynamics, which is modelled as a physical process, and the government policy, which is modelled as the adjoining controller. Our approach enables compositionality, where either the plant or the controller could be replaced by an alternative model. Our work is inspired by the engineering approach for the design of Cyber-Physical Systems (CPSs). Consequently, we term the new framework Compositional Cyber-Physical Epidemiology (CCPE). We created different classes of controllers and applied these to control the disease in New Zealand and Italy. Our controllers closely follow government decisions based on their published data. We not only reproduce the pandemic progression faithfully in New Zealand and Italy but also show the tradeoffs produced by differing control actions.

Uncertainty Theory Based Partitioning for Cyber-Physical Systems with Uncertain Reliability Analysis

2022 ◽  
Vol 27 (3) ◽  
pp. 1-19
Author(s):  
Si Chen ◽  
Guoqi Xie ◽  
Renfa Li ◽  
Keqin Li
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Uncertainty Theory ◽  
Critical Issue ◽  
Cyber Physical System ◽  
Physical Systems ◽  
Uncertain Variables ◽  
Uncertainty Model ◽  
First Time ◽  
Enhancement Algorithm

Reasonable partitioning is a critical issue for cyber-physical system (CPS) design. Traditional CPS partitioning methods run in a determined context and depend on the parameter pre-estimations, but they ignore the uncertainty of parameters and hardly consider reliability. The state-of-the-art work proposed an uncertainty theory based CPS partitioning method, which includes parameter uncertainty and reliability analysis, but it only considers linear uncertainty distributions for variables and ignores the uncertainty of reliability. In this paper, we propose an uncertainty theory based CPS partitioning method with uncertain reliability analysis. We convert the uncertain objective and constraint into determined forms; such conversion methods can be applied to all forms of uncertain variables, not just for linear. By applying uncertain reliability analysis in the uncertainty model, we for the first time include the uncertainty of reliability into the CPS partitioning, where the reliability enhancement algorithm is proposed. We study the performance of the reliability obtained through uncertain reliability analysis, and experimental results show that the system reliability with uncertainty does not change significantly with the growth of task module numbers.

scholarly journals Phenomenological model of the generation of the seismic mode «drumbeats» earthquakes accompanying the eruption of Kizimen volcano in 2011-2012

2020 ◽  
pp. 86-101
Author(s):  
А.А. Шакирова ◽  
П.П. Фирстов ◽  
Р.И. Паровик
Keyword(s):  
Lava Flow ◽  
Phenomenological Model ◽  
Nonlinear Oscillator ◽  
Time Intervals ◽  
Stick Slip ◽  
Slip Mechanism ◽  
Long Time ◽  
The Mathematical Model ◽  
First Time ◽  
Mode Generation

Извержение вулкана Кизимен в 2011-2012 гг. характеризовалось устойчивым, почти равномерным выжиманием вязкого лавового потока объемом 0.3 км³. Формирование лавового потока сопровождалось возникновением квазипериодических землетрясений режима «drumbeats» с энергетическими классами Ks<7, регистрируемых на длительных временных участках. Показано, что землетрясения генерировались движением фронта вязкого лавового потока, что в практике вулканологических исследований наблюдалось впервые. Предложена феноменологическая модель генерации сейсмического режима «drumbeats». Движение фронта лавового потока по склону вулкана происходило в результате прерывистого скольжения с включением механизма «stick-slip» и возбуждением автоколебательного процесса с генерацией сейсмического режима «drumbeats». Правдоподобность феноменологической модели режима ««drumbeats» на качественном уровне подтверждена математической моделью дробного нелинейного осциллятора. The eruption of the Kizimen volcano in 2011-2012 characterized by stable, almost uniform squeezing of a viscous lava flow with a volume of 0.3 km³. The formation of the lava flow was accompanied by the occurrence of quasiperiodic earthquakes of the “drumbeats” mode with energy classes Ks < 7, recorded at long time intervals. Shown that earthquakes were generated by the movement of the front of a viscous lava flow, which was observed for the first time in the practice of volcanological research. A phenomenological model of “drumbeats” seismic mode generation is proposed. The movement of the front of the lava flow along the slope of the volcano occurred because of intermittent sliding with the inclusion of the «stick-slip» mechanism and the initiation of a self-oscillating process with the generation of a seismic mode «drumbeats». The mathematical model of a fractional nonlinear oscillator qualitatively confirms the plausibility of the phenomenological model of the “drumbeats” mode.

THE (UNKNOWN) IMPACT OF THE FOURTH INDUSTRIAL REVOLUTION IN EDUCATION

2018 ◽  
Author(s):  
Marco Neves
Keyword(s):  
Artificial Intelligence ◽  
Mass Production ◽  
Industrial Revolution ◽  
Social Economic ◽  
Cyber Physical Systems ◽  
Physical Systems ◽  
The Third ◽  
Fourth Industrial Revolution ◽  
Time Machines ◽  
First Time

Today we are living in the cusp of a new industrial revolution that differs from all the previous ones. It´s been coined as the Fourth Industrial Revolution (FIR) at the 2011 Hannover Fair. The first industrial revolution powered mainly by the steam engine, the second one by the advent of electrification, mass production and division of labor and the third one by the upcoming of internet, computers, networks and digital machines. What differs the FIR from all the others is that this one is on the edge of artificial intelligence, digital ubiquity, cyber-physical systems and even on the way to “Singularity”: where for the first time machines acquired capabilities that we only consider possible in humans. This means that we are fencing tremendous changes in what concerns to all the aspects of life, i.e. social, economic, cultural and, collaterally, in labor market.

Generalized Harmonic Oscillators: Velocity Dependent Frequencies

2001 ◽  
Author(s):  
Ronald E. Mickens
Keyword(s):  
Nonlinear Oscillator ◽  
First Integral ◽  
Harmonic Oscillators ◽  
System Of Equations ◽  
Research Grants ◽  
Physical Systems ◽  
New Class ◽  
Generalized Harmonic Oscillators ◽  
Special Cases ◽  
Oscillator Equations

Abstract Preliminary results are given on a new class of nonlinear oscillator equations that generalize those of the usual linear harmonic case. These equations take the form ẋ = f(x)y and ẏ = −g(y)x, where f(x) and g(y) are continuous with first derivatives, and f(0) &gt; 0, g(0) &gt; 0. Of interest is the fact that these equations have a first-integral, i.e., there exists a function H(x,y) such that along a particular trajectory in the (x,y) phase space, H(x,y) = constant. We work out several general results related to this system of equations and illustrate them with several special cases that correspond to models of physical systems. The work reported here was supported in part by research grants from DOE and the MBRS-SCORE Program at Clark Atlanta University.

scholarly journals Advanced virtual prototyping for cyber-physical systems using RISC-V: implementation, verification and challenges

2021 ◽  
Vol 65 (1) ◽  
Author(s):  
Vladimir Herdt ◽  
Rolf Drechsler
Keyword(s):  
Operating System ◽  
Virtual Prototyping ◽  
Cyber Physical Systems ◽  
Design Flow ◽  
System Level ◽  
Bare Metal ◽  
Instruction Set ◽  
Physical Systems ◽  
Virtual Prototypes ◽  
First Time

AbstractVirtual prototypes (VPs) are crucial in today’s design flow. VPs are predominantly created in SystemC transaction-level modeling (TLM) and are leveraged for early software development and other system-level use cases. Recently, virtual prototyping has been introduced for the emerging RISC-V instruction set architecture (ISA) and become an important piece of the growing RISC-V ecosystem. In this paper, we present enhanced virtual prototyping solutions tailored for RISC-V. The foundation is an advanced open source RISC-V VP implemented in SystemC TLM and designed as a configurable and extensible platform. It scales from small bare-metal systems to large multi-core systems that run applications on top of the Linux operating system. Based on the RISC-V VP, this paper also discusses advanced VP-based verification approaches and open challenges. In combination, we provide for the first time an integrated and unified overview and perspective on advanced virtual prototyping for RISC-V.

scholarly journals Theoretical and Experimental Study on the Effective Piezoelectric Properties of 1-3 Type Cement-Based Piezoelectric Composites

Materials ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 1698 ◽  
Author(s):  
Jun Zhu ◽  
Zhi Wang ◽  
Xingyi Zhu ◽  
Bo Yang ◽  
Chuanqing Fu
Keyword(s):  
Piezoelectric Properties ◽  
Volume Fraction ◽  
Homogenization Method ◽  
Asymptotic Homogenization ◽  
Piezoelectric Composites ◽  
Physical Systems ◽  
Asymptotic Homogenization Method ◽  
Proper Volume ◽  
Predicted Values ◽  
First Time

The double asymptotic homogenization method originated for analyzing physical systems containing two or more length scales was adopted to predict the characteristic of 1-3 type cement-based piezoelectric composites for the first time. The piezoelectric properties of 1-3 type cement-based piezoelectric composites were measured and comparisons between the experimental data and predicted values validate the effectiveness of the present analytical model. Moreover, numerical discussions and experiments show that one should choose proper volume fraction of constituents to achieve the best performance of the 1-3 type cement-based piezoelectric composites.

On Coexistence of Fractional-Order Hidden Attractors

2018 ◽  
Vol 13 (9) ◽  
Author(s):  
Manashita Borah
Keyword(s):  
Fractional Order ◽  
Real Life ◽  
Fractional Dimension ◽  
Fractional Dynamics ◽  
Hidden Attractors ◽  
Physical Systems ◽  
Memristive System ◽  
First Time ◽  
Theoretical Analyses ◽  
Hyperchaotic Systems

Abstract This paper proposes new fractional-order (FO) models of seven nonequilibrium and stable equilibrium systems and investigates the existence of chaos and hyperchaos in them. It thereby challenges the conventional generation of chaos that involves starting the orbits from the vicinity of unstable manifold. This is followed by the discovery of coexisting hidden attractors in fractional dynamics. All the seven newly proposed fractional-order chaotic/hyperchaotic systems (FOCSs/FOHSs) ranging from minimum fractional dimension (nf) of 2.76 to 4.95, exhibit multiple hidden attractors, such as periodic orbits, stable foci, and strange attractors, often coexisting together. To the best of the our knowledge, this phenomenon of prevalence of FO coexisting hidden attractors in FOCSs is reported for the first time. These findings have significant practical relevance, because the attractors are discovered in real-life physical systems such as the FO homopolar disc dynamo, FO memristive system, FO model of the modulation instability in a dissipative medium, etc., as analyzed in this work. Numerical simulation results confirm the theoretical analyses and comply with the fact that multistability of hidden attractors does exist in the proposed FO models.

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