SYNCHRONIZATION OF SLOWLY ROTATING PENDULUMS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250128 ◽  
Author(s):  
K. CZOLCZYNSKI ◽  
P. PERLIKOWSKI ◽  
A. STEFANSKI ◽  
T. KAPITANIAK
Keyword(s):  
Initial Conditions ◽  
Basins Of Attraction ◽  
System Parameters ◽  
Initial Transient ◽  
Horizontal Beam ◽  
Parallel Surface ◽  
Wide Range ◽  
Phase Differences

We study synchronization of a number of rotating pendulums mounted on a horizontal beam which can roll on the parallel surface. It has been shown that after the initial transient, different states of pendulums synchronization occur. We derive the analytical equations for the estimation of the phase differences between phase synchronized pendulums. After the study of the basins of attraction of different synchronization states, we argue that the observed phenomena are robust as they occur for a wide range of both initial conditions and system parameters.

scholarly journals Bifurcations and Multistability in a Model of Cytokine-Mediated Autoimmunity

2019 ◽  
Vol 29 (03) ◽  
pp. 1950034 ◽  
Author(s):  
Farzad Fatehi ◽  
Yuliya N. Kyrychko ◽  
Robert Molchanov ◽  
Konstantin B. Blyuss
Keyword(s):  
T Cells ◽  
Chronic Infection ◽  
Initial Conditions ◽  
Cell Activity ◽  
Basins Of Attraction ◽  
Activity Analysis ◽  
Steady States ◽  
System Parameters ◽  
Stability And Bifurcations

This paper investigates the dynamics of immune response and autoimmunity with particular emphasis on the role of regulatory T cells (Tregs), T cells with different activation thresholds, and cytokines in mediating T cell activity. Analysis of the steady states yields parameter regions corresponding to regimes of normal clearance of viral infection, chronic infection, or autoimmune behavior, and the boundaries of stability and bifurcations of relevant steady states are found in terms of system parameters. Numerical simulations are performed to illustrate different dynamical scenarios, and to identify basins of attraction of different steady states and periodic solutions, highlighting the important role played by the initial conditions in determining the outcome of immune interactions.

Hidden Attractors and Dynamical Behaviors in an Extended Rikitake System

2015 ◽  
Vol 25 (02) ◽  
pp. 1550028 ◽  
Author(s):  
Zhouchao Wei ◽  
Wei Zhang ◽  
Zhen Wang ◽  
Minghui Yao
Keyword(s):  
Hopf Bifurcation ◽  
Initial Conditions ◽  
Dynamics Analysis ◽  
Hidden Attractor ◽  
Hidden Attractors ◽  
System Parameters ◽  
Dynamical Behaviors ◽  
Rikitake System ◽  
Wide Range ◽  
Stable Equilibria

In this paper, an extended Rikitake system is studied. Several issues, such as Hopf bifurcation, coexistence of stable equilibria and hidden attractor, and dynamics analysis at infinity are investigated either analytically or numerically. Especially, by a simple linear transformation, the wide range of hidden attractors is noticed, and the Lyapunov exponents diagram is given. The obtained results show that the unstable periodic solution generated by Hopf bifurcation leads to the hidden attractor. The existence of hidden attractors that may render the system's behavior unpredictable not only depends on the value of system parameters but also on the value of initial conditions. The phenomena are important and potentially problematic in engineering applications.

Geometry of Basins of Attraction and Heteroclinic Connections in Coupled Bistable Systems

2014 ◽  
Vol 24 (10) ◽  
pp. 1430029 ◽  
Author(s):  
Daniel Lyons ◽  
Joseph M. Mahaffy ◽  
Sara Wang ◽  
Antonio Palacios ◽  
Visarath In
Keyword(s):  
Materials Science ◽  
Initial Conditions ◽  
Coupling Parameter ◽  
Fundamental Principle ◽  
Basins Of Attraction ◽  
Invariant Sets ◽  
Modeling And Analysis ◽  
Complex Engineered Systems ◽  
Bistable Systems ◽  
Wide Range

The fundamental principle of bistability is widely used across various disciplines, including biology, chemistry, mechanics, physics, electronics and materials science. As the need for more powerful, efficient and sensitive complex-engineered systems grow, networks of coupled bistable systems have gained significant attention in recent years. Modeling and analysis of such higher-dimensional systems is usually focused on finding conditions for the existence and stability of typical invariant sets, i.e. steady states, periodic solutions and chaotic sets. High-dimensionality leads to complex patterns of collective behavior. Which type of behavior is exhibited by a network depends greatly on the initial conditions. Thus, it is also important to study the geometric structure and evolution of the basins of attraction of such patterns. In this manuscript, a complete study of the basins of attraction of a ring of bistable systems, coupled unidirectionally, is presented. 3D visualizations are included to aid the discussion of the changes in the basins of attraction as the coupling parameter varies. The results are broad enough that they can be applied to a wide range of systems with similar coupling topologies.

scholarly journals On the generation of internal waves by river plumes in subcritical initial conditions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. Mendes ◽  
J. C. B. da Silva ◽  
J. M. Magalhaes ◽  
B. St-Denis ◽  
D. Bourgault ◽  
...  
Keyword(s):  
Numerical Modeling ◽  
Internal Waves ◽  
Coastal Waters ◽  
Initial Conditions ◽  
Spatial Scales ◽  
River Plumes ◽  
Wide Range ◽  
Near Shore ◽  
Generation Mechanisms ◽  
Douro River

AbstractInternal waves (IWs) in the ocean span across a wide range of time and spatial scales and are now acknowledged as important sources of turbulence and mixing, with the largest observations having 200 m in amplitude and vertical velocities close to 0.5 m s−1. Their origin is mostly tidal, but an increasing number of non-tidal generation mechanisms have also been observed. For instance, river plumes provide horizontally propagating density fronts, which were observed to generate IWs when transitioning from supercritical to subcritical flow. In this study, satellite imagery and autonomous underwater measurements are combined with numerical modeling to investigate IW generation from an initial subcritical density front originating at the Douro River plume (western Iberian coast). These unprecedented results may have important implications in near-shore dynamics since that suggest that rivers of moderate flow may play an important role in IW generation between fresh riverine and coastal waters.

scholarly journals The Impact of Initial Conditions in N-Body Simulations of Debris Discs

2015 ◽  
Vol 32 ◽  
Author(s):  
E. Thilliez ◽  
S. T. Maddison
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Parent Body ◽  
Dust Trapping ◽  
Physical Context ◽  
Disc Width ◽  
Wide Range ◽  
Belt Width ◽  
New Generation ◽  
The Impact

AbstractNumerical simulations are a crucial tool to understand the relationship between debris discs and planetary companions. As debris disc observations are now reaching unprecedented levels of precision over a wide range of wavelengths, an appropriate level of accuracy and consistency is required in numerical simulations to confidently interpret this new generation of observations. However, simulations throughout the literature have been conducted with various initial conditions often with little or no justification. In this paper, we aim to study the dependence on the initial conditions of N-body simulations modelling the interaction between a massive and eccentric planet on an exterior debris disc. To achieve this, we first classify three broad approaches used in the literature and provide some physical context for when each category should be used. We then run a series of N-body simulations, that include radiation forces acting on small grains, with varying initial conditions across the three categories. We test the influence of the initial parent body belt width, eccentricity, and alignment with the planet on the resulting debris disc structure and compare the final peak emission location, disc width and offset of synthetic disc images produced with a radiative transfer code. We also track the evolution of the forced eccentricity of the dust grains induced by the planet, as well as resonance dust trapping. We find that an initially broad parent body belt always results in a broader debris disc than an initially narrow parent body belt. While simulations with a parent body belt with low initial eccentricity (e ~ 0) and high initial eccentricity (0 < e < 0.3) resulted in similar broad discs, we find that purely secular forced initial conditions, where the initial disc eccentricity is set to the forced value and the disc is aligned with the planet, always result in a narrower disc. We conclude that broad debris discs can be modelled by using either a dynamically cold or dynamically warm parent belt, while in contrast eccentric narrow debris rings are reproduced using a secularly forced parent body belt.

scholarly journals Harmonic hybrid inflation

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Federico Carta ◽  
Nicole Righi ◽  
Yvette Welling ◽  
Alexander Westphal
Keyword(s):  
Domain Wall ◽  
Symmetry Breaking ◽  
Initial Conditions ◽  
Scalar Potential ◽  
Field Range ◽  
Slow Roll ◽  
Minimal Form ◽  
Wide Range ◽  
Hybrid Inflation ◽  
Type Iib String Theory

Abstract We present a mechanism for realizing hybrid inflation using two axion fields with a purely non-perturbatively generated scalar potential. The structure of the scalar potential is highly constrained by the discrete shift symmetries of the axions. We show that harmonic hybrid inflation generates observationally viable slow-roll inflation for a wide range of initial conditions. This is possible while accommodating certain UV arguments favoring constraints f ≲ MP and ∆ϕ60 ≲ MP on the axion periodicity and slow-roll field range, respectively. We discuss controlled ℤ2-symmetry breaking of the adjacent axion vacua as a means of avoiding cosmological domain wall problems. Including a minimal form of ℤ2-symmetry breaking into the minimally tuned setup leads to a prediction of primordial tensor modes with the tensor-to-scalar ratio in the range 10−4 ≲ r ≲ 0.01, directly accessible to upcoming CMB observations. Finally, we outline several avenues towards realizing harmonic hybrid inflation in type IIB string theory.

Numerical investigation of the propagation of shock waves in rigid porous materials: development of the computer code and comparison with experimental results

1996 ◽  
Vol 324 ◽  
pp. 163-179 ◽  
Author(s):  
A. Levy ◽  
G. Ben-Dor ◽  
S. Sorek
Keyword(s):  
Porous Materials ◽  
Initial Conditions ◽  
Computer Code ◽  
Experimental Results ◽  
Numerical Code ◽  
Materials Development ◽  
Numerical Predictions ◽  
Wide Range ◽  
Dimensional Version ◽  
The One

The governing equations of the flow field which is obtained when a thermoelastic rigid porous medium is struck head-one by a shock wave are developed using the multiphase approach. The one-dimensional version of these equations is solved numerically using a TVD-based numerical code. The numerical predictions are compared to experimental results and good to excellent agreements are obtained for different porous materials and a wide range of initial conditions.

BASIN CONFIGURATION OF A SIX-DIMENSIONAL MODEL OF AN ELECTRIC POWER SYSTEM

2002 ◽  
Vol 12 (06) ◽  
pp. 1333-1356 ◽  
Author(s):  
YOSHISUKE UEDA ◽  
HIROYUKI AMANO ◽  
RALPH H. ABRAHAM ◽  
H. BRUCE STEWART
Keyword(s):  
Power Systems ◽  
Power System ◽  
Initial Conditions ◽  
Electrical Power ◽  
Practical Importance ◽  
Intervention Strategy ◽  
Basins Of Attraction ◽  
Electric Power System ◽  
Point Of View ◽  
Electrical Power System

As part of an ongoing project on the stability of massively complex electrical power systems, we discuss the global geometric structure of contacts among the basins of attraction of a six-dimensional dynamical system. This system represents a simple model of an electrical power system involving three machines and an infinite bus. Apart from the possible occurrence of attractors representing pathological states, the contacts between the basins have a practical importance, from the point of view of the operation of a real electrical power system. With the aid of a global map of basins, one could hope to design an intervention strategy to boot the power system back into its normal state. Our method involves taking two-dimensional sections of the six-dimensional state space, and then determining the basins directly by numerical simulation from a dense grid of initial conditions. The relations among all the basins are given for a specific numerical example, that is, choosing particular values for the parameters in our model.

3D Printing — The Basins of Tristability in the Lorenz System

2017 ◽  
Vol 27 (08) ◽  
pp. 1750128 ◽  
Author(s):  
Anda Xiong ◽  
Julien C. Sprott ◽  
Jingxuan Lyu ◽  
Xilu Wang
Keyword(s):  
Lorenz System ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Basins Of Attraction ◽  
Symmetric Pair ◽  
State Space Approach ◽  
3D Printers ◽  
The Lorenz System ◽  
Almost All ◽  
Space Approach

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists with a symmetric pair of stable equilibrium points, and the resulting tri-stable system has three intertwined basins of attraction. The advent of 3D printers now makes it possible to visualize the topology of such basins of attraction as the results presented here illustrate.

MODELING NANOSECOND-PULSED SPARK DISCHARGE AND FLAME KERNEL EVOLUTION

2021 ◽  
pp. 1-22
Author(s):  
Joohan Kim ◽  
Vyaas Gururajan ◽  
Riccardo Scarcelli ◽  
Sayan Biswas ◽  
Isaac Ekoto
Keyword(s):  
Electrical Discharge ◽  
Internal Combustion Engines ◽  
Initial Conditions ◽  
Fuel Mixture ◽  
Spark Ignition ◽  
Combustion Stability ◽  
Flame Kernel ◽  
Wide Range ◽  
Challenging Environment ◽  
Kernel Growth

Abstract Dilute combustion, either using exhaust gas recirculation or with excess-air, is considered a promising strategy to improve the thermal efficiency of internal combustion engines. However, the dilute air-fuel mixture, especially under intensified turbulence and high-pressure conditions, poses significant challenges for ignitability and combustion stability, which may limit the attainable efficiency benefits. In-depth knowledge of the flame kernel evolution to stabilize ignition and combustion in a challenging environment is crucial for effective engine development and optimization. To date, comprehensive understanding of ignition processes that result in the development of fully predictive ignition models usable by the automotive industry does not yet exist. Spark-ignition consists of a wide range of physics that includes electrical discharge, plasma evolution, joule-heating of gas, and flame kernel initiation and growth into a self-sustainable flame. In this study, an advanced approach is proposed to model spark-ignition energy deposition and flame kernel growth. To decouple the flame kernel growth from the electrical discharge, a nanosecond pulsed high-voltage discharge is used to trigger spark-ignition in an optically accessible small ignition test vessel with a quiescent mixture of air and methane. Initial conditions for the flame kernel, including its thermodynamic state and species composition, are derived from a plasma-chemical equilibrium calculation. The geometric shape and dimension of the kernel are characterized using a multi-dimensional thermal plasma solver. The proposed modeling approach is evaluated using a high-fidelity computational fluid dynamics procedure to compare the simulated flame kernel evolution against flame boundaries from companion schlieren images.

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