Chaotic diffusion for particles moving in a time dependent potential well

Leonel, Edson D.; Kuwana, Célia Mayumi; Yoshida, Makoto; Oliveira, Juliano A. de

doi:10.1016/j.physleta.2020.126737

Cited by 3 publications

(2 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we are going to consider Figure 1 d, where the potential energy of the particle is given by

a , b ,

and

are control parameters. The most frequently potential well model studied is the model of Figure 1 c [ 12 ]. However, we will see later that using the model of Figure 1 d and fixing the Poincaré section on the position

make the results the same, but the fixed points are symmetrical, facilitating our studies.…”

Section: The Model and Mappingmentioning

confidence: 99%

“…Multiple reflections can also be observed when studying classical particles confined within time-dependent potential well or barriers. The dynamics of these particles is an object of study for many researchers [ 11 , 12 , 13 , 14 , 15 , 16 ]. We can find applications in classical mechanics, quantum mechanics and electromagnetism [ 17 , 18 , 19 ].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well

Graciano

Costa

Leonel

et al. 2022

Entropy

View full text Add to dashboard Cite

We study the dynamics of classical particles confined in a time-dependent potential well. The dynamics of each particle is described by a two-dimensional nonlinear discrete mapping for the variables energy en and phase ϕn of the periodic moving well. We obtain the phase space and show that it contains periodic islands, chaotic sea, and invariant spanning curves. We find the elliptic and hyperbolic fixed points and discuss a numerical method to obtain them. We study the dispersion of the initial conditions after a single iteration. This study allows finding regions where multiple reflections occur. Multiple reflections happen when a particle does not have enough energy to exit the potential well and is trapped inside it, suffering several reflections until it has enough energy to exit. We also show deformations in regions with multiple reflection, but the area remains constant when we change the control parameter NC. Finally, we show some structures that appear in the e0e1 plane by using density plots.

show abstract

“…In this paper, we are going to consider Figure 1 d, where the potential energy of the particle is given by

a , b ,

and

make the results the same, but the fixed points are symmetrical, facilitating our studies.…”

Section: The Model and Mappingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well

Graciano

Costa

Leonel

et al. 2022

Entropy

View full text Add to dashboard Cite

show abstract

Maximum entropy model of chaotic explosion and implosion of a large gas bubble in liquid

Waldo

2024

Physics of Fluids

View full text Add to dashboard Cite

A mathematical model for the chaotic explosion of a large gas bubble in a liquid is presented in which there is a maximum increase in entropy. It is shown that this requires that the acoustic radiation during the chaos must be minimal and that the spherical surface at the end of the chaos must be stable. Also, a model including the acoustic radiation is developed for the spherical phases of the explosion and implosion of the bubble during which there is no change in entropy. The (final) chaotic phase of the implosion is also modeled so that there is a maximum increase in entropy. There might be additional periods of the bubble during which the bubble explodes and implodes in a similar fashion as the first period. The calculations using this model are shown to agree reasonably well with the data. In particular, these calculations determined that the ratio of the duration of the second period of the bubble to the first period imply that the energy lost in the first period during its implosion is about 2/3 of the energy of the first period. Also, these calculations determine that only about 30% of the total energy is radiated and the rest is absorbed by the water for a total of about 2/3 of the total energy. This also agrees with the data. Furthermore, the data appear to scale with initial total energy as in the calculations using this chaos model.

show abstract

Investigating the Stickiness in a Potential Well

Graciano,

Szezech,

Batista

et al. 2024

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

In this work, we use the finite-time Lyapunov exponent (FTLE) for a version of the potential well model with an oscillating bottom. This model is described by a conservative two-dimensional mapping that exhibits a mixed phase space, namely it contains a sea of chaos and the regions of stability. Via FTLE, we show that throughout its orbit, an initial condition in the chaotic sea can become trapped in a certain region. We construct and analyze phase spaces for different ranges of Lyapunov exponents in finite time, highlighting these traps. For smaller and larger values of FTLE, we identified a very regular phase space and a phase space with more chaos. By means of low FTLE values, we observe some small regions in the phase space that present regularities. Therefore, we demonstrate that FTLE can be useful to identify the stickiness effect in a time-dependent potential well.

show abstract

Chaotic diffusion for particles moving in a time dependent potential well

Cited by 3 publications

References 21 publications

Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well

Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well

Maximum entropy model of chaotic explosion and implosion of a large gas bubble in liquid

Investigating the Stickiness in a Potential Well

Contact Info

Product

Resources

About