Chaotic dynamics and orbit stability in the parabolic oval billiard

Lopac, Vjera; Mrkonjić, Ivana; Radić, Danko

doi:10.1103/physreve.66.036202

Cited by 27 publications

(24 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This description of the billiard geometry and dynamics is consistent with our previous analysis of the elliptical stadium billiard (ESB) [30,33,34], which is a two-parameter generalization of the Bunimovich stadium billiard [4] and is a special case of the mushroom billiard [35,36,37].…”

Section: Introductionsupporting

confidence: 68%

“…In our previous work we analyzed several types of billiards with noncircular arcs (parabolic, hyperbolic, elliptical and generalized power-law), exhibiting mixed dynamics [30,31,32]. Next we investigated, in the full parameter space [33], the elliptical stadium billiards (ESB), first introduced by Donnay [7].…”

Section: Introductionmentioning

confidence: 99%

“…In our further description we refer to the impact points T(x, y) in the first quadrant, with no loss of generality for the obtained results. In the Poincaré sections the points P(x, v x ) are obtained by plotting the slope of the velocity direction v x = cos φ versus the x-coordinate of the intersection point with the x-axis, as explained in [30,31,32,33].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Chaotic properties of the truncated elliptical billiards

Lopac¹,

Šimić²

2011

Communications in Nonlinear Science and Numerical Simulation

Self Cite

View full text Add to dashboard Cite

Chaotic properties of symmetrical two-dimensional stadium-like billiards with elliptical arcs are studied numerically and analytically. For the two-parameter truncated elliptical billiard the existence and linear stability of several lowest-order periodic orbits are investigated in the full parameter space. Poincaré plots are computed and used for evaluation of the degree of chaoticity with the box-counting method. The limit of the fully chaotic behavior is identified with circular arcs. Above this limit, for flattened elliptical arcs, mixed dynamics with numerous stable elliptic islands is present, similarly as in the elliptical stadium billiards. Below this limit the full chaos extends over the whole region of elongated shapes and the existing orbits are either unstable or neutral. This is conspicuously different from the behavior in the elliptical stadium billiards, where the chaotic region is strictly bounded from both sides. To examine the mechanism of this difference, a generalization to a novel three-parameter family of boundary shapes is proposed and suggested for further evaluation.

show abstract

Section: Introductionsupporting

confidence: 68%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Chaotic properties of the truncated elliptical billiards

Lopac¹,

Šimić²

2011

Communications in Nonlinear Science and Numerical Simulation

Self Cite

View full text Add to dashboard Cite

show abstract

“…8, and such a behaviour can be describe by using the scaling hypotheses given by Eqs. (36)- (38). The acceleration exponent is b % 0:5 for all the values of l. However, the saturation exponent a and the crossover exponent z are rather different.…”

Section: A Numerical Results For the Case Of In-flight Dissipationmentioning

confidence: 89%

“…29 In case (ii), two examples are the Bunimovich stadium 30 and the Sinai billiard, 31 in such a cases, the time evolution of a single initial condition is enough to fill the entire phase space. Finally, case (iii), mixed type systems, in such a case, chaotic seas are generally surrounding KAM islands and invariant curves are observed [32][33][34][35][36][37][38][39][40] (and references in therein). If a time dependent perturbation is introduced in the boundary, @Q ¼ @QðtÞ, the system exchanges energy/velocity with the particle upon collision.…”

Section: Introductionmentioning

confidence: 99%

In-flight and collisional dissipation as a mechanism to suppress Fermi acceleration in a breathing Lorentz gas

Oliveira¹,

Leonel²

2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

Some dynamical properties for a time dependent Lorentz gas considering both the dissipative and non dissipative dynamics are studied. The model is described by using a four-dimensional nonlinear mapping. For the conservative dynamics, scaling laws are obtained for the behavior of the average velocity for an ensemble of non interacting particles and the unlimited energy growth is confirmed. For the dissipative case, four different kinds of damping forces are considered namely: (i) restitution coefficient which makes the particle experiences a loss of energy upon collisions; and in-flight dissipation given by (ii) F ¼ ÀgV 2 ; (iii) F ¼ ÀgV l with l 6 ¼ 1 and l 6 ¼ 2 and; (iv) F ¼ ÀgV, where g is the dissipation parameter. Extensive numerical simulations were made and our results confirm that the unlimited energy growth, observed for the conservative dynamics, is suppressed for the dissipative case. The behaviour of the average velocity is described using scaling arguments and classes of universalities are defined. We revisit the problem of non-interacting particles in a time dependent Lorentz gas. We describe the model by using a four dimensional nonlinear map. As it is known, the phase space of the Lorentz gas with static scatterers is fully chaotic and the velocity of the particle is constant. However, when a time dependent perturbation is introduced to the boundary, the energy is no longer conserved and the unlimited energy growth is observed for the conservative case. On the other hand, our results show that when dissipation is introduced into the system, either by collisional dissipation or dissipation during the flight, the unlimited energy growth is no longer observed. Depending on the strength of the dissipation and considering short time, the average velocity can either grows and reaches a constant plateau or decays until the particle reaches the state of rest. For the cases, when the dynamics does not stop between the scatterers, the behaviour of the average velocity is described by using scaling arguments and once the scaling exponents are known, classes of universalities are defined.

show abstract

Ultra-thin broadband solar absorber based on stadium-shaped silicon nanowire arrays

Mortazavifar

Salehi

Shahraki

et al. 2022

Front. Optoelectron.

View full text Add to dashboard Cite

This paper investigates how the dimensions and arrangements of stadium silicon nanowires (NWs) affect their absorption properties. Compared to other NWs, the structure proposed here has a simple geometry, while its absorption rate is comparable to that of very complex structures. It is shown that changing the cross-section of NW from circular (or rectangular) to a stadium shape leads to change in the position and the number of absorption modes of the NW. In a special case, these modes result in the maximum absorption inside NWs. Another method used in this paper to attain broadband absorption is utilization of multiple NWs which have different geometries. However, the maximum enhancement is achieved using non-close packed NW. These structures can support more cavity modes, while NW scattering leads to broadening of the absorption spectra. All the structures are optimized using particle swarm optimizations. Using these optimized structures, it is viable to enhance the absorption by solar cells without introducing more absorbent materials. Graphical Abstract

show abstract

Chaotic dynamics and orbit stability in the parabolic oval billiard

Cited by 27 publications

References 30 publications

Chaotic properties of the truncated elliptical billiards

Chaotic properties of the truncated elliptical billiards

In-flight and collisional dissipation as a mechanism to suppress Fermi acceleration in a breathing Lorentz gas

Ultra-thin broadband solar absorber based on stadium-shaped silicon nanowire arrays

Contact Info

Product

Resources

About