Our brain is not static

Our brain is not static

The phenomenon of chaotic scattering is very relevant in different fields of science and engineering. It has been mainly studied in the context of Newtonian mechanics, where the velocities of the particles are low in comparison with the speed of light.

In this talk, we analyze global properties such as the escape time distribution and the decay law of the Hénon-Heiles system in the context of special relativity. Our results show that the average escape time decreases with increasing values of the relativistic factor β. As a matter of fact, we have found a crossover point for which the KAM islands in the phase space are destroyed when β ≃ 0.4 [1].

On the other hand, the study of the survival probability of particles in the scattering region shows an algebraic decay for values of β ≤ 0.4, and this law becomes exponential for β > 0.4. Surprisingly, a scaling law between the exponent of the decay law and the β factor is uncovered where a quadratic fitting between them is found. The results of our numerical simulations agree faithfully with our qualitative arguments. Besides, we compute the basin entropy and the fractal dimension of the set of singularities of the scattering function in function of β [2].

Finally, we apply these results in the scattering in three-body problem in relativistic regime [3]. We expect this work to be useful for a better understanding of both chaotic and relativistic systems.

References

• [1] J. D. Bernal, J. M. Seoane, and M. A. F. Sanjuán. Global relativistic effects in chaotic scattering. Phys. Rev. E 95, 032205 (2017).
• [2] J. D. Bernal, J. M. Seoane, and M. A. F. Sanjuán. Basin entropy and fractal dimension in relativistic chaotic scattering. Phys. Rev. E 97 042214 (2018).
• [3] J. D. Bernal, J. M. Seoane, J. C. Vallejo, L. Huang, and M. A. F. Sanjuán. Influence of the gravitational radius o asymptotic behaviour of the relativistic Sitnikov problem. Phys. Rev. E 102 042204 (2020).

Speaker

 Kelly Iarosz, Universidade Tecnológica Federal do Paraná UTFPR

How to attend

If not a member of the Dept. Mathematical Science at the University of Essex, you can register your interest in attending the seminar and request the Zoom’s meeting password by emailing Dr Jesus Martinez-Garcia jesus.martinez-garcia@essex.ac.uk.