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The relaxation of a weakly collisional plasma, which is of fundamental interest to laboratory astrophysical plasmas, can be described by the self-consistent Boltzmann-Poisson equations with the Lenard-Bernstein collision operator. We perform a perturbative (linear and second-order) analysis of the Boltzmann-Poisson equations and obtain exact analytic solutions which resolve some longstanding controversies regarding the impact of weak collisions on the continuous spectra, the discrete Landau eigenmodes, and the decay of plasma echoes. We retain both damping and diffusion terms in the collision operator throughout our treatment.

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In the field of complex dynamics, multistable attractors have been gaining significant attention due to their unpredictability in occurrence and extreme sensitivity to initial conditions. Co-existing attractors are abundant in diverse systems ranging from climate to finance and ecological to social systems. In this article, we investigate a data-driven approach to infer different dynamics of a multistable system using an echo state network.

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Light bending and X-ray echoes from behind a supermassive black hole.

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Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA, USA.

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We report on measurements of the dynamics of the total magnetization and spin populations in an almost unit-filled lattice system comprising about 10^{4} spin S=3 chromium atoms, under the effect of dipolar interactions. The observed spin population dynamics is unaffected by the use of a spin echo and fully consistent with numerical simulations of the S=3 XXZ spin model. On the contrary, the observed magnetization decays slower than in simulations and, surprisingly, reaches a small but nonzero asymptotic value within the longest timescale.

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