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We study the capture of galactic dark matter particles in the Solar System produced by rotation of Jupiter. It is shown that the capture cross section is much larger than the area of Jupiter orbit being inversely diverging at small particle energy. We show that the dynamics of captured particles is chaotic and is well described by a simple symplectic dark map. This dark map description allows to simulate the scattering and dynamics of $10^{14}$ dark matter particles during the life time of the Solar System and to determine dark matter density profile as a function of distance from the Sun. The mass of captured dark matter in the radius of Neptune orbit is estimated to be $2 cdot 10^{15} g$. The radial density of captured dark matter is found to be approximately constant behind Jupiter orbit being similar to the density profile found in galaxies.
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We study the capture of galactic dark matter particles (DMP) in two-body and few-body systems with a symplectic map description. This approach allows modeling the scattering of $10^{16}$ DMPs after following the time evolution of the captured particle on about $10^9$ orbital periods of the binary system. We obtain the DMP density distribution inside such systems and determine the enhancement factor of their density in a center vicinity compared to its galactic value as a function of the mass ratio of the bodies and the ratio of the body velocity to the velocity of the galactic DMP wind. We find that the enhancement factor can be on the order of tens of thousands.
We study chaos and Levy flights in the general gravitational three-body problem. We introduce new metrics to characterize the time evolution and final lifetime distributions, namely Scramble Density $mathcal{S}$ and the LF index $mathcal{L}$, that are derived from the Agekyan-Anosova maps and homology radius $R_{mathcal{H}}$. Based on these metrics, we develop detailed procedures to isolate the ergodic interactions and Levy flight interactions. This enables us to study the three-body lifetime distribution in more detail by decomposing it into the individual distributions from the different kinds of interactions. We observe that ergodic interactions follow an exponential decay distribution similar to that of radioactive decay. Meanwhile, Levy flight interactions follow a power-law distribution. Levy flights in fact dominate the tail of the general three-body lifetime distribution, providing conclusive evidence for the speculated connection between power-law tails and Levy flight interactions. We propose a new physically-motivated model for the lifetime distribution of three-body systems and discuss how it can be used to extract information about the underlying ergodic and Levy flight interactions. We discuss mass ejection probabilities in three-body systems in the ergodic limit and compare it to previous ergodic formalisms. We introduce a novel mechanism for a three-body relaxation process and discuss its relevance in general three-body systems.
We derive a semi-analytic criterion for the presence of chaos in compact, eccentric multiplanet systems. Beyond a minimum semimajor-axis separation, below which the dynamics are chaotic at all eccentricities, we show that (i) the onset of chaos is determined by the overlap of two-body mean motion resonances (MMRs), like it is in two-planet systems; (ii) secular evolution causes the MMR widths to expand and contract adiabatically, so that the chaotic boundary is established where MMRs overlap at their greatest width. For closely spaced two-planet systems, a near-symmetry strongly suppresses this secular modulation, explaining why the chaotic boundaries for two-planet systems are qualitatively different from cases with more than two planets. We use these results to derive an improved angular-momentum-deficit (AMD) stability criterion, i.e., the critical system AMD below which stability should be guaranteed. This introduces an additional factor to the expression from Laskar and Petit (2017) that is exponential in the interplanetary separations, which corrects the AMD threshold toward lower eccentricities by a factor of several for tightly packed configurations. We make routines for evaluating the chaotic boundary available to the community through the open-source SPOCK package.
The assumption that complex systems function optimally at the edge of chaos seems applicable to the international system as well. In this paper I argue that the normal chaotic war dynamic of the European international system (1495-1945) was temporarily (1657-1763) interrupted by a more simplified dynamic, resulting in more intense Great Power wars and in a delay of the reorganization of the international system in the 18th century.
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated with the attractors at period-doubling accumulation points and at tangent bifurcations to describe features of glassy dynamics, critical fluctuations and localization transitions. We recall that trajectories pertaining to the routes to chaos form families of time series that are readily transformed into networks via the Horizontal Visibility algorithm, and this in turn facilitates establish connections between entropy and Renormalization Group properties. We discretize the replicator equation of game theory to observe the onset of chaos in familiar social dilemmas, and also to mimic the evolution of high-dimensional ecological models. We describe an analytical framework of nonlinear mappings that reproduce rank distributions of large classes of data (including Zipfs law). We extend the discussion to point out a common circumstance of drastic contraction of configuration space driven by the attractors of these mappings. We mention the relation of generalized entropy expressions with the dynamics along and at the period doubling, intermittency and quasi-periodic routes to chaos. Finally, we refer to additional natural phenomena in complex systems where these conditions may manifest.
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