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Register a new userThe dynamics of asteroid rotation, governed by YORP effect: the kinematic ansatz
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The main motivation of this research is the analytical exploration of the dynamics of asteroid rotation when it moves in elliptic orbit through Space. According to the results of Efroimsky, Frouard (2016), various perturbations (collisions, close encounters, YORP effect) destabilize the rotation of a small body (asteroid), deviating it from the initial-current spin state. This yields evolution of the spin towards rotation about maximal-inertia axis due to the process of nutation relaxation or to the proper spin state corresponding to minimal energy with a fixed angular momentum. We consider in our research the aforementioned spin state of asteroid but additionally under non-vanishing influence of the effects of non-gravitational nature (YORP effect), which is destabilizing the asteroid rotation during its motion far from giant planets. Meanwhile, new solutions for asteroid rotation dynamics in case of negligible (time-dependent) applied torques have been obtained in our development. New method for solving Euler equations for rigid body rotation is suggested; an elegant example for evolution of spin towards the rotation about maximal-inertia axis is calculated.
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We have presented in this communication a new solving procedure for the dynamics of non-rigid asteroid rotation, considering the final spin state of rotation for a small celestial body (asteroid). The last condition means the ultimate absence of the applied external torques (including short-term effect from torques during collisions, long-term YORP effect, etc.). Fundamental law of angular momentum conservation has been used for the aforementioned solving procedure. The system of Euler equations for dynamics of non-rigid asteroid rotation has been explored with regard to the existence of an analytic way of presentation of the approximated solution. Despite of various perturbations (such as collisions, YORP effect) which destabilize the rotation of asteroid via deviating from the current spin state, the inelastic (mainly, tidal) dissipation reduces kinetic energy of asteroid. So, evolution of the spinning asteroid should be resulting by the rotation about maximal-inertia axis with the proper spin state corresponding to minimal energy with a fixed angular momentum. Basing on the aforesaid assumption (component K_1 is supposed to be fluctuating near the given appropriate constant of the fixed angular momentum), we have obtained that 2-nd component K_2 is the solution of appropriate Riccati ordinary differential equation of 1-st order, whereas component K_3 should be determined via expression for K_2.
Stochastic kinematic description of a complex dynamics is shown to dictate an energetic and thermodynamic structure. An energy function $varphi(x)$ emerges as the limit of the generalized, nonequilibrium free energy of a Markovian dynamics with vanishing fluctuations. In terms of the $ ablavarphi$ and its orthogonal field $gamma(x)perp ablavarphi$, a general vector field $b(x)$ can be decomposed into $-D(x) ablavarphi+gamma$, where $ ablacdotbig(omega(x)gamma(x)big)=$ $- ablaomega D(x) ablavarphi$. The matrix $D(x)$ and scalar $omega(x)$, two additional characteristics to the $b(x)$ alone, represent the local geometry and density of states intrinsic to the statistical motion in the state space at $x$. $varphi(x)$ and $omega(x)$ are interpreted as the emergent energy and degeneracy of the motion, with an energy balance equation $dvarphi(x(t))/dt=gamma D^{-1}gamma-bD^{-1}b$, reflecting the geometrical $|D ablavarphi|^2+|gamma|^2=|b|^2$. The partition function employed in statistical mechanics and J. W. Gibbs method of ensemble change naturally arise; a fluctuation-dissipation theorem is established via the two leading-order asymptotics of entropy production as $epsilonto 0$. The present theory provides a mathematical basis for P. W. Andersons emergent behavior in the hierarchical structure of complexity science.
Perpendicularly magnetized materials have attracted tremendous interest due to their high anisotropy, which results in extremely narrow, nano-sized domain walls. As a result, the recently studied current-induced domain wall motion (CIDWM) in these materials promises to enable a novel class of data, memory, and logic devices. In this letter, we propose the spin Hall effect as a radically new mechanism for CIDWM. We are able to carefully tune the net spin Hall current in depinning experiments on Pt/Co/Pt nanowires, offering unique control over CIDWM. Furthermore, we determine that the depinning efficiency is intimately related to the internal structure of the domain wall, which we control by small fields along the nanowire. This new manifestation of CIDWM offers a very attractive new degree of freedom for manipulating domain wall motion by charge currents, and sheds light on the existence of contradicting reports on CIDWM in perpendicularly magnetized materials.
Any population of asteroids, like asteroid families, will disperse in semi-major axis due to the Yarkovsky effect. The amount of drift is modulated by the asteroid spin state evolution which determines the balance between the diurnal and seasonal Yarkovsky force. The asteroids spin state is, in turn, controlled in part by the YORP effect. The otherwise smooth evolution of an asteroid can be abruptly altered by collisions, which can cause impulsive changes in the spin state and can move the asteroid onto a different YORP track. In addition, collisions may also alter the YORP parameters by changing the superficial features and overall shape of the asteroid. Thus, the coupling between YORP and Yarkovsky is also strongly affected by the impact history of each body. To investigate this coupling we developed a statistical code modeling the time evolution of semi--major axis under YORP-Yarkovsky coupling. It includes the contributions of NYORP (normal YORP), TYORP (tangential YORP) and collisions whose effects are deterministically calculated and not added in a statistical way. We find that both collisions and TYORP increase the dispersion of a family in semi-major axis by making the spin axis evolution less smooth and regular. We show that the evolution of a familys structure with time is complex and collisions randomize the YORP evolution. In our test families we do not observe the formation of a YORP-eye in the semi-major axis vs. diameter distribution, even after a long period of time. If present, the YORP-eye might be a relic of an initial ejection velocity pattern of the collisional fragments.
We estimate the expected magnitudes of the Schumann resonance fields immediately after the Chicxulub impact and show that they exceed their present-day values by about $5times 10^4$ times. Long-term distortion of the Schumann resonance parameters is also expected due to the enviromental impact of the Chicxulub event. If Schumann resonances play a regulatory biological role, as some studies indicate, it is possible that the excitation and distortion of Schumann resonances as a result of the asteroid/comet impact was a possible stress factor, which, among other stress factors associated with the impact, contributed to the demise of dinosaurs.
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