Asymptotic velocity of relativistic E × B drift

Asymptotic velocity is defined as the Cesàro limit of velocity. As such, its existence has been proved for bounded interaction potentials. This is known to be wrong in celestial mechanics with four or more bodies. Here, we show for a class of pair potentials including the homogeneous ones of degree − α for α ∈(0, 2), that asymptotic velocities exist for up to four bodies, dimension three or larger, for any energy and almost all initial conditions on the energy surface. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.

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Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2021135 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Giovanni Colombo ◽

Paolo Gidoni ◽

Emilio Vilches

Keyword(s):

Periodic Solution ◽

Asymptotic Stability ◽

Periodic Solutions ◽

Finite Time ◽

Dry Friction ◽

Average Velocity ◽

Well Posedness ◽

Asymptotic Velocity ◽

Sweeping Processes

<p style='text-indent:20px;'>We study the asymptotic stability of periodic solutions for sweeping processes defined by a polyhedron with translationally moving faces. Previous results are improved by obtaining a stronger <inline-formula><tex-math id="M1">\begin{document}$ W^{1,2} $\end{document}</tex-math></inline-formula> convergence. Then we present an application to a model of crawling locomotion. Our stronger convergence allows us to prove the stabilization of the system to a running-periodic (or derivo-periodic, or relative-periodic) solution and the well-posedness of an average asymptotic velocity depending only on the gait adopted by the crawler. Finally, we discuss some examples of finite-time versus asymptotic-only convergence.</p>

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Gravity assists near Venus for reaching positions over ecliptic. Resonant asymptotic velocity

Keldysh Institute Preprints ◽

10.20948/prepr-2018-222 ◽

2018 ◽

pp. 1-20

Author(s):

Yury Filippovich Golubev ◽

Alexey Vasilyevich Grushevskii ◽

Victor Vladimirovich Korianov ◽

Andrey Georgievich Tuchin ◽

Denis Andreevich Tuchin

Keyword(s):

Asymptotic Velocity ◽

Gravity Assists

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Asymptotic velocity defect profile in an incipient-separating axisymmetric flow

AIAA Journal ◽

10.2514/3.12337 ◽

1995 ◽

Vol 33 (1) ◽

pp. 94-101 ◽

Cited By ~ 3

Author(s):

Rakesh K. Singh ◽

Ram S. Azad

Keyword(s):

Axisymmetric Flow ◽

Velocity Defect ◽

Asymptotic Velocity ◽

Defect Profile

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Bounds on the velocity of spread of infection for a spatially connected epidemic process

Journal of Applied Probability ◽

10.2307/3212977 ◽

1980 ◽

Vol 17 (3) ◽

pp. 839-845 ◽

Cited By ~ 6

Author(s):

M. J. Faddy ◽

I. H. Slorach

Keyword(s):

Asymptotic Velocity ◽

Epidemic Process ◽

Lower Bounding ◽

Stochastic Epidemic ◽

Spread Of Infection

The simple (non-spatial) stochastic epidemic is generalised to allow infected individuals to move forward through a system of spatially connected colonies C1, C2, C3, ·· ·each containing susceptible individuals. Upper and lower bounding processes are considered, to establish bounds on the asymptotic velocity of forward spread of the infection through these spatially connected colonies. These bounds are shown to be asymptotically equivalent under certain conditions, and some simulations reveal other features of the process.

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