Linear Dissipative Force as a Result of Discrete Time Collisions
Goriachkin, Vasilii LU
and Turova, Tatyana
LU
(2020)
In Markov Processes and Related Fields
26(2).
p.315-337
- Abstract
We consider two models: one describes the particle movement under the influence of external force and friction, and another one describes the movement of a particle, which is acted upon by the same external force but it additionally collides with other particles of much lighter masses. We establish conditions for these two models to be equivalent in some sense. We also considered deterministic and stochastic models for collisions, in first case assuming that the time intervals between the collisions are constant, and in another case when these intervals are random independent random variables. For various examples of the external force we find parameters which yield asymptotic equivalence of the velocities of the particle in different... (More)
We consider two models: one describes the particle movement under the influence of external force and friction, and another one describes the movement of a particle, which is acted upon by the same external force but it additionally collides with other particles of much lighter masses. We establish conditions for these two models to be equivalent in some sense. We also considered deterministic and stochastic models for collisions, in first case assuming that the time intervals between the collisions are constant, and in another case when these intervals are random independent random variables. For various examples of the external force we find parameters which yield asymptotic equivalence of the velocities of the particle in different models. We also provide conditions when the trajectories of the particles in different models are close to each other in the Chebyshev norm over a certain finite period of time. Our results confirm that a linear dissipative force such as e.g., friction, can well be modelled by the collisions with external light particles if their masses and the time-intervals between the collisions satisfy certain condition. The latter is proved here to be universal for different forms of the external force.
(Less)
- author
- Goriachkin, Vasilii
LU
and Turova, Tatyana
LU
- organization
- publishing date
- 2020
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- dissipative force, Euler’s approximation method, friction, particles collision
- in
- Markov Processes and Related Fields
- volume
- 26
- issue
- 2
- pages
- 23 pages
- publisher
- Polymat Ltd
- external identifiers
-
- scopus:85147775301
- ISSN
- 1024-2953
- project
- Critical Scaling in Particle Systems and Random Graphs
- language
- English
- LU publication?
- yes
- id
- 281c0b59-c5ec-44d9-880c-f43adb961e90
- date added to LUP
- 2023-02-20 15:29:30
- date last changed
- 2023-09-25 03:48:59
@article{281c0b59-c5ec-44d9-880c-f43adb961e90,
abstract = {{<p>We consider two models: one describes the particle movement under the influence of external force and friction, and another one describes the movement of a particle, which is acted upon by the same external force but it additionally collides with other particles of much lighter masses. We establish conditions for these two models to be equivalent in some sense. We also considered deterministic and stochastic models for collisions, in first case assuming that the time intervals between the collisions are constant, and in another case when these intervals are random independent random variables. For various examples of the external force we find parameters which yield asymptotic equivalence of the velocities of the particle in different models. We also provide conditions when the trajectories of the particles in different models are close to each other in the Chebyshev norm over a certain finite period of time. Our results confirm that a linear dissipative force such as e.g., friction, can well be modelled by the collisions with external light particles if their masses and the time-intervals between the collisions satisfy certain condition. The latter is proved here to be universal for different forms of the external force.</p>}},
author = {{Goriachkin, Vasilii and Turova, Tatyana}},
issn = {{1024-2953}},
keywords = {{dissipative force; Euler’s approximation method; friction; particles collision}},
language = {{eng}},
number = {{2}},
pages = {{315--337}},
publisher = {{Polymat Ltd}},
series = {{Markov Processes and Related Fields}},
title = {{Linear Dissipative Force as a Result of Discrete Time Collisions}},
volume = {{26}},
year = {{2020}},
}