Spatio-angular order in populations of self-aligning objects: Formation of oriented patches

Alex Mogilner, Leah Edelstein-Keshet

Research output: Contribution to journalArticle

68 Citations (Scopus)

Abstract

We consider a class of models for the dynamic behaviour of ensembles of objects whose interactions depend on angular orientations as well as spatial positions. The "objects" could be particles, molecules, cells or organisms. We show how processes such as mutual alignment, pattern formation, and aggregation are describable by sets of partial differential equations containing convolution terms. Kernels of these convolutions are functions that describe the intensity of interaction of the objects at various relative angles and distances to one another. Such models appear to contain a rich diversity of possible behaviour and dynamics, depending on details of the kernels involved. They are also of great generality, with applications in the natural sciences, including physics and biology. In the latter, the examples that fall into such class include molecular, cellular, as well as social phenomena. Analysis of the equations, and predictions in several test cases are presented. This paper is related to Mogilner and Edelstein-Keshet (1995) in which the spatially-homogeneous version of these models was investigated.

Original languageEnglish (US)
Pages (from-to)346-367
Number of pages22
JournalPhysica D: Nonlinear Phenomena
Volume89
Issue number3-4
StatePublished - 1996
Externally publishedYes

Fingerprint

Patch
Convolution
convolution integrals
kernel
Natural sciences
Pattern Formation
biology
Interaction
organisms
partial differential equations
Dynamic Behavior
Partial differential equations
Biology
Aggregation
Alignment
Ensemble
Agglomeration
Physics
Partial differential equation
alignment

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Spatio-angular order in populations of self-aligning objects : Formation of oriented patches. / Mogilner, Alex; Edelstein-Keshet, Leah.

In: Physica D: Nonlinear Phenomena, Vol. 89, No. 3-4, 1996, p. 346-367.

Research output: Contribution to journalArticle

Mogilner, Alex ; Edelstein-Keshet, Leah. / Spatio-angular order in populations of self-aligning objects : Formation of oriented patches. In: Physica D: Nonlinear Phenomena. 1996 ; Vol. 89, No. 3-4. pp. 346-367.
@article{b9bdb07fe5154319bc675d81e541d272,
title = "Spatio-angular order in populations of self-aligning objects: Formation of oriented patches",
abstract = "We consider a class of models for the dynamic behaviour of ensembles of objects whose interactions depend on angular orientations as well as spatial positions. The {"}objects{"} could be particles, molecules, cells or organisms. We show how processes such as mutual alignment, pattern formation, and aggregation are describable by sets of partial differential equations containing convolution terms. Kernels of these convolutions are functions that describe the intensity of interaction of the objects at various relative angles and distances to one another. Such models appear to contain a rich diversity of possible behaviour and dynamics, depending on details of the kernels involved. They are also of great generality, with applications in the natural sciences, including physics and biology. In the latter, the examples that fall into such class include molecular, cellular, as well as social phenomena. Analysis of the equations, and predictions in several test cases are presented. This paper is related to Mogilner and Edelstein-Keshet (1995) in which the spatially-homogeneous version of these models was investigated.",
author = "Alex Mogilner and Leah Edelstein-Keshet",
year = "1996",
language = "English (US)",
volume = "89",
pages = "346--367",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "3-4",

}

TY - JOUR

T1 - Spatio-angular order in populations of self-aligning objects

T2 - Formation of oriented patches

AU - Mogilner, Alex

AU - Edelstein-Keshet, Leah

PY - 1996

Y1 - 1996

N2 - We consider a class of models for the dynamic behaviour of ensembles of objects whose interactions depend on angular orientations as well as spatial positions. The "objects" could be particles, molecules, cells or organisms. We show how processes such as mutual alignment, pattern formation, and aggregation are describable by sets of partial differential equations containing convolution terms. Kernels of these convolutions are functions that describe the intensity of interaction of the objects at various relative angles and distances to one another. Such models appear to contain a rich diversity of possible behaviour and dynamics, depending on details of the kernels involved. They are also of great generality, with applications in the natural sciences, including physics and biology. In the latter, the examples that fall into such class include molecular, cellular, as well as social phenomena. Analysis of the equations, and predictions in several test cases are presented. This paper is related to Mogilner and Edelstein-Keshet (1995) in which the spatially-homogeneous version of these models was investigated.

AB - We consider a class of models for the dynamic behaviour of ensembles of objects whose interactions depend on angular orientations as well as spatial positions. The "objects" could be particles, molecules, cells or organisms. We show how processes such as mutual alignment, pattern formation, and aggregation are describable by sets of partial differential equations containing convolution terms. Kernels of these convolutions are functions that describe the intensity of interaction of the objects at various relative angles and distances to one another. Such models appear to contain a rich diversity of possible behaviour and dynamics, depending on details of the kernels involved. They are also of great generality, with applications in the natural sciences, including physics and biology. In the latter, the examples that fall into such class include molecular, cellular, as well as social phenomena. Analysis of the equations, and predictions in several test cases are presented. This paper is related to Mogilner and Edelstein-Keshet (1995) in which the spatially-homogeneous version of these models was investigated.

UR - http://www.scopus.com/inward/record.url?scp=0001499542&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001499542&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001499542

VL - 89

SP - 346

EP - 367

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3-4

ER -