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 language | English (US) |
|---|---|
| Pages (from-to) | 346-367 |
| Number of pages | 22 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 89 |
| Issue number | 3-4 |
| State | Published - 1996 |
| Externally published | Yes |
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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 journal › Article
}
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.
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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 -