## INTERACTING MANY-PARTICLE SYSTEMS OF DIFFERENT PARTICLE TYPES CONVERGE TO A SORTED STATE

Publication: Research - peer-review › Journal article – Annual report year: 2010

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**INTERACTING MANY-PARTICLE SYSTEMS OF DIFFERENT PARTICLE TYPES CONVERGE TO A SORTED STATE.** / Kokkendorff, Simon Lyngby; Starke, Jens; Hummel, N.

Publication: Research - peer-review › Journal article – Annual report year: 2010

### Harvard

*S I A M Journal on Applied Mathematics*, vol 70, no. 7, pp. 2534-2555. DOI: 10.1137/070700693

### APA

*S I A M Journal on Applied Mathematics*,

*70*(7), 2534-2555. DOI: 10.1137/070700693

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*S I A M Journal on Applied Mathematics*. 2010, 70(7). 2534-2555. Available: 10.1137/070700693

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TY - JOUR

T1 - INTERACTING MANY-PARTICLE SYSTEMS OF DIFFERENT PARTICLE TYPES CONVERGE TO A SORTED STATE

AU - Kokkendorff,Simon Lyngby

AU - Starke,Jens

AU - Hummel,N.

PY - 2010

Y1 - 2010

N2 - We consider a model class of interacting many-particle systems consisting of different types of particles defined by a gradient flow. The corresponding potential expresses attractive and repulsive interactions between particles of the same type and different types, respectively. The introduced system converges by self-organized pattern formation to a sorted state where particles of the same type share a common position and those of different types are separated from each other. This is proved in the sense that we show that the property of being sorted is asymptotically stable and all other states are unstable. The models are motivated from physics, chemistry, and biology, and the principal investigations can be useful for many systems with interacting particles or agents. The models match particularly well a system in neuroscience, namely the axonal pathfinding and sorting in the olfactory system of vertebrates.

AB - We consider a model class of interacting many-particle systems consisting of different types of particles defined by a gradient flow. The corresponding potential expresses attractive and repulsive interactions between particles of the same type and different types, respectively. The introduced system converges by self-organized pattern formation to a sorted state where particles of the same type share a common position and those of different types are separated from each other. This is proved in the sense that we show that the property of being sorted is asymptotically stable and all other states are unstable. The models are motivated from physics, chemistry, and biology, and the principal investigations can be useful for many systems with interacting particles or agents. The models match particularly well a system in neuroscience, namely the axonal pathfinding and sorting in the olfactory system of vertebrates.

KW - neuroscience

KW - self-organization

KW - gradient flows

KW - stability

KW - pattern formation

KW - many-particle systems

KW - olfactory system

U2 - 10.1137/070700693

DO - 10.1137/070700693

M3 - Journal article

VL - 70

SP - 2534

EP - 2555

JO - S I A M Journal on Applied Mathematics

T2 - S I A M Journal on Applied Mathematics

JF - S I A M Journal on Applied Mathematics

SN - 0036-1399

IS - 7

ER -