An exclusion process for modelling fungal hyphal growth

Evans, Martin R.; Sugden, Kate

doi:10.1016/j.physa.2007.04.078

Cited by 40 publications

(46 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The physics of many non-equilibrium processes ranging from ionic conductors [1] and spin transport [2] to biological transport [3,4,5,6,7,8] can be described by driven diffusive systems. These are systems held out of equilibrium, for instance, by the environment driving a current of particles or energy through them.…”

Section: Introductionmentioning

confidence: 99%

Phase diagrams of two-lane driven diffusive systems

Evans¹,

Kafri²,

Sugden³

et al. 2011

J. Stat. Mech.

View full text Add to dashboard Cite

Abstract. We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagrams for the asymmetric exclusion process coupled to various second lanes: a diffusive lane; an asymmetric exclusion process with advection in the same direction as the first lane, and an asymmetric exclusion process with advection in the opposite direction. The competing currents on the two lanes naturally lead to a very rich phenomenology and we find a variety of phase diagrams. It is shown that the stability analysis is equivalent to an 'extremal current principle' for the total current in the two lanes. We also point to classes of models where both the stability analysis and the extremal current principle fail.arXiv:1103.4677v1 [cond-mat.stat-mech]

show abstract

Section: Introductionmentioning

confidence: 99%

Phase diagrams of two-lane driven diffusive systems

Evans¹,

Kafri²,

Sugden³

et al. 2011

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

“…In 46,47,48,49 the dynamically extending exclusion process (DEEP) has been introduced as a model for fungal growth. In the DEEP not all particles are removed from the system as they reach the end, but with some probability form a new lattice site.…”

Section: Applications and Related Modelsmentioning

confidence: 99%

Exclusive queueing processes and their application to traffic systems

Arita

Schadschneider

2014

Math. Models Methods Appl. Sci.

View full text Add to dashboard Cite

The dynamics of pedestrian crowds has been studied intensively in recent years, both theoretically and empirically. However, in many situations pedestrian crowds are rather static, e.g. due to jamming near bottlenecks or queueing at ticket counters or supermarket checkouts. Classically such queues are often described by the M/M/1 queue that neglects the internal structure (density profile) of the queue by focussing on the system length as the only dynamical variable. This is different in the Exclusive Queueing Process (EQP) in which the queue is considered on a microscopic level. It is equivalent to a Totally Asymmetric Exclusion Process (TASEP) of varying length. The EQP has a surprisingly rich phase diagram with respect to the arrival probability α and the service probability β. The behavior on the phase transition line is much more complex than for the TASEP with a fixed system length. It is nonuniversal and depends strongly on the update procedure used. In this article, we review the main properties of the EQP. We also mention extensions and applications of the EQP and some related models.

show abstract

“…An earlier example is the dynamically extending exclusion process (DEEP) introduced in [ 7,8,9,10] as a model for fungal growth. In contrast to the EQP, the DEEP has no mechanism for reducing the system length and therefore the length of the system is always diverging.…”

Section: Introductionmentioning

confidence: 99%

Density profiles of the exclusive queuing process

Arita

Schadschneider

2012

J. Stat. Mech.

View full text Add to dashboard Cite

The exclusive queueing process (EQP) incorporates the exclusion principle into classic queueing models. It can be interpreted as an exclusion process of variable system length. Here we extend previous studies of its phase diagram by identifying subphases which can be distinguished by the number of plateaus in the density profiles. Furthermore the influence of different update procedures (parallel, backward-ordered, continuous time) is determined.

show abstract

An exclusion process for modelling fungal hyphal growth

Cited by 40 publications

References 15 publications

Phase diagrams of two-lane driven diffusive systems

Phase diagrams of two-lane driven diffusive systems

Exclusive queueing processes and their application to traffic systems

Density profiles of the exclusive queuing process

Contact Info

Product

Resources

About