arXiv subjects

Ina Humpert

Publications and source records attributed to Ina Humpert.

3 recordsLinked to original sources

arXiv2021

Dynamic optimal transport on networks

We study a dynamic optimal transport problem on a network. Despite the cost for transport along the edges, an additional cost, scaled with a parameter $\kappa$, has to be paid for interchanging mass between edges and vertices. We show existence f minimisers using duality and discuss the relationship of the model to other metrics such as Fisher-Rao and the classical Wasserstein metric. Finally, we examine the limiting behaviour of the model in terms of the parameter $\kappa$.

math.AP↗

arXiv2019

On the Role of Vesicle Transport in Neurite Growth: Modelling and Experiments

The processes that determine the establishment of the complex morphology of neurons during development are still poorly understood. We present experiments that use live imaging to examine the role of vesicle transport and propose a lattice-based model that shows symmetry breaking features similar to a neuron during its polarization. In a otherwise symmetric situation our model predicts that a difference in neurite length increases the growth potential of the longer neurite indicating that vesicle transport can be regarded as a major factor in neurite growth.

q-bio.SC↗

arXiv2018

On Fokker-Planck Equations with In- and Outflow of Mass

Motivated by modeling transport processes in the growth of neurons, we present results on (nonlinear) Fokker-Planck equations where the total mass is not conserved. This is either due to in- and outflow boundary conditions or to spatially distributed reaction terms. We are able to prove exponential decay towards equilibrium using entropy methods in several situations. As there is no conservation of mass it is difficult to exploit the gradient flow structure of the differential operator which renders the analysis more challenging. In particular, classical logarithmic Sobolev inequalities are not applicable any more. Our analytic results are illustrated by extensive numerical studies.

math.AP↗