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pro vyhledávání: '"Hillen, Thomas"'
Many transport processes in ecology, physics and biochemistry can be described by the average time to first find a site or exit a region, starting from an initial position. Typical mathematical treatments are based on formulations that allow for vari
Externí odkaz:
http://arxiv.org/abs/2404.00400
In this paper we study a broad class of non-local advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the non-local presence of others. Our model allows for different non-local
Externí odkaz:
http://arxiv.org/abs/2312.09692
The employment of nonlocal PDE models to describe biological aggregation and other phenomena has gained considerable traction in recent years. For cell populations, these methods grant a means of accommodating essential elements such as cell adhesion
Externí odkaz:
http://arxiv.org/abs/2307.14396
Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection-diffusion model with nonlocal advection terms describing the species
Externí odkaz:
http://arxiv.org/abs/2305.14954
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a corresponding energy
Externí odkaz:
http://arxiv.org/abs/2206.07398
Publikováno v:
In Nonlinear Analysis: Real World Applications August 2024 78
Non-local advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modelling non-local advection mathematicall
Externí odkaz:
http://arxiv.org/abs/2106.06383
Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic level, yet thei
Externí odkaz:
http://arxiv.org/abs/2101.04647
Autor:
Buttenschön, Andreas, Hillen, Thomas
In this manuscript, we consider the modelling of cellular adhesions, which is a key interaction between biological cells. Continuum models of the diffusion-advection-reaction type have long been used in tissue modelling. In 2006, Armstrong, Painter,
Externí odkaz:
http://arxiv.org/abs/2001.00286