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pro vyhledávání: '"35Q92"'
In the present study, we consider the Extra-Membrane-Intra model (EMI) for the simulation of excitable tissues at the cellular level. We provide the (possibly large) system of partial differential equations (PDEs), equipped with ad hoc boundary condi
Externí odkaz:
http://arxiv.org/abs/2409.13432
The development of mathematical models of cancer informed by time-resolved measurements has enabled personalised predictions of tumour growth and treatment response. However, frequent cancer monitoring is rare, and many tumours are treated soon after
Externí odkaz:
http://arxiv.org/abs/2409.12844
Autor:
Eckardt, Maria, Surulescu, Christina
We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or decay, ac
Externí odkaz:
http://arxiv.org/abs/2409.12657
Autor:
Potts, Jonathan R.
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a rigorous, non-speculative way. Howe
Externí odkaz:
http://arxiv.org/abs/2409.10147
In this study, we explore a mathematical model for tissue growth focusing on the interplay between multiple cell subpopulations with distinct phenotypic characteristics. The model addresses the dynamics of tissue growth influenced by phenotype-depend
Externí odkaz:
http://arxiv.org/abs/2409.02904
Chemotaxis describes the intricate interplay of cellular motion in response to a chemical signal. We here consider the case of slab geometry which models chemotactic motion between two infinite membranes. Like previous works, we are particularly inte
Externí odkaz:
http://arxiv.org/abs/2408.17243
The standard Poisson-Boltzmann model for molecular electrostatics assumes a sharp variation of the permittivity and salt concentration along the solute-solvent interface. The discontinuous field parameters are not only difficult numerically, but also
Externí odkaz:
http://arxiv.org/abs/2408.14500
Autor:
Knosalla, Piotr, Lankeit, Johannes
This paper concerns the asymptotics of certain parabolic-elliptic chemotaxis-consumption systems with logistic growth and constant concentration of chemoattractant on the boundary. First we prove that in two dimensional bounded domains there exists a
Externí odkaz:
http://arxiv.org/abs/2408.10080
Autor:
He, Jingning, Wu, Hao
We analyze a diffuse interface model that describes the dynamics of incompressible viscous two-phase flows, incorporating mechanisms such as chemotaxis, active transport, and long-range interactions of Oono's type. The evolution system couples the Na
Externí odkaz:
http://arxiv.org/abs/2408.09514
Autor:
Bhattacharya, Apratim
The Poisson-Nernst-Planck (PNP) equations form a coupled parabolic-elliptic system, which models the transport of charged particles under the influence of diffusion and electric force. In this paper, we rigorously derive a homogenized model for the P
Externí odkaz:
http://arxiv.org/abs/2408.08831