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Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications
The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM.
Multiscale Modeling of Granular Flows with Application to Crowd Dynamics
A new multiscale modeling technique relies on a recently introduced measure-theoretic approach, which allows one to manage the microscopic and the macroscopic scale under a unique framework and in the resulting coupled model the two scales coexist and share information.
Mathematical modeling of vehicular traffic: a discrete kinetic theory approach
A discrete velocity mathematical model for vehicular traffic along a one-way road using the kinetic scale to capture the probabilistic essence of the interactions among the vehicles and offers the opportunity of a profitable analytical investigation of the relevant global features of the system.
Multiscale Modeling of Pedestrian Dynamics
This paper presents an overview of the modeling of Crowd Dynamics by time-Evolving Measures and generalizations of the Multiscale Approach.
On the dynamics of social conflicts: looking for the Black Swan
Modelling the modeling of social competition, possibly resulting in the onset of extreme conflicts, makes use of the framework of the kinetic theory for active particles, where nonlinear interactions among subjects are modeled according to game-theoretical principles.
Non-local first-order modelling of crowd dynamics: A multidimensional framework with applications
Alzheimer's disease: a mathematical model for onset and progression.
- M. Bertsch, B. Franchi, N. Marcello, M. C. Tesi, A. Tosin
- BiologyMathematical medicine and biology : a journal of…
- 16 March 2015
A mathematical model for the onset and progression of Alzheimer's disease based on transport and diffusion equations is proposed, which is in good qualitative agreement with clinical images of the disease distribution in the brain which vary from early to advanced stages.
Time-Evolving Measures and Macroscopic Modeling of Pedestrian Flow
This paper introduces a new model of pedestrian flow, formulated within a measure-theoretic framework. It consists of a macroscopic representation of the system via a family of measures which, pushed…
Mechanics and Chemotaxis in the Morphogenesis of Vascular Networks
A unified view of the morphogenetic process is provided in terms of physical mechanisms and mathematical modeling of the formation of vascular networks in vitro.
Complex Systems and Society: Modeling and Simulation
This work aims to foster the interdisciplinary dialogue between mathematicians and socio-economic scientists by taking into account a multidisciplinary approach that will encourage the transfer of knowledge, ideas, and methodology from one discipline to the other.