Zobrazeno 1 - 10
of 18
pro vyhledávání: '"Patacchini, F. S."'
Publikováno v:
European Journal of Applied Mathematics, 1-18, 2023
Motivated by applications in data science, we study partial differential equations on graphs. By a classical fixed-point argument, we show existence and uniqueness of solutions to a class of nonlocal continuity equations on graphs. We consider genera
Externí odkaz:
http://arxiv.org/abs/2209.15552
We analyze free energy functionals for macroscopic models of multi-agent systems interacting via pairwise attractive forces and localized repulsion. The repulsion at the level of the continuous description is modeled by pressure-related terms in the
Externí odkaz:
http://arxiv.org/abs/1803.01915
Autor:
Cañizo, J. A., Patacchini, F. S.
Publikováno v:
Calculus of Variations & PDE 57(24), 2018
Under suitable technical conditions we show that minimisers of the discrete interaction energy for attractive-repulsive potentials converge to minimisers of the corresponding continuum energy as the number of particles goes to infinity. We prove that
Externí odkaz:
http://arxiv.org/abs/1612.09233
The classical Johnson-Mehl-Avrami-Kolmogorov approach for nucleation and growth models of diffusive phase transitions is revisited and applied to model the growth of ferrite in multiphase steels. For the prediction of mechanical properties of such st
Externí odkaz:
http://arxiv.org/abs/1608.03821
We show that the support of any local minimizer of the interaction energy consists of isolated points whenever the interaction potential is of class $C^2$ and mildly repulsive at the origin; moreover, if the minimizer is global, then its support is f
Externí odkaz:
http://arxiv.org/abs/1607.08660
We prove the convergence of a particle method for the approximation of diffusive gradient flows in one dimension. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles and preserves the gradient flo
Externí odkaz:
http://arxiv.org/abs/1605.08086
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting scheme preserv
Externí odkaz:
http://arxiv.org/abs/1512.03029
Publikováno v:
Archive for Rational Mechanics and Analysis 217(3):1197-1217, 2015
The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not H-stable, which
Externí odkaz:
http://arxiv.org/abs/1405.5428
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