Zobrazeno 1 - 7
of 7
pro vyhledávání: '"Francesco S. Patacchini"'
Publikováno v:
Analysis and Applications. 19:965-1017
We investigate a model for collective behavior with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure-valued solutions (defined via mass transport) on sphere, as well as investigate the mean-field particle app
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6c48c40bb468879da51f8184d59a804f
https://doi.org/10.1142/s0219530521500081
https://doi.org/10.1142/s0219530521500081
Autor:
Francesco S. Patacchini, Dejan Slepčev
We study the approximation of the nonlocal-interaction equation restricted to a compact manifold $\mathcal{M}$ embedded in $\mathbb{R}^d$, and more generally compact sets with positive reach (i.e. prox-regular sets). We show that the equation on $\ma
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::776f320aa29180198d694c4ca4773d8b
Publikováno v:
Archive for rational mechanics and analysis, 2019, Vol.232(3), pp.1165-1206 [Peer Reviewed Journal]
Archive for Rational Mechanics and Analysis, 232 (3)
Archive for Rational Mechanics and Analysis, 232 (3)
In this paper we devote our attention to a class of weighted ultrafast diffusion equations arising from the problem of quantisation for probability measures. These equations have a natural gradient flow structure in the space of probability measures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4295051770e1e70f70536e7b0b9077bd
http://dro.dur.ac.uk/26697/
http://dro.dur.ac.uk/26697/
As a counterpoint to classical stochastic particle methods for diffusion, we develop a deterministic particle method for linear and nonlinear diffusion. At first glance, deterministic particle methods are incompatible with diffusive partial different
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f98c42d8a1e748a371f48b6e48f51707
http://hdl.handle.net/10044/1/66347
http://hdl.handle.net/10044/1/66347
Publikováno v:
Calculus of Variations and Partial Differential Equations. 57
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5aa659c0d94cab266f1d58fd9797224f
https://doi.org/10.1007/s00526-017-1289-3
https://doi.org/10.1007/s00526-017-1289-3
Publikováno v:
Zimmer, J, Patacchini, F, Hömberg, D & Sakamoto, K 2017, ' A revisited Johnson-Mehl-Avrami-Kolmogorov model and the evolution of grain-size distributions in steel ', IMA Journal of Applied Mathematics, vol. 82, no. 4, pp. 763-780 . https://doi.org/10.1093/imamat/hxx012
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::05b6cd111216db7ea2cdc027ed249f29
http://arxiv.org/abs/1608.03821
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f7463a6edca5948e0e7d6e2406eb11f9
http://arxiv.org/abs/1607.08660
http://arxiv.org/abs/1607.08660