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22 results on '"Patacchini, F"'

1. On a Class of Nonlocal Continuity Equations on Graphs

Author

Esposito, A., Patacchini, F. S., and Schlichting, A.

Subjects
Mathematics - Analysis of PDEs, 35R02, 35R06, 35A01, 35A02
Abstract

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 general interpolation functions, which give rise to a variety of different dynamics, e.g., the nonlocal interaction dynamics coming from a solution-dependent velocity field. Our analysis reveals structural differences with the more standard Euclidean space, as some analogous properties rely on the interpolation chosen.

Published
2022
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2. Existence of ground states for aggregation-diffusion equations

Author

Carrillo, J. A., Delgadino, M. G., and Patacchini, F. S.

Subjects
Mathematics - Analysis of PDEs
Abstract

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 functional making it energetically favorable to spread, while the attraction is modeled through nonlocal forces. We give conditions on general entropies and interaction potentials for which neither ground states nor local minimizers exist. We show that these results are sharp for homogeneous functionals with entropies leading to degenerate diffusions while they are not sharp for fast diffusions. The particular relevant case of linear diffusion is totally clarified giving a sharp condition on the interaction potential under which the corresponding free energy functional has ground states or not., Comment: 21 pages

Published
2018
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3. Discrete minimisers are close to continuum minimisers for the interaction energy

Author

Cañizo, J. A. and Patacchini, F. S.

Subjects
Mathematics - Analysis of PDEs
Abstract

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 the discrete interaction energy $\Gamma$-converges in the narrow topology to the continuum interaction energy. As an important part of the proof we study support and regularity properties of discrete minimisers: we show that continuum minimisers belong to suitable Morrey spaces and we introduce the set of empirical Morrey measures as a natural discrete analogue containing all the discrete minimisers., Comment: 37 pages, 1 figure

Published
2016
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4. A revisited Johnson-Mehl-Avrami-Kolmogorov model and the evolution of grain-size distributions in steel

Author

Hömberg, D., Patacchini, F. S., Sakamoto, K., and Zimmer, J.

Subjects
Condensed Matter - Materials Science
Abstract

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 steels, a deeper knowledge of the grain structure is essential. To this end, a Fokker-Planck evolution law for the volume distribution of ferrite grains is developed and shown to exhibit a log-normally distributed solution. Numerical parameter studies are given and confirm expected properties qualitatively. As a preparation for future work on parameter identification, a strategy is presented for the comparison of volume distributions with area distributions experimentally gained from polished micrograph sections., Comment: 16 pages, 19 figures

Published
2016
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5. Geometry of minimizers for the interaction energy with mildly repulsive potentials

Author

Carrillo, J. A., Figalli, A., and Patacchini, F. S.

Subjects
Mathematics - Analysis of PDEs
Abstract

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 finite. In addition, for some class of potentials we prove the validity of a uniform upper bound on the cardinal of the support of a global minimizer. Finally, in the one-dimensional case, we give quantitative bounds., Comment: In this updated version we corrected a couple of misprints and added details to the proof of Lemma 2.4. 10 pages, 1 figure

Published
2016
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6. Convergence of a particle method for diffusive gradient flows in one dimension

Author

Carrillo, J. A., Patacchini, F. S., Sternberg, P., and Wolansky, G.

Subjects
Mathematics - Analysis of PDEs
Abstract

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 flow structure at the particle level. The strategy of the proof is based on an abstract result for the convergence of curves of maximal slope in metric spaces., Comment: In this updated version we have corrected a few misprints. 28 pages, 1 figure

Published
2016
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7. Numerical Study of a Particle Method for Gradient Flows

Author

Carrillo, J. A., Huang, Y., Patacchini, F. S., and Wolansky, G.

Subjects
Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis
Abstract

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 preserves the gradient flow structure at the particle level, and enables us to obtain a gradient descent formulation after time discretisation. We give several simulations to illustrate the validity of this method, as well as a detailed study of one-dimensional aggregation-diffusion equations., Comment: 27 pages, 21 figures

Published
2015
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8. Existence of Compactly Supported Global Minimisers for the Interaction Energy

Author

Cañizo, J. A., Carrillo, J. A., and Patacchini, F. S.

Subjects
Mathematics - Analysis of PDEs
Abstract

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 is the complementary assumption to that in classical results on thermodynamic limits in statistical mechanics. The proof is based on a uniform control on the local mass around each point of the support of a global minimiser, together with an estimate on the size of the "gaps" it may have. The class of potentials for which we prove existence of global minimisers includes power-law potentials and, for some range of parameters, Morse potentials, widely used in applications. We also show that the support of local minimisers is compact under suitable assumptions., Comment: Final version after referee reports taken into account

Published
2014
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12. Health care for older people in Italy: The U.L.I.S.S.E. Project (Un link informatico sui servizi sanitari esistenti per l'anziano - a computerized network on health care services for older people)

Author

Lattanzio F, Mussi C, Scafato E, Ruggiero C, Dell'Aquila G, Pedone C, Mammarella F, Galluzzo L, Salvioli G, Senin U, Carbonin PU, Bernabei R, Cherubini A, Laguzzi E, Cucinotta D, Arnone G, Rozzini R, Cassinadri A, Putzu P, Porceddu C, Zaru C, Abate G, Di Iorio A, Abate M, Guglielmi M, Foschini N, Battaglini C, Fellin R, Volpato S, Cavalieri M, Fotini S, Guerra G, Rossi L, Masotti G, Fumagalli S, Odetti P, Cataldi A, Monacelli F, Nicita Mauro V, Basile G, Maltese G, Nicita Mauro C, Pellicciotti F, Scotto R, Vaccina A, Minnucci A, Forte L, Lo Storoto MR, Licata G, Tuttolomondo A, Barbagallo M, Dominguez LJ, De Leo M, Belvedere M, Putignano E, Longo A, Mancioli G, Patacchini F, Palmari N, Ierardi BA, Marino P, Soldato M, Pilotto A, Paris F, Forconi S, Guerrini M, De Paduanis GA, De Palma A, Boschi S, Molaschi M, Poli L, De Colle P, Bonoldi G, Puricelli S, Pellegrini R, Consolaro E, Bosello O, Zivelonghi A, Gravic G, Guariento S, Di Francesco V, Tua E, Pisaturo A, Lacava R, Gareri P, Borgia R, Cristiano VN, Palummeri, Pescetelli, Galdi M, Bochicchio GB, Solimano A, Brugaletta S, Carnazza L, Gallitto E, Albano G, Schipani G, Conte, Pagella A, Perrero L, Sabato V, Marella L, Schiavina, Zacco B, Scaglia L, Virgilio A, Iera M, Doria, Pansini L, Boni N, Inzitari M, Aramini I, Musante S, Cavagnaro P, Riello F, De Alfieri W, Pescetelli P, Trecca R, Di Iusto, Zamboni V, Cuppone R, Foschi, Marino S, Simone M, Scarlata A, Battegazzore C, Morucci R, Luchetti M, Menculini G, Cichetti G, Orlando I, Fantoni B, Ognibene G, Gobbi C, Cascone A, Avanzi GL, Casu A, Zeni S, Santin S, Scotti G, Cappella C, Penzo P., TOIGO, GABRIELE, Lattanzio, F, Mussi, C, Scafato, E, Ruggiero, C, Dell'Aquila, G, Pedone, C, Mammarella, F, Galluzzo, L, Salvioli, G, Senin, U, Carbonin, Pu, Bernabei, R, Cherubini, A, Laguzzi, E, Cucinotta, D, Arnone, G, Rozzini, R, Cassinadri, A, Putzu, P, Porceddu, C, Zaru, C, Abate, G, Di Iorio, A, Abate, M, Guglielmi, M, Foschini, N, Battaglini, C, Fellin, R, Volpato, S, Cavalieri, M, Fotini, S, Guerra, G, Rossi, L, Masotti, G, Fumagalli, S, Odetti, P, Cataldi, A, Monacelli, F, Nicita Mauro, V, Basile, G, Maltese, G, Nicita Mauro, C, Pellicciotti, F, Scotto, R, Vaccina, A, Minnucci, A, Forte, L, Lo Storoto, Mr, Licata, G, Tuttolomondo, A, Barbagallo, M, Dominguez, Lj, De Leo, M, Belvedere, M, Putignano, E, Longo, A, Mancioli, G, Patacchini, F, Palmari, N, Ierardi, Ba, Marino, P, Soldato, M, Pilotto, A, Paris, F, Forconi, S, Guerrini, M, De Paduanis, Ga, De Palma, A, Boschi, S, Molaschi, M, Poli, L, Toigo, Gabriele, De Colle, P, Bonoldi, G, Puricelli, S, Pellegrini, R, Consolaro, E, Bosello, O, Zivelonghi, A, Gravic, G, Guariento, S, Di Francesco, V, Tua, E, Pisaturo, A, Lacava, R, Gareri, P, Borgia, R, Cristiano, Vn, Palummeri, Pescetelli, Galdi, M, Bochicchio, Gb, Solimano, A, Brugaletta, S, Carnazza, L, Gallitto, E, Albano, G, Schipani, G, Conte, Pagella, A, Perrero, L, Sabato, V, Marella, L, Schiavina, Zacco, B, Scaglia, L, Virgilio, A, Iera, M, Doria, Pansini, L, Boni, N, Inzitari, M, Aramini, I, Musante, S, Cavagnaro, P, Riello, F, De Alfieri, W, Pescetelli, P, Trecca, R, Di, Iusto, Zamboni, V, Cuppone, R, Foschi, Marino, S, Simone, M, Scarlata, A, Battegazzore, C, Morucci, R, Luchetti, M, Menculini, G, Cichetti, G, Orlando, I, Fantoni, B, Ognibene, G, Gobbi, C, Cascone, A, Avanzi, Gl, Casu, A, Zeni, S, Santin, S, Scotti, G, Cappella, C, and Penzo, P.

Subjects
computerized network, Health care, service, elderly
Abstract

Objectives: The U.L.I.S.S.E. study is aimed at describing older patients who are cared for in hospitals, home care or nursing homes in Italy. Design: The U.L.I.S.S.E. study is an observational multicenter prospective 1-year study. Setting: Overall, 23 acute geriatric or internal medicine hospital units, 11 home care services and 31 nursing homes participated in the study. Measurements: The patient’s evaluation was performed using comprehensive geriatric assessment instruments, i.e. the interRAI Minimum Data Set, while data on service characteristics were recorded using ad-hoc designed questionnaires. Results: The older subjects who are in need of acute and long term care in Italy have similar characteristics: their mean age is higher than 80 years, they have a high level of disability in ADL, an important multimorbidity, and are treated with several drugs. The prevalence of cognitive impairment is particularly high in nursing homes, where almost 70% of residents suffer from it and 40% have severe cognitive impairment. On the other hand, there is a shortage of health care services, which are heterogeneous and fragmented. Conclusions: Health care services for older people in Italy are currently inadequate to manage the complexity of the older patients. An important effort should be undertaken to create a more integrated health care system.

Published
2010

13. Existence of Compactly Supported Global Minimisers for the Interaction Energy

Author

Ca��izo, J. A., Carrillo, J. A., and Patacchini, F. S.

Subjects
Mathematics (miscellaneous), Mathematics - Analysis of PDEs, Mechanical Engineering, FOS: Mathematics, Analysis, Analysis of PDEs (math.AP)
Abstract

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 is the complementary assumption to that in classical results on thermodynamic limits in statistical mechanics. The proof is based on a uniform control on the local mass around each point of the support of a global minimiser, together with an estimate on the size of the "gaps" it may have. The class of potentials for which we prove existence of global minimisers includes power-law potentials and, for some range of parameters, Morse potentials, widely used in applications. We also show that the support of local minimisers is compact under suitable assumptions., Final version after referee reports taken into account

Published
2014

15. Health care for older people in Italy: The U.L.I.S.S.E. Project (Un link informatico sui servizi sanitari esistenti per l'anziano - a computerized network on health care services for older people)

Author

Lattanzio, F, Mussi, C, Scafato, E, Ruggiero, C, Dell'Aquila, G, Pedone, C, Mammarella, F, Galluzzo, L, Salvioli, G, Senin, U, Carbonin, Pu, Bernabei, R, Cherubini, A, STUDY GROUP LAGUZZI E, U. L. I. S. S. E., Cucinotta, D, Arnone, G, Rozzini, R, Cassinadri, A, Putzu, P, Porceddu, C, Zaru, C, Abate, G, DI IORIO, A, Abate, M, Guglielmi, M, Foschini, N, Battaglini, C, Fellin, R, Volpato, S, Cavalieri, M, Fotini, S, Guerra, G, Rossi, L, Masotti, G, Fumagalli, S, Odetti, Patrizio, Cataldi, A, Monacelli, Fiammetta, NICITA MAURO, V, Basile, G, Maltese, G, NICITA MAURO, C, Pellicciotti, F, Scotto, R, Vaccina, A, Minnucci, A, Forte, L, LO STOROTO MR, Licata, G, Tuttolomondo, A, Barbagallo, M, Dominguez, Lj, DE LEO, M, Belvedere, M, Putignano, E, Longo, A, Mancioli, G, Patacchini, F, Palmari, N, Ierardi, Ba, Marino, P, Soldato, M, Pilotto, A, Paris, F, Forconi, S, Guerrini, M, DE PADUANIS GA, DE PALMA, A, Boschi, S, Molaschi, M, Poli, L, Toigo, G, DE COLLE, P, Bonoldi, G, Puricelli, S, Pellegrini, R, Consolaro, E, Bosello, O, Zivelonghi, A, Gravic, G, Guariento, S, DI FRANCESCO, V, Tua, E, Pisaturo, A, Lacava, R, Gareri, P, Borgia, R, Cristiano, Vn, Palummeri, Pescetelli, Galdi, M, Bochicchio, Gb, Solimano, A, Brugaletta, S, Carnazza, L, Gallitto, E, Albano, G, Schipani, G, Conte, Pagella, A, Perrero, L, Sabato, V, Marella, L, Schiavina, Zacco, B, Scaglia, L, Virgilio, A, Iera, M, Doria, Pansini, L, Boni, N, Inzitari, M, Aramini, I, Musante, S, Cavagnaro, P, Riello, F, DE ALFIERI, W, Pescetelli, P, Trecca, R, Iusto, Di, Zamboni, V, Cuppone, R, Foschi, Marino, S, Simone, M, Scarlata, A, Battegazzore, C, Morucci, R, Luchetti, M, Menculini, G, Cichetti, G, Orlando, I, Fantoni, B, Ognibene, G, Gobbi, C, Cascone, A, Avanzi, Gl, Casu, A, Zeni, S, Santin, S, Scotti, G, Cappella, C, and Penzo, P.

Subjects
residenzialità, non autosufficienza, cura anziani, servizio sanitario
Published
2010

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