-
Previous Article
Comparative model accuracy of a data-fitted generalized Aw-Rascle-Zhang model
- NHM Home
- This Issue
-
Next Article
Asymptotic behaviour of flows on reducible networks
Variational evolution of one-dimensional Lennard-Jones systems
1. | Dipartimento di Matematica, Università di Roma 'Tor Vergata', via della Ricerca Scientifica, 00133 Roma |
2. | Dipartimento di Matematica, Università di Trento, via Sommarive 14, 38123 Povo, Italy |
3. | Dipartimento di Matematica 'F. Casorati', Università di Pavia, via Ferrata, 1-27100 Pavia |
References:
[1] |
L. Ambrosio, Minimizing movements,, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5), 19 (1995), 191.
|
[2] |
L. Ambrosio and A. Braides, Energies in $SBV$ and variational models in fracture mechanics,, in Homogenization and Applications to Material Sciences (Nice, (1995), 1.
|
[3] |
L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems,, Oxford University Press, (2000).
|
[4] |
L. Ambrosio and N. Gigli, A user's guide to optimal transport,, in Modelling and Optimisation of Flows on Networks (eds. B. Piccoli and M. Rascle), (2062), 1. Google Scholar |
[5] |
L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures,, Lectures in Mathematics ETH, (2008).
|
[6] |
A. Braides, $\Gamma$-convergence for Beginners,, Oxford University Press, (2002).
doi: 10.1093/acprof:oso/9780198507840.001.0001. |
[7] |
A. Braides, Local Minimization, Variational Evolution and $\Gamma$-Convergence, Lecture Notes in Mathematics, 2094,, Springer, (2014).
doi: 10.1007/978-3-319-01982-6. |
[8] |
A. Braides, M. S. Gelli and M. Novaga, Motion and pinning of discrete interfaces,, Arch. Ration. Mech. Anal., 95 (2010), 469.
doi: 10.1007/s00205-009-0215-z. |
[9] |
A. Braides, A. J. Lew and M. Ortiz, Effective cohesive behavior of layers of interatomic planes,, Arch. Ration. Mech. Anal., 180 (2006), 151.
doi: 10.1007/s00205-005-0399-9. |
[10] |
A. Braides and L. Truskinovsky, Asymptotic expansions by Gamma-convergence,, Cont. Mech. Therm., 20 (2008), 21.
doi: 10.1007/s00161-008-0072-2. |
[11] |
G. Dal Maso, An Introduction to $\Gamma$-Convergence,, Birkhäuser, (1993).
doi: 10.1007/978-1-4612-0327-8. |
[12] |
E. De Giorgi, New problems on minimizing movements,, in Boundary Value Problems for Partial Differential Equations and Applications, (1993), 81.
|
[13] |
N. Gigli, On the heat flow on metric measure spaces: Existence, uniqueness and stability,, Calc. Var. Partial Differential Equations, 39 (2010), 101.
doi: 10.1007/s00526-009-0303-9. |
[14] |
M. Gobbino, Gradient flow for the one-dimensional Mumford-Shah functional,, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 27 (1998), 145.
|
[15] |
E. Sandier and S. Serfaty, Gamma-convergence of gradient flows and application to Ginzburg-Landau,, Comm. Pure Appl. Math., 57 (2004), 1627.
doi: 10.1002/cpa.20046. |
show all references
References:
[1] |
L. Ambrosio, Minimizing movements,, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5), 19 (1995), 191.
|
[2] |
L. Ambrosio and A. Braides, Energies in $SBV$ and variational models in fracture mechanics,, in Homogenization and Applications to Material Sciences (Nice, (1995), 1.
|
[3] |
L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems,, Oxford University Press, (2000).
|
[4] |
L. Ambrosio and N. Gigli, A user's guide to optimal transport,, in Modelling and Optimisation of Flows on Networks (eds. B. Piccoli and M. Rascle), (2062), 1. Google Scholar |
[5] |
L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures,, Lectures in Mathematics ETH, (2008).
|
[6] |
A. Braides, $\Gamma$-convergence for Beginners,, Oxford University Press, (2002).
doi: 10.1093/acprof:oso/9780198507840.001.0001. |
[7] |
A. Braides, Local Minimization, Variational Evolution and $\Gamma$-Convergence, Lecture Notes in Mathematics, 2094,, Springer, (2014).
doi: 10.1007/978-3-319-01982-6. |
[8] |
A. Braides, M. S. Gelli and M. Novaga, Motion and pinning of discrete interfaces,, Arch. Ration. Mech. Anal., 95 (2010), 469.
doi: 10.1007/s00205-009-0215-z. |
[9] |
A. Braides, A. J. Lew and M. Ortiz, Effective cohesive behavior of layers of interatomic planes,, Arch. Ration. Mech. Anal., 180 (2006), 151.
doi: 10.1007/s00205-005-0399-9. |
[10] |
A. Braides and L. Truskinovsky, Asymptotic expansions by Gamma-convergence,, Cont. Mech. Therm., 20 (2008), 21.
doi: 10.1007/s00161-008-0072-2. |
[11] |
G. Dal Maso, An Introduction to $\Gamma$-Convergence,, Birkhäuser, (1993).
doi: 10.1007/978-1-4612-0327-8. |
[12] |
E. De Giorgi, New problems on minimizing movements,, in Boundary Value Problems for Partial Differential Equations and Applications, (1993), 81.
|
[13] |
N. Gigli, On the heat flow on metric measure spaces: Existence, uniqueness and stability,, Calc. Var. Partial Differential Equations, 39 (2010), 101.
doi: 10.1007/s00526-009-0303-9. |
[14] |
M. Gobbino, Gradient flow for the one-dimensional Mumford-Shah functional,, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 27 (1998), 145.
|
[15] |
E. Sandier and S. Serfaty, Gamma-convergence of gradient flows and application to Ginzburg-Landau,, Comm. Pure Appl. Math., 57 (2004), 1627.
doi: 10.1002/cpa.20046. |
[1] |
Mathias Schäffner, Anja Schlömerkemper. On Lennard-Jones systems with finite range interactions and their asymptotic analysis. Networks & Heterogeneous Media, 2018, 13 (1) : 95-118. doi: 10.3934/nhm.2018005 |
[2] |
Irina Berezovik, Wieslaw Krawcewicz, Qingwen Hu. Dihedral molecular configurations interacting by Lennard-Jones and Coulomb forces. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 1879-1903. doi: 10.3934/dcdss.2019124 |
[3] |
Thomas Hudson. Gamma-expansion for a 1D confined Lennard-Jones model with point defect. Networks & Heterogeneous Media, 2013, 8 (2) : 501-527. doi: 10.3934/nhm.2013.8.501 |
[4] |
Antonin Chambolle, Francesco Doveri. Minimizing movements of the Mumford and Shah energy. Discrete & Continuous Dynamical Systems - A, 1997, 3 (2) : 153-174. doi: 10.3934/dcds.1997.3.153 |
[5] |
Antonio Tribuzio. Perturbations of minimizing movements and curves of maximal slope. Networks & Heterogeneous Media, 2018, 13 (3) : 423-448. doi: 10.3934/nhm.2018019 |
[6] |
Christopher J. Larsen. Local minimality and crack prediction in quasi-static Griffith fracture evolution. Discrete & Continuous Dynamical Systems - S, 2013, 6 (1) : 121-129. doi: 10.3934/dcdss.2013.6.121 |
[7] |
Juan Carlos Marrero, D. Martín de Diego, Diana Sosa. Variational constrained mechanics on Lie affgebroids. Discrete & Continuous Dynamical Systems - S, 2010, 3 (1) : 105-128. doi: 10.3934/dcdss.2010.3.105 |
[8] |
Mariano Giaquinta, Paolo Maria Mariano, Giuseppe Modica. A variational problem in the mechanics of complex materials. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 519-537. doi: 10.3934/dcds.2010.28.519 |
[9] |
Pedro D. Prieto-Martínez, Narciso Román-Roy. Higher-order mechanics: Variational principles and other topics. Journal of Geometric Mechanics, 2013, 5 (4) : 493-510. doi: 10.3934/jgm.2013.5.493 |
[10] |
Eliot Fried. New insights into the classical mechanics of particle systems. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1469-1504. doi: 10.3934/dcds.2010.28.1469 |
[11] |
Kaizhi Wang. Action minimizing stochastic invariant measures for a class of Lagrangian systems. Communications on Pure & Applied Analysis, 2008, 7 (5) : 1211-1223. doi: 10.3934/cpaa.2008.7.1211 |
[12] |
Brian Straughan. Shocks and acceleration waves in modern continuum mechanics and in social systems. Evolution Equations & Control Theory, 2014, 3 (3) : 541-555. doi: 10.3934/eect.2014.3.541 |
[13] |
Khalid Addi, Samir Adly, Hassan Saoud. Finite-time Lyapunov stability analysis of evolution variational inequalities. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1023-1038. doi: 10.3934/dcds.2011.31.1023 |
[14] |
Shengji Li, Chunmei Liao, Minghua Li. Stability analysis of parametric variational systems. Numerical Algebra, Control & Optimization, 2011, 1 (2) : 317-331. doi: 10.3934/naco.2011.1.317 |
[15] |
Oscar E. Fernandez, Anthony M. Bloch, P. J. Olver. Variational Integrators for Hamiltonizable Nonholonomic Systems. Journal of Geometric Mechanics, 2012, 4 (2) : 137-163. doi: 10.3934/jgm.2012.4.137 |
[16] |
Paulo Cesar Carrião, Olimpio Hiroshi Miyagaki. On a class of variational systems in unbounded domains. Conference Publications, 2001, 2001 (Special) : 74-79. doi: 10.3934/proc.2001.2001.74 |
[17] |
Fei Xu, Ross Cressman, Vlastimil Křivan. Evolution of mobility in predator-prey systems. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3397-3432. doi: 10.3934/dcdsb.2014.19.3397 |
[18] |
Gianni Dal Maso, Flaviana Iurlano. Fracture models as $\Gamma$-limits of damage models. Communications on Pure & Applied Analysis, 2013, 12 (4) : 1657-1686. doi: 10.3934/cpaa.2013.12.1657 |
[19] |
François Gay-Balma, Darryl D. Holm, Tudor S. Ratiu. Variational principles for spin systems and the Kirchhoff rod. Journal of Geometric Mechanics, 2009, 1 (4) : 417-444. doi: 10.3934/jgm.2009.1.417 |
[20] |
Sergio Grillo, Marcela Zuccalli. Variational reduction of Lagrangian systems with general constraints. Journal of Geometric Mechanics, 2012, 4 (1) : 49-88. doi: 10.3934/jgm.2012.4.49 |
2018 Impact Factor: 0.871
Tools
Metrics
Other articles
by authors
[Back to Top]