Thermalization of a driven bi-stable FPU chain

Continuum Mechanics and Thermodynamics

Volumn 22, Issue 6, 2010, Pages 679-698

  Efendiev, Yalchin R ^a   Truskinovsky, Lev ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

Author keywords

Bi stable elements; Ergodicity; Fermi Pasta Ulam system; Latent heat; Statistical mechanics; Thermolization

Indexed keywords

BISTABLES; CANONICAL DISTRIBUTIONS; DYNAMICAL BEHAVIORS; ENERGY WELLS; EQUIPARTITION; ERGODICITY; FERMI-PASTA-ULAM CHAIN; FERMI-PASTA-ULAM SYSTEM; HAMILTONIAN DYNAMICS; QUASI-STATIC; SPINODALS; TEMPERATURE OSCILLATIONS; THERMALIZATION; THERMOLIZATION; TIME-AVERAGED;

DYNAMICAL SYSTEMS; STATISTICAL MECHANICS;

LATENT HEAT;

EID: 78650177881     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-010-0166-5     Document Type: Article

References (26)

1. Balk, A.M., Cherkaev, A.V., Slepyan, L.I.: Dynamics of chains with non-monotone stress-strain relations. I. Model and numerical experiments. J. Mech. Phys. Solids 49, 131-148 (2001)
2. Berdichevsky, V.: Thermodynamics of Chaos and Order. Addison Wesley, New York (1997)
3. Blanc, F.L.X., Le Bris, C., Patz, C.: Finite-temperature coarse-graining of one-dimensional models: Mathematical analysis and computational approaches. J. Nonlinear Sci. 20(2), 241-275 (2010)
4. Campbell, D.K., Rosenau, P., Zaslavsky, G.M.: The Fermi-Pasta-Ulam problem-the first fifty years. Chaos 15, 015101 (2005)
5. Cardin, F., Favretti, M.: On the Helmholtz-Boltzmann thermodynamics of mechanical systems. Contin. Mech. Thermodyn. 16, 15-29 (2004)
6. da Fonseca, C., Petronilho, J.: Explicit inverse of a tridiagonal k-toeplitz matrix. Numer. Math. 100, 457-482 (2005)
7. Dreyer, W., Kunik, M.: Cold, thermal and oscillator closure of the atomic chain. J. Phys. A 33, 2097-2129 (2000)
8. Fedelich, B., Zanzotto, G.: Hysteresis in discrete systems of possibly interacting elements with a double-well energy. J. Nonlinear Sci. 2, 319-342 (1992)
9. Fermi, E., Pasta, J., Ulam, S.: Studies of Nonlinear Problems. Los Alamos Technical Reports, Document LA-1940 (1955)
10. Ford, J.: The Fermi-Pasta-Ulam problem: Paradox turns discovery. Physics Reports, pp. 271-310 (1992)
11. Gallavotti, E.G.: The Fermi-Pasta-Ulam Problem. Springer, New York (2007)
12. Giada Basile, S.O., Spohn, H.: Energy transport in stochastically perturbed lattice dynamics. Arch. Ration. Mech. Anal. 195(1), 171-203 (2010)
13. Jackson, E.: Perspectives of Nonlinear Dynamics. Cambridge University Press, Cambridge (1991)
14. Kastner, O.: Molecular-dynamics of a 2D model of the shape memory effect, part II: Thermodynamics of a small system. J. Mech. Phys. Solids 18, 63-81 (2006)
15. Müller, I., Seelecke, S.: Thermodynamic aspects of shape memory alloys. Math. Comput. Model. 34, 1307-1355 (2001) (Topics in the mathematical modelling of smart materials)
16. Muller, I., Villaggio, P.: A model for an elastoplastic body. Arch. Ration. Mech. Anal. 65, 25-46 (1977)
17. Ngan, S., Truskinovsky, L.: Thermoelastic aspects of nucleation in solids. J. Mech. Phys. Solids. 50, 1193-1229 (2002)
18. Puglisi, G., Truskinovsky, L.:Mechanics of a discrete chain with bi-stable elements. J. Mech. Phys. Solids. 48, 1-27 (2000)
19. Puglisi, G., Truskinovsky, L.: Thermodynamics of rate independent plasticity. J. Mech. Phys. Solids 53, 655-679 (2005)
20. Stuart, A., Humphries, A.: Dynamical Systems and Numerical Analysis. Cambridge University Press, Cambridge (1996)
21. Truskinovsky, L.: Nucleation and growth in elastodynamics. In:Duxbury, P.M., Pence, T. (eds.) Dynamics of Crystal Surfaces and Interfaces, pp. 185-197. Plenum, New York (1997)
22. Truskinovsky, L., Vainchtein, A.: About the origin of the nucleation peak in transformational plasticity. J. Mech. Phys. Solids 52, 1421-1446 (2004)
23. von Neumann, J.: Proposal and analysis of a numerical method for the treatment of hydrodynamical shock problem, 1944. In: John von Neumann Collected Works, vol. 6, no. 26. Macmillan, New York (1963)
24. Weinan, E., Ming, P.: Cauchy-born rule and the stability of crystalline solids: Dynamic problems. Acta Math. Appl. Sin. Engl. Ser. 23(4), 529-550 (2007)
25. Weissert,T.:The Genesis of Simulations in Dynamics: Pursuing the Fermi-Pasta-Ulam Problem. Springer, NewYork (1997)
26. Yoshikawa, T.: Transition from mechanical equilibrium to thermal equilibrium in a chain of unstable springs. Phys. Lett. A 307, 13-21 (2003)