Inertial and self interactions in structured continua: Liquid crystals and magnetostrictive solids
Tóm tắt
Evolution equations for liquid crystals and for magnetostrictive solids are discussed within the framework of a theory of continua with microstructure that allows for mechanical self-interactions and non-standard inertial terms.
Tài liệu tham khảo
Brown, W.F., ‘Electric and magnetic forces: a direct calculation’,Am. J. Phys.,19 (1951), 290–304 and 333–350.
Brown, W.F.,Micromagnetics, John Wiley & Sons (Interscience), 1963.
Brown, W.F.,Magnetoelastic Interactions, Springer-Verlag, 1966.
Chandrasekhar, S.,Liquid Crystals, 2nd ed., Cambridge University Press, 1992.
DeGennes, P.G. and Prost, J.P.,The Physics of Liquid Crystals, 2nd ed., Clarendon Press, 1993.
DeSimone, A. and Podio Guidugli, P., ‘On the continuum theory of deformable ferromagnetic solids’, to appear inArch. Rat. Mech. Anal. (1995).
Ericksen, J.L., ‘Anisotropic fluids’,Arch. Rat. Mech. Anal.,4 (1960), 231–237.
Ericksen, J.L., ‘Conservation laws for liquid crystals’,Trans. Soc. Rheol.,5 (1961), 23–34.
Feynman, R.,The Feynman Lectures on Physics, Addison-Wesley, 1964, Vol. 2, Chapter 34.
Gurtin, M.E. and Podio Guidugli, P., ‘On the formulation of balance laws for structured continua’,Z.A.M.P.,43 (1992), 181–190.
Gurtin, M.E. and Williams, W.O., ‘On the first law of thermodynamics’,Arch. Rat. Mech. Anal.,42 (1971), 77–92.
Leslie, F.M., ‘Some constitutive equations for liquid crystals’,Arch. Rat. Mech. Anal.,28 (1968), 265–283.
Maugin, G.A.,Continuum Mechanics of Electromagnetic Solids, North-Holland, Amsterdam, 1988.
Marrucci, G. and Greco, F., ‘Flow behavior of liquid crystalline polymers’, in Prigogine, I. and Rice, S.A. (Eds),Advances in Chemical Physics, Volume LXXXVI, John Wiley & Sons, 1993, pp. 331–404.
Podio Guidugli, P., ‘Inertia and invariance’,Annali Mat. Pura Appl., in press, (1994).
Serrin, J., ‘The equations of continuum mechanics as a consequence of invariance and thermodynamical principles’,Lecture at the Conference on Nonlinear Analysis and Partial Differential Equations, Rutgers University, May 1990.
Serrin, J., ‘The equations of continuum mechanics as a consequence of group invariance’,Lecture at the Conference on Advances in Modern Continuum Dynamics, Isola d'Elba, June 1991.
Tiersten, H.F., ‘Coupled magnetomechanical equations for magnetically saturated insulators’,J.Math. Phys.,5 (1964), 1298–1318.
Tiersten, H.F.,A Development of the Equations of Electromagnetism in Material Continua, Springer-Verlag, 1990.
Williams, W.O., Review ofContinua with Microstructure, by G. Capriz, Springer-Verlag, 1989.SIAM Review 33, (1991), 161–163.