论演化方程的结构<sup>*</sup>

J．巴德; 孙博华

论演化方程的结构^*

德国波鸿大学力学所

基金项目: * 德国洪堡基金和德国科学基金

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出版历程
- 收稿日期: 1994-08-16
- 刊出日期: 1995-08-15

Remarks on the Structure of Evolution Equations

J. Badur,
Sun Bohua

Ruhr-Universitat Bochum, Lehrsiuhl fur AIIgemeine Mechanik, D-4780 Bochum 1, Germany

摘要

摘要: 本文对演化方程进行了讨论,从而能够唯象地描述微观结构行为,如Maxwell气体的部分可逆流动、恢复性、结构松弛以及从光散射和分子动力学得到的其它实验结果。讨论所得结果涉及Zaremba补充式(ansatz)的重新评价,可用来解决输运方程中具有显着非线性的问题。
- 演化方程 /
- 唯象描述 /
- 微观结构方程 /
- Zaremba补充式
Abstract: In the paper the evolution equations are discussed so as to enable a phenomenological description of microstruchtral behaviour e.g. partially reversible flow of Maxwellian gas, recovery structural relaxation and other experimental results coming from light scattering and molecular dynamics.The result deals with the revaluation of Zaremba's ansatz.It leads to resolution of problems with substantial and available nonlinearities in the transport equation.
- evolution equation /
- phenomenological description /
- microstructural behaviour /
- Zaremba’s ansatz

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参考文献(25)

[1]	L. G. Colin, Extended non-equilibrium thermodynamics, scope and limitations, Revista Mex. Fisica, 34(1988), 344-366.
[2]	Z.H. Guo, Time derivatives of tensor fields in nonlinear continuum mechanics, Arch. Mech. Stosow, 15(1963), 131-163.
[3]	Maria Heckl and I. Müller, Frame dependence, entropy, entropy flux, and wave speeds in mixtures of gases, Acta Mech., 50(1983), 71-95.
[4]	D. Jou, J. Cassas-Vazquez and G. Lebon, Extended irreversible thermodynamics, Rep. Ping. Plps., 51(1988), 1105-1179.
[5]	J. Kestin, A note on the relation between the hypothesis of local equilibrium and the Clausius-Duhem inequality, J. Non-Eguilib. Thernrodvrr., 18(1990), 193-212.
[6]	J. Kestin, Local-equilibrium formalism applied to mechanics of solids. Int. J. Solids. Strue., 29(1992), 1827-1836.
[7]	J. Kestin, Thermodynamics (an essey) in: Zagadnienia Maszyn Przelpyuouych, Proc, of Conf on 90th Aniversary of Robert Szewalski, ed, S. Burka Gdansk(1993),,319-334.
[8]	I.-L. Liu and I. Müller, on the thermodynamics and thermostatics of fluids in electromagnetic field, Arch. Rutiorral Meclr. Anal., 46(1972), 149-176.
[9]	I.-L. Liu, On thermodynamics of viscoelasticity, in: Proc. 2nd Int. Conf. Nonlinear Mech., Beijing, ed. Z. H. Guo(1993), 174-177.
[10]	G. A. Maugin and C. Trimarco, Pseudomomentum and material forces in nonlinear elasticity: variational formmulations and application to brittle fructure, Acta Mech., 94 (1992), 1-28.
[11]	I. Müller, Zum Paradoxon der Wärmeleitungstheorie, Z. für Physik, 198(1967), 329-344
[12]	I. Müller and K. Wilmanski, Extended thermodynamics of a non-Newtonian fluid, Rheo. Acta, 25(1986), 335-349.
[13]	I. Müller, On the frame dependence of stress and heat flux, Arch. Rational Mech. Anal., 45(1972), 241-250
[14]	I. Müller, The structure of extended thermodynamics, in Trends in Applications of Mathematics to Mechanics, eds. W. Schneider, H. Troger, F. Zigler, Longman Sci.& Tech.(1992), 164-173.
[15]	I. Müller and T. Ruggeri, Extended thermodynamics, in Spriuger Tracts Natur. Phil., ed. C. Truesdell, 37(1993)
[16]	L. Natanson, Sur les lois de la diffusion, Bull. lnt. l'Acad. Sci. Letters. Cracovie (A) (1901),335-348.
[17]	L. Restuccia and B. Maruszewski, Diffusion and dislocation influence on the dynamics of elastic bodies, Int. J. Engn. Sci., 29(1991).1053-1063.
[18]	H. Stumpf and J. Badur. On missine links of rate-independent elastoplasticitv at finite strain, Mech. Res. Comm., 17, 5 (1990), 353-364.
[19]	H. Stumpf and J. Badur, On a generalization of elasto-plastic models within the frame of extended thermodynamics, ZAMM, 72 (1993), T211-214.
[20]	H. Stumpf and J. Badur, On surface objective rates, Quart. Appl. Math., 51 (1993),161-186.
[21]	B.H. dun, A simple review of elasto-plastic models, CERECAM Report No. 252, University of-Cape Town South Africa(1994), 1-55.
[22]	B.H. Sun and J. Badur, Some remarks on the multiplicative ecomposition within elasto-plasticity.
[23]	C. Truesdell and R. Toupin, The classical field theories, Hand. der Phys., Bd III/I, ed. S.Fllüge (1960), 226-793. (appendix by J. L. Ericksen, 794-858).
[24]	K. Wilmanski, Thermodynamics of a heat conducting Maxwellian fluid, Arch, Mech. Stosow, 40 (1988), 217-232.
[25]	S. Zaremna, Sur une forme perfectionee de la theorie de la relaxation, Bull. Int. I'Acad.Sci. Lettres Cracovie (CI. Sci. Math. Natur.) A (1903), 594-614.