A personal appreciation of Walter Noll. (English) Zbl 1412.01029
Summary: Walter Noll is personally acknowledged to have been an inspirational teacher and an exemplar in his analysis of fundamental concepts and relations in Continuum Mechanics. Attention is drawn to unfounded criticisms of two aspects of his work and how considerations of local spatial and temporal averaging of microscopic behaviour can complement and inform the continuum viewpoint. Remarks on such considerations briefly summarise the results of published works which both utilised Noll’s direct notation and attempted to emulate his precision and clarity.
MSC:
| 01A70 | Biographies, obituaries, personalia, bibliographies |
| 74-03 | History of mechanics of deformable solids |
| 76-03 | History of fluid mechanics |
Biographic References:
Noll, WalterReferences:
| [1] | Noll, W.: Lectures on the foundations of continuum mechanics and thermodynamics. Arch. Ration. Mech. Anal. 52, 62-92 (1973) · Zbl 0284.73002 · doi:10.1007/BF00249093 |
| [2] | Noll, W.: Die Herleitung der Grundgleichungen der Thermomechanik der Kontinua aus der statistischen Mechanik. J. Ration. Mech. Anal. 4, 627-646 (1955) · Zbl 0065.19405 |
| [3] | Noll, W.: On the theory of surface interactions (2005), 14 pp., published on the website www.math.cmu.edu/ wn0g/noll |
| [4] | Noll, W.: Thoughts on the concept of stress. J. Elast. 100, 25-32 (2010) · Zbl 1272.74007 · doi:10.1007/s10659-010-9247-8 |
| [5] | Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291-323 (1975) · Zbl 0326.73001 · doi:10.1007/BF00261375 |
| [6] | Murdoch, A.I., Cohen, H.: Symmetry considerations for material surfaces. Arch. Ration. Mech. Anal. 72, 61-98 (1979) · Zbl 0424.73063 · doi:10.1007/BF00250737 |
| [7] | Murdoch, A.I., Cohen, H.: Symmetry considerations for material surfaces: addendum. Arch. Ration. Mech. Anal. 76, 393-400 (1981) · Zbl 0468.73003 · doi:10.1007/BF00249972 |
| [8] | Noll, W.: Contributions to Natural Philosophy. Research Report 04-CAN-0187, Center for Nonlinear Analysis, Carnegie-Mellon University (2004) |
| [9] | Noll, W.: A mathematical theory of the mechanical behaviour of continuous media. Arch. Ration. Mech. Anal. 2, 197-226 (1958) · Zbl 0083.39303 · doi:10.1007/BF00277929 |
| [10] | Truesdell, C.; Noll, W.; Flügge, S. (ed.), The non-linear field theories of mechanics (1965), Berlin · Zbl 0137.19501 |
| [11] | Rivlin, R.S.: A note on the simple fluid. J. Non-Newton. Fluid Mech. 11, 209-213 (1982) · Zbl 0489.76010 · doi:10.1016/0377-0257(82)85023-4 |
| [12] | Murdoch, A.I.: On unfounded criticism of the simple fluid of Noll. J. Non-Newton. Fluid Mech. 12, 387-392 (1983) · Zbl 0528.76006 · doi:10.1016/0377-0257(83)85012-5 |
| [13] | Rivlin, R.S., Smith, G.F.: On the fallacy in a paper by A.I. Murdoch. J. Non-Newton. Fluid Mech. 12, 393-394 (1983) · doi:10.1016/0377-0257(83)85013-7 |
| [14] | Murdoch, A.I.: Reply to the note “On the fallacy in a paper by A.I. Murdoch” by R.S. Rivlin and G.F. Smith. J. Non-Newton. Fluid Mech. 15, 247-248 (1984) · doi:10.1016/0377-0257(84)80009-9 |
| [15] | Müller, I.: On the frame dependence of stress and heat flux. Arch. Ration. Mech. Anal. 45, 241-250 (1973) · Zbl 0243.76051 · doi:10.1007/BF00251375 |
| [16] | Silhavy, M.: The Mechanics and Thermomechanics of Continuous Media. Springer, Berlin (1997) · Zbl 0870.73004 · doi:10.1007/978-3-662-03389-0 |
| [17] | Gurtin, M.E., Fried, E., Anand, L.: The Mechanics and Thermodynamics of Continua. Cambridge University Press, Cambridge (2010) · doi:10.1017/CBO9780511762956 |
| [18] | Murdoch, A.I.: On material frame-indifference, intrinsic spin, and certain constitutive relations motivated by the kinetic theory of gases. Arch. Ration. Mech. Anal. 83, 185-194 (1983) · Zbl 0533.76077 · doi:10.1007/BF00282161 |
| [19] | Noll, W.: The genesis of Truesdell’s nonlinear field theories of mechanics. J. Elast. 70, 23-30 (2003) · Zbl 1039.01527 · doi:10.1023/B:ELAS.0000005581.36943.75 |
| [20] | Roberts, P. H.; Donnelly, R. J.; Dyke, M. (ed.); Vincentini, W. G. (ed.); Wehausen, J. V. (ed.), Superfluid mechanics, No. 6 (1974), Palo Alto |
| [21] | Hills, R.N., Roberts, P.H.: Superfluid mechanics for a high density of vortex lines. Arch. Ration. Mech. Anal. 66, 43-71 (1977) · Zbl 0399.76008 · doi:10.1007/BF00250851 |
| [22] | Piquet, J.: Turbulent Flows, revised 2nd printing edn. Springer, Berlin (2001) · Zbl 0928.76003 |
| [23] | Rivlin, R. S.; Kanninen, M. G. (ed.); Adler, D. (ed.); Rosenfield, A. R. (ed.); Jaffee, R. I. (ed.), Red herrings and sundry unidentified fish in nonlinear continuum mechanics, 117-134 (1970), New York |
| [24] | Jog, C.S.: Continuum Mechanics, 3rd edn. Cambridge University Press, Cambridge (2015) · doi:10.1017/CBO9781316134054 |
| [25] | Murdoch, A.I.: Objectivity in classical continuum physics: a rationale for discarding the ‘principle of invariance under superposed rigid body motions’ in favour of purely objective considerations. Contin. Mech. Thermodyn. 15, 309-320 (2003) · Zbl 1068.74515 · doi:10.1007/s00161-003-0121-9 |
| [26] | Murdoch, A.I.: On material frame-indifference. Proc. R. Soc. Lond. A 380, 417-426 (1983) · Zbl 0486.73001 · doi:10.1098/rspa.1982.0050 |
| [27] | Murdoch, A.I.: Physical Foundations of Continuum Mechanics. Cambridge University Press, Cambridge (2012) · Zbl 1280.82001 · doi:10.1017/CBO9781139028318 |
| [28] | Irving, J.H., Kirkwood, J.: The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. J. Chem. Phys. 18, 817-829 (1950) · doi:10.1063/1.1747782 |
| [29] | Murdoch, A.I.: Some primitive concepts in continuum mechanics regarded in terms of objective space-time averaging: the key role played by inertial observers. J. Elast. 84, 69-97 (2006) · Zbl 1103.74010 · doi:10.1007/s10659-005-9048-7 |
| [30] | Truesdell, C.: Rational Thermodynamics. McGraw Hill, New York (1969) · Zbl 0598.73002 |
| [31] | Bowen, R. M.; Eringen, A. C. (ed.), Theory of mixtures (1976), New York |
| [32] | Gurtin, M.E., Oliver, M.L., Williams, W.O.: On balance of forces for mixtures. Q. Appl. Math. 30, 527-530 (1973) · Zbl 0259.76048 · doi:10.1090/qam/99715 |
| [33] | Murdoch, A.I.: On spatially-averaged electrokinetics of point charges and Maxwell’s equations. J. Elast. 131, 75-109 (2018) · Zbl 1419.78002 · doi:10.1007/s10659-017-9647-0 |
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