Scott Spector

Biographical Sketch

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Education.
1978
1975
1974
1970
  Ph.D. in Mathematics, Carnegie Mellon University.
  M.S., Carnegie Mellon University.
  B.S., Carnegie Mellon University.
  White Plains High School, White Plains, NY.
Experience.
2012-date
2004-2012
1990-2012
1984-1990
1981-1984
1982-1983
1978-1981
  Professor and Distinguished Scholar Emeritus, Southern Illinois University.
  Distinguished Scholar, Southern Illinois University.
  Professor, Southern Illinois University.
  Associate Professor, Southern Illinois University.
  Assistant Professor, Southern Illinois University.
  Post-doctoral Fellow, IMA, University of Minnesota.
  Assistant Professor, University of Tennessee, Knoxville.
Editorial Board Membership.
Journal of Elasticity      
Research Interests.
Nonlinear Elasticity, Continuum Mechanics, Calculus of Variations, Partial Differential Equations.
Society Memberships.
Kappa Sigma
Society for Natural Philosophy -(Secretary 1986-87, 1990-91, 1999-2004, 2007-2008, Member of the Board of Directors, 1985-2018)
Tau Beta Pi
Other.
Featured Review in Mathematical Reviews, August 1996, 96h:73017
1997 Outstanding Researcher, College of Science, Southern Illinois University at Carbondale
2000 Outstanding Scholar, Southern Illinois University at Carbondale

Publications .
  • Uniqueness of equilibrium with sufficiently small strains in finite elasticity (with  D. E. Spector).  To appear: Archive for Rational Mechanics and Analysis.
  • On the uniqueness of energy minimizers in finite elasticity J. Elasticity 133 (2018), 73-103 (with  J. Sivaloganathan).
  • On the global stability of compressible elastic cylinders in tension, J. Elasticity 120 (2015), 161-195 (with  J. Sivaloganathan). MR3367697
  • A note on the convexity of C h(det C) , J. Elasticity 118 (2015), 251-256. MR3302185
  • A product property of Sobolev spaces with application to elliptic estimates, Rend. Semin. Mat. Univ. Padova 131 (2014), 67–76 (with  H. C. Simpson). ABSTRACT. MR3217751
  • On the stability of incompressible elastic cylinders in uniaxial extension, J. Elasticity 105 (2011), 313-330 (with  J. Sivaloganathan). ABSTRACT MR3217751
  • On irregular weak solutions of the energy-momentum equations, Proc. Royal Soc. Edinburgh 141A (2011), 193-203  (with  J. Sivaloganathan). ABSTRACT MR2773446
  • On the global stability of incompressible elastic bars in uniaxial extension, Proc. Royal Soc. Lond. Ser. A 466 (2010), 1167--1176 (with  J. Sivaloganathan). ABSTRACT   MR 2011c:74064
  • On the symmetry of energy minimising deformations in nonlinear elasticity II: Compressible materials Arch. Ration. Mech. Anal. 196 (2010), 395--431 (with  J. Sivaloganathan). ABSTRACT MR2609950
  • On the symmetry of energy minimising deformations in nonlinear elasticity I: Incompressible materials, Arch. Ration. Mech. Anal. 196 (2010), 363--394 (with  J. Sivaloganathan). ABSTRACT MR2609949
  • Applications of estimates near the boundary to regularity of solutions in linearized elasticity SIAM J. Math. Anal. 41 (2009), 923--935 (with  H. C. Simpson). ABSTRACT  MR 2011c:35137
  • Energy minimising properties of the radial cavitation solution in incompressible nonlinear elasticity, J. Elasticity 93 (2008), 177-187 (with J. Sivaloganathan). ABSTRACT MR 2010a:74012
  • On bifurcation in finite elasticity: Buckling of a rectangular rod, J. Elasticity 92 (2008), 277-326 (with H. C. Simpson). ABSTRACT MR 2009e:74017.
  • Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity, Anal. Non Lineaire 25 (2008), 201-213 (with  J. Sivaloganathan). ABSTRACT MR 2009c:74012.
  • A Variational Approach to Modelling Initiation of Fracture in Nonlinear Elasticity, IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics (A. B. Movchan, ed.), Springer, 2004, pp. 295-306 (with J. Sivaloganathan). ABSTRACT
  • The convergence of regularized minimizers for cavitation problems in nonlinear elasticity, SIAM J. Appl. Math 66 (2006), 736-757 (with J. Sivaloganathan and V. Tilakraj). ABSTRACT MR 2007m:74055.
  • Myriad radial cavitating equilibria in nonlinear elasticity, SIAM J. Appl. Math. 63 (2003), 1461-1473 (with J. Sivaloganathan). MR 2005c:74009.
  •  On cavitation, configurational forces and implications for fracture in a nonlinearly elastic material, J. Elasticity 67 (2002), 25-49 (with J. Sivaloganathan). ABSTRACT MR 2004e:74037.
  • A construction of infinitely many singular weak solutions to the equations of nonlinear elasticity, Proc. Royal Soc. Edinburgh 132A (2002), 985-992 (with J. Sivaloganathan). MR 2003f:74004.
  • An explicit radial cavitation solution in nonlinear elasticity, Math. Mech. Solids 7 (2002), 87-93 (with K. A. Pericak-Spector and J. Sivaloganathan). MR 2003c:74008.
  • On the existence of minimizers with prescribed singular points in nonlinear elasticity,  J. Elasticity 59 (2000), 83-113 (with J. Sivaloganathan). ABSTRACT MR 2002h:74013.
  • On the optimal location of singularities arising in variational problems of nonlinear elasticity, J. Elasticity 58 (2000), 191-224 (with J. Sivaloganathan). ABSTRACT MR 2002d:74006.
  • The representation theorem for linear, isotropic tensor functions in even dimensions,  J. Elasticity 57 (1999), 157-164 (with K. A. Pericak-Spector and J. Sivaloganathan). MR 2001i:74005.
  • An isoperimetric estimate and W1,p-quasiconvexity in nonlinear elasticity, Calc. Var. Partial Differential Equations 8 (1999), 159-176 (with S. Müller and J. Sivaloganathan). MR 2000c:74023.
  •  Dynamic cavitation with shocks in nonlinear elasticity, Proc. Royal Soc. Edinburgh. 127A (1997), 837-857 (with K. A. Pericak-Spector). MR 98j:73028.
  •  Invertibility and a topological property of Sobolev maps, SIAM J. Math. Anal. 27 (1996), 959-976 (with S. Müller and Q. Tang). MR 97e:46041.
  •  An existence theory for nonlinear elasticity that allows for cavitation, Arch. Rational Mech. Anal. 131 (1995), 1-66 (with S. Müller). Featured Review - MR 96h:73017.
  • On the representation theorem for linear, isotropic tensor functions, J. Elasticity 39 (1995), 181-185 (with K. A. Pericak-Spector). MR 96g:73005.
  •  Linear deformations as global minimizers in nonlinear elasticity, Q. Appl. Math. 52 (1994), 59-64. MR 94m:73026.
  •  Existence of singular minimizers in three-dimensional nonlinear elasticity, Workshop on the Mathematical Theory of Nonlinear and Inelastic Material Behaviour, Darmstadt, Germany, May 25-27, 1992 (ed. H.-D. Alber), Bonner Mathematische Schriften 239 (1993), 21-31 (with S. Müller). MR 95i:73029.
  • Remarks on W1,p-quasiconvexity, interpenetration of matter, and function spaces for elasticity, Anal. Non Lineaire 9 (1992), 263-280 (with R. D. James). MR 93h:73013.
  • The formation of filamentary voids in solids, J. Mech. Phys. Solids 39 (1991), 783-813 (with R. D. James). MR 93d:73059.
  •  Some necessary conditions at an internal boundary for minimizers in finite elasticity, J. Elasticity 26 (1991), 203-122 (with H. C. Simpson). MR 93g:73071.
  •  Necessary conditions at the boundary for minimizers in finite elasticity, Arch. Rational Mech. Anal. 107 (1989), 105-125 (with H. C. Simpson) MR 90i:73057.
  •  Nonuniqueness for a hyperbolic system: Cavitation in nonlinear elastodynamics, Arch. Rational Mech. Anal. 101 (1988), 293-317 (with K. A. Pericak-Spector) MR 89e:73013.
  • On the positivity of the second variation in finite elasticity, Arch. Rational Mech. Anal. 98 (1987), 1-30 (with H. C. Simpson). MR 88i:73033.
  •  On the failure of the complementing condition and nonuniqueness in linear elastostatics, J. Elasticity 15 (1985), 229-231 (with H. C. Simpson). MR 86m:73011.
  •  On the absence of bifurcation for elastic bars in uniaxial tension, Arch. Rational Mech. Anal. 85 (1984), 171-199. MR 85c:73038.
  •  On barrelling for a special material in finite elasticity, Q. Appl. Math. 42 (1984), 99-111 (with H. C. Simpson). MR 85e:73031.
  •  Some monotonicity results for ratios of modified Bessel functions, Q. Appl. Math. 42 (1984), 95-98 (with H. C. Simpson). MR 85d:33021.
  •  On barrelling instabilities in finite elasticity, J. Elasticity 14 (1984), 103-125 (with H. C. Simpson). MR 85m:73028.  
  • On copositive matrices and strong ellipticity for isotropic elastic materials, Arch. Rational Mech. Anal. 84 (1983), 55-68 (with H. C. Simpson). MR 84m:73018.
  • On uniqueness for the traction problem in finite elasticity, J. Elasticity 12 (1982), 367-383. MR 84d:73038.
  • On Gibbs stability in the classical theory of fluid mixtures, ZAMP 32 (1981), 286-295. MR 82i:80003.
  • On monotonicity of the optimal strain path in linear viscoelasticity, Q. Appl. Math. 38 (1980), 369-372 MR 82c:73035.
  • On uniqueness and bifurcation in nonlinear viscoelasticity, Arch. Rational Mech. Anal. 72 (1980), 303-313 (with M. E. Gurtin and D. W. Reynolds). MR 80k:73038.
  • On continuous dependence in finite elasticity, Q. Appl. Math. 38 (1980), 135-138. MR 81f:73020.
  •  On uniqueness in finite elasticity with general loading, J. Elasticity 10 (1980), 145-161. MR 81g:73059.
  • On stability and uniqueness in finite elasticity, Arch. Rational Mech. Anal. 70 (1979), 153-165 (with M. E. Gurtin). MR 80j:73022.
  • On the sign of the specific heat, Q. J. Mech. Appl. Math. 29, (1976), 493-497 (with M. E. Gurtin). MR 55 #7142.


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