Robert P. Lipton


Partial list of preprints and reprints:

  1. Numerical analysis of nonlocal fracture models in Holder space," arXiv.1701.02818v3 [math.NA] 25 Jan 2017. (With Prashant Jah.) (Link to arXiv)
  2. Effective Maxwell's equations for perfectly conducting split ring resonators , 2016. Submitted for publication. (With Ben Schweizer.)
  3. Numerical verification of a bond-based softening peridynamic model for small displacements: deducing material parameters from classical linear theory, 2016. Submitted for publication. (With Patrick Diehl and Mark Alexander Schiweitzer.)
  4. Novel metamaterial surfaces from perfectly conducting subwavelength corrugations, 2016. Submitted for publication. (With Anthony Polizzi and Lokendra Thakur.)
  5. Creating Band Gaps in Periodic Media. September 6, 2016 (With Robert Viator), arXiv:1607.02365v2 [math.AP](Link to arXiv)
  6. Cohesive Dynamics and Brittle Fracture. Journal of Elasticity, 124, Issue 2, 2016, pp. 143-191. (PDF)
  7. Erratum: Cohesive Dynamics and Brittle Fracture. Journal of Elasticity, 125, Issue 1, 2016, pp. 137. (PDF)
  8. Uncertain Loading and Quantifying Maximum Energy Concentration within Composite Structures. Journal of Computational Physics, 325, (2016), pp. 38-52. (With Paul Sinz and Michael Stuebner), (PDF)
  9. Multiscale Analysis of an Abstract Evolution Equation with Applications to Nonlocal Models for Heterogeneous Media. ESAIM: M2AN, 50 Number 5, 2016, pp. 1425-1455. (With Qiang Du and Tadele Mengesha). (PDF)
  10. Complex Fracture Nucleation and Evolution with Nonlocal Elastodynamics. February 2, 2015 (With Stewart Silling and Richard Lehoucq), arXiv:1602.00247(Link to arXiv)
  11. Bloch Waves in Crystals and Periodic High Contrast Media. ESAIM M2AN. June 16, 2016. (With Robert Viator). (PDF)
  12. Peridynamics, Fracture, and Nonlocal Continuum Models. SIAM News, Volume 47, Number 3, April 2014. (With Qiang Du). (Link to SIAM News)
  13. Dynamic Brittle Fracture as a Small Horizon Limit of Peridynamics.Journal of Elasticity. January 3, 2014. DOI 10.1007/s10659-013-9463-0 (PDF)
  14. Multiscale Methods for Engineering Double Negative Metamaterials. Photonics and Nanostructures - Fundamentals and Applications, 11 (2013) 442-452. (With Yue Chen). (PDF)
  15. Resonance and Double Negative Behavior in Metamaterials. Archchive for Rational Mechanics and Analysis, March 4, 2013 (DOI) 10.1007/s00205-013-0634-8. (With Yue Chen). (Link)
  16. Double Negative Dispersion Relations from Coated Plasmonic Rods. (With Yue Chen). Multiscale Modeling and Simulation, SIAM 11 (2013) 191-212(Link)
  17. Machine Computation Using the Exponentially Convergent Multiscale Spectral Generalized Finite Element Method. (With Ivo Babuska and Xu Huang). To Appear in Mathematical Modeling and Numerical Analysis (M2AN) 2013. (PDF)
  18. Optimal Local Approximation Spaces for Generalized Finite Element Methods with Application to Multiscale Problems. (With Ivo Babuska). Multiscale Modeling and Simulation, SIAM 9 (2011) 373-406. (PDF)
  19. Tunable Double Negative Band Structure from Non-Magnetic Coated Rods. (With Yue Chen). New Journal of Physics Volume 12 August 2010. (Link)
  20. Correctors and field fluctuations for the pε(x)-Laplacian with rough exponents. J. Math. Anal. Appl. 372 (2010) 448�469. (With Silvia Jimenez). (PDF)
  21. Optimal lower bounds on the local stress inside random thermoelastic composites. Acta Mechanica. DOI 10.1007/s00707-009-0273-1, 15 Jan. 2010 (With Yue Chen). (PDF)
  22. Sub-wavelength plasmonic crystals: dispersion relations and effective properties. Proc. Roy. Soc. London A. Published online Feb 10,2010 doi: 10.1098/rspa.2009.0542. (With Santiago Fortes and Stephen Shipman). (PDF)
  23. Convergent Power Series for Fields in Positive or Negative High-Contrast Periodic Media. (With Santiago Fortes and Stephen Shipman). Communications in Partial Differential Equations 36 (2011) 1016--1043. (PDF)
  24. Representation formulas for L-infinity norms of weakly convergent sequencies of gradient fields in homogenization. arXiv:1009.4429v2 [math.AP] 23 Sep 2010 (With Tadele Mengesha). Mathematical Modeling and Numerical Analysis (M2AN) 46 (2012) 1121--1146. (Link)
  25. Multiscale Dynamics of Heterogeneous Media in the Peridynamic Formulation. Journal of Elasticity (Online First), Dec. 8, 2010, pp. 1--33, DOI 10.1007/s10659-010-9291-4. (With Bacim Alali). (PDF)
  26. Optimal lower bounds on local stress inside random media. SIAM Journal On Applied Mathematics 70, 2009, pp. 1260--1282. (With Bacim Alali). (PDF)
  27. The penetration function and its application to microscale problems. BIT Numerical Mathematics 48, 2008, pp. 167--187. (With Ivo Babuska and Michael Stuebner). (PDF).
  28. Local field assessment inside multiscale composite architectures. Multiscale Modeling and Simulation, SIAM 6, 2007, pp. 937--962. (With Timothy Breitzman and Endel Iarve). (PDF)
  29. Bounds for the torsional rigidity of shafts with arbitrary cross sections containing cylindrically orthotropic fibers. Proc. Roy. Soc. London A436, 2007, pp. 3291--3309. (With Tungyang Chen.) (PDF)
  30. Homogenization and field concentrations in heterogeneous media. arXiv.math AP / 0603172v1 7Mar 2006. SIAM Journal on Mathematical Analysis, 38, 2006, pp. 1048--1059. (PDF)
  31. Inverse homogenization and design of microstructure for pointwise stress control. The Quarterly Journal of Mechanics and Applied Mathematics, 59, 2006, pp. 139--161. (With Michael Stuebner.) (PDF)
  32. Optimal lower bounds on the hydrostatic stress amplification inside random two-phase elastic composites." Journal of the Mechanics and Physics of Solids, 53, 2005, pp. 2471--2481. (PDF)
  33. Optimal design of composite structures for strength and stiffness: an inverse homogenization approach. Structural and Multidisciplinary Optimization, 33, 2007, pp. 351--362. (With Michael Stuebner.) (PDF)

  34. Optimal lower bounds on the dilatational strain inside random two-phase elastic composites subjected to hydrostatic loading. Mechanics of Materials, 38, 2006, pp. 833--839. (PDF)

  35. Exact scaling laws for electrical conductivity properties of nematic polymer nano-composite monodomains. Advanced Functional Materials, 15, 2005, pp. 627--638. (With Zheng Z., Forest M. G., Zhou R., and Wang A) (PDF)

  36. Configurations of nonlinear materials with electric fields that minimize L^p norms. Physica B, 338, 2003, pp. 48--53. (PDF)

  37. Bounds and extremal confgurations for the torsional rigidity of coated fiber reinforced shafts. SIAM J. Applied Mathematics, 65, 2004, pp. 299--315. (With Tungyang Chen.) (PDF)

  38. Homogenization theory and the assessment of extreme field values in composites with random microstructure. SIAM J. Applied Mathematics, 65, 2004, pp. 475--493. (PDF)

  39. Optimal lower bounds on the electric-field concentration in composite media. Journal of Applied Physics, vol. 96, 2004, pp. 2821--2827. (PDF)

  40. Bounds on the distribution of extreme values for the stress in composite materials. Journal of the Mechanics and Physics of Solids, vol. 52, 2004, pp. 1053--1069. (PDF)

  41. Assessment of the local stress state through macroscopic variables. Philosophical Transactions Mathematical, Physical & Engineering Sciences, vol. 361, 2003, pp. 921--946. (PDF)

  42. Relaxation through homogenization for optimal design problems with gradient constraints. Journal of Optimization Theory and Applications, vol. 114, 2002, pp. 27--54. (PDF)

  43. Stress constrained G closure and relaxation of structural design problems. Quarterly of Applied Mathematics. vol. LXII, 2004, pp. 295--321. (PDF)

  44. Design of functionally graded composite structures in the presence of stress constraints. International Journal of Solids and Structures, vol. 39, 2002, pp. 2575--2586. (PDF)

  45. Optimal inequalities for gradients of solutions of elliptic equations occurring in two-phase heat conductors. SIAM Journal on Mathematical Analysis, vol. 32 (2001), no. 5, 1081--1093. (PDF)

  46. Optimal design of gradient fields with applications to electrostatics. Nonlinear Partial Differential Equations and Their Applications: College de France Seminare Volume XIV, D. Cioranescu and J.-L. Lions Editors. Studies in Applied Mathematics and its Applications, vol. 31, Elsevier, Amsterdam, 2002, pp. 509--532. (With Ani Velo). (PDF)

  47. Bounds for the effective conductivity of a composite with imperfect interface. Proceedings of the Royal Society of London, vol. 457 (2001), 1501--1517. (With D.R.S. Talbot). (PDF)

  48. Optimal bounds on electric field fluctuations for random composites. Journal of Applied Physics, vol. 88, 2000, pp. 4287--4293. (PDF)

  49. The effect of the interface on the dc transport properties of nonlinear composite materials. Journal of Applied Physics vol. 86 no. 3, 1999, pp. 1480-1487. (With David R.S. Talbot.) (PDF)

  50. Optimal fiber configurations for maximum torsional rigidity. Archive for Rational Mechanics and Analysis, vol. 144, 1998, pp. 79--106. (PDF)

  51. An isoperimetric inequality for the torsional rigidity of imperfectly bonded fiber reinforced cylinders. Journal of Elasticity. 55 (1999), no. 1, 1--10. (PDF)

  52. The Second Stekloff eigenvalue and energy dissipation inequalities for functionals with surface energy. SIAM Journal on Mathematical Analysis, vol. 29 (1998), no. 3, 673--680. (PDF)

  53. On existence of energy minimizing configurations for mixtures of two imperfectly bonded conductors. Recent advances in structural modelling and optimization. Control Cybernet. 27 (1998), no. 2, 217--234.

  54. Variational methods, bounds, and size effects for two phase composites with coupled heat and mass transport processes at the two phase interface. Journal of the Mechanics and Physics of Solids, vol. 47, 1999, pp. 1699--1736. (PDF)

  55. Influence of interfacial surface conduction on the DC electrical conductivity of particle reinforced composites. Proceedings Royal Society of London, Mathematical, Physical and Engineering Sciences, vol. 454, 1998, 1371-1382. (PDF)

  56. Variational methods, size effects and extremal microgeometries for elastic composites with imperfect interface. Mathematical Models and Methods in Applied Sciences. 5 (1995), 1139--1173. (With Bogdan Vernescu.) (PDF)

  57. Critical radius size effects and inverse problems for composites with imperfect interface. Journal of Applied Physics. 79 (1996), 8964--8966. (With Bogdan Vernescu.) (PDF)

  58. Design of particle reinforced heat conducting composites with interfacial thermal barriers. Journal of Composite Materials. 32 (1998), 1322--1331. (PDF)

  59. Reciprocal relations, bounds and size effects for composites with highly conducting interface. SIAM Journal on Applied Math. 57 (1997), 347--363. (PDF)

  60. Reinforced Mindlin Plates with Extremal Stiffness. Int. J. Solids and Structures. 28 (1997), 3691--3704. (PDF)

  61. Composites with imperfect interface. Proceedings of the Royal Society of London A 452 (1996), 329--358. (With B. Vernescu.) (PDF)

  62. A saddle-point theorem with application to structural optimization. Journal of Optimization Theory and Applications. 81 (1994), 549--567. (PDF)

  63. Homogenization of two-phase emulsions. Proceedings of the Royal Society of Edinburgh 124A (1994), 1119--1134. (With Bogdan Vernescu.) (PDF)

  64. Inequalities for electric and elastic polarization tensors with applications to random composites. Journal of the Mechanics and Physics of Solids. 41 (1993), 809--833. (PDF)

  65. Optimal bounds on effective elastic tensors for orthotropic composites. Proceedings of the Royal Society of London. 443 (1994), 399--410. (PDF)

  66. Optimal design and relaxation for reinforced plates subject to random transverse loads. Probabilistic Engineering Mechanics. 9 (1994), 167--177. (PDF)

  67. Laminar elastic composites with crystallographic symmetry SIAM Journal on Applied Mathematics. 50 (1990), 683--702. (With Richard James and Adam Lutoborsky) (PDF)

  68. Saturation of the even order bounds on effective moduli by finite-rank laminates. Journal of Applied Physics. 67 (1990), 7300--7306. (PDF)

  69. Darcy's law for slow viscous flow past a stationary array of bubbles. Proceedings of the Royal Society of Edinburgh. 114A (1990), 71--79 (With Marco Avellaneda.) (PDF)

  70. Optimal bounds for the effective energy of a mixture of isotropic, incompressible, elastic materials. Archive for Rational Mechanics and Analysis. 102 (1988), 331--350. (With Robert V. Kohn). (PDF)

  71. On the effective elasticity of a two-dimensional homogenized incompressible elastic composite. Proceedings of the Royal Society of Edinburgh. 110A (1988), 45--61. (PDF)

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