Research Activities

 

Research Interests:

 

              Continuum Mechanics

                  Elasticity and Viscoelasticity

                  Fracture Mechanics

                  Nanomechanics

                  Mechanics of Biological Materials

                  Modeling in Cardio-Vascular Mechanics

                  Modeling in Cardio-Vascular Disease

                  Mathematical Ecology

                  Partial Differential Equations

                  Integral Equations

                  Chemical Physics

 

Representative Recent Publications:

 

J. R. Walton, L. A. Rivera-Rivera, R. R. Lucchese and J. W. Bevan, Canonical Force Distributions in Pairwise Interatomic Interaction from the Perspective of the Hellmann-Feynman Theorem, J. Phys. Chem. A, 120(20), 3718-3725, 2016.

 

J. R. Walton, L. A. Rivera-Rivera, R. R. Lucchese and J. W. Bevan, A Canonical Approach to Forces in Molecules, Chem. Phys., 474, 52-58, 2016.

 

J. R. Walton, L. A. Rivera-Rivera, R. R. Lucchese and J. W. Bevan, Canonical Approaches to Applications of the Virial Theorem, J. Phys. Chem. A, 120, 817-823, 2016.

 

J. R. Walton and A. Y. Zemlyanova, A Rigid Stamp Indentation into a Semi-Plane with a Curvature-Dependent Surface Tension on the Boundary,  SIAM J. Appl. Math., 76 (2), 618-640, 2016.

 

J. R. Walton, L. A. Rivera-Rivera, R. R. Lucchese and J. W. Bevan, A Canonical Approach to Multi-Dimensional van der Waals, Hydrogen-Bonded and Halogen-Bonded Potentials, Chem. Phys., 469-470, 60-64, 2016.

 

R. Parshad, J. R. Walton and X.-Y. Wang, Stochastic Models for the Trojan Y-Chromosome Eradication Strategy of an Invasive Species, J. Biol. Dyn., 10 (1), 179-199, 2015.

 

J. R. Walton, L. A. Rivera-Rivera, R. R. Lucchese and J. W. Bevan, From  H2+ the Multidimensional Potential for the Intermolecular Interaction Ar×HBr:  A Canonical Approach, Chem. Phys. Lett., 639,  63-66, 2015.

 

J. R. Walton, L. A. Rivera-Rivera, R. R. Lucchese and J. W. Bevan, Canonical Potentials and Spectra within the Born-Oppenheimer Approximation,  J. Phys. Chem. A, 119 (25), 6753-6758, 2015.

 

J. R. Walton, L. A. Rivera-Rivera, R. R. Lucchese and J. W. Bevan, A General Transformation to Canonical Form for Potentials in Pairwise Interatomic Interactions,  Phys. Chem. Chem. Phys., 17, 14805-14810, 2015.

 

M. Muddamallappa and J. R. Walton, On the direct numerical simulation of plane-strain fracture in a class of strain-limiting anisotropic elastic bodies, Int. J. Frac., 192 (2), 217-232, 2015.

 

M. Bulíček, J. Málek, K. R. Rajagopal and J. R. Walton, Existence of Solutions for the Anti-Plane Stress for a New Class of ``Strain-Limiting’’ Elastic Bodies,  Calc. Var. & PDE, 54 (2), 2115-2147,  2015.

 

L. Ferguson, M. Muddamallappa and J. R. Walton, Numerical Simulation of Mode-III Fracture Incorporating Surface Mechanics, Int. J. Frac.,  192 (1), 47-56, 2015.

 

T. Mai and J. R. Walton, On Monotonicity for Strain-Limiting Theories of Elasticity, J. Elast., 120 (1), 39-65, 2015.

 

K. Gou, M. Mallikarjuna, K. R. Rajagopal and J. R. Walton, Modeling Fracture in the Context of a Strain-Limiting Theory of Elasticity:  A Single Plane-Strain Crack, Int. J. Engng. Sci., 88, 73-82, 2015.

 

T. Mai and J. R. Walton, On Strong Ellipticity for Implicit and Strain-Limiting Theories of Elasticity, Math. Mech. Solids,  20 (2), 121-139, 2015.

 

R. R. Lucchese, C. K. Rosales, L. A. Rivera-Rivera, B. A. McElmurry, J. W. Bevan and J. R. Walton, A Unified Perspective on the Nature of Bonding in Pairwise Interatomic Interaction, J. Phys. Chem. A, 118, 6287-6298, 2014.

 

Kun Gou and Jay R. Walton, Reconstruction of Nonuniform Residual Stress for Soft Hyperelastic Tissue via Inverse Spectral Techniques, Int. J. Engng. Sci.,  82, 46-73, 2014.

 

Katie Storey, May Boggess, Rana D. Parshad, Jay R. Walton and Xueying Wang, Analysis of the Trojan Y-Chromosome eradication strategy for an invasive species,  J. Math. Biol., 68(7), 1731-1756, 2014.

J. R. Walton, Plane-Strain Fracture with Curvature-Dependent Surface Tension:  Mixed-Mode Loading, J. Elast., 114(1), 127-142, 2014.

S. Joshi and J. R. Walton, Reconstruction of the Residual Stresses in a Hyperelastic Body Using Ultrasound Techniques, Int. J. Eng. Sci., 70, 46-72, 2013.

 

A. Y. Zemlyanova and J. R. Walton, Modeling of a Curvilinear Planar Crack with a Curvature-Dependent Surface Tension, SIAM J. Appl. Math., 72(5), 1474-1492, 2012.

 

K. Gou, S. Joshi and J. R. Walton, Recovery of Material Parameters of Soft Hyperelastic Tissue by an Inverse Spectral Technique, Int. J. Eng. Sci., 56, 1-16, 2012.

 

J. R. Walton, A Note on Fracture Models Incorporating Surface Elasticity,  J. Elast., 109(1), 95-102, 2012.

 

M. Fujiwara, G. Pfeiffer, M. Boggess, S. Day and J. R. Walton, Coexistence of Competing Stage-Structured Populations, Scientific Reports, 1, Article #107, doi:  10.1038/srep00107, 2011.

 

K. R. Rajagopal and J. R. Walton, Modeling Fracture in the Context of a Strain-Limiting Theory of Elasticity, Int. J. Frac., 169(1), 39-48, 2011.

 

Yuliya Gorb and Jay R. Walton, Dependence of the Frequency Spectrum of Small Amplitude Vibrations Superimposed on Finite Deformations of a Nonlinear, Cylindrical Elastic Body on Residual Stress, Int. J. Eng. Sci, 48, 1289-1312, 2010.

 

T. L. Leise, J. R. Walton and Y. Gorb, Reconsidering the Boundary Conditions for a Dynamic Transient Mode I Crack Problem, Int. J. Frac., 162(1-2), 69-76, 2010.

 

A. Ibragimov, L. R. Ritter and J. R. Walton, Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis, SIAM J. Appl. Math., 70(7), 2150-2185, 2010.

T. Sendova and J. R. Walton, A New Approach to the Modeling and Analysis of Fracture through Extension of Continuum Mechanics to the Nanoscale, Math. Mech. Solids, 15(3), 368-413, 2010.

 

A. I. Ibragimov, C. J. McNeal, L. R. Ritter and J. R. Walton, Stability Analysis of a Model of Atherogenesis: An Energy Estimate Approach II, J.  Comp. & Math. Meth. Med., 11(1), 67-88, 2010.

 

E. Aulisa, A. I. Ibragimov, P. Valko and J. R. Walton, Mathematical Framework of the Well Productivity Index for Fast Forchheimer (Non-Darcy) Flows in Porous Media, Math. Mod. Meth. Appl. Sci., 19(8), 1241-1275, 2009.

 

E. Aulisa, A. I. Ibragimov, and J. R. Walton, A New Method for Evaluating the Productivity Index for Nonlinear Flows, SPE Journal, 14(4), 693-706, 2009.

 

A. I. Ibragimov, C. J. McNeal, L. R. Ritter and J. R. Walton, Stability Analysis of a Model of Atherogenesis: An Energy Estimate Approach, J. Comp. & Math. Meth. Med., 9 (2), pp. 121-142, 2008.

 

E.-S. Oh, J. R. Walton and J. C. Slatter, A theory of fracture based upon an extension of continuum mechanics to the nanoscale, J. Appl. Mech. 73 (5), pp. 792-798, 2006.

 

E._S. Oh, J. R. Walton, D. C. Lagoudas and J. C. Slattery, Evolution of stresses in a simple class of oxidation problems, Acta Mechanica 181, pp. 231-255, 2006.

 

A. I. Ibragimov, C. J. McNeal, L. R. Ritter and J. W. Walton, A Mathematical Model of Atherogenisis as an Inflammatory Response, Math. Med. & Biol., 22 (4), pp.305-333, 2005.

 

Z. Wang, A. L. McIntosh, B. A. McElmurry, J. R. Walton R. R. Lucchese and J. W. Bevan, An improved morphed potential for Ar:HBr based upon scaling the experimental dissociation energy, J. Phys. Chem., 109, pp. 8168--8179, 2005.

 

J. D. Humphrey, G. Cote, J. R. Walton, G. A. Meininger and G. Laine, A new paradigm for graduate research and training in the biomedical sciences and engineering, Advances in Physiology Education, 29, pp.98-102, 2005.

 

D. Khalmanova and J. R. Walton, Dynamic, steady-state crack propagation in a transversely isotropic viscoelastic body, Int. J. Frac., 131 (2), pp. 107-129, 2005.

 

A. I. Ibragimov, D. Khalmanova, P. Valko and J. R. Walton, On a Mathematical Model of the Productivity Index of a Well from Reservoir Engineering, SIAM J. Appl. Math., 65, No. 6, pp.1952--1980, 2005.

 

T. Sendova and J. R. Walton, On Strong Ellipticity for Isotropic Hyperelastic Materials Based upon Logarithmic Strain, Int. J. Non-Linear Mech., 40, No. 2-3, pp. 195-212, 2004.

 

T. L. Leise and J. R. Walton, An analytical and numerical study of a dynamically accelerating semi-infinite crack in a linear viscoelastic material, Int. J. Frac., 127, No.2, pp. 101-117, 2004.

 

J. R. Walton and J. P. Wilber, Deformations of a neo-Hookean elastic wedge revisited, Math. Mech. of Solids, 9, pp. 307-327, 2004.

 

T. L. Leise and J. R. Walton, A solution method for a dynamically accelerating semi-infinite crack in a linear viscoelastic material, SIAM Appl. Math., 64, No. 1, pp. 94-107, 2003.

 

L-I. Palade, J. R. Walton and A. Farina, A New Constitutive Equation that Models Extensional Strain Hardening Based on Evolving Natural Configurations:\ \ Stability Analysis, Int.~J.~Non-linear Mech., 39 No.3,pp. 379-387, 2004.

 

J. R. Walton, Vibrations of a Neo-Hookean Elastic Wedge, Int. J. Non-Linear Mech., 38, pp. 1285-1296, 2003.