Vladimir A. Volpert Vladimir A. Volpert



Professor of Applied Mathematics
Ph. D., Institute of Chemical Physics, USSR Academy of Sciences

E-mail address: v-volpert@northwestern.edu



Current Graduate Students:

Anna Tikhomirova
Esteban Urdiales



Advisor and Advisee



Previous Graduate Students:

Daniel Schult (1996)
Philip Goldfeder (1998)
Christopher Raymond (1999)
Cynthia Spade (2000)
Jeffrey Beck (2003)
Michael Perry (2003)
Laura Ritter (2003)
Divya Devadoss (2004)
Donna Comissiong (2005)



Research Interests:

Mathematical theory of combustion
Mathematical theory of frontal polymerization
Nonlinear analysis and bifurcation theory
Traveling wave solutions of parabolic systems
Asymptotic analysis and perturbation methods
Mathematical biology




JOURNAL PUBLICATIONS SINCE 1992

    VIT.A. VOLPERT, VL.A. VOLPERT, S.P. DAVTYAN, I.N. MEGRABOVA, N.F. SURKOV, Two-dimensional combustion modes in condensed flow, SIAM J. Appl. Math. 52 (1992), No. 2, pp. 368-383

    K.G. SHKADINSKY, B.J. MATKOWSKY, V.A. VOLPERT, Mathematical modeling of SHS processes, Int'l J. Self-Propagating High-Temperature Synthesis 1 (1992), No. 1, pp. 46-53

    B.J. MATKOWSKY, V.A. VOLPERT, Coupled nonlocal complex Ginzburg-Landau equations in gasless combustion, Physica D 54 (1992), pp. 203-219

    B.J. MATKOWSKY, V.A. VOLPERT, Nonlocal amplitude equations in reaction diffusion systems, Random and Computational Dynamics 1 (1992), No. 1, pp. 33-58

    K.G. SHKADINSKY, G.V. SHKADINSKAYA, B.J. MATKOWSKY, V.A. VOLPERT, Combustion synthesis of a porous layer, Combust. Sci. Technol. 88 (1992), pp. 247-270

    K.G. SHKADINSKY, G.V. SHKADINSKAYA, B.J. MATKOWSKY, V.A. VOLPERT, Combustion of porous samples with deformation of high temperature products, Int'l J. Self-Propagating High-Temperature Synthesis 1 (1992), No. 3, pp. 371-391

    K.G. SHKADINSKY, G.V. SHKADINSKAYA, B.J. MATKOWSKY, V.A. VOLPERT, Self-compaction or expansion in combustion synthesis of porous materials, Combust. Sci. Technol. 88 (1992), pp. 271-292

    K.G. SHKADINSKY, G.V. SHKADINSKAYA, B.J. MATKOWSKY, V.A. VOLPERT, Two-front traveling waves in filtration combustion, SIAM J. Appl. Math. 53 (1993), No. 1, pp. 128-140

    K.G. SHKADINSKY, G.V. SHKADINSKAYA, B.J. MATKOWSKY, V.A. VOLPERT, Filtration combustion with self-deformation, Journal of Material Synthesis and Processing 1 (1993), No. 4, pp. 245-274

    B.J. MATKOWSKY, V.A. VOLPERT, Stability of plane wave solutions of complex Ginzburg-Landau equations, Quarterly of Applied Mathematics LI (1993), No. 2, pp. 265-281

    VIT.A. VOLPERT, VL.A. VOLPERT, Propagation of frontal polymerization-crystallization waves, Euro. J. Appl. Math. 5 (1994), pp. 201-215

    B.J. MATKOWSKY, V.A. VOLPERT, Spiral gasless condensed phase combustion, SIAM J. Appl. Math. 54 (1994), No. 1, pp. 132-146

    VIT.A. VOLPERT, VL.A. VOLPERT, AND J.A. POJMAN, Effect of thermal expansion on stability of reaction front propagation, Chem. Eng. Sci. 49 (1994), No. 14, pp. 2385-2388

    A.P. ALDUSHIN, B.J. MATKOWSKY, V.A. VOLPERT, Interaction of gasless and filtration combustion, Combust. Sci. Technol. 99 (1994), No. 1-3, pp. 75-103

    A.P. ALDUSHIN, B.J. MATKOWSKY, K.G. SHKADINSKY, G.V. SHKADINSKAYA, V.A. VOLPERT, Combustion of porous samples with melting and flow of reactants, Combust. Sci. Technol. 99 (1994), No. 4-6, pp. 313-343

    K.G. SHKADINSKY, G.V. SHKADINSKAYA, B.J. MATKOWSKY, V.A. VOLPERT, Combustion of porous samples with oscillatory deformation of products, Int'l J. Self-Propagating High-Temperature Synthesis 3 (1994), No. 1, pp. 1-16

    A.P. ALDUSHIN, B.J. MATKOWSKY, V.A. VOLPERT, Enhancement of gasless combustion synthesis by counterflow gas filtration, Combust. Sci. Technol. 103 (1995), No. 1-6, pp. 1-20

    A.J. BERNOFF, R. KUSKE, B.J. MATKOWSKY, V.A. VOLPERT, Mean field effects for counterpropagating traveling wave solutions of reaction-diffusion systems, SIAM J. Appl. Math. 55 (1995), No. 2, pp. 485-519

    A.P. ALDUSHIN, B.J. MATKOWSKY, V.A. VOLPERT, Stoichiometric combustion waves and their stability, Combustion and Flame 101 (1995), No. 1/2, pp. 15-25

    B.J. MATKOWSKY, D.A. SCHULT, V.A. VOLPERT, A.C. FERNANDEZ-PELLO, Propagation and extinction of forced opposed flow smolder wave, Combustion and Flame 101 (1995), No. 4, pp. 471-490

    B.J. MATKOWSKY, D.A. SCHULT, V.A. VOLPERT, A.C. FERNANDEZ-PELLO, Forced forward smolder combustion, Combustion and Flame 104 (1996), No. 1, pp. 1-26

    VIT.A. VOLPERT, VL.A. VOLPERT, J.A. POJMAN, S. SOLOVYOV, Hydrodynamic stability of a polymerization front, Euro. J. Appl. Math. 7 (1996), pp. 303-320

    C.S. RAYMOND, V.A. VOLPERT, Stability of uniformly propagating SHS waves in porous solids with melting and flow of reactants, Chem. Eng. Sci. 51 (1996), No. 19, pp. 4443-4462

    C.S. RAYMOND, V.A. VOLPERT, Stabilization of gasless combustion waves by high melting temperature additives, Int'l J. Self-Propagating High-Temperature Synthesis 5 (1996), No. 3, pp. 197-207

    V.A. VOLPERT, Combustion waves with wide reaction zones, Applied Mathematics Letters 10 (1997), No. 4, pp. 59-64

    K.G. SHKADINSKY, G.V. SHKADINSKAYA, V.A. VOLPERT, Stability of "liquid flame" combustion waves, Chem. Eng. Sci. 52 (1997), No. 9, pp.1415-1428.

    P.M. GOLDFEDER, V.A. VOLPERT, V.M. ILYASHENKO, A. KHAN, J.A. POJMAN, S.E. SOLOVYOV, Mathematical modeling of free radical polymerization fronts, Journal of Physical Chemistry Part B 101 (1997), pp. 3474-3482.

    VL.A. VOLPERT, VIT.A. VOLPERT, Condensed phase reaction waves with variable thermo-physical characteristics, Comb. Sci. Technol. 127 (1997), No. 1-6, pp. 29-53

    C.S. RAYMOND, K.G. SHKADINSKY, V.A. VOLPERT, Gravitational effects on liquid flame thermite systems, Comb. Sci. Technol., 131 (1998), No. 1-6, pp. 107-129

    VL.A. VOLPERT, VIT.A. VOLPERT, V.M. ILYASHENKO, J.A. POJMAN, Frontal polymerization in a porous medium, Chem. Eng. Sci. 53 (1998), No. 9, pp. 1655-1665

    P.M. GOLDFEDER, V.A. VOLPERT, Nonadiabatic frontal polymerization, Journal of Engineering Mathematics 34 (1998), No. 3, pp. 301-318

    P.M. GOLDFEDER, V.A. VOLPERT, A model of frontal polymerization including the gel effect, Mathematical Problems in Engineering 4 (1998), pp. 377-391

    P.M. GOLDFEDER, V.A. VOLPERT, A model of frontal polymerization using complex initiation, Mathematical Problems in Engineering 5 (1999), No. 2, pp. 139-160

    C.S. RAYMOND, V.A. VOLPERT, An asymptotic model of condensed phase combustion with inert melting, Applied Mathematics Letters 12 (1999), No. 3, pp. 89-94

    C.A. SPADE, V.A. VOLPERT, Mathematical modeling of interfacial gel polymerization, Mathematical and Computer Modelling 30 (1999), pp. 67-73

    D.A. SCHULT, V.A. VOLPERT, Linear stability analysis of thermal free radical polymerization waves, Int'l J. SHS 8 (1999), No. 4, pp. 417-440

    C.A. SPADE, V.A. VOLPERT, On the steady-state approximation in thermal free radical frontal polymerization, Chem. Eng. Sci. 55 (2000), No. 3, pp. 641-654

    C.A. SPADE, V.A. VOLPERT, Mathematical modeling of interfacial gel polymerization for weak and strong gel effects, Macromolecular Theory and Simulations 9 (2000), No. 1, pp. 26-46

    C.A. SPADE, V.A. VOLPERT, Linear stability analysis of nonadiabatic free radical polymerization waves, Combustion Theory and Modelling 5 (2001), pp. 21-39

    C.S. RAYMOND, A. BAYLISS, B.J. MATKOWSKY, V.A. VOLPERT, Transitions to chaos in condensed phase combustion with reactant melting, Int'l J. Self-Propagating High-Temperature Synthesis 10 (2001), No. 2, pp. 133-149

    A.I. VOLPERT, V.A. VOLPERT, Traveling wave solutions of parabolic systems with discontinuous nonlinear terms, Nonlinear Analysis 49 (2002), No. 1, pp. 113-139

    D.A. SCHULT, C.A. SPADE, V.A. VOLPERT, Dopant distribution in isothermal frontal polymerization, Applied Mathematics Letters 15 (2002), No. 6, pp. 749-754

    J.A. POJMAN, J. MASERE, E. PETRETTO, M. RUSTICI, D-S HUH, M.S. KIM, V.A. VOLPERT, The effect of reactor geometry on frontal polymerization spin modes, Chaos 12 (2002), No. 1, pp. 56-65

    L.K. GROSS, V.A. VOLPERT, Weakly nonlinear stability analysis of frontal polymerization, Studies in Applied Mathematics 110 (2003), No. 4, pp. 351-376

    M.F. PERRY, V.A. VOLPERT, L.L. LEWIS, H.A. NICHOLS, J.A. POJMAN, Free-radical frontal copolymerization: The dependence of the front velocity on the monomer feed composition and reactivity ratios, Macromolecular Theory and Simulations 12 (2003), pp. 276-286

    L.R. RITTER, W.E. OLMSTEAD, V.A. VOLPERT, Initiation of free-radical polymerization waves, SIAM J. Appl. Math. 53 (2003), pp. 1831-1848

    J.M. BECK, V.A. VOLPERT, Gapped gapless packing structures, Journal of Colloid and Interface Science 262 (2003), pp. 162-170

    J.M. BECK, V.A. VOLPERT, Nonlinear dynamics in a simple model of solid flame microstructure, Physica D 182 (2003), No. 1-2, pp. 86-102.

    J.M. BECK, V.A. VOLPERT, A simple model of two dimensional solid flame microstructure, Combustion Theory and Modelling 7 (2003), No. 4, pp. 795-812

    M.F. PERRY, V.A. VOLPERT, Self-propagating free-radical binary frontal polymerization, Journal of Engineering Mathematics 49 (2004), pp. 359-372

    M.F. PERRY, V.A. VOLPERT, Linear stability analysis of two monomer systems of frontal polymerization, Chemical Engineering Science 59 (2004), pp. 3451-3460

    A. HEIFETZ, L.R. RITTER, W.E. OLMSTEAD, V.A. VOLPERT, A numerical analysis of initiation of polymerization waves, Mathematical and Computer Modelling 41 (2005), pp. 271-285

    D.M.G. COMISSIONG, L.K. GROSS, V.A. VOLPERT, Nonlinear dynamics of frontal polymerization with autoacceleration, Journal of Engineering Mathematics 53 (2005), pp. 59-78

    L.L. LEWIS, C.S. DEBISSCHOP, J.A. POJMAN, V. A. VOLPERT, Isothermal frontal polymerization: Confirmation of the mechanism and determination of factors affecting the front velocity, front shape, and propagation distance with comparison to mathematical modeling, Journal of Polymer Science Part A: Polymer Chemistry, 43 (2005), pp. 5774-5786

    D.E. DEVADOSS, V.A. VOLPERT, Mathematical modeling of radially propagating polymerization waves with the gel effect, Applied Mathematics and Computation 172 (2006), pp 1036-1053

    D.E. DEVADOSS, V.A. VOLPERT, Modeling isothermal free-radical frontal polymerization with gel effect using free volume theory, with and without inhibition, Journal of Mathematical Chemistry 39 (2006), pp. 73-105

    D.E. DEVADOSS, J.A. POJMAN, V.A. VOLPERT, Mathematical modeling of thiol-ene frontal polymerization, Chemical Engineering Science 61 (2006), pp. 1261-1275

    D.M.G. COMISSIONG, L.K. GROSS, V.A. VOLPERT, Frontal polymerization in the presence of an inert material, Journal of Engineering Mathematics 54 (2006), pp. 389-402

    A.A. NEPOMNYASHCHY, A.A. GOLOVIN, A.E. TIKHOMIROVA AND V.A. VOLPERT, Nucleation and growth of droplets at a liquid-gas interface, Phys. Rev. E 74 (2006), pp. 021605-1-021605-10

    A.E. TIKHOMIROVA AND V.A. VOLPERT, Nonlinear dynamics of endothelial cells, Appl. Math. Lett. 20 (2007), No. 2, pp. 163-169

    Also

    A. I. VOLPERT, Vit. A. VOLPERT, Vl. A. VOLPERT, Traveling wave solutions of parabolic systems, Translations of Mathematical Monographs, Vol. 140 (1994), 448 pp., American Mathematical Society, Providence, RI (pdf file)

    V. A. VOLPERT, Dynamics of thermal polymerization waves, In: Self-Assembly, Pattern Formation and Growth Phenomena in Nano-Systems, Proceedings of NATO ASI; Golovin, A. A.; Nepomnyashchy, A. A. Eds.; Springer; 2006, pp. 195-245