## Alexander Panchenko## Professor## Neill Hall Room 329## Phone: (509) 335-3127## Email: panchenko@math.wsu.edu |

##### Publications

- A method for tomographic diagnostics of a jet exhaust.
*Vestnik of Kharkov Polytechnic University,*7 (1992), no. 260, 73-86. (Russian). - Inverse source problem of radiation transfer: a special case of the attenuated Radon transform.
*Inverse Problems*, 9 (1993), 321-338. - Generalized projection and section theorems in diffraction tomography. in: Applied Problems of Radon Transform. AMS Translations, series 2, v. 162 (1994) , 33-43.
- R. P. Gilbert and A. Panchenko. Acoustics of a stratified poroelastic composite.
*Zetitschrift fur Analysis und ihre Anwendungen*, 18 (1999), 977-1001. - Quasi-exponential solutions for some PDE with coefficients of limited regularity. In: Direct and inverse problems of mathematical physics, Kluwer, Dordrecht, 2000, 161-184.
- L. Ehrenpreis, P. Kuchment and A. Panchenko. The exponential X-Ray transform and John's Equation.
I. Range description.
*Contemporary Mathematics*, 251 (2000), 173-188. - On a differential operator containing a large complex parameter.
*Applicable Analysis*, 74 (2000), 1-26. - An inverse problem for the magnetic Schroedinger Equation and quasi-exponential solutions of nonsmooth
partial differential equations.
*Inverse Problems*, 18 (2002), no.5, 1421-1434. - V. Harik, R. P. Gilbert and A. Panchenko. Vibration of two bonded periodic composites.
*International Journal of Solids and Structures*,**40**(2002), no. 12, 3177-3193. - R. P. Gilbert and A. Panchenko. Effective acoustic equations for a nonconsolidated medium with
microstructure. In:
*Acoustics, mechanics and the related topics of mathematical analysis*, World Scientific, River Edge, NJ, (2002), 164-170. - L. Paivarinta, A. Panchenko and G. Uhlmann. Complex geometrical optics solutions for Lipschitz
conductivity.
*Revista Matematica Iberoamericana*,**19**(2003), 56-72. - R. P. Gilbert and A. Panchenko. Effective acoustic equations of a two-phase medium with microstructure.
*Mathematical and Computer Modelling*,**39**, no. 13, (2004), 1431-1448. - L. Berlyand, L. Borcea and A. Panchenko. Network approximation for effective viscosity of highly
concentrated suspensions with complex geometry.
*SIAM Journ. Math. Analysis*,**36**(5), 2005, 1580-1628. - R. P. Gilbert, A. Panchenko and X. Xie. Homogenization of a viscoelastic matrix in linear frictional
contact.
*Math. Models and Methods in Applied Sciences*,**28**, (2005), 309-328. - R. P. Gilbert, A. Panchenko and X. Xie. A prototype homogenization model for acoustics of granular
materials.
*International Journal of Multiscale Computational Engineering*,**4**, (5{6), 2006, 585-600. - L. Berlyand and A. Panchenko. Strong and weak blow up of the viscous dissipation rates for concentrated
suspensions.
*Journal of Fluid Mechanics*, 578 (2007), 1-34. - M. C. Calderer and A. Panchenko. Young measures and order-disorder transition in liquid crystal
flows.
*SIAM Journ. Math. Analysis*,**38**, no. 5 (2007), 1642-1659. - M. Fang, R. P. Gilbert, A. Panchenko and A. Vasilic, Homogenizing the time harmonic acoustics of
bone: the monophasic case.
*Mathematical and Computer Modeling*,**46**, 3-4, (2007), 331-340. - K. A. Ariyawansa, L. Berlyand and A. Panchenko. A network model of geometrically constrained
deformations of granular materials.
*Networks and Heterogeneous Media*., (2008),**3**(1), 125-148. - A. Panchenko. G-convergence and homogenization of viscoelastic flows. Submitted.
- A. Cherkaev, A. Kouznetsov and A. Panchenko. Still states of bistable lattices, compatibility, and phase
transition.
*Continuum Mechanics and Thermodynamics*, (2010),**22**(6-8), 421-444. - S. J. Mesarovic, R. Baskaran and A. Panchenko, Thermodynamic coarsening of dislocation mechanics
and the size-dependent continuum crystal plasticity.
*J. Mech. Phys. Solids***58**(2010), no. 3, 311329. - R. P. Gilbert, A. Panchenko and A. Vasilic, Acoustic propagation in a random saturated medium:
the monophasic case.
*Math. Methods in Appl. Sciences*, (2010), Published online 09/20/2010, DOI 10.1002/mma/1360. - R. P. Gilbert, A. Vasilic and A. Panchenko, Homogenization of cancellous bone with an interstitial
non-Newtonian
fluid.
*Non-linear Analysis*, to appear. - A. Panchenko, L. I. Barannyk and R. P. Gilbert. Closure method for spatially averaged dynamics of
particle chains.
*Nonlinear Analysis: Real World Applications*, 12 (2011), 1681-1697. - A. Tartakovsky, A. Panchenko and K Ferris. Dimension reduction method for ODE
fluid models.
*J. Comp. Phys.*, 230 (2011), 8554-8572. - A. Panchenko, L.L. Barannyk, K.Cooper. Deconvolution closure for mesoscopic continuum models of particle systems. Submitted.
- A. Panchenko, A. Tartakovsky. Discrete models of fluids: spatial averaging, closure, and model reduction. Submitted.