Current Research Interests

Data Science. Feature extraction from networks. Learning network dynamics from limited time-series. Statistical inference on networks. Application areas: plant biology, neuroscience.

Dynamics of active particle systems and active materials. Mathematics of robotic swarms. Analysis and simulation of self-organizing particle systems possessing some means of self-propulsion and decision-making capability.

Continuum theories of large particle systems. The main question is how to produce a continuum description of a large system of atoms or molecules (think of a fluid) starting from the atomistic equations of motion for the particles. This is the Sixth Hilbert Problem, still largely unsolved.

Students interested in either analysis or computing are welcome. If desired, a MS degree in Statistics can be obtained in parallel with the Ph.D in Math. Career opportunities with National Labs, Academia, and Industry are likely.

Publications

1. A method for tomographic diagnostics of a jet exhaust. Vestnik of Kharkov Polytechnic University, 7 (1992), no. 260, 73--86. (Russian).


2. Inverse source problem of radiation transfer: a special case of the attenuated Radon transform. Inverse Problems, 9 (1993), 321--338.


3. Generalized projection and section theorems in diffraction tomography. in: Applied Problems of Radon Transform. AMS Translations, series 2, v. 162 (1994) , 33--43.


4. R. P. Gilbert and A. Panchenko. Acoustics of a stratified poroelastic composite. Zetitschrift fur Analysis und ihre Anwendungen, 18 (1999), 977--1001.


5. Quasi-exponential solutions for some PDE with coefficients of limited regularity. In: Direct and inverse problems of mathematical physics, Kluwer, Dordrecht, 2000, 161--184.


6. 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.


7. On a differential operator containing a large complex parameter. Applicable Analysis, 74 (2000), 1-26.


8. 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.


9. 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.


10. 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.


11. L. Paivarinta, A. Panchenko and G. Uhlmann. Complex geometrical optics solutions for Lipschitz conductivity. Revista Matematica Iberoamericana, 19 (2003), 56-72.


12. 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.


13. 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.


14. 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.


15. 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.


16. 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.


17. 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.


18. 18. M. Fang, R. P. Gilbert, A. Panchenko and A. Vasilic, Homogenizing the time-harmonic acoustics of bone: The monophasic case. Mathematical and Computer Modelling, 46, 3-4, (2007), 331--340.


19. 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.


20. M. C. Calderer, A. DeSimone, D. Golovaty, and A. Panchenko, On an effective model for ferronematic liquid crystals. Proceedings of ICIAM-07, published in Proceedings on Applied Mathematics and Mechanics (2007) 7 (1), 1130401-1130402.


21. A. Cherkaev, A. Kouznetsov, and A. Panchenko. Still sates of bistable lattices, compatibility, and phase transition. Continuum Mechanics and Thermodynamics, (2010), 22 (6-8), 421-444.


22. R. P. Gilbert, A. Panchenko, and A. Vasilic. Homogenizing acoustics of cancellous bone with an interstitial non-Newtonian fluid. Nonlinear Analysis: Theory, Methods, and Applications, 74 (2011), 1005-1018.


23. R. P. Gilbert, A. Panchenko and A. Vasilic. Acoustic propagation in a random saturated medium: the monophasic case. Mathematical Methods in the Applied Sciences, (2010), 33, 18, 2206-2214.


24. S. Dj. Mesarovic, R. Baskaran and A. Panchenko. Thermodynamic coarsening of dislocation mechanics and the size-dependent continuum crystal plasticity. Journal of the Mechanics and Physics of Solids, (2010), 58, no. 3, 311-329.


25. A. Panchenko, L. L. Barannyk, and R. P. Gilbert. Closure method for spatially averaged dynamics of particle chains. Nonlinear Analysis: Real World Applications, 12 (3), (2011), 1681-1697.


26. A. Tartakovsky, A. Panchenko, and K. Ferris. Dimension reduction method for ODE fluid models. Journal of Computational Physics, 230, (2011), 8554-8572.


27. R. P. Gilbert, A. Panchenko, and A. Vasilic. Biphasic Acoustic Behavior of a Non-periodic Porous Medium In Poromechanics V: Proceedings of the Fifth Biot Conference on Poromechanics. Ed. by Ch. Hellmich, B. Pichler; and D. Adam, ASCE Publishing, 2013, 1981-1990.


28. R. P. Gilbert, A. Panchenko, A. Vasilic, and Yongzhi Xu. Homogenizing the Ultrasonic Response of Wet Cortical Bone. In Poromechanics V: Proceedings of the Fifth Biot Conference on Poromechanics. Ed. by Ch. Hellmich, B. Pichler; and D. Adam, ASCE Publishing, 2013, 1097-1106.


29. A. Panchenko, A. Tartakovsky. Discrete models of fluids: spatial averaging, closure, and model reduction. SIAM J. Appl. Math, 74 (2), (2014), 477-515.


30. R. P. Gilbert, A. Panchenko, and A. Vasilic. Acoustic propagation in a random saturated medium: the biphasic case. Applicable Analysis, 93 (4), (2014), 676-697.


31. M. C. Calderer, A. DeSimone, D. Golovaty, and A. Panchenko. Effective models for nematic liquid crystals composites with ferromagnetic inclusions. SIAM J. Appl. Math., 74 (2) (2014), 247-262.


32. L. L. Barannyk and A. Panchenko. Optimizing performance of deconvolution closure for large ODE systems. IMA J. Appl. Math., 80 (4) (2015), 1099-1123. doi:10.1093/imamat/hxu042.


33. D. Hinz, A. Panchenko, T.-Y. Kim, and E. Fried. Motility versus fluctuations: Mixtures of self-propelled and passive particles. Soft Matter, 10 (2014), 9082-9089, DOI: 10.1039/C4SM01562B.


34. A. Tartakovsky and A. Panchenko. Pairwise Force Smooth Particle Hydrodynamics for multiphase flow: surface tension and contact line dynamics. Journal of Computational Physics, 305 (2016), 1119-1146.


35. D. Hinz, A. Panchenko, T.-Y. Kim, and E. Fried. Particle-based simulation of self-motile suspensions. Computer Physics Communications, 196 (2015), 45-57.


36. V. Oles, A. Panchenko, and A. Smertenko. Modeling hormonal control of cambium proliferation. PLOS one, (2017), doi:10.1371/journal.pone.0171927.


37. A. Panchenko, D. Hinz and E. Fried. Spatial averaging of a dissipative particle dynamics model for active suspensions. Physics of Fluids, 30 (2018), 033331, https://doi.org/10.1063/1.5024746.