Selected Papers:

  N.B. Murphy, E. Cherkaev, K. Golden, Anderson transition for classical transport in composite materials, Physical Review Letters, Vol. 118, 036401, 5 pp., 2017.  DOI: https://doi.org/10.1103/PhysRevLett.118.0364012016 (pdf)

 N Wellander, S Guenneau, E Cherkaev, Two-scale cut-and-projection convergence; homogenization of quasiperiodic structures, Math. Meth. Appl. Sci, 2017. doi:10.1002/mma.4345  (pdf)    

M. Kordy,  E. Cherkaev, P. Wannamaker, Null space correction and adaptive model order reduction in multi-frequency Maxwell's problem, Advances in Computational Mathematics, 2017, Vol. 43, pp. 171–193. https://doi.org/10.1007/s10444-016-9482-z (pdf)

N.B. Murphy, E. Cherkaev, J. Zhu, J. Xin, K. Golden, Spectral analysis and computation of effective diffusivities in space-time periodic incompressible flows, CAM 15-63, UCLA, 2015. Annals of Mathematical Sciences and Applications, 2017, Vol. 2, N. 1, 3-66.  DOI: http://dx.doi.org/10.4310/AMSA.2017.v2.n1.a1 (pdf)

 N.B. Murphy, E. Cherkaev, J. Zhu, J. Xin, K. Golden, Spectral analysis and computation of effective diffusivities for steady random flows, under review, 2016 (pdf)

B. Osting, J. Marzuola, E. Cherkaev, An Isoperimetric inequality for an integral operator on flat tori, Illinois Journal of Mathematics, 2015, Vol. 59, N. 3, 773-793.    arXiv:1510.08410 (pdf)

C. Strong, D. Foster, E. Cherkaev, I. Eisenman, K.M. Golden, On the definition of marginal ice zone width, Journal of Atmospheric and Oceanic Technology, Vol. 34, pp. 1565-1584, doi: 10.1175/JTECH-D-16-0171.1, 2017. 

M. Kordy,  E. Cherkaev, P. Wannamaker, Null space correction and adaptive model order reduction in multi-frequency Maxwell's problem, Advances in Computational Mathematics, 2017, Vol. 43, pp. 171–193. https://doi.org/10.1007/s10444-016-9482-z (pdf)

M. Kordy, E. Cherkaev, P. Wannamaker, M. Sommer, Subspace Gauss-Newton method for a low rank approximation of the Jacobian,  submitted, 2016.

M. Kordy, E. Cherkaev, P. Wannamaker, Adaptive model order reduction  for the Jacobian calculation in inverse multi-frequency problem for Maxwell's equations, Applied Numerical Mathematics, Vol. 109, pp. 1-18. doi: 10.1016/j.apnum.2016.02.010, 2016 (pdf)

M. Kordy, P. Wannamaker, V. Maris, E. Cherkaev, G. Hill,  3-D magnetotelluric inversion including topography using deformed hexahedral edge finite elements and direct solvers parallelized on SMP computers - Part I: forward problem and parameter Jacobians, Geophysical Journal International, 2016, 204 (1), 74-93, doi: 10.1093/gji/ggv410 (pdf)

M. Kordy, P. Wannamaker, V. Maris, E. Cherkaev, G. Hill, 3-dimensional magnetotelluric inversion including topography using deformed hexahedral edge finite elements and direct solvers parallelized on symmetric multiprocessor computers - Part II: direct data-space inverse solution, Geophysical Journal International, 2016,  204 (1), 94-110, doi: 10.1093/gji/ggv411 (pdf)

R. Mihaila, D. Ruhela, E. Keough, E. Cherkaev, S. Chang, B. Galinski, R. Bartz, D. Brown, B. Howell, J. Cunningham,

Mathematical modeling: A tool for optimization of lipid nanoparticle mediated delivery of siRNA, Molecular Therapy - Nucleic Acids, Vol 7, pp 246-255, 16 June 2017. DOI: http://dx.doi.org/10.1016/j.omtn.2017.04.003

N.B. Murphy, E. Cherkaev, C. Hohenegger, and K.M. Golden, Spectral measure computations for composite media, Communications in Mathematical Sciences, Vol. 13, No. 4, pp. 827-864, 2015  (pdf)

M. Kordy, E. Cherkaev, P. Wannamaker, Variational formulation for Maxwell's equations with Lorentz gauge: Existence
and uniqueness of solution, International Journal of Numerical Analysis & Modeling, IJNAM, 2015, Vol. 12, No. 4, pp. 731-749  (pdf)

A. Gully, J. Lin, E. Cherkaev, K.M. Golden, Bounds on the complex permittivity of polycrystalline materials by analytic continuation, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences (including cover), Vol. 471, Issue 2174, 17 pp., doi: 10.1098/rspa.2014.0702, 2015. (pdf)

O. Levy, E. Cherkaev, Effective medium approximations for anisotropic composites with arbitrary component orientation, J. Appl. Phys., 2013,  114, 164102; doi: 10.1063/1.4826616 (pdf)

M. Kordy, V. Maris, P. Wannamaker, E. Cherkaev, 3D Edge Finite Element solution for scattered electric field using a direct solver parallelized on an SMP Workstation,  5th International Symposium on Three-Dimensional Electromagnetics, Sapporo, Japan, May 7–9, 2013 (pdf)

C. Orum, E. Cherkaev, K. Golden, Recovery of inclusion separations in strongly heterogeneous composites from effective property measurements, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol. 468, pp. 784-809, doi:10.1098/rspa.2011.0527, 2012.  (pdf)

 E. Cherkaev, C. Bonifasi-Lista, Characterization of structure and properties of bone by spectral measure method, J Biomech., 2011, 44(2):345-351 (pdf)

 

 K. Golden, B. Murphy, E. Cherkaev, Spectral analysis and connectivity of porous microstructures in bone. J Biomech., 2011, 44(2):337-344.  (pdf)

 

D. Zhang, E. Cherkaev, M. Lamoureux, Stieltjes representation of the 3D Bruggeman effective medium and  Pade approximation, Applied Mathematics and Computation, v 217,  pp 7092-7107, 2011,  doi:10.1016/j.amc.2011.01.020  (pdf.file)

 D. Zhang, M. Lamoureux, G. Margarve, E. Cherkaev, Rational approximation for estimation of quality Q factor and phase velocity in linear, viscoelastic, isotropic media, Computational Geosciences, Vol 15, N 1, pp 117-133, 2011   (pdf.file)

 

A. Cherkaev, E. Cherkaev, S. Leelavanichkul, Principles of Optimization of Structures Against an Impact, Continuum Models and Discrete Systems Symposia (CMDS-12), Journal of Physics: Conference Series 319 (2011) 012021,
 doi:10.1088/1742-6596/319/1/012021 (pdf.file)
 

E. Cherkaev, D. Zhang, Pade approximations in inverse homogenization and numerical simulation of electromagnetic fields in composites, 2010 URSI International Symposium on  Electromagnetic Theory (EMTS), 10.1109/URSI-EMTS.2010.5637164, 2010, pp 580-583 (pdf.file)

 

 C. Bonifasi-Lista, E. Cherkaev, and Y.N. Yeni,  Analytical approach to recovering bone porosity from effective complex shear modulus,  Journal of Biomechanical Engineering, 2009, v. 131, N. 12, pp. 121003-1 - 121003-8,  doi:10.1115/1.4000082 (pdf.file)

 H. Bertete-Aguirre, E. Cherkaev, Stable parameter estimation method applied to characterization of plume transport in environmental inverse problems, SAGEEP 2010, Proceedings, Vol. 2, 711-714. 

 C. Bonifasi-Lista, E. Cherkaev, Electrical impedance spectroscopy as a potential tool for recovering bone porosity, Physics in Medicine and Biology, 54 (2009) 3063-3082. doi: 10.1088/0031-9155/54/10/007 (pdf.file)

 D. Zhang, E. Cherkaev, Reconstruction of spectral function from effective permittivity of a composite material using rational function approximations, Journal of Computational Physics, 228 (2009) 5390-5409, doi:10.1016/j.jcp.2009.04.014 (pdf.file)

  C. Bonifasi-Lista, E. Cherkaev, Analytical relations between effective material properties and microporosity: Application to bone mechanics, International Journal of Engineering Science, 46 (2008), 12, 1239-1252. doi:10.1016/j.ijengsci.2008.06.011 

E. Cherkaev, Inverse homogenization with diagonal Pade approximants, PAMM, Special Issue: ICIAM07, Vol 7,  N 1, 2008, pp 1042001 - 1042002. doi 10.1002/pamm.200701047 (pdf.file)

 E. Cherkaev and A. Cherkaev, Minimax optimization problem of structural design, International Journal of Computers and Structures, 2008, Vol 86/13-14, 1426-1435 (pdf file)

 

 D. Zhang, E. Cherkaev, Pade approximations for identification of air bubble volume from temperature- or frequency-dependent permittivity of a two-component mixture, Inverse Problems in Science and Engineering,  2008,  16, 4, pp. 425-445. 

 

 E. Cherkaev,  M.-J. Ou,  De-Homogenization: Reconstruction of moments of the spectral measure of composite, 2008 Inverse Problems 24 065008 (19pp), doi: 10.1088/0266-5611/24/6/065008 

 E. Cherkaev, A. Cherkaev, Robust optimal design for the worst case scenario, ECCM2006: III European Conference on Computational Mechanics, Solids, Structures, and Coupled Problems in Engineering, C.A.Mota Soares et al. (eds.), 2006, Springer Science.

 

 C. Bonifasi-Lista, E. Cherkaev, Identification of bone structure from effective measurements, III European Conf. on Computational Mechanics, Solids, Structures, C.A.Mota Soares et al. (eds.) 2006, Springer Science.

 C. Bonifasi-Lista, E. Cherkaev, Identification of bone microstructure from effective complex modulus, Vibration Problems ICOVP 2005, Springer Proceedings in Physics, Vol. 111, E. Inan, A. Kiris  (Eds.), 2006, pp. 91-96

 

 A. Cherkaev,  E. Cherkaev, L. Slepyan, Dynamics of structures with bistable links, Vibration Problems ICOVP 2005, Springer Proceedings in Physics, Vol. 111, E. Inan, A. Kiris  (Eds.), 2006, pp. 111-122.  

  M-J. Ou and E. Cherkaev, On the integral representation formula for a two-component elastic composite, Mathematical Methods in the Applied Sciences, 2006, Vol. 29, Issue 6, pp 655-664.

• A. Cherkaev, E. Cherkaev, L. Slepyan,  Transition waves in  bistable structures  I:  Delocalization of damage.  J. Mech. Phys. Solids,  v 53/2, pp 383-405, 2005 (pdf)
   
  
• L. Slepyan, A. Cherkaev,  E. Cherkaev,  Transition waves in  bistable  structures  II:  Analytical solution, wave speed, and energy dissipation. J. Mech. Phys. Solids, v  53/2, pp 407-436, 2005 (pdf)

• E. Cherkaev,  A. Cherkaev,  Principal compliance and robust optimal design, Journal of Elasticity, 2003, v.72, 71-98. Also in: The Rational Spirit in Modern Continuum Mechanics,  Essays and Papers Dedicated to the Memory of Clifford Ambrose Truesdell III, 2003 (pdf.file).
   
  
• E. Cherkaev, Spectral coupling of effective properties of a random mixture,  IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, A.B. Movchan, ed., Kluwer Academic Press, 2003, 304-313 (pdf.file)

• E. Cherkaev, D. Zhang, Coupling  of the effective properties  of a  random  mixture through the reconstructed spectral representation, ETOPIM Proceedings, Physica B, 2003, 338, 1-4, 16-23 (pdf.file)


• E. Cherkaev,  Inverse homogenization for evaluation of effective  properties of a mixture,  Inverse Problems, 2001, 17, 1203-1218  (pdf.file)


• H. Bertete-Aguirre, E. Cherkaev, M. Oristaglio,  Non-smooth gravity problem with total variation penalization functional,  Geophys. Journal International,  2002, 149, 499-507 (pdf.file)

• E. Cherkaev, A new inversion method for dissipating electromagnetic problem, Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation, A. Bermudez  et al., eds., SIAM, 2000, 637-642  (pdf.file)
 
•  E. Cherkaeva and K. Golden, Inverse bounds for microstructural  parameters of composite media derived from complex permittivity  measurements,  Waves in Random Media, 1998, 8, 437-450 (pdf.file)
  

• A. Cherkaev, E. Cherkaeva, Optimal design for uncertain loading conditions, Homogenization,  V. Berdichevsky, V. Jikov, and G.Papanicolaou, eds., World Scientific, 1999, 193-213 (pdf.file)
  
 
• A. Cherkaev, E. Cherkaeva, Structural optimization and biological "designs", Solid Mechanics and its Applications, v. 69: Synthesis in Bio Solid Mechanics, P. Pedersen and M.Bendsoe, eds., 1999, 247-264 (ps.file)

• H. Bertete-Aguirre, E. Cherkaeva,  M. Oristaglio, Non-smooth gravity problem.  68-th Ann. Meeting, Soc. Exploration Geophys., 1998 (ps.file)

•  K.M. Golden, D. Borup, M. Cheney, E. Cherkaeva, M.S. Dawson, Kung-Hau Ding, A.K. Fung, D. Isaacson, S.A. Johnson, A.K. Jordan, J.A. Kong, Ronald Kwok, Son V. Nghiem, R.G. Onstott, J.Sylvester, D.P. Winebrenner, I.H.H. Zabel, Inverse electromagnetic scattering for sea ice. IEEE Trans. on Geoscience and Remote Sensing, 1998, 36, 5, 1675-1704.

• E. Cherkaeva,  A.C. Tripp, On optimal design of transient electromagnetic waveforms. Expanded Abstracts, 67th Ann. Meeting, Soc. Exploration Geophys., 1997,  438-441 (ps.file)

• A.C. Tripp, E. Cherkaeva, J. Hulen, Bounds on the complex conductivity of geophysical mixtures. Geophysical Prospecting, 1998, 46, 6,  589-601 (pdf.file)

• E. Cherkaeva, A.C. Tripp, Source optimization in the inverse geoelectrical problem. In:  Inverse Problems in Geophysical Applications, eds. H.W. Engl, A. Louis, and W. Rundell, SIAM, Philadelphia, 1997,  240-256  ( pdf.file)
 
• E. Cherkaeva, Optimal source control and  resolution in nondestructive testing. Structural and Multidisciplinary Optimization,  1997,  13,  1,  12-16 (ps.file)
 
• E.Cherkaeva,  A.C. Tripp,  Optimal survey design using focused resistivity arrays.  IEEE, Trans. Geoscience and Remote Sensing, 1996, 34, 2, 358-366 (pdf.file)
 
• E. Cherkaeva, A.C. Tripp, Inverse conductivity problem for  inexact  measurements, Inverse Problems, 1996, 12, 869-883 (pdf.file)
 
• E. Cherkaeva, A. Cherkaev, Bounds for detectability of material damage by noisy electrical measurements.  In: Structural and Multidisciplinary Optimization,  N. Olhoff and G.I.N. Rozvany eds, Pergamon, 1995, 543-548 ( pdf.file).