# Random Media and Disordered Materials

**"Multiple Ginzburg-Landau Vortices Pinned by Randomly Distributed Small Holes"**(with V. Mityushev and S. D. Ryan),*submitted*(2016), pdf.**"Complexity reduction in many particles systems with random initial data"**(with P.E. Jabin, M. Potomkin),__SIAM/ASA Journal of Uncertainty Quantification__, 4(1), pp. 446-474 (2016), pdf.**"Rayleigh Approximation for ground states of the Bose and Coulomb glasses"**(with S. D. Ryan, V. Mityushev, and V. M. Vinokur),__Scientific Reports: Nature Publishing Group__, 5, 7821 (2015), pdf.**"Rise of Correlations of Transformation Strains in Random Polycrystals"**(with O. Bruno and A. Novikov),__SIAM J. Math. Analysis__, v.40, n.4, pp. 15501584 (2008).-
**"Ginzburg-Landau model of a liquid crystal with random inclusions"**(with E. Khruslov),__Journal of Mathematical Physics__, 46, pp. 095107:1-15 (2005), pdf. **"Discrete Network Approximation for Highly-Packed Composites with Irregular Geometry in Three Dimensions"**(with Y. Gorb and A. Novikov), in__Lecture Notes in Computational Science and Engineering__, editors B. Engquist, P. Lotstedt and O. Runborg, Springer Verlag (2004), pdf.**"Increase and Decrease of the Effective Conductivity of Two Phase Composites due to Polydispersity"**(with V. Mityushev),__Journal of Statistical Physics__, 118, 3/4 pp 481-509 (2005), pdf.**"Random network model for heat transfer in high contrast composite materials"**(with D. Gerenrot and J. Phillips),__IEEE Transactions on Advanced Packaging__, 26:4, pp. 410-417 (2003), pdf.**"Generalized Clausius-Mosotti formula for random composite with circular fibers"**(with V. Mityushev),__Journal of Statistical Physics__, 102, 1/2 pp. 115-145 (2001), pdf.**"Asymmetric Strain-Stress Distribution Function for Crystal with Random Point Defects"**In the book__Homogenization__, ed. V. Berdichevsky, V. Jikov and G. Papanicolaou, World Scientific, 179-192 (1999), pdf.**"First-Passage Percolation, Semi-Directed Bernoulli Percolation, and Failure in Brittle Materials"**(with M. Rintoul and S. Torquato)__Journal of Statistical Physics__, 91, 3/4, 603-623 (1998), pdf.**"Non-Gaussian Limiting Behavior of the Percolation Threshold in a Large System"**(with J.Wehr),__Communications in Mathematical Physics__, 185, 73-92 (1997), pdf.**"The Probability Distribution of the Percolation Threshold in a Large System"**(with J. Wehr),__Journal of Physics A: Mathematics and General__, 28:24, 7127-7133 (1995), pdf.**"The accuracy of O'Doherty-Anstey approximation for wave propagation in highly disordered stratiffied media"**(with R. Burridge),__Wave Motion__, 21:3, 357-373 (1995), pdf.**"Exact Result for the Effective Conductivity of a Continuum Percolation Model"**(with K. Golden),__Physical Review B__, 50 (4):2114-2117 (1994), pdf.**"Exactly solvable random model and IR spectroscopy of strained defective lattice"**(with N. Chukanov and V. Dubovitskii),__Chemical Physics Letters__, 181, No. 5:450-454 (1991), pdf.**"The localization problem for a random elastic continuum with dispersion"**(with S. Molchanov),__Mathematics Notes, USSR Academy__, 49, No. 3:346-348 (1991), pdf.