Leonid Berlyand

Leonid Berlyand is a Soviet and American mathematician. He is known for his works on homogenization and Ginzburg–Landau theory.

Leonid Berlyand
BornSeptember 20, 1957
Kharkov, Ukraine
NationalityUSSR, then United States
Alma materNational University of Kharkov
Known forworks on homogenization
Scientific career
FieldsApplied mathematics, homogenization, mathematical biology
InstitutionsNational University of Kharkov, Semenov Institute of Chemical Physics, Penn State University
Doctoral advisorEvgeny Khruslov

Life and career

Berlyand was born in Kharkov on September 20, 1957. His father, Viktor Berlyand, was a mechanical engineer, and his mother, Mayya Genkina, an electronics engineer. Upon his graduation in 1979 from the department of mathematics and mechanics at the National University of Kharkov, he began his doctoral studies at the same university and earned a Ph. D. in 1984. His Ph. D. thesis studied the homogenization of elasticity problems. He worked at the Semenov Institute of Chemical Physics in Moscow. In 1991 he moved to the United States and started working at Pennsylvania State University, where he has served as a full professor since 2003. He has held long-term visiting positions at Princeton University, the California Institute of Technology, the University of Chicago, the Max Planck Institute for Mathematics in the Sciences, Argonne and Los Alamos National Laboratories. His research has drawn support from the National Science Foundation(NSF),[1] NIH/NIGMS,[2] the Applied Mathematics Program of the DOE Office of Sciences,[3] BSF (the Bi-National Science Foundation USA-Israel)[4] and the NATO Science for Peace and Security Section. Berlyand has authored roughly 100 works on homogenization theory and PDE/variational problems in biology and material science. He has organized a number of professional conferences and serves as a co-director of the Center for Mathematics of Living and Mimetic Matter at Penn State University. He has supervised 17 graduate students and ten postdoctoral fellows.[5][6]

Research

Drawing upon fundamental works in classical homogenization theory, Berlyand advanced the methods of homogenization in many versatile applications. He obtained mathematical results applicable to diverse scientific areas including biology, fluid mechanics, superconductivity, elasticity, and material science. His mathematical modeling explains striking experimental result in the collective swimming of bacteria.[7] His homogenization approach to multi-scale problems was transformed into a practical computational tool by introducing a concept of polyharmonic homogenization which led to a new type of multiscale finite elements.[8] Together with H. Owhadi, he introduced a "transfer-of-approximation" modeling concept, based on the similarity of the asymptotic behavior of the errors of Galerkin solutions for two elliptic PDEs.[9][10] He also contributed to mathematical aspects of the Ginzburg–Landau theory of superconductivity/superfluidity by introducing a new class of semi-stiff boundary problems.[11]

Awards and honors

Membership in professional associations

Editorship

Books (author)
  • "Introduction to Network Approximation for Materials Modeling" (with A. Kolpakov and A. Novikov), Cambridge University Press, 2012.
  • "Getting Acquainted with Homogenization and Multiscale" (with V. Rybalko), part of the Compact Textbooks in Mathematics book series, Springer, 2018.

Selected publications
  • "Phase-Field Model of Cell Motility: Traveling Waves and Sharp Interface Limit" (with M. Potomkin and V. Rybalko), Comptes Rendus Mathématique, 354(10), pp. 986–992 (2016)
  • "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)
  • "Flexibility of bacterial flagella in external shear results in complex swimming trajectories" (with M. Tournus, A. Kirshtein, and I. Aranson), Journal of the Royal Society Interface 12 (102) (2014)
  • "Vortex phase separation in mesoscopic superconductors" (with O. Iaroshenko, V. Rybalko, V. M. Vinokur), Scientific Reports: Nature Publishing Group 3 (2013)
  • "Effective viscosity of bacterial suspensions: A three-dimensional PDE model with stochastic torque" (with B.M. Haines, I.S. Aranson, D.A. Karpeev), Comm. Pure Appl. Anal., v. 11(1), pp. 19–46 (2012)
  • "Flux norm approach to finite dimensional homogenization approximations with non-separated scales and high contrast" (with H. Owhadi), Arch. Rat. Mech. Anal. , v. 198, n. 2, pp. 677–721 (2010)
  • "Solutions with Vortices of a Semi-Stiff Boundary Value Problem for the Ginzburg-Landau Equation" (with V. Rybalko), J. European Math. Society v. 12 n. 6, pp. 1497–1531 (2009)
  • "Fictitious Fluid Approach and Anomalous Blow-up of the Dissipation Rate in a 2D Model of Concentrated Suspensions" (with Y. Gorb and A. Novikov), Arch. Rat. Mech. Anal., v. 193, n. 3, pp. 585–622, (2009), DOI:10.1007/s00205-008-0152-2
  • "Effective Viscosity of Dilute Bacterial Suspensions: A Two-Dimensional Model" (with B. Haines, I. Aronson, and D. Karpeev), Physical Biology, 5:4, 046003 (9pp) (2008)
  • "Ginzburg-Landau minimizers with prescribed degrees. Capacity of the domain and emergence of vortices" (with P. Mironescu), Journal of Functional Analysis, v. 239, n. 1, pp. 76–99 (2006)
  • "Network Approximation in the Limit of Small Interparticle Distance of the Effective Properties of a High-Contrast Random Dispersed Composite" (with A. Kolpakov), Archive for Rational Mechanics and Analysis, 159, pp. 179–227 (2001)
  • "Non-Gaussian Limiting Behavior of the Percolation Threshold in a Large System" (with J.Wehr), Communications in Mathematical Physics, 185, 73–92 (1997), pdf.
  • "Large Time Asymptotics of Solutions to a Model Combustion System with Critical Nonlinearity" (with J. Xin), Nonlinearity, 8:161–178 (1995)
  • "Asymptotics of the Homogenized Moduli for the Elastic Chess-Board Composite" (with S. Kozlov), Archive for Rational Mechanics and Analysis, 118, 95–112 (1992)

References
  1. One of NSF-DMREF grants
  2. Berlyand's NIH/NSF grants
  3. One of the DOE grants
  4. One of BSF gants
  5. Berlyand on the site of the Sports Concussion Research Center at the Penn State University
  6. Berlyand's personal page at the site of the Penn State University
  7. L. Berlyand, M. Tournus, A. Kirshtein, I. Aranson. Flexibility of bacterial flagella in external shear results in complex swimming trajectories, Journal of the Royal Society Interface 12 (102) (2014)
  8. H. Owhadi, L. Zhang, L. Berlyand, Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization, ESAIM: Mathematical Modelling and Numerical Analysis. Special issue, 48 (2), pp. 517–552 (2014)
  9. William W. Symes, Xin Wang. Subgrid wave modeling by transfer‐of‐approximation. SEG Technical Program Expanded Abstracts 2011: pp. 2909–2914
  10. X. Wang. Transfer-of-approximation Approaches for Subgrid Modeling, Ph. D. Thesis, Rice University
  11. L. Berlyand, V. Rybalko. Solutions with Vortices of a Semi-Stiff Boundary Value Problem for the Ginzburg-Landau Equation, J. European Math. Society v. 12 n. 6, pp.1497–1531 (2009)
  12. "Former Winners of the C. I. Noll Award for Excellence in Teaching — Eberly College of Science". science.psu.edu. Retrieved 2017-11-26.
  13. Seminar "Time, chaos and mathematics" at the Moscow State University
  14. Berlyand's award at the Twitter of the Penn State University
  15. Berlyand in the list of managing editors of Networks&Heterogeneous media
  16. Berlyand in the list of the Editorial Board of the International Journal for Multiscale Computational Engineering
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