Leonid Berlyand

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Leonid Berlyand is affiliated with the following schools: Pennsylvania State University, National University of Kharkiv

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Leonid Berlyand

Mathematics

#1880

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#2986

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Measure Theory

#4140

World Rank

#4878

Historical Rank

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Mathematics

Why Is Leonid Berlyand Influential?

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According to Wikipedia, Leonid Berlyand is a Soviet and American mathematician, a professor of Penn State University. He is known for his works on homogenization, Ginzburg–Landau theory, mathematical modeling of active matter and mathematical foundations of deep learning.

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Leonid Berlyand's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization (2012) (136)
Flux Norm Approach to Finite Dimensional Homogenization Approximations with Non-Separated Scales and High Contrast (2009) (104)
Three-dimensional model for the effective viscosity of bacterial suspensions. (2009) (89)
Network Approximation in the Limit of¶Small Interparticle Distance of the¶Effective Properties of a High-Contrast¶Random Dispersed Composite (2001) (87)
Generalized Clausius–Mossotti Formula for Random Composite with Circular Fibers (2001) (86)
Viscosity of bacterial suspensions: hydrodynamic interactions and self-induced noise. (2011) (85)
Effective viscosity of dilute bacterial suspensions: a two-dimensional model (2008) (60)
Introduction to the Network Approximation Method for Materials Modeling (2013) (47)
A Model of Hydrodynamic Interaction Between Swimming Bacteria (2008) (45)
Correlation properties of collective motion in bacterial suspensions (2013) (42)
Increase and Decrease of the Effective Conductivity of Two Phase Composites due to Polydispersity (2005) (40)
Error of the Network Approximation for Densely Packed Composites with Irregular Geometry (2002) (34)
Ginzburg-Landau minimizers with prescribed degrees. Capacity of the domain and emergence of vortices (2006) (33)
On uniqueness of vector-valued minimizers of the Ginzburg-Landau functional in annular domains (2002) (32)
Strong and weak blow-up of the viscous dissipation rates for concentrated suspensions (2007) (31)
Network Approximation for Effective Viscosity of Concentrated Suspensions with Complex Geometry (2005) (29)
Flexibility of bacterial flagella in external shear results in complex swimming trajectories (2015) (28)
The accuracy of the O'Doherty-Anstey approximation for wave propagation in highly disordered stratified media (1995) (28)
Asymptotics of the effective conductivity of composites with closely spaced inclusions of optimal shape (2005) (27)
Symmetry Breaking in Annular Domains for a Ginzburg-Landau Superconductivity Model (2001) (26)
Effective shear viscosity and dynamics of suspensions of micro-swimmers from small to moderate concentrations (2011) (26)
Large time asymptotics of solutions to a model combustion system with critical nonlinearity (1995) (23)
Solutions with vortices of a semi-stiff boundary value problem for the Ginzburg–Landau equation (2007) (22)
Minimax Critical Points in Ginzburg-Landau Problems with Semi-Stiff Boundary Conditions: Existence and Bubbling (2014) (21)
Effective viscosity of bacterial suspensions: a three-dimensional PDE model with stochastic torque. (2011) (20)
Nonexistence of Ginzburg-Landau minimizers with prescribed degree on the boundary of a doubly connected domain (2006) (20)
Continuum limit for three-dimensional mass-spring networks and discrete Korn's inequality (2006) (19)
A Kinetic Model for Semidilute Bacterial Suspensions (2013) (18)
Random network model for heat transfer in high contrast composite materials (2003) (18)
Fictitious Fluid Approach and Anomalous Blow-up of the Dissipation Rate in a 2D Model of Concentrated Suspensions (2006) (17)
The averaging of the diffusion equation in a porous medium with weak absorption (1990) (16)
Asymptotics of the homogenized moduli for the elastic chess-board composite (1992) (15)
Discrete network approximation for highly-packed composites with irregular geometry in three dimensions (2005) (15)
Ginzburg-Landau minimizers in perforated domains with prescribed degrees (2008) (15)
Homogenization of a Ginzburg–Landau model for a nematic liquid crystal with inclusions (2005) (15)
Global minimizers for a p-Ginzburg-Landau-type energy in R 2 (2009) (14)
Homogenized Non-Newtonian Viscoelastic Rheology of a Suspension of Interacting Particles in a Viscous Newtonian Fluid (2004) (14)
Rayleigh approximation to ground state of the Bose and Coulomb glasses (2015) (14)
Two-parameter homogenization for a Ginzburg-Landau problem in a perforated domain (2008) (13)
Fictitious Fluid Approach and Anomalous Blow-up of the Dissipation Rate in a Two-Dimensional Model of Concentrated Suspensions (2009) (13)
The probability distribution of the percolation threshold in a large system (1995) (13)
Collision of microswimmers in a viscous fluid. (2013) (13)
On an evolution equation in a cell motility model (2015) (13)
Focusing of active particles in a converging flow (2017) (12)
Effective viscosity of puller-like microswimmers: a renormalization approach (2013) (12)
Bifurcation of traveling waves in a Keller-Segel type free boundary model of cell motility (2017) (11)
Frequency-Dependent Acoustics of Composites with Interfaces (2000) (10)
Surface anchoring controls orientation of a microswimmer in nematic liquid crystal (2020) (10)
Homogenization of Harmonic Maps and Superconducting Composites (1999) (10)
Sharp interface limit in a phase field model of cell motility (2014) (10)
Ginzburg-Landau minimizers with prescribed degrees . Emergence of vortices and existence / nonexistence of the minimizers (2006) (9)
Phase-Field Model of Cell Motility: Traveling Waves and Sharp Interface Limit (2016) (9)
Vortex phase separation in mesoscopic superconductors (2013) (9)
Ginzburg–Landau minimizers with prescribed degrees: dependence on domain (2003) (8)
Complexity Reduction in Many Particle Systems with Random Initial Data (2013) (8)
Flagella bending affects macroscopic properties of bacterial suspensions (2016) (8)
Nonlinear dielectric response of periodic composite materials (2007) (8)
TRANSPORT PROPERTIES OF DENSELY PACKED COMPOSITES. EFFECT OF SHAPES AND SPACINGS OF INCLUSIONS (2004) (8)
Radially symmetric minimizers for a p-Ginzburg Landau type energy in $${\mathbb R^2}$$ (2011) (7)
Self‐Propulsion and Shear Flow Align Active Particles in Nozzles and Channels (2020) (7)
Radially symmetric minimizers for a $p$-Ginzburg Landau type energy in $\R^2$ (2010) (7)
Exactly solvable random model and IR spectroscopy of a strained defective lattice (1991) (7)
A new approach to homogenization with arbitrarily rough and high contrast coefficients for scalar and vectorial problems (2009) (7)
Homogenization of the Ginzburg-Landau functional with a surface energy term (1999) (7)
The homogenized model of small oscillations of complex fluids (2008) (6)
Ginzburg–Landau model of a liquid crystal with random inclusions (2005) (6)
Global Energy Matching Method for Atomistic-to-Continuum Modeling of Self-Assembling Biopolymer Aggregates (2010) (6)
Minimizers of the magnetic Ginzburg-Landau functional in simply connected domain with prescribed degree on the boundary (2011) (6)
Near boundary vortices in a magnetic Ginzburg-Landau model: their locations via tight energy bounds (2010) (6)
Competition between the surface and the boundary layer energies in a Ginzburg–Landau model of a liquid crystal composite (2002) (6)
A KINETIC MODEL FOR SEMI-DILUTE BACTERIAL SUSPENSIONS (2013) (6)
Effective Properties of Superconducting and Superfluid Composites (1998) (5)
Effective elastic moduli of a soft medium with hard polygonal inclusions and extremal behavior of effective Poisson's ratio (1995) (5)
Homogenized description of multiple Ginzburg-Landau vortices pinned by small holes (2013) (5)
Effective Rheological Properties in Semi-dilute Bacterial Suspensions (2015) (5)
Minimal model of directed cell motility on patterned substrates. (2017) (5)
Asymptotic analysis of an array of closely spaced absolutely conductive inclusions (2006) (5)
A new approach to homogenization with arbitrarily rough coefficients for scalar and vectorial problems with localized and global pre-computing (2009) (4)
Existence and stability of superconducting solutions for the Ginzburg-Landau equations in the presence of weak electric currents (2014) (4)
On the convergence of formally diverging neural net-based classifiers (2018) (4)
Stability for the Training of Deep Neural Networks and Other Classifiers (2020) (4)
Non-Gaussian Limiting Behavior of the Percolation Threshold in a Large System (1997) (4)
Stability of steady states and bifurcation to traveling waves in a free boundary model of cell motility (2019) (4)
Continuum Approximations to Systems of Correlated Interacting Particles (2018) (4)
First-Passage Percolation, Semi-Directed Bernoulli Percolation, and Failure in Brittle Materials (1998) (4)
A two scale (cid:2) -convergence approach for random non-convex homogenization (2016) (3)
Getting Acquainted with Homogenization and Multiscale (2018) (3)
Capacity of a multiply-connected domain and nonexistence of Ginzburg-Landau minimizers with prescribed degrees on the boundary. (2006) (3)
The Effective Conductivity of Densely Packed High Contrast Composites With Inclusions of Optimal Shape (2004) (3)
On approximation of Ginzburg–Landau minimizers by S1-valued maps in domains with vanishingly small holes (2018) (2)
Emergence of traveling waves and their stability in a free boundary model of cell motility (2021) (2)
A network model of geometrically constrained deformations of granular materials (2008) (2)
A two scale $$\Gamma $$Γ-convergence approach for random non-convex homogenization (2016) (2)
A Kinetic Approach to Active Rods Dynamics in Confined Domains (2019) (2)
Effective shear viscosity and dynamics of suspensions of micro-swimmers at moderate concentrations (2009) (2)
Non-uniqueness in a nonlinear sharp interface model of cell motility (2014) (2)
Existence of Superconducting Solutions for a Reduced Ginzburg-Landau Model in the Presence of Strong Electric Currents (2016) (2)
Homogenization of a Ginzburg–Landau functional (2005) (1)
Renormalized Ginzburg-Landau energy and location of near boundary vortices (2012) (1)
Rise of Correlations of Transformation Strains in Random Polycrystals (2008) (1)
Introduction to the Network Approximation Method for Materials Modeling: Application of the method of complex variables (2012) (1)
Introduction to Stochastic Homogenization (2018) (1)
Dynamics and steady state of squirmer motion in liquid crystal (2022) (1)
Introduction to the Network Approximation Method for Materials Modeling: References (2012) (1)
Asymptotic stability of contraction-driven cell motion. (2021) (1)
Reactivity of crystals with defects (1990) (1)
Pinning by holes of multiple vortices in homogenization for Ginzburg-Landau problems (2011) (1)
Interaction of microswimmers in viscoelastic liquid crystals (2022) (1)
Finite dimensional approximation of solutions of divergence form equations with rough and high contrast coefficients (2009) (1)
Kinetic models of swimming bacteria in semi-dilute limit Project : Coarse-graining techniques for modeling highly heterogeneous complex biomaterials (2011) (0)
Modeling of collective swimming in random bacterial suspensions (2012) (0)
Numerics for percolation and polydispersity via network models (2012) (0)
Γ-Convergence in Nonlinear Homogenization Problems (2018) (0)
Two-parameter homogenization for a GL problem in a perforated domain (2006) (0)
Effective shear and extensional viscosities of concentrated disordered suspensions of rigid particles. (2004) (0)
Coarse-graining computation of collective swimming in biosuspensions. Project: Coarse-graining techniques for modeling highly heterogeneous complex biomaterials (2011) (0)
Formal Two-Scale Asymptotic Expansions and the Corrector Problem (2018) (0)
Boundary conditions in PDE model of collisions of swimmers (2012) (0)
Eeective Elastic Moduli of a Soft Medium with Hard Polygonal Inclusions and Extremal Behavior of Eeective Poisson's Ratio (1995) (0)
PDE models of collective swimming in bacterial suspensions (2012) (0)
Phase field model of cell motility : sharp interface limit in subcritical case (0)
Continuum Approximations to Systems of Correlated Interacting Particles (2018) (0)
EngagedScholarship@CSU EngagedScholarship@CSU A Kinetic Model for Semidilute Bacterial Suspensions A Kinetic Model for Semidilute Bacterial Suspensions (2020) (0)
An Atomistic to Continuum Model for Biopolymers Self-Assembled Aggregation (2009) (0)
On approximation of Ginzburg-Landau minimizers by $\mathbb S^1$-valued maps in domains with vanishingly small holes (2017) (0)
Supplementary material from "Flagellar bending affects macroscopic properties of bacterial suspensions" (2017) (0)
COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: The asymptotic behaviour of solutions of the first boundary-value problem of elasticity theory in domains with a finely-grained boundary (1983) (0)
Examples of Explicit Effective Coefficients: Laminated Structures and 2D Checkerboards (2018) (0)
ASYMMETRIC STRAIN-STRESS DISTRIBUTION FUNCTION FOR CRYSTAL WITH RANDOM POINT DEFECTS (1999) (0)
Network method for nonlinear composites (2012) (0)
On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau system (2019) (0)
Mini-Workshop: PDE Models of Motility and Invasion in Active Biosystems (2018) (0)
A MODEL FOR GRANULAR STATICS WITH IMPENETRABILITY CONSTRAINTS (0)
Effective Rheological Properties in Semi-dilute Bacterial Suspensions (2016) (0)
Finite Dimensional Approximations for Continuum Multiscale Problems (2017) (0)
Introduction to the Network Approximation Method for Materials Modeling: Background and motivation for the introduction of network models (2012) (0)
Homogenization of harmonic maps with large number of vortices and applications in superconductivity and superfluidity (2001) (0)
Vortex phase separation in mesoscopic (2013) (0)
The localization problem for a random elastic continuum with dispersion (1991) (0)
Network approximation for boundary-value problems with discontinuous coefficients and a finite number of inclusions (2012) (0)
Multiple Ginzburg–Landau vortices pinned by randomly distributed small holes (2018) (0)
An Example of a Nonlinear Problem: Homogenization of Plasticity and Limit Loads (2018) (0)
Emergence of traveling waves and their stability analysis in a free boundary model of cell motility (2020) (0)
What Is Homogenization and Multiscale? First Examples (2018) (0)
On the limit p → ∞ of global minimizers for a p-Ginzburg-Landau-type energy (2013) (0)
Introduction to the Network Approximation Method for Materials Modeling: Review of mathematical notions used in the analysis of transport problems in densely-packed composite materials (2012) (0)
Focusing of Active Rods in a Converging Flow (2018) (0)
Effect Of Shapes And Spacings Of Inclusions OnTransport Properties Of Densely PackedComposites (2003) (0)
Compensated Compactness and Oscillating Test Functions (2018) (0)
Renormalization Group Technique for Asymptotic Behavior of a Thermal Diffisive Model with Critical Nonlinearity (2007) (0)
Brief History and Surprising Examples in Homogenization (2018) (0)
Modeling of collective swimming of bacteria (2011) (0)
Two-Scale Convergence (2018) (0)
A novel multi-scale loss function for classification problems in machine learning (2021) (0)
Phase field model of cell motility: sharp interface limit in sub-critical case (2013) (0)
Flux Norm Approach to Homogenization Problems with non-separated Scales (2009) (0)
The network approximation theorem for an infinite number of bodies (2012) (0)
Flagella bending aﬀects macroscopic properties of bacterial suspensions Electronic Supplementary Material (2017) (0)
Continuum Limits for Discrete Problems with Fine Scales (2018) (0)
Surface anchoring controls orientation of a microswimmer in nematic liquid crystal (2020) (0)
Numerical homogenization on approach for stokesian suspensions. (2012) (0)
A network model for granular statics with impenetrability constraints (2006) (0)
Network approximation for potentials of bodies (2012) (0)

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