Berlyand, Leonid, Owhadi, Houman
We consider divergence-form (elliptic, parabolic and hyperbolic) equations (or systems of equations for elasticity) with rough ($L^\infty(\Omega)$, $\Omega \subset \R^d$) coefficients that, in...
An atomistic to continuum model for biopolymers self-assembled aggregation (2009)
Berlyand, Leonid, Fedorov, Maxim V., Zhang, Lei
We want to address the following problem of hierarchical modeling of the structure of biopolymer self-assembly, and relate the marcoscale mechanical and geometrical property to their microscale...
Rise of correlations of transformation strains in random polycrystals (2008)
Berlyand, Leonid, Bruno, Oscar, Novikov, Alexei
We investigate the statistics of the transformation strains that arise in random martensitic polycrystals as boundary conditions cause its component crystallites to undergo martensitic phase...
Effective Viscosity of Dilute Bacterial Suspensions: A Two-Dimensional Model (2008)
Haines, Brian M., Aranson, Igor S., Berlyand, Leonid, Karpeev, Dmitry A.
Suspensions of self-propelled particles are studied in the framework of two-dimensional (2D) Stokesean hydrodynamics. A formula is obtained for the effective viscosity of such suspensions in the...
Two-parameter homogenization for a Ginzburg-Landau problem in a perforated domain (2008)
Berlyand, Leonid, Mironescu, Petru
Let $A$ be an annular type domain in $\R^2$. Let $A_\delta$ be a perforated domain obtained by punching periodic holes of size $\delta$ in $A$; here, $\delta$ is sufficiently small. Suppose that $\J$...
Two-parameter homogenization for a Ginzburg-Landau problem in a perforated domain (2008)
Berlyand, Leonid, Mironescu, Petru
Let $A$ be an annular type domain in $\R^2$. Let $A_\delta$ be a perforated domain obtained by punching periodic holes of size $\delta$ in $A$; here, $\delta$ is sufficiently small. Suppose that $\J$...
A network model for granular statics with impenetrability constraints (2006)
Ariyawansa, K. A., Berlyand, Leonid, Panchenko, Alexander
We study quasi-static deformation of dense granular packings. The packing is deformed by imposing external boundary conditions, which model engineering experiments such as shear and compression. We...
Berlyand, Leonid, Gorb, Yuliya, Novikov, Alexei
We present a two-dimensional (2D) mathematical model of a highly concentrated suspension or a thin film of the rigid inclusions in an incompressible Newtonian fluid. Our objectives are two-fold: (i)...
Berlyand, Leonid, Golovaty, Dmitry, Rybalko, Volodymyr
Suppose that $\omega\subset\Omega\subset R^2$. In the annular domain $A=\Omega\setminus\bar\omega$ we consider the class $J$ of complex valued maps having degree 1 on $\partial \Omega$ and on...
Berlyand, Leonid, Panchenko, Alexander
We study effective shear viscosity $\mu^\star$ and effective extensional viscosity $\lambda^\star$ of concentrated non-colloidal suspensions of rigid spherical particles. The focus is on the...
Berlyand, Leonid, Golovaty, Dmitry, Movchan, Alexander, Phillips, Jonathan
We analyse transport properties of fluid/solid and solid/solid composites containing finite arrays of closely spaced rigid inclusions when a host medium is either an elastic matrix or an...