Related papers: Irregularity of polymer domain boundaries in two-d…
We study the complexity of geometric problems on spaces of low fractal dimension. It was recently shown by [Sidiropoulos & Sridhar, SoCG 2017] that several problems admit improved solutions when the input is a pointset in Euclidean space…
We consider various random models (directed polymer, random ferromagnets, spin-glasses) in their disorder-dominated phases, where the free-energy cost $F(L)$ of an excitation of length $L$ presents fluctuations that grow as a power-law…
We study the motion of an ideal incompressible fluid in a perforated domain. The porous medium is composed of inclusions of size $a$ separated by distances $\tilde d$ and the fluid fills the exterior. We analyse the asymptotic behavior of…
Motivated by the study of trace for Schramm-Loewner evolutions, we consider evolutions of planar domains governed by ordinary differential equations with holomorphic vector fields $F$ defined on the upper half plane $\mathbb{H}$. We show a…
The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of…
We present simulations that show that an ideal two-dimensional foam with a finite contact angle develops an inhomogeneity for high liquid fraction $\phi$. In liquid-liquid emulsions this inhomogeneity is known as flocculation. In the case…
We study the temporal growth pattern of surface fluctuations on a series of spinodally unstable polymer films where the degree of instability is controlled by the film thickness. For films in the deep spinodal region, the growth rate…
We study the depinning phase transition of a directed polymer in a $d$-dimensional space by a periodic potential localized on a straight line. We give exact formulas in all dimensions for the critical pinning we need to localize the…
We study directed polymers subject to a quenched random potential in d transversal dimensions. This system is closely related to the Kardar-Parisi-Zhang equation of nonlinear stochastic growth. By a careful analysis of the perturbation…
We show that a known condition for having rough basin boundaries in bistable 2D maps holds for high-dimensional bistable systems that possess a unique nonattracting chaotic set embedded in their basin boundaries. The condition for roughness…
Diffusion properties of a self-avoiding polymer embedded in regularly distributed obstacles with spacing a=20 and confined in two dimensions is studied numerically using the extended bond fluctuation method which we have developed recently.…
Perfectly Matched Layers (PML) has become a very common method for the numerical approximation of wave and wave-like equations on unbounded domains. This technique allows one to obtain accurate solutions while working on a finite…
Nominal two-dimensional (2D) shear layers have been studied extensively, and their principal dynamics are well understood. In practical configurations, however, the behavior of such shear layers is affected by proximal surfaces. In this…
In this work, we have studied the temporal evolution of some properties of a sample of superactive regions with the aim to single out the most significant for flare activity forecasting. We have investigated properties of 14 superactive…
Incompressible 3D Euler equations develop high vorticity in very thin pancake-like regions from generic large-scale initial conditions. In this work we propose an exact solution of the Euler equations for the asymptotic pancake evolution.…
By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…
This study reports a general scenario for the out-of-equilibrium features of collapsing polymeric architectures. We use molecular dynamics simulations to characterize the coarsening kinetics, in bad solvent, for several macromolecular…
The paper presents a short overview of the theoretical, numerical and experimental works on the critical behavior of a dilute polymer solution of long-flexible polymer chains confined in semi-infinite space restricted by a surface or in a…
We use Langevin dynamics (LD) simulations to investigate single-file diffusion (SFD) in a dilute solution of flexible linear polymers inside a narrow tube with periodic boundary conditions (a torus). The transition from SFD, where the time…
We establish the regularity results for solutions of nonlocal Venttsel' problems in polygonal and piecewise smooth two-dimensional domains.