Related papers: Maze solvers demystified and some other thoughts
Similarity solutions play an important role in many fields of science. The recent book of Barenblatt (1996) discusses many examples. Often, outstanding unresolved issues are whether a similarity solution is dynamically attractive, and if it…
How finite-sized material lines stretch in chaotic (mono-scale) and turbulent (multi-scale) flows remains a central but unresolved problem that governs mixing, transport and reaction. We show elongation is controlled by a finite-sampling…
Computing a polygon defining a set of planar points is a classical problem of modern computational geometry. In laboratory experiments we demonstrate that a concave hull, a connected alpha-shape without holes, of a finite planar set is…
We study the new geometric flow that was introduced in [11] that evolves a pair of map and (domain) metric in such a way that it changes appropriate initial data into branched minimal immersions. In the present paper we focus on the…
Drop condensation and evaportation as a result of the gradient in vapor concentration are important in both engineering and natural systems. One of the interesting natural examples is transpiration on plant leaves. Most of water in the…
We report a new type of drop instability, where the density difference between the drop and the solvent is negative. We show that the drop falls inside the solvent down to a minimum height, then fragmentation takes place and secondary…
In this work we study and expand a model describing the dynamics of a unicellular slime mold, Physarum Polycephalum (PP), which was proposed to simulate the ability of PP to find the shortest path connecting two food sources in a maze. The…
We prove local well-posedness for the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable…
We present a mechanistic model of drug release from a multiple emulsion into an external surrounding fluid. We consider a single multi-layer droplet where the drug kinetics are described by a pure diffusive process through different liquid…
A multicomponent extension of our recent theory of simple fluids [ U.M.B. Marconi and S. Melchionna, Journal of Chemical Physics, 131, 014105 (2009) ] is proposed to describe miscible and immiscible liquid mixtures under inhomogeneous, non…
Mathematical modeling is an important theoretical tool which provides researchers with quantification of the permeability of dialyzing systems in renal replacement therapy. In the paper we provide a short review of the most successful…
Over the last two decades, scientific literature has been blooming with various means of simulating epithelial cell colonies. Each of these simulations can be separated by their respective efficiency (expressed in terms of consumed…
We analyze response of a macromolecule near to a substrate; the substrate is tiled in the sequential and specific manner so that repeat units of the macromolecule may have different response on its adsorption in different directions onto…
We consider a situation commonly encountered in microfluidics: two streams of miscible liquids are brought at a junction to flow side by side within a microchannel, allowing solutes to diffuse from one stream to the other and possibly…
Recent studies suggest that cosolute mixtures may exert significant non-additive effects upon protein stability. The corresponding liquid-vapor interfaces may provide useful insight into these non-additive effects. Accordingly, in this work…
This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation. The solution properties of this regularization are investigated via a sequence of numerical simulations whose…
The experimental literature on the motion of mesoscopic probe particles through polymer solutions is systematically reviewed. The primary focus is the study of diffusive motion of small probe particles. Comparison is made with measurements…
The electrolyte (comprising of solute ions and solvents) flow-through the porous media is frequently encountered in nature or in many engineering applications, such as the electrochemical systems, manufacturing of composites, oil…
Liquid phase exfoliation (LPE) is the most promising method for the low-cost, scalable production of two-dimensional nanosheets from their bulk counterparts. Extensive exfoliation occurs in most solvents due to the huge amount of energy…
Streamer electrical discharges are often investigated with computer simulations of density models (also called drift-diffusion-reaction models). We review these models, detailing their physical foundations, their range of validity and the…