Related papers: Maze solvers demystified and some other thoughts
Nature is remarkably adept at using interfaces to build structures, encapsulate reagents, and regulate biological processes. Inspired by Nature, we describe flexible polymer-based ribbons, termed "mesoscale polymers" (MSPs), to modulate…
The dynamics of biological polymers, including proteins, RNA, and DNA, occur in very high-dimensional spaces. Many naturally-occurring polymers can navigate a vast phase space and rapidly find their lowest free energy (folded) state. Thus,…
In this paper we have discussed a unique general algorithm for exploring and solving any kind of line maze with another simple one for simple mazes without loops or loops having highest two branches none of which are inward. For the general…
Minimal surface problems arise naturally in many soft matter systems whose free energies are dominated by surface or interface energies. Of particular interest are the shapes, stability and mechanical stresses of minimal surfaces spanning…
We review recent advances in the design, synthesis, and modeling of active fluids. Active fluids have been at the center of many technological innovations and theoretical advances over the past two decades. Research on this new class of…
Microfluidic multipoles (MFMs) have been realized experimentally and hold promise for "open-space" biological and chemical surface processing. Whereas convective flow can readily be predicted using hydraulic-electrical analogies, the design…
Diffusive motion of regulatory enzymes on biopolymers with eventual capture at a reaction site is a common feature in cell biology. Using a lattice gas model we study the impact of diffusion and capture for a microtubule polymerase and a…
Incompressible flows can be effective mixers by appropriately advecting a passive tracer to produce small filamentation length scales. In addition, diffusion is generally perceived as beneficial to mixing due to its ability to homogenise a…
The capability to accurately predict flood flows via numerical simulations is a key component of contemporary flood risk management practice. However, modern flood models lack the capacity to accurately model flow interactions with linear…
We study a reaction-diffusion model posed on two distinct spatial scales that accounts for diffusion, aggregation, fragmentation, and deposition of populations of colloidal particles within a porous material. In this model, the macroscopic…
Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
We study the flow of fluid in porous media in dimensions $d=2$ and 3. The medium is modeled by bond percolation on a lattice of $L^d$ sites, while the flow front is modeled by tracer particles driven by a pressure difference between two…
We study the long-time behavior of the solutions of a two-component reaction-diffusion system on the real line, which describes the basic chemical reaction $A <=> 2 B$. Assuming that the initial densities of the species $A, B$ are bounded…
We theoretically study physical properties of one-dimensionally and regularly placed solutes. The solute is rigid-body, has arrow-like shape, and changes its direction up or down. If the solutes are immersed in continuum solvent, nothing…
The effective mixing behavior of solutes in porous media is fundamentally connected to the development of a local mixing interface between the two initial solutions, which is characterized by a complex lamellar structure. The deformation of…
We consider the evolution of fronts by mean curvature in the presence of obstacles. We construct a weak solution to the flow by means of a variational method, corresponding to an implicit time-discretization scheme. Assuming the regularity…
Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it…
Hypothesis Understanding the scission of rod-like micelles under mechanical forces is crucial for optimizing their stability and behavior in industrial applications. This study investigates how micelle length, flexibility, and external…
Mixing describes the process by which solutes evolve from an initial heterogeneous state to uniformity under the stirring action of a fluid flow. Fluid stretching forms thin scalar lamellae which coalesce due to molecular diffusion. Owing…