Related papers: Effective medium theory of permeation through idea…
We study the diffusion process through an ideal polymer network, using numerical methods. Polymers are modeled by random walks on the bonds of a two-dimensional square lattice. Molecules occupy the lattice cells and may jump to the…
We develop an effective medium approach to the mechanics of disordered, semiflexible polymer networks and study the response of such networks to uniform and nonuniform strain. We identify distinct elastic regimes in which the contributions…
Disordered spring networks can exhibit rigidity transitions, due to either the removal of materials in over-constrained networks or the application of strain in under-constrained ones. While an effective medium theory (EMT) exists for the…
We study epidemic processes using a metapopulation approach on the line featuring random transport rates between arbitrarily distant sites. An average transport network is found using a recently developed variant of the effective medium…
We formulate an effective medium (mean field) theory of a material consisting of randomly distributed nodes connected by straight slender rods, hinged at the nodes. Defining novel wavelength-dependent effective elastic moduli, we calculate…
Transfer matrix theory (TMT) is used to study the effective-medium theory (EMT) of one dimensional metamaterials (1D MMs). 1D MMs with equal diagonal elements of periodic transfer matrix are defined as 1D perfect MMs (1D PMMs), which can be…
Recent experimental observations of anisotropic conductivity in stretched polymer electrolytes films of the polyethylene oxide family are discussed. The main experimental observations, enhancement of the ionic diffusion and conductivity in…
Effective medium theory of transport in disordered systems, whose basis is the replacement of spatial disorder by temporal memory, is extended in several practical directions. Restricting attention to a 1-dimensional system with bond…
The convergence between effective medium theory and pore-network modelling is examined. Electrical conductance on two and three-dimensional cubic resistor networks is used as an example of transport through composite materials or porous…
Here, we present an overview of recent developments in the characterization of electromagnetic and quantum metamaterials using effective medium methods. It is highlighted that both electromagnetic and electronic systems can be homogenized…
We study the diffusion of gas molecules through a two-dimensional network of polymers with the help of Monte Carlo simulations. The polymers are modeled as non-interacting random walks on the bonds of a two-dimensional square lattice, while…
We consider the random walk on a lattice with random transition rates and arbitrarily long-range jumps. We employ Bruggeman's effective medium approximation (EMA) to find the disorder averaged (coarse-grained) dynamics. The EMA procedure…
Tracer-diffusion of small molecules through dense systems of chain polymers is studied within an athermal lattice model, where hard core interactions are taken into account by means of the site exclusion principle. An approximate mapping of…
This paper focuses on the time-harmonic electromagnetic (EM) scattering problem in a general medium which may possess a nontrivial topological structure. We model this by an inhomogeneous and possibly anisotropic medium with embedded…
An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…
The embedded topic model (ETM) is a widely used approach that assumes the sampled document-topic distribution conforms to the logistic normal distribution for easier optimization. However, this assumption oversimplifies the real…
Major efforts in recent years have been directed towards understanding molecular transport in polymeric membranes, in particular reverse osmosis and nanofiltration membranes. Transition-state theory is an increasingly common approach to…
Recent experiments have demonstrated that the nonlinear elasticity of in vitro networks of the biopolymer actin is dramatically altered in the presence of a flexible cross-linker such as the abundant cytoskeletal protein filamin. The basic…
We start from a low-energy effective field theory for interacting fermions on the lattice and expand in the hopping parameter to derive the nearest-neighbor interactions for a lattice gas model. In this model the renormalization of…
We build an effective medium theory for two-dimensional photonic crystals comprising a rectangular lattice of dielectric cylinders with the incident electric field polarized along the axis of the cylinders. In particular, we discuss the…