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The equations of motion in a macroscopically inhomogeneous porous medium saturated by a fluid are derived. As a first verification of the validity of these equations, a two-layer rigid frame porous system considered as one single porous…
Engineering simple, artificial models of living cells allows synthetic biologists to study cellular functions under well-controlled conditions. Reconstituting multicellular behaviors with synthetic cell-mimics is still a challenge because…
The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications…
The problem of diffusion in a porous medium with a spatially varying porosity is considered. The particular microstructure analyzed comprises a collection of impenetrable spheres, though the methods developed are general. Two different…
This work uncovers the low-dimensional nature the complex dynamics of actuated separated flows. Namely, motivated by the problem of model-based predictive control of separated flows, we identify the requirements on a model-based observer…
This paper presents a simple tool for characterising the timescale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in…
A mathematical model is developed, to jointly analyze elastic and inelastic scattering data of fluctuating membranes within a single theoretical framework. The model builds on a non-homogeneously clipped time-dependent Gaussian random…
Spatiotemporal disorder has been recently associated to the occurrence of anomalous nonergodic diffusion of molecular components in biological systems, but the underlying microscopic mechanism is still unclear. We introduce a model in which…
The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g. in soil layers in contact with the atmosphere)…
Random lateral translocation of lipids and proteins is a universal process on membrane surfaces. Local aggregation or organization of lipids and proteins can be induced when this lateral random diffusion is mediated by the electrostatic…
In this paper, we derive an effective model for transport processes in periodically perforated elastic media, taking into account, e.g., cyclic elastic deformations as they occur in lung tissue due to respiratory movement. The underlying…
A microscopic bubble of soluble gas always dissolves in finite time in an under-saturated fluid. This diffusive process is driven by the difference between the gas concentration near the bubble, whose value is governed by the internal…
Using Monte Carlo simulations we investigate some new aspects of the phase diagram and the behavior of the diffusion coefficient in an associating lattice gas (ALG) model on different regions of the phase diagram. The ALG model combines a…
Water molecules play an important role in providing unique environments for biological reactions on cell membranes. It is widely believed that water molecules form bridges that connect lipid molecules and stabilize cell membranes. Using…
We study the flow of a micropolar fluid in a thin domain with microstructure, i.e. a thin domain with thickness $\varepsilon$ which is perforated by periodically distributed solid cylinders of size $a_\varepsilon$. A main feature of this…
The rheology of pressure-driven flows of two-dimensional dense monodisperse emulsions in neutral wetting microchannels is investigated by means of mesoscopic lattice simulations, capable of handling large collections of droplets, in the…
A mathematical model describing the erosion or leaching of a solid material by a flowing fluid in a column is developed. This involves an advection-diffusion equation coupled to a linear kinetic reaction describing the mass transfer between…
We propose here a model for solidification of a liquid contents of an elastic bottle in a freezer. The main goal is to explain the occurrence of high stresses inside the bottle. As a by-product, we derive a formula for the undercooling…
We consider the classical problem of particle diffusion in $d$-dimensional radially-symmetric systems with absorbing boundaries. A key quantity to characterise such diffusive transport is the evolution of the proportion of particles…
Using analytical calculations and computer simulations we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the…