Related papers: Diffusion in a slab: different approaches
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish local…
The problem of a bouncing ball on a non-planar surface is investigated. We discovered that surface undulation adds a horizontal component to the impact force, which acquires a random character. Some aspects of Brownian motion are found in…
The purpose of this paper is to provide a formula for the effective diffusion operator obtained by projecting the 3-dimensional diffusion equation onto a 2-dimensional plane, assuming reflective boundary conditions at two surfaces in…
We study fluctuations of particle absorption by a three-dimensional domain with multiple absorbing patches. The domain is in contact with a gas of interacting diffusing particles. This problem is motivated by living cell sensing via…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
The linear intensity profile of multiply scattered light in a slab geometry extrapolates to zero at a certain distance beyond the boundary. The diffusion equation with this "extrapolated boundary condition" has been used in the literature…
The Langevin equation is a common tool to model diffusion at a single-particle level. In non-homogeneous environments, such as aqueous two-phase systems or biological condensates with different diffusion coefficients in different phases,…
The stationary phase method is applied to diffusion by a potential barrier for an incoming wave packet with energies greater then the barrier height. It is observed that a direct application leads to paradoxical results. The correct…
Constant flux atom deposition into a porous medium is shown to generate a dense overlayer and a diffusion profile. Scaling analysis shows that the overlayer acts as a dynamic control for atomic diffusion in the porous substrate. This is…
This review article examines the complex dynamics of thin-film flows of granular suspensions spreading over rigid solid substrates with free air interfaces. Such systems feature an involved coupling of the free-surface dynamics with the…
Since the famous 1926 paper by Richardson, the relative diffusion of two particles in a turbulent liquid has attracted a lot of interest. The motion of a single particle on the other hand is usually considered not to be especially…
Phase field models for two-phase flow with a surfactant soluble in possibly both fluids are derived from balance equations and an energy inequality so that thermodynamic consistency is guaranteed. Via a formal asymptotic analysis, they are…
Interfering liquid surface waves are generated by electrically driven vertical oscillations of two or more equispaced pins immersed in a liquid (water). The corresponding intensity distribution, resulting from diffraction of monochromatic…
We consider subdiffusion of a particle in a one-dimensional system with a thin partially permeable wall. Passing through the wall, the particle can be absorbed with a certain probability. We call such a wall partially permeable partially…
For reaction-diffusion processes without exclusion, in which the particles can exist in the same site of a one-dimensional lattice, we study all the integrable models which can be obtained by imposing a boundary condition on the master…
The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. In particular, such problems describe chemical reactions and biological processes in which…
Various model problems of ``transport-limited dissolution'' in two dimensions are analyzed using time-dependent conformal maps. For diffusion-limited dissolution (reverse Laplacian growth), several exact solutions are discussed for the…
A non-equilibrium thermodynamics model able to analyze the combined effect of diffusion and adsorption in porous materials is proposed. The model considers the coupled dynamics of the diffusive phase, described by a diffusion type equation,…
We compare the behavior of propagating and evanescent light waves in absorbing media with that of electrons in the presence of inelastic scattering. The imaginary part of the dielectric constant results primarily in an exponential decay of…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…