Related papers: Diffusion of tangential tensor fields: numerical i…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…
An accurate and comprehensive numerical solution to the parabolic free boundary problem arising from thin film flow with both velocity and temperature distribution at large Reynolds numbers is obtained using a modified Keller box method. A…
The present investigation discusses the flow and heat transfer characteristics of a steady three dimensional Sisko fluid. The flow is induced due to bidirectional stretching sheet. The influence of power-law index and stretching ratio on…
We present a position Langevin equation for overdamped particle motion on rough two-dimensional surfaces. A Brownian Dynamics algorithm is suggested to evolve this equation numerically, allowing for the prediction of effective (projected)…
A fully discrete finite element method, based on a new weak formulation and a new time-stepping scheme, is proposed for the surface diffusion flow of closed curves in the two-dimensional plane. It is proved that the proposed method can…
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…
A pair of Direct Numerical Simulations is used to investigate curvature and pressure effects. One has a Gaussian test bump and a straight opposite wall, while the other has a straight test wall and a blowing/suction distribution on an…
Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures with self-affine roughness is studied by analytic and numerical methods. Numerical simulations were performed via the lattice-Boltzmann approach, using a new boundary…
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…
A combination of reaction-diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system's state and geometry over time. These systems can be…
A particle is thrown tangentially on a surface. It is shown that for some surfaces and for special initial velocities the thrown particle leaves immediately the surface, and for special conditions it never leaves the surface. The conditions…
We investigate the propagation of surface waves along a spatially dispersive graphene sheet, including substrate effects. The proposed analysis derives the admittances of an equivalent circuit of graphene able to handle spatial dispersion,…
Due to ample applications from medical services to industrial activities, the study of flow and heat transfer through a curved duct has attracted considerable attention to the researchers. In this paper, a comprehensive numerical study is…
An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a…
For a fissured medium, we analyze the impact that the geometry of the cracks, has in the phenomenon of preferential fluid flow. Using finite volume meshes we analyze the mechanical energy dissipation due to gravity, curvature of the surface…
A normal-diffusion theory for heat transfer in many-body systems via carriers of thermal photons is developed. The thermal conductivity tensor is rigorously derived from fluctuational electrodynamics as a coefficient of diffusion term for…
We perform a study on the evolution of helical quantum turbulence at different temperatures by solving numerically the Gross-Pitaevskii and the Stochastic Ginzburg-Landau equations, using up to $4096^3$ grid points with a pseudospectral…
Calculating the thermal diffusivity of solid materials is commonly carried out using the laser flash experiment. This classical experiment considers a small (usually thin disc-shaped) sample of the material with parallel front and rear…