相关论文: A fractal graph model of capillary type systems
We develop an index theory for variational problems on noncompact quantum graphs. The main results are a spectral flow formula, relating the net change of eigenvalues to the Maslov index of boundary data, and a Morse index theorem, equating…
The hierarchy and fine tuning of the gauge coupling constants are described on the base of topological invariants (Chern classes interpreted as filling factors) characterizing a collection of fractional topological fluids emerging from…
This paper investigates fractional torsional rigidity on compact, connected metric graphs, a novel extension of the classical concept to nonlocal operators. The fractional torsional rigidity is defined as the $L^1$-norm of the fractional…
Capillary phenomena are involved in many industrial processes, especially those dealing with composite manufacturing. However, their modelling is still challenging. Therefore, a finite element setting is proposed to better investigate this…
In this lecture we present an overview of the physics of irreversible fractal growth process, with particular emphasis on a class of models characterized by {\em quenched disorder}. These models exhibit self-organization, with critical…
The capillary time-step constraint is the dominant limitation on the applicable time-step in many simulations of interfacial flows with surface tension and, consequently, governs the execution time of these simulations. We propose a…
We study the gravity-driven flow of two fluid phases in a one-dimensional homogeneous porous column when history dependence of the pressure difference between the phases (capillary pressure) is taken into account. In the hyperbolic limit,…
Contact of a fluid with a solid or an elastic wall is investigated. The wall exerts molecular forces on the fluid which is locally strongly nonhomogeneous. The problem is approached with a fluid energy of the second gradient form and a wall…
We identify incompressible planar linear flows that are generalizations of the well known one-parameter family characterized by the ratio of in-plane extension to (out-of-plane) vorticity. The latter `canonical' family is classified into…
One-dimensional blood flow model accuracy has been verified in many studies. This work is about introducing gravity into a one-dimensional model. For this purpose, gravitational force was introduced into the existing model. The boundary…
We study single-phase flow in a fractured porous medium at a macroscopic scale that allows to model fractures individually. The flow is governed by Darcy's law in both fractures and porous matrix. We derive a new mixed-dimensional model,…
Three-dimensional X-ray microtomography, coupled to rheometric measurements, enables a morphology-resolved reconstruction of capillary stresses at the grain scale in unsaturated wet granular materials. Liquid domains are automatically…
We study capillary-gravity surface waves for fluid flows governed by Darcy's law. This includes flows in vertical Hele-Shaw cells and in porous media (the one-phase Muskat problem) with finite or infinite depth. The free boundary is acted…
Channel formation and branching is widely seen in physical systems where movement of fluid through a porous structure causes the spatiotemporal evolution of the medium in response to the flow, in turn causing flow pathways to evolve. We…
The motion of a gas-liquid interface along a solid wall is influenced by the capillary forces resulting from the interface's shape and its interaction with the solid, where it forms a dynamic contact angle. Capillary models play a…
Recent experimental studies on the instability appearance of capillary jets have revealed the capabilities of linear spatiotemporal instability analysis to predict the parametrical map where steady jetting or dripping takes place. In this…
The fabric of porous and fractured media contains solid regions (grains) and voids. The space conducting fluids is a system of connected voids with variable geometries. Relative to the grain sizes, the voids can be voluminous with three…
We applied a hybrid-dimensional flow model to pressure transients recorded during pumping experiments conducted at the Reiche Zeche underground research laboratory to study the normal opening behavior of fractures due to fluid injection.…
We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of {F}orchheimer-type and is subject to a mixed mass and volumetric flux boundary condition. The governing equations are reduced to a…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…