Related papers: Variational Pattern Selection
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…
We use a lattice gas cellular automata model in the presence of random dynamic scattering sites and quenched disorder in the two-phase immiscible model with the aim of producing an interface dynamics similar to that observed in Hele-Shaw…
A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics. In the present paper, using the variational method for solving nonlinear boundary problems of…
A unique pattern selection in the absolutely unstable regime of a driven, nonlinear, open-flow system is analyzed: The spatiotemporal structures of rotationally symmetric vortices that propagate downstream in the annulus of the rotating…
We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it…
Feature selection problems have been extensively studied for linear estimation, for instance, Lasso, but less emphasis has been placed on feature selection for non-linear functions. In this study, we propose a method for feature selection…
To wield an object means to hold and move it in a way that exploits its functions. When humans wield tools -- such as writing with a pen or cutting with scissors -- our hands would reach very specific poses, often drastically different from…
We study viscous fingering of an air-nematic interface in a radial Hele-Shaw cell when periodically switching on and off an electric field, which reorients the nematic and thus changes its viscosity, as well as the surface tension and its…
Interactions between neighboring cells are essential for generating or refining patterns in a number of biological systems. We propose a discrete filtering approach to predict how networks of cells modulate spatially varying input signals…
A hierarchy of mathematical models describing viscosity-stratified flow in a Hele-Shaw cell is constructed. Numerical modelling of jet flow and development of viscous fingers with the influence of inertia and friction is carried out.…
Hele-Shaw problems are prototypes to study the interface dynamics. Linear theory suggests the existence of self-similar patterns in a Hele-Shaw flow. That is, with a specific injection flux the interface shape remains unchanged while its…
A unique pattern selection in the absolutely unstable regime of driven, nonlinear, open-flow systems is reviewed. It has recently been found in numerical simulations of propagating vortex structures occuring in Taylor-Couette and…
We investigate the viscous fingering instability that arises when air is injected from the end of an oil-filled, compliant channel. We show that induced axial and transverse depth gradients foster novel pattern formation. Moreover, the…
The first stages of finger formation in a Hele-Shaw cell with lifting plates are investigated by means of linear stability analysis. The equation of motion for the pressure field (growth law) results to be that of the directional…
The pattern selection problem in binary-mixture convection in an extended channel with a lateral through-flow is presented. The through-flow breaks left--right parity and changes pattern dynamics dramatically. The problem is studied based…
We derive a formula describing the evolution of tip-splittings of Saffman-Taylor fingers in a Hele-Shaw cell, at zero surface tension.
We analyze a recent experiment of Sharon \textit{et al.} (2003) on the coarsening, due to surface tension, of fractal viscous fingering patterns (FVFPs) grown in a radial Hele-Shaw cell. We argue that an unforced Hele-Shaw model, a natural…
The complex behaviour of air-liquid interfaces driven into Hele-Shaw channels at high speeds could arise from oscillatory dynamics; yet, both the physical and dynamical mechanisms that lead to interfacial oscillations remain unclear. We…
The increasing availability of geometric data has motivated the need for information processing over non-Euclidean domains modeled as manifolds. The building block for information processing architectures with desirable theoretical…
In this paper, we present a novel interface-driven adaptive variational procedure using a fully Eulerian description of fluid-structure interaction. The proposed fully-Eulerian procedure involves a fixed background unstructured mesh on…