Related papers: Wetting of gradient fields: pathwise estimates
A new method for interface tracking is presented. The interface representation, based on domain decomposition, provides the interface location explicitly, yet is Eulerian. This allows for well established finite difference methods on…
In adaptive networks fragmentation transitions have been observed in which the network breaks into disconnected components. We present an analytical approach for calculating the transition point in general adaptive network models. Using the…
We consider a three-dimensional Ising model in a transverse magnetic field, $h$ and a bulk field $H$. An interface is introduced by an appropriate choice of boundary conditions. At the point $(H=0,h=0)$ spin configurations corresponding to…
A lattice model for active matter is studied numerically, showing that it displays wettings transitions between three distinctive phases when in contact with an impenetrable wall. The particles in the model move persistently, tumbling with…
We analyse features of the patterns formed from a simple model for a martensitic phase transition. This is a fragmentation model that can be encoded by a general branching random walk. An important quantity is the distribution of the…
In earlier work \cite{bedeaux/vdW/I, bedeaux/vdW/II, bedeaux/vdW/III} a systematic extension of the van der Waals square gradient model to non-equilibrium one-component systems was given. In this work the focus was on heat and mass transfer…
Interpretability methods for deep neural networks mainly focus on the sensitivity of the class score with respect to the original or perturbed input, usually measured using actual or modified gradients. Some methods also use a…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
A simple one-dimensional microscopic model of the depinning transition of an interface from an attractive hard wall is introduced and investigated. Upon varying a control parameter, the critical behaviour observed along the transition line…
Recent studies of wetting in a two-component square-gradient model of interfaces in a fluid mixture, showing three-phase bulk coexistence, have revealed some highly surprising features. Numerical results show that the density profile paths,…
Hypothesis Emerging energy-related technologies deal with multiscale hierarchical structures, intricate surface morphology, non-axisymmetric interfaces, and complex contact lines where wetting is difficult to quantify with classical…
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…
We consider two-dimensional ($d=2$) systems with short-ranged microscopic interactions, where interface unbinding (wetting) transitions occur in the limit of vanishing temperature $T$. For $T=0$ the transition is characterized by…
The paper introduces hidden grid background oriented schlieren for quantitative study and visualization of natural convection heat transfer. In this technique, the refractive index variation, induced by the temperature gradient, is encoded…
The unbinding properties of an interface near structured wedges are investigated by discrete models with short range interactions. The calculations demonstrate that interface unbinding take place in two stages: $i$) a continuous…
Integrated Gradients has become a popular method for post-hoc model interpretability. De-spite its popularity, the composition and relative impact of different regions of the integral path are not well understood. We explore these effects…
Many popular feature-attribution methods for interpreting deep neural networks rely on computing the gradients of a model's output with respect to its inputs. While these methods can indicate which input features may be important for the…
We study a stationary wetting problem on rough and inhomogeneous solid surfaces. We derive a new formula for the apparent contact angle by asymptotic two-scale homogenization method. The formula reduces to a modified Wenzel equation for…
We study the wetting model, which considers a random walk constrained to remain above a hard wall, but with additional pinning potential for each contact with the wall. This model is known to exhibit a wetting phase transition, from a…
We study 2D wedge wetting using a continuum interfacial Hamiltonian model which is solved by transfer-matrix methods. For arbitrary binding potentials, we are able to exactly calculate the wedge free-energy and interface height distribution…