The transition to dripping in the gravity-driven flow of a liquid film under an inclined plate is investigated at zero Reynolds number. …

We consider a 2D model of an autophoretic particle in which the particle has a circular shape and emits/absorbs a solute that diffuses …

In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve variable-coefficient elliptic interface …

In this work, a new hybrid neural-network and finite-difference method is developed for solving Poisson equation in a regular domain …

In this paper, a new Discontinuity Capturing Shallow Neural Network (DCSNN) for approximating $d$-dimensional piecewise continuous …

In this paper, a shallow Ritz-type neural network for solving elliptic equations with delta function singular sources on an interface …

The motion of an autophoretic spherical particle in a simple fluid is analyzed. This motion is powered by a chemical species which is …

In this paper, we introduce a mesh-free physics-informed neural network for solving partial differential equations on surfaces. Based …

We explore flow of a completely wetting fluid in a funnel, with particular focus on contact line instabilities at the fluid front. …

We consider the Cahn-Hilliard (CH) equation with a Burgers-type convective term that is used as a model of coarsening dynamics in …

We propose a simple and efficient class of direct solvers for Poisson equation in finite or infinite domains related to spherical …

A simple and efficient spectral method is formulated to solve Poisson equation in an annular domain. The solver relies on the Fourier …

The swimming of a rigid phoretic particle in an isotropic fluid is studied numerically as a function of the dimensionless solute …

The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of …

A numerical continuation method is developed to follow time-periodic travelling- wave solutions of both local and non-local evolution …

We discuss the behavior of partially wetting liquids on a rotating cylinder using a model that takes into account the effects of …

A mesoscopic continuum model is employed to analyze the transport mechanisms and structure formation during the redistribution stage of …

We consider a coating flow of nematic liquid crystal (NLC) fluid film on an inclined substrate. Exploiting the small aspect ratio in …

We analyze coherent structures in nonlocal dispersive active-dissipative nonlinear systems, using as a prototype the …

The flow of nematic liquid crystals down an inclined substrate is studied. Under the usual long wave approximation, a fourth-order …

We investigate a weakly nonlinear equation that arises in the modelling of wave dynamics on a liquid film flowing down an inclined …

We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free …

We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth-order …

We study contact line induced instabilities for a thin film of fluid under destabilizing gravitational force in three-dimensional …

Experiments by Poulard and Cazabat [Langmuir 21, 6270 (2005)] on spreading droplets of nematic liquid crystal (NLC) reveal a …

A series of experiments [C. Poulard and A. M. Cazabat, “Spontaneous spreading of nematic liquid crystals” Langmuir 21, 6270 …

We consider free surface instabilities of films flowing on inverted substrates within the framework of lubrication approximation. We …

We develop a simple Dufort-Frankel type scheme for solving the time-dependent Gross-Pitaevskii equation (GPE). The GPE is a nonlinear …

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