# Publications

### On the transition to dripping of an inverted liquid film

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

### A Reduced Model for a Phoretic Swimmer

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

### A cusp-capturing PINN for elliptic interface problems

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

### A hybrid neural-network and finite-difference method for solving Poisson equation with jump discontinuities on interfaces

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

### A Discontinuity Capturing Shallow Neural Network for Elliptic Interface Problems

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

### A Shallow Ritz Method for elliptic problems with Singular Sources

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

### Spontaneous locomotion of phoretic particles in three dimensions

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

### A shallow physics-informed neural network for solving partial differential equations on surfaces

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

### Thin liquid films in a funnel

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

### Effect of driving on coarsening dynamics in phase-separating systems

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

### A direct Poisson solver in spherical geometry with an application to diffusiophoretic problems

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

### Fast spectral solver for Poisson equation in an annular domain

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

### Chaotic swimming of phoretic self-propelled particles

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

### Two-dimensional pulse dynamics and the formation of bound states on electrified falling films

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

### Continuation methods for time-periodic travelling-wave solutions to evolution equations

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

### Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder

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

### Instabilities of layers of deposited molecules on chemically stripe patterned substrates: Ridges vs. drops

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

### Three-dimensional coating flow of nematic liquid crystal on an inclined substrate

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

### Coherent structures in non-local dispersive active-dissipative systems

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

### Modeling flow of nematic liquid crystal down an incline

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

### Numerical study of a non-local weakly nonlinear model for a liquid film sheared by a turbulent gas

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

### Note on the hydrodynamic description of thin nematic films: strong anchoring model

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

### Modelling spreading dynamics of nematic liquid crystals in three spatial dimensions

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

### Thin films flowing down inverted substrates: Three-dimensional flow

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

### Defect modeling in spreading nematic droplets

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

### Modeling and simulations of the spreading and destabilization of nematic droplets

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

### Thin films flowing down inverted substrates: two dimensional flow

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

### A simple Dufort-Frankel type scheme for the Gross-Pitaevskii equation of Bose-Einstein condensates on different geometries

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