A hybrid neural-network and MAC scheme for Stokes interface problems
In this paper, we present a hybrid neural-network and MAC (Marker-And-Cell) scheme for solving Stokes equations with singular forces on …
Distinguishing Methicillin-resistant Staphylococcus aureus from Methicillin-sensitive Strains by Combining Fe3O4 Magnetic Nanoparticle-based Affinity Mass Spectrometry with A Machine Learning Strategy
Pathogenic bacteria, including drug-resistant variants such as methicillin-resistant Staphylococcus aureus (MRSA), can cause severe …
Motility and swimming: universal description and generic trajectories
Autonomous locomotion is a ubiquitous phenomenon in biology and in physics of active systems at microscopic scale. This includes …
Variability of morphology in beat-to-beat photoplethysmographic waveform quantified with unsupervised wave-shape manifold learning for clinical assessment
We investigated the beat-to-beat fluctuation of the photoplethysmography (PPG) waveform. The motivation is that morphology variability …
A cusp-capturing PINN for elliptic interface problems
In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve discontinuous-coefficient elliptic interface …
An efficient neural-network and finite-difference hybrid method for elliptic interface problems with applications
A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain …
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 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 …
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 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 …
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 …
