Te-Sheng Lin

National Yang Ming Chiao Tung University · Applied Mathematics

Pathogenic bacteria, including drug-resistant variants such as methicillin-resistant Staphylococcus aureus (MRSA), can cause severe infections in the human body. Early detection of MRSA is essential for clinical diagnosis and proper treatment, considering the distinct therapeutic strategies for methicillin-sensitive S. aureus (MSSA) and MRSA infect...

Autonomous locomotion is a ubiquitous phenomenon in biology and in physics of active systems at microscopic scale. This includes prokaryotic, eukaryotic cells (crawling and swimming) and artificial swimmers. An outstanding feature is the ability of these entities to follow complex trajectories, ranging from straight, curved (circular, helical...),...

In this paper, we present a novel hybrid method for solving a Stokes interface problem in a regular domain with jump discontinuities on an interface. Our approach combines the expressive power of neural networks with the convergence of finite difference schemes to achieve efficient implementations and accurate results. The key concept of our method...

Coffee is a daily essential, with prices varying based on taste, aroma, and chemical composition. However, distinguishing between different coffee beans is challenging due to time-consuming and destructive sample pretreatment. This study presents a novel approach for directly analyzing single coffee beans through mass spectrometry (MS) without the...

The transition to dripping in the gravity-driven flow of a liquid film under an inclined plate is investigated at zero Reynolds number. Computations are carried out on a periodic domain assuming either a fixed fluid volume or a fixed flow rate for a hierarchy of models: two lubrication models with either linearised curvature or full curvature (the...

We consider a two-dimensional (2-D) model of an autophoretic particle. Beyond a certain emission/absorption rate (characterized by a dimensionless Péclet number, $Pe$ ) the particle is known to undergo a bifurcation from a non-motile to a motile state, with different trajectories, going from a straight to a chaotic motion by increasing $Pe$ . From...

The transition to dripping in the gravity-driven flow of a liquid film under an inclined plate is investigated at zero Reynolds number. Computations are carried out on a periodic domain assuming either a fixed fluid volume or a fixed flow rate for a hierarchy of models: two lubrication models with either linearised curvature or full curvature (the...

In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve variable-coefficient elliptic interface problems whose solution is continuous but has discontinuous first derivatives on the interface. To find such a solution using neural network representation, we introduce a cusp-enforced level set function as an addition...

In this work, a new hybrid neural-network and finite-difference method is developed for solving Poisson equation in a regular domain with jump discontinuities on an embedded irregular interface. Since the solution has low regularity across the interface, when applying finite difference discretization to this problem, an additional treatment account...

In this paper, a new Discontinuity Capturing Shallow Neural Network (DCSNN) for approximating d-dimensional piecewise continuous functions and for solving elliptic interface problems is developed. There are three novel features in the present network; namely, (i) jump discontinuities are accurately captured, (ii) it is completely shallow, comprisin...

In this paper, a shallow Ritz-type neural network for solving elliptic equations with delta function singular sources on an interface is developed. There are three novel features in the present work; namely, (i) the delta function singularity is naturally removed, (ii) level set function is introduced as a feature input, (iii) it is completely shal...

The motion of an autophoretic spherical particle in a simple fluid is analyzed. This motion is powered by a chemical species which is absorbed or emitted by the particle and which diffuses and is advected in the surrounding fluid. The transition from the nonmotile to the motile state occurs if the Péclet number Pe (defined as the ratio of the solut...

In this paper, we introduce a mesh-free physics-informed neural network for solving partial differential equations on surfaces. Based on the idea of embedding techniques, we write the underlying surface differential equations using conventional Cartesian differential operators. With the aid of level set function, the surface geometrical quantities,...

Locomotion is essential for living cells. It enables bacteria and algae to explore space for food, cancer to spread, and immune system to fight infections. Motile cells display trajectories of intriguing complexity, from regular (e.g. circular, helical, and so on) to irregular motions (run-tumble), the origin of which has remained elusive for over...

We consider a 2D model of an autophoretic particle in which the particle has a circular shape and emits/absorbs a solute that diffuses and is advected by the suspending fluid. Beyond a certain emission/absorption rate (characterized by a dimensionless P\'eclet number, $Pe$) the particle is known to undergo a bifurcation from a non motile to a motil...

Autonomous locomotion is a ubiquitous phenomenon in biology and in physics of active systems at microscopic scale. This includes prokaryotic, eukaryotic cells (crawling and swimming) and artificial swimmers. An outstanding feature is the ability of these entities to follow complex trajectories, ranging from straight, curved (circular, helical...),...

In this paper, a shallow Ritz-type neural network for solving elliptic problems with delta function singular sources on an interface is developed. There are three novel features in the present work; namely, (i) the delta function singularity is naturally removed, (ii) level set function is introduced as a feather input, (iii) it is completely shall...

In this paper, a new Discontinuity Capturing Shallow Neural Network (DCSNN) for approximating $d$-dimensional piecewise continuous functions and for solving elliptic interface problems is developed. There are three novel features in the present network; namely, (i) jump discontinuity is captured sharply, (ii) it is completely shallow consisting of...

We consider the Cahn–Hilliard (CH) equation with a Burgers-type convective term that is used as a model of coarsening dynamics in laterally driven phase-separating systems. In the absence of driving, it is known that solutions to the standard CH equation are characterized by an initial stage of phase separation into regions of one phase surrounded...

We explore contact line instabilities of a thin films flowing in a funnel. The funnel geometry involves additional azimuthal curvature, and it also leads to a convergent flow and corresponding thickening of the film, which may play a role in determining the stability properties. Many different limiting cases are identified. We report experimental f...

We propose a simple and efficient class of direct solvers for Poisson equation in finite or infinite domains related to spherical geometry. The solver was developed based on truncated spherical harmonics expansion, where the differential mode equations were solved by second-order finite difference method without handling coordinate singularities. T...

The swimming of a rigid phoretic particle in an isotropic fluid is studied numerically as a function of the dimensionless solute emission rate (or Péclet number Pe). The particle sets into motion at a critical Pe. Whereas the particle trajectory is straight at a small enough Pe, it is found that it loses its stability at a critical Pe in favor of a...

We consider the Cahn-Hilliard (CH) equation with a Burgers-type convective term that is used as a model of coarsening dynamics in driven phase-separating systems. In the absence of driving, it is known that solutions to the standard CH equation are characterized by an initial stage of phase separation into regions of one phase surrounded by the oth...

The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model, which is valid in the presence of weak inerti...

A numerical continuation method is developed to follow time-periodic travelling-wave solutions of both local and non-local evolution partial differential equations (PDEs). It is found that the equation for the speed of the moving coordinate can be derived naturally from the governing equations together with a condition that breaks the translational...

The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling-wave solutions on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model derived on the basis of thin-film the...

We discuss the behavior of partially wetting liquids on a rotating cylinder using the model of Thiele [J. Fluid Mech. 671, 121-136 (2011)] that takes into account the effects of gravity, viscosity, rotation, surface tension and wettability. Such a system can be considered as a prototype for many other systems where the interplay of spatial heteroge...

A mesoscopic continuum model is employed to analyze the transport mechanisms and structure formation during the redistribution stage of deposition experiments where organic molecules are deposited on a solid substrate with periodic stripe-like wettability patterns. Transversally invariant ridges located on the more wettable stripes are identified a...

We consider a coating flow of nematic liquid crystal (NLC) fluid film on an inclined substrate. Exploiting the small aspect ratio in the geometry of interest, a fourth-order nonlinear partial differential equation is used to model the free surface evolution. Particular attention is paid to the interplay between the bulk elasticity and the anchoring...

We analyze coherent structures in nonlocal dispersive active-dissipative nonlinear systems, using as a prototype the Kuramoto-Sivashinsky (KS) equation with an additional nonlocal term that contains stabilizing/destabilizing and dispersive parts. As for the local generalized Kuramoto-Sivashinsky (gKS) equation (see, e.g., [T. Kawahara and S. Toh, P...

We investigate a weakly nonlinear equation that arises in the modelling of wave dynamics on a liquid film flowing down an inclined plane when a turbulent gas flows above it. The model is the Kuramoto-Sivashinsky equation with an additional non-local term multiplied by a parameter representing the relative importance of the turbulent gas. The non-lo...

The flow of nematic liquid crystals down an inclined substrate is studied. Under the usual long wave approximation, a fourth-order nonlinear parabolic partial differential equation of the diffusion type is derived for the free surface height. The model accounts for elastic distortions of the director field due to different anchoring conditions at t...

We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The influence of elastic distortion energy and of imposed anchoring variations at the substrate are explored through lin...

We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for the film thickness in order to provide a solid basis for further investigation: several conflicting models exi...

We study contact line induced instabilities for a thin film of fluid under destabilizing gravitational force in three dimensional setting. In the previous work (Phys. Fluids, {\bf 22}, 052105 (2010)), we considered two dimensional flow, finding formation of surface waves whose properties within the implemented long wave model depend on a single par...

Experiments by Poulard and Cazabat [Langmuir 21, 6270 (2005)] on spreading droplets of nematic liquid crystal (NLC) reveal a surprisingly rich variety of behavior, including at least two different emerging length scales resulting from a contact line instability. In earlier work [Cummings, Lin, and Kondic, Phys. Fluids 23, 043102 (2011)] we modified...

We study contact line induced instabilities for thin film of complete and partially wetting fluids spreading down an inclined plane with inclination angle ranging from 0 to pi. It is found that a contact line may lead to free surface instability without any additional perturbations. We investigate the effect of both inclination angle and of contact...

A series of experiments [C. Poulard and A. M. Cazabat, ``Spontaneous spreading of nematic liquid crystals,'' Langmuir 21, 6270 (2005)] on spreading droplets of nematic liquid crystal (NLC) reveals a surprisingly rich variety of behaviors. Small droplets can either be arrested in their spreading, spread stably, destabilize without spreading (corruga...

Experiments by Poulard & Cazabat ootnotetextC. Poulard, A. M. Cazabat, Langmuir, 6270, vol. 21 (2005) on spreading droplets of nematic liquid crystal reveal a surprisingly rich variety of behavior, including at least two different emerging lengthscales resulting from a contact line instability. In earlier work ootnotetextL. J. Cummings, T.-S. Lin,...

We consider free surface instabilities of films flowing on inverted substrates within the framework of lubrication approximation. We allow for the presence of fronts and related contact lines, and explore the role which they play in instability development. It is found that a contact line, modeled by a commonly used precursor film model, leads to f...

A series of experiments involving spreading of nematic liquid crystal drops on solid substrates ootnotetextPoulard and Cazabat, Langmuir, 6270, vol. 21 (2005) have uncovered a surprisingly rich variety of behavior. The drops can either be arrested in their spreading, spread stably, or destabilize with or without spreading. We propose a relatively s...

We study free surface instabilities of spreading thin films exposed to destabilizing body force (gravity) on partially wetting substrates. For completely wetting films on inverted substrates, we have uncovered rich structure of convective and absolute instabilities which evolve due to contact line presence. ootnotetextT.-S. Lin, L. Kondic, Phys. Fl...

We consider free surface instabilities of films hanging on inverted substrates within the framework of lubrication approximation. Contrary to all the previous works, we include fluid fronts in formulation. It is found that the presence of contact lines leads to free surface instabilities of convective type without any additional natural or excited...

We develop a simple Dufort-Frankel-type scheme for solving the time-dependent Gross-Pitaevskii equation (GPE). The GPE is a nonlinear Schrödinger equation describing the Bose-Einstein condensation (BEC) at very low temperature. Three different geometries including 1D spherically symmetric, 2D cylindrically symmetric, and 3D anisotropic Cartesian do...