Browsing by Author "Lin, Te-Sheng"

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A direct Poisson solver in spherical geometry with an application to diffusiophoretic problems
(2020-05-15)
Lin, Te-Sheng
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Hu, Wei-Fan
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Misbah, Chaouqi
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應用數學系
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Department of Applied Mathematics
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. The solver was further extended to study the dynamics of a diffusiophoretic particle suspended in Stokes flow. Numerical experiments suggested that the particle can achieve a self-sustained unidirectional motion at moderate Peclet numbers, whereas the particle motion becomes chaotic in high Peclet number regimes. The statistical analysis illustrates the run-and-tumble-like nature at short times and diffusive nature at long times without any source of noise. (C) 2020 Elsevier Inc. All rights reserved.
Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder
(2016-08)
Lin, Te-Sheng
;
Rogers, Steven
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Tseluiko, Dmitri
;
Thiele, Uwe
;
應用數學系
We discuss the behavior of partially wetting liquids on a rotating cylinder using a model 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 heterogeneity and a lateral driving force in the proximity of a first-or second-order phase transition results in intricate behavior. So does a partially wetting drop on a rotating cylinder undergo a depinning transition as the rotation speed is increased, whereas for ideally wetting liquids, the behavior only changes quantitatively. We analyze the bifurcations that occur when the rotation speed is increased for several values of the equilibrium contact angle of the partially wetting liquids. This allows us to discuss how the entire bifurcation structure and the flow behavior it encodes change with changing wettability. We employ various numerical continuation techniques that allow us to track stable/unstable steady and time-periodic film and drop thickness profiles. We support our findings by time-dependent numerical simulations and asymptotic analyses of steady and time-periodic profiles for large rotation numbers. Published by AIP Publishing.
Chaotic Swimming of Phoretic Particles
(2019-12-03)
Hu, Wei-Fan
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Lin, Te-Sheng
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Rafai, Salima
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Misbah, Chaouqi
;
應用數學系
The swimming of a rigid phoretic particle in an isotropic fluid is studied numerically as a function of the dimensionless solute emission rate (or Peclet 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 meandering motion. When Pe is increased further, the particle meanders at a short scale but its trajectory wraps into a circle at a larger scale. Increasing even further, Pe causes the swimmer to escape momentarily the circular trajectory in favor of chaotic motion, which lasts for a certain time, before regaining a circular trajectory, and so on. The chaotic bursts become more and more frequent as Pe increases, until the trajectory becomes fully chaotic, via the intermittency scenario. The statistics of the trajectory is found to be of the run-and-tumble-like nature at a short enough time and of diffusive nature at a long time without any source of noise.
COHERENT STRUCTURES IN NONLOCAL DISPERSIVE ACTIVE-DISSIPATIVE SYSTEMS
(2015-01-01)
Lin, Te-Sheng
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Pradas, Marc
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Kalliadasis, Serafim
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Papageorgiou, Demetrios T.
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Tseluiko, Dmitri
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, Phys. Fluids, 31 (1988), pp. 2103-2111]), we show that sufficiently strong dispersion regularizes the chaotic dynamics of the KS equation, and the solutions evolve into arrays of interacting pulses that can form bound states. We analyze the asymptotic characteristics of such pulses and show that their tails tend to zero algebraically but not exponentially, as for the local gKS equation. Since the Shilnikov-type approach is not applicable for analyzing bound states in nonlocal equations, we develop a weak-interaction theory and show that the standard first-neighbor approximation is no longer applicable. It is then essential to take into account long-range interactions due to the algebraic decay of the tails of the pulses. In addition, we find that the number of possible bound states for fixed parameter values is always finite, and we determine when there is long-range attractive or repulsive force between the pulses. Finally, we explain the regularizing effect of dispersion by showing that, as dispersion is increased, the pulses generally undergo a transition from absolute to convective instability. We also find that for some nonlocal operators, increasing the strength of the stabilizing/destabilizing term can have a regularizing/deregularizing effect on the dynamics.
Instabilities of Layers of Deposited Molecules on Chemically Stripe Patterned Substrates: Ridges versus Drops
(2015-09-29)
Honisch, Christoph
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Lin, Te-Sheng
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Heuer, Andreas
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Thiele, Uwe
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Gurevich, Svetlana V.
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 as very important transient states and their linear stability is analyzed accompanied by direct numerical simulations of the fully nonlinear evolution equation for two-dimensional substrates. It is found that there exist two different instability modes that lead to different nonlinear evolutions that result (i) at large ridge volume in the formation of bulges that spill from the more wettable stripes onto the less wettable bare substrate and (ii) at small ridge volume in the formation of small droplets located on the more wettable stripes. In addition, the influence of different transport mechanisms during redistribution is investigated focusing on the cases of convective transport with no-slip at the substrate, transport via diffusion in the film bulk and via diffusion at the film surface. In particular, it is shown that the transport process does neither influence the linear stability thresholds nor the sequence of morphologies observed in the time simulation, but only the ratio of the time scales of the different process phases.
Tracking Dynamic Arterial Pressure Waveform on Vasoactive Medication Via Manifold Learning Method
(2019-04-01)
Lin, Yu-Ting
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Lin, Te-Sheng
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Wu, Hau-tieng
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Chang, Cheng-Hsi
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Wang, Shen-Chih