scikit-finite-diff, a new tool for PDE solving

Cellier, Nicolas; Ruyer-Quil, Christian

doi:10.21105/joss.01356

Cited by 12 publications

(6 citation statements)

References 3 publications

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“…The model and its parameters are detailed in the Supplementary Method 2 . The numerical solution was obtained in Python using the PDE solver scikit-finite-diff package 58 .…”

Section: Methodsmentioning

confidence: 99%

Optogenetic spatial patterning of cooperation in yeast populations

Le Bec,

Pouzet,

Cordier

et al. 2024

Nat Commun

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Microbial communities are shaped by complex metabolic interactions such as cooperation and competition for resources. Methods to control such interactions could lead to major advances in our ability to better engineer microbial consortia for synthetic biology applications. Here, we use optogenetics to control SUC2 invertase production in yeast, thereby shaping spatial assortment of cooperator and cheater cells. Yeast cells behave as cooperators (i.e., transform sucrose into hexose, a public good) upon blue light illumination or cheaters (i.e., consume hexose produced by cooperators to grow) in the dark. We show that cooperators benefit best from the hexoses they produce when their domain size is constrained between two cut-off length-scales. From an engineering point of view, the system behaves as a bandpass filter. The lower limit is the trace of cheaters’ competition for hexoses, while the upper limit is defined by cooperators’ competition for sucrose. Cooperation mostly occurs at the frontiers with cheater cells, which not only compete for hexoses but also cooperate passively by letting sucrose reach cooperators. We anticipate that this optogenetic method could be applied to shape metabolic interactions in a variety of microbial ecosystems.

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“…The model and its parameters are detailed in the Supplementary Method 2 . The numerical solution was obtained in Python using the PDE solver scikit-finite-diff package 58 .…”

Section: Methodsmentioning

confidence: 99%

Optogenetic spatial patterning of cooperation in yeast populations

Le Bec,

Pouzet,

Cordier

et al. 2024

Nat Commun

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“…Lately, there have been several attempts at simplifying the process of translating the mathematical formulation of a PDE to a numerical implementation on the computer. Most notably, the finite-difference approach has been favored by the packages scikit-finite-d iff (Cellier & Ruyer-Quil, 2019) and Devito (Louboutin et al, 2019). Conversely, finiteelement and finite-volume methods provide more flexibility in the geometries considered and have been used in major packages, including FEniCS (Alnaes et al, 2015), FiPy (Guyer, Wheeler, & Warren, 2009), pyclaw (Ketcheson et al, 2012), and SfePy (Cimrman, Lukeš, & Rohan, 2019).…”

Section: Methodsmentioning

confidence: 99%

py-pde: A Python package for solving partial differential equations

Zwicker¹

2020

JOSS

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Partial differential equations (PDEs) play a central role in describing the dynamics of physical systems in research and in practical applications. However, equations appearing in realistic scenarios are typically non-linear and analytical solutions rarely exist. Instead, such systems are solved by numerical integration to provide insight into their behavior. Moreover, such investigations can motivate approximative solutions, which might then lead to analytical insight.

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“…In this section, we present some time-dependent numerical simulations of the three-equation full and approximate models (4.2), (4.10), and (4.17), (4.16) and the no-slip model (4.17), (4.19) with outlet open boundary conditions and forcing at the inlet (open flow). Computations have been performed using finite differences and the method of lines, which can be easily employed in the case of evolution equations (Cellier & Ruyer-Quil 2019), for which the system of partial differential equations can be written as where the indices refer to temporal or spatial derivatives; and is the vector that contains the unknowns (in this particular case , and ). The spatial derivatives of our system (6.1) are first discretised and replaced by algebraic approximations using second-order central finite differences.…”

Section: Time-dependent Simulationsmentioning

confidence: 99%

“…In this section, we present some time-dependent numerical simulations of the three-equation and two-equation full models (27,35) with periodic boundary conditions (closed flow), and with outlet open boundary conditions and forcing at the inlet (open flow). Computations have been performed using finite differences and the method of lines, which can be easily employed in the case of evolution equations [34], for which the system of partial differential equations can be written as…”

Section: Time-dependent Simulationsmentioning

confidence: 99%

Falling film on an anisotropic porous medium

2022

Self Cite

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The stability and dynamics of a falling liquid film over an anisotropic porous medium are studied using a one-domain approach. Our stability analysis shows a significant departure from the effective no-slip boundary condition in the isotropic case. Anisotropy does not affect the threshold of linear instability. However, a non-trivial dual effect of anisotropy on the film stability is observed depending on the permeability of the porous medium. This dual effect results from the net balance of the enhancement of viscous diffusion at the top Brinkman sublayer and the mitigation of viscous damping in the core Darcy sublayer. Three-equation models have been derived from the lubrication theory approximation in terms of the exact mass balance and averaged momentum balances in the porous and liquid layers. In the nonlinear regime, anisotropy has a dual effect by damping capillary waves at large permeabilities and enhancing them at low permeabilities. Anisotropy also affects wave speeds and shapes, modifies travelling-wave branches of solutions, affects the development of a time-periodic wavetrain by inlet forcing and alters the noise-driven dynamics of the flow. These effects result from the mitigation of mass exchange at the liquid–porous interface and the contribution of the cross-stream permeability in the Brinkman top sublayer to the viscous diffusion.

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scikit-finite-diff, a new tool for PDE solving

Abstract: Scikit-FDiff is a new tool for Partial Differential Equation (PDE) solving, written in pure Python, that focuses on reducing the time between the development of the mathematical model and the numerical solving.

Cited by 12 publications

References 3 publications

Optogenetic spatial patterning of cooperation in yeast populations

Optogenetic spatial patterning of cooperation in yeast populations

py-pde: A Python package for solving partial differential equations

Falling film on an anisotropic porous medium

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