Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes

Scroggs, Matthew W.; Dokken, Jørgen S.; Richardson, Chris N.; Wells, Garth N.

doi:10.1145/3524456

Cited by 99 publications

(38 citation statements)

References 32 publications

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“…The system is time discretized according to established methods ( 58 ). Assuming that the total free energy of the system decreases to a minimum with time, we use the built-in Newtonian solver in the FEniCS environment to approximate the forward evolution of the system in time.…”

Section: Methodsmentioning

confidence: 99%

Nucleation of the destruction complex on the centrosome accelerates degradation of β-catenin and regulates Wnt signal transmission

Lach

Qiu

Kajbaf

et al. 2022

Proc. Natl. Acad. Sci. U.S.A.

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Wnt signal transduction is controlled by the destruction complex (DC), a condensate comprising scaffold proteins and kinases that regulate β-catenin stability. Overexpressed DC scaffolds undergo liquid–liquid phase separation (LLPS), but DC mesoscale organization at endogenous expression levels and its role in β-catenin processing were previously unknown. Here, we find that DC LLPS is nucleated by the centrosome. Through a combination of CRISPR-engineered custom fluorescent tags, finite element simulations, and optogenetic tools that allow for manipulation of DC concentration and multivalency, we find that centrosomal nucleation drives processing of β-catenin by colocalizing DC components to a single reaction crucible. Enriching GSK3β partitioning on the centrosome controls β-catenin processing and prevents Wnt-driven embryonic stem cell differentiation to mesoderm. Our findings demonstrate the role of nucleators in controlling biomolecular condensates and suggest tight integration between Wnt signal transduction and the cell cycle.

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Section: Methodsmentioning

confidence: 99%

Nucleation of the destruction complex on the centrosome accelerates degradation of β-catenin and regulates Wnt signal transmission

Lach

Qiu

Kajbaf

et al. 2022

Proc. Natl. Acad. Sci. U.S.A.

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“…We simulate biofilm structures using the Cahn-Hilliard equations with the Dolfin platform from FEniCSx (61). We initialize the field of u ( x ) as where ν is a uniformly distributed random number between -1 and 1, x is the voxel position in a 56 × 56 × 56 grid, c r = 0.1, c 0 = 0.5, h ( x ) is height at location x , x 0 = 0.15 and c ra = 0.15.…”

Section: Methodsmentioning

confidence: 99%

“…M λ∇u • n = 0 on ∂Ω, (7) with the Dolfin platform from FEniCSx (61). We initialize the field of u(x) as…”

Section: Methodsmentioning

confidence: 99%

Spatial distribution of bacteria and extracellular polymeric substances impacts nanoparticle penetration in biofilms

Coppens

Belpaire

Pešek

et al. 2022

Preprint

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Extracellular polymeric substances (EPS) in bacterial biofilms complicate treatment by inactivating drugs and slowing down diffusion. Through enhanced penetration and resistance to degradation in bacterial biofilms, nanoparticle (NP) carriers can help improve biofilm treatment. However, the way in which biofilm architecture influences the diffusive properties and penetration of NPs in biofilms is still poorly understood. In this work, we combined single particle tracking (SPT) and confocal laser scanning microscopy (CLSM) in Salmonella biofilms with simulations of a Brownian dynamics model to quantify how macro- (spatial organization of the bacteria) and micro- (EPS dependent) structure of the biofilm affects NP penetration. In CLSM images we observed immobilization of NPs in the EPS, which allows shielding of bacteria from the NPs, an effect that was more pronounced in dispersed biofilms, grown in nutrient-rich conditions, than in compacted biofilms, grown in nutrient-poor conditions. SPT experiments revealed anomalous diffusion, with an increased probability for small displacements near clusters of bacteria. Simulations of a Brownian dynamics model revealed that EPS reinforces shielding by affecting the pore structure of the biofilm. Finally, in virtual biofilms with varying spatial distribution of bacteria, we found that even for the same number of bacteria, dispersed biofilm structures provide more shielding than biofilms organized in dense, compacted clusters, even when accounting for decreased NP diffusivity.

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“… FEM models of each room are computed and used as a reference for the proposed BEM eigensolver. The FEM operators were created using FEniCSx [14] and the FEM eigenproblem was solved using the SLEPc4py Python package. The SLEPc4py solver is set to use the same block SS contour integral based method proposed for BEM [15], but for a Polynomial Eigenvalue Problem (PEP), This is done to ensure that the converged eigenvalues are all ones within the integration contour, expediting comparison between BEM and FEM.…”

Section: Numerical Examplesmentioning

confidence: 99%

A Boundary Element Method (BEM) Solver for Low Frequency Room Modes

Cicero

Hargreaves

2023

inter noise

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Room modes are known to be problematic in small critical listening environments. They degrade the acoustic quality at low frequencies, producing peaks and nulls in the frequency domain and ringing in the time domain. The Finite Element Method (FEM) is currently the easiest way to predict such resonances for arbitrarily shaped rooms. This solves for mode frequencies and shapes, as well as Q-factors and decay rates. Such 'eigenfrequency' solvers are commonplace in FEM, but FEM has the disadvantage of needing to mesh the entire air volume in the room. The Boundary Element Method (BEM) avoids this and only requires a simple boundary mesh, but solution of its eigenfrequency problems is much more challenging and appears in only a few academic papers. Here we transfer those approaches to Room Acoustics. We implement the block Sakurai-Sugiura method, which uses a contour integral in the complex frequency plane to convert the BEM eigenfrequency problem, which is usually non-linear in wavenumber, into a standard linear eigenfrequency problem that is straightforward to solve. The method is demonstrated through application to a cuboid room and an irregularly shaped room, both with impedance boundary conditions. Results are validated against FEM and discussed.

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Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes

Cited by 99 publications

References 32 publications

Nucleation of the destruction complex on the centrosome accelerates degradation of β-catenin and regulates Wnt signal transmission

Nucleation of the destruction complex on the centrosome accelerates degradation of β-catenin and regulates Wnt signal transmission

Spatial distribution of bacteria and extracellular polymeric substances impacts nanoparticle penetration in biofilms

A Boundary Element Method (BEM) Solver for Low Frequency Room Modes

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