Stencils with isotropic discretization error for differential operators

We report a hybrid numerical method for the solution of the model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes are solved using the stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretisation of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level in both cases. The methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results. The Galilean invariance of the model is tested and found to be satisfactory. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations.

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“…Eq. A3 has been systematically derived by imposing conditions of rotational invariance and isotropy of the operator [46]. Eq.…”

Section: Discussionmentioning

confidence: 99%

Lattice-Boltzmann-Langevin simulations of binary mixtures

2011

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“…This type of system is ideal if one is interested in self-organization based on chemical gradients. Indeed, resolving diffusion on a structured grid is well documented (Douglas and Gunn, 1964;Patra and Karttunen, 2006;Strikwerda, 2004). However, it is a poor system to use when implementing mechanical properties, as the structured grid has trouble dealing with deformation and representing complex geometries.…”

Section: Structured Grid Modelsmentioning

confidence: 99%

The physics of organoids: a biophysical approach to understanding organogenesis

Dahl-Jensen

Grapin-Botton

2017

Development

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Organoids representing a diversity of tissues have recently been created, bridging the gap between cell culture and experiments performed in vivo. Being small and amenable to continuous monitoring, they offer the opportunity to scrutinize the dynamics of organ development, including the exciting prospect of observing aspects of human embryo development live. From a physicist's perspective, their ability to self-organize -to differentiate and organize cells in space -calls for the identification of the simple rules that underlie this capacity. Organoids provide tractable conditions to investigate the effects of the growth environment, including its molecular composition and mechanical properties, along with the initial conditions such as cell number and type(s). From a theoretical standpoint, different types of in silico modeling can complement the measurements performed in organoids to understand the role of chemical diffusion, contact signaling, differential cell adhesion and mechanical controls. Here, we discuss what it means to take a biophysical approach to understanding organogenesis in vitro and how we might expect such approaches to develop in the future.

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“…TABLE I. Summary of crit for either operator with 1 APE step and c SW ¼ 1, as determined from direct measurements at these couplings (with error bars) and through the fit (21 C. Comparing the scaling of decay constants at fixed r 0 M P The decay constants F , F " ss , F " cc are determined from the improved and renormalized current…”

Section: A Scale Setting and Overall Tuning Strategymentioning

confidence: 99%

Brillouin improvement for Wilson fermions

Dürr

Koutsou

2011

Phys. Rev. D

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We present a parameter-free Wilson-type lattice Dirac operator with an 81-point stencil for the covariant derivative and the Laplacian, which attempts to minimize the breaking of rotational symmetry near the boundary of the Brillouin zone. The usefulness of this ''Brillouin operator'' in practical applications is explored by studying the scaling of pseudoscalar decay constants in quenched QCD, with rather good results in the physical charm region. We also investigate the suitability of this operator as a kernel to the overlap procedure. Here, the resulting overlap operator is found to be cheaper to construct and significantly better localized than the variety with the standard Wilson kernel.

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Stencils with isotropic discretization error for differential operators

Cited by 63 publications

References 16 publications

Lattice-Boltzmann-Langevin simulations of binary mixtures

Lattice-Boltzmann-Langevin simulations of binary mixtures

The physics of organoids: a biophysical approach to understanding organogenesis

Brillouin improvement for Wilson fermions

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