A C++ expression system for partial differential equations enables generic simulations of biological hydrodynamics

Singh, Abhinav; Incardona, Pietro; Sbalzarini, Ivo F.

doi:10.1140/epje/s10189-021-00121-x

Cited by 8 publications

(3 citation statements)

References 44 publications

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“…Finally, we perform a strong scaling benchmark of the computation time with increasing numbers of CPU cores with both codes implemented in the parallel computing library OpenFPM [11,26] in C++ and run on the same hardware. The results in Fig.…”

Section: Resultsmentioning

confidence: 99%

Mesh-free collocation for surface differential operators

Shrivastava¹,

Alejandra²,

Incardona³

et al. 2022

Preprint

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We present a mesh-free collocation scheme to discretize intrinsic surface differential operators over surface point clouds with given normal vectors. The method is based on Discretization-Corrected Particle Strength Exchange (DC-PSE), which generalizes finite difference methods to mesh-free point clouds and moving Lagrangian particles. The resulting Surface DC-PSE method is derived from an embedding theorem, but we analytically reduce the operator kernels along the surface normals, resulting in an embedding-free, purely surface-intrinsic computational scheme. We benchmark the scheme by discretizing the Laplace-Beltrami operator on a circle and a sphere, and present convergence results for both explicit and implicit solvers. We then showcase the algorithm on the problem of computing mean curvature of an ellipsoid and of the Stanford Bunny by evaluating the surface divergence of the normal vector field with the proposed Surface DC-PSE method.

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Section: Resultsmentioning

confidence: 99%

Mesh-free collocation for surface differential operators

Shrivastava¹,

Alejandra²,

Incardona³

et al. 2022

Preprint

Self Cite

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“…Differential operators are discretized with second-order accu-racy using Discretization-Corrected Particle Strength Exchange (DC-PSE) [22]. The force balance is solved at every time step with a pressure correction scheme to impose incompressibility [23,24]. For the hydrodynamic boundary conditions, we enforce stress freeness (σ tot xy = σ tot yz = 0) at the x = y = 0 and x = y = L planes and fix the integration constant by imposing zero flow velocity at x = L/2, y = L/2.…”

mentioning

confidence: 99%

“…More simulation details can be found in supplementary information. The simulation computer code is implemented using the scalable computing library OpenFPM [25] and a template expression language for partial differential equations [23].…”

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confidence: 99%

Three Dimensional Spontaneous Flow Transition in Active Polar Fluids

Shrivastava¹,

Vagne²,

Jülicher³

et al. 2023

Preprint

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Active liquid crystals exhibit spontaneous flow when sufficient active stress is generated by internal molecular mechanisms. This is also referred to as active Fréedericksz transition. We show this transition in three dimensions and study its dependence on the boundary conditions. Using nonlinear numerical solutions and linear perturbation analysis, we find an out-of-plane transition under extensile active stress for perpendicular polarity anchoring at the boundary, whereas parallel anchoring permits both in-plane flow under contractile stress and out-of-plane wrinkling under extensile stress.Active fluids are out-of-equilibrium materials driven by energy injection at the microscopic scale [1, 2]. Active materials can have a polar or nematic alignment symmetry of the orientation vector field, and the constituents of the material allow it to generate contractile or extensile active stress. Prominent examples of active fluids are found in living matter across scales, from the cytoskeleton [3, 4] and tissues [5][6][7] to collective behavior in flocks [8]. The hydrodynamic theory of incompressible active polar fluids describes the dynamics of such active liquid crystals at long wavelengths. A key behavior of active polar fluids is their ability to generate spontaneous flow under confinement and sufficient active stress. It has been shown in two dimensions (2D) that spontaneous flow can emerge due to a Fréedericksz-type transition first observed in passive liquid crystals [9]. The passive Fréedericksz transition describes the change of an isotropic state to an anisotropic state under the influence of external electric or magnetic fields [10]. In active liquid crystals, the transition is driven by active molecular processes causing spontaneous material flow [11][12][13].Recent works suggest such instabilities to also exist in three-dimensional (3D) active polar fluids [14]. For example, an extensile active fluid was found to exhibit a bending instability in a simplified model [15], and flow-aligning active fluids were found to display coherent motion in 3D channels upon increased activity [16]. Furthermore, It has been shown that 3D contractile active fluids dampen out-of-plane perturbations, whereas extensile fluids amplify them in the absence of boundary effects [17]. 3D active fluids under confinement behave fundamentally different from their 2D counterparts. Notably, they exhibit flow due to buckling under extensile active stress, which is not possible in 2D for rigid boundaries [18]. Experimentally, this instability has been observed in microtubule assays capable of generating extensile active stresses [18,19].Here, we consider the active Ericksen-Leslie hydrodynamic model and show that the instability exists in 3D. We consider a thick active polar film, which is the 3D extension of a Fréedericksz cell, with anchoring of the polarity and stress-free boundary conditions on the walls. We show how the steady-state spontaneous flow depends on the polarity boundary conditions and the sign of active stress. We derive a...

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A Meshfree Collocation Scheme for Surface Differential Operators on Point Clouds

Singh,

Foggia,

Incardona

et al. 2023

J Sci Comput

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We present a meshfree collocation scheme to discretize intrinsic surface differential operators over scalar fields on smooth curved surfaces with given normal vectors and a non-intersecting tubular neighborhood. The method is based on discretization-corrected particle strength exchange (DC-PSE), which generalizes finite difference methods to meshfree point clouds. The proposed Surface DC-PSE method is derived from an embedding theorem, but we analytically reduce the operator kernels along surface normals to obtain a purely intrinsic computational scheme over surface point clouds. We benchmark Surface DC-PSE by discretizing the Laplace–Beltrami operator on a circle and a sphere, and we present convergence results for both explicit and implicit solvers. We then showcase the algorithm on the problem of computing Gauss and mean curvature of an ellipsoid and of the Stanford Bunny by approximating the intrinsic divergence of the normal vector field. Finally, we compare Surface DC-PSE with surface finite elements (SFEM) and diffuse-interface finite elements (DI FEM) in a validation case.

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A C++ expression system for partial differential equations enables generic simulations of biological hydrodynamics

Cited by 8 publications

References 44 publications

Mesh-free collocation for surface differential operators

Mesh-free collocation for surface differential operators

Three Dimensional Spontaneous Flow Transition in Active Polar Fluids

A Meshfree Collocation Scheme for Surface Differential Operators on Point Clouds

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