Related papers: Arbitrary Lagrangian--Eulerian finite element meth…
We present a theory that combines the framework of irreversible thermodynamics with modified integral theorems to model arbitrarily curved and deforming membranes immersed in bulk fluid solutions. We study the coupling between the mechanics…
Diffusion in cell membranes is not just simple two-dimensional Brownian motion, but typically depends on the timescale of the observation. The physical origins of this anomalous sub-diffusion are unresolved, and model systems capable of…
An interfacial regularized Stokeslet scheme is presented to predict the motion of solid bodies (e.g. proteins or gel-phase domains) embedded within flowing lipid bilayer membranes. The approach provides a numerical route to calculate…
We present the numerical methods and GPU-accelerated implementation underlying a Total Lagrangian finite element framework for finite-deformation flexible multibody dynamics, introduced in the companion paper [1]. The framework supports…
A novel method for complex fluid-structure interaction (FSI) involving large structural deformation and motion is proposed. The new approach is based on a hybrid fluid formulation that combines the advantages of purely Eulerian (fixed-grid)…
In this paper, we present a novel interface-driven adaptive variational procedure using a fully Eulerian description of fluid-structure interaction. The proposed fully-Eulerian procedure involves a fixed background unstructured mesh on…
As a sequel to our previous work [C. Ma, Q. Zhang and W. Zheng, SIAM J. Numer. Anal., 60 (2022)], [C. Ma and W. Zheng, J. Comput. Phys. 469 (2022)], this paper presents a generic framework of arbitrary Lagrangian-Eulerian unfitted finite…
Morphological change of bilayer membrane in vivo is not a spontaneous procedure but modulated by various types of proteins in general. Most of these modulations are associated with the localization of related proteins in the crowded lipid…
Laminated glass structures are formed by stiff layers of glass connected with a compliant plastic interlayer. Due to their slenderness and heterogeneity, they exhibit a complex mechanical response that is difficult to capture by…
Cell blebs are protrusions of the cell membrane and can be instrumental for cell migration. We derive a continuum model for the mechanical and geometrical aspects of the onset of blebbing in terms of a force balance. It is abstract and…
Consider a lipid membrane with a free exposed edge. The energy describing this membrane is quadratic in the extrinsic curvature of its geometry; that describing the edge is proportional to its length. In this note we determine the boundary…
An energy stable finite element scheme within arbitrary Lagrangian Eulerian (ALE) framework is derived for simulating the dynamics of millimetric droplets in contact with solid surfaces. Supporting surfaces considered may exhibit…
This paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are demonstrated for a range of benchmark…
This work is in the field of multi-material compressible fluid flows simulation. The proposed scheme is eulerian and related to finite volumes methods, but in a Lagrange-Remap formalism on regular orthogonal meshes. The Lagrangian scheme is…
Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be…
In this work we present a novel second order accurate well balanced Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gasdynamics with gravity in cylindrical…
Random lateral translocation of lipids and proteins is a universal process on membrane surfaces. Local aggregation or organization of lipids and proteins can be induced when this lateral random diffusion is mediated by the electrostatic…
Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…
This review describes the analytical calculation of lateral pressure profile in lipid membrane with finite curvature. The derivation is based on the previously developed microscopic model of flexible strings [1,2]. According to this theory…
We develop a mixed finite element domain decomposition method on non-matching grids for the Biot system of poroelasticity. A displacement-pressure vector mortar function is introduced on the interfaces and utilized as a Lagrange multiplier…