Membrane remodeling due to mixture of multiple curvature proteins: Insights from mesoscopic continuum modeling

We present an extension of the Monte Carlo based mesoscopic membrane model where the membrane is represented as a dynamically triangulated surface and the proteins are modeled as anisotropic inclusions formulated as in-plane nematic field variables adhering to the deformable elastic sheet. The local orientation of the nematic field lies in the local tangent plane of the membrane and is free to rotate in this plane. Protein-membrane interactions are modeled as anisotropic spontaneous curvatures of the membrane and protein-protein interactions are modeled by the splay and bend terms of Frank's free energy for nematic liquid crystals. In the extended model, we have augmented the Hamiltonian to study membrane deformation due to a mixture of multiple types of curvature generating proteins. This feature opens the door for understanding how multiple different kinds of curvature-generating proteins may be working in a coordinated manner to induce desired membrane morphologies. For example, among other things, we study membrane deformations and tubulation due to a mixture of positive and negative curvature proteins as mimics of various proteins from BAR domain family working together for curvature formation and stabilization. We also study the effect of membrane anisotropy, which manifests as membrane localization and differential binding affinity of a given curvature protein, leading to insights into the tightly regulated cargo sorting and transport processes. Our simulation results show different morphologies of deformed vesicles that depend on the curvatures and densities of the participating proteins as well as on the protein-protein and membrane-proteins interactions.

Modelling Clamping Force Deflection in Dexel-Based Material Removal Simulations

Machining simulations of material removal that predict workpiece quality are a key factor in gaining an understanding of the possible causes of manufacturing defects. Particularly in the case of thin-walled workpieces, as are frequently produced in the aerospace industry, the workpiece stiffness is of utmost importance. Form deviations on the final workpiece can result due to the the process force or the clamping situation. This article presents a method for modelling the deformation due to the clamping force in dexel-based material removal simulations. To prevent distortion of the dexel model, triangulated surface meshes are generated separately for the start and end points of a dexel field by means of a Delaunay triangulation for the final contour. With the help of an FE simulation of the near contour state, the resulting displacements for the corner points of the triangles are determined and then inversely displaced. Subsequently, the new start and end points of the machined dexels are determined through a 2D interpolation. The method is validated for flatness and roundness deviations using two specimen workpieces. It shows that the prediction can be significantly improved, especially for thin-walled components.

Deformation of membrane vesicles due to chiral surface proteins

Chiral, rod-like molecules can self-assemble into cylindrical membrane tubules and helical ribbons. They have been successfully modeled using the theory of chiral nematics. Models have also predicted the role of chiral lipids in forming nanometer-sized membrane buds in the cell. However, in most theoretical studies, the membrane shapes are considered fixed (cylinder, sphere, saddle, etc.), and their optimum radius of curvatures are found variationally by minimizing the energy of the composite system consisting of membrane and chiral nematics. Numerical simulations have only recently started to consider membrane deformation and chiral orientation simultaneously. Here we examine how deformable, closed membrane vesicles and chiral nematic rods mutually influence each other's shape and orientation, respectively, using Monte-Carlo (MC) simulation on a closed triangulated surface. For this, we adopt a discrete form of chiral interaction between rods, originally proposed by Van der Meer et al. (1976) for off-lattice simulations. In our simulation, both conical and short cylindrical tubules emerge, depending on the strength of the chiral interaction and the intrinsic chirality of the molecules. We show that the Helfrich-Prost term, which couple nematic tilt with local membrane curvature in continuum models, can account for most of the observations in the simulation. At higher chirality, our theory also predicts chiral tweed phase on cones, with varying bandwidths.

Single and multiple springback technique for construction and control of thick prismatic mesh layers

We suggest an algorithm for construction of semi-structured thick prismatic mesh layers which guarantees an absence of inverted prismatic cells in resulting layer and allows one to control near-surface mesh orthogonality. Initial mesh is modelled as a thin layer of highly compressed prisms made of hyperelastic material glued to the triangulated surface. In order to compute robust normals at the vertices of the surface mesh we use quadratic programming algorithm based on the nearest ball concept. This pre-stressed material expands, possibly with self-penetration and extrusion to exterior of computational domain until target layer thickness is attained. Special preconditioned relaxation procedure is proposed based on the solution of stationary springback problem. It is shown that preconditioner can handle very stiff problems. Once an offset prismatic mesh is constructed, self-intersections are eliminated using iterative prism cutting procedure.Next, variational advancing front procedure is applied for refinement and precise orthogonalization of prismatic layer near boundaries. We demonstrate that resulting mesh layer is ‘almost mesh-independent’ in a sense that the dependence of thickness and shape of the layer on mesh resolution and triangle quality is weak. It is possible to apply elastic springback technique sequentially layer by layer. We compare single springback technique with multiple springback technique in terms of mesh quality, stiffness of local variational problems and mesh orthogonality or/and layer thickness balance.

INFLUENCE OF GEOMETRY RECOVERY ON STRESS STATE OF OPTIMIZED PARTS

This paper discusses the influence of geometry recovery on actual stress fields within load-carrying parts that have to be reconstructed from the resulting surfaces obtained by topology optimization procedures. A typical result of a topology optimization process is a triangulated surface which represents the boundary of the optimized part. In a production environment, this triangulated surface is mostly used to reconstruct a proper CAD model of the optimized part. This process is by far not automated and may require significant skills and efforts. Unfortunately, it also unavoidably introduces variations in the geometry of the optimized part. Although visually these variations might seem to be rather minor, they may very quickly introduce significant stress field variations. These variations may result in harmful locally increased stress levels and even significant stress concentrations. To get more insight into these phenomena, the topology of a quasi-two-dimensional example part is optimized. The resulting geometry is then reconstructed with various levels of precision. For the obtained geometries, the stress fields are studied numerically. It is shown that stress field variations are indeed such that they may influence significantly the probability of fatigue crack initiation and consequently the service life of the part. Obviously, the geometry recovery after topology optimization should be done very carefully, especially if the part will be subject to cyclic loading during operation.

A Clustering-Based Bubble Method for Generating High-Quality Tetrahedral Meshes of Geological Models

High-quality mesh generation is critical in the finite element analysis of displacements and stabilities of geological bodies. In this paper, we propose a clustering-based bubble method for generating high-quality tetrahedral meshes of geological models. The proposed bubble method is conducted based on the spatial distribution of the point set of given surface meshes using the clustering method. First, the inputted geological models consisting of triangulated surface meshes are divided into several parts based on spatial distribution of point set, which can be used for the determination of the positions and radii of initial bubbles. Second, a procedure based on distance of nearby bubbles is used to obtain the initial size of bubbles. Third, by enforcing the forces acting on bubbles, all bubbles inside the 3D domain reach an equilibrium state by the motion control equations. Finally, the center nodes of the bubbles can form a high-quality node distribution in the domain, and then the required tetrahedral mesh is generated. Comparative benchmarks are presented to demonstrate that the proposed method is capable of generating highly well-shaped tetrahedral meshes of geological models.

Detailed 3D Fault Representations for the 2019 Ridgecrest, California, Earthquake Sequence

ABSTRACT We present new 3D source fault representations for the 2019 M 6.4 and M 7.1 Ridgecrest earthquake sequence. These representations are based on relocated hypocenter catalogs expanded by template matching and focal mechanisms for M 4 and larger events. Following the approach of Riesner et al. (2017), we generate reproducible 3D fault geometries by integrating hypocenter, nodal plane, and surface rupture trace constraints. We used the southwest–northeast-striking nodal plane of the 4 July 2019 M 6.4 event to constrain the initial representation of the southern Little Lake fault (SLLF), both in terms of location and orientation. The eastern Little Lake fault (ELLF) was constrained by the 5 July 2019 M 7.1 hypocenter and nodal planes of M 4 and larger aftershocks aligned with the main trend of the fault. The approach follows a defined workflow that assigns weights to a variety of geometric constraints. These main constraints have a high weight relative to that of individual hypocenters, ensuring that small aftershocks are applied as weaker constraints. The resulting fault planes can be considered averages of the hypocentral locations respecting nodal plane orientations. For the final representation we added detailed, field-mapped rupture traces as strong constraints. The resulting fault representations are generally smooth but nonplanar and dip steeply. The SLLF and ELLF intersect at nearly right angles and cross on another. The ELLF representation is truncated at the Airport Lake fault to the north and the Garlock fault to the south, consistent with the aftershock pattern. The terminations of the SLLF representation are controlled by aftershock distribution. These new 3D fault representations are available as triangulated surface representations, and are being added to a Community Fault Model (CFM; Plesch et al., 2007, 2019; Nicholson et al., 2019) for wider use and to derived products such as a CFM trace map and viewer (Su et al., 2019).

ABOUT SMOOTH INTERPOLATION OF A TRIANGULATED SURFACE

A method and algorithm for rebuilding a surface triangulation in three-dimensional space defined by an STL file is proposed. An initial surface in 3D space (STL file) is represented as a polyhedron composed of triangular faces. The method is based on the analytical representation of the surface as a piecewise polynomial function. This function is built on a polyhedral surface composed of triangles and satisfies the following requirements: 1) within one face, the function is an algebraic polynomial of the third degree; 2) the function is continuous on the entire surface and preserves the continuity of the first partial derivatives; 3) the surface determined by the function passes through the vertices of the initial triangulated surface. The restructuring of computational meshes is required in cases of distortion of the shape of cells when solving problems of mathematical physics using mesh methods (finite-difference, FEM, etc.). Cell distortion can be due to various reasons. These can be large distortions of moving Lagrangian meshes in the calculations in the current configuration, with instability of the hourglass type, with distortion of the faces of the interface between interacting gaseous, liquid and elastoplastic bodies. The rebuilding of the mesh reduces to solving the problem of constructing a smooth surface passing through the nodes of an existing triangulated surface or part of it. Later the nodes of the new mesh are placed on the constructed smooth surface with existing requirements for the size and shape of the cells. The construction of a smooth piecewise polynomial surface is based on the ideas of spline approximation and reduces to the building of a cubic polynomial on each triangular face, taking into account the smooth conjugation of polynomial pieces of the surface constructed on adjacent faces. The proposed method for rebuilding surface triangulation can be useful for calculating the motion of deformable bodies when solving problems of the dynamics of continuous media on immovable Euler grids.

A Physics-Based Estimation of Mean Curvature Normal Vector for Triangulated Surfaces

In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based derivation is equivalent to the discrete Laplace-Beltrami operator approach in the literature. This work, in addition to providing an alternative expression to calculate the mean curvature normal vector, can be further extended to other mesh structures, including non-triangular and heterogeneous meshes.