Related papers: Bone Adaptation as a Geometric Flow
We describe a method for modeling the geometry of porous materials. The approach enables the independent selection of crucial parameters, including porosity, pore size distribution, pore shape, and connectivity. Consequently, it can…
Over the past few years, we developed a mathematically rigorous method to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. We have proved the existence of a geometric transformation…
We present a particle method for estimating the curvature of interfaces in volume-of-fluid simulations of multiphase flows. The method is well suited for under-resolved interfaces, and it is shown to be more accurate than the parabolic…
Bone's mechanostat theory describes the adaptation of bone tissues to their mechanical environment. Many experiments have investigated and observed such structural adaptation. However, there is still much uncertainty about how to define the…
In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric…
This work proposes a gradient-based method to design bone implants using triply-periodic minimal surfaces (TPMS) of spatially varying thickness to maximize bone in-growth. Bone growth into the implant is estimated using a finite element…
The response of many materials to applied forces and boundary constraints depends upon internal geometric changes at multiple submacroscopic levels. Hierarchical structured deformations provide a mathematical setting for the description of…
In this work we present a new conceptual model to describe fluid flow in a porous media system in presence of a large fault. Geological faults are often modeled simply as interfaces in the rock matrix, but they are complex structure where…
The unsteady motion of a gas-liquid interface, such as during splashing or atomization, often results in complex liquid structures embedded in the ambient fluid. Here we explore the use of skeletonization to identify the minimum amount of…
The smoothed particle hydrodynamics (SPH) method has been increasingly used to study fluid problems in recent years; but its computational cost can be high if high resolution is required. In this study, an adaptive resolution method based…
Coordinate-based neural networks parameterizing implicit surfaces have emerged as efficient representations of geometry. They effectively act as parametric level sets with the zero-level set defining the surface of interest. We present a…
We introduce in this paper new and very effective numerical methods based on neural networks for the approximation of the mean curvature flow of either oriented or non-orientable surfaces. To learn the correct interface evolution law, our…
We introduce variational approximations for curve evolutions in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples include the hyperbolic plane, the hyperbolic disk,…
A geometric analysis of protein folding, which complements many of the models in the literature, is presented. We examine the process from unfolded strand to the point where the strand becomes self-interacting. A central question is how it…
Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides…
Orthotropic shell structures are ubiquitous in biology and engineering, from bacterial cell walls to reinforced domes. We present a rescaling transformation that maps an orthotropic shallow shell to an isotropic one with a different local…
When considering flows in biological membranes, they are usually treated as flat, though more often than not, they are curved surfaces, even extremely curved, as in the case of the endoplasmic reticulum. Here, we study the topological…
The biological functions of proteins often depend on dynamic structural ensembles. In this work, we develop a flow-based generative modeling approach for learning and sampling the conformational landscapes of proteins. We repurpose highly…
In microsurgery, lasers have emerged as precise tools for bone ablation. A challenge is automatic control of laser bone ablation with 4D optical coherence tomography (OCT). OCT as high resolution imaging modality provides volumetric images…
Detailed understanding of the coupling between fluid flow and solid deformation in porous media is crucial for the development biomedical devices and novel energy technologies relating to a wide range of geological and biological processes.…