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We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface, and then derive simple…
The deformation barriers standing in the quasi-molecular shape path have been determined in the actinide region within a macroscopic-microscopic energy derived from a generalized liquid drop model, the algebraic droplet model shell…
We present a rotation equivariant, quasi-monolithic graph neural network framework for the reduced-order modeling of fluid-structure interaction systems. With the aid of an arbitrary Lagrangian-Eulerian formulation, the system states are…
Investigating blood flow in the cardiovascular system is crucial for assessing cardiovascular health. Computational approaches offer some non-invasive alternatives to measure blood flow dynamics. Numerical simulations based on traditional…
We studied numerically the dynamics of colliding rigid bodies in a Newtonian fluid. The finite element method is used to solve the fluid-body interaction and the fluid motion is described in the Arbitrary-Lagrangian-Eulerian framework. To…
Current state-of-the-art methods for image segmentation form a dense image representation where the color, shape and texture information are all processed together inside a deep CNN. This however may not be ideal as they contain very…
We consider steady nonlinear free surface flow past an arbitrary bottom topography in three dimensions, concentrating on the shape of the wave pattern that forms on the surface of the fluid. Assuming ideal fluid flow, the problem is…
We outline a generic, flexible, modular, yet efficient framework to the computation of energies and states for general nanoscopic systems with a focus on semiconductor quantum dots. The approach utilizes the configuration interaction…
We consider a liquid bridge between two identical spheres and provide approximate expressions for the capillary force and the exposed surface area of the liquid bridge as functions of the liquid bridge's total volume and the sphere…
We propose a distributed cubic regularization of the Newton method for solving (constrained) empirical risk minimization problems over a network of agents, modeled as undirected graph. The algorithm employs an inexact, preconditioned Newton…
For a long time, the point cloud completion task has been regarded as a pure generation task. After obtaining the global shape code through the encoder, a complete point cloud is generated using the shape priorly learnt by the networks.…
Volumetric image segmentation with convolutional neural networks (CNNs) encounters several challenges, which are specific to medical images. Among these challenges are large volumes of interest, high class imbalances, and difficulties in…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…
The general Helfrich shape equation determined by minimizing the curvature free energy describes the equilibrium shapes of the axisymmetric lipid bilayer vesicles in different conditions. It is a non-linear differential equation with…
Having a finite interfacial thickness, the phase-field models supply a way to model the fluid interfaces, which allows the calculations of the interface movements and deformations on the fixed grids. Such modeling is applied to the…
We consider capillary surfaces that are constructed by bounded generating curves. This class of surfaces includes radially symmetric and lower dimensional fluid-fluid interfaces. We use the arc-length representation of the differential…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
Accurate simulation of blood flow in deformable vessels is critical in cardiovascular research for understanding disease progression and informing clinical decision-making. However, due to the thin-walled nature of arteries, traditional…
In this paper we propose a novel numerical scheme for the Canham-Helfrich-Evans bending energy based on a three-field lifting procedure of the distributional shape operator to an auxiliary mean curvature field. Together with its energetic…
We introduce a novel numerical framework for the exploration of Blaschke--Santal\'o diagrams, which are efficient tools characterizing the possible inequalities relating some given shape functionals. We introduce a parametrization of convex…