Related papers: A robust method for calculating interface curvatur…
Event-based motion field estimation is an important task. However, current optical flow methods face challenges: learning-based approaches, often frame-based and relying on CNNs, lack cross-domain transferability, while model-based methods,…
Image segmentation is an essential component in many image processing and computer vision tasks. The primary goal of image segmentation is to simplify an image for easier analysis, and there are two broad approaches for achieving this: edge…
We consider the spreading of a thin two-dimensional droplet on a planar substrate as a prototype system to compare the contemporary model for contact line motion based on interface formation of Shikhmurzaev [Int. J. Multiphas. Flow 19, 589…
This paper presents a new monolithic free-surface formulation that exhibits correct kinetic and potential energy behavior. We focus in particular on the temporal energy behavior of two-fluids flow with varying densities. Correct energy…
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
We present a robust numerical method for solving incompressible, immiscible two-phase flows. The method extends the monolithic phase conservative level set method with embedded redistancing by Quezada de Luna et al. [38] and a semi-implicit…
In two-phase flow, the presence of inter-phasal surface - the interface - causes additional terms to appear in LES formulation. Those terms were ignored in contemporary works, for the lack of model and because the authors expected them to…
In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network for solving partial differential equations on static and evolving surfaces. For the static surface case, with the aid of level set function, the…
The dynamics of compressible liquid-vapor flow depends sensitively on the microscale behavior at the phase boundary. We consider a sharp-interface approach, and propose a multiscale model to describe liquid-vapor flow accurately, without…
We present a fully-explicit, iteration-free, weakly-compressible method to simulate immiscible incompressible two-phase flows. To update pressure, we circumvent the computationally expensive Poisson equation and use the general pressure…
Estimation of the level set of a function (i.e., regions where the function exceeds some value) is an important problem with applications in digital elevation mapping, medical imaging, astronomy, etc. In many applications, the function of…
We focus on a geometrical inverse problem that involves recovering discontinuities in electrical conductivity based on boundary measurements. This problem serves as a model to introduce a shape recovery technique that merges the…
High-quality surface normal can help improve geometry estimation in problems faced by autonomous vehicles, such as collision avoidance and occlusion inference. While a considerable volume of literature focuses on densely scanned indoor…
We investigate the level set method (LSM) in a specific quantum context; namely the dipole transition moment for a system with a nontrivial Morse potential. We draw equal moment sets in the two-dimensional space of two important parameters…
Insoluble surfactants adsorbed at liquid-liquid or gas-liquid interfaces alter interfacial tension, leading to variations in the normal stress jump and generating tangential Marangoni stresses that can dramatically affect the flow dynamics.…
Approximating PDEs on surfaces by the diffuse interface approach allows us to use standard numerical tools to solve these problems. This makes it an attractive numerical approach. We extend this approach to vector-valued surface PDEs and…
For many applications, we need to use techniques to represent convex shapes and objects. In this work, we use level set method to represent shapes and find a necessary and sufficient condition on the level set function to guarantee the…
Accurate modeling of moving boundaries and interfaces is a difficulty present in many situations of computational mechanics. We use the eXtreme Mesh deformation approach (X-Mesh) to simulate the interaction between two immiscible flows…
This paper presents a new representation of curve dynamics, with applications to vortex filaments in fluid dynamics. Instead of representing these filaments with explicit curve geometry and Lagrangian equations of motion, we represent…
Frequently, the design of physicochemical processes requires screening of large numbers of alternative designs with complex geometries. These geometries may result in conformal meshes which introduce stability issues, significant…