相关论文: Geometry of Valley Growth

Growth in crystals can be { usually } described by field equations such as the Kardar-Parisi-Zhang (KPZ) equation. While the crystalline structure can be characterized by Euclidean geometry with its peculiar symmetries, the growth dynamics…

The simulation of vehicular wireless channels using geometry-based radio channel models is computationally intensive when the number of scatterers is significantly high. In this paper, we propose a new geometry-based stochastic channel…

Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…

This paper describes a study based on computational fluid dynamics (CFD) and deep neural networks that focusing on predicting the flow field in differently distorted U-shaped pipes. The main motivation of this work was to get an insight…

We propose a scheme for the construction of deformed matrix geometries using Landau models. The Landau models are practically useful tools to extract matrix geometries. The level projection method however cannot be applied straightforwardly…

Metastable vaterite crystals were synthesized by increasing the pH and consequently the saturation states of Ca and CO3 containing solutions using an ammonia diffusion method. SEM and TEM analyses indicate that vaterite grains produced by…

Objective: ascending aortic aneurysm growth prediction is still challenging in clinics. In this study, we evaluate and compare the ability of local and global shape features to predict ascending aortic aneurysm growth. Material and methods:…

We study the effect of fluid flow on three-dimensional (3D) dendrite growth using a phase-field model on an adaptive finite element grid. In order to simulate 3D fluid flow, we use an averaging method for the flow problem coupled to the…

We examine the molecular dynamics of crystal growth in the presence of surface melting and surface impurities, and from this propose a detailed microscopic model for the growth of ice from the vapor phase. Our model naturally accounts for…

We investigated the pressure-driven flow in curved channels at low aspect ratio, the latter being the ratio between the channel height (along the axial direction) and width (along the radial direction). The dynamics was studied numerically,…

The formation of pyramid-like structures in thin-film growth on substrates with a quadratic symmetry, e.g., {001} surfaces, is shown to exhibit anisotropic scaling as there exist two length scales with different time dependences. Analytical…

Vesicles are becoming a quite popular model for the study of red blood cells (RBCs). This is a free boundary problem which is rather difficult to handle theoretically. Quantitative computational approaches constitute also a challenge. In…

Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…

The process of morphogenesis, which can be defined as an evolution of the form of an organism, is one of the most intriguing mysteries in the life sciences. It is clear, that gene expression patterns cannot explain the development of the…

The demographics of Kepler planets provide a key testbed for models of planet formation and evolution, particularly for explaining the radius valley separating super-Earths and sub-Neptunes. A primordial interpretation based on differences…

In spite of considerable progress, computing curvature in Volume of Fluid (VOF) methods continues to be a challenge. The goal is to develop a function or a subroutine that returns the curvature in computational cells containing an interface…

In this work, we look at Score-based generative models (also called diffusion generative models) from a geometric perspective. From a new view point, we prove that both the forward and backward process of adding noise and generating from…

The innumerable shapes of plant leaves present a challenge to the explanatory power of biophysical theory. A model is needed that can produce these shapes with a small set of parameters. This paper presents a simple model of leaf shape…

Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding existing spatial…

Soft bodies flowing in a channel often exhibit parachute-like shapes usually attributed to an increase of hydrodynamic constraint (viscous stress and/or confinement). We show that the presence of a fluid membrane leads to the reverse…