Related papers: Simple analytic equation for airfoil shape descrip…
In a recent paper, a new 3-parameter class of Abel type equations, so-called AIR, all of whose members can be mapped into Riccati equations, is shown. Most of the Abel equations with solution presented in the literature belong to the AIR…
This study presents a comprehensive mathematical framework for modeling the flight dynamics of a six-degree-of-freedom fixed-wing aircraft as a rigid body with three control surfaces: rudder, elevators, and ailerons. The framework consists…
We propose two deep learning models that fully automate shape parameterization for aerodynamic shape optimization. Both models are optimized to parameterize via deep geometric learning to embed human prior knowledge into learned geometric…
We study a singular parabolic equation of the total variation type in one dimension. The problem is a simplification of the singular curvature flow. We show existence and uniqueness of weak solutions. We also prove existence of weak…
The inverse approach is computationally efficient in aerodynamic design as the desired target performance distribution is prespecified. However, it has some significant limitations that prevent it from achieving full efficiency. First, the…
We are seeing a Cambrian explosion of 3D shape representations for use in machine learning. Some representations seek high expressive power in capturing high-resolution detail. Other approaches seek to represent shapes as compositions of…
This research examines the aerodynamic performance of wavy (corrugated) airfoils, focusing specifically on analyzing the impact of two angles of attack: the airfoil's angle of attack and the tail's angle of attack (beta). Simulations were…
We present functional forms allowing a broader range of analytic solutions to common economic equilibrium problems. These can increase the realism of pen-and-paper solutions or speed large-scale numerical solutions as computational…
Shape analysis methods have in the past few years become very popular, both for theoretical exploration as well as from an application point of view. Originally developed for planar curves, these methods have been expanded to higher…
Aerodynamic performance evaluation is an important part of the aircraft aerodynamic design optimization process; however, traditional methods are costly and time-consuming. Despite the fact that various machine learning methods can achieve…
The field of scientific machine learning and its applications to numerical analyses such as CFD has recently experienced a surge in interest. While its viability has been demonstrated in different domains, it has not yet reached a level of…
Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire…
The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms…
Computational Fluid Dynamics (CFD) has become an indispensable tool in the optimization design, and evaluation of aircraft aerodynamics. However, solving the Navier-Stokes (NS) equations is a time-consuming, memory demanding and…
This is not a new result. Purpose of this work is to describe a method to search the analytical expression of the general real solution of the two-dimensional Laplace differential equation. This thing is not easy to find in scientific…
A potential motion of ideal incompressible fluid with a free surface and infinite depth is considered in two-dimensional geometry. A time-dependent conformal mapping of the lower complex half-plane of the auxiliary complex variable $w$ into…
Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We…
We propose a mathematical model for fluids in multiphase flows in order to establish a solid theoretical foundation for the study of their complex topology, large geometric deformations, and topological changes such as merging. Our modeling…
In the calculation of thermodynamic properties and three dimensional structures of macromolecules, such as proteins, it is important to have a good algorithm for computing solvent accessible surface area of macromolecules. Here we propose a…
This paper introduces a new method to stylize 3D geometry. The key observation is that the surface normal is an effective instrument to capture different geometric styles. Centered around this observation, we cast stylization as a shape…