Lecture

Surface Curvature and Assimilation

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

PHYS-108: General physics : fluids and electromagnetism

Le cours couvre deux grands chapitres de la physique: l'étude des fluides et l'électromagnétisme. Une introduction aux ondes est également faite pour pouvoir étudier les solutions des équations de l'hydrodynamique et des équations de Maxwell. ...

Description

This lecture covers the main concepts related to surface curvature, including the law of place, main curvature, and how to assimilate a curve on an arbitrary surface. It also delves into examples such as soap bubbles and capillarity, explaining the behavior of interfaces and liquid/gas interactions. Furthermore, it explores fluid mechanics, focusing on the description of moving fluids and the thermal speeds of atoms and molecules. The different types of flow, such as laminar and turbulent flow, are discussed in detail, highlighting their characteristics and behaviors.

Instructor

Christian Gabriel Theiler

Christian Theiler obtained his Master’s degree in physics from ETH Zurich in 2007 and his PhD from EPFL in 2011. He then joined MIT as a postdoctoral associate to work on the Alcator C-Mod tokamak. In 2014, he returned to EPFL as a EUROfusion fellow, to join the TCV tokamak team. Two years later, he was named Tenure Track Assistant Professor in Plasma Physics at EPFL. Christian’s research focuses on tokamak boundary physics and related diagnostic techniques. He has contributed to the understanding of the formation, propagation, and control of turbulent plasma structures, called blobs, and gained new insights on the structure of transport barriers in the plasma periphery in different high-confinement regimes. His current research focuses on detachment physics and turbulence characteristics in conventional and alternative divertor magnetic geometries.

Official source

Ontological neighbourhood

Mathematics

Geometry: Differential geometry

Related concepts (32)

Gaussian curvature

In differential geometry, the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ1 and κ2, at the given point: The Gaussian radius of curvature is the reciprocal of Κ. For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature zero everywhere. The Gaussian curvature can also be negative, as in the case of a hyperboloid or the inside of a torus.

Principal curvature

In differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by the eigenvalues of the shape operator at that point. They measure how the surface bends by different amounts in different directions at that point. At each point p of a differentiable surface in 3-dimensional Euclidean space one may choose a unit normal vector. A normal plane at p is one that contains the normal vector, and will therefore also contain a unique direction tangent to the surface and cut the surface in a plane curve, called normal section.

Scalar curvature

In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the geometry of the metric near that point. It is defined by a complicated explicit formula in terms of partial derivatives of the metric components, although it is also characterized by the volume of infinitesimally small geodesic balls.

Turbulence

In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers. Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent.

Riemann curvature tensor

In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common way used to express the curvature of Riemannian manifolds. It assigns a tensor to each point of a Riemannian manifold (i.e., it is a tensor field). It is a local invariant of Riemannian metrics which measures the failure of the second covariant derivatives to commute. A Riemannian manifold has zero curvature if and only if it is flat, i.

Related lectures (64)

Curvature and Inflection Points

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Gaussian Curvature and Geodesics

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Turbulence: Numerical Flow Simulation

Explores turbulence characteristics, simulation methods, and modeling challenges, providing guidelines for choosing and validating turbulence models.

Conservation Laws and Bernoulli Equation