Algebraic geometry | Differential algebra
In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions Pε, where ε is a small number, or a vector of small quantities. The infinitesimal conditions are the result of applying the approach of differential calculus to solving a problem with constraints. The name is an analogy to non-rigid structures that deform slightly to accommodate external forces. Some characteristic phenomena are: the derivation of first-order equations by treating the ε quantities as having negligible squares; the possibility of isolated solutions, in that varying a solution may not be possible, or does not bring anything new; and the question of whether the infinitesimal constraints actually 'integrate', so that their solution does provide small variations. In some form these considerations have a history of centuries in mathematics, but also in physics and engineering. For example, in the geometry of numbers a class of results called isolation theorems was recognised, with the topological interpretation of an open orbit (of a group action) around a given solution. Perturbation theory also looks at deformations, in general of operators. (Wikipedia).
Elastic Deformation and Plastic Deformation | Mechanical Properties of Solids | Don't Memorise
Deformation is simply a change in the shape of a body caused by a Force. But what can be Elastic Deformation and Plastic Deformations? (Mechanical Properties of Solids) We know that when a Spring is Stretched or Compressed it goes back to original shape when released. Why is that? what i
From playlist Physics
Physics, Torque (1 of 13) An Explanation
Explains what torque is, the definition, how it is described and the metric units. Also presented are two examples of how to calculate the torque produced by a force. Torque is a turning force. It is a measure of how much force acting on an object that causes the object to rotate. The ob
From playlist Mechanics
Stress-strain curves and modulus of elasticity
When we apply a stress to a material we get a strain. But how much? The amount of strain will be proportional to the modulus of elasticity also known as Young's modulus or the materials stiffness. Yount's modulus is the slope of the stress vs strain curve during the elastic deformation reg
From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020
Physics - Mechanics: Ch 17 Tension and Weight (1 of 11) What is Tension?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is tension and how to calculate tension using the free-body diagram. Next video in this series can be seen at: https://youtu.be/BxUhaktD8PA
From playlist PHYSICS MECHANICS 1: INTRO, VECTORS, MOTION, PROJECTILE MOTION, NEWTON'S LAWS
Material behavior (introduction)
While we will use the approximation of a linear elastic solid throughout this course, this video is a quick peak at real material behavior. Created for Mechanics of Solids and Structures course at Olin College.
From playlist Lectures for mechanics of solids and structures
Physics - Mechanics: Stress and Strain (11 of 16) Ex. 2: Cutting Steel Sheet
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the force needed to cut through a steel sheet.
From playlist PHYSICS 10.5 STRESS AND STRAIN
What is length contraction? Length contraction gives the second piece (along with time dilation) of the puzzle that allows us to reconcile the fact that the speed of light is constant in all reference frames.
From playlist Relativity
Stress & Strain - Elastic Modulus & Shear Modulus Practice Problems - Physics
This physics video tutorial provides practice problems associated with the elastic modulus and shear modulus of materials. It explains how to calculate the stress and strain of materials when an external force is applied. Stress is the ratio of force and area. Strain is the ratio of the
From playlist New Physics Video Playlist
Craig Kaplan - Parquet Deformations: the tiles, they are a-changin - CoM Apr 2021
A Parquet Deformation is a tessellation that evolves gradually in space, a kind of animation expressed in a single drawing. William Huff developed Parquet Deformations and used them as an exercise for architecture and design students for decades. For a computer scientist, they also represe
From playlist Celebration of Mind 2021
Chelsea Walton, "An Invitation to Noncommutative Algebra," the 2021 NAM Claytor-Woodard Lecture
Chelsea Walton, Rice University, gives the NAM Claytor-Woodard Lecture on "An invitation to Noncommutative Algebra," on January 9, 2021 at the Joint Mathematics Meetings
From playlist Useful math
Line operators and geometry in 3d N=4 gauge theory by Tudor Dimofte
Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries
From playlist Quantum Fields, Geometry and Representation Theory
Stéphane Mallat: "Scattering Invariant Deep Networks for Classification, Pt. 1"
Graduate Summer School 2012: Deep Learning, Feature Learning "Scattering Invariant Deep Networks for Classification, Pt. 1" Stéphane Mallat, École Polytechnique Institute for Pure and Applied Mathematics, UCLA July 18, 2012 For more information: https://www.ipam.ucla.edu/programs/summer
From playlist GSS2012: Deep Learning, Feature Learning
Cécile Sykes: Cell-like membranes are shaped by actin dynamics...
The detailed mechanisms of many cell functions such as motility, traffic, division or filopodia formation is difficult to address due to cell complexity. In all these functions, a common observation is that cytoskeleton assembly correlates with membrane deformation based on active forces.
From playlist Mathematics in Science & Technology
Twisted S-duality by Philsang Yoo
PROGRAM QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Professor Stéphane Mallat: "High-Dimensional Learning and Deep Neural Networks"
The Turing Lectures: Mathematics - Professor Stéphane Mallat: High-Dimensional Learning and Deep Neural Networks Click the below timestamps to navigate the video. 00:00:07 Welcome by Professor Andrew Blake, Director, The Alan Turing Institute 00:01:36 Introduction by Professo
From playlist Turing Lectures
AlgTop0: Introduction to Algebraic Topology
This is the Introductory lecture to a beginner's course in Algebraic Topology given by N J Wildberger of the School of Mathematics and Statistics at UNSW in 2010. This first lecture introduces some of the topics of the course and three problems. His YouTube site "Insights into Mathematic
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Mohamed Boucetta: On the geometry of noncommutative deformations
Recording during the meeting "Workshop on Differential Geometry and Nonassociative Algebras" the November 12, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians
From playlist Geometry
Deformation via dislocation motion
Deformation can occur as dislocations move through a material. Edge and screw dislocations move in perpendicular directions to achieve the same deformation. Edge dislocations move with shear force direction while screw dislocations move perpendicular. Dislocation density can be calculated
From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020
Hooke's Law | Mechanical Properties of Solids | Don't Memorise
Hooke's law is the law that is widely used in engineering. In simple terms, Hooke's law experiment relates the Change in Deformation in spring with the Applied Force! Watch this video to find out the relation & learn what is Hooke's law (Mechanical Properties of Solids) In this video, w
From playlist Physics