The Multi Phase Topology Optimisation is a simulation technique based on the principle of the finite element method which is able to determine the optimal distribution of two or more different materials in combination under thermal and mechanical loads. The objective of optimization is to minimize the component's elastic energy. Conventional topology optimisation methods which simulate adaptive bone mineralization have the disadvantage that there is a continuous change of mass by the growth process. However, MPTO keeps all initial material concentrations and uses methods adapted for molecular dynamics to find energy minimum. Applying MPTO to Mechanically loaded components with a high number of different material densities, the optimization results show graded and sometimes anisotropic porosity distributions which are very similar to natural bone structures. This allows the macro- and microstructure of a mechanical component in one step. This method uses the Rapid Prototyping techniques, 3D printing and selective laser sintering to produce very stiff, light weight components with graded porosities calculated by MPTO. (Wikipedia).
Local linearity for a multivariable function
A visual representation of local linearity for a function with a 2d input and a 2d output, in preparation for learning about the Jacobian matrix.
From playlist Multivariable calculus
Multivariable Calculus: Cross Product
In this video we explore how to compute the cross product of two vectors using determinants.
From playlist Multivariable Calculus
Plotting Points Using Cylindrical Coordinates: Dynamic & Modifiable Illustrator
Link: https://www.geogebra.org/m/tV6CZy9Y
From playlist Multivariable Calculus: Dynamic Interactives!
From rotating impellers stirring air into a liquid, to a turbulent jet entering a moving flow, mixing processes are essential to almost every industrial application you can think of. Omar Matar and his research group at Imperial College London are experts in running numerical simulations t
From playlist Fluid Dynamics
Adding Vectors Geometrically: Dynamic Illustration
Link: https://www.geogebra.org/m/tsBer5An
From playlist Trigonometry: Dynamic Interactives!
Plotting Points Using Spherical Coordinates: Dynamic & Modifiable Illustrator
Link: https://www.geogebra.org/m/h9xS5ZZs
From playlist Multivariable Calculus: Dynamic Interactives!
A.Marveggio:Approximation of multiphase mean curvature flow by means of Allen-Cahn phase-field model
The evolution of interfaces by mean curvature flow features the occurrence of topology changes and geometric singularities. An alternative approach for the description of the underlying dynamics is that of phase-field models of Allen-Cahn type, which replace sharp interfaces with diffuse i
From playlist "SPP meets TP": Variational methods for complex phenomena in solids
Mean angle is not a usual average. Means on circle - Intro to directional statistics (3B1B SoME1)
How to indicate the mean direction (or average direction) of the wind? How to calculate the mean position (or average position) on the circle? [Timestamps below] This video shows that such a simple thing like mean or average changes its meaning for the points belonging to the circle or wh
From playlist Summer of Math Exposition Youtube Videos
3 Squares Problem: Trigonometric Identity (Proof Without Words)
Link: https://www.geogebra.org/m/w8r7rn9Q
From playlist Trigonometry: Dynamic Interactives!
Area of a Regular Polygon: 2 Conceptual Approaches
Links: https://www.geogebra.org/m/aHvgEm9v https://www.geogebra.org/m/wxJFqM9P
From playlist Geometry: Dynamic Interactives!
The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from. #mathematics #DomainOfScience If you would like to buy a poster of this map, they are available here: No
From playlist Math Art
Optimisation algorithms for computer vision and machine learning
Bio Pankaj is a second year PhD student in the Engineering Science department at University of Oxford and an enrichment year student at The Alan Turing Institute. His research interests lie in optimisation and machine learning. At Oxford, he is a member of the OVAL group under Prof. Pawan
From playlist Short Talks
DDPS | Turbulent disperse two-phase flows: simulations and data-driven modeling
In this DDPS talk from Aug. 26, 2021, University of Michigan Assistant Professor in Mechanical Engineering and Aerospace Engineering Jesse Capecelatro discusses a data-driven framework for model closure of the multiphase Reynolds Average Navier—Stokes (RANS) equations. Description: Turbu
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
Topological Sort Algorithm | Graph Theory
How to find the topological sort of a directed acyclic graph Shortest path on a Directed Acyclic Graph (DAG): https://www.youtube.com/watch?v=TXkDpqjDMHA Github source code link: https://github.com/williamfiset/algorithms#graph-theory 0:00 Intro 0:18 Topological sort real life examples
From playlist Graph Theory Playlist
Function Comparision - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Rahul Savani: Polymatrix Games Algorithms and Applications
Polymatrix games are multi-player games that capture pairwise interactions between players. They are defined by an underlying interaction graph, where nodes represent players, and every edge corresponds to a two-player strategic form (bimatrix) game. This talk will be a short survey that w
From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"
Circumgalacitc medium-a laboratory for astrophysical fluid dynamics by Prakriti Pal choudhury
DISCUSSION MEETING FLUIDS DAY ORGANIZERS: Rama Govindarajan, Samriddhi Sankar Ray and Gaurav Tomar DATE : 20 January 2020 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The fluid mechanics community in Bangalore has expanded enormously with different physics and engineering departments
From playlist Fluids Day 2020
Multiphase and multi-scale AGN feedback processes - Dominika Wylezalek
Institute for Advanced Study / Princeton University Joint Astrophysics Colloquium Topic: Multiphase and multi-scale AGN feedback processes Speaker: Dominika Wylezalek Affiliation: University of Heidelberg Date: November 22, 2022 AGN feedback is now widely considered to be one of the main
From playlist Natural Sciences
Multiplicacion de Matrizes 2x2 por 2x2
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Multiplicacion de Matrizes 2x2 por 2x2
From playlist Álgebra
Modeling Batteries Using Simulink and Simscape
Learn about equivalent circuits and why you’d want to use them. In this video, you will learn to: - Use equivalent circuits to represent the dynamic behavior of a battery cell. - Identify how to parameterize the equivalent circuit based on measurement data using parameter estimation. -
From playlist Hybrid Electric Vehicles