Numerical analysis | Functional analysis | Computational fluid dynamics | Applied mathematics

Explicit algebraic stress model

The algebraic stress model arises in computational fluid dynamics. Two main approaches can be undertaken. In the first, the transport of the turbulent stresses is assumed proportional to the turbulent kinetic energy; while in the second, convective and diffusive effects are assumed to be negligible. Algebraic stress models can only be used where convective and diffusive fluxes are negligible, i.e. source dominated flows. In order to simplify the existing EASM and to achieve an efficient numerical implementation the underlying tensor basis plays an important role. The five-term tensor basis that is introduced here tries to combine an optimum of accuracy of the complete basis with the advantages of a pure 2d concept. Therefore a suitable five-term basis is identified. Based on that the new model is designed and validated in combination with different eddy-viscosity type background models. (Wikipedia).

Explicit algebraic stress model
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Section (3 5) Implicit Derivatives

Applied Calculus – Section (3.5) – Implicit Derivatives This lecture discusses compares explicit and implicit functions. We work out an example that can be differentiated both explicitly and implicitly and show equivalent results. Examples are worked out which invoke other derivative rules

From playlist Applied Calculus

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Implicit differentiation COMPLETELY EXPLAINED! (KristaKingMath)

► My Derivatives course: https://www.kristakingmath.com/derivatives-course Implicit differentiation is the method you use to find a derivative when you can't define the original equation explicitly. Explicitly defined equations are equations that are solved for y in terms of x. In other w

From playlist Calculus I

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An Introduction to Stress and Strain

This video is an introduction to stress and strain, which are fundamental concepts that are used to describe how an object responds to externally applied loads. Stress is a measure of the distribution of internal forces that develop within a body to resist these applied loads. There are

From playlist Mechanics of Materials / Strength of Materials

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R - Latent Growth (Curve) Example

Lecturer: Dr. Erin M. Buchanan Missouri State University Summer 2016 This video covers an example of how to perform a latent growth model with steps over intercepts, random intercepts, random slopes, slopes, covariance, and residuals. Lavaan and the growth() functions are used. Lecture

From playlist Structural Equation Modeling

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State of Stress. Part 4.

Relationship between the shear and axial strain is demonstrated. Lectures for Mechanics of Solids and Structures course at Olin College.

From playlist Lectures for mechanics of solids and structures

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Normal Stress and Normal Strain | Mechanical Properties of Solids | Don't Memorise

Stress and strain are basically classified into two types of stress and types of strain: Normal Stress/ Normal Strain and Shear Stress/ Shear Strain. To know what they mean, watch the video! (Mechanical Properties of Solids) In this video, we will learn: 0:00 Introduction 0:09 Types of

From playlist Physics

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Calculus 1 Lecture 2.7: Implicit Differentiation

Calculus 1 Lecture 2.7: Implicit Differentiation

From playlist Calculus 1 (Full Length Videos)

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R - Full Structural Equation Models Lecture

Lecturer: Dr. Erin M. Buchanan Missouri State University Summer 2016 This lecture covers how to program reflexive and formative indicators in lavaan, their interpretation, and how to use them. We talk about how to convert from a measurement model only to a full structural model. Lectur

From playlist Structural Equation Modeling

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Abstract Algebra | Injective Functions

We give the definition of an injective function, an outline of proving that a given function is injective, and a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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Padma Srinivasan - Conductors and minimal discriminants of hyperelliptic curves - AGONIZE conference

Conductors and minimal discriminants are two measures of degeneracy of the singular fiber in a family of hyperelliptic curves. In genus one, the Ogg–Saito formula shows that these two invariants are equal, and in genus two, Qing Liu showed that they are related by an inequality. In this ta

From playlist Arithmetic Geometry is ONline In Zoom, Everyone (AGONIZE)

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Clément Hongler - Ising model, (para)fermions, and field theory

In the last 20 years, parafermionic observables have allowed one to rigorously connect lattice models and conformal field theories. I'll present old and recent results and discuss new perspectives (there will new pictures!). Clément Hongler (EPFL)

From playlist 100…(102!) Years of the Ising Model

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The ABC Conjecture, Brian Conrad (Stanford) [2013]

slides for this talk: https://drive.google.com/file/d/1J04zXCQYgn9MdgDUo63rH719cruiQJVo/view?usp=sharing The ABC Conjecture Brian Conrad [Stanford University] Stony Brook Mathematics Colloquium Video September 12, 2013 http://www.math.stonybrook.edu/Videos/Colloquium/video_slides.php?

From playlist Number Theory

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Initial Theta Data - part 04 - Existence and Examples

Here we use the last part of Papa Silverman to show how one can construct initial theta data.

From playlist Initial Theta Data

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Analytic Geometric Langlands-correspondence: Relations to Conformal (Lecture 2) by Joerg Teschner

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 Pandi

From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)

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Analytic Geometric Langlands-correspondence: Relations to Conformal ..(Lecture 3) by Joerg Teschner

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 Pandi

From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)

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Bartomeu Fiol - Radiation from Matrix Models

I give an overview of work characterizing radiation in generic four-dimensional conformal field theories. I argue that for theories with conformal scalars, the radiated energy is not positive definite and the radiated power is not Lorentz invariant. I then determine the coupling dependence

From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday

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An Arithmetic Refinement of Homological Mirror Symmetry for the 2-Torus - Yanki Lekili

Yanki Lekili University of Cambridge November 9, 2012 We establish a derived equivalence of the Fukaya category of the 2-torus, relative to a basepoint, with the category of perfect complexes on the Tate curve over Z[[q]]. It specializes to an equivalence, over Z, of the Fukaya category o

From playlist Mathematics

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Elliptic Curves - Lecture 8a - Weierstrass models, discriminant, and j-invariant

This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/

From playlist An Introduction to the Arithmetic of Elliptic Curves

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10 Adjoint state method

We show the connection between the method of adjoints in optimal control to the implicit function theorem ansatz. We relate the costate or adjoint state variable to Lagrange multipliers.

From playlist There and Back Again: A Tale of Slopes and Expectations (NeurIPS-2020 Tutorial)

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Serre Duality on Character Varieties and Explicit Reciprocity Laws by Otmar Venjakob

PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla

From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)

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Projection (linear algebra) | Tensor | Computational fluid dynamics | Algebraic equation