Video yükleniyor...

Video Yüklenemedi

Ana Sayfaya Dön

Finite Element Methods use fine meshes only where greater detail is needed, allowing the focusing behavior of a convex lens to be simulated accurately without the cost of refining the entire domain.

mathelirium's profile picture

Mathelirium

35,849 subscribers

16,128 görüntüleme • 2 ay önce •via X (Twitter)

LIVE

Anya Rossi• Live Now

Private livecam show

0 Yorum

Yorum bulunmuyor

Orijinal gönderinin yorumları burada görünecek

Benzer Videolar

Vikram Sarabhai Space Centre (VSSC), Indian Space Research Organisation, Thiruvananthapuram, is organising National Finite Element Developers' / FEAST Users’ meet (NAFED08) on February 01, 2025, at IIT Hyderabad. FEAST (Finite Element Analysis for STructures), a general purpose finite element software is completely an indigenous development complying with industry standard practices. To promote the usage of FEAST and enhance its capabilities through collaboration, NAFED is being conducted annually since 2016. The objective of the meet is to bring together domain experts and software developers within the country in the field of finite element and numerical methods. The central focus of the meet will be on the usage of FEAST software for solving complex engineering problems and consolidate usage feedbacks to enhance the software. Developers from academia and start-ups are given an opportunity to showcase their possible collaborative work and interact with FEAST software developers on how to interface their work with FEAST as external modules using python scripting. Events like a competition for design and analysis of structures using FEAST and a Quiz competition for students on finite element analysis are also planned as part of the meet. For further details visit the meet link:
3:07

Vikram Sarabhai Space Centre (VSSC), Indian Space Research Organisation, Thiruvananthapuram, is organising National Finite Element Developers' / FEAST Users’ meet (NAFED08) on February 01, 2025, at IIT Hyderabad. FEAST (Finite Element Analysis for STructures), a general purpose finite element software is completely an indigenous development complying with industry standard practices. To promote the usage of FEAST and enhance its capabilities through collaboration, NAFED is being conducted annually since 2016. The objective of the meet is to bring together domain experts and software developers within the country in the field of finite element and numerical methods. The central focus of the meet will be on the usage of FEAST software for solving complex engineering problems and consolidate usage feedbacks to enhance the software. Developers from academia and start-ups are given an opportunity to showcase their possible collaborative work and interact with FEAST software developers on how to interface their work with FEAST as external modules using python scripting. Events like a competition for design and analysis of structures using FEAST and a Quiz competition for students on finite element analysis are also planned as part of the meet. For further details visit the meet link:

ISRO

74,297 görüntüleme • 1 yıl önce

A Physics-Informed Neural Network (PINN) is trying to learn a solution to the Klein-Gordon PDE PINNs are neural nets trained to satisfy a partial differential equation. They use a simple trick of baking the PDE residual straight into the loss. They came out of a very practical pain point. Classical PDE pipelines can be amazing, but they often demand a lot of setup work such as meshes, stencils, and stability tuning. Once you build a solver, it’s usually tied to one geometry and one discretization choice. A PINN flips the workflow. You represent the solution itself as a smooth function uᵩ(x,t) and you enforce the physics wherever you choose to sample the domain.
1:00

A Physics-Informed Neural Network (PINN) is trying to learn a solution to the Klein-Gordon PDE PINNs are neural nets trained to satisfy a partial differential equation. They use a simple trick of baking the PDE residual straight into the loss. They came out of a very practical pain point. Classical PDE pipelines can be amazing, but they often demand a lot of setup work such as meshes, stencils, and stability tuning. Once you build a solver, it’s usually tied to one geometry and one discretization choice. A PINN flips the workflow. You represent the solution itself as a smooth function uᵩ(x,t) and you enforce the physics wherever you choose to sample the domain.

Mathelirium

56,467 görüntüleme • 5 ay önce

A Lens Is a Physical Fourier Computer A lens does not only bend light. It computes with the wave. Send several Gaussian beams into the lens, and the field after the glass is no longer just focused. The lens adds a quadratic phase, lets the wave propagate, and converts angle into position at the focal plane. That detector plane is the Fourier plane.
1:00

A Lens Is a Physical Fourier Computer A lens does not only bend light. It computes with the wave. Send several Gaussian beams into the lens, and the field after the glass is no longer just focused. The lens adds a quadratic phase, lets the wave propagate, and converts angle into position at the focal plane. That detector plane is the Fourier plane.

Mathelirium

34,713 görüntüleme • 3 ay önce

The entire universe itself is finite (creation). Just like u having the ability to lift a cup of water (which is finite) whenever u wish via "kasb" and it wouldn't be shirk or kufr according to asharis, controlling the ENTIRE universe however one wishes with ALL its atoms ..
1:36

The entire universe itself is finite (creation). Just like u having the ability to lift a cup of water (which is finite) whenever u wish via "kasb" and it wouldn't be shirk or kufr according to asharis, controlling the ENTIRE universe however one wishes with ALL its atoms ..

Muwahhid

20,449 görüntüleme • 7 ay önce

Higuruma is the only character in the entire jjk verse to have grown faster than Yuji. He was able to use domain amplification, and RCT in the span of just three months of becoming a sorcerer. Bro rivals Gojo in terms of pure potential.
0:53

Higuruma is the only character in the entire jjk verse to have grown faster than Yuji. He was able to use domain amplification, and RCT in the span of just three months of becoming a sorcerer. Bro rivals Gojo in terms of pure potential.

𝙰𝚗𝚒𝚖𝚎 𝙵𝚕𝚒𝚡

57,689 görüntüleme • 7 gün önce

Do you actually know what convex optimization is in the geometric, guarantee-theoretic sense or have you only met it through solvers and loss curves? Convexity is rare comfort in optimization...there are no spurious local minima, no surprise traps, and inequalities you can use like tools instead of prayers. So, what is this convexity? Let x = (x₁, x₂) and let f(x) be convex. Plot the surface z = f(x). Pick a contact point x₀. The local slope is the gradient p = ∇f(x₀). That p is exactly the data that defines the supporting plane: z = f(x₀) + p · (x − x₀). Thus, f is said to be convex because for every x, f(x) ≥ f(x₀) + p · (x − x₀). So the plane at x₀ can slide under the surface, but it never slices through it. Not near the point...everywhere. Now for here is the interesting part: The slope becomes a coordinate system! Rewrite the same plane as z = p · x − b, where b is the offset. Because the plane passes through (x₀, f(x₀)), the offset is forced to be b = p · x₀ − f(x₀). And that number isn’t just geometry trivia. It’s the convex conjugate: f*(p) = sup over x ( p · x − f(x) ). At a differentiable contact point, the supporting plane touches f tightly enough that the supremum is achieved at x₀, giving the identity f*(p) = p · x₀ − f(x₀) when p = ∇f(x₀). So one moving contact point gives two linked readouts: primal position x₀ dual position (slope) p = ∇f(x₀) dual offset f*(p) One surface. Two worlds. #ConvexOptimization #Optimization #MachineLearning #SignalProcessing #AppliedMath #Engineering
0:50

Do you actually know what convex optimization is in the geometric, guarantee-theoretic sense or have you only met it through solvers and loss curves? Convexity is rare comfort in optimization...there are no spurious local minima, no surprise traps, and inequalities you can use like tools instead of prayers. So, what is this convexity? Let x = (x₁, x₂) and let f(x) be convex. Plot the surface z = f(x). Pick a contact point x₀. The local slope is the gradient p = ∇f(x₀). That p is exactly the data that defines the supporting plane: z = f(x₀) + p · (x − x₀). Thus, f is said to be convex because for every x, f(x) ≥ f(x₀) + p · (x − x₀). So the plane at x₀ can slide under the surface, but it never slices through it. Not near the point...everywhere. Now for here is the interesting part: The slope becomes a coordinate system! Rewrite the same plane as z = p · x − b, where b is the offset. Because the plane passes through (x₀, f(x₀)), the offset is forced to be b = p · x₀ − f(x₀). And that number isn’t just geometry trivia. It’s the convex conjugate: f*(p) = sup over x ( p · x − f(x) ). At a differentiable contact point, the supporting plane touches f tightly enough that the supremum is achieved at x₀, giving the identity f*(p) = p · x₀ − f(x₀) when p = ∇f(x₀). So one moving contact point gives two linked readouts: primal position x₀ dual position (slope) p = ∇f(x₀) dual offset f*(p) One surface. Two worlds. #ConvexOptimization #Optimization #MachineLearning #SignalProcessing #AppliedMath #Engineering

Mathelirium

38,506 görüntüleme • 7 ay önce

“The cost of inaction is greater than the cost of action” Economist Mariana Mazzucato explains that cuts, like to the winter fuel payments, can actually be more costly in the long term #bbcqt
0:51

“The cost of inaction is greater than the cost of action” Economist Mariana Mazzucato explains that cuts, like to the winter fuel payments, can actually be more costly in the long term #bbcqt

BBC Question Time

81,750 görüntüleme • 1 yıl önce

The VIPER Titanium Money Clip is constructed from 100% solid American titanium and was designed using the latest 3D modelling and finite element analysis software. This premium money clip is engineered to hold up to 60 folded bill & cards without the bulk of a wallet.
0:42

The VIPER Titanium Money Clip is constructed from 100% solid American titanium and was designed using the latest 3D modelling and finite element analysis software. This premium money clip is engineered to hold up to 60 folded bill & cards without the bulk of a wallet.

Superior Titanium Products, Inc.

5,420,043 görüntüleme • 3 yıl önce

A Million-Dollar Storm Mathematics Still Cannot Tame. Turbulence matters because it is the default behavior of real fluids once motion becomes strong enough, e.g. air over wings, blood through vessels, weather in the atmosphere, water in oceans, fuel in engines, and flow in pipes and turbines. We can write down the Navier-Stokes equations for all of this, but in 3D one of the deepest open questions is still whether smooth solutions always stay smooth, or can break down in finite time. That is crucial because it asks whether the basic equations of fluid motion remain mathematically under control forever, or can form a true singularity where the theory itself breaks. Solve that and you got yourself a million dollars
0:33

A Million-Dollar Storm Mathematics Still Cannot Tame. Turbulence matters because it is the default behavior of real fluids once motion becomes strong enough, e.g. air over wings, blood through vessels, weather in the atmosphere, water in oceans, fuel in engines, and flow in pipes and turbines. We can write down the Navier-Stokes equations for all of this, but in 3D one of the deepest open questions is still whether smooth solutions always stay smooth, or can break down in finite time. That is crucial because it asks whether the basic equations of fluid motion remain mathematically under control forever, or can form a true singularity where the theory itself breaks. Solve that and you got yourself a million dollars

Mathelirium

30,056 görüntüleme • 4 ay önce

MeshSplatting: Differentiable Rendering with Opaque Meshes Contributions: (i) An end-to-end optimization of mesh-based scene representations retains visual quality while training 2× faster than current state-of-the-art methods. (ii) Rather than a polygon soup, we generate a connected mesh by refining the vertex locations of a restricted Delaunay triangulation. (iii) Triangles are naturally connected to each other, and quantities stored within vertices are smoothly interpolated across each triangle. (iv) The optimization is aware that the triangles should be opaque, allowing direct high-quality rendering in standard game engines (see Fig. 1), opening the door for classical techniques like the use of depth buffers and occlusion culling [1, 22].
0:49

MeshSplatting: Differentiable Rendering with Opaque Meshes Contributions: (i) An end-to-end optimization of mesh-based scene representations retains visual quality while training 2× faster than current state-of-the-art methods. (ii) Rather than a polygon soup, we generate a connected mesh by refining the vertex locations of a restricted Delaunay triangulation. (iii) Triangles are naturally connected to each other, and quantities stored within vertices are smoothly interpolated across each triangle. (iv) The optimization is aware that the triangles should be opaque, allowing direct high-quality rendering in standard game engines (see Fig. 1), opening the door for classical techniques like the use of depth buffers and occlusion culling [1, 22].

MrNeRF

15,322 görüntüleme • 8 ay önce

The entire world is watching what is happening in India under Sanghis. And I deeply appreciate that the mask is off, allowing the world to see the genuine face of Hindutva. This vulgar display of unhinged behavior is good for India's future.
1:00

The entire world is watching what is happening in India under Sanghis. And I deeply appreciate that the mask is off, allowing the world to see the genuine face of Hindutva. This vulgar display of unhinged behavior is good for India's future.

Darab Farooqui

58,915 görüntüleme • 7 ay önce

"India will be one of the only oil refining hubs in a few years. The world is losing 200,000 barrels of refining capacity a year in Europe. America hasn't set up a new refinery in 50 years. But India is boosting refining capacity to 320 million tons by 2030," says minister Puri
0:49

"India will be one of the only oil refining hubs in a few years. The world is losing 200,000 barrels of refining capacity a year in Europe. America hasn't set up a new refinery in 50 years. But India is boosting refining capacity to 320 million tons by 2030," says minister Puri

Shashank Mattoo

49,732 görüntüleme • 3 ay önce

Can Spacetime Move Faster Than Light? In 1994, Miguel Alcubierre proposed a strange solution to Einstein’s field equations: A Spacetime geometry where a compact region could be transported without the object inside locally breaking the speed of light. The idea is not that a ship accelerates through space faster than light. The local interior remains comparatively calm. The violent part is the surrounding geometry. Space contracts in front of the bubble, expands behind it, and forms a moving transport shell that carries the interior region forward. A simplified form of the Alcubierre metric is ds² = −dt² + [dx − vₛ f(rₛ)dt]² + dy² + dz² where f(rₛ) shapes the warp bubble and vₛ describes the motion of its centre. The physics is still highly speculative, especially because the original construction requires exotic stress-energy, but the mathematical idea is powerful. #GeneralRelativity #AlcubierreDrive #WarpDrive #Spacetime #EinsteinEquations #Relativity #Physics #Astrophysics #Cosmology
0:56

Can Spacetime Move Faster Than Light? In 1994, Miguel Alcubierre proposed a strange solution to Einstein’s field equations: A Spacetime geometry where a compact region could be transported without the object inside locally breaking the speed of light. The idea is not that a ship accelerates through space faster than light. The local interior remains comparatively calm. The violent part is the surrounding geometry. Space contracts in front of the bubble, expands behind it, and forms a moving transport shell that carries the interior region forward. A simplified form of the Alcubierre metric is ds² = −dt² + [dx − vₛ f(rₛ)dt]² + dy² + dz² where f(rₛ) shapes the warp bubble and vₛ describes the motion of its centre. The physics is still highly speculative, especially because the original construction requires exotic stress-energy, but the mathematical idea is powerful. #GeneralRelativity #AlcubierreDrive #WarpDrive #Spacetime #EinsteinEquations #Relativity #Physics #Astrophysics #Cosmology

Mathelirium

37,986 görüntüleme • 1 ay önce

Five years ago, OpenAI trained a 5-fingered humanoid hand to solve a Rubik’s Cube using RL and domain randomization, pushing the boundaries of sim-to-real for fine-motor tasks. It underscored the value of creating sufficiently complex simulated worlds in which robots can learn.
2:46

Five years ago, OpenAI trained a 5-fingered humanoid hand to solve a Rubik’s Cube using RL and domain randomization, pushing the boundaries of sim-to-real for fine-motor tasks. It underscored the value of creating sufficiently complex simulated worlds in which robots can learn.

The Humanoid Hub

66,761 görüntüleme • 1 yıl önce

Element 115 "a night of splendor but where is the soul?"
2:20

Element 115 "a night of splendor but where is the soul?"

Mouthy Buddha

12,603 görüntüleme • 5 ay önce

Aether is a type of energy that can be classified as the Fifth Element and in the past was even part of the periodic table. This energy is present in everything. There are safe ways to capture and use this energy, but unfortunately it has been taken from us and hidden. The higher it is, the greater its presence, perhaps hence the reason for so many towers in the past. The higher you are, the greater the presence of the æther.
1:04

Aether is a type of energy that can be classified as the Fifth Element and in the past was even part of the periodic table. This energy is present in everything. There are safe ways to capture and use this energy, but unfortunately it has been taken from us and hidden. The higher it is, the greater its presence, perhaps hence the reason for so many towers in the past. The higher you are, the greater the presence of the æther.

Bronze Giant

384,691 görüntüleme • 1 yıl önce

I think most of the players didn't notice this detail during the walkthrough, but Iuno's domain has a tiny detail where you can interact with small moons. 4K: #WutheringWaves #WuWa #鳴潮
4:40

I think most of the players didn't notice this detail during the walkthrough, but Iuno's domain has a tiny detail where you can interact with small moons. 4K: #WutheringWaves #WuWa #鳴潮

Naru

23,371 görüntüleme • 11 ay önce

Melania Trump: The widespread of abusive behavior in the digital domain affect the daily lives of our children, families, and communities… My commitment to the Be Best initiative underscores the importance of online safety
1:58

Melania Trump: The widespread of abusive behavior in the digital domain affect the daily lives of our children, families, and communities… My commitment to the Be Best initiative underscores the importance of online safety

Acyn

1,572,697 görüntüleme • 1 yıl önce

Ask anyone who’s taken a course in Ordinary Differential Equations (ODEs) what a solution to an ODE represents geometrically, and most of them won’t have a clean answer. When I first took ordinary differential equations, the pattern was always the same. Early on it turns into a speedrun of methods: separation of variables, integrating factors, variation of parameters, Bernoulli, exact equations. Then pretty quickly the course slides into hammer-picking. Spot the form, apply the recipe, move on. Too mechanical! And the real problem is what you don’t walk away with. You leave with a toolkit, but without a feel for what a differential equation even is, especially geometrically. That matters because in real modeling the equations you meet are rarely nice enough to reward memorised recipes. So you get trained to solve toy forms, while the actual subject stays blurry. The behavior. The flow. The shape of solutions. It wasn't until I watched the first lecture of Professor Arthur Mattuck that I realized I didn’t actually know what a solution to a differential equation represents geometrically. His point is almost embarrassingly simple. A first-order ODE is a slope field, and a solution is a curve that stays tangent to that field everywhere. The math breakdown: Write the ODE as dy/dx = f(x,y). At each point (x,y), attach a tiny line segment with slope f(x,y). A function y = y₁(x) is a solution exactly when its graph follows those slopes. At every x, the slope of the curve equals the slope prescribed by the field at the point on the curve. That’s the one line that ties both viewpoints together: y₁′(x) = f(x, y₁(x)). So solving the ODE and drawing an integral curve are the same statement in two languages. Once you see that, you stop obsessing over whether you can write y(x) in closed form. You start asking the questions that actually matter. Where do solutions flow. Where do they get trapped. Where do they blow up. Where does existence or uniqueness fail because the field isn’t even defined? That’s the perspective shift I wish every ODE course forces early. It’s also why I keep pairing math with animation. #DifferentialEquations #ODEs #VectorFields #AppliedMathematics #Mathematics #
20:13

Ask anyone who’s taken a course in Ordinary Differential Equations (ODEs) what a solution to an ODE represents geometrically, and most of them won’t have a clean answer. When I first took ordinary differential equations, the pattern was always the same. Early on it turns into a speedrun of methods: separation of variables, integrating factors, variation of parameters, Bernoulli, exact equations. Then pretty quickly the course slides into hammer-picking. Spot the form, apply the recipe, move on. Too mechanical! And the real problem is what you don’t walk away with. You leave with a toolkit, but without a feel for what a differential equation even is, especially geometrically. That matters because in real modeling the equations you meet are rarely nice enough to reward memorised recipes. So you get trained to solve toy forms, while the actual subject stays blurry. The behavior. The flow. The shape of solutions. It wasn't until I watched the first lecture of Professor Arthur Mattuck that I realized I didn’t actually know what a solution to a differential equation represents geometrically. His point is almost embarrassingly simple. A first-order ODE is a slope field, and a solution is a curve that stays tangent to that field everywhere. The math breakdown: Write the ODE as dy/dx = f(x,y). At each point (x,y), attach a tiny line segment with slope f(x,y). A function y = y₁(x) is a solution exactly when its graph follows those slopes. At every x, the slope of the curve equals the slope prescribed by the field at the point on the curve. That’s the one line that ties both viewpoints together: y₁′(x) = f(x, y₁(x)). So solving the ODE and drawing an integral curve are the same statement in two languages. Once you see that, you stop obsessing over whether you can write y(x) in closed form. You start asking the questions that actually matter. Where do solutions flow. Where do they get trapped. Where do they blow up. Where does existence or uniqueness fail because the field isn’t even defined? That’s the perspective shift I wish every ODE course forces early. It’s also why I keep pairing math with animation. #DifferentialEquations #ODEs #VectorFields #AppliedMathematics #Mathematics #

Mathelirium

40,841 görüntüleme • 6 ay önce