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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

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16,218 просмотров • 4 месяцев назад •via X (Twitter)

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A Luneburg lens bends an Electromagnetic wave without a curved boundary. Instead its dielectric constant changes continuously from the centre to the edge. This forces different parts of the wavelength to travel at different speeds. Here, we solve the full 2D TM EM wave equation on an unstructured triangular mesh using the Finite Element Method (FEM).

A Luneburg lens bends an Electromagnetic wave without a curved boundary. Instead its dielectric constant changes continuously from the centre to the edge. This forces different parts of the wavelength to travel at different speeds. Here, we solve the full 2D TM EM wave equation on an unstructured triangular mesh using the Finite Element Method (FEM).

Mathelirium

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This is an animation of a Photonic Molecule. Light becomes trapped inside a tiny ring and then coupled into another without the two ever touching. The scene is evolved from Maxwell's equations using Finite Difference Time Domain (FDTD) on a dense Yee grid.

This is an animation of a Photonic Molecule. Light becomes trapped inside a tiny ring and then coupled into another without the two ever touching. The scene is evolved from Maxwell's equations using Finite Difference Time Domain (FDTD) on a dense Yee grid.

Mathelirium

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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:

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

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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.

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

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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.

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

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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 ..

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Muwahhid

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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.

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

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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

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

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Diffusion models spend the same compute on a blank wall as on a face. But you often know in advance where the detail will be. Introducing Level-of-Token (LoT) Diffusion: we turn that knowledge into a multiresolution token layout, with fine tokens where detail is needed and coarse tokens elsewhere. 1/9🧵

Diffusion models spend the same compute on a blank wall as on a face. But you often know in advance where the detail will be. Introducing Level-of-Token (LoT) Diffusion: we turn that knowledge into a multiresolution token layout, with fine tokens where detail is needed and coarse tokens elsewhere. 1/9🧵

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This is a visualization of a Rydberg wavepacket. In simple terms it is a way of showing an electron in a very highly excited quantum state. The Math comes from the Schrödinger equation for hydrogen where the electron is described by a wavefunction rather than as a tiny ball moving on a fixed path. The yellow sphere at the centre is the proton, not the electron. The colored 3D surface around it shows places where the electron is more likely to be, i.e. a probability cloud.

This is a visualization of a Rydberg wavepacket. In simple terms it is a way of showing an electron in a very highly excited quantum state. The Math comes from the Schrödinger equation for hydrogen where the electron is described by a wavefunction rather than as a tiny ball moving on a fixed path. The yellow sphere at the centre is the proton, not the electron. The colored 3D surface around it shows places where the electron is more likely to be, i.e. a probability cloud.

Mathelirium

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“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

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BBC Question Time

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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.

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Superior Titanium Products, Inc.

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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].

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].

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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.

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.

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thanks for all the love on this, i'll publish for you to play soon in the meantime here's a demo of some new mechanics: - bending light around a black hole - splitting with a prism - focusing with a convex lens more physics - puzzles - levels coming soon :]

thanks for all the love on this, i'll publish for you to play soon in the meantime here's a demo of some new mechanics: - bending light around a black hole - splitting with a prism - focusing with a convex lens more physics - puzzles - levels coming soon :]

AA

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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.

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.

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

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"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

"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

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