theCFDguy @theCFDguy

The fix for AI enshittification in learning and teaching is quite simple - go back to in person tests and exams. But, we have far too many admins and incompetent academics who will make it very difficult to implement the simple solutions.

We can already build excellent Digital Twins of engineering assets, especially for structures, with existing ingredients (CAD, Simulation models, ROMs, sensors and actuators). What's missing is the integrated frameworks connecting different tools and deploying the DT models.

Where lines meet at right angles, Pythagoras revealed a hidden poetry of numbers. 🎬credit: eeanimation

New paper in @PhysRevFluids! We introduce VIVALDy, a hybrid generative reduced-order model for turbulent flows! journals.aps.org/prfluids/abstr… Using only cylinder displacement, the model reconstructs the turbulent wake in VIV by combining β-VAE–GANs, masked convolutions,and transformers

Area of circle

The same reason why we have Physics-Informed Machine Learning frameworks which are expensive and fragile. It's the trend, aka AI hype.

Nateinthewild | Nate Luebbe @nateinthewild

3 weeks ago

Am I missing something here? The robot is pushing packages from left to right, wouldn’t a conveyor belt do this exact same job at 10x efficiency and 1% the cost?

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I hope Engineers working in industries and government agencies will follow the safety and reliability standard even more stringently. Otherwise, the AI-slop designs are going to cause irreparable damage to our infrastructure and our lives.

adam @adamdotnew

3 weeks ago

Opus 4.7 vs GPT 5.5 at CAD Who wins?

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Noether’s Theorem is one of the most profound and elegant discoveries in the history of physics. Published by Emmy Noether in 1918, it reveals a deep and fundamental connection between symmetries in nature and the conservation laws of physics. In simple terms, Noether’s Theorem states that every continuous symmetry of the laws of physics gives rise to a corresponding conserved quantity. A symmetry means the physical laws remain unchanged under a certain transformation, such as shifting forward or backward in time, moving through space, or rotating an object. The conserved quantity is something that remains constant over time, like energy, linear momentum, angular momentum, or electric charge. For example, because the laws of physics do not change over time, energy is conserved. Because the laws are the same everywhere in space, momentum is conserved. Because the laws look the same in all directions, angular momentum is conserved. Before Noether’s work, scientists treated conservation laws as independent fundamental rules. Her theorem showed that these laws are not arbitrary. They are natural consequences of deeper symmetries in the universe. This insight is incredibly powerful. It allows physicists to discover conserved quantities simply by identifying the symmetries present in a theory. The theorem has become a cornerstone of modern physics, playing a central role in quantum field theory, the Standard Model of particle physics, and general relativity. By shifting our focus from individual conservation laws to the underlying symmetries, Noether’s Theorem changed the way physicists approach fundamental questions about reality. Many major advances in theoretical physics since 1918 have been guided by the search for new symmetries. Noether’s Theorem teaches us that the beautiful symmetries we observe in nature are the true reason why energy, momentum, charge, and other quantities remain conserved. It remains one of the deepest and most influential ideas in all of physics.

Visualization of Stokes' Theorem.

Nikola Tesla invented this valve over a century ago, and NASA still uses the same idea today.

The Navier-Stokes equations are a set of partial differential equations that describe the motion of viscous, fluid substances by balancing forces acting on a fluid element with its change in momentum. Based on Newton’s second law, they are fundamental in engineering and physics, often solved numerically, and are known for their complexity in modeling turbulent flows.

There's an integral so elegant, so mysterious that it shows up everywhere—from physics to probability to quantum mechanics. It's called the Gaussian integral. This integral defines the shape of the normal distribution, also known as the bell curve. It's why test scores cluster around an average, why errors in measurements behave predictably, and why the universe tends to have a most likely outcome even within randomness. And its answer—this is it. Not an approximation, not a coincidence, just pure mathematical magic.

In mathematics, beauty is truth, and truth is beauty

A visual proof that the volume and surface area of a torus is the same as a cylinder (with radius r and height 2πR).

The "Basel Problem" was one of the most famous challenges in 17th-century mathematics. It asked for the precise sum of the reciprocals of the squares of the natural numbers. It defeated many of the top mathematicians, including Jacob Bernoulli, Johann Bernoulli, Daniel Bernoulli, Leibniz, Stirling, de Moivre and others. In 1734, at the age of 28, Leonhard Euler stunned the mathematical world by proving that the sum equals π²/6.

Onion math.

257 years ago, Joseph Fourier was born on this day. In 1822, Fourier showed that any wave can be broken down into an infinite sum of sine waves, using a technique now called the Fourier transform. The Fourier transform is like a recipe generator. You input a complicated wave and you get back its ingredients, the amplitude and frequency of each component sine wave. Fourier analysis is an essential part of modern technology. Its applications range from JPEG compression and image recognition to quantum physics and MRI's. Fourier theory has two components: basic building blocks and labels. Imagine a child's toy castle. This castle can be disassembled into individual building blocks. And these building blocks can then be sorted by color into bins and labeled. Similarly, the Fourier transform disassembles a complex wave into individual sine waves. These are like the building blocks. Each sine wave can be labeled with its frequency, or how quickly it oscillates per second. The labels on the bins are more than just a way to organize things. They can be used to rebuild the original complex wave and as an efficient shorthand for communicating information. For example, when you send a voice message, your phone doesn't transmit an entire complex sound wave. Instead, it breaks it down and sends just the labels or frequencies of the component sine waves. The receiver's phone then reverses this process, converting the labels back into the contents of the bins to reconstruct the message’s original sound wave.

mesh morphing - #interFoam dynamic mesh