Max Gaspari

Great #BlackHoleWeather team dinner tonight: welcome party for Giovanni & Otello, plus celebration for @filippobarbani papers submissions! Super fun and warm evening with the crew, enjoying some very proper Emilian physics fuel: tigelle e crescentine. Nothing like good food, good Lambrusco, and fun discussions to recharge the spirit! #BHWcuisine

The Lorenz attractor is the mathematical basis of the well-known "butterfly effect." It's derived from the Lorenz equations, a set of three ordinary differential equations developed as a simplified mathematical model for weather prediction.

It’s okay to go at your own pace. Typically, the spinning crushed cores of exploded stars spin rapidly when they form. Some whirl around hundreds of times per second. But astronomers found one that turns just once every 18 minutes or so! #MondayMotivation

You're looking at the home of 40 billion stars! 🌟 Messier 95 is a barred spiral galaxy about 33 million light-years away, with glowing arms full of star birth activity: go.nasa.gov/4uxYDLp

Mach 3 flow past a sphere creates a detached bow shock, air compresses, heats, even ionizes into plasma. A perfect shape turns chaotic, shedding vortices with massive wave drag. Pure speed alone creates structure, heat, and turbulence.

🚀 Exponax v0.2.0 — fast & differentiable PDE solvers in JAX New: 3D Navier-Stokes on a single GPU, wave equation stepper, improved dealiasing & memory efficiency 4096² / 256³ on 24GB consumer GPUs 10k² / 512³ on A100/H100 📦 pip install exponax github.com/Ceyron/exponax

“We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning.” — Werner Heisenberg, Physics and Philosophy

GPT-5.2 derived a new result in theoretical physics. We’re releasing the result in a preprint with researchers from @the_IAS, @VanderbiltU, @Cambridge_Uni, and @Harvard. It shows that a gluon interaction many physicists expected would not occur can arise under specific conditions. openai.com/index/new-resu…

To celebrate Valentine's Day, the @chandraxray team has released a new image of the Cocoon Nebula (officially named IC 5146). This heart-shaped nebula is a region in the Milky Way galaxy where new stars are forming. Read more: chandra.si.edu/photo/2026/hea…

this zoomed/rescaled view of a CPU is 🤯 youtube.com/watch?v=QtW1lQ…

That’s it for our Brownian motion mini-series!🫡 We started from “continuous everywhere, differentiable nowhere”, built quadratic variation, watched infinite zero crossings and local time, pushed out to the law of the iterated logarithm, then used Itô’s formula and Itô integrals for real, before showing how SDEs actually arise in practice (random phasor fields in Rayleigh scattering, log-price in Black-Scholes). If you really digest the ideas in these ~8 posts, you’re basically armed to walk into any serious Stochastic Calculus/SDE course anywhere. Support us by buying a coffee at buymeacoffee.com/mathelirium In parting, we hook our complex Ornstein-Uhlenbeck SDE (Rayleigh scattering) to what's called its Fokker-Planck PDE. An SDE is for a single path: dΨ(t) = -λ Ψ(t) dt + σ dZ(t). Now, write Ψ(t) = (X(t), Y(t)), then the drift is a(x,y)=(-λx, -λy) and the diffusion is isotropic with matrix (σ^2/2) I, so the density p(x,y,t) obeys the forward equation: ∂p/∂t = -∇·(a p) + (σ^2/2) Δp = -∂x[(-λx)p] - ∂y[(-λy)p] + (σ^2/2)(∂xx p + ∂yy p). That’s the link...the SDE moves points and the Fokker-Planck moves probability mass. So the same randomness shows up as individual trajectories Ψ(t) in the complex plane and as a smooth density p(x,y,t) flowing under that PDE. In the animation, that’s the OU swarm inside the fog on the left, and the Rayleigh radius law |Ψ(t)| as a time-radius strip on the right. #BrownianMotion #StochasticCalculus #ProbabilityTheory #ItoCalculus #SDEs #MathTwitter

#BHW2025 Workshop – open questions from participants (proof of "HI" = human intelligence)😆

#BHW2025 Workshop – DAY 4 Dinner party & group photo

#BHW2025 Workshop – DAY1 Gaspari @max_gasp talk: "#BlackHoleWeather Introduction" dropbox.com/scl/fi/rctn5hp…

#BHW2025 Workshop – DAY5 Gaspari @max_gasp "Closing remarks"

#BHW2025 Workshop – DAY5 Romero talk: "Subarcminute tSZ Observations and Ties to BlackHoleWeather"

#BHW2025 Workshop – DAY5 Johnson talk: "Optical/UV IFU Observations of AGN Feeding and Feedback"

#BHW2025 Workshop – DAY5 Molendi talk: "AGN Feedback Shaping the Baryon Content of Halos"

#BHW2025 Workshop – DAY5 Fournier talk: "Probing ICM Turbulence with Exascale MHD Simulations"

#BHW2025 Workshop – DAY4 Reefe talk: "Coronal Gas in the CGM of BCGs"