A collage of images of Schrödinger, his 100-year-old paper and his equation. The Schrödinger equation was integral to changing the way the world saw chemistry as a science. Credit: Madeline Monroe/TKH ...

Abstract: This paper studies the problem of output feedback stabilization of a nonlinear diffusion equation, generally referred to as the generalized porous media equation. This equation occurs in a ...

A hundred years ago this week, at the height of the quantum revolution, Austrian physicist Erwin Schrödinger submitted a manuscript for publication. Its centerpiece was an innocuous-looking equation ...

All the tech we rely on, from cars to smartphones, was engineered using physics. You don’t need to know the science to use these things. But a well-rounded human should understand at least some of the ...

To mathematicians, equations are art. Just as many are moved by a painting or piece of music, to those who appreciate and understand math, expressions of numbers, variables, operations and relations ...

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On Wednesday, Stability AI released weights for Stable Diffusion 3 Medium, an AI image-synthesis model that turns text prompts into AI-generated images. Its arrival has been ridiculed online, however, ...

feq(i,j,1)=w(1)*rho(i,j)*(1.+3.*u); feq(i,j,2)=w(2)*rho(i,j)*(1.+3.*v); feq(i,j,3)=w(3)*rho(i,j)*(1.-3.*u); feq(i,j,4)=w(4)*rho(i,j)*(1.-3.*v); feq(i,j,5)=w(5)*rho(i ...

It’s hard to miss how much attention AI image generators alone have attracted in recent months. With good reason, because they demonstrate the progress of deep learning models in a vivid and playful ...

Abstract: In this research, we present two Numerical algorithms for studying the dynamics of spatially extended coupled nonlinear reaction-diffusion model. The difference in this work is to model a ...

On Tuesday, Stability AI launched Stable Diffusion XL Turbo, an AI image-synthesis model that can rapidly generate imagery based on a written prompt. So rapidly, in fact, that the company is billing ...