Dernières nouvelles sur les fractales

System identification is an important methodology used in control theory and constitutes the first step of control design. It is known that many real systems can be better characterized by fractional-order models. However, it is often quite complex and difficult to apply classical control theory methods analytically for fractional-order models....

The simultaneous estimation of coefficients and the initial conditions for model fractional parabolic systems of porous media is reduced to the minimization of a least-squares cost functional. This inverse problem uses information about the pressures at a finite number of space time points. The Frechet gradient of the cost functional...

Toyota Research Institute of North America (TRINA) has developed a new simulation-driven inverse design methodology to accelerate the research and development process for fuel cell flow field plates. The methodology sets key performance objectives and directs algorithms to generate structural flow field forms that fulfill those objectives. The TRINA team...

Cardiac diseases are one of the leading mortality factors in modern, industrialized societies, which cause high expenses in public health systems. Due to high costs, developing analytical methods to improve cardiac diagnostics is essential. The heart's electric activity was first modeled using a set of nonlinear differential equations. Following this,...

For every $alpha < 1/3$, we construct an explicit divergence-free vector field $mathbf{b}(t,x)$ which is periodic in space and time and belongs to $C^0_t C^{alpha}_x cap C^{alpha}_t C^0_x$ such that the corresponding scalar advection-diffusion equation $$partial_t theta^kappa + mathbf{b} cdot nabla theta^kappa - kappa Delta theta^kappa = 0$$ exhibits anomalous...

MIT engineers’ new technique analyzes the 3D organization of the genome at a resolution 100 times higher than before....

MIT engineers’ new technique analyzes the 3D organization of the genome at a resolution 100 times higher than before....

This is today’s edition of The Download, our weekday newsletter that provides a daily dose of what’s going on in the world of technology. Artificial intelligence is infiltrating health care. We shouldn’t let it make all the decisions. Would you trust medical advice generated by artificial intelligence? It’s a question raised by...

An example of the fractal structures in spin ice, together with a famous example of a fractal (the Mandelbrot set) on top of a photograph of water ice. Image: Jonathan N. Hallén, Cavendish Laboratory, University of Cambridge.The nature and properties of materials depend strongly on dimension. Life in a one-dimensional...

Ann Reardon is probably the last person whose content you’d expect to be banned from YouTube. A former Australian youth worker and a mother of  three, she has her own cookbook, has baked for the BBC, and once made a coin-size apple pie for two baby chicks. Since 2011 she’s...

When water flows through a bed of ground espresso beans, ultimately resulting in a delicious latte, the water is undergoing a process called percolation. The water slowly meanders through the coffee at just the right rate to extract the rich coffee flavors. In general, percolation refers to liquids filtering through...

All countries in the world urgently need to adapt to climate change but are not yet in a good position to do so. It’s urgent because we are not even adapted to the present climate. This fact is underscored by recent weather-related calamities, such as flooding in Central Europe and...