Related papers: Predictive Scaling Laws for Spherical Rotating Dyn…
We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory…
We make use of the formalism described in a previous paper [Martins {\it et al.} Phys. Rev. D90 (2014) 043518] to address general features of wiggly cosmic string evolution. In particular, we highlight the important role played by poorly…
Scaling laws for the thrust production and energetics of self-propelled or fixed-velocity three-dimensional rigid propulsors undergoing pitching motions are presented. The scaling relations extend the two-dimensional scaling laws presented…
Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their…
The mechanism by which the Earth's magnetic field is generated is thought to be thermal convection in the metallic liquid iron core. Computational considerations previously restricted most numerical simulations to a regime where the…
Empirically, large-scale deep learning models often satisfy a neural scaling law: the test error of the trained model improves polynomially as the model size and data size grow. However, conventional wisdom suggests the test error consists…
Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic…
Many spiral galaxies host magnetic fields with energy densities comparable to those of the turbulent and thermal motions of their interstellar gas. However, quantitative comparison between magnetic field properties inferred from observation…
Dense suspensions of particles dispersed in liquids are central to industrial and geophysical processes and serve as model systems for out-of-equilibrium soft matter. At high particle concentrations, they exhibit stress-dependent rheology,…
Magnetic fields pervade astrophysical systems and strongly influence their dynamics. Because magnetic diffusion is usually much faster than system evolution, ancient fields cannot explain the present magnetization of planets, stars, and…
In machine learning, the scaling law describes how the model performance improves with the model and data size scaling up. From a learning theory perspective, this class of results establishes upper and lower generalization bounds for a…
In this Letter, the 2-dimensional dense flow of polygonal particles on an incline with a flat frictional inferior boundary is analyzed by means of contact dynamics discrete element simulations, in order to develop boundary conditions for…
The irregular polarity reversals of the Earth's magnetic field have attracted much interest during the last decades. Despite the fact that recent numerical simulations of the geodynamo have shown nice polarity transitions, the very reason…
We investigate non-linear scaling relations for two-dimensional gravitational collapse in an expanding background using a 2D TreePM code and study the strongly non-linear regime ($\bar\xi \leq 200$) for power law models. Evolution of these…
Passive scalar mixing (metals, molecules, etc.) in the turbulent interstellar medium (ISM) is critical for abundance patterns of stars and clusters, galaxy and star formation, and cooling from the circumgalactic medium. However, the…
Disclosure of scaling relationship between observable quantities gives direct information about dynamics of natural phenomenon. This is the main reason why scaling plays a key role in the methodology of natural sciences. In this talk, Part…
Human mobility patterns deeply affect the dynamics of many social systems. In this paper, we empirically analyze the real-world human movements based GPS records, and observe rich scaling properties in the temporal-spatial patterns as well…
Magnetic fields of low-mass stars and planets are thought to originate from self-excited dynamo action in their convective interiors. Observations reveal a variety of field topologies ranging from large-scale, axial dipole to more…
Neural scaling laws have revolutionized the design and optimization of large-scale AI models by revealing predictable relationships between model size, dataset volume, and computational resources. Early research established power-law…
We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an…