Related papers: Predictive Scaling Laws for Spherical Rotating Dyn…
Similarity scaling, when it can be justified, is a powerful tool for predicting properties of fluid flows and reducing the computational load when using mathematical models. Numerous publications describe different applications of this…
In rapidly rotating turbulence (Rossby number much less than unity), the standard mixing length theory for turbulent convection breaks and Coriolis force enters the force balance such that magnetic field eventually depends on rotation. By…
We present new scaling laws for the thrust production and power consumption of three-dimensional combined heaving and pitching hydrofoils by extending the three-dimensional pitching scaling laws introduced by Ayancik et al. (2019). New…
We present analytical examples of fluid dynamos that saturate through the action of the Coriolis and inertial terms of the Navier-Stokes equation. The flow is driven by a body force and is subject to global rotation and uniform sweeping…
Neural scaling laws--power-law relationships between generalization errors and characteristics of deep learning models--are vital tools for developing reliable models while managing limited resources. Although the success of large language…
Magnetised turbulence is ubiquitous in astrophysical systems, where it notoriously spans a broad range of spatial scales. Phenomenological theories of MHD turbulence describe the self-similar dynamics of turbulent fluctuations in the…
Additional physics beyond standard hydrodynamics is needed to fully model the intracluster medium (ICM); however, as we move to more sophisticated models, it is important to consider the role of magnetic fields and the way the fluid…
The competition between turbulent convection and global rotation in planetary and stellar interiors governs the transport of heat and tracers, as well as magnetic-field generation. These objects operate in dynamical regimes ranging from…
We consider magnetic fields generated by homogeneous isotropic and parity invariant turbulent flows. We show that simple scaling laws for dynamo threshold, magnetic energy and Ohmic dissipation can be obtained depending on the value of the…
It has been suggested in Hoyng (2009) that dynamo action can be analysed by expansion of the magnetic field into dynamo modes and statistical evaluation of the mode coefficients. We here validate this method by analysing a numerical…
Neural scaling laws define a predictable relationship between a model's parameter count and its performance after training in the form of a power law. However, most research to date has not explicitly investigated whether scaling laws can…
Mean-field galactic dynamo theory is the leading theory to explain the prevalence of regular magnetic fields in spiral galaxies, but its systematic comparison with observations is still incomplete and fragmentary. Here we compare…
Star-planet magnetic interactions (SPMI) occurring in the sub-Alfvenic regime can, in principle, induce stellar chromospheric hotspots. Currently, estimates of the power generated by SPMI primarily rely on analytical scaling laws that…
Tidal dissipation in planets and stars is one of the key physical mechanisms driving the evolution of star-planet and planet-moon systems. Several signatures of its action are observed in planetary systems thanks to their orbital…
One common approach for solving collisions between protoplanets in simulations of planet formation is to employ analytical scaling laws. The most widely used one was developed by Leinhardt & Stewart (2012) from a catalog of ~ 180 N-body…
The systematic variation of solar active region (AR) properties with their magnetic flux has been the subject of numerous studies but the proposed scaling laws still vary rather widely. A correct representation of these laws and the…
When training deep neural networks, a model's generalization error is often observed to follow a power scaling law dependent both on the model size and the data size. Perhaps the best known example of such scaling laws are for…
The discovery of dynamical models from data represents a crucial step in advancing our understanding of physical systems. Library-based sparse regression has emerged as a powerful method for inferring governing equations directly from…
This Letter reports scaling laws of free magnetic energy stored in a solar emerging flux region which is a key to understanding the energetics of solar active phenomena such as solar flares and coronal mass ejections. By performing…
This study employs molecular dynamics simulations to investigate droplet dynamics when a stationary droplet on a solid surface is struck by another droplet of similar size from above. The focus is on the jumping behavior of the merged…