Related papers: Predictive Scaling Laws for Spherical Rotating Dyn…
Numerical dynamo models always employ parameter values that differ by orders of magnitude from the values expected in natural objects. However, such models have been successful in qualitatively reproducing properties of planetary and…
Earth's magnetic field is generated by processes in the electrically conducting, liquid outer core, subsumed under the term `geodynamo'. In the last decades, great effort has been put into the numerical simulation of core dynamics following…
Numerical experiments of dynamo action designed to understand the generation of Earth's magnetic field produce different regime branches identified within bifurcation diagrams. Notable are distinct branches where the resultant magnetic…
Numerical simulations of convection driven rotating spherical shell dynamos have often been performed with rigid boundary conditions, as is appropriate for the metallic cores of terrestrial planets. Free-slip boundaries are more appropriate…
Magnetic field observations of low-mass stars reveal an increase of magnetic activity with increasing rotation rate. The so-called activity-rotation relation is usually attributed to changes in the underlying dynamo processes generating the…
In fluid dynamics, the scaling behaviour of flow length scales is commonly used to infer the governing force balance of a system. The key to a successful approach is to measure length scales that are representative of the energy contained…
Dynamo action in the Earth's outer core is expected to be controlled by a balance between pressure, Coriolis, buoyancy and Lorentz forces, with marginal contributions from inertia and viscous forces. Current numerical simulations of the…
Scaling laws arise and are eulogized across disciplines from natural to social sciences for providing pithy, quantitative, `scale-free', and `universal' power law relationships between two variables. On a log-log plot, the power laws…
Glorified dimensional analysis is used to derive scaling rules for internal and external magnetic field strengths and various time scales. Naive dimensional analysis is inconclusive because of multiple time scales, but physical arguments…
Galactic dynamo models have generally relied on input parameters that are very challenging to constrain. We address this problem by developing a model that uses observable quantities as input: the galaxy rotation curve, the surface…
The dynamo effect is the most popular candidate to explain the non-primordial magnetic fields of astrophysical objects. Although many systematic studies of parameters have already been made to determine the different dynamical regimes…
Rotational scaling relationships are examined for the degree of equipartition between magnetic and kinetic energies in stellar convection zones. These scaling relationships are approached from two paradigms, with first a glance at scaling…
The geodynamo features a broad separation between the large scale at which Earth's magnetic field is sustained against ohmic dissipation and the small scales of the turbulent and electrically conducting underlying fluid flow in the outer…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the…
This paper presents two interesting scaling laws, which relate some critical exponents in the critical behavior of spherically symmetric gravitational collapses. These scaling laws are independent of the details of gravity theory under…
This paper examines the consistency of the exact scaling laws for isotropic MHD turbulence in numerical simulations with large magnetic Prandtl numbers Pm and with Pm=1. The exact laws are used to elucidate the structure of the magnetic and…
This paper provides a brief overview of dynamo scaling relationships for the degree of equipartition between magnetic and kinetic energies. Three basic approaches are adopted to explore these scaling relationships, with a first look at two…
Neural scaling laws establish a predictable relationship between model performance and data or compute, offering crucial guidance for resource allocation in new domains and tasks. Yet such laws are most needed precisely where they are…
Here, we develop scaling laws for (1) the distribution of impact-induced heat within the mantle and (2) shape of the impact-induced melt based on more than 100 smoothed particle hydrodynamic (SPH) simulations. We use Legendre polynomials to…