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We describe quantum limits to field sensing that relate noise, geometry and measurement duration to fundamental constants, with no reference to particle number. We cast the Tesche and Clarke (TC) bound on dc-SQUID sensitivity as such a…
Motivated by the centering of biological objects in large cells, we study the generic properties of centering forces inside a ball (or a volume of spherical topology) in $n$ dimensions. We consider two scenarios : autonomous centering (in…
We analyse the results of direct numerical simulations of rotating convection in spherical shell geometries with stress-free boundary conditions, which develop strong zonal flows. Both the Ekman number and the Rayleigh number are varied. We…
We show that the thermodynamic dislocation theory (TDT) predicts a scaling relation between stresses, strain rates, and temperatures for steady-state deformations of crystalline solids, and that this relation is accurately obeyed by a wide…
The geomagnetic field has undergone hundreds of polarity reversals over Earth's history, at a variable pace. In numerical models of Earth's core dynamics, reversals occur with increasing frequency when the convective forcing is increased…
Compressed frictional granular matter cannot flow without dilation. Upon forced shearing to generate flow, the amount of dilation may depend on the initial preparation and a host of material variables. On the basis of both experiments and…
We derive a general dimensionless form for granular locomotion, which is validated in experiments and Discrete Element Method (DEM) simulations. The form instructs how to scale size, mass, and driving parameters in order to relate dynamic…
Active fluids exhibit complex turbulent-like flows at low Reynolds number. Recent work predicted that 2d active nematic turbulence follows universal scaling laws. However, experimentally testing these predictions is conditioned by the…
Hydrodynamic simulations have become irreplaceable in modern cosmology for exploring complex systems and making predictions to steer future observations. In Chapter 1, we begin with a philosophical discussion on the role of simulations in…
The climate is a forced and dissipative nonlinear system featuring non-trivial dynamics of a vast range of spatial and temporal scales. The understanding of the climate's structural and multiscale properties is crucial for the provision of…
The physical background of scaling laws of disk galaxies is reviewed. The match between analytically derived and observed scaling laws is briefly discussed. Accurate modeling of the fraction of baryons that end populating a disk, and the…
The control of energy dissipation in non-spherical particle contact remains an unresolved problem. Unlike spherical contact, where the interaction reduces to a one-dimensional normal oscillator, both the effective inertia and the effective…
Planetary cores are the seat of rich and complex fluid dynamics, in which the effects of rotation and magnetic field combine. The equilibria governing the strength of the magnetic field produced by the dynamo effect, the organisation and…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
Galaxies and the dark matter halos that host them are not spherically symmetric, yet spherical symmetry is a helpful simplifying approximation for idealised calculations and analysis of observational data. The assumption leads to an exact…
The dynamical equations describing the evolution of a physical system generally have a freedom in the choice of units, where different choices correspond to different physical systems that are described by the same equations. Since there…
The turbulent dynamo is a powerful mechanism that converts turbulent kinetic energy to magnetic energy. A key question regarding the magnetic field amplification by turbulence, is, on what scale, $k_{\rm p}$, do magnetic fields become most…
Using direct simulations of hydromagnetic turbulence driven by random polarized waves it is shown that dynamo action is possible over a wide range of magnetic Prandtl numbers from 10^-3 to 1. Triply periodic boundary conditions are being…
Time series forecasting plays a critical role in decision-making processes across diverse fields including meteorology, traffic, electricity, economics, finance, and so on. Especially, predicting returns on financial instruments is a…
Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic non-integrable models that are used to describe real experiments, which do not have the symmetry…