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We review recent insights into the dynamics of the solar convection zone obtained from global numerical simulations, focusing on two recent developments in particular. The first is quasi-cyclic magnetic activity in a long-duration dynamo…
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…
In this work 2D Ising systems were used to simulate the reversals of the Earth's magnetic field. Each spin was supposed to be a ring current in the Earth dynamo and the magnetization to be proportional to the field intensity. Given the…
Examples of cyclic (periodic) behavior in geophysical data abound. In many cases the primary period is known, such as in daily measurements of rain, temperature, and sea level. However, many time series of measurements contain cycles of…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
The calling card of solar magnetism is the sunspot cycle, during which sunspots regularly reverse their polarity sense every 11 years. However, a number of more complicated time-dependent behaviors have also been identified. In particular,…
Modern problems in magnetization dynamics require more and more the numerical determination of the spin-wave spectra and -dispersion in magnetic systems where analytic theories are not yet available. Micromagnetic simulations can be used to…
The periods of magnetic activity cycles in the Sun and solar-type stars do not exhibit a simple or even single trend with respect to rotation rate or luminosity. Dynamo models can be used to interpret this diversity, and can ultimately help…
Metasurfaces are extremely useful for controlling and manipulating electromagnetic waves. Full-wave numerical simulation is highly desired for their design and optimization, but it is notoriously difficult, even for two-dimensional…
An external description for aperiodically sampled MIMO linear systems has been developed. Emphasis is on the sampling period sequence, included among the variables to be handled. The computational procedure is simple and no use of…
The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
We describe computational tools that have been developed to simulate dynamical mass transfer in semi-detached, polytropic binaries that are initially executing synchronous rotation upon circular orbits. Initial equilibrium models are…
Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…
Recent measurements of durations of non-equilibrium processes provide valuable information on microscopic mechanisms and energetics. Comprehensive theory for corresponding experiments so far is well developed for single-particle systems…
This paper introduces a data-driven time embedding method for modeling long-range seasonal dependencies in spatiotemporal forecasting tasks. The proposed approach employs Dynamic Mode Decomposition (DMD) to extract temporal modes directly…
The level of solar magnetic activity, as exemplified by the number of sunspots and by energetic events in the corona, varies on a wide range of time scales. Most prominent is the 11-year solar cycle, which is significantly modulated on…
This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…
We propose a wavelet based method for the characterization of the scaling behavior of non-stationary time series. It makes use of the built-in ability of the wavelets for capturing the trends in a data set, in variable window sizes.…
Spin-dynamics techniques can now be used to study the deterministic time-dependent behavior of magnetic systems containing over 10^5 spins with quite good accuracy. This approach will be introduced, including the theoretical foundations of…