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We show how to compute the circular area invariant of planar curves, and the spherical volume invariant of surfaces, in terms of line and surface integrals, respectively. We use the Divergence Theorem to express the area and volume…
Particles transported in fluids are everywhere, occurring for example in indoor air, the atmosphere, the oceans, and engineering applications. In this study, a novel three-dimensional numerical framework -- the Palabos Turret is presented,…
A Hamiltonian two-field gyrofluid model is used to investigate the dynamics of an electron-ion collisionless plasma subject to a strong ambient magnetic field, within a spectral range extending from the magnetohydrodynamic (MHD) scales to…
We demonstrate the utility of the bispectrum, the Fourier three-point correlation function, for studying driving scales of magnetohydrodynamic (MHD) turbulence in the interstellar medium. We calculate the bispectrum by implementing a…
We describe the procedure used to flux calibrate the three-band submillimetre photometer in the Spectral and Photometric Imaging REceiver (SPIRE) instrument on the Herschel Space Observatory. This includes the equations describing the…
The classic, two-component, crust-superfluid model of a neutron star can be formulated as a noise-driven, linear dynamical system, in which the angular velocities of the crust and superfluid are tracked using a Kalman filter applied to…
In the Interstellar Medium (ISM), gas and dust evolve under magnetohydrodynamic (MHD) turbulence. This produces dense, non-linear structures that then seed star formation. Observationally and theoretically, turbulence is quantified by…
We introduce a novel approach for measuring the total curvature at every triangle of a discrete surface. This method takes advantage of the relationship between per triangle total curvature and the Dirichlet energy of the Gauss map. This…
Chiral particles are experimentally investigated while settling inwater with various turbulence intensity levels. The locations and orientations of the particles are tracked over time, allowing the close investigation of the particles'…
A new inversion method for determining near-surface shear currents from a measured wave spectrum is introduced. The method is straightforward to implement and starts from the existing state-of-the-art technique of assigning effective depths…
We present a novel, deterministic, and efficient method to detect whether a given rational space curve is symmetric. By using well-known differential invariants of space curves, namely the curvature and torsion, the method is significantly…
This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…
We propose a framework for a global description of the dynamics of complex flows via clusterized spatial representations of the flow, isolating and identifying local dynamics, retrieving different Space-Time Cluster-Based Network Models…
In this review many of the well known tools for the analysis of Complex systems are used in order to study the global coupling of the turbulent convection zone with the solar atmosphere where the magnetic energy is dissipated explosively.…
Traditional methods for solving physical equations in curved spaces, especially in fluid mechanics and general relativity, rely heavily on the use of Christoffel symbols. These symbols provide the necessary corrections to account for…
Magnetic geometry has a significant effect on the level of turbulent transport in fusion plasmas. Here, we model and analyze this dependence using multiple machine learning methods and a dataset of > 200,000 nonlinear simulations of…
Measures of discrepancy between probability distributions (statistical distance) are widely used in the fields of artificial intelligence and machine learning. We describe how certain measures of statistical distance can be implemented as…
Predicting the outcome of jet-milling based on the knowledge of process parameters and starting material properties is a task still far from being accomplished. Given the technical difficulties in measuring thermodynamics, flow properties…
The complex interaction between shocks and plasma turbulence is extremely important to address crucial features of energy conversion in a broad range of astrophysical systems. We study the interaction between a supercritical, perpendicular…
We present a novel method for calculating interface curvature on 3D unstructured meshes from piecewise-linear interface reconstructions typically generated in the volume of fluid method. Interface curvature is a necessary quantity to…