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Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…
The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…
We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical…
Characteristic modes of a spherical shell are found analytically as spherical harmonics normalized to radiate unitary power and to fulfill specific boundary conditions. The presented closed-form formulas lead to a proposal of precise…
We investigate the stress response function of a layer of grains, i.e. the stress profile in response to a localized overload. The shape of the profile is very sensitive to the packing arrangement, and is thus a good signature of the…
Accurate angular quadratures are crucial for the numerical solution of three-dimensional (3D) radiative transfer problems, especially when the spectral line polarisation produced by the scattering of anisotropic radiation is included. There…
Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets…
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…
High-precision stellar analyses require hydrodynamic 3D modeling. Such models predict changes across stellar disks of spectral line shapes, asymmetries, and wavelength shifts. For testing models in stars other than the Sun, spatially…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
A new iterative solver is proposed to efficiently calculate the ground state electronic structure in Density Functional Theory calculations. This algorithm is particularly useful for simulating physical systems considered difficult to…
We develop two new highly efficient estimators to measure the polarization (Stokes parameters) in experiments that constrain the position angle of individual photons such as scattering and gas-pixel-detector polarimeters, and analyse in…
Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…
Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…
Various parametric representations have been proposed to model the speech signal. While the performance of such vocoders is well-known in the context of speech processing, their extrapolation to singing voice synthesis might not be…
Solar spectropolarimetric inversion -- inferring atmospheric conditions from the Stokes vector -- is a key diagnostic tool for understanding solar magnetism, but traditional inversion methods are computationally expensive and sensitive to…
We review the algebraic definition of the efficiency of a polarization modulation scheme, which is commonly adopted for solar and stellar spectro-polarimetry applications, and generalize it to allow distinct states of the modulation cycle…
The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…
A general theoretical framework is developed for interpreting spectropolarimetric observations of optically thin emission line scattering from small dust particles. Spatially integrated and spatially resolved line profiles of both scattered…
Spectral synthesis is a powerful tool with which to find the fundamental parameters of stars. Models are usually restricted to single values of temperature and gravity, and assume spherical symmetry. This approximation breaks down for…