Related papers: An empirical formula for the distribution function…
We develop a model of thin turbulent accretion discs supported by magnetic pressure of turbulent magnetic fields. This applies when the turbulent kinetic and magnetic energy densities are greater than the thermal energy density in the disc.…
The coefficient of restitution of colliding viscoelastic spheres is analytically known as a complete series expansion in terms of the impact velocity where all (infinitely many) coefficients are known. While beeing analytically exact, this…
We provide a computational method for quickly determining the correct distribution of optically active nanoparticles for a desired response. This is achieved by simulating the optical response of single nanoparticles and performing a…
We have investigated a weighted chi-square distribution of the variable $\xi$ which is a weighted sum of squared normally distributed independent variables whose weights are cosines of angles $\phi_k=2\pi k/N$, where $k \in \{0,1,...,N-1\}$…
We derive the central stellar velocity dispersion function for quiescent galaxies in 280 massive clusters with $\log (M_{200} / M_{\odot}) > 14$ in IllustrisTNG300. The velocity dispersion function is an independent tracer of the dark…
The velocity distribution of neighbouring stars is deduced from the Hipparcos proper motions. We have used a classical Schwarzschild decomposition and also developed a dynamical model for quasi-exponential stellar discs. This model is a 3-D…
We extend models of our Galaxy based on distribution functions (DFs) that are analytic functions of the action integrals to extended distribution functions (EDFs), which have an analytic dependence on metallicity as well. We use a simple,…
Translational diffusion coefficients are routinely estimated from molecular dynamics simulations. Linear fits to mean squared displacement (MSD) curves have become the de facto standard, from simple liquids to complex biomacromolecules.…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…
We explore the evolution of the mass distribution of dust in collision-dominated debris disks, using the collisional code introduced in our previous paper. We analyze the equilibrium distribution and its dependence on model parameters by…
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
In quantitative finance, it is often necessary to analyze the distribution of the sum of specific functions of observed values at discrete points of an underlying process. Examples include the probability density function, the hedging…
We study the distribution of the exponential functional $I(\xi,\eta)=\int_0^{\infty} \exp(\xi_{t-}) \d \eta_t$, where $\xi$ and $\eta$ are independent L\'evy processes. In the general setting using the theories of Markov processes and…
We investigate the reliability of mass estimators based on the observable velocity dispersion and half-light radius $R_\mathrm{h}$ for dispersion-supported galaxies. We show how to extend them to flattened systems and provide simple…
We prove the formula for the second order "thick" distributional derivative of 1/r in 3 dimensional Euclidean space. This formula generalizes the well known Frahm formulas for the distributional derivatives of 1/r.
The stellar velocity ellipsoid of the solar neighbour is re-examined using intermediate-old mono-abundances stellar groups with high quality chemistry data together with parallaxes and proper motions from Gaia DR1. We find the average…
We introduce novel finite element schemes for curve diffusion and elastic flow in arbitrary codimension. The schemes are based on a variational form of a system that includes a specifically chosen tangential motion. We derive optimal $L^2$-…
We present a novel positive potential-density pair expansion for modelling galaxies, based on the Miyamoto-Nagai (MN) disc. By using three sets of such discs, each one of them aligned along each symmetry axis, we are able to reconstruct a…
Starting from the equations of collisionless linear gyrokinetics for magnetised plasmas with an imposed inhomogeneous magnetic field, we present the first known analytical, closed-form solution for the resulting velocity-space integrals in…