Related papers: Self-consistent dynamical models with a finite ext…
Galaxies, dark matter haloes, and star clusters have a finite extent, yet most simple dynamical models have an infinite extent. The default method to generate dynamical models with a finite extent is to apply an energy truncation to the…
The standard method to generate dynamical models with a finite extent is to apply a truncation in binding energy to the distribution function. This approach has the disadvantages that one cannot choose the density to start with, that the…
We present a new step in our systematic effort to develop self-consistent dynamical models with a finite radial extent. The focus is on models with simple analytical density profiles allowing for analytical calculations of many dynamical…
Fully analytical dynamical models usually have an infinite extent, while real star clusters, galaxies, and dark matter haloes have a finite extent. The standard method for generating dynamical models with a finite extent consists of taking…
Two new families of self-consistent axisymmetric truncated equilibrium models for the description of quasi-relaxed rotating stellar systems are presented. The first extends the spherical King models to the case of solid-body rotation. The…
Simple analytical models, such as the Hernquist model, are very useful tools to investigate the dynamical structure of galaxies. Unfortunately, most of the analytical distribution functions are either isotropic or of the Osipkov-Merritt…
We present self-consistent triaxial stellar systems that have analytic distribution functions (DFs) expressed in terms of the actions. These provide triaxial density profiles with cores or cusps at the centre. They are the first…
The truncation of stellar discs is not abrupt but characterized by a continuous distancing from the exponential profile. There exists a truncation curve, $t(r)$, ending at a truncation radius, $r_t$. We present here a theoretical model in…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
Deterministic closures for coarse-grained turbulence models help reproduce mean statistics, but often fail to capture the finite-time growth of uncertainty. Using the framework of shell models as a quantitative multi-scale testbed, we…
Recent advances in diffusion models bring state-of-the-art performance on image generation tasks. However, empirical results from previous research in diffusion models imply an inverse correlation between density estimation and sample…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…
We study truncations of hierarchical equations of motion (HEOM) for finite-dimensional open quantum systems. We prove that for finite-dimensional approximations constructed with a Schur-complement type of terminator, the spectrum converges…
We study analytically the development of gravitational instability in an expanding shell having finite thickness. We consider three models for the radial density profile of the shell: (i) an analytic uniform-density model, (ii) a…
We demonstrate that discontinuous shear thickening (DST) can occur even in moderately dense, inertial suspensions of hydrodynamically interacting, frictionless soft particles. Using the Lubrication-Friction Discrete Element Method, our…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of…
We propose a new method for generating equilibrium models of spherical systems of collisionless particles that are finite in extent, but whose central regions resemble dark matter halos from cosmological simulations. This method involves…