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Approximating nonlinear dynamics with a truncated perturbative expan- sion may be accurate for a while, but it in general breaks down at a long time scale that is one over the small expansion parameter. There are interesting occasions in…
We present a family of spherical models for elliptical galaxies and bulges consisting of a stellar component and a central black hole. All models in this family share the same stellar density profile, which has a steep central cusp. The…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
It is well known that the density and anisotropy profile in the inner regions of a stellar system with positive phase-space distribution function are not fully independent. Here we study the interplay between density profile and orbital…
Statler (1987) demonstrated that self-consistent triaxial models with the perfect density law could be constructed for virtually any choice of axis ratios. His experiments are repeated here using triaxial mass models based on Jaffe's…
We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is analytically computed and is shown to be fractal and/or absolutely continuous according to the value…
The analytical phase-space distribution function (DF) of spherical self--consistent galaxy (or cluster) models, embedded in a dark matter halo, where both density distributions follow the Hernquist profile, with different total masses and…
A model one-dimensional self consistent steady state collisionless self-gravitating system in which all the particles have the same energy is presented. This has the remarkable property that the position and velocity of the particles…
In this Part 2 we study further experimental properties of two-layer exchange flows in a stratified inclined duct (SID), which are turbulent, strongly-stratified, shear-driven, and continuously-forced. We analyse the same state-of-the-art…
Analytic results for the asymptotic decay of the electron density matrix in insulators have been obtained in all three dimensions ($D=1 - 3$) for a tight-binding model defined on a simple cubic lattice. The anisotropic decay length is shown…
We present a general formalism for studying generalized Holographic Dark Energy (HDE) models in which we use a dimensionless form of the area-entropy of cosmological horizons. The future event horizon is applied though the formalism can…
Although density functional theory provides reliable predictions for the static properties of simple fluids under confinement, a theory of comparative accuracy for the transport coefficients has yet to emerge. Nonetheless, there is evidence…
Numerical dynamo models always employ parameter values that differ by orders of magnitude from the values expected in natural objects. However, such models have been successful in qualitatively reproducing properties of planetary and…
Simulated dark matter profiles are often modelled as a `NFW' density profile rather than a single power law. Recently, attention has turned to the rather rigorous power-law behaviour exhibited by the `pseudo phase-space density' of the dark…
We develop a flexible set of action-based distribution functions (DFs) for stellar haloes. The DFs have five free parameters, controlling the inner and outer density slope, break radius, flattening and anisotropy respectively. The DFs…
We consider a spatially flat FLRW universe. We assume that it is filled with dark energy in the form of logotropic dark fluid coupled with dark matter in the form of a perfect fluid having a barotropic equation of state. We employ dynamical…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
We demonstrate the existence of distribution functions that can be used to represent spherical massless cored stellar systems embedded in cuspy dark matter halos with constant mildly tangential velocity anisotropy. In particular, we derive…
Synthesizing fully developed three-dimensional turbulent velocity fields remains a long-standing problem in fluid mechanics and an open challenge for generative modeling. The difficulty arises from the coexistence of extreme dimensionality,…
Frequency-dependent acoustical loss due to a multitude of physical mechanisms is commonly modeled by multiple relaxations. For discrete relaxation distributions, such models correspond with causal wave equations of integer-order temporal…