Related papers: Flattened stellar systems based on distribution fu…
The presence of spiral structure in isolated galaxies is a problem that has only been partially explained by theoretical models. Because the rate and pattern of star formation in the disk must depend only on mechanisms internal to the disk,…
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 standard method of modelling axisymmetric stellar systems begins from the assumption that mass follows light. The gravitational potential is then derived from the luminosity distribution, and a unique two-integral distribution function…
A phase-space distribution function of the steady state in galaxy models that admits regular orbits overall in the phase-space can be represented by a function of three action variables. This type of distribution function in Galactic models…
Two main features of the observable distribution of visible matter are the space correlations of galaxy positions and the mass function of galaxies. As discussed in Pietronero and Sylos Labini on this issue ([1], see also [2],[3]), the…
We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…
Active filaments, such as microtubules with attached cargo-carrying motor proteins, are important dynamic structures for fluid transport in and around living cells. The mathematical models of active filaments appearing in the literature…
This paper presents an angle-based approach for distributed formation shape stabilization of multi-agent systems in the plane. We develop an angle rigidity theory to study whether a planar framework can be determined by angles between…
We have used a combination of high resolution cosmological N-body simulations and semi-analytic modelling of galaxy formation to investigate the processes that determine the spatial distribution of galaxies in cold dark matter (CDM) models.…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…
We show that, in conserved-mass transport processes, the steady-state distribution of mass in a subsystem is uniquely determined from the functional dependence of variance of the subsystem mass on its mean, provided that joint mass…
We discuss a reaction-diffusion model in one dimension subjected to an external driving force. Each lattice site may be occupied by at most one particle. The particles hop with asymmetric rates (the sum of which is one) to the right or left…
We construct a normal form suited to {\it fast driven systems}. We call so systems including actions ${\rm I}$, angles {$\psi$}, and one fast coordinate $y$, moving under the action of a vector--field $N$ depending only on ${\rm I}$ and $y$…
This study presents a distributed gradient-based approach to solve system optimal dynamic traffic assignment (SODTA) formulated based on the cell transmission model. The algorithm distributes SODTA into local sub-problems, who find optimal…
We use dynamical models that include bulk rotation, velocity dispersion anisotropy and both stars and dark matter to explore the conditions that give rise to the early-type galaxy scaling relations referred to as the Fundamental Plane (FP)…
We recently derived, using the density-of-states approximation, analytic distribution functions for the outcomes of direct single-binary scatterings (Stone & Leigh 2019). Using these outcome distribution functions, we present in this paper…
Starting from the hypothesis that the Galaxy's dark halo responded adiabatically to the infall of baryons, we have constructed a self-consistent dynamical model of the Galaxy that satisfies a large number of observations, including…
The magnetic activity of solar-type stars generally increases with stellar rotation rate. The increase, however, saturates for fast rotation. The Babcock-Leighton mechanism of stellar dynamos saturates as well when the mean tilt-angle of…
We analyze the structure of stochastic dynamics near either a stable or unstable fixed point, where force can be approximated by linearization. We find that a cost function that determines a Boltzmann-like stationary distribution can always…