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We present a hybrid study that combines a concise review of scalar-field cosmology with new analytic developments that integrate averaging reductions for oscillatory regimes with dynamical-systems techniques. For oscillatory fields, we…
The gravitational influence of a planet on a nearby disk provides a powerful tool for detecting and studying extrasolar planetary systems. Here we demonstrate that gaps can be opened in dynamically cold debris disks at the mean-motion…
Triaxial dynamical models of massive galaxies observed in the ATLAS3D project can provide new insights into the complex evolutionary processes that shape galaxies. The ATLAS3D survey is ideal as the sample comprises a good mix of fast and…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
We consider the three-dimensional bounded motion of a test particle around razor-thin disk configurations, by focusing on the adiabatic invariance of the vertical action associated with disk-crossing orbits. We find that it leads to an…
Over the course of the recent decades, $N$-body simulations have become a standard tool for quantifying the gravitational perturbations that ensue in planet-forming disks. Within the context of such simulations, massive non-central bodies…
We investigate the regular or chaotic nature of star orbits moving in the meridional plane of an axially symmetric galactic model with a disk and a spherical nucleus. We study the influence of some important parameters of the dynamical…
We present a new asymptotic strategy for general micro-macro models which analyze complex viscoelastic fluids governed by coupled multiscale dynamics. In such models, the elastic stress appearing in the macroscopic continuum equation is…
The discrete kinetic model is used to study the propagation of sound waves in system of hard-disk-like rotating stars (or vortex gases). The anomalous (negative) attenuation or amplification which is possibly due to the binary collision of…
We discuss various analytical approximation methods for following the evolution of cosmological density perturbations into the strong (i.e. nonlinear) clustering regime. These methods can be classified into five types: (i) simple…
Grid-based magnetohydrodynamic (MHD) simulations have proven invaluable for the study of astrophysical accretion disks. However, the fact that angular momentum transport in disks is mediated by MHD turbulence (with structure down to very…
A general method is presented for constructing distribution functions for flat systems whose surface density and Toomre's Q number profile is given. The purpose of these functions is to provide plausible galactic models and assess their…
Nonlinear stochastic motion presents significant challenges for Bayesian particle tracking. To address this challenge, this paper proposes a framework to construct an invertible transformation that maps the nonlinear state-space model (SSM)…
System of partial differential equations with a convolution terms and non-local nonlinearity describing oscillations of plate due to Berger approach and with accounting for thermal regime in terms of Coleman-Gurtin and Gurtin-Pipkin law and…
We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…
Recently, continuous-time dynamical systems have proved useful in providing conceptual and quantitative insights into gradient-based optimization, widely used in modern machine learning and statistics. An important question that arises in…
This paper explores cosmological scenarios in a scalar-tensor theory of gravity, including both a non-minimal coupling with scalar curvature of the form $R\phi^2$ and a non-minimal derivative coupling of the form…
It is well understood that dynamic instability is among the primary drivers of forecast uncertainty in chaotic, physical systems. Data assimilation techniques have been designed to exploit this phenomena, reducing the effective dimension of…
In this work, two new axisymmetric models for the Galactic mass distribution are presented. Motivated by recent results, these two models include the contribution of a stellar thin disc and of a thick disc, as massive as the thin…
We present a new three-parameter family of self-consistent equilibrium models for quasi-relaxed stellar systems that are subject to the combined action of external tides and rigid internal rotation. These models provide an idealised…