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Gravity-driven flows of liquid films are frequent in nature and industry, such as in landslides, lava flow, cooling of nuclear reactors, and coating processes. In many of these cases, the liquid is non-Newtonian and has particular…
We study rapidly accreting, gravitationally unstable disks with a series of global, three dimensional, numerical experiments using the code ORION. In this paper we conduct a numerical parameter study focused on protostellar disks, and show…
The formation of disk galaxies is one of the most outstanding problems in modern astrophysics and cosmology. We review the progress made by numerical simulations carried out on large parallel supercomputers. Recent progress stems from a…
In this paper, we study the propagation and stability of nonlinear sound waves in accretion disks. Using the shearing box approximation, we derive the form of these waves using a semi-analytic approach and go on to study their stability.…
Using a hydrodynamic adaptive mesh refinement code, we simulate the growth and evolution of a galaxy, which could potentially host a supermassive black hole, within a cosmological volume. Reaching a dynamical range in excess of 10 million,…
We present a non-linear numerical model for a geometrically thin accretion disk with the addition of stochastic non-linear fluctuations in the viscous parameter. These numerical realizations attempt to study the stochastic effects on the…
We describe methods for setting up self-consistent disk-bulge-halo galaxy models. The bulge and halo distribution functions (\df) are functions of $E$ and $L_z$ only. The halo's flattening and rotation can be specified. The disk \df\ is a…
The Nystr\"om method is a widely used technique for improving the scalability of kernel-based algorithms, including kernel ridge regression, spectral clustering, and Gaussian processes. Despite its popularity, the numerical stability of the…
We confirm that a high rate of shear at the center is able to stabilize an entire stellar disk against bar-forming (m=2) modes, irrespective of the dark halo density. Our simulations of unstable power-law disks also yield the growth rate…
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on $\mathbb{R}^{d}$. Under standard spectral stability assumptions, we establish Lyapunov stability of the front against fully…
Warped H I gas layers in the outer regions of spiral galaxies usually display a noticeably twisted structure. This structure almost certainly arises primarily as a result of differential precession in the H I disk as it settles toward a…
We use the Stripe 82 proper motion catalogue of Bramich et al. (2008) to study the kinematics of Galactic disk stars in the solar neighborhood. We select samples of dwarf stars with reliable spectra and proper motions. They have cylindrical…
Recent observations have shown that star-forming galaxies like our own Milky Way evolve kinematically into ordered thin disks over the last ~8 billion years since z=1.2, undergoing a process of "disk settling." For the first time, we study…
Dynamical simulations are a fundamental tool for studying the secular evolution of disc galaxies. Even at their maximum resolution, they still follow a limited number of particles and typically resolve scales of the order of a few tens of…
A satellite galaxy or dark matter subhalo that passes through a stellar disk may excite coherent oscillations in the disk perpendicular to its plane. We determine the properties of these modes for various self-gravitating plane symmetric…
Numerical simulations based on radial basis functions have been developed for systems with complex geometries and have been successfully applied across various fields, including seismology, coastal hydrodynamics, and biology. However,…
It is shown that pure exponential discs in spiral galaxies are capable of supporting slowly varying discrete global lopsided modes, which can explain the observed features of lopsidedness in the stellar discs. Using linearized fluid…
We are carrying out a programme of non-linear time-dependent numerical calculations to study the evolution of the thermal instability driven by radiation pressure in transonic accretion discs around black holes. In our previous studies we…
The data obtained by the recent modern sky surveys enable detailed studies of the stellar distribution in the multi-dimensional space spanned by spatial coordinates, velocity and metallicity, from the solar neighborhood all the way out to…
To obtain a simple description of a geometrically thin magnetic accretion disk, we apply the method of asymptotic expansion. For the first time we write a full set of stationary asymptotic approximation equations of a thin magnetic…