Related papers: Numerical simulations of general gravitational sin…
I review recent progress from $N$-body simulations in our understanding of the secular evolution of isolated disk galaxies. I describe some of the recent controversies in the field which have been commonly attributed to numerics. The…
Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being…
This paper presents reflections on the validity of a series of mathematical methods and technical assumptions that are encrusted in macrophysics (related to gravitational interaction), that seem to have little or no physical significance.…
Numerical simulations are becoming a more effective tool for conducting detailed investigations into the evolution of our universe. In this article, we show how the framework of numerical relativity can be used for studying cosmological…
Many properties of current \emph{ab initio} approaches to the quantum many-body problem, both perturbational or otherwise, are related to the singularity structure of Rayleigh--Schr\"odinger perturbation theory. A numerical procedure is…
Numerical Relativity is a multidisciplinary field including relativity, magneto-hydrodynamics, astrophysics and computational methods, among others, with the aim of solving numerically highly-dynamical, strong-gravity scenarios where no…
Since the breakthrough papers from 2005/2006, the field of numerical relativity has experienced a growth spurt that took the two-body problem in general relativity from the category of "really-hard-problems" to the realm of…
We provide a brief overview of recent advances and outstanding issues in simulations of interstellar turbulence, including isothermal models for interior structure of molecular clouds and larger-scale multiphase models designed to simulate…
A new and very general technique for simulating solid-fluid suspensions has been described in a previous paper (Part I); the most important feature of the new method is that the computational cost scales with the number of particles. In…
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…
Numerical simulations of galaxy formation require a number of parameters. Some of these are intrinsic to the numerical integration scheme (eg the timestep), while others describe the physical model (eg the gas metallicity). In this paper,…
We briefly review some of the scientific challenges and epistemological issues related to climate science. We discuss the formulation and testing of theories and numerical models, which, given the presence of unavoidable uncertainties in…
Future quantum computers are anticipated to be able to perform simulations of quantum many-body systems and quantum field theories that lie beyond the capabilities of classical computation. This will lead to new insights and predictions for…
We present an overview of recent developments in the numerical solution of Horndeski gravity theories, which are the class of all scalar-tensor theories of gravity that have second order equations of motion. We review several methods that…
Several methodologies are developed for large-scale atomistic simulations with fully quantum mechanical description of electron systems. The important methodological concepts are (i) generalized Wannier state, (ii) Krylov subspace and (iii)…
This note emphasizes the role of multi-scale wave structures and junction conditions in many fields of physics, from the dynamics of fluids with non-convex equations of state to the study of gravitational singularities and bouncing…
This paper is devoted to the study of simulating a large class of self-similar processes. Since most current simulation approaches are limited to case-by-case studies, every existing approach has its constraints and flaws; hence a general…
Numerical simulations are a versatile tool providing insight into the complicated process of structure formation in cosmology. This process is mainly governed by gravity, which is the dominant force on large scales. To date, a century after…
After quick survey of some key results and open questions about the structure of singularities of minimal surfaces, we discuss recent work~\cite{Sim23} on singularities of stable minimal hypersurfaces, including some simplifications of the…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…