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Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…
Over the past decades, kinetic description of granular materials has received a lot of attention in mathematical community and applied fields such as physics and engineering. This article aims to review recent mathematical results in…
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…
Numerical simulations are playing an increasingly important role in modern science. In this work it is suggested to use a numerical study of the famous perihelion motion of the planet Mercury (one of the prime observables supporting…
Vastly different time and length scales are a common problem in numerical simulations of astrophysical phenomena. Here, we present an approach to numerical modeling of such objects on the example of Type Ia supernova simulations. The…
The development of both ground- and space-based gravitational wave detectors provides new opportunities to observe the radiation from binaries containing neutron stars and black holes. Numerical simulations in 3-D are essential for…
Numerical simulation is an important method for verifying the quantum circuits used to simulate low-energy nuclear states. However, real-world applications of quantum computing for nuclear theory often generate deep quantum circuits that…
Recent developments in quantum annealing techniques have been indicating potential advantage of quantum annealing for solving NP-hard optimization problems. In this article we briefly indicate and discuss the beneficial features of quantum…
This document is both a synthesis of current notions about complex systems, and a practical approach description. A disambiguation is proposed and exposes possible reasons for controversies related to causation and emergence. Theoretical…
I begin with a brief history of N-body simulation and visualization and then go on to describe various methods for creating images and animations of modern simulations in cosmology and galactic dynamics. These techniques are incorporated…
We present numerical simulations of binary black hole systems which for the first time last for about one orbital period for close but still separate black holes as indicated by the absence of a common apparent horizon. An important part of…
Numerical Relativity has been using orbifolds for a long time, although they appear under different names in the literature. We review orbifolds previously used in simulations also discuss some that have not been used yet but are likely to…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
We review progress towards direct simulation of quantum dynamics in many-body systems, using recently developed stochastic gauge techniques. We consider master equations, canonical ensemble calculations and reversible quantum dynamics are…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
We present the analysis of a suite of simulations of a Virgo mass galaxy cluster. Undertaken within the framework of standard cold dark matter cosmology, these simulations were performed at differing resolutions and with increasingly…
We review the state of the art of three dimensional numerical simulations of solar and stellar dynamos. We summarize fundamental constraints of numerical modelling and the techniques to alleviate these restrictions. Brief summary of the…
The universe is permeated by a network of filaments, sheets, and knots collectively forming a "cosmic web.'' The discovery of the cosmic web, especially through its signature of absorption of light from distant sources by neutral hydrogen…
I briefly discuss recent results of numerical simulations addressing the generation of a cosmological gravitational wave background produced by turbulence sources in the early universe. Contribution to the 2021 Gravitation session of the…
The standard paradigm of cosmology assumes General Relativity (GR) is a valid theory for gravity at scales in which it has not been properly tested. Developing novel tests of GR and its alternatives is crucial if we want to give strength to…