Related papers: Accurate initial conditions for cosmological N-bod…
The precise tuning required to observe critical phenomena in gravitational collapse poses a challenge for most numerical codes. First, threshold estimation searches may be obstructed by the appearance of coordinate singularities, indicating…
An important class of physical systems that are of interest in practice are input-output open quantum systems that can be described by quantum stochastic differential equations and defined on an infinite-dimensional underlying Hilbert…
In the last decades cosmological N-body dark matter simulations have enabled ab initio studies of the formation of structure in the Universe. Gravity amplified small density fluctuations generated shortly after the Big Bang, leading to the…
Understanding the dynamics of quantum systems is crucial in many areas of physics, but simulating many-body systems presents significant challenges due to the large Hilbert space to navigate and the exponential growth of computational…
Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…
Computable estimates for the error of finite element discretisations of parabolic problems in the $L^\infty(0,T; L^2)$ norm are developed, which exhibit constant effectivities (the ratio of the estimated error to the true error) with…
We investigate the curvature perturbations induced by the randomness of the quantum tunneling process during cosmological first-order phase transitions (PTs) and for the first time ultilize curvature perturbations to constrain the PT…
We report on a series of tests of agreement between three types of N-body simulations: PM, P$^3$M, and Tree codes. We find good agreement in both the individual and the statistical properties only on scales larger than the mean…
Micromagnetics depends on high-fidelity numerical methods for magnetization dynamics. This work proposes a third-order temporal accuracy scheme for the Landau-Lifshitz-Gilbert equation, addressing accuracy-efficiency trade-offs in existing…
Cosmological N-Body simulations have become an essential tool for studying formation of large scale structure. These simulations are computationally challenging even though the available computing power gets better every year. A number of…
The aim of these lecture notes is to familiarize graduate students and beginning postgraduates with the basic ideas of linear cosmological perturbation theory and of structure formation scenarios. We present both the Newtonian and the…
This paper addresses the class of continuous-time nonlinear programming problems with equality and inequality constraints. The paper presents necessary optimality conditions of the sequential form. To be more precise, a sequence of…
Programmable quantum simulators such as superconducting quantum processors and ultracold atomic lattices represent rapidly developing emergent technology that may one day qualitatively outperform existing classical computers. Yet, apart…
We develop a pivot-shifted Carleman linearization framework for quantum algorithms solving quadratic nonlinear ordinary differential equations. By shifting the dynamics by a pivot state prior to Carleman lifting, and combining this with a…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
Numerous previous studies have investigated the phenomenon wherein initially spherical N-body systems are distorted to triaxial shapes. We report on an investigation of a previously described orbital instability that should oppose…
We initiate the study of extended excitations in the long-range O(N) model. We focus on line and surface defects and we discuss the challenges of a naive generalization of the simplest defects in the short-range model. To face these…
How condensed-matter simulations depend on the number of molecules being simulated ($N$) is sometimes itself a valuable piece of information. Liquid crystals provide a case in point. Light scattering and $2d$-IR experiments on…
The effects of particle discreteness in N-body simulations of Lambda Cold Dark Matter (LambdaCDM) are still an intensively debated issue. In this paper we explore such effects, taking into account the scatter caused by the randomness of the…
We present a method to construct semi-numerical ``simulations'', which can efficiently generate realizations of halo distributions and ionization maps at high redshifts. Our procedure combines an excursion-set approach with first-order…