Related papers: EXP: N-body integration using basis function expan…
The many-body problem can in general not be solved exactly, and one of the most prominent approximations is to build perturbation expansions. A huge variety of expansions is possible, which differ by the quantity to be expanded, the…
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…
I review recent progress in numerically simulating the formation and evolution of galaxies in hierarchically clustering universes. Special emphasis is given to results based on high-resolution gas dynamical simulations using the N-body…
Modeling interacting galaxies to reproduce observed systems is still a challenge due to the extended parameter space (among other problems). Orbit and basic galaxy parameters can be tackled by fast simulation techniques like the restricted…
We present a numerical code for multi-component simulation of the galactic evolution. Our code includes the following parts: $N$-body is used to evolve dark matter, stellar dynamics and dust grains, gas dynamics is based on TVD-MUSCL scheme…
In early Solar System numerical simulations, where chaos is a primary driver, it is difficult to explore parameter space in a systematic way. In such simulations, stable configurations are hard to come by, and often require special…
Aims. The orbital structure of galaxies is strongly influenced by the accuracy of the force calculation during orbit integration. We explore the accuracy of force calculations for two expansion methods and determine which one is preferable…
Two questions that naturally arise in N-body simulations of stellar systems are: (1) How can we compare experiments that employ different types of softened gravity? (2) Given a particular type of softened gravity, which choices of the…
We established and estimate the full asymptotic expansion in integer powers of 1 N of the [ $\sqrt$ N ] first marginals of N-body evolutions lying in a general paradigm containing Kac models and non-relativistic quantum evolution. We prove…
Particle-mesh simulations trade small-scale accuracy for speed compared to traditional, computationally expensive N-body codes in cosmological simulations. In this work, we show how a data-driven model could be used to learn an effective…
Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations…
We provide a systematic analysis of the multipolar gravitational waveform, energy and angular momentum fluxes emitted by a nonspinning test particle orbiting a Kerr black hole along equatorial, eccentric orbits. These quantities are…
Upcoming Large Scale Structure surveys aim to achieve an unprecedented level of precision in measuring galaxy clustering. However, accurately modeling these statistics may require theoretical templates that go beyond second-order…
I present empirical measurements of the rate of relaxation in N-body simulations of stable spherical systems and distinguish two separate types of relaxation: energy diffusion that is largely independent of particle mass, and energy…
We present methods for emulating the matter power spectrum by combining information from cosmological $N$-body simulations at different resolutions. An emulator allows estimation of simulation output by interpolating across the parameter…
We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size $n$, the smoothing spline estimator can be expressed as a linear combination of $n$ basis functions,…
This paper presents a simple and effective new numerical scheme for the computation of electrostatic fields exterior to a collection of close-to-touching discs. The method is presented in detail for the two-cylinder case. The key idea is to…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…
We consider the common problem setting of an elastic sphere impacting on a flexible beam. In contrast to previous studies, we analyze the modal energy distribution induced by the impact, having in mind the particular application of impact…
This paper presents a new technique to calculate the evolution of a quantum wavefunction in a chosen spatial basis by minimizing the accumulated action. Introduction of a finite temporal basis reduces the problem to a set of linear…