Related papers: Perturbation-theory informed integrators for cosmo…
We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…
We study symplectic numerical integration of mechanical systems with a Hamiltonian specified in non-canonical coordinates and its application to guiding-center motion of charged plasma particles in magnetic confinement devices. The…
Trajectory prediction (TP) is crucial for ensuring safety and efficiency in modern air traffic management systems. It is, for example, a core component of conflict detection and resolution tools, arrival sequencing algorithms, capacity…
We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These…
We consider the growth of primordial dark matter halos seeded by three crossed initial sine waves of various amplitudes. Using a Lagrangian treatment of cosmological gravitational dynamics, we examine the convergence properties of a…
We present high--spatial resolution studies of the density field as predicted by Lagrangian perturbation approximations up to the third order. The first--order approximation is equivalent to the ``Zel'dovich approximation'' for the type of…
Cosmology is entering an era of percent level precision due to current large observational surveys. This precision in observation is now demanding more accuracy from numerical methods and cosmological simulations. In this paper, we study…
Cosmological correlators offer a remarkable window into the high-energy physics governing Universe's earliest moments, with the tantalising prospect of discovering new particles. However, extracting new physics from these observables…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly…
The linear matter power spectrum is an essential ingredient in all theoretical models for interpreting large-scale-structure observables. Although Boltzmann codes such as CLASS or CAMB are very efficient at computing the linear spectrum,…
Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for…
Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost…
We study the effect of nonperturbative corrections associated with the behavior of particles after shell crossing on the matter power spectrum. We compare their amplitude with the perturbative terms that can be obtained within the fluid…
Recently, our group developed explicit symplectic methods for curved spacetimes that are not split into several explicitly integrable parts, but are via appropriate time transformations. Such time-transformed explicit symplectic integrators…
We present a formulation of cosmological perturbation theory where the Boltzmann hierarchies that evolve the neutrino phase-space distributions are replaced by integrals that can be evaluated easily with fast Fourier transforms. The…
Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the…
This paper proposes several explicit and implicit multistep frequency response optimized integrators considering first or second order derivative. A prediction-based method aiming at accelerating a novel power system transient simulation…
We present a new method for developing time step controllers based on a technique from the field of machine learning. This method is applicable to stable time integrators that have an embedded scheme, i.e., that have local error estimation…
Magnetic quadrupoles are essential components of particle accelerators like the Large Hadron Collider. In order to study numerically the stability of the particle beam crossing a quadrupole, a large number of particle revolutions in the…