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In many practical situations, the useful signal is contained in a low-dimensional subspace, drown in noise and interference. Many questions related to the estimation and detection of the useful signal arise. Because of their particular…
It is shown that there are static spacetimes with timelike curvature singularities which appear completely nonsingular when probed with quantum test particles. Examples include extreme dilatonic black holes and the fundamental string…
I describe approaches to the study of black hole spacetimes via numerical relativity. After a brief review of the basic formalisms and techniques used in numerical black hole simulations, I discuss a series of calculations from axisymmetry…
This is a review of recent progress concerning generic spacelike singularities in general relativity. For brevity the main focus is on singularities in vacuum spacetimes, although the connection with, and the role of, matter for generic…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
A review on numerical simulations of galaxy formation is given. Different numerical methods to solve collisionless and gas dynamical systems are outlined and one particular simulation technique, Smoothed Particle Hydrodynamics, is discussed…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
Estimating the number of spikes in a spiked model is an important problem in many areas such as signal processing. Most of the classical approaches assume a large sample size $n$ whereas the dimension $p$ of the observations is kept small.…
The electric field distributions and space-time singularity curves are computed for ultrashort pulsed Laguerre-Gaussian laser beams having spatial chirp. Due to the breaking of cylindrical symmetry by the spatial chirp, the singularities…
Motivated by studies of indirect measurements in quantum mechanics, we investigate stochastic differential equations with a fixed point subject to an additional infinitesimal repulsive perturbation. We conjecture, and prove for an important…
The application of numerical relativity to cosmological spacetimes is providing new insights into the behavior of Einstein's equations, beyond common approximations. In order for simulations to be performed as accurately and efficiently as…
One way to understand more about spacetime singularities is to construct solutions of the Einstein equations containing singularities with prescribed properties. The heuristic ideas of the BKL picture suggest that oscillatory singularities…
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…
This is the first part in a series of two papers, where we consider a specific microscopic model of spacetime. In our model Planck size quantum black holes are taken to be the fundamental building blocks of space and time. Spacetime is…
For problems in astrophysics, planetary science and beyond, numerical simulations are often limited to simulating fewer particles than in the real system. To model collisions, the simulated particles (aka superparticles) need to be inflated…
Solar limb and disc spicule quasi- periodic motions have been reported for a long time, strongly suggesting that they are oscillating. In order to clear up the origin and possibly explain some solar limb and disc spicule quasi-periodic…
The shape space of k labelled points on a plane can be identified with the space of pure quantum states of dimension k-2. Hence, the machinery of quantum mechanics can be applied to the statistical analysis of planar configurations of…
We consider superfluidity and quantum vorticity in rotating spacetimes. The system is described by a complex scalar satisfying a nonlinear Klein-Gordon equation. Rotation terms are identified and found to lead to the transfer of angular…
In this work we have used for the first time pseudo-spectral methods to perform numerical simulations of spherically symmetric black hole formations on a Friedman-Robertson-Walker universe. With these methods, the differential equations…