Related papers: Positioning in a flat two-dimensional space-time: …
Unruh-DeWitt detectors interacting locally with a quantum field are systems under consideration for relativistic quantum information processing. In most works, the detectors are assumed to be point-like and, therefore, couple with the same…
We introduce an operational approach to the use of pulsating sources, located at spatial infinity, for defining a relativistic positioning and navigation system, based on the use of four-dimensional bases of null four-vectors, in flat…
In a static spacetime, the Killing time can be used to measure the time required for signals or objects to propagate between two of its orbits. By further restricting to spherically symmetric cases, one obtains a natural association between…
In recent years many studies of urban mobility based on large data sets have been published: most of them based on crowdsourced GPS data or smart-card data. We present, what is to our knowledge the first, exploration of public transport…
The nonlinear stability of Minkowski spacetime has been one of the central achievements in the mathematical theory of general relativity and, more broadly, in the analysis of nonlinear geometric wave equations. Since the seminal work of…
This paper proposes a globally and exponentially convergent predictive observer for attitude and position estimation based on landmark measurements and velocity (angular and linear) readings. It is assumed that landmark measurements are…
Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems…
Relativistic positioning systems are interesting {\em technical objects} for applications around the Earth and in the Solar system. But above all else, they are basic {\em scientific objects} allowing developing relativity from its own…
Global navigation satellite systems use appropriate satellite constellations to get the coordinates of an user -close to Earth- in an almost inertial reference system. We have simulated both GPS and GALILEO constellations. Uncertainties in…
We study the orbits of two interacting particles described by a fully relativistic classical mechanical Hamiltonian. We use two sets of initial conditions. In the first set (dynamics 1) the system's center of mass is at rest. In the second…
We investigate the limitations of length measurements by accelerated observers in Minkowski spacetime brought about via the hypothesis of locality, namely, the assumption that an accelerated observer at each instant is equivalent to an…
Minkowski diagrams in 1+1 dimensional flat space-time are given a strictly geometric derivation, directly from two gedanken experiments incorporating the principle of the constancy of the velocity of light and the principle of (special)…
Real-world systems can be strongly influenced by time delays occurring in self-coupling interactions, due to unavoidable finite signal propagation velocities. When the delays become significantly long, complicated high-dimensional phenomena…
We give a closed expression for the Minkowski (1+1)-dimensional metric in the radar coordinates of an arbitrary non-inertial observer O in terms of O's proper acceleration. Knowledge of the metric allows the non-inertial observer to perform…
We present here a method for the relativistic positioning in spacetime based on the reception of pulses from sources of electromagnetic signals whose worldline is known. The method is based on the use of a four-dimensional grid covering the…
Physicists have been interested in accelerated observers for quite some time. Since the advent of special relativity, many authors have tried to understand these observers in the framework of Minkowski spacetime. One of the most important…
Delays are inherent to most dynamical systems. Besides shifting the process in time, they can significantly affect their performance. For this reason, it is usually valuable to study the delay and account for it. Because they are dynamical…
Takens' Embedding Theorem asserts that when the states of a hidden dynamical system are confined to a low-dimensional attractor, complete information about the states can be preserved in the observed time-series output through the delay…
Delay coordinates are a widely used technique to pass from observations of a dynamical system to a representation of the dynamical system as an embedding in Euclidean space. Current proofs show that delay coordinates of a given dynamical…
We derive relativistic Maxwell-Bloch equations for potential applications in astronomical environments, where various radiative processes are known to occur, including the maser action and Dicke's superradiance. We show that for both…