Related papers: Analysis of short-term Polarization Stability usin…
The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the It\^{o} stochastic differential equation. It is assumed that the noise…
It has already been shown that microlensing can give rise to a non-zero variable polarisation signal. Here we use realistic simulations to demonstrate the additional information that can be gained from polarimetric observations of lensing…
Metrology experiments can be limited by the noise produced by the laser involved via small fluctuations in the laser's power or frequency. Typically, active power stabilization schemes consisting of an in-loop sensor and a feedback control…
Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent…
With the forthcoming release of high precision polarization measurements, such as from the Planck satellite, it becomes critical to evaluate the performance of estimators for the polarization fraction and angle. These two physical…
Complex architectures for wireless communications, digital electronics and space-based navigation interlink several oscillator-based devices such as clocks, transponders and synthesizers. Estimators characterizing their stability are…
We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…
Quantifying the optical chirality of a sample requires the precise measurement of the rotation of the plane of linear polarisation of the transmitted light. Central to this notion is that the sample needs to be exposed to light of a defined…
We study an Allen-Cahn equation perturbed by a multiplicative stochastic noise which is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive uniform energy bounds…
This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation, where the source is represented by white noise. The study examines the well-posedness of the direct problem and derives…
We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally…
The power spectral density in Fourier frequency domain, and the different variants of the Allan deviation (ADEV) in dependence on the averaging time are well established tools to analyse the fluctuation properties and frequency instability…
Polarization imaging can yield crucial information in multiple applications of remote sensing, such as characterization of clouds, aerosols, and the Aurora Borealis. Some applications require sub-percent polarimetric sensitivity and…
A theoretical framework is introduced to model the dynamical changes of the state of polarization during transmission in coherent fibre-optic systems. The model generalizes the one-dimensional phase noise random walk to higher dimensions,…
Improvement in time resolution sometimes introduces short-range random noises into temporal data sequences. These noises affect the results of power-spectrum analyses and the Detrended Fluctuation Analysis (DFA). The DFA is one of useful…
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…
Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…
Electricity systems are experiencing increased effects of randomness and variability due to emerging stochastic assets. The increased effects introduce new uncertainties into power systems that can impact system operability and reliability.…
Ensuring the long-term reproducibility of data analyses requires results stability tests to verify that analysis results remain within acceptable variation bounds despite inevitable software updates and hardware evolutions. This paper…
In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…