Related papers: Equivalence between Geometric Frequency and Lagran…
Time-frequency scattering is a mathematical transformation of sound waves. Its core purpose is to mimick the way the human auditory system extracts information from its environment. In the context of improving the artificial intelligence of…
The gamma difference distribution is defined as the difference of two gamma distributions, with in general different shape and rate parameters. Starting with knowledge of the corresponding characteristic function, a second order linear…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
The advection-diffusion equation is studied via a global Lagrangian coordinate transformation. The metric tensor of the Lagrangian coordinates couples the dynamical system theory rigorously into the solution of this class of partial…
In recent work [1] we uncovered intriguing connections between Otto's characterisation of diffusion as entropic gradient flow [16] on one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other.…
Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…
In this paper we are interested in the mathematical and numerical analysis of the time-dependent Galbrun equa- tion in a rigid duct. This equation models the acoustic propagation in presence of flow [1]. We propose a regu- larized…
We investigate Lagrangian relative dispersion in direct numerical simulation of two-dimensional inverse cascade turbulence. The analysis is performed by using both standard fixed time statistics and an exit time approach. Our results are in…
Dynamics, the physical change in time and a pillar of natural sciences, can be regarded as an emergent phenomenon when the system of interest is part of a larger, static one. This "relational approach to time", in which the system's…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
An exact series representation of the even frequency moments of the dynamic structure factor is derived. Truncations are proposed that allow to evaluate the explicitly unknown second, fourth and fifth frequency moments for the finite…
Measurement devices always add noise to the signal of interest and it is necessary to evaluate the variance of the results. This article focuses on stationary random processes whose Power Spectrum Density is a power law of frequency. For…
An exact analogy of electromagnetic fields and particles can be found in continuum mechanics of a turbulent perfect fluid with voids. Deviations of the turbulence from a homogeneous isotropic state correspond to electromagnetic fields: with…
The power grid frequency is the central observable in power system control, as it measures the balance of electrical supply and demand. A reliable frequency forecast can facilitate rapid control actions and may thus greatly improve power…
Electromagnetic and gravitational central-field problems are studied with relativistic quantum mechanics on curved space-time backgrounds. Corrections to the transition current are identified. Analogies of the gravitational and…
Friction incorporates the close connection between classical mechanics in irreversible thermodynamics. The translation to a quantum mechanical foundation is not trivial and requires a generalization of the Lagrange function. A change to…
By viewing a velocity gradient in a fluid as an internal disturbance and treating it as a constraint on the wave function of a system, a linear evolution equation for the wave function is obtained from the Lagrange multiplier method. It…
We study the interaction among gravitational and electromagnetic plane waves by means of an analogue electromagnetic model of gravity, where the gravitational properties are encoded in the electromagnetic properties of a material in flat…
The irreducible representations of the extended Galilean group are used to derive the symmetric and asymmetric wave equations. It is shown that among these equations only a new asymmetric wave equation is fundamental. By being fundamental…
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…