Related papers: Higher order minimum entropy approximations in rad…
In this paper, we present a high order finite difference solver for anisotropic diffusion problems based on the first-order hyperbolic system method. In particular, we demonstrate that the construction of a uniformly accurate fifth-order…
One way of getting insight into non-Gaussian measures, posed on infinite dimensional Hilbert spaces, is to first obtain best fit Gaussian approximations, which are more amenable to numerical approximation. These Gaussians can then be used…
Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…
Solving the continuum radiative transfer equation in high opacity media requires sophisticated numerical tools. In order to test the reliability of such tools, we present a benchmark of radiative transfer codes in a 2D disc configuration.…
A new set of discrete ordinates is proposed for one-dimensional radiative transfer in spheres with central symmetry. The set is structured with un-normalized circular functions. This resulted in a conservative and closed set of discrete…
Accurate characterization of entropy plays a pivotal role in capturing reversible and irreversible heating in supercapacitors during charging/discharging cycles. However, numerical methods that can faithfully capture entropy variation in…
The method of maximum entropy (ME) is extended to address the following problem: Once one accepts that the ME distribution is to be preferred over all others, the question is to what extent are distributions with lower entropy supposed to…
In this paper relations among some kinds of cumulative entropies and moments of order statistics are presented. By using some characterizations and the symmetry of a non negative and absolutely continuous random variable X, lower and upper…
Given a sequence composed of a limit number of characters, we try to "read" it as a "text". This involves to segment the sequence into "words". The difficulty is to distinguish good segmentation from enormous number of random ones.Aiming at…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state…
Motivated by recent findings, we discuss the existence of a direct and robust mechanism providing discontinuous absorbing transitions in short range systems with single species, with no extra symmetries or conservation laws. We consider…
(Abridged) We describe a new algorithm for solving the coupled frequency-integrated transfer equation and the equations of magnetohydrodynamics when the light-crossing time is only marginally shorter than dynamical timescales. The transfer…
In this paper, the moment matching techniques are adopted to obtain reduced-order closed-loop systems with reduced-order controllers that maintain the closed-loop stability and guarantee desired asymptotic performance, after revealing the…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
In this work we propose a novel method to ensure important entropy inequalities are satisfied semi-discretely when constructing reduced order models (ROMs) on nonlinear reduced manifolds. We are in particular interested in ROMs of systems…
The theory of heat transfer by electromagnetic radiation is based on the radiative transfer equation (RTE) for the radiation intensity, or equivalently on the Boltzmann transport equation (BTE) for the photon distribution. We focus in this…
A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small…
We propose a projection based multi-moment matching method for model order reduction of quadratic-bilinear systems. The goal is to construct a reduced system that ensures higher-order moment matching for the multivariate transfer functions…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…