Related papers: Using the maximum entropy distribution to describe…
Moment-closure methods are popular tools to simplify the mathematical analysis of stochastic models defined on networks, in which high dimensional joint distributions are approximated (often by some heuristic argument) as functions of lower…
We introduce an extensible multi-fluid moment model in the context of collisionless magnetic reconnection. This model evolves full Maxwell equations, and simultaneously moments of the Vlasov-Maxwell equation for each species in the plasma.…
We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an…
The magnetosphere of Mercury is studied using an implicit full particle in cell simulation (PIC). We use a hybrid simulation where ions are full particles and electrons are considered as a fluid to start a full PIC simulation where…
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…
We perform a three-dimensional (3D) global simulation of Earth's magnetosphere with kinetic reconnection physics to study the flux transfer events (FTEs) and dayside magnetic reconnection with the recently developed magnetohydrodynamics…
Simulations of large-scale plasma systems are typically based on a fluid approximation approach. These models construct a moment-based system of equations that approximate the particle-based physics as a fluid, but as a result lack the…
We propose a hybrid moment method for the multi-scale kinetic equations in the framework of the regularized moment method [7]. In this method, the fourth order moment system is chosen as the governing equations in the fluid region. When…
We explore the use of the method of Maximum Entropy (ME) as a technique to generate approximations. In a first use of the ME method the "exact" canonical probability distribution of a fluid is approximated by that of a fluid of hard…
We carry out particle-in-cell simulations of complex current sheets of the family of analytically found Vlasov--Maxwell equilibria that model a collisionless magnetopause and allow for arbitrary energy distributions and countercurrents of…
For the first time, we explore the tightly coupled interior-magnetosphere system of Mercury by employing a three-dimensional ten-moment multifluid model. This novel fluid model incorporates the non-ideal effects including the Hall effect,…
The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region…
The maximum entropy principle is applied to the formal derivation of isothermal, Euler-like equations for semiclassical fermions (electrons and holes) in graphene. After proving general mathematical properties of the equations so obtained,…
Maximum entropy distributions with discrete support in $m$ dimensions arise in machine learning, statistics, information theory, and theoretical computer science. While structural and computational properties of max-entropy distributions…
Using the recently developed ``Maximum Entropy'' (or ``least biased'') distribution function to truncate the moment hierarchy arising from kinetic theory, we formulate a far-from-equilibrium macroscopic theory that provides the possibility…
We derive some fluid-dynamic models for electron transport near a Dirac point in graphene. We start from a kinetic model constituted by a set of spinorial Wigner equations, we make suitable scalings (hydrodynamic or diffusive) of the model…
In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit,…
While semiconductor electronics is at heart of modern world, and now uses 5nm or smaller processes of single atoms, it seems there are missing models of actual electron currents in these scales - which could help with more conscious design…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
We simulate magnetic reconnection in the GEM problem using a two-fluid model with 10 moments for the electron fluid as well as the proton fluid. We show that use of 10 moments for electrons gives good qualitative agreement with the the…