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This paper complements the empirical justification of the revised scheme in Part I of this work with a mathematical justification leveraging a semi-discrete analysis framework for assessing the splitting error of process coupling methods.…
This is a sketch of a 321D approximation for stellar convection which is nonlocal, and thus has nonzero fluxes of KE (to be published in more detail elsewhere). Boundary conditions are discussed in a fluid dynamics context (i.e.,…
By suitable reformulations, we review the mathematical frameworks of six different approaches to the description of non-equilibrium dynamics with the purpose to set up a unified formulation of the Maximum Entropy Production (MEP) principle…
Climate model large ensembles are an essential research tool for analysing and quantifying natural climate variability and providing robust information for rare extreme events. The models simulated representations of reality are susceptible…
Nowadays, weather forecasts are commonly generated by ensemble forecasts based on multiple runs of numerical weather prediction models. However, such forecasts are usually miscalibrated and/or biased, thus require statistical…
The moving discontinuous Galerkin finite element method with interface condition enforcement (MDG-ICE) is applied to the case of viscous flows. This method uses a weak formulation that separately enforces the conservation law, constitutive…
Electric vertical takeoff and landing (eVTOL) aircraft operating in high-density urban airspace must maintain safe separation through tactical conflict resolution, yet the energy cost of such maneuvers has not been systematically…
The unsupervised and principled diagnosis of multi-scale data is a fundamental obstacle in modern scientific problems from, for instance, weather and climate prediction, neurology, epidemiology, and turbulence. Multi-scale data is…
We present 3-D hydrodynamical simulations of core convection with a stably stratified envelope of a \unit{25}{\Msun} star in the early phase of the main-sequence. We use the explicit gas-dynamics code \code{PPMstar} which tracks two fluids…
Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adaptation to combination MCC and combination to adaptation MCC, are developed to deal with the distributed estimation over network…
Mixture-of-Experts (MoE) models have gained popularity in achieving state-of-the-art performance in a wide range of tasks in computer vision and natural language processing. They effectively expand the model capacity while incurring a…
We introduce a new regularization model for incompressible fluid flow, which is a regularization of the EMAC formulation of the Navier-Stokes equations (NSE) that we call EMAC-Reg. The EMAC (energy, momentum, and angular momentum…
Dynamic stochastic general equilibrium (DSGE) models have been an ubiquitous, and controversial, part of macroeconomics for decades. In this paper, we approach DSGEs purely as statstical models. We do this by applying two common model…
We study the closure problem for continuum balance equations that model mesoscale dynamics of large ODE systems. The underlying microscale model consists of classical Newton equations of particle dynamics. As a mesoscale model we use the…
This paper introduces a method for spatial interpolation of extreme values, and in particular targets the case in which conventional data, resulting from a measurement for example, are available at only a few locations. To overcome this the…
Accurately assessing the potential for fault slip is essential in many subsurface operations. Conventional model-based history matching methods, which entail the generation of posterior geomodels calibrated to observed data, can be…
Diffusion coefficients are key thermophysical properties for modeling mass transport in liquids, but experimental data are scarce, making reliable prediction methods indispensable. In the present work, we introduce a new method for…
Most natural thermodynamic systems operate far from equilibrium, developing persistent currents and organizing into non-equilibrium stationary states (NESSs). Yet, the principles by which such systems self-organize, breaking equilibrium…
We study the formation and the dynamics of correlations in the velocity field for 1D and 2D cooling granular gases with the assumption of negligible density fluctuations (``Homogeneous Velocity-correlated Cooling State'', HVCS). It is shown…
In this work, Entropy-Stable (ES) schemes are formulated for the multicomponent compressible Euler equations. Entropy-conservative (EC) and ES fluxes are derived. Particular attention is paid to the limit case of zero partial densities…