Related papers: On a minimum set of equations for parameterisation…
The generalized Langrangian mean theory provides exact equations for general wave-turbulence-mean flow interactions in three dimensions. For practical applications, these equations must be closed by specifying the wave forcing terms. Here…
The framework of invariant parameterization is extended to higher-order closure schemes. We also define, for the first time, generalized invariant parameterization schemes, where symmetries of the corresponding original model are preserved…
The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the…
Many large scale numerical simulations of astrophysical plasmas must also reproduce the hydrogen ionization and the resulting emission spectrum, in some cases quite accurately. We describe a compact model hydrogen atom that can be readily…
Starting from coupled fluid-kinetic equations for the modeling of laden flows, we derive relevant viscous corrections to be added to asymptotic hydrodynamic systems, by means of Chapman-Enskog expansions and analyse the shock profile…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
We investigate a lattice model representing a granular gas in a thin channel. We deduce the hydrodynamic description for the model from the microscopic dynamics in the large system limit, including the lowest finite-size corrections. The…
The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization…
We introduce a new general framework for the approximation of evolution equations at low regularity and develop a new class of schemes for a wide range of equations under lower regularity assumptions than classical methods require. In…
A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of…
This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…
We give a framework for constructing generically optimal homotopies for parametrized polynomial systems from tropical data. Here, generically optimal means that the number of paths tracked is equal to the generic number of solutions. We…
Arctic sea ice plays an important role in the global climate. Sea ice models governed by physical equations have been used to simulate the state of the ice including characteristics such as ice thickness, concentration, and motion. More…
A method for finding reduced-order approximations of turbulent flow models is presented. The method preserves bounds on the production of turbulent energy in the sense of the $\curly{L}_2$ norm of perturbations from a notional laminar…
Simple models are used throughout the physical sciences as a means of developing intuition, capturing phenomenology, and qualitatively reproducing observations. In studies of microswimming, simple force-dipole models are commonplace,…
The Primitive Equations are a basic model in the study of large scale Oceanic and Atmospheric dynamics. These systems form the analytical core of the most advanced General Circulation Models. For this reason and due to their challenging…
The simulation and parameter optimization of coupled ocean circulation and ecosystem models in three space dimensions is one of the most challenging tasks in numerical climate research. Here we present a scientific toolkit that aims at…
Aerodynamic models are developed to describe coherent structures and transport processes in hurricanes moving over open seas. The models consist of the lower boundary layer and upper adiabatic layer. Except friction at the air/sea…
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…
Training nonlinear parametrizations such as deep neural networks to numerically approximate solutions of partial differential equations is often based on minimizing a loss that includes the residual, which is analytically available in…