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Such methodology can be used for any other reduced model problem that include multiple parameters and time consuming simulations.
Mixing in a turbulent spray jet is identified as a model problem that clarifies the role of large scale structures in the overall mixing process.
In this paper we propose and utilize a model problem that permits the theoretical analysis of iterative schemes for solving such problems.
As a way to reduce trucks' fuel burn, attention has been given lately to the development of a decision model (problem) that is designed to solve a variant of the standard vehicle routing problem, called the pollution routing problem (PRP), which minimizes the fuel burn or pollutants emission of trucks.
To develop and analyze new computational techniques for the Boltzmann equation based on model or approximation adaptivity, it is imperative to have disposal of a compliant model problem that displays the essential characteristics of the Boltzmann equation and that admits the extraction of highly accurate reference solutions.
We validate our method and illustrate the reduced computational cost and the ability to easily represent final state chemical non-equilibrium by studying a model problem that is motivated by the physics of the neutrino freeze-out processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component (e±-annihilation).
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The numerical method is tested by solving model problems that describe the coalescence of particles for both single and double initial distributions.
This methodology is demonstrated on three model problems that are representative of typical cardiovascular geometries: a stenosis, a vessel bifurcation modeled on Murray's law, and an end-to-side anastomosis.
Then we give some applications of the results in Sections 3 and 4 to two reaction-diffusion model problems that arise from nonstationary radiative heat transfer in a system of moving absolutely black bodies and a reaction-diffusion equation with nonlocal boundary flux conditions.
The final outcome is a rich formalism to represent and reason about relevant concepts in artificial intelligence, while still having a model checking problem that is no more computationally expensive than that of the less expressive quantified boolean logic.
This creates a problem for the inferences generally licensed by the standard model, a problem that is independent of, and perhaps even deeper than, the problem of intersecting lineages.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com