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For this model, an analytical solution for a D-optimal design is derived.
Based on a first principle "Newman model", an analytical model was developed to predict the enhance transfer rates.
Based on this model, an analytical formula providing the value of the axial deformation of the rigid ring and assessment of the shell's axial stiffness is derived.
Making use of the non-linear model, an analytical relation was found between the parameters of the system that define the region over which oscillatory instabilities are possible.
This paper builds upon research by Lee concerning the token flow model, an analytical model for the behavior of dataflow graphs with data-dependent control flow, by analyzing the properties of cycles of the schedule: sequences of actor executions that return the graph to its initial state.
From this model, an analytical expression for bullwhip is derived that is directly equivalent to the common statistical measure often used in simulation, statistical and empirical studies to quantify the bullwhip effect.
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Then, we verify the semi-analytical model against a numerical model and an analytical model.
The work contains a detailed FEM study, a comparison with an equivalent plate model and an analytical model and examines the limitations of the latter two.
In more complex models an analytical approach may not be possible.
In "Analytical modeling", an analytical modeling and description of our architectural framework is given.
None of us has a model that actually captures the real world, because no complex reality can be represented analytically and a model is an analytical way of representing reality.
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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