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Alternatively, one might consider using the integrated radiant intensity in the positive half-space, i.e., the sum η of the efficiencies of all transmitted propagating orders in the FMM analysis.
To get an idea of the far-field radiation pattern of the probe, we plot in Figure 6b the angular distribution of transmission efficiency η, which in FMM calculations means plotting the efficiencies η m of all propagating orders of the superperiodic grating.
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The problem is challenging due to its multiscale nature (temperature usually propagates orders of magnitude faster than moisture), different characters of the two fields (moisture exhibits boundary layers which are not present in the temperature field), extremely long integration times (30 years or more), and lack of viable error control mechanisms.
Using the analytic form of the solution, it is shown that the observed discrepancy is related to interaction between the damped hydrodynamic mode and a downstream propagating higher order acoustic mode.
For instance, companies need to understand how spam messages are propagated in order to protect their businesses.
Also known as snakes, they are deformable models that consist on evolving an interface which is propagated in order to recover the shape of the object of interest.
As an extension of previous work on low frequency fundamental mode acoustic transmission through the walls of rectangular ducts, results are presented here on the transmission of internally propagated higher order acoustic modes through the duct walls.
The transmission of sound energy, in the form of internally propagated higher order modes, through the walls of "flat-oval" air conditioning ducts is investigated by means of numerical solutions to the equations of motion for the duct walls and the acoustic wave equation governing sound propagation inside the duct.
It is then possible to reconstruct the sub-diffraction limit details by measuring the scattered propagating negative diffraction orders in the far-field [1].
"This film in no way is propagating violence in order to solve the problem.
Our experimental results on a number of benchmark problems demonstrate that propagating the multiset ordering constraint via a dedicated algorithm can be very beneficial.
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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