.. _sec:end:

End Matter
==========

Nomenclature
------------

+------------------------+----------------------------------------------------+
| **latin**                                                                   |
+------------------------+----------------------------------------------------+
| :math:`A`              | area                                               |
+------------------------+----------------------------------------------------+
| :math:`C_D`            | drag coefficient                                   |
+------------------------+----------------------------------------------------+
| :math:`d`              | diameter                                           |
+------------------------+----------------------------------------------------+
| :math:`e`              | restitution coefficient                            |
+------------------------+----------------------------------------------------+
| :math:`g`              | gravity magnitude                                  |
+------------------------+----------------------------------------------------+
| :math:`L_i`            | length in the :math:`i^{th}`-direction             |
+------------------------+----------------------------------------------------+
| :math:`\dot m`         | mass flow rate                                     |
+------------------------+----------------------------------------------------+
| :math:`M`              | bed mass                                           |
+------------------------+----------------------------------------------------+
| :math:`U`              | superficial (gas) velocity                         |
+------------------------+----------------------------------------------------+
| :math:`P`              | pressure                                           |
+------------------------+----------------------------------------------------+
| :math:`Q`              | volumetric flow rate                               |
+------------------------+----------------------------------------------------+
| :math:`R_{air}`        | specific gas constant for air                      |
+------------------------+----------------------------------------------------+
| :math:`t`              | time                                               |
+------------------------+----------------------------------------------------+
| :math:`T`              | temperature                                        |
+------------------------+----------------------------------------------------+
| :math:`v`              | velocity                                           |
+------------------------+----------------------------------------------------+
| :math:`V`              | volume                                             |
+------------------------+----------------------------------------------------+
| **greek**                                                                   |
+------------------------+----------------------------------------------------+
| :math:`\mu`            | friction coefficient (particles)                   |
|                        | or material viscosity (gas)                        |
+------------------------+----------------------------------------------------+
| :math:`\Psi`           | sphericity                                         |
+------------------------+----------------------------------------------------+
| **subscripts and superscripts**                                             |
+------------------------+----------------------------------------------------+
| :math:`atm`            | atmosphere                                         |
+------------------------+----------------------------------------------------+
| :math:`F`              | float (rotameter)                                  |
+------------------------+----------------------------------------------------+
| :math:`g`              | gas                                                |
+------------------------+----------------------------------------------------+
| :math:`lab`            | laboratory (conditions)                            |
+------------------------+----------------------------------------------------+
| :math:`obs`            | observed (conditions)                              |
+------------------------+----------------------------------------------------+
| :math:`p`              | particle                                           |
+------------------------+----------------------------------------------------+
| :math:`r`              | rise (through the bed)                             |
+------------------------+----------------------------------------------------+
| :math:`std`            | standard (conditions)                              |
+------------------------+----------------------------------------------------+
| :math:`x`,             |                                                    |
| :math:`y`,             | coordinate direction                               |
| :math:`z`              |                                                    |
+------------------------+----------------------------------------------------+

Acronyms
--------

+------------------------+----------------------------------------------------+
| CFD                    | Computational Fluid Dynamics                       |
+------------------------+----------------------------------------------------+
| DEM                    | Discrete Element Method                            |
+------------------------+----------------------------------------------------+
| HDPE                   | High-Density Polyethylene                          |
+------------------------+----------------------------------------------------+
| UQ                     | Uncertainty Quantification                         |
+------------------------+----------------------------------------------------+
| VSSUQ                  | Very Small-Scale experiment for UQ                 |
+------------------------+----------------------------------------------------+


.. _sec:refs:

References
----------

.. format:
   `name (year) <link>`_
   Title,
   *Journal*, **vol**, pp-pp.

*  `Hoomans, et al. (2001) <https://doi.org/10.1016/S0032-5910(00)00391-0>`_
   Experimental validation of granular dynamics simulations of gas-fluidised beds
   with homogenous in-flow conditions using positron emission particle tracking,
   *Powder Technology*, **116**, 166-177.

*  `Khanam and AlMaadeed (2015) <https://doi.org/10.1179/2055035915Y.0000000002>`_
   Processing and characterization of polyethylene-based composites,
   *Advanced Manufacturing: Polymer & Composites Science*, **1**, 63-79.

*  `LaMarche, et al. (2022) <https://doi.org/10.1002/aic.17643>`_
   Very small-scale, segregating-fluidized-bed experiments: A dataset for
   CFD-DEM validation and uncertainty quantification,
   *AIChE Journal*, **XXX**, yy-yy.

*  `Rosato, et al. (1987) <https://doi.org/10.1103/PhysRevLett.58.1038>`_
   Why the Brazil nuts are on top: Size segregation of particulate matter by
   shaking. *Physical Review Letters*, **58**, 1038-1040.

*  `Yuu, Umekage and Johno (2000) <https://doi.org/10.1016/S0032-5910(99)00277-6>`_
   Numerical simulation of air and particle motions in bubbling fluidized bed of
   small particles, *Powder Technology*, **110**, 158-168.


Appendices
----------

.. toctree::
   :maxdepth: 1

   appx_Ucalc


Acknowledgements
----------------

This work was supported by the U.S. Department of Energy under Grant No. DE-FE0026298.


Disclaimer
----------

This repository is released under the `MIT License <https://github.com/wfullmer/vssuq/blob/main/LICENSE>`_.