Badges: Zenodo, Beta (#200)

* Badges: Zenodo, Beta

Update badges to include Zenodo.org archive and beta-status.

* Zenodo: LDRD Note

.zenodo.json

@@ -49,6 +49,7 @@
     "license": {
       "id": "BSD-3-Clause-LBNL"
     },
+    "notes": "This work was supported by the Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory under U.S. Department of Energy Contract No. DE-AC02-05CH11231.",
     "language": "eng",
     "keywords": [
       "research",

README.md

@@ -1,13 +1,16 @@
 # pyAMReX
 
-[![Python3][api-py3]](https://www.python.org/) ![Python3 API: Alpha][dev-alpha]
-[![License AMReX](https://img.shields.io/badge/license-BSD--3--Clause--LBNL-blue.svg)](https://spdx.org/licenses/BSD-3-Clause-LBNL.html)  
+[![Python3][api-py3]](https://www.python.org/)
+![Python3 API: Beta][dev-beta]
+[![Discussions](https://img.shields.io/badge/chat-discussions-turquoise.svg)](https://github.com/AMReX-Codes/pyamrex/discussions)  
 ![linux](https://github.com/AMReX-Codes/pyamrex/workflows/linux/badge.svg?branch=development)
 ![macos](https://github.com/AMReX-Codes/pyamrex/workflows/macos/badge.svg?branch=development)
-![windows](https://github.com/AMReX-Codes/pyamrex/workflows/windows/badge.svg?branch=development)
+![windows](https://github.com/AMReX-Codes/pyamrex/workflows/windows/badge.svg?branch=development)  
+[![License pyAMReX](https://img.shields.io/badge/license-BSD--3--Clause--LBNL-blue.svg)](https://spdx.org/licenses/BSD-3-Clause-LBNL.html)
+[![DOI (source)](https://img.shields.io/badge/DOI%20(source)-10.5281/zenodo.8408733-blue.svg)](https://doi.org/10.5281/zenodo.8408733)
 
 [api-py3]: https://img.shields.io/badge/language-Python3-yellowgreen "Python3 API"
-[dev-alpha]: https://img.shields.io/badge/phase-alpha-yellowgreen "Status: Alpha"
+[dev-beta]: https://img.shields.io/badge/phase-beta-yellowgreen "Status: Beta"
 
 The Python binding pyAMReX bridges the worlds of block-structured codes and data science: it provides zero-copy application GPU data access for AI/ML, in situ analysis, application coupling and enables rapid, massively parallel prototyping.
 pyAMReX enhances the [Block-Structured AMR Software Framework AMReX](https://amrex-codes.github.io) and its applications.

setup.py

@@ -244,7 +244,7 @@ def build_extension(self, ext):
     # cmdclass={'test': PyTest},
     # platforms='any',
     classifiers=[
-        "Development Status :: 3 - Alpha",
+        "Development Status :: 4 - Beta",
         "Natural Language :: English",
         "Environment :: Console",
         "Environment :: GPU",