.. _theory_citations:

References and Citations
=========================

This page collects full bibliographic information for all works cited in the Theory section,
along with BibTeX entries for inclusion in LaTeX documents.



Primary References
------------------

.. _ref_he2024:

**He et al. PNAS 2024**
   He, H., Liang, H., Chu, M., Jiang, Z., de Pablo, J. J., Tirrell, M. V.,
   Narayanan, S., & Chen, W. "Transport coefficient approach for characterizing
   nonequilibrium dynamics in soft matter." *Proceedings of the National Academy
   of Sciences*, 121(31), e2401162121 (2024).

   **DOI**: `10.1073/pnas.2401162121 <https://doi.org/10.1073/pnas.2401162121>`_

   This paper introduces the transport coefficient framework :math:`J(t)` and the two-time
   correlation function :math:`c_2(\mathbf{q}, t_1, t_2)` as the central quantities for
   XPCS analysis of non-stationary systems. It derives the homodyne scattering formula for
   laminar flow and the connection to the Green-Kubo relation.

   **BibTeX**:

   .. code-block:: bibtex

      @article{He2024PNAS,
        author  = {He, Hongrui and Liang, Hao and Chu, Miaoqi and Jiang, Zhang and
                   de Pablo, Juan J and Tirrell, Matthew V and Narayanan, Suresh
                   and Chen, Wei},
        title   = {Transport coefficient approach for characterizing nonequilibrium
                   dynamics in soft matter},
        journal = {Proceedings of the National Academy of Sciences},
        year    = {2024},
        volume  = {121},
        number  = {31},
        pages   = {e2401162121},
        doi     = {10.1073/pnas.2401162121},
      }

.. _ref_he2025:

**He et al. PNAS 2025**
   He, H., Liang, H., Chu, M., Jiang, Z., de Pablo, J. J., Tirrell, M. V.,
   Narayanan, S., & Chen, W. "Bridging microscopic dynamics and rheology in
   the yielding of charged colloidal suspensions." *Proceedings of the National
   Academy of Sciences*, 122(42), e2514216122 (2025).

   **DOI**: `10.1073/pnas.2514216122 <https://doi.org/10.1073/pnas.2514216122>`_

   This companion paper applies the :math:`J(t)` framework to the yielding transition in
   repulsive (Andrade creep) and attractive (shear banding) colloidal suspensions.
   Introduces the multi-component heterodyne formula and non-Gaussian displacement analysis.

   **BibTeX**:

   .. code-block:: bibtex

      @article{He2025PNAS,
        author  = {He, Hongrui and Liang, Heyi and Chu, Miaoqi and Jiang, Zhang and
                   de Pablo, Juan J and Tirrell, Matthew V and Narayanan, Suresh
                   and Chen, Wei},
        title   = {Bridging microscopic dynamics and rheology in the yielding
                   of charged colloidal suspensions},
        journal = {Proceedings of the National Academy of Sciences},
        year    = {2025},
        volume  = {122},
        number  = {42},
        pages   = {e2514216122},
        doi     = {10.1073/pnas.2514216122},
      }


XPCS Methodology
-----------------

**Sutton et al. (2003)**
   Sutton, M. "A review of X-ray intensity fluctuation spectroscopy." *C. R. Physique*,
   9(5–6), 657–667 (2008).

   Review of XPCS technique, coherence requirements, and connection to dynamic light
   scattering.

   .. code-block:: bibtex

      @article{Sutton2008,
        author  = {Sutton, Mark},
        title   = {A review of X-ray intensity fluctuation spectroscopy},
        journal = {Comptes Rendus Physique},
        year    = {2008},
        volume  = {9},
        pages   = {657--667},
        doi     = {10.1016/j.crhy.2007.04.008},
      }

**Lumma et al. (2000)**
   Lumma, D., Lurio, L. B., Mochrie, S. G. J., and Sutton, M. "Area detector based photon
   correlation in the regime of short data batches: Data reduction for dynamic X-ray
   scattering." *Review of Scientific Instruments*, 71(9), 3274–3289 (2000).

   Introduces the two-time correlation matrix as a practical estimator for non-stationary
   XPCS. Defines the diagonal-averaging approximation.

   .. code-block:: bibtex

      @article{Lumma2000,
        author  = {Lumma, D. and Lurio, L. B. and Mochrie, S. G. J. and Sutton, M.},
        title   = {Area detector based photon correlation in the regime of short data batches},
        journal = {Review of Scientific Instruments},
        year    = {2000},
        volume  = {71},
        pages   = {3274--3289},
        doi     = {10.1063/1.1287334},
      }

**Duri et al. (2005)**
   Duri, A., et al. "Time-resolved-correlation: A new tool for studying temporally
   heterogeneous dynamics." *Journal of Physics: Condensed Matter*, 17, S3455 (2005).

   Establishes the two-time correlation function as a diagnostic for temporally heterogeneous
   ("aging") dynamics.

   .. code-block:: bibtex

      @article{Duri2005,
        author  = {Duri, A. and Bissig, H. and Trappe, V. and Cipelletti, L.},
        title   = {Time-resolved-correlation: A new tool for studying temporally
                   heterogeneous dynamics},
        journal = {Journal of Physics: Condensed Matter},
        year    = {2005},
        volume  = {17},
        pages   = {S3455},
        doi     = {10.1088/0953-8984/17/31/003},
      }


Stochastic Processes
--------------------

**Uhlenbeck & Ornstein (1930)**
   Uhlenbeck, G. E. and Ornstein, L. S. "On the theory of the Brownian motion."
   *Physical Review*, 36(5), 823–841 (1930).

   Original derivation of the Ornstein-Uhlenbeck process.

   .. code-block:: bibtex

      @article{UhlenbeckOrnstein1930,
        author  = {Uhlenbeck, G. E. and Ornstein, L. S.},
        title   = {On the theory of the {B}rownian motion},
        journal = {Physical Review},
        year    = {1930},
        volume  = {36},
        pages   = {823--841},
        doi     = {10.1103/PhysRev.36.823},
      }

**Kubo (1966)**
   Kubo, R. "The fluctuation-dissipation theorem." *Reports on Progress in Physics*,
   29(1), 255–284 (1966).

   Establishes the Green-Kubo relation connecting transport coefficients to velocity
   autocorrelation functions.

   .. code-block:: bibtex

      @article{Kubo1966,
        author  = {Kubo, Ryogo},
        title   = {The fluctuation-dissipation theorem},
        journal = {Reports on Progress in Physics},
        year    = {1966},
        volume  = {29},
        pages   = {255--284},
        doi     = {10.1088/0034-4885/29/1/306},
      }


Bayesian Methods
----------------

**Scott et al. (2016)**
   Scott, S. L., et al. "Bayes and big data: The consensus Monte Carlo algorithm."
   *International Journal of Management Science and Engineering Management*, 11(2), 78–88
   (2016).

   Introduces Consensus Monte Carlo for distributed posterior inference. The foundation
   of the CMC backend in homodyne.

   .. code-block:: bibtex

      @article{Scott2016,
        author  = {Scott, S. L. and Blocker, A. W. and Bonassi, F. V. and
                   Chipman, H. A. and George, E. I. and McCulloch, R. E.},
        title   = {Bayes and big data: The consensus {M}onte {C}arlo algorithm},
        journal = {International Journal of Management Science and Engineering Management},
        year    = {2016},
        volume  = {11},
        pages   = {78--88},
        doi     = {10.1080/17509653.2016.1142191},
      }

**Hoffman & Gelman (2014)**
   Hoffman, M. D. and Gelman, A. "The No-U-Turn Sampler: Adaptively setting path lengths
   in Hamiltonian Monte Carlo." *Journal of Machine Learning Research*, 15, 1593–1623 (2014).

   Introduces NUTS, the adaptive HMC sampler used in each CMC shard via NumPyro.

   .. code-block:: bibtex

      @article{HoffmanGelman2014,
        author  = {Hoffman, Matthew D. and Gelman, Andrew},
        title   = {The {N}o-{U}-{T}urn {S}ampler: Adaptively setting path lengths
                   in {H}amiltonian {M}onte {C}arlo},
        journal = {Journal of Machine Learning Research},
        year    = {2014},
        volume  = {15},
        pages   = {1593--1623},
      }

**Phan et al. (2019)**
   Phan, D., et al. "Composable effects for flexible and accelerated probabilistic
   programming in NumPyro." *arXiv:1912.11554* (2019).

   Describes the NumPyro probabilistic programming library used for NUTS sampling in
   homodyne's CMC backend.

   .. code-block:: bibtex

      @article{Phan2019NumPyro,
        author  = {Phan, Du and Pradhan, Neeraj and Jankowiak, Martin},
        title   = {Composable effects for flexible and accelerated probabilistic
                   programming in {NumPyro}},
        journal = {arXiv preprint arXiv:1912.11554},
        year    = {2019},
      }


Optimization
-------------

**More (1977)**
   Moré, J. J. "The Levenberg-Marquardt algorithm: Implementation and theory."
   In *Numerical Analysis*, Lecture Notes in Mathematics, vol. 630, pp. 105–116.
   Springer, Berlin, 1977.

   Canonical reference for the Levenberg-Marquardt algorithm used in the NLSQ optimizer.

   .. code-block:: bibtex

      @incollection{More1977,
        author    = {Mor{\'e}, J. J.},
        title     = {The {L}evenberg-{M}arquardt algorithm: Implementation and theory},
        booktitle = {Numerical Analysis},
        series    = {Lecture Notes in Mathematics},
        volume    = {630},
        pages     = {105--116},
        publisher = {Springer},
        year      = {1977},
        doi       = {10.1007/BFb0067700},
      }

**Hansen (2016)**
   Hansen, N. "The CMA evolution strategy: A tutorial." *arXiv:1604.00772* (2016).

   Comprehensive tutorial on CMA-ES, the global optimizer used for multi-scale NLSQ
   problems in homodyne.

   .. code-block:: bibtex

      @article{Hansen2016CMAes,
        author  = {Hansen, Nikolaus},
        title   = {The {CMA} evolution strategy: A tutorial},
        journal = {arXiv preprint arXiv:1604.00772},
        year    = {2016},
      }


JAX and Scientific Stack
-------------------------

**Bradbury et al. (2018)**
   Bradbury, J., et al. "JAX: composable transformations of Python+NumPy programs."
   Version 0.8, 2018. https://github.com/jax-ml/jax.

   The JAX library providing JIT compilation and automatic differentiation for all
   numerical kernels in homodyne.

   .. code-block:: bibtex

      @software{jax2018github,
        author    = {Bradbury, James and Frostig, Roy and Hawkins, Peter and
                     Johnson, Matthew James and Leary, Chris and Maclaurin, Dougal and
                     Necula, George and Paszke, Adam and VanderPlas, Jake and
                     Wanderman-Milne, Skye and Zhang, Qiao},
        title     = {{JAX}: composable transformations of {Python+NumPy} programs},
        url       = {https://github.com/jax-ml/jax},
        version   = {0.8},
        year      = {2018},
      }

**Gelman et al. (2013)**
   Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B.
   *Bayesian Data Analysis*, 3rd edition. CRC Press, 2013.

   Standard reference for Bayesian inference, posterior diagnostics (R-hat, ESS), and
   prior specification strategies.

   .. code-block:: bibtex

      @book{Gelman2013BDA,
        author    = {Gelman, Andrew and Carlin, John B. and Stern, Hal S. and
                     Dunson, David B. and Vehtari, Aki and Rubin, Donald B.},
        title     = {Bayesian Data Analysis},
        edition   = {3rd},
        publisher = {CRC Press},
        year      = {2013},
      }


Rheology
---------

**Andrade (1910)**
   Andrade, E. N. da C. "On the viscous flow in metals, and allied phenomena."
   *Proceedings of the Royal Society A*, 84, 1–12 (1910).

   Original characterization of the :math:`t^{1/3}` creep law that appears in
   repulsive colloidal suspensions under constant stress.

   .. code-block:: bibtex

      @article{Andrade1910,
        author  = {Andrade, E. N. da~C.},
        title   = {On the viscous flow in metals, and allied phenomena},
        journal = {Proceedings of the Royal Society A},
        year    = {1910},
        volume  = {84},
        pages   = {1--12},
        doi     = {10.1098/rspa.1910.0050},
      }


Citing Homodyne
-----------------

If you use homodyne in your research, please cite the primary PNAS 2024 paper.
Optionally cite the software package directly:

.. code-block:: bibtex

   @software{homodyne,
     title       = {Homodyne: JAX-first high-performance XPCS analysis},
     author      = {Chen, Wei and He, Hongrui},
     year        = {2024},
     url         = {https://github.com/imewei/homodyne},
     institution = {Argonne National Laboratory},
   }

**Example citation text** for a methods section:

   "XPCS data were analyzed using the transport coefficient approach [1] as
   implemented in the Homodyne software package [2]. The analysis employed
   the laminar flow mode with per-angle scaling to account for instrumental
   variations across detector positions."

   [1] He et al., PNAS 121(31), e2401162121 (2024). DOI: 10.1073/pnas.2401162121

   [2] https://github.com/imewei/homodyne


Acknowledgments
-----------------

If you use homodyne in your research, please consider acknowledging:

- U.S. Department of Energy, Office of Science, Basic Energy Sciences
- Advanced Photon Source User Facility at Argonne National Laboratory


Contact
--------

- **Principal Investigator**: Wei Chen (wchen@anl.gov), Argonne National Laboratory
- **Lead Developer**: Hongrui He
- **Technical Support**: `GitHub Issues <https://github.com/imewei/homodyne/issues>`_
