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

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

This paper introduces the transport coefficient framework \(J(t)\) and the two-time correlation function \(c_2(\mathbf{q}, t_1, t_2)\) 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:

@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},
}
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

This companion paper applies the \(J(t)\) 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:

@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.

@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.

@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.

@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.

@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.

@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.

@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.

@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.

@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.

@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.

@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.

@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.

@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 \(t^{1/3}\) creep law that appears in repulsive colloidal suspensions under constant stress.

@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:

@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