An up-to-date listing of publications can be found on Dan Rothman's Google Scholar Profile.
Some recent covers:
Below is a list of some highlights, thematically organized, with recent publications given some preference. Some of the links provide free access.
Kinetic complexity of the carbon cycle
DH Rothman, Earth's carbon cycle: A mathematical perspective, Bulletin of the American Mathematical Society 52, 47-64 (2015).
Y Cohen and DH Rothman, Mechanisms for mechanical trapping of geologically sequestered carbon dioxide, Proceedings of the Royal Society A 471:20140853 (2015). Postscript
C Follett, DJ Repeta, DH Rothman, L Xu, and C Santinelli, Hidden cycle of dissolved organic carbon in the deep ocean, Proceedings of the National Academy of Sciences 111, 16706–16711 (2014).
D Reeves, DH Rothman, Age dependence of mineral dissolution and precipitation rates, Global Biogeochemical Cycles 27, 906-919 (2013)
DC Forney, DH Rothman, Carbon transit through degradation networks, Ecological Monographs 84, 109-129 (2013)
DC Forney, DH Rothman, Common structure in the heterogeneity of plant-matter decay, Journal of The Royal Society Interface 9 (74), 2255-2267 (2012)
DH Rothman, DC Forney, Physical model for the decay and preservation of marine organic carbon, Science 316 (5829), 1325-1328 (2007)
Co-evolution of life and the environment
DH Rothman, Thresholds of catastrophe in the Earth system, Science Advances 3, e1700906 (2017).
DH Rothman, Mathematical expression of a global environmental catastrophe, Notices of the American Mathematical Society 64, 138-140 (2017).
DH Rothman, GP Fournier, KL French, EJ Alm, EA Boyle, C Cao, RE Summons, Methanogenic burst in the end-Permian carbon cycle, Proceedings of the National Academy of Sciences 111 (15), 5462–5467 (2014)
DH Rothman, JM Hayes, RE Summons, Dynamics of the Neoproterozoic carbon cycle, Proceedings of the National Academy of Sciences 100 (14), 8124-8129 (2003)
DH Rothman, Atmospheric carbon dioxide levels for the last 500 million years, Proceedings of the National Academy of Sciences 99 (7), 4167-4171 (2002)
DH Rothman, Global biodiversity and the ancient carbon cycle, Proceedings of the National Academy of Sciences 98 (8), 4305-4310 (2001)
Geometry of natural forms
Y Cohen, O Devauchelle, HF Seybold, RS Yi, P Szymczak, and DH Rothman, Path selection in the growth of rivers, Proceedings of the National Academy of Sciences, doi: 10.1073/pnas.1413883112 (2015).
AP Petroff, O Devauchelle, H Seybold, DH Rothman, Bifurcation dynamics of natural drainage networks, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, 20120365 (2013)
AP Petroff, NJ Beukes, DH Rothman, T Bosak, Biofilm Growth and Fossil Form, Physical Review X 3, 041012 (2013)
O Devauchelle, AP Petroff, HF Seybold, DH Rothman, Ramification of stream networks, Proceedings of the National Academy of Sciences 109 (51), 20832-20836 (2012)
AP Petroff, O Devauchelle, DM Abrams, AE Lobkovsky, A Kudrolli, DH Rothman, Geometry of valley growth, Journal of Fluid Mechanics 673, 245-254 (2011)
O Devauchelle, AP Petroff, AE Lobkovsky, DH Rothman, Longitudinal profile of channels cut by springs, Journal of Fluid Mechanics 667, 38-47 (2011)
DM Abrams, AE Lobkovsky, AP Petroff, KM Straub, B McElroy, DC Mohrig, A Kudrolli, DH Rothman, Growth laws for channel networks incised by groundwater flow, Nature Geoscience 2 (3), 193-196 (2009)
JP Grotzinger, DH Rothman, An abiotic model for stromatolite morphogenesis, Nature 383 (6599), 423-425 (1996)
Discrete fluids, interfacial flows, and porous media
DH Rothman and S Zaleski, Lattice-Gas Cellular Automata: Simple models of complex hydrodynamics, Cambridge University Press (1997). Free software and further information.
DH Rothman, S Zaleski, Lattice-gas models of phase separation: interfaces, phase transitions, and multiphase flow, Reviews of Modern Physics 66, 1417 (1994)