A major challenge in unraveling the behavior of discrete systems and structures consisting of dissipative, interacting particles is the complexity embodied in multiple time and length scales that ultimately play a role in macroscopic behavior. A universal feature in these systems is the transmission of energy and momentum through an evolving microstructure, via internal nonlinear dynamic interactions and coupling with physical boundaries and external fields. An understanding of the governing mechanics lies at the heart of developing much-needed predictive models to design efficient industrial bulk solids handling systems, to create innovative materials with specified properties, and to potentially mitigate the loss of property and humans lives brought about by geophysical flows, such as landslides and avalanches. While substantial progress towards this goal has been achieved over the last 30 years, a model capable of describing the gamut of phenomena remains an open question.
A novel interdisciplinary approach, combining the modern theory of dynamical systems coupled with the use of discrete element simulations and experiments, is being used to investigate a variety of granular flows, with an emphasis on the evolution of density engendered by the time-dependent motion of boundaries.
Of particular interest are the dynamics of individual particles, the transmission of force and energy through the system, and the resulting evolution of the microstructure.
We have derived an approximate dynamical systems model of the mass center of a one-dimensional column, and a more general three-dimensional, infinite dimensional continuum model in the form of an integro-partial differential equation as the long-wave limit of a system of discrete spheres that interact via dissipative contact models. Soft-sphere simulations featuring the Walton-Braun hysteretic models have been completed at NJIT over a broad parameter space that includes particle properties, input energy via the time-dependent motion of a boundary, as well as the influence of lateral periodicity and system size. For the column, strong quantitative agreement with discrete simulations has been achieved, as well as with experiments conducted at Birmingham University (UK) using Positron Emission Particle Tracking
. We are currently extending our simulation efforts using
Mercury DPM 
in collaboration with Twente University (Netherlands).
Our close interactive approach comprising simulations and experiments, coupled with dynamical modeling and analysis generates an effective synergy to advance the state-of-the-art in the study of granular flows, and promises to have an even greater impact on future research, including innovations in each of the component disciplines. The results so far have been extremely encouraging and the potential for further advances, both practical and theoretical, appears to be strong.
- A. D. Rosato, L. Zuo, D. Blackmore, H. Wu, D. Horntrop, D. Parker, C. Windows-Yule, "Tapped Granular Column Dynamics: Simulations, Experiments and Modeling",
J. Comp. Part. Mech
., (2015), DOI 10.1007/s40571-015-0075-2
- C. R. K. Windows-Yule, A. D. Rosato, D. J. Parker, A.R. Thornton, "Maximizing Energy Transfer in Vibrofluidized Granular Systems",
Phys. Rev. E
91 , 052203 (2015).
- D. Blackmore, A. D. Rosato, X. Tricoche, K. Urban, L. Zuo, "Analysis, Simulation, Visualization of 1D Tapping via Reduced Dynamical Systems Models",
273-74 , pg. 14-27 (2014).
- V. Ratnaswamy, A. D. Rosato, D. Blackmore, X. Tricoche, N. Ching, L. Zuo, "Evolution of Solids Fraction Surfaces in Taping: Simulation and Dynamical Systems Analysis",
14 , 163-168 (2012).
- D. Blackmore, A. D. Rosato, X. Tricoche, K. Urban, V. Ratnaswamy, "Tapping Dynamics of Granular Columns and Beyond",
Journal of Mechanics, Materials and Structures6 [1-4], 71-86 (2011).
- A. Rosato, O. Dybenko, V. Ratnaswamy, D. Horntrop, L. Kondic, "Microstructure Development in Tapped Granular Systems",
Physical Review E
81 , 061301 (2010).
 An imaging technique allowing granular dynamics to be studied in three-dimensional flows. (