The story Flatland helped 19th century readers understand the metaphorical role of the fourth dimension. Higher dimensions now help 21st century scientists to better understand our comparatively low-dimensional world. The pattern of coins packed on a tabletop or oranges piled on a grocer's stand have both similarities and differences. By examining similar problems in dimensions higher than two or three, we are able to obtain additional points of comparison. Similarly, progress in understanding dense particulate matter such as colloids, granular materials, glasses, or emulsions is starting to arise from comparing and contrasting the behavior of related phenomena in different spatial dimensions. A variety of experimental and theoretical techniques allow for this exploration, but interestingly, different approaches sometimes lead to differing answers as to how dimensionality influences a phenomenon. Some even argue that dimension plays little role on their subfield. Can we make sense of this conundrum? Since progress is taking place on many continents and in different fields (mathematics, engineering, and basic sciences), there is a need to bring researchers together for an extended and focused period of time to sketch the road ahead and to capture the momentum created by these often independent developments. This grant will help support the travel of graduate students and postdoctoral trainees from the US to a workshop addressing questions of dimensionality in dense particulate matter to be held in Dresden, Germany. These junior researchers will be enabled to present talks and posters to the international audience of experts in the various sub-fields. The participation of students and postdoctoral fellows in international workshops is key to training an internationally competitive workforce in this rapidly developing field for which university coursework does not yet exist. The workshop has two features that are aimed at encouraging junior researchers to build future collaborations with the international community: the pairing of formal talks with organized discussions, and the allotment of time for small-group interactions.
?From May 30-June 4 2010, more than 60 chemists, engineers, mathematicians, and physicists from 5 continents gathered for a workshop hosted by the Max Planck Institute for Complex Systems in Dresden, Germany. The title and goal of the workshop was to address the question "Particulate Matter: Does Dimensionality Matter?" This award supported the travel of 8 graduate students and postdocs to this international meeting. Intellectual Merits: The main focus of the conference was to better understand industrially-important materials, such as sand, glasses, colloids, foams, and emulsions by comparing their behavior -- and that of related models -- in 2, 3, and more dimensions. In the 19th century, looking at the world from a dimensional lens helped readers of the mathematical parable "Flatland" grasp the metaphorical role of the fourth dimension. Today, even higher dimensions help scientists shine new light on our relatively low-dimensional world. A flat layer of coins pushed together on a tabletop and a pile of oranges on a grocer's stand have both similarities and differences. They are both the densest possible packing of spheres in their respective dimensions, but the way in which they form, support stress, and rearrange, are different. Computers allow us to contrast similar systems in even higher dimensions. The scientific discussion was lively: not all participants agreed about the role of disorder and randomness, or even the importance of the number of dimensions. Through the meeting, certain lines of agreement have started to appear, as well as key regimes in which to conduct future investigations. Friction, polydispersity, temperature, and particle shape are important variables, but isolating the possible impact of dimensionality from these other factors is necessary if one hopes to make sense of the results. A particular emphasis on the dynamics and structure of disordered systems was noted. On the one hand, the role of dimensionality in theories of jamming and the glass transition led to animated discussions about the physical basis and range of validity of the many analytical approaches explored by various groups. The state of the question and the nature of the challenges ahead have become clearer as a result. On the other hand, the description of order and geometry in disordered systems using local parameters that are accessible in both simulations and experiments -- and a need to understand how these different measures differ from each other -- allowed the identification of parallel challenges in separate scientific communities. Several participating groups have been in a race to find the densest possible packing of tetrahedra. Record-holder Sharon Glotzer gave a lively presentation of the history of this race. Various novel techniques that this packing problem has spawned were also presented, which opened a line of conversation on combining analytical tools with computational methods in higher dimensions. Connections of packing problems to disordered biological systems were enlightening to many in the community, and will likely yield new research directions. Broader Impacts: The NSF funds allowed 8 US-based graduate students and postdocs to attend this international professional meeting, and obtain important exposure to the leading edge of the field. These participants presented posters and/or talks, and had extensive lively discussions with senior participants during meals and breaks. Female graduate students and postdocs in particular were observed to network extensively with each other and with senior participants. All of these activities lay the groundwork for future collaborations and research directions. Overall, the week-long meeting allowed the researchers to spend a focused period of time discussing these issues, allowing them develop ideas for future research directions, and to capture the momentum created by these often independent developments taking place around the world.
