Session T1: Prize Session: Buckley, Lilienfeld

Oliver E. Buckley Prize Talk: Exotic Order in Solids

Historically, solids were classified as crystalline or amorphous, the former being characterized by delta function Bragg peaks in their diffraction patterns. Quasicrystals are solids with long range quasiperiodic translational order and symmetries forbidden to crystals, and, like crystals, their diffraction spectra consist of discrete Bragg peaks. As such, both crystals and quasicrystals are easily identified by scattering, and their degree of perfection is readily quantified. These two classes, crystals and quasicrystals, while large, do not exhaust all the possibilities for ordered solids, and models of ordered materials which exhibit no Bragg scattering may be constructed. Consequently, a different criterion for the characterization of long range order (which would subsume crystals and quasicrystals) is needed for their description, as well as for the quantification of the extent of their order.   

Oliver E. Buckley Condensed Matter Prize Talk: Once upon a time in Kamchatka: The Search for Natural Quasicrystals

Twenty-five years ago, soon after the concept of quasicrystals was introduced\footnote{D. Levine and P.J. Steinhardt, PRL 53, 2477 (1984).} and the first examples were synthesized in the laboratory,\footnote{D. Shechtman, I. Blech, D. Gratias and J.W. Cahn, PRL 53, 1951 (1984).} the search for a naturally-forming quasicrystal began. For many years, the search was informal. However, beginning about a decade ago,\footnote{P.J. Lu, K. Deffeyes, P.J. Steinhardt, and N. Yao, PRL 87, \textbf{275507 (2001).}} a systematic search was developed that, through planning and much serendipity, led to the discovery this past year of a natural candidate embedded in a rock reported to have been found in a remote region on the northern Kamchatka peninsula.\footnote{L. Bindi, P.J. Steinhardt, N. Yao and P.J. Lu, Science 324, 1306 (2009).} The talk will describe the search for natural quasicrystals and the implications for physics and geology.   

Julius Edgar Lilienfeld Prize Talk: The Fermi Pasta Ulam (FPU) Problem and The Birth of Nonlinear Science

In 1953, Enrico Fermi, John Pasta, and Stan Ulam initiated a series of computer studies aimed at exploring how simple, multi-degree of freedom nonlinear mechanical systems obeying reversible deterministic dynamics evolve in time to an equilibrium state describable by statistical mechanics. Their expectation was that this would occur by mixing behavior among the many linear modes. Their intention was then to study more complex nonlinear systems, with the hope of modeling turbulence computationally. The results of this first study of the so-called Fermi-Pasta-Ulam (FPU) problem, which were published in 1955 and characterized by Fermi as a ``little discovery,'' showed instead of the expected mixing of linear modes a striking series of (near) recurrences of the initial state and no evidence of equipartition. This work heralded the beginning of both computational physics and (modern) nonlinear science. In particular, the work marked the first systematic study of a nonlinear system by digital computers (``experimental mathematics'') and led directly to the discovery of ``solitons,'' as well as to deep insights into deterministic chaos and statistical mechanics. In this talk, I will review the original FPU studies and show how they led to the understanding of two key paradigms of nonlinear science. Specifically, I will show how a continuum approximation to the original discrete system led to the discovery of ``solitions'' whereas a low-mode approximation led to an early example of ``deterministic chaos.'' I will close with a brief indication of how the recurrence phenomenon observed by behavior by FPU can be reconciled with mixing, equipartition, and statistical mechanics.   

Julius Edgar Lilienfeld Prize Talk: Catastrophic cascade of failures in interdependent networks

We study interdependent networks, where nodes fail in one network, cause dependent nodes in another network to also fail. We provide a framework for understanding the robustness of such interacting networks. We calculate the critical fraction of nodes that upon removal will lead to a failure cascade and to a complete fragmentation of two interdependent networks. Surprisingly, while for a single network a broader degree distribution results in the network being more robust to random failures, for interdependent networks, the broader the distribution is, the more vulnerable the networks become to random failures.