Applications of Statistical Physics to Complex Processes

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TECHNICAL SUMMARYThis award supports theoretical research and education to apply non-equilibrium statistical physics to fundamental natural processes, including interfaces in coarsening magnetic systems, stochastically-driven search algorithms, diffusion of Brownian particles in complex media, and evolutionary biology. The geometry of coarsening interfaces will be studied in the simplest geometrical setting of a single infinite right angle corner that separates two broken-symmetry ordered phases. In two dimensions, the smoothing of this corner interface can be exactly solved by constructing an isomorphism between the corner interface and an exclusion process. One of the goals of this work is to extend this approach to the challenging case of the three-dimensional corner by developing a mapping between the interface evolution and a 3-species exclusion process on the hexagonal lattice and then solving the latter model.The PI will construct optimized strategies for a searcher that seeks a target by detecting tracer particles that are steadily emitted by the target. The searcher adjusts its trajectory when tracers are detected so as to move closer to the source. A range of strategies will be studied in order to find the optimal search process as a function of fundamental parameters, such as the nature of the tracer motion, the tracer lifetime and its concentration. Another research project is to apply first-passage propagation as an efficient way to simulate diffusion in porous media and, as a byproduct, provide a novel way to reconstruct microscopic Brownian particle trajectories in a porous medium from first-passage information at widely separated time intervals. Such information would provide a non-invasive way to determine the micro-structure of porous media in a non-invasive manner.A complementary research effort will be focused on determining the number of species of a given mass in related animal groups. From basic features of fossil data, a minimalist diffusion-reaction model can be distilled that accounts for the observed broad distribution of the number of species of a given mass. The time dependence of this distribution will now be studied, both to describe the species abundance distribution in different epochs, and to understand how punctuated evolution manifests itself in the development of species abundance distributions.The research will contribute substantially to graduate education by providing the basis for the Ph.D. thesis research of several graduate students. Some of the research projects will be performed in collaboration with colleagues at the Santa Fe Institute (SFI) and at the newly-relocated Schlumberger research lab in Cambridge, Massachusetts. The project on species abundance has brought a more quantitative dimension to current SFI efforts to understand macro-scale phenomena within systems biology. The projects on first-passage propagation and trajectory reconstruction could provide Schlumberger scientists with new theoretical tools to help predict the physical properties of oil-bearing rocks.NONTECHNICAL SUMMARYThis award supports theoretical research and education to advance statistical physics to encompass physical and material systems that are far from equilibrium. Many important processes ranging from materials growth to the physical processes that support life are nonquilibrium systems that lack the intrinsic balance of (thermodynamic) forces that characterize equilibrium systems, a pillar in the conceptual foundations of statistical physics. Statistical physics has a broad reach and the research encompasses several problems, among them is to better understand of the process of coarsening in which interfaces that separate different phases in a material shrink and eventually disappear. This process is ubiquitous in materials science. The PI will also study diffusion through porous media with an aim to develop insights that will enable one to deduce the nature of the porous material without damaging the material. Finally, the PI will also apply the methods of nonequilibrium statistical mechanics to problems at the interface of the physical sciences with biology. Inspired in large part by fundamental problems in materials science, this research contributes to the further development of the powerful framework of statistical physics enabling insights into a wide range of problems that extend beyond materials science.The research will contribute substantially to graduate education by providing the basis for the Ph.D. thesis research of several graduate students. Some of the research projects will be performed in collaboration with colleagues at the Santa Fe Institute (SFI) and at the newly-relocated Schlumberger research lab in Cambridge, Massachusetts. The project on species abundance has brought a more quantitative dimension to current SFI efforts to understand macro-scale phenomena within systems biology. The projects on first-passage propagation and trajectory reconstruction could provide Schlumberger scientists with new theoretical tools to help predict the physical properties of oil-bearing rocks.