Applications of Statistical Physics to Complex Processes

该奖项支持理论研究和教育，将非平衡统计物理学应用于基本的自然过程，包括粗化磁系统中的界面，随机驱动的搜索算法，布朗粒子在复杂介质中的扩散，以及进化生物学。粗化界面的几何形状将在一个单一的无限直角角，分离两个破对称有序相的最简单的几何设置进行研究。在二维空间中，通过构造角界面与排斥过程之间的同构，可以精确地解决角界面的光滑问题。这项工作的目标之一是将这种方法扩展到具有挑战性的情况下的三维角落，通过开发一个映射之间的界面演化和一个3-物种的排斥过程的六边形lattice，然后解决后者model.The PI将构建优化的策略，寻找一个目标，通过检测示踪剂粒子的目标是稳定发射的目标。当探测到示踪剂时，探测器会调整其轨迹，以便更靠近源。一系列的战略将进行研究，以找到最佳的搜索过程作为基本参数的函数，如示踪剂运动的性质，示踪剂的寿命和浓度。另一个研究项目是将首次通过传播作为一种有效的方法来模拟多孔介质中的扩散，并作为副产品，提供了一种新的方法来重建微观布朗粒子轨迹在多孔介质中的首次通过信息在广泛分离的时间间隔。这些信息将提供一种非侵入性的方法来确定多孔介质的微观结构，以非侵入性的方式。一个补充的研究工作将集中在确定相关动物群体中给定质量的物种数量。从化石数据的基本特征，一个最低限度的扩散反应模型可以提炼，占观察到的广泛分布的物种数量的给定质量。现在将研究这种分布的时间依赖性，既要描述不同时期的物种多度分布，又要了解间断进化如何在物种多度分布的发展中表现出来。几个研究生的论文研究。 一些研究项目将与圣达菲研究所（SFI）和新搬迁的斯伦贝谢研究实验室（位于马萨诸塞州剑桥）的同事合作进行。物种丰富度项目为目前SFI了解系统生物学中宏观尺度现象的努力带来了更多的量化层面。第一通道传播和轨迹重建项目可以为斯伦贝谢科学家提供新的理论工具，帮助预测含油岩石的物理性质。非技术总结该奖项支持理论研究和教育，以推进统计物理学，包括远离平衡的物理和材料系统。从物质生长到支持生命的物理过程，许多重要的过程都是非平衡系统，它们缺乏平衡系统所特有的（热力学）力的内在平衡，而平衡系统是统计物理学概念基础的支柱。统计物理学具有广泛的影响力，研究包括几个问题，其中之一是更好地理解粗化过程，其中将材料中不同相分离的界面收缩并最终消失。这个过程在材料科学中无处不在。PI还将研究通过多孔介质的扩散，旨在发展见解，使人们能够在不损坏材料的情况下推断多孔材料的性质。最后，PI还将应用非平衡统计力学的方法来解决物理科学与生物学的界面问题。 该研究在很大程度上受到材料科学基本问题的启发，有助于进一步发展统计物理学的强大框架，使人们能够深入了解材料科学之外的广泛问题。该研究将为博士学位提供基础，从而为研究生教育做出重大贡献。几个研究生的论文研究。 一些研究项目将与圣达菲研究所（SFI）和新搬迁的斯伦贝谢研究实验室（位于马萨诸塞州剑桥）的同事合作进行。物种丰富度项目为目前SFI了解系统生物学中宏观尺度现象的努力带来了更多的量化层面。首次通过传播和轨迹重建项目可以为斯伦贝谢科学家提供新的理论工具，以帮助预测含油岩石的物理性质。

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.