Perturbed Fluctuations & Patterns

该奖项支持理论和计算研究以及教育活动，以了解边界对波动场的影响。波动的电磁场弥漫在空间中，解释了各种各样的现象，如热（黑体）辐射、中性物体之间的范德华力；流体和大分子的热运动是软物质固有的，例如聚合物和凝胶；而生物学提供了许多不平衡波动的例子。本研究将探讨限制波动场的边界的静态和动态扰动如何改变周围物体之间的能量传递和力，并影响粒子在表面上扩散的聚集模式。项目的具体任务包括但不限于：1。众所周知的黑体结果只适用于大于热波长的尺度。使用散射理论的工具，PI应该开发基本独立的示踪公式来处理热传递，以及相互作用的力，在不同温度下，适用于所有尺度的紧凑或扩展的物体集合。PI应考虑涉及运动和旋转物体的非平衡稳态，并计算辐射能量以及由于周围真空中电磁波动的改变而产生的耗散力和剪切力。PI将探索新的边界条件，以及由此产生的力定律，这些可能通过适当修改表面来实现；例如，通过刻蚀分形图案，或在一个渗透阈值。对于尺度不变的物体，如锥体或金字塔，波动引起的力具有由尺寸考虑决定的简单的通用形式。我们将探讨这些力对形状和几何形状的依赖性。PI将解决以下问题：如何在曲面上改变反应/扩散模式？平衡系统用统计场论的标准工具来描述，约束对象被表述为边界条件。散射振幅是一种编码物体对场的影响的有效方法，而物体之间的影响传递则由格林函数捕获。对于不平衡的系统，焦点转移到每个物体内部的波动源，但是物体之间的相互作用仍然通过散射振幅和格林函数的操作来捕获。对于曲面上的图案，我们将依靠微分几何的方法。预计在所有情况下都要结合分析和数值研究。人力资源的教育和发展是该项目的一个重要方面。该研究是跨学科的，旨在将统计物理学的方法应用于广泛的科学问题。这项研究与PI教授的课程密切相关，这些课程通过教科书和网络传播对更广泛的科学界产生影响。该奖项支持理论和计算研究，以及教育活动，以了解边界对波动场的影响。波动，无论是随机热运动的结果，还是海森堡著名的测不准原理的结果，在自然界中无处不在，在小系统中尤其明显。虽然波动意味着不确定性，但可以利用波动来操纵各种力量，实现理想的结果。具体的例子包括：1；真空远不是空的，而是随着量子和热源的电磁波动而脉动。真空中的物体改变了这些涨落，反过来又受到卡西米尔力和范德华力的影响。远离稳定平衡状态的浸入物体的运动研究较少，包括真空摩擦、辐射发射和短尺度上对经典黑体辐射结果的违背等现象。例如，后者可用于在短间隙上增加数量级的热传递。软物质中的热波动，例如接近临界流体混合物，会产生可控范围内的力，可用于将胶体组装成所需的图案。这些力是如何被边界的形状和结构所改变的，例如蚀刻特定的化学或几何图案？生物系统在不同的尺度上形成模式，从亚细胞到有机体，尽管或因为有非平衡波动。将探讨边界形状对涉及扩散的聚集过程的影响。人力资源的教育和发展是该项目的一个重要方面。该研究是跨学科的，旨在将统计物理学的方法应用于广泛的科学问题。这项研究与PI教授的课程密切相关，这些课程通过教科书和网络传播对更广泛的科学界产生影响。

TECHNICAL SUMMARYThis award supports theoretical and computational research, as well as educational activities, towards understanding the influence of boundaries on fluctuating fields. Fluctuating electromagnetic fields pervade space, accounting for phenomena as diverse as thermal (blackbody) radiation, van der Waalsforces between neutral objects; thermal motions of fluids and macromolecules are inherent to soft matter, for example polymers and gels; while biology provides many instances of out of equilibrium fluctuations. This research will explore how static and dynamic perturbations of the boundaries confining fluctuating fields modifies energy transfer and forces between surrounding bodies, and influences aggregation patterns of particles diffusing on the surfaces. Specific thrusts of the project include, but are not limited to: 1. The well known blackbody results are applicable only on scales larger than the thermal wavelength. Using tools from scattering theory, the PI shall develop basis independent trace formulae to treat heat transfer, as well as interaction forces, amongst a collection of objects, compact or extended, at different temperatures, applicable to all scales.2. The PI shall consider non-equilibrium steady states involving moving and rotating objects, and compute energy radiated as well dissipative and shear forces due to modifications of electromagnetic fluctuations in the surrounding vacuum.3. The PI shall explore the novel boundary conditions, and consequent force laws, that may be realized by appropriate modification of surfaces; for example by etching fractal patterns, or at a percolation threshold.4. Fluctuation induced forces for scale invariant objects, such as a cone or pyramid, have simple universal forms dictated by dimensional considerations. The dependence of these forces on shape and geometry will be explored.5. The PI will address the question: How are reaction/diffusion patterns modified on a curved surface?Systems in equilibrium are described by standard tools of statistical field theory, with the confining objects formulated as boundary conditions. Scattering amplitudes are an efficient way of encoding the influence of an object on the field, while transmission of influence between bodies in captured by Green's functions. For systems out of equilibrium, the focus shifts to fluctuating sources within each body, but the interactions between bodies are still captured by manipulations of scattering amplitudes and Green's functions. For patterns on curved surfaces we shall rely on methods from differential geometry. A combination of analytical and numerical studies is anticipated in all cases.Education and development of human resources are an important aspect of this project. The research is interdisciplinary, aimed at applying methods from statistical physics to a wide range of scientific problems. The research is closely linked to courses taught by the PI, which through textbooks and dissemination by the web have an impact on a broader scientific community.NONTECHNICAL SUMMARYThis award supports theoretical and computational research, as well as educational activities, towards understanding the influence of boundaries on fluctuating fields. Fluctuations, whether the result of the random thermal motion or a consequence of Heisenberg's famous uncertainty principle are ubiquitous in nature, and particularly pronounced in small systems. While fluctuations imply uncertainty, they can be utilized to manipulate forces and to achieve preferred outcomes. Specific examples include: 1. Far from empty, the vacuum pulsates with electromagnetic fluctuations of quantum and thermal origin. Objects in vacuum modify these fluctuations and in turn experience forces, the much studied Casimir and van der Waals forces. The motion of the immersed objects far from the steady state of equilibrium are less well studied and include phenomena such as friction of vacuum, emission of radiation, and violations of classical blackbody radiation results at short scales. The latter can for example be utilized to increase heat transfer across a short gap by orders of magnitude.2. Thermal fluctuations in soft matter, for example near critical fluid mixtures, result in forces of controllable range that can be used to assemble colloids into desired patterns. How are these forces modified by the shape and structure of the boundary, for example by etching specific chemical or geometrical patterns?3. Biological systems form patterns at different scales, from sub-cellular to organism, despite, or because of, non-equilibrium fluctuations. The influence of boundary shapes will be explored for aggregation processes that involve diffusion.Education and development of human resources are an important aspect of this project. The research is interdisciplinary, aimed at applying methods from statistical physics to a wide range of scientific problems. The research is closely linked to courses taught by the PI, which through textbooks and dissemination by the web have an impact on a broader scientific community.