This 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 Waals forces 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 SUMMARY
This 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.
