Steady advection-diffusion around finite absorbers in two-dimensional potential flows

We perform an exhaustive study of the simplest, nontrivial problem in advection-diffusion -- a finite absorber of arbitrary cross section in a steady two-dimensional potential flow of concentrated fluid. This classical problem has been studied extensively in the theory of solidification from a flowing melt, and it also arises in Advection-Diffusion-Limited Aggregation. In both cases, the fundamental object is the flux to a circular disk, obtained by conformal mapping from more complicated shapes. We construct the first accurate numerical solution using an efficient new method, which involves mapping to the interior of the disk and using a spectral method in polar coordinates. Our method also combines exact asymptotics and an adaptive mesh to handle boundary layers. Starting from a well-known integral equation in streamline coordinates, we also derive new, high-order asymptotic expansions for high and low P\'eclet numbers (\Pe). Remarkably, the `high' \Pe expansion remains accurate even for such low \Pe as $10^{-3}$. The two expansions overlap well near \Pe = 0.1, allowing the construction of an analytical connection formula that is uniformly accurate for all \Pe and angles on the disk with a maximum relative error of 1.75%. We also obtain an analytical formula for the Nusselt number ($\Nu$) as a function of the P\'eclet number with a maximum relative error of 0.53% for all possible geometries. Because our finite-plate problem can be conformally mapped to other geometries, the general problem of two-dimensional advection-diffusion past an arbitrary finite absorber in a potential flow can be considered effectively solved.Comment: 29 pages, 12 figs (mostly in color

Transport-limited aggregation and dense granular flow

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 141-153).In this thesis, transport of interacting particles is studied in two different physical systems. In the first part, a model for interfacial growth driven by general transport processes is proposed to generalize Laplacian growth such as diffusion-limited aggregation (DLA) and viscous fingering. The fractal properties, crossover in morphology, and relation between continuous and stochastic growth are studied in the context of a representative case, advection-diffusion-limited aggregation (ADLA). The model is extended on curved surfaces and the effect of curvature is also discussed. In the second part, dense granular flow inside silos and hoppers is investigated using high-speed imaging and the results are compared to existing theories. While mean velocity fields are in qualitative agreement, the diffusion and mixing of particles are contradictory to the microscopic assumptions. A new model for dense granular flow is suggested to resolve the inconsistency.by Jaehyuk Choi.Ph.D

Lineage of Eccentrics: The Popularization of Art History, or Rewriting Japanese Art History

In 1968, art historian Tsuji Nobuo categorized a number of Edo-era painters under the description Lineage of Eccentrics. These were artists not bound to any art historical schools, but whose work was characterized by displays of bizarre and fantastical images. Since then, the concept of kisō (eccentric ideas) has acted as a driving force and an academic support for the phenomenon of the Japanese art boom—the popularity of Japanese traditional art since the 2000s. It has also contributed to the rediscovery of its representative artist, Itō Jakuchū. The concept of kisō had an avant-gardist feature in that it denied conventional formality, and at the same time sought to become a new mainstream. In that pursuit, the concept enthusiastically embraced Western art styles such as Maniérisme and Surrealism in order to guarantee its universality. It also reflected the enthusiasm for postwar democracy by emphasizing the artless character of the populace. This effort in turn established a basis for writing pro-audience art history. Furthermore, the concept of kisō sought to expand its boundaries as a genre to include not only paintings, but also crafts and everyday objects, through the key concepts of asobi (playfulness) and kazari (decorativeness) in its media. This allowed the idea of kisō to extend its lifespan as a concept not limited to the Edo era, but one which pertained to the entirety of Japanese art. In conjunction with the Japanese art boom, the concept was employed in writing easily comprehensible art history by using, in place of art historical jargon, more familiar terms such as expression, freedom, playfulness, decorativeness, humor, and the grotesque. This rewritten art history has been visualized in the form of fun exhibitions curated around themes of happiness, cuteness, and joy. The idea of kisō rejected elitism and oriented itself toward the general public. This allowed it to coexist readily with contemporary Japanese art that actively adopted subculture as its major theme. Japanese Neo-pop, as exemplified by the work of Murakami Takashi, and Murakamis Superflat aesthetic, is known to have been greatly influenced by Tsujis Lineage of Eccentrics (2004), and it summons the painters of this lineage by means of parody and homage. The concept of kisō, at first glance, might appear to be inconsistent and illogical, as it has advanced by embracing and rebuilding conflicting elements: the universal and the specific, the mainstream and the avant-garde, the yin and yang, and so on. However, one may say that it has been this flexibility that has permitted it successfully to gain the popularity it has enjoyed