Art of Science 2011 competition, Princeton University
The Art of Science exhibition explores the interplay between science and art. These practices both involve the pursuit of those moments of discovery when what you perceive suddenly becomes more than the sum of its parts. Each piece in this exhibition is, in its own way, a record of such a moment.
(from top, left to right)
Chaos and geomagnetic reversals
Dept. of Astrophysical Sciences/ Princeton Plasma Physics Laboratory
The magnetic field of the Earth has reversed its polarity several hundred times during the past 160 million years. Polarity reversals are known to be strongly irregular and chaotic, and the reversal durations are relatively short (typically a few thousand years) compared with the constant polarity intervals between reversals. This image shows a simple deterministic model illustrating the geomagnetic reversals. The model is based on the non-linear interaction between two magnetic modes (dipole and quadrupole) and one velocity component of the Earth’s core flow, and the image shows typical trajectories in the 3D phase space. The corresponding strange attractor reproduces irregular reversals between two symmetrical states. While the behavior in a given polarity is strongly chaotic and seems random, the path followed by trajectories during a reversal is always the same: during a reversal, the magnetic field changes shape (from dipolar to quadrupolar structure), rather than simply vanishing.
Zhen James Xiang (GS)
Dept. of Electrical Engineering
As part of my research I am designing intelligent image decomposition algorithms that split an image into sub-images in a way that best captures important image structure. Natural images have structure. Understanding this structure and being able to decompose an image in a way that respects this structure is an important aspect of computational image processing. The algorithm used here recursively cuts an image into smaller rectangular pieces. For each cut, a larger rectangle is divided either horizontally or vertically into two equal smaller rectangles. This results in a division of the input image into many rectangular pieces, similar to those shown, organized into a data structure called a dyadic tree.
For each input image, our algorithm finds the dyadic tree that gives the most concise representation of the image as measured by its Haar wavelet transform coefficients computed on this tree. We have shown that this optimal tree provides the best approximation of the sublevel sets of the image and is useful in tasks such as removing unwanted noise in the image. To visualize how the decomposition algorithm works, I developed computer code that displays the resulting dyadic tree. The input image has been automatically cut into local rectangular pieces in a way carefully designed to achieve a useful global optimality. For clarity, only a partial decomposition of the input image has been shown. This visualization reminds us of the inspirations we receive from nature: that harmony is required between division and unity.
Dust to Dust, to Planets?
Xuening Bai (GS), James M. Stone (fac)
Dept. of Astrophysical Sciences
Planets form from the coagulation of tiny solid particles (dust) in a gaseous protoplanetary disk, requiring growth over 40 orders of magnitude in particle mass. A crucial stage in planet formation involves making kilometer-sized planetesimals from millimeter to centimeter sized pebbles. This image illustrates this process: aerodynamical interactions between the gas and the pebbles collect the latter into very dense clumps (bright regions), almost as if by design. In turn, these clumps become planetesimals: the building blocks of planets. The image is taken from a hydrodynamical simulation of a protoplanetary disk, in which the dynamics and feedback from millions of small solid particles is included self-consistently. The unstable clumping of particles was predicted in research conducted at Princeton by A. Youdin and J. Goodman.
Yunlai Zha (GS)
Dept. of Electrical Engineering
Arsenic sulphide dissolved in a solution displays colorful random patterns after being spin-coated and baked on a chrome-evaporated glass slide.
Patterning the embryo
Yoosik Kim (GS) and Stanislav Shvartsman (fac)
Dept. of Chemical and Biological Engineering
These images are vertical cross-sectional images of embryos of Drosophila melanogaster — otherwise known as the common fruit fly. The images, obtained using a confocal microscope, are of embryos stained with antibodies in order to visualize molecules that subdivide the embryo into three tissue types: muscle, nervous system, and skin. Obtaining such images is an engineering challenge since it requires upright positioning of a tiny embryo, which is ellipsoid in shape and only a half-millimeter long.
In collaboration with Lu lab at Georgia Tech, we have developed a microfluidic device to trap and orient a large number of embryos vertically. This technique can be used to quantify spatial profiles of signaling molecules, which can be used to develop mathematical models and eventually to understand the processes that drive the development of the embryo.