2008 Woodie Awards
Bubbles give insight into universe
Issue date: 5/1/08
Imagine blowing soap bubbles when you were younger. Picture the thin, sparkling film of soap spreading out across a loop of plastic or metal wire, slowly building into a fragile sphere that comes loose and floats away.
It turns out there is an entire branch of mathematics devoted to the study of this sort of phenomenon. Patrick Zulkowski, a Hopkins grad student, along with his advisor Chikako Mese, are conducting research into the minimal surfaces between closed curves, a somewhat abstract problem with real-world consequences.
This question goes back to Plateau's Problem, a famous dilemma that dates to the 19th century. Joseph Plateau, a Belgian physicist, was interested in soap films and their surfaces in a closed loop of wire. His study of their properties led to the formulation of Plateau's laws, which describe the structure and behavior of their surfaces.
The essential law governing their behavior is that the soap film, due to its natural surface tension, wants to form a film with the smallest area possible. In a free-floating soap bubble, surface tension causes bubbles to form a perfect sphere. Things are more complicated while the growing bubble is still attached to the wire.
Zulkowski, who received a bachelor's and master's from the University of Delaware, studies these surfaces. But what would higher math at Hopkins be without some extra complexity? His studies take place in a multidimensional space, far beyond the normal realm of our three- (or four-) dimensional lives.
In order to explain his work, Zulkowski makes an analogy to our world. A geodesic is the shortest connection between two points. Here, geodesic is just a fancy way of saying straight line. But those lines vary as you add more spatial dimensions. The shortest connection between Baltimore and Los Angeles would definitely be a little bent, since our planet is a ball and not a flat plane.
As you add dimensions, finding the least distance, the geodesic keeps on becoming more complicated as you move on from the plane to a sphere all the way up to unimaginable spaces - spaces that do exist according to mathematicians and physicists.
It turns out there is an entire branch of mathematics devoted to the study of this sort of phenomenon. Patrick Zulkowski, a Hopkins grad student, along with his advisor Chikako Mese, are conducting research into the minimal surfaces between closed curves, a somewhat abstract problem with real-world consequences.
This question goes back to Plateau's Problem, a famous dilemma that dates to the 19th century. Joseph Plateau, a Belgian physicist, was interested in soap films and their surfaces in a closed loop of wire. His study of their properties led to the formulation of Plateau's laws, which describe the structure and behavior of their surfaces.
The essential law governing their behavior is that the soap film, due to its natural surface tension, wants to form a film with the smallest area possible. In a free-floating soap bubble, surface tension causes bubbles to form a perfect sphere. Things are more complicated while the growing bubble is still attached to the wire.
Zulkowski, who received a bachelor's and master's from the University of Delaware, studies these surfaces. But what would higher math at Hopkins be without some extra complexity? His studies take place in a multidimensional space, far beyond the normal realm of our three- (or four-) dimensional lives.
In order to explain his work, Zulkowski makes an analogy to our world. A geodesic is the shortest connection between two points. Here, geodesic is just a fancy way of saying straight line. But those lines vary as you add more spatial dimensions. The shortest connection between Baltimore and Los Angeles would definitely be a little bent, since our planet is a ball and not a flat plane.
As you add dimensions, finding the least distance, the geodesic keeps on becoming more complicated as you move on from the plane to a sphere all the way up to unimaginable spaces - spaces that do exist according to mathematicians and physicists.
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