mathematics

Silas D. Alben

Silas D. Alben is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Silas D. Alben rather than just read about it. In short: Silas D. Alben is an American mathematician.

Key takeaways

Silas D. Alben belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Silas D. Alben to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Silas D. Alben from memory before moving on to harder problems.

Reference excerpt

Silas D. Alben is an American mathematician. He is Professor of Mathematics and Director of the Applied and Interdisciplinary Mathematics Program at the University of Michigan. His research addresses problems from biology (especially biomechanics) and engineering that can be studied with the tools of applied mathematics and continuum mechanics.

Biography

Education Silas Alben attended Harvard College where he received in 1999 A.B. degrees in Mathematics and Physics, magna cum laude. In 2000, he joined the Courant Institute of Mathematical Sciences at New York University, where he received a Ph.D. in Mathematics in 2004. His thesis Drag Reduction by Self-Similar Bending and a Transition to Forward Flight by a Symmetry-Breaking Instability was advised by Michael Shelley.

Research Alben's research focuses on problems in biomechanics, material science, and fluid mechanics. As a graduate student at NYU, Alben worked with Jun Zhang and Michael Shelley in investigating the dynamics of flexible structures and how such structures can become more aerodynamic by altering their shape. In this study, experiments visualized a short glass fiber deforming in fluid flow, and analysis showed how the fiber can reduce the drag force exerted by the fluid by changing its shape. This work was published 2002 in Nature under the title Drag Reduction Through Self-Similar Bending of a Flexible Body, and was the subject of various news articles in periodicals including The New York Times and others. As a Postdoctoral Fellow at Harvard, Alben collaborated with Ernst A. van Nierop and Michael P. Brenner in a paper titled "How Bumps on Whale Flippers Delay Stall: An Aerodynamic Model". The paper gave a mathematical model for this hydrodynamic phenomenon. This result, featured in MIT's Technology Review and Nature, provides a theoretical basis for potential improvements in using bumps for more stable airplanes, more agile submarines, and more efficient turbine blades. In 2007, Alben investigated (with Michael P. Brenner) the self-assembly of 3D structures from flat, elastic sheets. This experiment, featured in New Scientist, presented a new technique in nano construction; previously, the transformation of flat sheets to 3D structures was performed by random formation, but in this study, the addition of biases into the design of the sheets gave the possibility of predicting the resulting shape.

Honors and awards Alfred P. Sloan Foundation Research Fellow (2011)

References

External links Homepage U Michigan faculty profile

Worked examples

Example 1 — a first encounter with Silas D. Alben

Start with the simplest possible case. Write down what Silas D. Alben claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Silas D. Alben before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Silas D. Alben ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Silas D. Alben

In research: Silas D. Alben appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Silas D. Alben in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Silas D. Alben is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century American mathematicians, American fluid dynamicists, Courant Institute of Mathematical Sciences alumni, so understanding it makes those chapters shorter.
In everyday life: Look for Silas D. Alben outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Silas D. Alben in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Silas D. Alben means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Silas D. Alben out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Silas D. Alben in simple terms?

Silas D. Alben is an American mathematician.

Why does Silas D. Alben matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Silas D. Alben?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Silas D. Alben.