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Now showing items 1-10 of 17

#### Viscous fluid sheets

(Massachusetts Institute of Technology, 2007)

We present a general theory for the dynamics of thin viscous sheets. Employing concepts from differential geometry and tensor calculus we derive the governing equations in terms of a coordinate system that moves with the ...

#### Parabolic equations without a minimum principle

(Massachusetts Institute of Technology, 2007)

In this thesis, we consider several parabolic equations for which the minimum principle fails. We first consider a two-point boundary value problem for a one dimensional diffusion equation. We show the uniqueness and ...

#### Expressions for the generating function of the Donaldson invariants for CP²

(Massachusetts Institute of Technology, 2007)

The Donaldson invariants for CP2 were obtained as the u-plane integral from a N = 2 supersymmetric topological U(1)-gauge theory by Moore and Witten. We derive the generating function for the Donaldson invariants of CP2 ...

#### Multiscale modeling in granular flow

(Massachusetts Institute of Technology, 2007)

Granular materials are common in everyday experience, but have long-resisted a complete theoretical description. Here, we consider the regime of slow, dense granular flow, for which there is no general model, representing ...

#### Adaptive protocols for the quantum depolarizing channel

(Massachusetts Institute of Technology, 2007)

In the first part, we present a family of entanglement purification protocols that generalize four previous methods, namely the recurrence method, the modified recurrence method, and the two methods proposed by Maneva-Smolin ...

#### On quasi-categories as a foundation for higher algebraic stacks

(Massachusetts Institute of Technology, 2007)

We develop the basic theory of quasi-categories (a.k.a. weak Kan complexes or ([infinity], 1)- categories as in [BV73], [Joy], [Lur06]) from first principles, i.e. without reference to model categories or other ideas from ...

#### Dirac operators and monopoles with singularities

(Massachusetts Institute of Technology, 2007)

This thesis consists of two parts. In the first part of the thesis, we prove an index theorem for Dirac operators of conic singularities with codimension 2. One immediate corollary is the generalized Rohklin congruence ...

#### Order computations in generic groups

(Massachusetts Institute of Technology, 2007)

We consider the problem of computing the order of an element in a generic group. The two standard algorithms, Pollard's rho method and Shanks' baby-steps giant-steps technique, both use [theta](N^1/2) group operations to ...

#### Sampling-based algorithms for dimension reduction

(Massachusetts Institute of Technology, 2007)

Can one compute a low-dimensional representation of any given data by looking only at its small sample, chosen cleverly on the fly? Motivated by the above question, we consider the problem of low-rank matrix approximation: ...

#### The Ro (S¹)-graded equivariant homotopy of THH(Fp)

(Massachusetts Institute of Technology, 2007)

The main result of this thesis is the computation of ... for ... These RO(S¹)-graded TR-groups are the equivariant homotopy groups naturally associated to the S¹-spectrum THH(Fp), the topological Hochschild S¹-spectrum. ...