Browsing Department of Mathematics by Title
Now showing items 342361 of 828

I. A pressure Poisson method for the incompressible NavierStokes equations : II. Long time behavior of the KleinGordon equations
(Massachusetts Institute of Technology, 2011)In this thesis, we address two problems involving partial differential equations. In the first problem, we reformulate the incompressible NavierStokes equations into an equivalent pressure Poisson system. The new system ... 
Ideals in triangulated categories : phantoms, ghosts and skeleta
(Massachusetts Institute of Technology, 1997) 
Identifying boosted objects with Nsubjettiness and linear kmeans clustering
(Massachusetts Institute of Technology, 2011)In this thesis, I explore aspects of a new jet shape  Nsubjettiness  designed to identify boosted hadronicallydecaying objects (with a particular focus on tagging top quarks) at particle accelerators such as the Large ... 
Immersions of symmetric spaces,
(Massachusetts Institute of Technology, 1970) 
Improving a bounding result for weaklyscattered theories
(Massachusetts Institute of Technology, 2006)In this thesis, we effectively construct a predecessor function for the type definitions in the raw hierarchy for any weaklyscattered theory. Using this predecessor function, we improve a recent bounding result by Sacks ... 
The indecomposable integral representations of finite cyclic groups
(Massachusetts Institute of Technology, 1962) 
Index theorems and magnetic monopoles on asymptotically conic manifolds
(Massachusetts Institute of Technology, 2010)In this thesis, I investigate the index of Callias type operators on asymptotically conic manifolds (also known as asymptotically locally Euclidean manifolds or scattering manifolds) and give an application to the moduli ... 
Inducedcharge electroosmosis
(Cambridge University Press, 2004)We describe the general phenomenon of â€˜inducedcharge electroosmosis’ (ICEO) – the nonlinear electroosmotic slip that occurs when an applied field acts on the ionic charge it induces around a polarizable surface. ... 
Inducedcharge electrokinetics at large voltages
(Massachusetts Institute of Technology, 2008)The classical transport theory cannot explain the experimental behavior of electrochemical systems in the extreme operating conditions required by modern microfluidics devices. Some experimental puzzles include strange ... 
An infinite loop space structure for Ktheory of bimonoidal categories
(Massachusetts Institute of Technology, 2010)In recent work of BaasDundasRichterRognes, the authors introduce the notion of the K theory of a bimonoidal category R, and show that it is equivalent to the algebraic Ktheory space of the ring spectrum KR. In this ... 
Initial data to vacuum Einstein equations with asymptotic expansion
(Massachusetts Institute of Technology, 1998) 
The instability of timedependent jets
(Massachusetts Institute of Technology, 2002)The central focus of my thesis is to study the instability jets of various complexity by analyzing the linear and nonlinear dynamics. We applied this methodology to four different situations in order to learn the following. ... 
Instanton correction, wall crossing and mirror symmetry of Hitchin's moduli spaces
(Massachusetts Institute of Technology, 2011)We study two instanton correction problems of Hitchin's moduli spaces along with their wall crossing formulas. The hyperkahler metric of a Hitchin's moduli space can be put into an instantoncorrected form according to ... 
Integral geometry, Hamiltonian dynamics, and Markov Chain Monte Carlo
(Massachusetts Institute of Technology, 2016)This thesis presents applications of differential geometry and graph theory to the design and analysis of Markov chain Monte Carlo (MCMC) algorithms. MCMC algorithms are used to generate samples from an arbitrary probability ... 
Integration in finite terms with elementary functions and dilogarithms
(Massachusetts Institute of Technology, 1994) 
Interactions between combinatorics, lie theory and algebraic geometry via the Bruhat orders
(Massachusetts Institute of Technology, 1981) 
Intercalation dynamics in lithiumion batteries
(Massachusetts Institute of Technology, 2009)A new continuum model has been proposed by Singh, Ceder, and Bazant for the ion intercalation dynamics in a single crystal of rechargeablebattery electrode materials. It is based on the CahnHilliard equation coupled to ... 
The intersection homology with twisted coefficients of toric varieties
(Massachusetts Institute of Technology, 1991) 
Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
(Massachusetts Institute of Technology, 2006)We define a new family of open GromovWitten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian ... 
Introductory study of hypercomplex number systems and their applications in geometry
(Massachusetts Institute of Technology, 1931)