Chris Woodward

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We prove that the linearization functor from the category of Hamiltonian K-actions with group-valued moment maps in the sense of Lu, to the category of ordinary Hamiltonian K-actions, preserves products up to symplectic isomorphism. As an application, we give a new proof of the Thompson conjecture on singular values of matrix products and extend this result(More)
We realize Stasheff’s multiplihedron geometrically as the moduli space of stable quilted disks. This generalizes the geometric realization of the associahedron as the moduli space of stable disks. We show that this moduli space is the non-negative real part of a complex moduli space of stable scaled marked curves.
One of the simplest invariants of a symplectic manifold is the isomorphism class of the canonical line bundle. Suppose (M,ω) is a symplectic manifold. For any ω-compatible almost complex structure J one defines the canonical line bundle KM as the dual to the top exterior power of the tangent bundle TM , KM = detC(TM)∗. Since the space of ω-compatible almost(More)
Under stress, crystals irreversibly deform through complex dislocation processes that intermittently change the microscopic material shape through isolated slip events. These underlying processes can be revealed in the statistics of the discrete changes. Through ultraprecise nanoscale measurements on nickel microcrystals, we directly determined the size of(More)
The strain field of isolated screw and edge dislocation cores in aluminum are calculated using density-functional theory and a flexible boundary condition method. Nye tensor density contours and differential displacement fields are used to accurately bound Shockley partial separation distances. Our results of 5-7.5 A (screw) and 7.0-9.5 A (edge) eliminate(More)
In this manuscript, we extend on our prior work to show that under certain conditions cross-slip nucleation is athermal and spontaneous with zero activation energy in FCC elemental metals such as Ni and Cu, and L12 intermetallic compounds such as Ni3Al. Using atomistic simulations (molecular statics), we show that spontaneous cross-slip occurs at mildly(More)
Exact time-dependent density functionals remember both the entire history of the density and the initial wave function. We show that the two effects are intimately related, and all history dependence can be written as initial-state dependence, including that of the exchange-correlation kernel. For states that can be evolved from a ground state, all(More)