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Dartmouth College

2010

Mathematical models

Articles 1 - 4 of 4

Full-Text Articles in Physical Sciences and Mathematics

Long-Lived Time-Dependent Remnants During Cosmological Symmetry Breaking: From Inflation To The Electroweak Scale, Marcelo Gleiser, Noah Graham, Nikitas Stamatopoulos Aug 2010

Long-Lived Time-Dependent Remnants During Cosmological Symmetry Breaking: From Inflation To The Electroweak Scale, Marcelo Gleiser, Noah Graham, Nikitas Stamatopoulos

Dartmouth Scholarship

Through a detailed numerical investigation in three spatial dimensions, we demonstrate that long-lived time-dependent field configurations emerge dynamically during symmetry breaking in an expanding de Sitter spacetime. We investigate two situations: a single scalar field with a double-well potential and an SU(2) non-Abelian Higgs model. For the single scalar, we show that large-amplitude oscillon configurations emerge spontaneously and persist to contribute about 1.2% of the energy density of the Universe. We also show that for a range of parameters, oscillon lifetimes are enhanced by the expansion and that this effect is a result of parametric resonance. For the SU(2) case, …


Testing General Relativity With Current Cosmological Data, Scott F. Daniel, Eric V. Linder, Tristan L. Smith, Robert R. Caldwell Jun 2010

Testing General Relativity With Current Cosmological Data, Scott F. Daniel, Eric V. Linder, Tristan L. Smith, Robert R. Caldwell

Dartmouth Scholarship

Deviations from general relativity, such as could be responsible for the cosmic acceleration, would influence the growth of large-scale structure and the deflection of light by that structure. We clarify the relations between several different model-independent approaches to deviations from general relativity appearing in the literature, devising a translation table. We examine current constraints on such deviations, using weak gravitational lensing data of the CFHTLS and COSMOS surveys, cosmic microwave background radiation data of WMAP5, and supernova distance data of Union2. A Markov chain Monte Carlo likelihood analysis of the parameters over various redshift ranges yields consistency with general relativity …


Non-Gaussianity From Self-Ordering Scalar Fields, Daniel G. Figueroa, Robert R. Caldwell, Marc Kamionkowski Jun 2010

Non-Gaussianity From Self-Ordering Scalar Fields, Daniel G. Figueroa, Robert R. Caldwell, Marc Kamionkowski

Dartmouth Scholarship

The Universe may harbor relics of the post-inflationary epoch in the form of a network of self-ordered scalar fields. Such fossils, while consistent with current cosmological data at trace levels, may leave too weak an imprint on the cosmic microwave background and the large-scale distribution of matter to allow for direct detection. The non-Gaussian statistics of the density perturbations induced by these fields, however, permit a direct means to probe for these relics. Here we calculate the bispectrum that arises in models of self-ordered scalar fields. We find a compact analytic expression for the bispectrum, evaluate it numerically, and provide …


Low-Frequency Turbulence In A Linear Magnetized Plasma, B. N. Rogers, Paolo Ricci Mar 2010

Low-Frequency Turbulence In A Linear Magnetized Plasma, B. N. Rogers, Paolo Ricci

Dartmouth Scholarship

Plasma turbulence in a linear device is explored for the first time with three-dimensional global two-fluid simulations, focusing on the plasma parameters of the Large Plasma Device. Three instabilities are present in the simulations: the Kelvin-Helmholtz instability, a sheath-driven instability, and a resistive drift wave instability. The Kelvin-Helmholtz mode is shown to dominate the transport of plasma across the magnetic field. Simple scaling laws are obtained for the plasma profiles.