Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
Orienteering In Knowledge Spaces: The Hyperbolic Geometry Of Wikipedia Mathematics, Gregory Leibon, Daniel N. Rockmore
Orienteering In Knowledge Spaces: The Hyperbolic Geometry Of Wikipedia Mathematics, Gregory Leibon, Daniel N. Rockmore
Dartmouth Scholarship
In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example …
Information-Preserving Structures: A General Framework For Quantum Zero-Error Information, Robin Blume-Kohout, Hui Khoon Ng, David Poulin, Lorenza Viola
Information-Preserving Structures: A General Framework For Quantum Zero-Error Information, Robin Blume-Kohout, Hui Khoon Ng, David Poulin, Lorenza Viola
Dartmouth Scholarship
Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system’s ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures, to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected. We …
Perpendicular Ion Heating By Low-Frequency Alfvén-Wave Turbulence In The Solar Wind, Benjamin D. G. Chandran, Bo Li, Barrett N. Rogers, Eliot Quataert, Kai Germaschewski
Perpendicular Ion Heating By Low-Frequency Alfvén-Wave Turbulence In The Solar Wind, Benjamin D. G. Chandran, Bo Li, Barrett N. Rogers, Eliot Quataert, Kai Germaschewski
Dartmouth Scholarship
We consider ion heating by turbulent Alfvén waves (AWs) and kinetic Alfvén waves (KAWs) with wavelengths (measured perpendicular to the magnetic field) that are comparable to the ion gyroradius and frequencies ω smaller than the ion cyclotron frequency Ω. We focus on plasmas in which β < 1, where β is the ratio of plasma pressure to magnetic pressure. As in previous studies, we find that when the turbulence amplitude exceeds a certain threshold, an ion's orbit becomes chaotic. The ion then interacts stochastically with the time-varying electrostatic potential, and the ion's energy undergoes a random walk. Using phenomenological arguments, we derive an analytic expression for the rates at which different ion species are heated, which we test by simulating test particles interacting with a spectrum of randomly phased AWs and KAWs. We find that the stochastic heating rate depends sensitively on the quantity ε = δv ρ/v ⊥, where v ⊥ (v ∥) is the component of the ion velocity perpendicular (parallel) to the background magnetic field B 0, and δv ρ (δB ρ) is the rms amplitude of the velocity (magnetic-field) fluctuations at the gyroradius scale. In the case …
Noncommutative Topology And The World’S Simplest Index Theorem, Erik Van Erp
Noncommutative Topology And The World’S Simplest Index Theorem, Erik Van Erp
Dartmouth Scholarship
In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool …
Distance To The Sagittarius Dwarf Galaxy Using Macho Project Rr Lyrae Stars, Andrea Kunder, Brian Chaboyer
Distance To The Sagittarius Dwarf Galaxy Using Macho Project Rr Lyrae Stars, Andrea Kunder, Brian Chaboyer
Dartmouth Scholarship
We derive the distance to the northern extension of the Sagittarius (Sgr) dwarf spheroidal galaxy from 203 Sgr RR0 Lyrae stars found in the MACHO database. Their distances are determined differentially with respect to 288 Galactic bulge RR0 Lyrae stars also found in the MACHO data. We find a distance modulus difference of 2.41 mag at l = 5◦ and b =− 8◦ and that the extension of the Sgr galaxy toward the galactic plane is inclined toward us. Assuming R GC = 8 kpc, this implies the distance to these stars is (m − M) 0 = …
New Neighbors: Parallaxes Of 18 Nearby Stars Selected From The Lspm-North Catalog, Sébastien Lépine, John R. Thorstensen, Michael M. Shara, R. Michael Rich
New Neighbors: Parallaxes Of 18 Nearby Stars Selected From The Lspm-North Catalog, Sébastien Lépine, John R. Thorstensen, Michael M. Shara, R. Michael Rich
Dartmouth Scholarship
We present astrometric parallaxes for 18 suspected nearby stars selected from the LSPM-north proper motion catalog. 16 objects are confirmed to be main-sequence M dwarfs within 16 pc of the Sun, including three stars (LSPM J0011+5908, LSPM J0330+5413, and LSPM J0510+2714) which lie just within the 10 pc horizon. Two other targets (LSPM J1817+1328, LSPM J2325+1403) are confirmed to be nearby white dwarfs at distances of 14 and 22 pc, respectively. One of our targets, the common proper motion pair LSPM J0405+7116E + LSPM J0405+7116W, is revealed to be a triple system, with the western component resolved into a pair …
Inverse Spectral Results On Even Dimensional Tori, Carolyn Gordon, Pierre Guerini, Thomas Kappeler, David Webb
Inverse Spectral Results On Even Dimensional Tori, Carolyn Gordon, Pierre Guerini, Thomas Kappeler, David Webb
Dartmouth Scholarship
Given a Hermitian line bundle L over a flat torus M, a connection ∇ on L, and a function Q on M, one associates a Schrödinger operator acting on sections of L; its spectrum is denoted Spec(Q;L,∇). Motivated by work of V. Guillemin in dimension two, we consider line bundles over tori of arbitrary even dimension with “translation invariant” connections ∇, and we address the extent to which the spectrum Spec(Q;L,∇) determines the potential Q. With a genericity condition, we show that if the connection is invariant under the isometry of M defined by the map x→-x, then the spectrum …
Duan's Fixed Point Theorem: Proof And Generalization, Martin Arkowitz
Duan's Fixed Point Theorem: Proof And Generalization, Martin Arkowitz
Dartmouth Scholarship
Let X be an H-space of the homotopy type of a connected, finite CW-complex, f : X→X any map and pk : X→X the kth power map. Duan proved that pkf : X → X has a fixed point if k ≥ 2. We give a new, short and elementary proof of this. We then use rational homotopy to generalize to spaces X whose rational cohomology is the tensor product of an exterior algebra on odd dimensional generators with the tensor product of truncated polynomial algebras on even dimensional generators. The role of the power map …
Objectivity, Information, And Maxwell's Demon, Steven Weinstein
Objectivity, Information, And Maxwell's Demon, Steven Weinstein
Dartmouth Scholarship
This paper examines some common measures of complexity, structure, and information, with an eye toward understanding the extent to which complexity or information‐content may be regarded as objective properties of individual objects. A form of contextual objectivity is proposed which renders the measures objective, and which largely resolves the puzzle of Maxwell's Demon.
Boundary Volume And Length Spectra Of Riemannian Manifolds: What The Middle Degree Hodge Spectrum Doesn't Reveal, Carolyn S. Gordon, Juan P. Rossetti
Boundary Volume And Length Spectra Of Riemannian Manifolds: What The Middle Degree Hodge Spectrum Doesn't Reveal, Carolyn S. Gordon, Juan P. Rossetti
Dartmouth Scholarship
No abstract provided.