On Charge-3 Cyclic Monopoles

We determine the spectral curve of charge 3 BPS su(2) monopoles with C_3 cyclic symmetry. The symmetry means that the genus 4 spectral curve covers a (Toda) spectral curve of genus 2. A well adapted homology basis is presented enabling the theta functions and monopole data of the genus 4 curve to be given in terms of genus 2 data. The Richelot correspondence, a generalization of the arithmetic mean, is used to solve for this genus 2 curve. Results of other approaches are compared.Comment: 34 pages, 16 figures. Revision: Abstract added and a few small change

Cosmic bubble and domain wall instabilities III: The role of oscillons in three-dimensional bubble collisions

We study collisions between pairs of bubbles nucleated in an ambient false vacuum. For the first time, we include the effects of small initial (quantum) fluctuations around the instanton profiles describing the most likely initial bubble profile. Past studies of this problem neglect these fluctuations and work under the assumption that the collisions posess an exact SO(2,1) symmetry. We use three-dimensional lattice simulations to demonstrate that for double-well potentials, small initial perturbations to this symmetry can be amplified as the system evolves. Initially the amplification is well-described by linear perturbation theory around the SO(2,1) background, but the onset of strong nonlinearities amongst the fluctuations quickly leads to a drastic breaking of the original SO(2,1) symmetry and the production of oscillons in the collision region. We explore several single-field models, and we find it is hard to both realize inflation inside of a bubble and produce oscillons in a collision. Finally, we extend our results to a simple two-field model. The additional freedom allowed by the second field allows us to construct viable inflationary models that allow oscillon production in collisions. The breaking of the SO(2,1) symmetry allows for a new class of observational signatures from bubble collisions that do not posess azimuthal symmetry, including the production of gravitational waves which cannot be supported by an SO(2,1) spacetime.Comment: 35 pages + references, 26 figures. Submitted to JCAP. v2: Acknowledgments updates, no other change

Cosmic bubble and domain wall instabilities I: parametric amplification of linear fluctuations

This is the first paper in a series where we study collisions of nucleated bubbles taking into account the effects of small initial (quantum) fluctuations in a fully 3+1-dimensional setting. In this paper, we consider the evolution of linear fluctuations around highly symmetric though inhomogeneous backgrounds. We demonstrate that a large degree of asymmetry develops over time from tiny fluctuations superposed upon planar and SO(2,1) symmetric backgrounds. These fluctuations arise from zero-point vacuum oscillations, so excluding them by enforcing a spatial symmetry is inconsistent in a quantum treatment. We consider the limit of two colliding planar walls, with fluctuation mode functions characterized by the wavenumber transverse to the collision direction and a longitudinal shape along the collision direction $x$, which we solve for. Initially, the fluctuations obey a linear wave equation with a time- and space-dependent mass $m_{eff}(x,t)$. When the walls collide multiple times, $m_{eff}$ oscillates in time. We use Floquet theory to study the fluctuations and generalize techniques familiar from preheating to the case with many coupled degrees of freedom. This inhomogeneous case has bands of unstable transverse wavenumbers $k_\perp$ with exponentially growing mode functions. From the detailed spatial structure of the mode functions in $x$, we identify both broad and narrow parametric resonance generalizations of the homogeneous $m_{eff}(t)$ case of preheating. The unstable $k_\perp$ modes are longitudinally localized, yet can be described as quasiparticles in the Bogoliubov sense. We define an effective occupation number to show they are created in bursts for the case of well-defined collisions in the background. The transverse-longitudinal coupling accompanying nonlinearity radically breaks this localized particle description, with nonseparable 3D modes arising.Comment: 37 pages + references, 20 figures, submitted to JCA

Cosmic bubble and domain wall instabilities II: Fracturing of colliding walls

We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous paper, we demonstrated that at the linear level a subset of these fluctuations experience parametric amplification as a result of their coupling to the planar symmetric background. Here we study the full three-dimensional nonlinear dynamics using lattice simulations, including both the early time regime when the fluctuations are well described by linear perturbation theory as well as the subsequent stage of fully nonlinear evolution. We find that the nonplanar fluctuations have a dramatic effect on the overall evolution of the system. Specifically, once these fluctuations begin to interact nonlinearly the split into a planar symmetric part of the field and the nonplanar fluctuations loses its utility. At this point the colliding domain walls dissolve, with the endpoint of this being the creation of a population of oscillons in the collision region. The original (nearly) planar symmetry has been completely destroyed at this point and an accurate study of the system requires the full three-dimensional simulation.Comment: 23 pages + references, 13 figures. Submitted to JCAP. v2: Acknowledgements updated, no other change

Cruise aerodynamics of USB nacelle/wing geometric variations

Experimental results are presented on aerodynamic effects of geometric variations in upper surface blown nacelle configurations at high speed cruise conditions. Test data include both force and pressure measurements on two and three dimensional models powered by upper surface blowing nacelles of varying geometries. Experimental results are provided on variations in nozzle aspect ratio, nozzle boattail angle, and multiple nacelle installations. The nacelles are ranked according to aerodynamic drag penalties as well as overall installed drag penalties. Sample effects and correlations are shown for data obtained with the pressure model

Laser velocimeter applications to high-lift research

The application of the Lockheed-Georgia 2-D laser velocimeter (LV) burst-counter system to the flow field around a 2- and 3-element high-lift airfoil is discussed. The characteristic behavior of the confluent boundary layer (that is, the boundary layer existing downstream of a slot as it approaches and undergoes separation is evaluated. In this application, the LV represents all ideal instruments for nonintrusively probing into the narrow slots and cove areas characterizing mechanical high-lift systems. The work is being performed in the Lockheed-Georgia 10 x 30-inch low-speed test facility using a 9-inch (basic) chord section of the general aviation GAW-1 airfoil. The LV system employs a 4-W argon laser and operates in an off-axis, backscatter mode with a focus length of about 30 inches. Smoke is used as the seeding medium and is injected downstream of the model such that particle uniformity and size are constant upon completion of the tunnel circuit into the test area. The LV system is fully automated by utilizing a MAC-16 minicomputer for positioning, data acquisition, and preliminary data reduction

Empirical Aesthetics and the Philosophy of John Cage: A Literature Review and Experimental Study

This paper examines the musical philosophy of composer John Cage in terms of psychological theories and experimental design. A literature review was first conducted to extract testable hypotheses from Cage’s musical works, writings, and interviews relevant to theories and research in empirical aesthetics. A study was then devised to examine the relationships between cognitive appraisals of the interestingness, enjoyableness, orderliness, and musicality of general sound events, as well as to determine the influence of openness to experience and the effect of two intentional-listening strategies, inspired by Cage’s ideas, on these relationships. Participants (n = 21) completed an openness to experience questionnaire, listened to 20 sound recordings, and responded to each sound on a cognitive appraisal form. Participants were also randomly assigned to one of three groups (n = 7) and were encouraged to adopt one of two intentional listening strategies, or no strategy, depending on assignment. The analysis found significant relationships for interestingness, enjoyableness, and orderliness in predicting musicality, though scatter plot distributions suggest that orderliness is less essential to musicality than interestingness and enjoyableness. Openness to experience was found to be insignificant for all appraisals and relationships, as were the listening strategies, with one exception: appraisals of interestingness were found to decrease as a result of adopting a Cage-inspired listening strategy, though the validity of this result is suspect