Exponential asymptotics and higher-order Stokes phenomenon in singularly perturbed ODEs

Outside the area of exponential asymptotics, the concept of the higher-order Stokes phenomenon remains somewhat esoteric. The intention of this work is to provide several examples of relatively simple ordinary differential equations where the phenomenon arises, and to develop additional practical methodologies for its study. In particular, we show how the higher-order Stokes phenomenon may be derived through the hyperterminant representation of the late-term divergence of an asymptotic expansion developed by Olde Daalhuis (J. Comp. Appl. Math. vol. 76, 1996, pp. 255-264). Lower-order components of the factorial-over-power divergence are considered, for which late-late-term divergence arises. Borel resummation of these lower-order components reveals the higher-order Stokes phenomenon, in which new components of the late-terms of the expansion are smoothly switched on with an error function dependence. The techniques are firstly demonstrated with a second-order linear inhomogeneous ODE that exemplifies the simplest example of higher-order Stokes phenomena. Further examples studied include higher-order equations and eigenvalue problems.Comment: 28 pages, 6 figure

Intensity of Brillouin light scattering from spin waves in magnetic multilayers with noncollinear spin configurations: Theory and experiment

The scattering of photons from spin waves (Brillouin light scattering -- BLS) is a well-established technique for the study of layered magnetic systems. The information about the magnetic state and properties of the sample is contained in the frequency position, width, and intensity of the BLS peaks. Previously [Phys. Rev. B 67, 184404 (2003)], we have shown that spin wave frequencies can be conveniently calculated within the ultrathin film approach, treating the intralayer exchange as an effective bilinear interlayer coupling between thin virtual sheets of the ferromagnetic layers. Here we give the consequent extension of this approach to the calculation of the Brillouin light scattering (BLS) peak intensities. Given the very close relation of the BLS cross-section to the magneto-optic Kerr effect (MOKE), the depth-resolved longitudinal and polar MOKE coefficients calculated numerically via the usual magneto-optic formalism can be employed in combination with the spin wave precessional amplitudes to calculate full BLS spectra for a given magnetic system. This approach allows an easy calculation of BLS intensities even for noncollinear spin configurations including the exchange modes. The formalism is applied to a Fe/Cr/Fe/Ag/Fe trilayer system with one antiferromagnetically coupling spacer (Cr). Good agreement with the experimental spectra is found for a wide variety of spin configurations.Comment: 19 pages, 5 figure

The Physics of Miniature Worlds

This excerpt from a book length work on the history of the methodology of experimental physical models (physically similar systems) interwoven in Ludwig Wittgenstein's life begins in 1913-1914. It also discusses works by physicists around the same time that were thematically related to the philosophical topics he was working on: Ludwig Boltzmann, Wilhelm Ostwald, Edgar Buckingham, James Thomson, D'Arcy Wentworth Thompson, Henry Crew (and his new translation of Galileo's Two New Sciences during this period), Heike Kamerlingh Onnes, Van Der Waals, and Rayleigh (following up on the work of Gabriel Stokes), and Richard C Tolman. The landmark work at Britain's National Physical Laboratory in 1914 on Similar Motions by Stanton and Pannell, following up on Osborne Reynolds' work in Manchester, is also described and discussed. Connections between physics and the history of flight are mentioned, too: Penuad's successes, Boltzmann's relationship with engineer Otto Lilienthal, and the significance that Hermann von Helmholtz's landmark paper in meteorology which addressed the problem of steering aircraft, took on during this period

Precision Pointing of IBEX-Lo Observations

Post-launch boresight of the IBEX-Lo instrument onboard the Interstellar Boundary Explorer (IBEX) is determined based on IBEX-Lo Star Sensor observations. Accurate information on the boresight of the neutral gas camera is essential for precise determination of interstellar gas flow parameters. Utilizing spin-phase information from the spacecraft attitude control system (ACS), positions of stars observed by the Star Sensor during two years of IBEX measurements were analyzed and compared with positions obtained from a star catalog. No statistically significant differences were observed beyond those expected from the pre-launch uncertainty in the Star Sensor mounting. Based on the star observations and their positions in the spacecraft reference system, pointing of the IBEX satellite spin axis was determined and compared with the pointing obtained from the ACS. Again, no statistically significant deviations were observed. We conclude that no systematic correction for boresight geometry is needed in the analysis of IBEX-Lo observations to determine neutral interstellar gas flow properties. A stack-up of uncertainties in attitude knowledge shows that the instantaneous IBEX-Lo pointing is determined to within \sim 0.1\degr in both spin angle and elevation using either the Star Sensor or the ACS. Further, the Star Sensor can be used to independently determine the spacecraft spin axis. Thus, Star Sensor data can be used reliably to correct the spin phase when the Star Tracker (used by the ACS) is disabled by bright objects in its field-of-view. The Star Sensor can also determine the spin axis during most orbits and thus provides redundancy for the Star Tracker.Comment: 22 pages, 18 figure

A Characterization of the ALMA Phasing System at 345 GHz

The development of the Atacama Large Millimeter/submillimeter Array (ALMA) phasing system (APS) has allowed ALMA to function as an extraordinarily sensitive station for very long baseline interferometry (VLBI) at frequencies of up to 230 GHz (~1.3 mm). Efforts are now underway to extend use of the APS to 345 GHz (~0.87 mm). Here we report a characterization of APS performance at 345 GHz based on a series of tests carried out between 2015-2021, including a successful global VLBI test campaign conducted in 2018 October in collaboration with the Event Horizon Telescope (EHT).Comment: 22 pages, 11 figures, 7 tables, accepted for publication in PAS

Evolving outer heliosphere: Large-scale stability and time variations observed by the Interstellar Boundary Explorer

The first all-sky maps of Energetic Neutral Atoms (ENAs) from the Interstellar Boundary Explorer (IBEX) exhibited smoothly varying, globally distributed flux and a narrow ribbon of enhanced ENA emissions. In this study we compare the second set of sky maps to the first in order to assess the possibility of temporal changes over the 6 months between views of each portion of the sky. While the large-scale structure is generally stable between the two sets of maps, there are some remarkable changes that show that the heliosphere is also evolving over this short timescale. In particular, we find that (1) the overall ENA emissions coming from the outer heliosphere appear to be slightly lower in the second set of maps compared to the first, (2) both the north and south poles have significantly lower (similar to 10-15%) ENA emissions in the second set of maps compared to the first across the energy range from 0.5 to 6 keV, and (3) the knot in the northern portion of the ribbon in the first maps is less bright and appears to have spread and/or dissipated by the time the second set was acquired. Finally, the spatial distribution of fluxes in the southernmost portion of the ribbon has evolved slightly, perhaps moving as much as 6 degrees (one map pixel) equatorward on average. The observed large-scale stability and these systematic changes at smaller spatial scales provide important new information about the outer heliosphere and its global interaction with the galaxy and help inform possible mechanisms for producing the IBEX ribbon

Rotation, Equivalence Principle, and GP-B Experiment

The ultra-precise Gravity Probe B experiment measured the frame-dragging effect and geodetic precession on four quartz gyros. We use this result to test WEP II (Weak Equivalence Principle II) which includes rotation in the universal free-fall motion. The free-fall E\"otv\"os parameter eta for rotating body is < = 10**(-11) with four-order improvement over previous results. The anomalous torque per unit angular momentum parameter lambda is constrained to (-0.05 +- 3.67) \times 10**(-15) s-1, (0.24 +- 0.98) \times 10**(-15) s-1, and (0 +- 3.6) \times 10**(-13) s-1 respectively in the directions of geodetic effect, frame-dragging effect and angular momentum axis; the dimensionless frequency-dependence parameter {\kappa} is constrained to (1.75 +- 4.96) \times 10**(-17), (1.80 +- 1.34) \times 10**(-17), and (0 +- 3) \times 10**(-14) respectively.Comment: 9 pages, 2 figures, 3 table

Energy flow lines and the spot of Poisson-Arago

We show how energy flow lines answer the question about diffraction phenomena presented in 1818 by the French Academy: "deduce by mathematical induction, the movements of the rays during their crossing near the bodies". This provides a complementary answer to Fresnel's wave theory of light. A numerical simulation of these energy flow lines proves that they can reach the bright spot of Poisson-Arago in the shadow center of a circular opaque disc. For a monochromatic wave in vacuum, these energy flow lines correspond to the diffracted rays of Newton's Opticks

Epeak estimator for Gamma-Ray Bursts Observed by the Swift Burst Alert Telescope

We report a correlation based on a spectral simulation study of the prompt emission spectra of gamma-ray bursts (GRBs) detected by the Swift Burst Alert Telescope (BAT). The correlation is between the Epeak energy, which is the peak energy in the \nu F_\nu spectrum, and the photon index (\Gamma) derived from a simple power-law model. The Epeak - \Gamma relation, assuming the typical smoothly broken power-law spectrum of GRBs, is \log Epeak = 3.258 - 0.829\Gamma (1.3 < \Gamma < 2.3). We take into account not only a range of Epeak energies and fluences, but also distributions for both the low-energy photon index and the high-energy photon index in the smoothly broken power-law model. The distribution of burst durations in the BAT GRB sample is also included in the simulation. Our correlation is consistent with the index observed by BAT and Epeak measured by the BAT, and by other GRB instruments. Since about 85% of GRBs observed by the BAT are acceptably fit with the simple power-law model because of the relatively narrow energy range of the BAT, this relationship can be used to estimate Epeak when it is located within the BAT energy range.Comment: 27 pages, 31 figures, accepted for publication in Ap