Self-adjoint symmetry operators connected with the magnetic Heisenberg ring

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in the paper) and which yield consequently observables of the Heisenberg model. We prove the following results: (i) One can construct a self-adjoint idempotent symmetry operator from every irreducible character of every subgroup of S_N. This leads to a big manifold of observables. In particular every commutation symmetry yields such an idempotent. (ii) The set of all generating idempotents of a minimal right ideal R of C[S_N] contains one and only one idempotent which ist self-adjoint. (iii) Every self-adjoint idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k which are also self-adjoint and pairwise orthogonal. We give a computer algorithm for the calculation of such decompositions. Furthermore we present 3 additional algorithms which are helpful for the calculation of self-adjoint operators by means of discrete Fourier transforms of S_N. In our investigations we use computer calculations by means of our Mathematica packages PERMS and HRing.Comment: 13 page

Fluctuations of the Magnetization in Thin Films due to Conduction Electrons

A detailed analysis of damping and noise due to a {\it sd}-interaction in a thin ferromagnetic film sandwiched between two large normal metal layers is carried out. The magnetization is shown to obey in general a non-local equation of motion which differs from the the Gilbert equation and is extended to the non-adiabatic regime. To lowest order in the exchange interaction and in the limit where the Gilbert equation applies, we show that the damping term is enhanced due to interfacial effects but it also shows oscillations as a function of the film thickness. The noise calculation is however carried out to all orders in the exchange coupling constant. The ellipticity of the precession of the magnetization is taken into account. The damping is shown to have a Gilbert form only in the adiabatic limit while the relaxation time becomes strongly dependent on the geometry of the thin film. It is also shown that the induced noise characteristic of sd-exchange is inherently colored in character and depends on the symmetry of the Hamiltonian of the magnetization in the film. We show that the sd-noise can be represented in terms of an external stochastic field which is white only in the adiabatic regime. The temperature is also renormalized by the spin accumulation in the system. For large intra-atomic exchange interactions, the Gilbert-Brown equation is no longer valid

3D Surface Measurement for Medical Application—Technical Comparison of Two Established Industrial Surface Scanning Systems

In 3D mapping of flexible surfaces (e.g. human faces) measurement errors due to movement or positioning occur. Aggravated by equipment- or researcher-caused mistakes considerable deviations can result. Therefore first the appliances' precision handling and reliability in clinical environment must be established. Aim of this study was to investigate accuracy and precision of two contact-free 3D measurement systems (white light vs. laser). Standard specimens of known diameter for sphere deviation, touch deviation and plane deviation were tested. Both systems are appropriate for medical application acquiring solid data (<mm). The more complex white-light system shows better accuracy at 0.2s measuring time. The laser system is superior concerning robustness, while accuracy is poorer and input time (1.5-2.5s) longer. Due to the clinical demand the white-light system is superior in a laboratory environment, while the laser system is easier to handle under non-laboratory condition

The Evolution of PSR J0737-3039B and a Model for Relativistic Spin Precession

We present the evolution of the radio emission from the 2.8-s pulsar of the double pulsar system PSR J0737-3039A/B. We provide an update on the Burgay et al. (2005) analysis by describing the changes in the pulse profile and flux density over five years of observations, culminating in the B pulsar's radio disappearance in 2008 March. Over this time, the flux density decreases by 0.177 mJy/yr at the brightest orbital phases and the pulse profile evolves from a single to a double peak, with a separation rate of 2.6 deg/yr. The pulse profile changes are most likely caused by relativistic spin precession, but can not be easily explained with a circular hollow-cone beam as in the model of Clifton & Weisberg (2008). Relativistic spin precession, coupled with an elliptical beam, can model the pulse profile evolution well. This particular beam shape predicts geometrical parameters for the two bright orbital phases which are consistent and similar to those derived by Breton et al. (2008). However, the observed decrease in flux over time and B's eventual disappearance cannot be easily explained by the model and may be due to the changing influence of A on B.Comment: 20 pages, 18 figures, Accepted by ApJ on 2 August 201

Chromospheric seismology above sunspot umbrae

The acoustic resonator is an important model for explaining the three-minute oscillations in the chromosphere above sunspot umbrae. The steep temperature gradients at the photosphere and transition region provide the cavity for the acoustic resonator, which allows waves to be both partially transmitted and partially reflected. In this paper, a new method of estimating the size and temperature profile of the chromospheric cavity above a sunspot umbra is developed. The magnetic field above umbrae is modelled numerically in 1.5D with slow magnetoacoustic wave trains travelling along magnetic fieldlines. Resonances are driven by applying the random noise of three different colours---white, pink and brown---as small velocity perturbations to the upper convection zone. Energy escapes the resonating cavity and generates wave trains moving into the corona. Line of sight (LOS) integration is also performed to determine the observable spectra through SDO/AIA. The numerical results show that the gradient of the coronal spectra is directly correlated with the chromosperic temperature configuration. As the chromospheric cavity size increases, the spectral gradient becomes shallower. When LOS integrations is performed, the resulting spectra demonstrate a broadband of excited frequencies that is correlated with the chromospheric cavity size. The broadband of excited frequencies becomes narrower as the chromospheric cavity size increases. These two results provide a potentially useful diagnostic for the chromospheric temperature profile by considering coronal velocity oscillations

An Interface Region Imaging Spectrograph first view on Solar Spicules

Solar spicules have eluded modelers and observers for decades. Since the discovery of the more energetic type II, spicules have become a heated topic but their contribution to the energy balance of the low solar atmosphere remains unknown. Here we give a first glimpse of what quiet Sun spicules look like when observed with NASA's recently launched Interface Region Imaging Spectrograph (IRIS). Using IRIS spectra and filtergrams that sample the chromosphere and transition region we compare the properties and evolution of spicules as observed in a coordinated campaign with Hinode and the Atmospheric Imaging Assembly. Our IRIS observations allow us to follow the thermal evolution of type II spicules and finally confirm that the fading of Ca II H spicules appears to be caused by rapid heating to higher temperatures. The IRIS spicules do not fade but continue evolving, reaching higher and falling back down after 500-800 s. Ca II H type II spicules are thus the initial stages of violent and hotter events that mostly remain invisible in Ca II H filtergrams. These events have very different properties from type I spicules, which show lower velocities and no fading from chromospheric passbands. The IRIS spectra of spicules show the same signature as their proposed disk counterparts, reinforcing earlier work. Spectroheliograms from spectral rasters also confirm that quiet Sun spicules originate in bushes from the magnetic network. Our results suggest that type II spicules are indeed the site of vigorous heating (to at least transition region temperatures) along extensive parts of the upward moving spicular plasma.Comment: 6 pages, 4 figures, accepted for publication in ApJ Letters. For associated movies, see http://folk.uio.no/tiago/iris_spic

Detection of supersonic downflows and associated heating events in the transition region above sunspots

IRIS data allow us to study the solar transition region (TR) with an unprecedented spatial resolution of 0.33 arcsec. On 2013 August 30, we observed bursts of high Doppler shifts suggesting strong supersonic downflows of up to 200 km/s and weaker, slightly slower upflows in the spectral lines Mg II h and k, C II 1336 \AA, Si IV 1394 \AA, and 1403 \AA, that are correlated with brightenings in the slitjaw images (SJIs). The bursty behavior lasts throughout the 2 hr observation, with average burst durations of about 20 s. The locations of these short-lived events appear to be the umbral and penumbral footpoints of EUV loops. Fast apparent downflows are observed along these loops in the SJIs and in AIA, suggesting that the loops are thermally unstable. We interpret the observations as cool material falling from coronal heights, and especially coronal rain produced along the thermally unstable loops, which leads to an increase of intensity at the loop footpoints, probably indicating an increase of density and temperature in the TR. The rain speeds are on the higher end of previously reported speeds for this phenomenon, and possibly higher than the free-fall velocity along the loops. On other observing days, similar bright dots are sometimes aligned into ribbons, resembling small flare ribbons. These observations provide a first insight into small-scale heating events in sunspots in the TR.Comment: accepted by ApJ

High-resolution Observations of the Shock Wave Behavior for Sunspot Oscillations with the Interface Region Imaging Spectrograph

We present the first results of sunspot oscillations from observations by the Interface Region Imaging Spectrograph. The strongly nonlinear oscillation is identified in both the slit-jaw images and the spectra of several emission lines formed in the transition region and chromosphere. We first apply a single Gaussian fit to the profiles of the Mgii 2796.35 {\AA}, Cii 1335.71 {\AA}, and Si iv 1393.76 {\AA} lines in the sunspot. The intensity change is about 30%. The Doppler shift oscillation reveals a sawtooth pattern with an amplitude of about 10 km/s in Si iv. In the umbra the Si iv oscillation lags those of Cii and Mgii by about 3 and 12 s, respectively. The line width suddenly increases as the Doppler shift changes from redshift to blueshift. However, we demonstrate that this increase is caused by the superposition of two emission components. We then perform detailed analysis of the line profiles at a few selected locations on the slit. The temporal evolution of the line core is dominated by the following behavior: a rapid excursion to the blue side, accompanied by an intensity increase, followed by a linear decrease of the velocity to the red side. The maximum intensity slightly lags the maximum blueshift in Si iv, whereas the intensity enhancement slightly precedes the maximum blueshift in Mgii. We find a positive correlation between the maximum velocity and deceleration, a result that is consistent with numerical simulations of upward propagating magnetoacoustic shock waves.Comment: 5 figures, in ApJ. Correction of time lags (correct values are 3 and 12s) made on June 17 201

Homologous Helical Jets: Observations by IRIS, SDO and Hinode and Magnetic Modeling with Data-Driven Simulations

We report on observations of recurrent jets by instruments onboard the Interface Region Imaging Spectrograph (IRIS), Solar Dynamics Observatory (SDO) and Hinode spacecrafts. Over a 4-hour period on July 21st 2013, recurrent coronal jets were observed to emanate from NOAA Active Region 11793. FUV spectra probing plasma at transition region temperatures show evidence of oppositely directed flows with components reaching Doppler velocities of +/- 100 km/s. Raster Doppler maps using a Si IV transition region line show all four jets to have helical motion of the same sense. Simultaneous observations of the region by SDO and Hinode show that the jets emanate from a source region comprising a pore embedded in the interior of a supergranule. The parasitic pore has opposite polarity flux compared to the surrounding network field. This leads to a spine-fan magnetic topology in the coronal field that is amenable to jet formation. Time-dependent data-driven simulations are used to investigate the underlying drivers for the jets. These numerical experiments show that the emergence of current-carrying magnetic field in the vicinity of the pore supplies the magnetic twist needed for recurrent helical jet formation.Comment: 15 pages, 10 figures, accepted by Ap