1,512 research outputs found
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
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
The constitutive tensor of linear elasticity: its decompositions, Cauchy relations, null Lagrangians, and wave propagation
In linear anisotropic elasticity, the elastic properties of a medium are
described by the fourth rank elasticity tensor C. The decomposition of C into a
partially symmetric tensor M and a partially antisymmetric tensors N is often
used in the literature. An alternative, less well-known decomposition, into the
completely symmetric part S of C plus the reminder A, turns out to be
irreducible under the 3-dimensional general linear group. We show that the
SA-decomposition is unique, irreducible, and preserves the symmetries of the
elasticity tensor. The MN-decomposition fails to have these desirable
properties and is such inferior from a physical point of view. Various
applications of the SA-decomposition are discussed: the Cauchy relations
(vanishing of A), the non-existence of elastic null Lagrangians, the
decomposition of the elastic energy and of the acoustic wave propagation. The
acoustic or Christoffel tensor is split in a Cauchy and a non-Cauchy part. The
Cauchy part governs the longitudinal wave propagation. We provide explicit
examples of the effectiveness of the SA-decomposition. A complete class of
anisotropic media is proposed that allows pure polarizations in arbitrary
directions, similarly as in an isotropic medium.Comment: 1 figur
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