Term Graph Representations for Cyclic Lambda-Terms

We study various representations for cyclic lambda-terms as higher-order or as first-order term graphs. We focus on the relation between `lambda-higher-order term graphs' (lambda-ho-term-graphs), which are first-order term graphs endowed with a well-behaved scope function, and their representations as `lambda-term-graphs', which are plain first-order term graphs with scope-delimiter vertices that meet certain scoping requirements. Specifically we tackle the question: Which class of first-order term graphs admits a faithful embedding of lambda-ho-term-graphs in the sense that: (i) the homomorphism-based sharing-order on lambda-ho-term-graphs is preserved and reflected, and (ii) the image of the embedding corresponds closely to a natural class (of lambda-term-graphs) that is closed under homomorphism? We systematically examine whether a number of classes of lambda-term-graphs have this property, and we find a particular class of lambda-term-graphs that satisfies this criterion. Term graphs of this class are built from application, abstraction, variable, and scope-delimiter vertices, and have the characteristic feature that the latter two kinds of vertices have back-links to the corresponding abstraction. This result puts a handle on the concept of subterm sharing for higher-order term graphs, both theoretically and algorithmically: We obtain an easily implementable method for obtaining the maximally shared form of lambda-ho-term-graphs. Also, we open up the possibility to pull back properties from first-order term graphs to lambda-ho-term-graphs. In fact we prove this for the property of the sharing-order successors of a given term graph to be a complete lattice with respect to the sharing order. This report extends the paper with the same title (http://arxiv.org/abs/1302.6338v1) in the proceedings of the workshop TERMGRAPH 2013.Comment: 35 pages. report extending proceedings article on arXiv:1302.6338 (changes with respect to version v2: added section 8, modified Proposition 2.4, added Remark 2.5, added Corollary 7.11, modified figures in the conclusion

Surface motion in the pulsating DA white dwarf G 29-38

We present time-resolved spectrophotometry of the pulsating DA white dwarf G 29-38. As in previous broad-band photometry, the light curve shows the presence of a large number of periodicities. Many of these are combination frequencies, i.e., periodicities occurring at frequencies that are sums or differences of frequencies of stronger, real modes. We identify at least six real modes, and at least five combination frequencies. We measure line-of-sight velocities for our spectra and detect periodic variations at the frequencies of five of the six real modes, with amplitudes of up to 5 km/s. We argue that these variations reflect the horizontal surface motion associated with the g-mode pulsations. No velocity signals are detected at any of the combination frequencies, confirming that the flux variations at these frequencies do not reflect physical pulsation, but rather mixing of frequencies due to a non-linear transformation in the outer layers of the star. We discuss the amplitude ratios and phase differences found for the velocity and light variations, as well as those found for the real modes and their combination frequencies, both in a model-independent way and in the context of models based on the convective-driving mechanism. In a companion paper, we use the wavelength dependence of the amplitudes of the modes to infer their spherical degree.Comment: 12 pages, 5 figures, mn.sty. Accepted for publication in MNRA

Mode identification from time-resolved spectroscopy of the pulsating white dwarf G 29-38

We have used time-resolved spectroscopy to measure the colour dependence of pulsation amplitudes in the DAV white dwarf G 29-38. Model atmospheres predict that mode amplitudes should change with wavelength in a manner that depends on the spherical harmonic degree l of the mode. This dependence arises from the convolution of mode geometry with wavelength-dependent limb darkening. Our analysis of the six largest normal modes detected in Keck observations of G 29-38 reveals one mode with a colour dependence different from the other five, permitting us to identify the l value of all six modes and to test the model predictions. The Keck observations also show pulsation amplitudes that are unexpectedly asymmetric within absorption lines. We show that these asymmetries arise from surface motions associated with the non-radial pulsations (which are discussed in detail in a companion paper). By incorporating surface velocity fields into line profile calculations, we are able to produce models that more closely resemble the observations.Comment: 10 pages, 9 figures, mn.sty. Accepted for publication in MNRA

A Quantitative Non-radial Oscillation Model for the Subpulses in PSR B0943+10

In this paper, we analyze time series measurements of PSR B0943+10 and fit them with a non-radial oscillation model. The model we apply was first developed for total intensity measurements in an earlier paper, and expanded to encompass linear polarization in a companion paper to this one. We use PSR B0943+10 for the initial tests of our model because it has a simple geometry, it has been exhaustively studied in the literature, and its behavior is well-documented. As prelude to quantitative fitting, we have reanalyzed previously published archival data of PSR B0943+10 and uncovered subtle but significant behavior that is difficult to explain in the framework of the drifting spark model. Our fits of a non-radial oscillation model are able to successfully reproduce the observed behavior in this pulsar.Comment: 45 pages, 16 figures, accepted Ap

Molecular Feshbach dissociation as a source for motionally entangled atoms

We describe the dissociation of a diatomic Feshbach molecule due to a time-varying external magnetic field in a realistic trap and guide setting. An analytic expression for the asymptotic state of the two ultracold atoms is derived, which can serve as a basis for the analysis of dissociation protocols to generate motionally entangled states. For instance, the gradual dissociation by sequences of magnetic field pulses may delocalize the atoms into macroscopically distinct wave packets, whose motional entanglement can be addressed interferometrically. The established relation between the applied magnetic field pulse and the generated dissociation state reveals that square-shaped magnetic field pulses minimize the momentum spread of the atoms. This is required to control the detrimental influence of dispersion in a recently proposed experiment to perform a Bell test in the motion of the two atoms [C. Gneiting and K. Hornberger, Phys. Rev. Lett. 101, 260503 (2008)].Comment: 12 pages, 3 figures; corresponds to published versio

Quartic double solids with ordinary singularities

We study the mixed Hodge structure on the third homology group of a threefold which is the double cover of projective three-space ramified over a quartic surface with a double conic. We deal with the Torelli problem for such threefolds.Comment: 14 pages, presented at the Conference Arnol'd 7

Time-resolved optical spectroscopy of the pulsating DA white dwarf HS 0507+0434B: New constraints on mode identification and pulsation properties

We present a detailed analysis of time-resolved optical spectra of the ZZ Ceti white dwarf, HS 0507+0434B. Using the wavelength dependence of observed mode amplitudes, we deduce the spherical degree, l, of the modes, most of which have l=1. The presence of a large number of combination frequencies (linear sums or differences of the real modes) enabled us not only to test theoretical predictions but also to indirectly infer spherical and azimuthal degrees of real modes that had no observed splittings. In addition to the above, we measure line-of-sight velocities from our spectra. We find only marginal evidence for periodic modulation associated with the pulsation modes: at the frequency of the strongest mode in the lightcurve, we measure an amplitude of 2.6+/-1.0 km/s, which has a probability of 2% of being due to chance; for the other modes, we find lower values. Our velocity amplitudes and upper limits are smaller by a factor of two compared to the amplitudes found in ZZ Psc. We find that this is consistent with expectations based on the position of HS 0507+0434B in the instability strip. Combining all the available information from data such as ours is a first step towards constraining atmospheric properties in a convectionally unstable environment from an observational perspective.Comment: 16 pages, 12 figs.; accepted for publication in A&