Solar-wind predictions for the Parker Solar Probe orbit

The scope of this study is to model the solar-wind environment for the Parker Solar Probe's unprecedented distances down to 9.86 Rs in its mission phase during 2018-2025. The study is performed within the CGAUSS project which is the German contribution to the PSP mission as part of the WISPR imager on PSP. We present an empirical solar-wind model for the inner heliosphere which is derived from OMNI and Helios data. The sunspot number (SSN) and its predictions are used to derive dependencies of solar-wind parameters on solar activity and to forecast them for the PSP mission. The frequency distributions for the solar-wind key parameters magnetic field strength, proton velocity, density, and temperature, are represented by lognormal functions, considering the velocity distribution's bi-componental shape. Functional relations to the SSN are compiled using OMNI data and based on data from both Helios probes, the parameters' frequency distributions are fitted with respect to solar distance. Thus, an empirical solar-wind model for the inner heliosphere is derived, accounting for solar activity and solar distance. The inclusion of SSN predictions and the extrapolation down to PSP's perihelion region enables us to estimate the solar-wind environment for PSP's planned trajectory during its mission duration. This empirical model yields estimated solar-wind values for PSP's 1st perihelion in 2018 at 0.16 au: 87 nT, 340 km s-1, 214 cm-3 and 503000 K. The estimates for PSP's first closest perihelion, occurring in 2024 at 0.046 au, are 943 nT, 290 km s-1, 2951 cm-3, and 1930000 K. Since the modeled velocity and temperature values below approximately 20 Rs appear overestimated in comparison with existing observations, this suggests that PSP will directly measure solar-wind acceleration and heating processes below 20 Rs as planned.Comment: 14 pages, 14 figures, 4 tables, accepted for publication in A&

Experimental results for the Poincar\'e center problem (including an Appendix with Martin Cremer)

We apply a heuristic method based on counting points over finite fields to the Poincar\'e center problem. We show that this method gives the correct results for homogeneous non linearities of degree 2 and 3. Also we obtain new evidence for Zoladek's conjecture about general degree 3 non linearitiesComment: 16 pages, 2 figures, source code of programs at http://www-ifm.math.uni-hannover.de/~bothmer/strudel/. Added references, the result of Example 6.2 is not new. Added two new sections on rationally reversible systems. The 4th codim 7 component we saw only experimentally can now also be identified geometrical

Significance of log-periodic signatures in cumulative noise

Using methods introduced by Scargle in 1978 we derive a cumulative version of the Lomb periodogram that exhibits frequency independent statistics when applied to cumulative noise. We show how this cumulative Lomb periodogram allows us to estimate the significance of log-periodic signatures in the S&P 500 anti-bubble that started in August 2000.Comment: 14 pages, 7 figures; AMS-Latex; introduction rewritten, some points of the exposition clarified. Author-supplied PDF file with high resolution graphics is available at http://btm8x5.mat.uni-bayreuth.de/~bothmer

Geometric Syzygies of Canonical Curves of even Genus lying on a K3-Surface

Based on a recent result of Voisin [2001] we describe the last nonzero syzygy space in the linear strand of a canonical curve C of even genus g=2k lying on a K3 surface, as the ambient space of a k-2-uple embedded P^{k+1}. Furthermore the geometric syzygies constructed by Green and Lazarsfeld [1984] from g^1_{k+1}'s form a non degenerate configuration of finitely many rational normal curves on this P^{k+1}. This proves a natural generalization of Green's conjecture [1984], namely that the geometric syzygies should span the space of all syzygies, in this case.Comment: 29 pages; 5 figure

Geometric syzygies of elliptic normal curves and their secant varieties

We show that the linear syzygy spaces of elliptic normal curves, their secant varieties and of bielliptic canonical curves are spanned by geometric syzygies.Comment: 31 Pages; AMSlate

Generic Syzygy Schemes

For a finite dimensional vector space G we define the k-th generic syzygy scheme Gensyz_k(G) by explicit equations. We show that the syzygy scheme Syz(f) of any syzygy in the linear strand of a projective variety X which is cut out by quadrics is a cone over a linear section of a corresponding generic syzygy scheme. We also give a geometric description of Gensyz_k(G) for k=0,1,2. In particular Gensyz_2(G) is the union of a Pl"ucker embedded Grassmannian and a linear space. From this we deduce that every smooth, non-degenerate projective curve C which is cut out by quadrics and has a p-th linear syzygy of rank p+3 admits a rank 2 vector bundle E with det E = O_C(1) and h^0(E) at least p+4.Comment: 12 Pages. This paper is a completely rewritten version of the first part of math.AG/0108078. It also contains several new result

Observational features of equatorial coronal hole jets

Collimated ejections of plasma called "coronal hole jets" are commonly observed in polar coronal holes. However, such coronal jets are not only a specific features of polar coronal holes but they can also be found in coronal holes appearing at lower heliographic latitudes. In this paper we present some observations of "equatorial coronal hole jets" made up with data provided by the STEREO/SECCHI instruments during a period comprising March 2007 and December 2007. The jet events are selected by requiring at least some visibility in both COR1 and EUVI instruments. We report 15 jet events, and we discuss their main features. For one event, the uplift velocity has been determined as about 200 km/s, while the deceleration rate appears to be about 0.11 km/s2, less than solar gravity. The average jet visibility time is about 30 minutes, consistent with jet observed in polar regions. On the basis of the present dataset, we provisionally conclude that there are not substantial physical differences between polar and equatorial coronal hole jets.Comment: 9 pages, 8 figures, 1 table, accepted for publication in Annales Geophysicae, Special Issue:'Three eyes on the Sun-multi-spacecraft studies of the corona and impacts on the heliosphere