On the flow map for 2D Euler equations with unbounded vorticity

In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Holder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an arbitrarily poor modulus of continuity of the flow map.Comment: http://iopscience.iop.org/0951-7715/24/9/013/ for published versio

The change in the inclination angle of the non-eclipsing binary SS Lacertae: future eclipses

Eclipses in the 14.4-day period double-lined binary SS Lac were observed photographically and visually early in the 20th century, but stopped some 50 or 60 years ago. This has been explained by the presence of a distant third star in the system, which has now been detected spectroscopically with a period of 679 days. The plane of the orbit of the binary is changing relative to the line of sight in response to perturbations from this third object. A recent analysis by Milone et al. (M00) of all photometric material available for the system, including a re-measurement of original Harvard plates, has confirmed earlier reports of changes in the depth of the eclipses as a function of time, which are due to the third star. In this paper we discuss our detailed analysis of the eclipse amplitude measurements, and extract from them information on the change in the inclination angle of the binary over the last century. Our use of a much improved ephemeris for the system by Torres & Stefanik was found to be crucial, and prompted us to re-determine all the amplitudes from the historical data at our disposal, including the Harvard material used by M00. Systematically lower measurements on the branches of the minima were properly accounted for, and we made use of both a linear approximation to the time variation of the inclination angle and a more realistic model based on the theory of three-body interactions ("regression of the nodes" effect). The nodal cycle is found to be about 600 yr, within which TWO eclipse "seasons" occur, each lasting about 100 yr. The non-eclipsing status of the system is expected to continue until the beginning of the 23rd century.Comment: 32 pages, including figures and tables. Accepted for The Astronomical Journal, April 200

SphinX soft X-ray spectrophotometer: Science objectives, design and performance

The goals and construction details of a new design Polish-led X-ray spectrophotometer are described. The instrument is aimed to observe emission from entire solar corona and is placed as a separate block within the Russian TESIS X- and EUV complex aboard the CORONAS-PHOTON solar orbiting observatory. SphinX uses silicon PIN diode detectors for high time resolution measurements of the solar spectra in the range 0.8–15 keV. Its spectral resolution allows for discerning more than hundred separate energy bands in this range. The instrument dynamic range extends two orders of magnitude below and above these representative for GOES. The relative and absolute accuracy of spectral measurements is expected to be better than few percent, as follows from extensive ground laboratory calibrations

Absolute dimensions of the unevolved B-type eclipsing binary GG Orionis

We present photometric observations in B and V as well as spectroscopic observations of the detached, eccentric 6.6-day double-lined eclipsing binary GG Ori, a member of the Orion OB1 association. Absolute dimensions of the components, which are virtually identical, are determined to high accuracy (better than 1% in the masses and better than 2% in the radii) for the purpose of testing various aspects of theoretical modeling. We obtain M(A) = 2.342 +/- 0.016 solar masses and R(A) = 1.852 +/- 0.025 solar radii for the primary, and M(B) = 2.338 +/- 0.017 solar masses and R(B) = 1.830 +/- 0.025 solar radii for the secondary. The effective temperature of both stars is 9950 +/- 200 K, corresponding to a spectral type of B9.5. GG Ori is very close to the ZAMS, and comparison with current stellar evolution models gives ages of 65-82 Myr or 7.7 Myr depending on whether the system is considered to be burning hydrogen on the main sequence or still in the final stages of pre-main sequence contraction. We have detected apsidal motion in the binary at a rate of dw/dt = 0.00061 +/- 0.00025 degrees per cycle, corresponding to an apsidal period of U = 10700 +/- 4500 yr. A substantial fraction of this (approximately 70%) is due to the contribution from General Relativity.Comment: To appear in The Astronomical Journal, December 200

SphinX: The Solar Photometer in X-Rays

Solar Photometer in X-rays (SphinX) was a spectrophotometer developed to observe the Sun in soft X-rays. The instrument observed in the energy range ≈ 1 - 15 keV with resolution ≈ 0.4 keV. SphinX was flown on the Russian CORONAS-PHOTON satellite placed inside the TESIS EUV and X telescope assembly. The spacecraft launch took place on 30 January 2009 at 13:30 UT at the Plesetsk Cosmodrome in Russia. The SphinX experiment mission began a couple of weeks later on 20 February 2009 when the first telemetry dumps were received. The mission ended nine months later on 29 November 2009 when data transmission was terminated. SphinX provided an excellent set of observations during very low solar activity. This was indeed the period in which solar activity dropped to the lowest level observed in X-rays ever. The SphinX instrument design, construction, and operation principle are described. Information on SphinX data repositories, dissemination methods, format, and calibration is given together with general recommendations for data users. Scientific research areas in which SphinX data find application are reviewed

The most plausible explanation of the cyclical period changes in close binaries: the case of the RS CVn-type binary WW Dra

We searched the orbital period changes in 182 EA-type (including the 101 Algol systems used by \cite{hal89}), 43 EB-type and 53 EW-type binaries with known both the mass ratio and the spectral type of their secondary components. We reproduced and improved the same diagram as Hall's (1989) according to the new collected data. Our plots do not support the conclusion derived by \cite{hal89} that all cases of cyclical period changes are restricted to binaries having the secondary component with spectral types later than F5. The presence of period changes also among stars with secondary component of early type indicates that the magnetic activity is one cause, but not the only one, for the period variation. It is discovered that cyclic period changes, likely due to the presence of a third body are more frequent in EW-type binaries among close binaries. Therefore, the most plausible explanation of the cyclical period changes is the LTTE via the presence of a third body. By using the century-long historical record of the times of light minimum, we analyzed the cyclical period change in the Algol binary WW Dra. It is found that the orbital period of the binary shows a $\sim112.2 \textbf{\textrm{yr}}$ cyclic variation with an amplitude of $\sim0.1977\textbf{\textrm{days}}$. The cyclic oscillation can be attributed to the LTTE via a third body with a mass no less than $6.43 M_{\odot}$. However, no spectral lines of the third body were discovered indicating that it may be a candidate black hole. The third body is orbiting the binary at a distance shorter than 14.4 AU and it may play an important role in the evolution of this system.Comment: 9 pages, 5 figures, published by MNRA

Muscle architecture in relation to function

Animal muscles generate forces and induce movements at desirable rates. These roles are interactive and must be considered together. Performance of the organism and survival of the species also involve potential optimization of control and of energy consumption. Further, individual variability arising partly via ontogeny and partly from phylogenetic history often has pronounced and sometime conflicting effects on structures and their uses. Hence, animal bodies are generally adequate for their tasks rather than being elegantly matched to them. For muscle, matching to role is reflected at all levels of muscular organization, from the nature of the sarcoplasm and contractile filaments to architectural arrangements of the parts and whole of organs.Vertebrate muscles are often analyzed by mapping their placement and then "explaining" this on the basis of currently observed roles. A recent alternative asks the obverse; given a mass of tissue that may be developed and maintained at a particular cost, what predictions do physical principles permit about its placement. Three architectural patterns that deserve discussion are the classical arrangement of fibers in pinnate patterns, the more recent assumption of sarcomere equivalence, and the issue of compartmentation. All have potential functional implications. 1. 1. The assumption of equivalence of the sarcomeres of motor units allows predictions of the fiber length between sites of origin and insertion. In musculoskeletal systems that induce rotation, the observed (but not the pinnation-associated) insertion angle will differ with the radial lines on which the fibers insert. In a dynamic contraction inducing rotation, a shift of moment arm has no effect for muscles of equal mass.2. 2. Classical pinnate muscles contain many relatively short fibers positioned in parallel but at an angle to the whole muscle, reducing the per fiber force contribution. However, the total physiological cross-section and total muscle force are thus increased relative to arrangements with fibers parallel to the whole muscle. Equivalent muscles may be placed in various volumetric configurations matching other demands of the organism. The loss of fiber force due to (pinnate, not equivalent) angulation is compensated for by the reduced shortening of fibers in multipinnate arrays.3. 3. Compartmentation, i.e., the subdivision of muscles into independently controlled, spatially discrete volumes, is likely ubiquitous. Differential activation of the columns of radial arrays may facilitate change of vector and with this of function. Compartmentation is apt to be particularly important in strap muscles with short fiber architecture; their motor units generally occupy columnar, rather than transversely stacked, subdivisions; this may affect recovery from fiber atrophy and degeneration. Transverse and columnar stacking occur; both may have historical, as well as functional causes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29529/1/0000616.pd