The effect of elliptic shape on the period ratio P-1/P-2 of emerging coronal loops

Aims. We determine the effect of an elliptical shape on the period ratio for the standing transversal oscillations of a longitudinally stratified coronal loop throughout its emergence from the low solar atmosphere into the ubiquitously magnetised corona. Methods. Under the assumption that elliptical curvature has a negligible effect on eigenfrequencies, the equation that describes the projection of a density profile onto a magnetic flux tube with elliptical shape is obtained in a gravitationally stratified atmosphere. The effect of the elliptical shape on the period ratio of the fundamental mode to the first harmonic (P-1/P-2) at various stages of emergence is determined, assuming that the oscillation periods are much shorter than the characteristic time scale of loop emergence. Results. We find that there are two separate cases of elliptical shape that occur, the minor ellipse and the major ellipse. It is then shown how the period ratio P-1/P-2 is dependent upon the ellipticity (epsilon), the parameter characterising the stage of emergence (lambda) and the density scale height (H). Ellipticity is found to make an important contribution to P-1/P-2 for the minor ellipse when compared to its counterpart of standing oscillations of stratified loops with semi-circle or circle-arc shape. The major ellipse was found to have a lesser effect on the period ratio of standing oscillations. We also find the value of P-1/P-2 is dependent upon the stage of emergence of the loop, where the greatest contribution from emergence to the ratio of P-1/P-2 is when the loop is almost fully emerged. The important implication for magneto-seismological interpretations of the observations of oscillating coronal loops is that measurements of ellipticity and stage of emergence should supplement observations of oscillation periods and should be considered when applying observed frequencies of the fundamental mode and first harmonic to determine the diagnostic properties of these oscillating loops, e. g. the density scale height or strength of magnetic field. Neglecting the determination of ellipticity and stage of emergence may result in a 35% error in estimating density scale height

Magnetohydrodynamic waves in a compressible magnetic flux tube with elliptical cross-section

Aims. The propagation of magnetohydrodynamic (MHD) waves in a finite, compressible magnetic flux tube with an elliptical cross-section embedded in a magnetic environment is investigated. Methods. We present the derivation of the general dispersion relation of linear magneto-acoustic wave propagation for a compressible magnetic flux tube with elliptical cross-section in a plasma with finite beta. The wave modes of propagation for the n = 0 (symmetric) sausage and n = 1 (anti-symmetric) kink oscillations are then examined within the limit of the thin flux tube approximation. Results. It is shown that a compressible magnetic tube with elliptical cross-section supports slow and fast magneto-acoustic waves. In the thin tube approximation, the slow sausage mode and the slow and fast kink modes are found in analogue to a circular cross-section. However, the kink modes propagate with different phase speeds depending on whether the axial displacement takes place along the major or minor axis of the ellipse. This feature is present in both the slow and the fast bands, providing two infinite sets of slow kink modes and two infinite sets of fast kink modes, i.e. each corresponding cylindrical mode splits into two sets of modes due to the ellipticity. The difference between the phase speeds along the different axis is dependent on the ratio of the lengths of the two axes. Analytical expressions for the phase speeds are found. We show that the sausage modes do not split due to the introduced ellipticity and only the phase speed is modified when compared to the appropriate cylindrical counterpart. The percentage difference between the periods of the circular and elliptical cross-sections is also calculated, which reaches up to 21% for oscillations along the major axis. The level of difference in period could be very important in magneto-seismological applications, when observed periods are inverted into diagnostic properties (e. g. magnetic field strength, gravitational scale height, tube expansion parameter). Also shown is the perturbation of focal points of the elliptical cross-section for different modes. It is found that the focal points are unperturbed for the sausage mode, but are perturbed for all higher modes

String theory and the Kauffman polynomial

We propose a new, precise integrality conjecture for the colored Kauffman polynomial of knots and links inspired by large N dualities and the structure of topological string theory on orientifolds. According to this conjecture, the natural knot invariant in an unoriented theory involves both the colored Kauffman polynomial and the colored HOMFLY polynomial for composite representations, i.e. it involves the full HOMFLY skein of the annulus. The conjecture sheds new light on the relationship between the Kauffman and the HOMFLY polynomials, and it implies for example Rudolph's theorem. We provide various non-trivial tests of the conjecture and we sketch the string theory arguments that lead to it.Comment: 36 pages, many figures; references and examples added, typos corrected, final version to appear in CM

Quasi-fission reactions as a probe of nuclear viscosity

Fission fragment mass and angular distributions were measured from the ^{64}Ni+^{197}Au reaction at 418 MeV and 383 MeV incident energy. A detailed data analysis was performed, using the one-body dissipation theory implemented in the code HICOL. The effect of the window and the wall friction on the experimental observables was investigated. Friction stronger than one-body was also considered. The mass and angular distributions were consistent with one-body dissipation. An evaporation code DIFHEAT coupled to HICOL was developed in order to predict reaction time scales required to describe available data on pre-scission neutron multiplicities. The multiplicity data were again consistent with one-body dissipation. The cross-sections for touch, capture and quasi-fission were also obtained.Comment: 25 pages REVTeX, 3 tables, 13 figures, submitted to Phys. Rev

Chern-Simons Invariants of Torus Links

We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus links and we obtain an analogous formula for Kauffman invariants. We also derive a formula for cable knots. We use our results to test a recently proposed conjecture that relates HOMFLY and Kauffman invariants.Comment: 20 pages, 5 figures; v2: minor changes, version submitted to AHP. The final publication is available at http://www.springerlink.com/content/a2614232873l76h6

On the properties of slow mhd sausage waves within small-scale photospheric magnetic structures

The presence of magneto-acoustic waves in magnetic structures in the solar atmosphere is well-documented. Applying the technique of solar magneto-seismology (SMS) allows us to infer the background properties of these structures. Here, we aim to identify properties of the observed magneto-acoustic waves and study the background properties of magnetic structures within the lower solar atmosphere. Using the Dutch Open Telescope (DOT) and Rapid Oscillations in the Solar Atmosphere (ROSA) instruments, we captured two series of high-resolution intensity images with short cadence of two isolated magnetic pores. Combining wavelet analysis and empirical mode decomposition (EMD), we determined characteristic periods within the cross-sectional (i.e., area) and intensity time series. Then, by applying the theory of linear magnetohydrodynamics (MHD), we identified the mode of these oscillations within the MHD framework. Several oscillations have been detected within these two magnetic pores. Their periods range from 3 to 20 minutes. Combining wavelet analysis and EMD enables us to confidently find the phase difference between the area and intensity oscillations. From these observed features, we concluded that the detected oscillations can be classified as slow sausage MHD waves. Further, we determined several key properties of these oscillations such as the radial velocity perturbation, magnetic field perturbation and vertical wavenumber using solar magnetoseismology. The estimated range of the related wavenumbers reveals that these oscillations are trapped within these magnetic structures. Our results suggest that the detected oscillations are standing harmonics, and, this allows us to estimate the expansion factor of the waveguides by employing SMS. The calculated expansion factor ranges from 4-12

Interferometric Bell-state preparation using femtosecond-pulse-pumped Spontaneous Parametric Down-Conversion

We present theoretical and experimental study of preparing maximally entangled two-photon polarization states, or Bell states, using femtosecond pulse pumped spontaneous parametric down-conversion (SPDC). First, we show how the inherent distinguishability in femtosecond pulse pumped type-II SPDC can be removed by using an interferometric technique without spectral and amplitude post-selection. We then analyze the recently introduced Bell state preparation scheme using type-I SPDC. Theoretically, both methods offer the same results, however, type-I SPDC provides experimentally superior methods of preparing Bell states in femtosecond pulse pumped SPDC. Such a pulsed source of highly entangled photon pairs is useful in quantum communications, quantum cryptography, quantum teleportation, etc.Comment: 11 pages, two-column format, to appear in PR

Atmospheric Heating and Wind Acceleration: Results for Cool Evolved Stars based on Proposed Processes

A chromosphere is a universal attribute of stars of spectral type later than ~F5. Evolved (K and M) giants and supergiants (including the zeta Aurigae binaries) show extended and highly turbulent chromospheres, which develop into slow massive winds. The associated continuous mass loss has a significant impact on stellar evolution, and thence on the chemical evolution of galaxies. Yet despite the fundamental importance of those winds in astrophysics, the question of their origin(s) remains unsolved. What sources heat a chromosphere? What is the role of the chromosphere in the formation of stellar winds? This chapter provides a review of the observational requirements and theoretical approaches for modeling chromospheric heating and the acceleration of winds in single cool, evolved stars and in eclipsing binary stars, including physical models that have recently been proposed. It describes the successes that have been achieved so far by invoking acoustic and MHD waves to provide a physical description of plasma heating and wind acceleration, and discusses the challenges that still remain.Comment: 46 pages, 9 figures, 1 table; modified and unedited manuscript; accepted version to appear in: Giants of Eclipse, eds. E. Griffin and T. Ake (Berlin: Springer