Pfaffian Solutions for the Manin-Radul-Mathieu SUSY KdV and SUSY sine-Gordon Equations

We reduce the vectorial binary Darboux transformation for the Manin-Radul supersymmetric KdV system in such a way that it preserves the Manin-Radul-Mathieu supersymmetric KdV equation reduction. Expressions in terms of bosonic Pfaffians are provided for transformed solutions and wave functions. We also consider the implications of these results for the supersymmetric sine-Gordon equation.Comment: 10 pages, LaTeX2e with AMSLaTeX and Babel package

Massive Domain Wall Fermions on Four-dimensional Anisotropic Lattices

We formulate the massive domain wall fermions on anisotropic lattices. For the massive domain wall fermion, we find that the dispersion relation assumes the usual form in the low momentum region when the bare parameters are properly tuned. The quark self-energy and the quark field renormalization constants are calculated to one-loop in bare lattice perturbation theory. For light domain wall fermions, we verified that the chiral mode is stable against quantum fluctuations on anisotropic lattices. This calculation serves as a guidance for the tuning of the parameters in the quark action in future numerical simulations.Comment: 36 pages, 14 figures, references adde

On the Witten Rigidity Theorem for Stringc^c Manifolds

We establish the family rigidity and vanishing theorems on the equivariant $K$-theory level for the Witten type operators on String$^c$ manifolds introduced by Chen-Han-Zhang.Comment: arXiv admin note: substantial text overlap with arXiv:1104.3972, and with arXiv:math/0001014, arXiv:math/9912108 by other author

Contracting and Erupting Components of Sigmoidal Active Regions

It is recently noted that solar eruptions can be associated with the contraction of coronal loops that are not involved in magnetic reconnection processes. In this paper, we investigate five coronal eruptions originating from four sigmoidal active regions, using high-cadence, high-resolution narrowband EUV images obtained by the Solar Dynamic Observatory (SDO}). The magnitudes of the flares associated with the eruptions range from the GOES-class B to X. Owing to the high-sensitivity and broad temperature coverage of the Atmospheric Imaging Assembly (AIA) onboard SDO, we are able to identify both the contracting and erupting components of the eruptions: the former is observed in cold AIA channels as the contracting coronal loops overlying the elbows of the sigmoid, and the latter is preferentially observed in warm/hot AIA channels as an expanding bubble originating from the center of the sigmoid. The initiation of eruption always precedes the contraction, and in the energetically mild events (B and C flares), it also precedes the increase in GOES soft X-ray fluxes. In the more energetic events, the eruption is simultaneous with the impulsive phase of the nonthermal hard X-ray emission. These observations confirm the loop contraction as an integrated process in eruptions with partially opened arcades. The consequence of contraction is a new equilibrium with reduced magnetic energy, as the contracting loops never regain their original positions. The contracting process is a direct consequence of flare energy release, as evidenced by the strong correlation of the maximal contracting speed, and strong anti-correlation of the time delay of contraction relative to expansion, with the peak soft X-ray flux. This is also implied by the relationship between contraction and expansion, i.e., their timing and speed.Comment: Accepted for publication in Ap

Linear analysis of three-dimensional instability of non-Newtonian liquid jets

The instability behaviour of non-Newtonian liquid jets moving in an inviscid gaseous environment is investigated theoretically for three-dimensional disturbances. The corresponding dispersion relation between the wave growth rate and the wavenumber is derived. Results for axisymmetrical non-Newtonian jets, the Newtonian jets, and the inviscid jets are recovered, and it is shown that two-dimensional disturbances are the most dangerous for the considered set of parameters