Discovery of KiloHertz Quasi-Periodic Oscillations in 4U 1735-44

We discovered a single kHz quasi-periodic oscillation (QPO) near 1150 Hz in the Rossi X-ray Timing Explorer X-ray light curve of the low mass X-ray binary and atoll source 4U 1735-44. The rms amplitude of this peak was 2-3%, and the FWHM 6-40 Hz. There are indications that the kHz QPO frequency decreased from 1160 Hz to 1145 Hz when the count rate increased, which would be quite different from what is observed in other atoll sources for which kHz QPOs have been discovered. In the X-ray color-color diagram and hardness-intensity diagram the source traced out the curved branch (the so-called banana branch) which has been found by previous instruments. The kHz QPO was only detected when the source was at the lowest count rates during our observations, i.e. on the lower part of the banana branch. When 4U 1735-44 was at higher count rates, i.e. on the upper part of the banana branch and at higher inferred mass accretion rate with respect to that on the lower part of the banana branch, the QPO was not detected. Besides the kHz QPO we discovered a low frequency QPO with a frequency near 67 Hz, together with a complex broad peaked noise component below 30 Hz. This 67 Hz QPO may be related to the magnetospheric beat-frequency QPO, which is observed on the horizontal branch of Z sources. This idea is supported by the (peaked) noise found in both 4U 1735-44 and Z sources at frequencies just below the QPO frequency.Comment: 9 pages, including 2 figures. Accepted for publication in ApJ Letter

Surface Acoustic Wave induced Transport in a Double Quantum Dot

We report on non-adiabatic transport through a double quantum dot under irradiation of surface acoustic waves generated on-chip. At low excitation powers, absorption and emission of single and multiple phonons is observed. At higher power, sequential phonon assisted tunneling processes excite the double dot in a highly non-equilibrium state. The present system is attractive for studying electron-phonon interaction with piezoelectric coupling.Comment: 4 pages, 3 figure

Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps

Closed form expressions in terms of multi-sums of products have been given in \cite{Tranclosedform, KRQ} of integrals of sine-Gordon, modified Korteweg-de Vries and potential Korteweg-de Vries maps obtained as so-called $(p,-1)$-traveling wave reductions of the corresponding partial difference equations. We prove the involutivity of these integrals with respect to recently found symplectic structures for those maps. The proof is based on explicit formulae for the Poisson brackets between multi-sums of products.Comment: 24 page

Neutrix Calculus and Finite Quantum Field Theory

In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series. We apply neutrix calculus, developed in connection with asymptotic series and divergent integrals, to QFT,obtaining finite renormalizations. While none of the physically measurable results in renormalizable QFT is changed, quantum gravity is rendered more manageable in the neutrix framework.Comment: 10 pages; LaTeX; version to appear in J. Phys. A: Math. Gen. as a Letter to the Edito

A 695-Hz quasi-periodic oscillation in the low-mass X-ray binary EXO 0748-676

We report the discovery of a 695-Hz quasi-periodic oscillation (QPO) in data taken with the Rossi X-ray Timing Explorer of the low-mass X-ray binary (LMXB) EXO 0748-676. This makes EXO 0748-676 the second dipping LMXB, after 4U 1915-05, that shows kHz QPOs. Comparison with other sources suggests that the QPO corresponds to the lower frequency peak of the kHz QPO pair often observed in other LMXBs. The QPO was found in the only observation done during an outburst of the source in early 1996. This observation is also the only one in which the ~1 Hz QPO recently found in EXO 0748-676 is not present.Comment: 6 pages, accepted for publication in Part 1 of The Astrophysical Journa

Discontinuities without discontinuity: The Weakly-enforced Slip Method

Tectonic faults are commonly modelled as Volterra or Somigliana dislocations in an elastic medium. Various solution methods exist for this problem. However, the methods used in practice are often limiting, motivated by reasons of computational efficiency rather than geophysical accuracy. A typical geophysical application involves inverse problems for which many different fault configurations need to be examined, each adding to the computational load. In practice, this precludes conventional finite-element methods, which suffer a large computational overhead on account of geometric changes. This paper presents a new non-conforming finite-element method based on weak imposition of the displacement discontinuity. The weak imposition of the discontinuity enables the application of approximation spaces that are independent of the dislocation geometry, thus enabling optimal reuse of computational components. Such reuse of computational components renders finite-element modeling a viable option for inverse problems in geophysical applications. A detailed analysis of the approximation properties of the new formulation is provided. The analysis is supported by numerical experiments in 2D and 3D.Comment: Submitted for publication in CMAM