Convex integration for Lipschitz mappings and counterexamples to regularity

We study Lispchitz solutions of partial differential relations $\nabla u\in K$, where $u$ is a vector-valued function in an open subset of $R^n$. In some cases the set of solutions turns out to be surprisingly large. The general theory is then used to construct counter-examples to regularity of solutions of Euler-Lagrange systems satisfying classical ellipticity conditions.Comment: 28 pages published versio

Reheating after Supercooling in the Chiral Phase Transition

The chirally symmetric quark-gluon plasma produced in energetic heavy-ion collisions is predicted to supercool at the late stages of its evolution. The thermal energy is then transformed into the potential energy associated with an energetically unfavorable field configuration. Since the system is in an unstable state it eventually rolls down to the true minimum of the effective chiral potential. When this motion is described in terms of the sigma-model, we find that the energy of the coherent $\sigma-$field is very efficiently converted into pionic excitations due to anharmonic oscillations around this minimum. The system is expected to partially thermalize before its disintegration.Comment: Final version accepted for publication, 8 pages, REVTe

Interpolation with circular basis functions

In this paper we consider basis function methods for solving the problem of interpolating data over distinct points on the unit circle. In the special case where the points are equally spaced we can appeal to the theory of circulant matrices which enables an investigation into the stability and accuracy of the method. This work is a further extension and application of the research of Cheney, Light and Xu ([W.A. Light and E.W. Cheney, J. Math. Anal. Appl., 168:110–130, 1992] and [Y. Xu and E.W. Cheney, Computers Math. Applic., 24:201–215, 1992]) from the early nineties

Submillimeter polarization and variability of quasar PKS 1830-211

Polarization from active galactic nuclei is interpreted as a signpost of the role of magnetic fields in the launch and collimation of their relativistic radio jets. Here, we report the detection of a clear polarization signal from ALMA observations of the gravitationally lensed quasar PKS 1830-211 at submillimeter wavelengths (Band 9, 650 GHz). Applying a differential-polarimetry technique to the two compact lensed images of the quasar, we estimate a fractional polarization of ~5% for one lensed image, while the other appears nearly unpolarized, which implies that the polarization activity varies on a timescale of a few weeks. With additional ALMA Band 7 and 8 (between 300-500 GHz) concomitant data, we constrain a Faraday rotation of a few $10^5$ rad m$^{-2}$. We also observe flux-density variability of ~10% within one hour in Band 9. This work illustrates that a differential analysis can extract high-accuracy information (flux-density ratio and polarimetry) free of calibration issues from resolved sources in the submillimeter domain.Comment: 7 pages, 6 figures, accepted for publications in A&

Using gravitational lensed images to investigate the intrinsic AGN variability

We discuss about how the relative flux densities among the images of gravitationally-lensed active galactic nuclei, AGN, can be used to study the intrinsic AGN variability with high accuracy. Multi-frequency monitoring observations of resolved gravitational lenses can allow us to detect signals of very weak variability and also provide information about the jet opacity and structure. As an example, we investigate the variability of the flux-density ratio between the two lensed images of the blazar B0218+357, using dual-frequency cm-wave observations. Similar to our previously reported submm-wave observations of the lensed blazar PKS1830-211, we observe a clear chromatic variability, starting short before an increase in the flux-density of the blazar. The evolution of the flux-density ratios between the blazar images shows a more clear and rich structure than that of the mere lightcurves of each individual image. The accuracy in the ratio measurements is allowing us to see variability episodes in the blazar that are weaker than the natural scatter in the absolute flux-density measurements. A simple opacity model in the jet is used to consistently explain the difference between the flux-density-ratio evolution at the two frequencies.Comment: 5 pages, 2 figures. Accepted for publication in A&A. Final versio

Piezoelectric transducer

Transducer consists of a hybrid thin film and a piezoelectric transistor that acts as a stress-sensitive device with built-in gain. It provides a stress/strain transducer that incorporates a signal amplification stage and sensor in a single package

Microscopic Description of Deeply Virtual Compton Scattering off Spin-0 Nuclei

We evaluate within a microscopic calculation the contributions of both coherent and incoherent deeply virtual Compton scattering from a spin-0 nucleus. The coherent contribution is obtained when the target nucleus recoils as a whole, whereas for incoherent scattering break-up configurations for the final nucleus into a an outgoing nucleon and an $A-1$ system are considered. The two processes encode different characteristics of generalized parton distributions.Comment: 7 pages, 3 figure