Gravitational Collapse of Cylindrical Shells Made of Counter-Rotating Dust Particles

The general formulas of a non-rotating dynamic thin shell that connects two arbitrary cylindrical regions are given using Israel's method. As an application of them, the dynamics of a thin shell made of counter-rotating dust particles, which emits both gravitational waves and massless particles when it is expanding or collapsing, is studied. It is found that when the models represent a collapsing shell, in some cases the angular momentum of the dust particles is strong enough to halt the collapse, so that a spacetime singularity is prevented from forming, while in other cases it is not, and a line-like spacetime singularity is finally formed on the symmetry axis.Comment: To appear in Phys. Rev.

Production of biochars from crop residues for the remediation of trace elements contaminated soils

Biochar is the solid material obtained from thermochemical conversion of biomass under oxygen-limited conditions (pyrolysis), which can be applied as soil ameliorant [1]. In general, biochar properties are very heterogeneous due to the diverse pyrolytic conditions and the wide variety of organic residues used as feedstock [2,3]. This study intends to discern the relationship between feedstock, pyrolysis conditions and biochar properties with the goal of producing biochar with a high potential for the stabilization of trace elements in contaminated soils. For that purpose, biochars were produced using four different feedstock (rice husk, pruned olive trees, olive pit and “alperujo”, a byproduct of olive oil production) and two contrasting pyrolysis systems: a batch reactor (temperature ranged from 350 to 600 ºC; reaction time from 0.5 to 4 h under N2 atmosphere with a heating and cooling rate of XY K s-1) and a continuously feed reactor with a screw conveyor (Pyreka reactor; 500 ºC, residence time 12 min and N2 flux). Biochars were characterized by determining their pH, water holding capacity (WHC), elemental composition (C, H, N), ash content, internal structure by micro-computed tomography and chemical composition by field emission scanning electron microscopy with energy dispersive X-ray spectroscopy. To complete the characterization, Brunauer-Emmett-Teller specific surface area (SSABET; N2 adsorptive) and solid-state 13C-NMR spectroscopy were performed. Biochars produced in the batch reactor showed that pH, WHC, TC, SSABET, ash content and aromaticity increased with temperature and reaction time. Rice husk biochars showed the highest WHC (> 100%), while olive pit biochars the lowest ones. Rice husk and olive pit biochars had the highest aromaticity (between 75 and 91% of aryl carbon). The H/Cat ratio decreased with increasing pyrolysis temperature, which suggests an increase in the condensation degree of the aromatic structures. SSABET surface area ranged from 20 to 100 m2 g-1 and increased with temperature. Biochars produced in the batch reactor resulted in greater SSA values than Pyreka biochars. The pyrolysis conditions of 500 ºC and 2 h at the batch reactor resulted in similar biochars than those produced by the Pyreka reactor at 500 ºC and 12 min. Taking into account the necessity of applying biochar to soil for remediation purposes, we selected those biochars of high stability (ratio H/Cat ≤ 0.7 & high aromaticity by 13C NMR spectroscopy), great capacity for the sorption and stabilization of trace elements2 (SSABET ≥ 100 m2g-1; pH ≥9) and good potential to act as soil amendment (high WHC). The pyrolysis conditions finally selected were 500 ºC and 2 hours for the steel-batch reactor and 500 ºC and 12 min for the continuous reactor. At these conditions, rice husk biochars showed the most appropriate characteristics to be used as soil amendment for trace-elements contaminated soils

Nonclassical statistics of intracavity coupled χ(2)\chi^{(2)} waveguides: the quantum optical dimer

A model is proposed where two $\chi^{(2)}$ nonlinear waveguides are contained in a cavity suited for second-harmonic generation. The evanescent wave coupling between the waveguides is considered as weak, and the interplay between this coupling and the nonlinear interaction within the waveguides gives rise to quantum violations of the classical limit. These violations are particularly strong when two instabilities are competing, where twin-beam behavior is found as almost complete noise suppression in the difference of the fundamental intensities. Moreover, close to bistable transitions perfect twin-beam correlations are seen in the sum of the fundamental intensities, and also the self-pulsing instability as well as the transition from symmetric to asymmetric states display nonclassical twin-beam correlations of both fundamental and second-harmonic intensities. The results are based on the full quantum Langevin equations derived from the Hamiltonian and including cavity damping effects. The intensity correlations of the output fields are calculated semi-analytically using a linearized version of the Langevin equations derived through the positive-P representation. Confirmation of the analytical results are obtained by numerical simulations of the nonlinear Langevin equations derived using the truncated Wigner representation.Comment: 15 pages, 8 figures, submitted to Phys. Rev.

Analysis of Agglomerative Clustering

The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes a hierarchy of approximate solutions to this problem (for all values of $k$) is the agglomerative clustering algorithm with the complete linkage strategy. For decades, this algorithm has been widely used by practitioners. However, it is not well studied theoretically. In this paper, we analyze the agglomerative complete linkage clustering algorithm. Assuming that the dimension $d$ is a constant, we show that for any $k$ the solution computed by this algorithm is an $O(\log k)$-approximation to the diameter $k$-clustering problem. Our analysis does not only hold for the Euclidean distance but for any metric that is based on a norm. Furthermore, we analyze the closely related $k$-center and discrete $k$-center problem. For the corresponding agglomerative algorithms, we deduce an approximation factor of $O(\log k)$ as well.Comment: A preliminary version of this article appeared in Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS '11), March 2011, pp. 308-319. This article also appeared in Algorithmica. The final publication is available at http://link.springer.com/article/10.1007/s00453-012-9717-