The Stationary Phase Method for a Wave Packet in a Semiconductor Layered System. The applicability of the method

Using the formal analysis made by Bohm in his book, {\em "Quantum theory"}, Dover Publications Inc. New York (1979), to calculate approximately the phase time for a transmitted and the reflected wave packets through a potential barrier, we calculate the phase time for a semiconductor system formed by different mesoscopic layers. The transmitted and the reflected wave packets are analyzed and the applicability of this procedure, based on the stationary phase of a wave packet, is considered in different conditions. For the applicability of the stationary phase method an expression is obtained in the case of the transmitted wave depending only on the derivatives of the phase, up to third order. This condition indicates whether the parameters of the system allow to define the wave packet by its leading term. The case of a multiple barrier systems is shown as an illustration of the results. This formalism includes the use of the Transfer Matrix to describe the central stratum, whether it is formed by one layer (the single barrier case), or two barriers and an inner well (the DBRT system), but one can assume that this stratum can be comprise of any number or any kind of semiconductor layers.Comment: 15 pages, 4 figures although figure 4 has 5 graph

The Case of H2_2C3_3O Isomers, Revisited: Solving the Mystery of the Missing Propadienone

To date, two isomers of H$_2$C$_3$O have been detected, namely, propynal (HCCCHO) and cylclopropenone (c-H$_2$C$_3$O). A third, propadienone (CH$_2$CCO), has thus far eluded observers despite the fact that it is the lowest in energy of the three. This previously noted result is in contradiction of the minimum energy principle, which posits that the abundances of isomers in interstellar environments can be predicted based on their relative stabilities - and suggests, rather, the importance of kinetic over thermodynamic effects in explaining the role of such species. Here, we report results of \textit{ab initio} quantum chemical calculations of the reaction between H and (a) HC$_3$O, (b) H$_2$C$_3$O (both propynal and propadienone), and (c) CH$_2$CHCO. We have found that, among all possible reactions between atomic hydrogen and either propadienone or propynal, only the destruction of propadienone is barrierless and exothermic. That this destruction pathway is indeed behind the non-detection of CH$_2$CCO is further suggested by our finding that the product of this process, the radical CH$_2$CHCO, can subsequently react barrierlessly with H to form propenal (CH$_2$CHCHO) which has, in fact, been detected in regions where the other two H$_2$C$_3$O isomers are observed. Thus, these results not only shed light on a previously unresolved astrochemical mystery, but also further highlight the importance of kinetics in understanding the abundances of interstellar molecules.Comment: ApJ, accepted: 14 pages, 2 figure

Momentum distributions of α\alpha-particles from decaying low-lying 12^{12}C-resonances

The complex scaled hyperspherical adiabatic expansion method is used to compute momentum and energy distributions of the three $\alpha$-particles emerging from the decay of low-lying $^{12}$C-resonances. The large distance continuum properties of the wave functions are crucial and must be accurately calculated. We discuss separately decays of natural parity states: two $0^+$, one $1^{-}$, three $2^+$, one $3^-$, two $4^+$, one $6^+$, and one of each of unnatural parity, $1^{+}$, $2^-$, $3^+$, $4^-$. The lowest natural parity state of each $J^{\pi}$ decays predominantly sequentially via the $^{8}$Be ground state whereas other states including unnatural parity states predominantly decay directly to the continuum. We present Dalitz plots and systematic detailed momentum correlations of the emerging $\alpha$-particles.Comment: 11 pages, 7 figures, accepted for publication in Physical Review

Housing cycles in the major euro area countries.

The recent burst of the house price bubble in the United States and its spillover effects on real economies worldwide has rekindled the interest in the role of housing in the business cycle. In this paper, we investigate the relationships between housing cycles among the four major euro area countries (Germany, France, Italy and Spain) over the sample 1980q1 – 2008q4. Our main findings are that GDP cycles between 1.5 and 8 years show a high degree of comovement across these four countries, reflecting trade linkages. In contrast comovements in housing market cycles between 1.5 and 8 years are much weaker, idiosyncratic factors playing a major role. House prices are even less related across countries than quantities (residential investment, building permits, housing starts …). We find however much stronger relationships since 1999, i.e. in the common monetary policy period.Housing cycles, synchronisation measures, euro area countries.

Gravitational shocks as a key ingredient of Gamma-Ray Bursts

We identify a novel physical mechanism that may be responsible for energy release in $\gamma$-ray bursts. Radial perturbations in the neutron core, induced by its collision with collapsing outer layers during the early stages of supernova explosions, can trigger a gravitational shock, which can readily eject a small but significant fraction of the collapsing material at ultra-relativistic speeds. The development of such shocks is a strong-field effect arising in near-critical collapse in General Relativity and has been observed in numerical simulations in various contexts, including in particular radially perturbed neutron star collapse, albeit for a tiny range of initial conditions. Therefore, this effect can be easily missed in numerical simulations if the relevant parameter space is not exhaustively investigated. In the proposed picture, the observed rarity of $\gamma$-ray bursts would be explained if the relevant conditions for this mechanism appear in only about one in every $10^4-10^5$ core collapse supernovae. We also mention the possibility that near-critical collapse could play a role in powering the central engines of Active Galactic Nuclei.Comment: 9 pages, 3 figure

On computing distance function for Level Set Method using USFEM/Rothe as stabilized formulation

En este trabajo se ha utilizado la formulación estabilizada de elementos finitos Unusual Stabilized Finite Element Method (USFEM) asociada al método de Rothe para resolver el problema del redistanciamiento en el método de Funciones de Nivel. Se ha utilizado el método de Rothe primero para el avance de la solución en el pseudotiempo y la formulación USFEM para la solución del problema advectivo–reactivo en estado estacionario, para cada paso de tiempo resultante. Se han hecho ejemplos en 2D y se han comparado sus resultados con el esquema de estabilización SUPG, incrementado con un operador de captura de discontinuidades no lineal.In this work we use the Unusual Stabilized Finite Element Method (USFEM) associated to Rothes method for solving the redistancing problem in the Level Set Method . Rothes method is used first for advancing the solution in (pseudo)time and USFEM for solving the resulting steady advective–reaction problem in each time step. Several 2D problems are solved and results compared with SUPG scheme supplemented with a nonlinear discontinuity–capturing operator.Peer Reviewe

Adjusting ROC curve for Covariates with AROC R package

The ability of a medical test to differentiate between diseased and non-diseased states is of vital importance and must be screened by statistical analysis for reliability and improvement. The receiver operating characteristic (ROC) curve remains a popular method of marker analysis, disease screening and diagnosis. Covariates in this field related to the subject’s characteristics are incorporated in the analysis to avoid bias. The covariate adjusted ROC (AROC) curve was proposed as a method of incorporation. The AROC R-package was recently released and brings various methods of estimation based on multiple authors work. The aim of this study was to explore the AROC package functionality and usability using real data noting its possible limitations. The main methods of the package were capable of incorporating different and multiple variables, both categorical and continuous, in the AROC curve estimation. When tested for the same data, AROC curves are generated with no statistical differences, regardless of method. The package offers a variety of methods to estimate the AROC curve complemented with predictive checks and pooled ROC estimation. The package offers a way to conduct a more thorough ROC and AROC analysis, making it available for any R user.This work has been supported by FCT - Fundação para a Ciência e Tecnologia within the R&D Units Project Scope: UIDB/00319/202

The Dirichlet Obstruction in AdS/CFT

The obstruction for a perturbative reconstruction of the five-dimensional bulk metric starting from the four-dimensional metric at the boundary,that is, the Dirichlet problem, is computed in dimensions $6\leq d\leq 10$ and some comments are made on its general structure and, in particular, on its relationship with the conformal anomaly, which we compute in dimension $d=8$.Comment: 13 pages, references added (this paper supersedes hep-th/0206140, "A Note on the Bach Tensor in AdS/CFT", which has been withdrawn

The Influence of Dual-Recycling on Parametric Instabilities at Advanced LIGO

Laser interferometers with high circulating power and suspended optics, such as the LIGO gravitational wave detectors, experience an optomechanical coupling effect known as a parametric instability: the runaway excitation of a mechanical resonance in a mirror driven by the optical field. This can saturate the interferometer sensing and control systems and limit the observation time of the detector. Current mitigation techniques at the LIGO sites are successfully suppressing all observed parametric instabilities, and focus on the behaviour of the instabilities in the Fabry-Perot arm cavities of the interferometer, where the instabilities are first generated. In this paper we model the full dual-recycled Advanced LIGO design with inherent imperfections. We find that the addition of the power- and signal-recycling cavities shapes the interferometer response to mechanical modes, resulting in up to four times as many peaks. Changes to the accumulated phase or Gouy phase in the signal-recycling cavity have a significant impact on the parametric gain, and therefore which modes require suppression.Comment: 9 pages, 11 figures, 2 ancillary file

alpha particle momentum distributions from 12C decaying resonances

The computed $\alpha$ particle momentum distributions from the decay of low-lying $^{12}$C resonances are shown. The wave function of the decaying fragments is computed by means of the complex scaled hyperspherical adiabatic expansion method. The large-distance part of the wave functions is crucial and has to be accurately calculated. We discuss energy distributions, angular distributions and Dalitz plots for the $4^+$, $1^+$ and $4^-$ states of $^{12}$C.Comment: 6 pages, 4 figures. Proceedings of the SOTANCP2008 conference held in Strasbourg in May 200