Finding next-to-shortest paths in a graph

We study the problem of finding the next-to-shortest paths in a graph. A next-to-shortest $(u,v)$-path is a shortest $(u,v)$-path amongst $(u,v)$-paths with length strictly greater than the length of the shortest $(u,v)$-path. In constrast to the situation in directed graphs, where the problem has been shown to be NP-hard, providing edges of length zero are allowed, we prove the somewhat surprising result that there is a polynomial time algorithm for the undirected version of the problem

The temporal evolution of the energy flux across scales in homogeneous turbulence

A temporal study of energy transfer across length scales is performed in 3D numerical simulations of homogeneous shear flow and isotropic turbulence. The average time taken by perturbations in the energy flux to travel between scales is measured and shown to be additive. Our data suggests that the propagation of disturbances in the energy flux is independent of the forcing and that it defines a `velocity' that determines the energy flux itself. These results support that the cascade is, on average, a scale-local process where energy is continuously transmitted from one scale to the next in order of decreasing size.Comment: Accepted for publication as a Letter in Physics of Fluid

Open charm meson in nuclear matter at finite temperature beyond the zero range approximation

The properties of open charm mesons, $D$, $\bar D$, $D_s$ and $\bar D_s$ in nuclear matter at finite temperature are studied within a self-consistent coupled-channel approach. The interaction of the low lying pseudoscalar mesons with the ground state baryons in the charm sector is derived from a $t$-channel vector-exchange model. The in-medium scattering amplitudes are obtained by solving the Lippmann-Schwinger equation at finite temperature including Pauli blocking effects, as well as $D$, $\bar D$, $D_s$ and $\bar D_s$ self-energies taking their mutual influence into account. We find that the in-medium properties of the $D$ meson are affected by the $D_s$-meson self-energy through the intermediate $D_s Y$ loops coupled to $DN$ states. Similarly, dressing the $\bar{D}$ meson in the $\bar{D}Y$ loops has an influence over the properties of the $\bar{D}_s$ meson.Comment: 23 pages, 9 figures, 2 table

On the evolution of the molecular line profiles induced by the propagation of C-shock waves

We present the first results of the expected variations of the molecular line emission arising from material recently affected by C-shocks (shock precursors). Our parametric model of the structure of C-shocks has been coupled with a radiative transfer code to calculate the molecular excitation and line profiles of shock tracers such as SiO, and of ion and neutral molecules such as H13CO+ and HN13C, as the shock propagates through the unperturbed medium. Our results show that the SiO emission arising from the early stage of the magnetic precursor typically has very narrow line profiles slightly shifted in velocity with respect to the ambient cloud. This narrow emission is generated in the region where the bulk of the ion fluid has already slipped to larger velocities in the precursor as observed toward the young L1448-mm outflow. This strongly suggests that the detection of narrow SiO emission and of an ion enhancement in young shocks, is produced by the magnetic precursor of C-shocks. In addition, our model shows that the different velocity components observed toward this outflow can be explained by the coexistence of different shocks at different evolutionary stages, within the same beam of the single-dish observations.Comment: 7 pages, 4 figures, accepted for publication in Ap

The magnetic precursor of L1448-mm: Excitation differences between ion and neutral fluids

Shock modelling predicts an electron density enhancement within the magnetic precursor of C-shocks. Previous observations of SiO, H13CO+, HN13C and H13CN toward the young L1448-mm outflow showed an over-excitation of the ion fluid that was attributed to an electron density enhancement in the precursor. We re-visit this interpretation and test if it still holds when we consider different source morphologies and kinetic temperatures for the observed molecules, and also give some insight on the spatial extent of the electron density enhancement around L1448-mm. We estimate the opacities of H13CO+ and HN13C by observing the J=3\to2 lines of rarer isotopologues to confirm that the emission is optically thin. To model the excitation of the molecules, we use the large velocity gradient (LVG) approximation with updated collisional coefficients to i) re- analyse the observations toward the positions where the over-excitation of H13CO+ has previously been observed [i.e. toward L1448- mm at offsets (0,0) and (0,-10)], and ii) to investigate if the electron density enhancement is still required for the cases of extended and compact emission, and for kinetic temperatures of up to 400 K. We also report several lines of SiO, HN13C and H13CO+ toward new positions around this outflow, to investigate the spatial extent of the over-excitation of the ions in L1448-mm. From the isotopologue observations, we find that the emission of H13CO+ and HN13C from the precursor is optically thin if this emission is extended. Using the new collisional coefficients, an electron density enhancement is still needed to explain the excitation of H13CO+ for extended emission and for gas temperatures of\le 400 K toward L1448-mm (0,-10), and possibly also toward L1448-mm (0,0). For compact emission the data cannot be fitted. We do not find any evidence for the over-excitation of the ion fluid toward the newly observed positions around L1448-mm. The observed line emission of SiO, H13CO+ and HN13C toward L1448-mm (0,0) and (0,-10) is consistent with an electron density enhancement in the precursor component, if this emission is spatially extended. This is also true for the case of high gas temperatures (\le400 K) toward the (0,-10) offset. The electron density enhancement seems to be restricted to the southern, redshifted lobe of the L1448-mm outflow. Interferometric images of the line emission of these molecules are needed to confirm the spatial extent of the over-excitation of the ions and thus, of the electron density enhancement in the magnetic precursor of L1448-mm.Comment: Accepted for publication in A&A; 9 pages, 3 figure