Quadratic Maps in Two Variables on Arbitrary Fields

Let $\mathbb{F}$ be a field of characteristic different from $2$ and $3$, and let $V$ be a vector space of dimension $2$ over $\mathbb{F}$. The generic classification of homogeneous quadratic maps $f\colon V\to V$ under the action of the linear group of $V$, is given and efficient computational criteria to recognize equivalence are provided.Comment: 12 pages, no figure

A Cellular Automaton Model for the Traffic Flow in Bogota

In this work we propose a car cellular automaton model that reproduces the experimental behavior of traffic flows in Bogot\'a. Our model includes three elements: hysteresis between the acceleration and brake gaps, a delay time in the acceleration, and an instantaneous brake. The parameters of our model were obtained from direct measurements inside a car on motorways in Bogot\'a. Next, we simulated with this model the flux-density fundamental diagram for a single-lane traffic road and compared it with experimental data. Our simulations are in very good agreement with the experimental measurements, not just in the shape of the fundamental diagram, but also in the numerical values for both the road capacity and the density of maximal flux. Our model reproduces, too, the qualitative behavior of shock waves. In addition, our work identifies the periodic boundary conditions as the source of false peaks in the fundamental diagram, when short roads are simulated, that have been also found in previous works. The phase transition between free and congested traffic is also investigated by computing both the relaxation time and the order parameter. Our work shows how different the traffic behavior from one city to another can be, and how important is to determine the model parameters for each city.Comment: 14 pages and 13 figures (gzipped tar file). Submitted to Int.J.Mod.Phys.C. Minor changes, specially at references and typoes, plus a clearer summary of the CA rule

A 300 GHz "Always-in-Focus" Focusing System for Target Detection

A focusing system for a 300 GHz radar with 5 m target distance and 10 mm diameter spot size resolution is proposed. The focusing system is based on a Gaussian telescope scheme and its main parameters have been de¬signed using Gaussian beam quasi-optical propagation theory with an in-house developed MATLAB® based analysis tool. Then, this approach has been applied to a real focusing system based on two elliptical mirrors in order to reduce the distortion and cross-polar level and a plane mirror to provide scanning capabilities. The over¬all system has been simulated with a full-wave electromag¬netic simulator and its behavior is presented. With this approach, the focusing system always works "in-focus" since the only mirror that is rotated when scanning is the output plane mirror, so the beam is almost not distorted. The design process, although based in the well-known Gaussian beam quasi-optical propagation theory, provides a fast and accurate method and minimizes the overall size of the mirrors. As a consequence, the size of the focusing system is also reduced

Molecular gas in low-metallicity starburst galaxies: Scaling relations and the CO-to-H2_2 conversion factor

We study the molecular content and the star formation efficiency of 21 Blue Compact Dwarfs (BCDs). We present CO(1-0) and (2-1) observations, further supplemented with additional CO measurements and multiwavelength ancillary data from the literature. We find the CO luminosity to be correlated with the stellar and HI masses, SFR tracers, the size of the starburst and its metallicity. BCDs appear offset from the Schmidt-Kennicutt (SK) law, showing extremely low ($\lesssim$0.1 Gyr) H2 and H2+HI depletion timescales. The departure from the SK law is smaller when considering H2+HI rather than H2 only, and is larger for BCDs with lower metallicity and higher specific SFR. Thus, the molecular fraction and H2 depletion timescale of BCDs is found to be strongly correlated with metallicity. Using this and assuming that the empirical correlation found between the specific SFR and galaxy-averaged H2 depletion timescale of more metal-rich galaxies extends to lower masses, we derive a metallicity-dependent CO-to-H2 conversion factor $\alpha_{CO, Z} \propto (Z/Z_{\odot})^{-y}$, with $y=1.5(\pm 0.3)$ in qualitative agreement with previous determinations, dust-based measurements, and recent model predictions. Our results suggest that in vigorously star-forming dwarfs the fraction of H2 traced by CO decreases by a factor of about 40 from $Z \sim Z_{\odot}$ to $Z \sim 0.1 Z_{\odot}$, leading to a strong underestimation of the H2 mass in metal-poor systems when a Galactic $\alpha_{CO, MW}$ is considered. Adopting $\alpha_{CO, Z}$ we find that departures from the SK law are partially resolved. Our results suggest that starbursting dwarfs have shorter depletion gas timescales and lower molecular fractions compared to normal late-type disc galaxies even accounting for the molecular gas not traced by CO emission in metal-poor environments, raising additional constraints to model predictions (Abridged).Comment: 18 pages, 14 Figures, 4 Tables: Accepted for publication in A&

First clear evidence of quantum chaos in the bound states of an atomic nucleus

We study the spectral fluctuations of the $^{208}$Pb nucleus using the complete experimental spectrum of 151 states up to excitation energies of $6.20$ MeV recently identified at the Maier-Leibnitz-Laboratorium at Garching, Germany. For natural parity states the results are very close to the predictions of Random Matrix Theory (RMT) for the nearest-neighbor spacing distribution. A quantitative estimate of the agreement is given by the Brody parameter $\omega$, which takes the value $\omega=0$ for regular systems and $\omega \simeq 1$ for chaotic systems. We obtain $\omega=0.85 \pm 0.02$ which is, to our knowledge, the closest value to chaos ever observed in experimental bound states of nuclei. By contrast, the results for unnatural parity states are far from RMT behavior. We interpret these results as a consequence of the strength of the residual interaction in $^{208}$Pb, which, according to experimental data, is much stronger for natural than for unnatural parity states. In addition our results show that chaotic and non-chaotic nuclear states coexist in the same energy region of the spectrum.Comment: 9 pages, 1 figur

Solid flow drives surface nanopatterning by ion-beam irradiation

Ion Beam Sputtering (IBS) is known to produce surface nanopatterns over macroscopic areas on a wide range of materials. However, in spite of the technological potential of this route to nanostructuring, the physical process by which these surfaces self-organize remains poorly under- stood. We have performed detailed experiments of IBS on Si substrates that validate dynamical and morphological predictions from a hydrodynamic description of the phenomenon. Our results elucidate flow of a nanoscopically thin and highly viscous surface layer, driven by the stress created by the ion-beam, as a description of the system. This type of slow relaxation is akin to flow of macroscopic solids like glaciers or lead pipes, that is driven by defect dynamics.Comment: 12 pages, 4 figure

Spin splitting in a polarized quasi-two-dimensional exciton gas

We have observed a large spin splitting between "spin" $+1$ and $-1$ heavy-hole excitons, having unbalanced populations, in undoped GaAs/AlAs quantum wells in the absence of any external magnetic field. Time-resolved photoluminescence spectroscopy, under excitation with circularly polarized light, reveals that, for high excitonic density and short times after the pulsed excitation, the emission from majority excitons lies above that of minority ones. The amount of the splitting, which can be as large as 50% of the binding energy, increases with excitonic density and presents a time evolution closely connected with the degree of polarization of the luminescence. Our results are interpreted on the light of a recently developed model, which shows that, while intra-excitonic exchange interaction is responsible for the spin relaxation processes, exciton-exciton interaction produces a breaking of the spin degeneracy in two-dimensional semiconductors.Comment: Revtex, four pages; four figures, postscript file Accepted for publication in Physical Review B (Rapid Commun.