Rate of decoherence for an electron weakly coupled to a phonon gas

We study the dynamics of an electron weakly coupled to a phonon gas. The initial state of the electron is the superposition of two spatially localized distant bumps moving towards each other, and the phonons are in a thermal state. We investigate the dynamics of the system in the kinetic regime and show that the time evolution makes the non-diagonal terms of the density matrix of the electron decay, destroying the interference between the two bumps. We show that such a damping effect is exponential in time, and the related decay rate is proportional to the total scattering cross section of the electron-phonon interaction.Comment: 27 pages, 2 figure

Constrained energy minimization and orbital stability for the NLS equation on a star graph

We consider a nonlinear Schr\"odinger equation with focusing nonlinearity of power type on a star graph ${\mathcal G}$, written as $i \partial_t \Psi (t) = H \Psi (t) - |\Psi (t)|^{2\mu}\Psi (t)$, where $H$ is the selfadjoint operator which defines the linear dynamics on the graph with an attractive $\delta$ interaction, with strength $\alpha < 0$, at the vertex. The mass and energy functionals are conserved by the flow. We show that for $0<\mu<2$ the energy at fixed mass is bounded from below and that for every mass $m$ below a critical mass $m^*$ it attains its minimum value at a certain \hat \Psi_m \in H^1(\GG) , while for $m>m^*$ there is no minimum. Moreover, the set of minimizers has the structure {\mathcal M}={e^{i\theta}\hat \Psi_m, \theta\in \erre}. Correspondingly, for every $m<m^*$ there exists a unique $\omega=\omega(m)$ such that the standing wave $\hat\Psi_{\omega}e^{i\omega t}$ is orbitally stable. To prove the above results we adapt the concentration-compactness method to the case of a star graph. This is non trivial due to the lack of translational symmetry of the set supporting the dynamics, i.e. the graph. This affects in an essential way the proof and the statement of concentration-compactness lemma and its application to minimization of constrained energy. The existence of a mass threshold comes from the instability of the system in the free (or Kirchhoff's) case, that in our setting corresponds to \al=0.Comment: 26 pages, 1 figur

Variational properties and orbital stability of standing waves for NLS equation on a star graph

We study standing waves for a nonlinear Schr\"odinger equation on a star graph {$\mathcal{G}$} i.e. $N$ half-lines joined at a vertex. At the vertex an interaction occurs described by a boundary condition of delta type with strength $\alpha\leqslant 0$. The nonlinearity is of focusing power type. The dynamics is given by an equation of the form $i \frac{d}{dt}\Psi_t = H \Psi_t - | \Psi_t |^{2\mu} \Psi_t$, where $H$ is the Hamiltonian operator which generates the linear Schr\"odinger dynamics. We show the existence of several families of standing waves for every sign of the coupling at the vertex for every $\omega > \frac{\alpha^2}{N^2}$. Furthermore, we determine the ground states, as minimizers of the action on the Nehari manifold, and order the various families. Finally, we show that the ground states are orbitally stable for every allowed $\omega$ if the nonlinearity is subcritical or critical, and for $\omega<\omega^\ast$ otherwise.Comment: 36 pages, 2 figures, final version appeared in JD

Robust monomer-distribution biosignatures in evolving digital biota

Because organisms synthesize component molecules at rates that reflect those molecules' adaptive utility, we expect a population of biota to leave a distinctive chemical signature on their environment that is anomalous given the local (abiotic) chemistry. We observe the same effect in the distribution of computer instructions used by an evolving population of digital organisms, and characterize the robustness of the evolved signature with respect to a number of different changes in the system's physics. The observed instruction abundance anomaly has features that are consistent over a large number of evolutionary trials and alterations in system parameters, which makes it a candidate for a non-Earth-centric life-diagnosticComment: 22 pages, 4 figures, 1 table. Supplementary Material available from C

Comparison of the properties of two fossil groups of galaxies with the normal group NGC 6034 based on multiband imaging and optical spectroscopy

We collected multiband imaging and spectroscopy for two fossil groups (RX J1119.7+2126 and 1RXS J235814.4+150524) and one normal group (NGC 6034). We computed photometric redshifts in the central zones of each group, combining previous data with the SDSS five-band data. For each group we investigated the red sequence (RS) of the color-magnitude relation and computed the luminosity functions, stellar population ages and distributions of the group members. Spectroscopy allowed us to investigate the large-scale surroundings of these groups and the substructure levels in 1RXS J235814.4+150524 and NGC 6034. The large-scale environment of 1RXS J235814.4+150524 is poor, though its galaxy density map shows a clear signature of the surrounding cosmic web. RX J1119.7+2126 appears to be very isolated, while the cosmic environment of NGC 6034 is very rich. At the group scale, 1RXS J235814.4+150524 shows no substructure. Galaxies with recent stellar populations seem preferentially located in the group outskirts. A RS is discernable for all three groups in a color-magnitude diagram. The luminosity functions based on photometric redshift selection and on statistical background subtraction have comparable shapes, and agree with the few points obtained from spectroscopic redshifts. These luminosity functions show the expected dip between first and second brightest galaxies for the fossil groups only. Their shape is also regular and relatively flat at faint magnitudes down to the completeness level for RX J1119.7+2126 and NGC 6034, while there is a clear lack of faint galaxies for 1RXS J235814.4+150524. RX J1119.7+2126 is definitely classified as a fossil group; 1RXS J235814.4+150524 also has properties very close to those of a fossil group, while we confirm that NGC 6034 is a normal group.Comment: Accepted in A&A, english-improved, 5 jpeg figures, and shortened abstrac

Fast solitons on star graphs

We define the Schr\"odinger equation with focusing, cubic nonlinearity on one-vertex graphs. We prove global well-posedness in the energy domain and conservation laws for some self-adjoint boundary conditions at the vertex, i.e. Kirchhoff boundary condition and the so called $\delta$ and $\delta'$ boundary conditions. Moreover, in the same setting we study the collision of a fast solitary wave with the vertex and we show that it splits in reflected and transmitted components. The outgoing waves preserve a soliton character over a time which depends on the logarithm of the velocity of the ingoing solitary wave. Over the same timescale the reflection and transmission coefficients of the outgoing waves coincide with the corresponding coefficients of the linear problem. In the analysis of the problem we follow ideas borrowed from the seminal paper \cite{[HMZ07]} about scattering of fast solitons by a delta interaction on the line, by Holmer, Marzuola and Zworski; the present paper represents an extension of their work to the case of graphs and, as a byproduct, it shows how to extend the analysis of soliton scattering by other point interactions on the line, interpreted as a degenerate graph.Comment: Sec. 2 revised; several misprints corrected; added references; 32 page

A Possible Case of Neurogenic Pulmonary Edema in a Sheep following Intracranial Surgery

A 3-year-old female crossbred sheep weighing 64 kg was anaesthetized for intracranial surgery as a part of a research project. Premedication and induction of anesthesia were uneventful as well as tracheal intubation. Anesthesia was maintained with isoflurane in a 50% mixture of oxygen and air, fentanyl (5-15 µg kg-1h-1) and lidocaine (1.8 mg kg-1h-1). During anesthesia, an increased alveolar-arterial oxygen gradient was calculated on the basis of arterial blood gas analysis: inspiratory fraction of oxygen was increased and a recruitment manoeuvre was performed. After 210 minutes of anesthesia, the sheep was let recover with oxygen supplementation under monitoring of pulse-oxymetry, capnography, inspired and expired oxygen, temperature and invasive blood pressure. At tracheal extubation no signs of regurgitation or aspiration were noticed. Twenty-five minutes later, the sheep showed deterioration of neurological status and clonic seizure responsive to diazepam. After transient tachycardia, blood pressure rose acutely and sinus bradycardia followed. Severe tachypnea started in few minutes accompanied by loud respiratory noises and harsh diffuse crackles on both sides of the thorax. Foamy blood nasal exudates discharged from the nostrils. Neurogenic pulmonary edema as a sequel of increased intracranial pressure was suspected and treated with intravenous mannitol (0.5 gkg-1) and furosemide (4 mgKg-1). Hypoxemia was successfully managed with oxygen supplementation. Motor and cognitive functions improved progressively and were deemed normal within 12 hours from the episode, when arterial partial pressure of oxygen was 11.7 kPa (88 mmHg) at room air

A fountain of droplets

A vessel is plunged upside down into a pool of 50 cSt silicone oil. An air bell is then created. This bell is vertically shaken at 60 Hz that leads to the oscillation of the air/oil interface. The edges of the immersed vessel generate surface waves that propagate towards the center of the bell. When the amplitude of the oscillation increases, wave amplitude increases. We study the influence of the angle between successive sides on the wave patterns. Two kinds of vessel have been studied: a triangular and a square prism. The shape of the air/oil meniscus depends on the angle between the sides of the considered prism. As the amplitude of the oscillation is increased, the triple line, which is the contact line between the solid and the air/oil interface, moves up and down. Above a given acceleration that depends on the immersion depth and on the shape vessel, wave goes under the corner edge of the bell. During the oscillation, the wave generates at the edges presents a singularity that leads eventually to a jet and a drop ejection. A drop is ejected at each oscillation. More complicated ejection can be produced with further increase of the amplitude. This is a sample arXiv article illustrating the use of fluid dynamics videos.Comment: 3 pages, 2 figures, 2 movies (high-res and low-res

SINGLE BUILDING POINT CLOUD SEGMENTATION: TOWARDS URBAN DATA MODELING AND MANAGEMENT

To manage urban areas, a key step is the development of a geometric survey and its subsequent analysis and processing in order to provide useful information, and to become a good basis for urban modeling. Surveys of urban areas can be developed with various technologies, such as Aerial Laser Scanning, Unmanned Aerial Systems photogrammetry, and Mobile Mapping Systems. To make the resulting point clouds useful for subsequent steps, it is necessary to segment them into classes representing urban elements. On the other hand, there are 2D land representations that provide a variety of information related to the elements in the urban environment, which are linked to databases that have information content related to them. In this context, the element identified as interesting for urban management of the built heritage is the individual building unit. This paper presents an automated method for using map datasets to segment individual building units on a point cloud of an urban area. A unique number is then assigned to the segmented points, linking them directly to the corresponding element in the map database. The resulting point cloud thus becomes a container of the information in the map database, and a basis for possible city modeling. The method was successfully tested on the historic city of Sabbioneta (northern Italy), using two point clouds, one obtained through the use of a Mobile Mapping System and one obtained with Unmanned Aerial System photogrammetry. Two cartographic databases were used, one opensource (OpenStreetMap) and one provided by the regional authorities (regional cartographic database)