Geometry of Gaussian free field sign clusters and random interlacements

For a large class of amenable transient weighted graphs $G$, we prove that the sign clusters of the Gaussian free field on $G$ fall into a regime of strong supercriticality, in which two infinite sign clusters dominate (one for each sign), and finite sign clusters are necessarily tiny, with overwhelming probability. Examples of graphs belonging to this class include regular lattices like $\mathbb{Z}^d$, for $d \geqslant 3$, but also more intricate geometries, such as Cayley graphs of suitably growing (finitely generated) non-Abelian groups, and cases in which random walks exhibit anomalous diffusive behavior, for instance various fractal graphs. As a consequence, we also show that the vacant set of random interlacements on these objects, introduced by Sznitman in arXiv:0704.2560, and which is intimately linked to the free field, contains an infinite connected component at small intensities. In particular, this result settles an open problem from arXiv:1010.1490.Comment: 73 page

Non-adiabatic Electron Pumping through Interacting Quantum Dots

We study non-adiabatic charge pumping through single-level quantum dots taking into account Coulomb interactions. We show how a truncated set of equations of motion can be propagated in time by means of an auxiliary-mode expansion. This formalism is capable of treating the time-dependent electronic transport for arbitrary driving parameters. We verify that the proposed method describes very precisely the well-known limit of adiabatic pumping through quantum dots without Coulomb interactions. As an example we discuss pumping driven by short voltage pulses for various interaction strengths. Such finite pulses are particular suited to investigate transient non-adiabatic effects, which may be also important for periodic drivings, where they are much more difficult to reveal.Comment: 11 pages, 4 figure

How do STEM students use digital and non-digital learning resources?

We create online/digital resources in various formats for our students, and expect them to be digital natives who can use them effectively, but what evidence do we have that this is the case? This session reports on research carried out looking at how students actually study. Students on 3 STEM second year modules which have study materials supplied in different formats (from entirely online to mostly book based) were surveyed, and in-depth interviews carried out

Managing uncertainty in complex stochastic models: design and emulation of a Rabies model

In this paper we present a novel method for emulating a stochastic, or random output, computer model and show its application to a complex rabies model. The method is evaluated both in terms of accuracy and computational efficiency on synthetic data and the rabies model. We address the issue of experimental design and provide empirical evidence on the effectiveness of utilizing replicate model evaluations compared to a space-filling design. We employ the Mahalanobis error measure to validate the heteroscedastic Gaussian process based emulator predictions for both the mean and (co)variance. The emulator allows efficient screening to identify important model inputs and better understanding of the complex behaviour of the rabies model

Wireless ad hoc Sensor Networks for City Street Light Maintenance

Wireless embedded devices, especially those of the open source hardware/software kind have seen rapid growth in recent years. This kind of devices when combined with ad hoc networks and sensor data can be a low-cost and highly scalable solution to many applications. In this paper we describe the experience of taking this concept of network infrastructure, developing application infrastructure and applying it, as a prototype, to a practical situation for a medium-sized city in the Buenos Aires province outer area, Argentina. We implement a novel sensor data delivery platform using open source hardware and software focused on streetlight maintenance at a fraction of the commercial implementation costs. To the extent of our knowledge this is the first system developed, deployed and documented in a Latin American country. Also presented in this paper is the system architecture as well as the design of hardware and software components as well as the results obtained.Sociedad Argentina de Informática e Investigación Operativ

Generating Galton-Watson trees using random walks and percolation for the Gaussian free field

The study of Gaussian free field level sets on supercritical Galton-Watson trees has been initiated by Ab\"acherli and Sznitman in Ann. Inst. Henri Poincar\`e Probab. Stat., 54(1):173--201, 2018}. By means of entirely different tools, we continue this investigation and generalize their main result on the positivity of the associated percolation critical parameter $h_*$ to the setting of arbitrary supercritical offspring distribution and random conductances. A fortiori, this provides a positive answer to the open question raised at the end of the aforementioned article. What is more, in our setting it also establishes a rigorous proof of the physics literature mantra that positive correlations facilitate percolation when compared to the independent case. Our proof proceeds by constructing the Galton-Watson tree through an exploration via finite random walk trajectories. This exploration of the tree progressively unveils an infinite connected component in the random interlacements set on the tree, which is stable under small quenched noise. Using a Dynkin-type isomorphism theorem, we then infer the strict positivity of the critical parameter $h_* .$ As a byproduct of our proof we obtain the transience of the random interlacement set and the level sets of the Gaussian free field above small positive levels on such Galton-Watson trees.Comment: 38 pages 1 figur

Accretion Disks around Young Stars: Lifetimes, Disk Locking and Variability

We report the findings of a comprehensive study of disk accretion and related phenomena in four of the nearest young stellar associations spanning 6-30 million years in age, an epoch that may coincide with the late stages of planet formation. We have obtained ~650 multi-epoch high-resolution optical spectra of 100 low-mass stars that are likely members of the eta Chamaeleontis (~6 Myr), TW Hydrae (~8 Myr), beta Pictoris (~12 Myr) and Tucanae-Horologium (~30 Myr) groups. Our data were collected over 12 nights between 2004 December - 2005 July on the Magellan Clay 6.5m telescope. Based on H$\alpha$ line profiles, along with a variety of other emission lines, we find clear evidence of on-going accretion in three out of 11 eta Cha stars and two out of 32 TW Hydrae members. None of the 57 beta Pic or Tuc-Hor members shows measurable signs of accretion. Together, these results imply significant evolution of the disk accretion process within the first several Myr of a low-mass star's life. While a few disks can continue to accrete for up to ~10 Myr, our findings suggest that disks accreting for beyond that timescale are rather rare. This result provides an indirect constraint on the timescale for gas dissipation in inner disks and, in turn, on gas giant planet formation. All accretors in our sample are slow rotators, whereas non-accretors cover a large range in rotational velocities. This may hint at rotational braking by disks at ages up to ~8 Myr. Our multi-epoch spectra confirm that emission-line variability is common even in somewhat older T Tauri stars, among which accretors tend to show particularly strong variations. Thus, our results indicate that accretion and wind activity undergo significant and sustained variations throughout the lifetime of accretion disks.Comment: to appear in The Astrophysical Journa

A Comprehensive View of Circumstellar Disks in Chamaeleon I: Infrared Excess, Accretion Signatures and Binarity

We present a comprehensive study of disks around 81 young low-mass stars and brown dwarfs in the nearby ~2-Myr-old Chamaeleon I star-forming region. We use mid-infrared photometry from the Spitzer Space Telescope, supplemented by findings from ground-based high-resolution optical spectroscopy and adaptive optics imaging. We derive disk fractions of 52 (+/-6) % and 58 (+6/-7) % based on 8-micron and 24-micron colour excesses, respectively, consistent with those reported for other clusters of similar age. Within the uncertainties, the disk frequency in our sample of K3-M8 objects in Cha I does not depend on stellar mass. Diskless and disk-bearing objects have similar spatial distributions. There are no obvious transition disks in our sample, implying a rapid timescale for the inner disk clearing process; however, we find two objects with weak excess at 3-8 microns and substantial excess at 24 microns, which may indicate grain growth and dust settling in the inner disk. For a sub-sample of 35 objects with high-resolution spectra, we investigate the connection between accretion signatures and dusty disks: in the vast majority of cases (29/35) the two are well correlated, suggesting that, on average, the timescale for gas dissipation is similar to that for clearing the inner dust disk. The exceptions are six objects for which dust disks appear to persist even though accretion has ceased or dropped below measurable levels. Adaptive optics images of 65 of our targets reveal that 17 have companions at (projected) separations of 10-80 AU. Of the five <20 AU binaries, four lack infrared excess, possibly indicating that a close companion leads to faster disk dispersal. The closest binary with excess is separated by ~20 AU, which sets an upper limit of ~8 AU for the outer disk radius. (abridged)Comment: accepted for publication in the Astrophysical Journa