Thermodynamics of the dead-zone inner edge in protoplanetary disks

In protoplanetary disks, the inner boundary between the turbulent and laminar regions could be a promising site for planet formation, thanks to the trapping of solids at the boundary itself or in vortices generated by the Rossby wave instability. At the interface, the disk thermodynamics and the turbulent dynamics are entwined because of the importance of turbulent dissipation and thermal ionization. Numerical models of the boundary, however, have neglected the thermodynamics, and thus miss a part of the physics. The aim of this paper is to numerically investigate the interplay between thermodynamics and dynamics in the inner regions of protoplanetary disks by properly accounting for turbulent heating and the dependence of the resistivity on the local temperature. Using the Godunov code RAMSES, we performed a series of 3D global numerical simulations of protoplanetary disks in the cylindrical limit, including turbulent heating and a simple prescription for radiative cooling. We find that waves excited by the turbulence significantly heat the dead zone, and we subsequently provide a simple theoretical framework for estimating the wave heating and consequent temperature profile. In addition, our simulations reveal that the dead-zone inner edge can propagate outward into the dead zone, before staling at a critical radius that can be estimated from a mean-field model. The engine driving the propagation is in fact density wave heating close to the interface. A pressure maximum appears at the interface in all simulations, and we note the emergence of the Rossby wave instability in simulations with extended azimuth. Our simulations illustrate the complex interplay between thermodynamics and turbulent dynamics in the inner regions of protoplanetary disks. They also reveal how important activity at the dead-zone interface can be for the dead-zone thermodynamic structure.Comment: 16 pages, 16 figures. Accepted in Astronomy and Astrophysic

Distributed anonymous function computation in information fusion and multiagent systems

We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes, with bounded computation and storage capabilities that do not scale with the network size. Our goal is to characterize the class of functions that can be computed within this model. In our main result, we exhibit a class of non-computable functions, and prove that every function outside this class can at least be approximated. The problem of computing averages in a distributed manner plays a central role in our development

Distributed anonymous discrete function computation

We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes. In this model, each node has bounded computation and storage capabilities that do not grow with the network size. Furthermore, each node only knows its neighbors, not the entire graph. Our goal is to characterize the class of functions that can be computed within this model. In our main result, we provide a necessary condition for computability which we show to be nearly sufficient, in the sense that every function that satisfies this condition can at least be approximated. The problem of computing suitably rounded averages in a distributed manner plays a central role in our development; we provide an algorithm that solves it in time that grows quadratically with the size of the network

Residence time of symmetric random walkers in a strip with large reflective obstacles

We study the effect of a large obstacle on the so called residence time, i.e., the time that a particle performing a symmetric random walk in a rectangular (2D) domain needs to cross the strip. We observe a complex behavior, that is we find out that the residence time does not depend monotonically on the geometric properties of the obstacle, such as its width, length, and position. In some cases, due to the presence of the obstacle, the mean residence time is shorter with respect to the one measured for the obstacle--free strip. We explain the residence time behavior by developing a 1D analog of the 2D model where the role of the obstacle is played by two defect sites having a smaller probability to be crossed with respect to all the other regular sites. The 1D and 2D models behave similarly, but in the 1D case we are able to compute exactly the residence time finding a perfect match with the Monte Carlo simulations

Continuous-time average-preserving opinion dynamics with opinion-dependent communications

We study a simple continuous-time multi-agent system related to Krause's model of opinion dynamics: each agent holds a real value, and this value is continuously attracted by every other value differing from it by less than 1, with an intensity proportional to the difference. We prove convergence to a set of clusters, with the agents in each cluster sharing a common value, and provide a lower bound on the distance between clusters at a stable equilibrium, under a suitable notion of multi-agent system stability. To better understand the behavior of the system for a large number of agents, we introduce a variant involving a continuum of agents. We prove, under some conditions, the existence of a solution to the system dynamics, convergence to clusters, and a non-trivial lower bound on the distance between clusters. Finally, we establish that the continuum model accurately represents the asymptotic behavior of a system with a finite but large number of agents.Comment: 25 pages, 2 figures, 11 tex files and 2 eps file

Manipulation of Giant Faraday Rotation in Graphene Metasurfaces

Faraday rotation is a fundamental magneto-optical phenomenon used in various optical control and magnetic field sensing techniques. Recently, it was shown that a giant Faraday rotation can be achieved in the low-THz regime by a single monoatomic graphene layer. Here, we demonstrate that this exceptional property can be manipulated through adequate nano-patterning, notably achieving giant rotation up to 6THz with features no smaller than 100nm. The effect of the periodic patterning on the Faraday rotation is predicted by a simple physical model, which is then verified and refined through accurate full-wave simulations.Comment: 4 pages, 5 figures, submitted to Applied Physics Letter