Super-hydrodynamic limit in interacting particle systems

This paper is a follow-up of the work initiated in [3], where it has been investigated the hydrodynamic limit of symmetric independent random walkers with birth at the origin and death at the rightmost occupied site. Here we obtain two further results: first we characterize the stationary states on the hydrodynamic time scale and show that they are given by a family of linear macroscopic profiles whose parameters are determined by the current reservoirs and the system mass. Then we prove the existence of a super-hyrdrodynamic time scale, beyond the hydrodynamic one. On this larger time scale the system mass fluctuates and correspondingly the macroscopic profile of the system randomly moves within the family of linear profiles, with the randomness of a Brownian motion.Comment: 22 page

Large Radio Telescopes for Anomalous Microwave Emission Observations

We discuss in this paper the problem of the Anomalous Microwave Emission (AME) in the light of ongoing or future observations to be performed with the largest fully steerable radio telescope in the world. High angular resolution observations of the AME will enable astronomers to drastically improve the knowledge of the AME mechanisms as well as the interplay between the different constituents of the interstellar medium in our galaxy. Extragalactic observations of the AME have started as well, and high resolution is even more important in this kind of observations. When cross-correlating with IR-dust emission, high angular resolution is also of fundamental importance in order to obtain unbiased results. The choice of the observational frequency is also of key importance in continuum observation. We calculate a merit function that accounts for the signal-to-noise ratio (SNR) in AME observation given the current state-of-the-art knowledge and technology. We also include in our merit functions the frequency dependence in the case of multifrequency observations. We briefly mention and compare the performance of four of the largest radiotelescopes in the world and hope the observational programs in each of them will be as intense as possible.Comment: Review accepted for publication in Advances in Astronom

Collective decision making in dynamic environments

Abstract: Collective decision making is the ability of individuals to jointly make a decision without any centralized leadership, but only relying on local interactions. A special case is represented by the best-of-n problem, whereby the swarm has to select the best option among a set of n discrete alternatives. In this paper, we perform a thorough study of the best-of-n problem in dynamic environments, in the presence of two options (n=2). Site qualities can be directly measured by agents, and we introduce abrupt changes to these qualities. We introduce two adaptation mechanisms to deal with dynamic site qualities: stubborn agents and spontaneous opinion switching. Using both computer simulations and ordinary differential equation models, we show that: (i) The mere presence of the stubborn agents is enough to achieve adaptability, but increasing its number has detrimental effects on the performance; (ii) the system adaptation increases with increasing swarm size, while it does not depend on agents’ density, unless this is below a critical threshold; (iii) the spontaneous switching mechanism can also be used to achieve adaptability to dynamic environments, and its key parameter, the probability of switching, can be used to regulate the trade-off between accuracy and speed of adaptation

Tunnelling in nonlocal evolution equations

We study "tunnelling" in a one-dimensional, nonlocal evolution equation by assigning a penalty functional to orbits which deviate from solutions of the evolution equation. We discuss the variational problem of computing the minimal penalty for orbits which connect two stable, stationary solutions

A fitness model for the Italian Interbank Money Market

We use the theory of complex networks in order to quantitatively characterize the formation of communities in a particular financial market. The system is composed by different banks exchanging on a daily basis loans and debts of liquidity. Through topological analysis and by means of a model of network growth we can determine the formation of different group of banks characterized by different business strategy. The model based on Pareto's Law makes no use of growth or preferential attachment and it reproduces correctly all the various statistical properties of the system. We believe that this network modeling of the market could be an efficient way to evaluate the impact of different policies in the market of liquidity.Comment: 5 pages 5 figure

Large deviations for the macroscopic motion of an interface

We study the most probable way an interface moves on a macroscopic scale from an initial to a final position within a fixed time in the context of large deviations for a stochastic microscopic lattice system of Ising spins with Kac interaction evolving in time according to Glauber (non-conservative) dynamics. Such interfaces separate two stable phases of a ferromagnetic system and in the macroscopic scale are represented by sharp transitions. We derive quantitative estimates for the upper and the lower bound of the cost functional that penalizes all possible deviations and obtain explicit error terms which are valid also in the macroscopic scale. Furthermore, using the result of a companion paper about the minimizers of this cost functional for the macroscopic motion of the interface in a fixed time, we prove that the probability of such events can concentrate on nucleations should the transition happen fast enough

Current reservoirs in the simple exclusion process

We consider the symmetric simple exclusion process in the interval $[-N,N]$ with additional birth and death processes respectively on $(N-K,N]$, $K>0$, and $[-N,-N+K)$. The exclusion is speeded up by a factor $N^2$, births and deaths by a factor $N$. Assuming propagation of chaos (a property proved in a companion paper "Truncated correlations in the stirring process with births and deaths") we prove convergence in the limit $N\to \infty$ to the linear heat equation with Dirichlet condition on the boundaries; the boundary conditions however are not known a priori, they are obtained by solving a non linear equation. The model simulates mass transport with current reservoirs at the boundaries and the Fourier law is proved to hold

Multi-mode TES bolometer optimization for the LSPE-SWIPE instrument

In this paper we explore the possibility of using transition edge sensor (TES) detectors in multi-mode configuration in the focal plane of the Short Wavelength Instrument for the Polarization Explorer (SWIPE) of the balloon-borne polarimeter Large Scale Polarization Explorer (LSPE) for the Cosmic Microwave Background (CMB) polarization. This study is motivated by the fact that maximizing the sensitivity of TES bolometers, under the augmented background due to the multi-mode design, requires a non trivial choice of detector parameters. We evaluate the best parameter combination taking into account scanning strategy, noise constraints, saturation power and operating temperature of the cryostat during the flight.Comment: in Journal of Low Temperature Physics, 05 January 201

Stability of planar fronts for a non--local phase kinetics equation with a conservation law in D≤3D \le 3

We consider, in a $D-$dimensional cylinder, a non--local evolution equation that describes the evolution of the local magnetization in a continuum limit of an Ising spin system with Kawasaki dynamics and Kac potentials. We consider sub--critical temperatures, for which there are two local spatially homogeneous equilibria, and show a local nonlinear stability result for the minimum free energy profiles for the magnetization at the interface between regions of these two different local equilibrium; i.e., the planar fronts: We show that an initial perturbation of a front that is sufficiently small in $L^2$ norm, and sufficiently localized yields a solution that relaxes to another front, selected by a conservation law, in the $L^1$ norm at an algebraic rate that we explicitly estimate. We also obtain rates for the relaxation in the $L^2$ norm and the rate of decrease of the excess free energy