Analysis of the seismic site effects along the ancient Via Laurentina (Rome)

This paper presents an evaluation of the Local Seismic Response (LSR) along the route of the ancient Roman road Via Laurentina, which has been exposed in several areas of southwest Rome over the last decade during the construction of new buildings and infrastructures. It is an example of LSR analysis applied to ancient and archaeological sites located in alluvial valleys with some methodological inferences for the design of infrastructure and urban planning. Since the ancient road does not cross the alluvial valley (namely the Fosso di Vallerano Valley) normal to its sides, it was not possible to directly perform 2D numerical modelling to evaluate the LSR along the road route. Therefore, outputs of 2D numerical models, obtained along three cross sections that were normal oriented respect to the valley, were projected along the route of the Via Laurentina within a reliable buffer attributed according to an available high-resolution geological model of the local subsoil. The modelled amplification functions consider physical effects due to both the 2D shape of the valley and the heterogeneities of the alluvial deposits. The 1D and 2D amplification functions were compared to output that non-negligible effects are related to the narrow shape of the fluvial valley and the lateral contacts between the lithotecnical units composing the alluvial fill. The here experienced methodology is suitable for applications to the numerical modelling of seismic response in case of linear infrastructures (i.e., roads, bridges, railways) that do not cross the natural system along physically characteristic directions (i.e. longitudinally or transversally)

A spatial stochastic model for rumor transmission

We consider an interacting particle system representing the spread of a rumor by agents on the $d$-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0,1,2}. Here 0 stands for ignorants, 1 for spreaders and 2 for stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate \lambda. At rate \alpha a spreader becomes a stifler due to the action of other (nearest neighbor) spreaders. Finally, spreaders and stiflers forget the rumor at rate one. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability

Two repelling random walks on Z\mathbb Z

We consider two interacting random walks on $\mathbb{Z}$ such that the transition probability of one walk in one direction decreases exponentially with the number of transitions of the other walk in that direction. The joint process may thus be seen as two random walks reinforced to repel each other. The strength of the repulsion is further modulated in our model by a parameter $\beta \geq 0$. When $\beta = 0$ both processes are independent symmetric random walks on $\mathbb{Z}$, and hence recurrent. We show that both random walks are further recurrent if $\beta \in (0,1]$. We also show that these processes are transient and diverge in opposite directions if $\beta > 2$. The case $\beta \in (1,2]$ remains widely open. Our results are obtained by considering the dynamical system approach to stochastic approximations.Comment: 17 pages. Added references and corrected typos. Revised the argument for the convergence to equilibria of the vector field. Improved the proof for the recurrence when beta belongs to (0,1); leading to the removal of a previous conjectur

Scaling limit for a drainage network model

We consider the two dimensional version of a drainage network model introduced by Gangopadhyay, Roy and Sarkar, and show that the appropriately rescaled family of its paths converges in distribution to the Brownian web. We do so by verifying the convergence criteria proposed by Fontes, Isopi, Newman and Ravishankar.Comment: 15 page

Lattice Gauge Theories and the Heisenberg Antiferromagnetic Chain

We study the strongly coupled 2-flavor lattice Schwinger model and the SU(2)-color QCD_2. The strong coupling limit, even with its inherent nonuniversality, makes accurate predictions of the spectrum of the continuum models and provides an intuitive picture of the gauge theory vacuum. The massive excitations of the gauge model are computable in terms of spin-spin correlators of the quantum Heisenberg antiferromagnetic spin-1/2 chain.Comment: Proceedings LATTICE99 (spin models), 3 page