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

Testing Closed String Field Theory with Marginal Fields

We study the feasibility of level expansion and test the quartic vertex of closed string field theory by checking the flatness of the potential in marginal directions. The tests, which work out correctly, require the cancellation of two contributions: one from an infinite-level computation with the cubic vertex and the other from a finite-level computation with the quartic vertex. The numerical results suggest that the quartic vertex contributions are comparable or smaller than those of level four fields.Comment: 14 pages, LaTeX. v2: New references to work of Beccaria and Rampino, and Taylor. Improved numerical analysis at the end of section

Salophen and salen oxo vanadium complexes as catalysts of sulfides oxidation with H 2O 2: Mechanistic insights

The application of V(V) catalysts in oxidation of sulfides with peroxides offers an efficient procedure, that is compatible with different functional groups, and leads to good yields and selectivities. However, the understanding of the factors affecting the reactivity of different catalysts is still far to be complete. An experimental and theoretical study on a series of V(V) complexes containing variously substituted salen and salophen ligands is reported with the aim to correlate the activity of the catalysts with the electronic character of the vanadium center. The results obtained indicate that steric factors play a major role in determining the outcome of the reaction, often overcoming the electronic effects. Theoretical results suggest the intervention in the catalytic cycle of an hydroperoxo vanadium species

Ultrafast Momentum Imaging of Pseudospin-Flip Excitations in Graphene

The pseudospin of Dirac electrons in graphene manifests itself in a peculiar momentum anisotropy for photo-excited electron-hole pairs. These interband excitations are in fact forbidden along the direction of the light polarization, and are maximum perpendicular to it. Here, we use time- and angle-resolved photoemission spectroscopy to investigate the resulting unconventional hot carrier dynamics, sampling carrier distributions as a function of energy and in-plane momentum. We first show that the rapidly-established quasi-thermal electron distribution initially exhibits an azimuth-dependent temperature, consistent with relaxation through collinear electron-electron scattering. Azimuthal thermalization is found to occur only at longer time delays, at a rate that depends on the substrate and the static doping level. Further, we observe pronounced differences in the electron and hole dynamics in n-doped samples. By simulating the Coulomb- and phonon-mediated carrier dynamics we are able to disentangle the influence of excitation fluence, screening, and doping, and develop a microscopic picture of the carrier dynamics in photo-excited graphene. Our results clarify new aspects of hot carrier dynamics that are unique to Dirac materials, with relevance for photo-control experiments and optoelectronic device applications.Comment: 23 pages, 12 figure

A solution to the 4-tachyon off-shell amplitude in cubic string field theory

We derive an analytic series solution of the elliptic equations providing the 4-tachyon off-shell amplitude in cubic string field theory (CSFT). From such a solution we compute the exact coefficient of the quartic effective action relevant for time dependent solutions and we derive the exact coefficient of the quartic tachyon coupling. The rolling tachyon solution expressed as a series of exponentials $e^t$ is studied both using level-truncation computations and the exact 4-tachyon amplitude. The results for the level truncated coefficients are shown to converge to those derived using the exact string amplitude. The agreement with previous work on the subject, both on the quartic tachyon coupling and on the CSFT rolling tachyon, is an excellent test for the accuracy of our off-shell solution.Comment: 26 pages, 5 figure

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)

La cooperazione transfrontaliera tra Italia e Tunisia: esperienze e prospettive

The article presents the main results of a field research conducted be-tween 2012 and 2013 on the Italy-Tunisia border, aimed at investigating regional development options through policies and practices of cross-border cooperation. Starting from the specific context of the Italy-Tunisia border, the article presents the main aims, achievements, limits and prospects for cross-border cooperation across the channel of Sicily, also in light of the perceptions and expectations of local private and public stakeholders. The priorities to be addressed at different scales in order to improve the impact of the cooperation between Sicily and Tunisia in-clude, in our opinion, the support to democratization in Tunisia and to the local civil society; to pay attention to the social as well as the eco-nomic aspects of cooperation; to ensure to local actors both political and financial support; to improve the cross-border cooperation instrument through a better targeting; the setting of a coherent multilevel political framework for addressing each of these issues effectively