Random Balls Model With Dependence

In this article, we consider a configuration of weighted random balls in $\mathbb{R}^d$ generated according to a Poisson point process. The model investigated exhibits inhomogeneity, as well as dependence between the centers and the radii and heavy tails phenomena. We investigate the asymptotic behavior of the total mass of the configuration of the balls at a macroscopic level. Three different regimes appear depending on the intensity parameters and the zooming factor. Among the three limiting fields, two are stable while the third one is a Poisson integral bridging between the two stable regimes. For some particular choices of the inhomogeneity function, the limiting fields exhibit isotropy or self-similarity.Comment: 28 page

The Interfacial-Organized Monolayer Water Hindering the Aggregation of Nanographene: Both in Stacking and Sliding Assembly Pathways

A computational investigation was carried out to understand the aggregation of nanoscale graphene with two typical assembly pathways of stacking assembly and sliding assembly in water. The interfacial-organized monolayer water film (MWF) hindering the aggregation of nanographene in both stacking and sliding assembly pathways was reported for the first time. By means of potential mean forces (PMFs) calculation, no energy barrier was observed during the sliding assembly of two graphene nanosheets, while the PMF profiles could be impacted by the contact forms of nanographene and the MWF within the interplate of two graphene nanosheets. To explore the potential physical basis of the hindering-role of self-organized interfacial water, the dynamical and structural properties as well as the status of hydrogen bonds (H-bonds) for interfacial water were investigated. We found that the compact, ordered structure and abundant H-bonds of the MWF could be taken as the fundamental aspects of the hindering-role of interfacial water for the hydrophobic assembly of nanographene. These findings are displaying a potential to further understand the hydrophobic assembly which mostly dominate the behaviors of nanomaterials, proteins etc. in aqueous solutions.Comment: 33 pages, 7 figures, 1 tabl

Phase Diagram, Scalar-Pseudoscalar Meson Behavior and Restoration of Symmetries in (2+1) Polyakov-Nambu-Jona-Lasinio Model

We explore the phase diagram and the modification of mesonic observables in a hot and dense medium using the (2+1) Polyakov-Nambu-Jona-Lasinio model. We present the phase diagram in the ($T,\,\mu_B$)-plane, with its isentropic trajectories, paying special attention to the chiral critical end point (CEP). Chiral and deconfinement transitions are examined. The modifications of mesonic observables in the medium are explored as a tool to analyze the effective restoration of chiral symmetry for different regions of the phase diagram. It is shown that the meson masses, namely that of the kaons, change abruptly near the CEP, which can be relevant for its experimental search.Comment: 25 pages, 11 figures, 2 table

Applications of Distributed Optimal Control in Economics-The Case of Forest Management

This paper presents a theoretical model to find the optimal selective-logging regime of a size-distributed forest. The law of motion of the economic model is governed by a partial differential equation that describes the evolution of the forest stock over time. To find the solution of the resulting distributed optimal control problem, we propose a numerical solution technique known as "Escalator Boxcar Train" used in Biology, for the study of dynamics of physiologically structured populations. The empirical part of the paper determines the optimal selective-logging regime of a size-distributed forest, that is, the selective logging that maximizes the discounted net benefits from timber production of a stand of pinus sylvestris, over an infinite time horizon, and compares the selective logging with the clear-cutting regime.Distributed optimal control, diameter-distributed forest, Escalator Boxcar Train.