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

Non equilibrium stationary state for the SEP with births and deaths

We consider the symmetric simple exclusion process in the interval \La_N:=[-N,N]\cap\mathbb Z with births and deaths taking place respectively on suitable boundary intervals $I_+$ and $I_-$, as introduced in De Masi et al. (J. Stat. Phys. 2011). We study the stationary measure density profile in the limit $N\to\infty

The subgrid-scale scalar variance under supercritical pressure conditions

To model the subgrid-scale (SGS) scalar variance under supercritical-pressure conditions, an equation is first derived for it. This equation is considerably more complex than its equivalent for atmospheric-pressure conditions. Using a previously created direct numerical simulation (DNS) database of transitional states obtained for binary-species systems in the context of temporal mixing layers, the activity of terms in this equation is evaluated, and it is found that some of these new terms have magnitude comparable to that of governing terms in the classical equation. Most prominent among these new terms are those expressing the variation of diffusivity with thermodynamic variables and Soret terms having dissipative effects. Since models are not available for these new terms that would enable solving the SGS scalar variance equation, the adopted strategy is to directly model the SGS scalar variance. Two models are investigated for this quantity, both developed in the context of compressible flows. The first one is based on an approximate deconvolution approach and the second one is a gradient-like model which relies on a dynamic procedure using the Leonard term expansion. Both models are successful in reproducing the SGS scalar variance extracted from the filtered DNS database, and moreover, when used in the framework of a probability density function (PDF) approach in conjunction with the β-PDF, they excellently reproduce a filtered quantity which is a function of the scalar. For the dynamic model, the proportionality coefficient spans a small range of values through the layer cross-stream coordinate, boding well for the stability of large eddy simulations using this model

Optimal multi-objective discrete decision making using a multidirectional modified Physarum solver

This paper will address a bio-inspired algorithm able to incrementally grow decision graphs in multiple directions for discrete multi-objective optimization. The algorithm takes inspiration from the slime mould Physarum Polycephalum, an amoeboid organism that in its plasmodium state extends and optimizes a net of veins looking for food. The algorithm is here used to solve multi-objective Traveling Salesman and Vehicle Routing Problems selected as representative examples of multi-objective discrete decision making problems. Simulations on selected test case showed that building decision sequences in two directions and adding a matching ability (multidirectional approach) is an advantageous choice if compared with the choice of building decision sequences in only one direction (unidirectional approach). The ability to evaluate decisions from multiple directions enhances the performance of the solver in the construction and selection of optimal decision sequences