Large deviations of the empirical flow for continuous time Markov chains

We consider a continuous time Markov chain on a countable state space and prove a joint large deviation principle for the empirical measure and the empirical flow, which accounts for the total number of jumps between pairs of states. We give a direct proof using tilting and an indirect one by contraction from the empirical process.Comment: Minor revision, to appear on Annales de l'Institut Henri Poincare (B) Probability and Statistic

Large deviation principles for nongradient weakly asymmetric stochastic lattice gases

We consider a lattice gas on the discrete d-dimensional torus $(\mathbb{Z}/N\mathbb{Z})^d$ with a generic translation invariant, finite range interaction satisfying a uniform strong mixing condition. The lattice gas performs a Kawasaki dynamics in the presence of a weak external field E/N. We show that, under diffusive rescaling, the hydrodynamic behavior of the lattice gas is described by a nonlinear driven diffusion equation. We then prove the associated dynamical large deviation principle. Under suitable assumptions on the external field (e.g., E constant), we finally analyze the variational problem defining the quasi-potential and characterize the optimal exit trajectory. From these results we deduce the asymptotic behavior of the stationary measures of the stochastic lattice gas, which are not explicitly known. In particular, when the external field E is constant, we prove a stationary large deviation principle for the empirical density and show that the rate function does not depend on E.Comment: Published in at http://dx.doi.org/10.1214/11-AAP805 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Large deviations for a stochastic model of heat flow

We investigate a one dimensional chain of $2N$ harmonic oscillators in which neighboring sites have their energies redistributed randomly. The sites $-N$ and $N$ are in contact with thermal reservoirs at different temperature $\tau_-$ and $\tau_+$. Kipnis, Marchioro, and Presutti \cite{KMP} proved that this model satisfies {}Fourier's law and that in the hydrodynamical scaling limit, when $N \to \infty$, the stationary state has a linear energy density profile $\bar \theta(u)$, $u \in [-1,1]$. We derive the large deviation function $S(\theta(u))$ for the probability of finding, in the stationary state, a profile $\theta(u)$ different from $\bar \theta(u)$. The function $S(\theta)$ has striking similarities to, but also large differences from, the corresponding one of the symmetric exclusion process. Like the latter it is nonlocal and satisfies a variational equation. Unlike the latter it is not convex and the Gaussian normal fluctuations are enhanced rather than suppressed compared to the local equilibrium state. We also briefly discuss more general model and find the features common in these two and other models whose $S(\theta)$ is known.Comment: 28 pages, 0 figure

Large deviations for diffusions: Donsker-Varadhan meet Freidlin-Wentzell

We consider a diffusion process on $\mathbb R^n$ and prove a large deviation principle for the empirical process in the joint limit in which the time window diverges and the noise vanishes. The corresponding rate function is given by the expectation of the Freidlin-Wentzell functional per unit of time. As an application of this result, we obtain a variational representation of the rate function for the Gallavotti-Cohen observable in the small noise and large time limits

scale adaptive simulations of a swirl stabilized spray flame using flamelet generated manifold

Abstract The present work describes the main findings derived from CFD simulations of the swirl stabilized spray flame experimentally investigated by Sheen [1] . Scale Adaptive Simulations (SAS) have been performed using Flamelet Generated Manifold (FGM) for combustion modelling and a Eulerian-Lagrangian approach for liquid phase description. Results highlight the capabilities of SAS in predicting the main characteristics of the analysed turbulent spray flame, leading to appreciable enhancements with respect to RANS results in terms of both velocity and temperature distributions

Analysis of the GT26 single-shaft gas turbine performance and emissions

Abstract The progressive developments in terms of gas turbine materials as well as blade cooling systems have led to a continuous growth in the turbine inlet temperature (TIT) and the overall pressure ratio (OPR). This means higher thermal efficiency and power output. Other techniques to achieve better performance can be the adoption of a heat recovery system, an intercooler system or the reheat, as well as a combined cycle application. Furthermore, the higher the TIT and OPR the higher the NOx emissions. Nowadays, with an always stricter emissions legislation, it is particularly important to keep emission levels as low as possible. In the present work, a performance analysis has been conducted with the in-house modular tool ESMS (Equation Solver Modular System). The software simply represents the engine with separate blocks, solving the energy and the continuity equations. Firstly, the design process has been performed on the Ansaldo Energia GT26 machine, equipped with reheat, based on the manufacturer datasheet. Secondly, off-design simulations have been done, changing respectively the fuel mass flow in the 1st burner (EV) and in the 2nd burner (SEV). Therefore, both TIT and power output change. A sensitivity analysis of the thermal efficiency η and the power output with respect to both fuel flows shows how, for part load operations with a half of the design power output, it is better to change the SEV fuel flow only. It can also demonstrate that the high-pressure turbine (HPT) power output is more insensitive to SEV fuel flow than the low-pressure turbine (LPT) one. EV fuel flow variations affect both the HPT and the LPT behaviour. Eventually, a correlation for the NOx emissions has been characterized and results illustrate that NOx emissions are strictly related to the EV fuel flow: in fact, the O2 level in the SEV burner is sensibly lower than in the first one, thus contributing to lower emissions

Lagrangian phase transitions in nonequilibrium thermodynamic systems

In previous papers we have introduced a natural nonequilibrium free energy by considering the functional describing the large fluctuations of stationary nonequilibrium states. While in equilibrium this functional is always convex, in nonequilibrium this is not necessarily the case. We show that in nonequilibrium a new type of singularities can appear that are interpreted as phase transitions. In particular, this phenomenon occurs for the one-dimensional boundary driven weakly asymmetric exclusion process when the drift due to the external field is opposite to the one due to the external reservoirs, and strong enough.Comment: 10 pages, 2 figure

methane swirl stabilized lean burn flames assessment of scale resolving simulations

Abstract The reliable prediction of the turbulent combustion process in lean flames is of paramount importance in the design of gas turbine combustors. The present work presents an assessment of the capabilities of Flamelet Generated Manifold (FGM) in the framework of Reynolds-Averaged Navier-Stokes (RANS) and Large-Eddy Simulation (LES) At this purpose the TECFLAM swirl burner consisting of a strongly swirling, unconfined natural gas flame was chosen. Results highlight that RANS-FGM succeeds in predicting the main characteristics of the reacting flow field and species concentrations. However, only LES is capable of reproducing the actual turbulent mixing between swirling flow and co-flow, thus leading to appreciable enhancements with respect to RANS results