L2L^2-stability near equilibrium for the 44 waves kinetic equation

We consider the four waves spatial homogeneous kinetic equation arising in wave turbulence theory. We study the long-time behaviour and existence of solutions around the Rayleigh-Jeans equilibrium solutions. For cut-off'd frequencies, we show that for dispersion relations weakly perturbed around the quadratic case, the linearized operator around the Rayleigh-Jeans equilibria is coercive. We then pass to the fully nonlinear operator, showing an $L^2$ - stability for initial data close to Rayleigh-Jeans.Comment: 23 pages, 1 figur

The economic valuation, pricing and promotion of recycled water

This thesis topic is the evaluation of recycled water in Crete, Greece. Recycled water is a derivative of fresh water and as such it can be regarded as a good of a similar nature to fresh water (at least for some of its uses such as irrigation). The departure point for this research was given by specific articles and principles of the 60/2000 Water Framework Directive. According to them, recycled water evaluation can be viewed as a corollary of this directive. Since Crete is a European region with intense water shortage problems, this was a good opportunity to apply the suggestions of the directive: solve the problem of water shortage internally (i. e. in Crete, with the island's own means and plans, since Crete can be regarded as a single river basin district), make the most of marginal waters while at the same time enhancing the environment. The evaluation of recycled water has been implemented through the involvement of two distinctive groups of people: farmers and consumers. Therefore, on the one hand, the research asks farmers whether they would be willing to use recycled water of certain qualities for the irrigation of olive trees and tomatoes and on the other hand, the research asks consumers whether they would be willing to use and pay for food products irrigated with recycled water. Results show there is social acquiescence on recycled water usage. This is confirmed by the correspondence of willingness to use recycled water between farmers and consumers. Conclusions from the willingness to use and willingness to pay models provide useful pricing and marketing signals for recycled water. Besides the evaluation of recycled water, another part of the research dealt with the role water plays in the production of olive oil and the confirmation of irrigation water shortages

Quantitative studies and Hydrodynamical limits for interacting particle systems

The main results of my work contribute to the mathematical study of microscopic non-equilibrium systems that were first introduced in order to derive macroscopic physical laws such as Fourier's law. In particular the main objective is to determine the scaling of the spectral gap, i.e. the relaxation rate, in terms of the number of the particles for a paradigmatic model describing heat transport, the chain of oscillators. The mathematical study of this model started at the end of $90$s and it is challenging due to the degeneracy of the dynamics as the noise is not assumed to act to all the degrees of freedom, leading to lack of ellipticity and coercivity. We give bounds on the spectral gap for weak nonlinearities of the chain, i.e. perturbations around linear homogeneous chains and also a complete answer for the linear, homogeneous and disordered, chain of oscillators as well as $d$-dimensional grids of oscillators. The methods range from hypocoercivity inspired techniques, in the sense of Villani, to spectral analysis of discrete Schrödinger operators. Moreover we study heat conduction in gases addressing, with both analytic and probabilistic techniques, the question of the existence, and properties, of a non-equilibrium steady state for the nonlinear BGK model, introduced by Bhatnagar, Gross and Krook, with diffusive boundary conditions. The case that we address concerns large boundary temperatures away from the equilibrium case. Furthermore, besides non-equilibrium phenomena in many particle systems, this thesis deals with the question of deriving nonlinear diffusion equations from microscopic stochastic processes. We present a new, quantitative, unified method to show that the particle densities of one-dimensional processes on a periodic lattice, including the zero-range and simple exclusion jump processes as well as diffusion processes of Ginzburg-Landau type, converge to the solution of a nonlinear diffusion equation with an explicit, uniform in time, convergence rate. We discuss how we can extend the result to all the dimensions. Finally a study of the scaling of the spectral gap for all the mean field $\mathcal{O}(n)$ models of Ginzburg-Landau type using semiclassical tools, is included in this thesis. This concerns the spectral gap as a function of the number of particles, spins, for the dynamics below and at the critical temperature, with and without an external magnetic field.EPSR

Economic valuation in Web surveys:A review of the state of the art and best practices

This paper is a review of the currently existent economic valuation surveys (with stated preference methods) developed for and administered through the web. Valuation surveys that employ stated preference techniques are not particularly verbose about the details of their web development or administration. Web surveys for economic valuation are a new, interest raising field, given the worldwide continually increasing computer literacy and internet access. Currently most web valuation studies are concerned with the valuation of a topic of interest (mostly from environmental and energy economics) and hardly few, if any at all, are concerned with the experimentation on the web opportunities themselves and the effect they have on the results of the studies. The paper also presents the advantages of web survey and contributes to consolidating an informed state of the art for field practitioners, developers and reviewers of relevant papers

Properties of Non-Equilibrium Steady States for the non-linear BGK equation on the torus

We study the non-linear BGK model in 1d coupled to a spatially varying thermostat. We show existence, local uniqueness and linear stability of a steady state when the linear coupling term is large compared to the non-linear self interaction term. This model possesses a non-explicit spatially dependent non-equilibrium steady state. We are able to successfully use hypocoercivity theory in this case to prove that the linearised operator around this steady state posesses a spectral gap.Comment: 41 page

Sustainable technologies in Greek tourist accommodation : a quantitative review

This paper is the second part of a review on sustainable technologies pertinent in Greek tourist accommodation. The first part was a qualitative review while the current paper is a quantitative review. Namely, this paper provides figures and data that describe the quantitative picture of sustainable hotels in Greece. The topic is unique because the analysis presented herein has been largely fragmented in various reports, webpages and the records of relevant organizations. The reason we focus on Greek reality is the importance of tourism for the Greek economy. This review will help first hoteliers to benchmark their businesses to the ideal sustainable reference point and second policy makers to obtain a quantitative overview of hotel sustainability in Greece and provide insight as to the measures that should be established for the promotion and improvement of sustainability in Greek hotels and the subsequent design of useful measures and policies.peer-reviewe

Spectral analysis and phase transitions for long-range interactions in harmonic chains of oscillators

We consider chains of $N$ harmonic oscillators in two dimensions coupled to two Langevin heat reservoirs at different temperatures - a classical model for heat conduction introduced by Lebowitz, Lieb, and Rieder \cite{RLL67}. We extend our previous results \cite{BM20} significantly by providing a full spectral description of the full Fokker-Planck operator allowing also for the presence of a constant external magnetic field for charged oscillators. We then study oscillator chains with additional next-to-nearest-neighbor interactions and find that the spectral gap undergoes a phase transition if the next-to-nearest-neighbour interactions are sufficiently strong and may even cease to exist for oscillator chains of finite length

Quantitative Rates of Convergence to Non-equilibrium Steady State for a Weakly Anharmonic Chain of Oscillators

AbstractWe study a 1-dimensional chain of N weakly anharmonic classical oscillators coupled at its ends to heat baths at different temperatures. Each oscillator is subject to pinning potential and it also interacts with its nearest neighbors. In our set up both potentials are homogeneous and bounded (with N dependent bounds) perturbations of the harmonic ones. We show how a generalised version of Bakry–Emery theory can be adapted to this case of a hypoelliptic generator which is inspired by Baudoin (J Funct Anal 273(7):2275-2291, 2017). By that we prove exponential convergence to non-equilibrium steady state in Wasserstein–Kantorovich distance and in relative entropy with quantitative rates. We estimate the constants in the rate by solving a Lyapunov-type matrix equation and we obtain that the exponential rate, for the homogeneous chain, has order bigger than $$N^{-3}$$ N - 3 . For the purely harmonic chain the order of the rate is in $$[N^{-3},N^{-1}]$$ [ N - 3 , N - 1 ] . This shows that, in this set up, the spectral gap decays at most polynomially with N.</jats:p