Exploring families of energy-dissipation landscapes via tilting -- Three types of EDP convergence

This paper revolves around a subtle distinction between two concepts: passing to the limit in a family of gradient systems, on one hand, and deriving effective kinetic relations on the other. The two concepts are strongly related, and in many examples they even appear to be the same. Our main contributions are to show that they are different, to show that well-known techniques developed for the former may give incorrect results for the latter, and to introduce new tools to remedy this. The approach is based on the Energy-Dissipation Principle that provides a variational formulation to gradient-flow equations that allows one to apply techniques from Γ-convergence of functional on states and functionals on trajectories

A framework of nonequilibrium statistical mechanics. II. Coarse-graining

For a given thermodynamic system, and a given choice of coarse-grained state variables, the knowledge of a force-flux constitutive law is the basis for any nonequilibrium modeling. In the first paper of this series we established how, by a generalization of the classical fluctuation-dissipation theorem (FDT), the structure of a constitutive law is directly related to the distribution of the fluctuations of the state variables. When these fluctuations can be expressed in terms of diffusion processes, one may use Green-Kubo-type coarse-graining schemes to find the constitutive laws. In this paper we propose a coarse-graining method that is valid when the fluctuations are described by means of general Markov processes, which include diffusions as a special case. We prove the success of the method by numerically computing the constitutive law for a simple chemical reaction $A \rightleftarrows B$. Furthermore, we show that one cannot find a consistent constitutive law by any Green-Kubo-like scheme.Comment: This paper and its precursor (I) replace the previous paper arXiv:1809.07253. Now the content and the presentation style are more targeted to physicists, with particular emphasis on the applications to specific physical systems. The theoretical and the practical aspects have been separated from each other in the two paper

A framework of nonequilibrium statistical mechanics. I. Role and type of fluctuations

Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processes and elaborate the general recipes for evaluating dynamic material properties, which characterize force-flux constitutive laws, by statistical mechanics. Markov processes with continuous trajectories are conveniently characterized by stochastic differential equations and lead to Green-Kubo-type formulas for dynamic material properties. Markov processes with discontinuous jumps include transitions over energy barriers with the rates calculated by Kramers. We describe a unified approach to Markovian fluctuations and demonstrate how the appropriate type of fluctuations (continuous versus discontinuous) is reflected in the mathematical structure of the phenomenological equations.Comment: This paper and its continuation (II) replace the previous paper arXiv:1809.07253. Now the content and the presentation style are more targeted to physicists, with particular emphasis on the applications to specific physical systems. The theoretical and the practical aspects have been separated from each other in the two paper

Singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities

We consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities. The dependence on the spatial coordinates comes from the presence of a potential and of a function representing a saturation effect. We investigate the existence of nontrivial nonnegative solutions concentrating around local minima of both the potential and of the saturation function. Necessary conditions to locate the possible concentration points are also given

Education in mine waste engineering: the experience of "SIGEO" Master's Course

On 19th July 1985 the failure of two tailings dams at the service of a fluorite mine in the Stava Valley (Italy) caused the death of 268 people and severe environmental and socioeconomic damage. Similar accidents have happened in Sgorigrad (Bulgaria, 1966), Aberfan (U.K., 1966), Buffalo Creek (USA, 1972), Aznalcollar (Spain, 1998), Taoshi (China, 2008) and many other places worldwide. The European Union has recognized the seriousness of the problems concerning the management and disposal of mining waste (over 400 million tonnes per year worldwide). With the 2006/21/CE Directive, the EU has urged all member States to carry out censuses, monitoring and consolidation of existing structures under the supervision of qualified experts. These experts should be provided with interdisciplinary knowledge that is difficult to attain during normal degree courses. For this reason, the Trento and Modena-Reggio Emilia Universities and the Turin Polytechnic have set up a post-graduate Master’s Course in “Analysis and Management of Geotechnical Structures”. The article describes the interdisciplinary approach adopted in the course and aims to stimulate the sharing of this initiative among other European Universities

FTY720/fingolimod decreases hepatic steatosis and expression of fatty acid synthase in diet-induced nonalcoholic fatty liver disease in mice

Nonalcoholic fatty liver disease (NAFLD), a leading cause of liver dysfunction, is a metabolic disease that begins with steatosis. Sphingolipid metabolites, particularly ceramide and sphingosine-1-phosphate (S1P), have recently received attention for their potential roles in insulin resistance and hepatic steatosis. FTY720/fingolimod, a prodrug for the treatment of multiple sclerosis, is phosphorylated in vivo to its active phosphorylated form by sphingosine kinase 2 and has been shown to interfere with the actions of S1P and to inhibit ceramide biosynthesis. Therefore, in this study we investigated the effects of FTY720 in a diet-induced animal model of NAFLD (DIAMOND) that recapitulates the hallmarks of the human disease. The oral administration of FTY720 to these mice fed a high-fat diet and sugar water improved glucose tolerance and reduced steatosis. In addition to decreasing liver triglycerides, FTY720 also reduced hepatic sphingolipid levels, including ceramides, monohexosylceramides, and sphingomyelins, particularly the C16:0 and C24:1 species, as well as S1P and dihydro-S1P. FTY720 administration decreased diet-induced fatty acid synthase (FASN) expression in DIAMOND mice without affecting other key enzymes in lipogenesis. FTY720 had no effect on the expression of SREBP-1c, which transcriptionally activates FASN. However, in agreement with the notion that the active phosphorylated form of FTY720 is an inhibitor of histone deacetylases, FTY720-P accumulated in the liver, and histone H3K9 acetylation was markedly increased in these mice. Hence, FTY720 might be useful for attenuating FASN expression and triglyceride accumulation associated with steatosis. Keywords: lipogenesis; sphingolipids; sphingosine-1-phosphate