Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Internal Model Principle: extension to the switching case and applications

This thesis deals with a novel control approach based on the extension of the well-known Internal Model Principle to the case of periodic switched linear exosystems. This extension, inspired by power electronics applications, aims to provide an effective design method to robustly achieve the asymptotic tracking of periodic references with an infinite number of harmonics. In the first part of the thesis the basic components of the novel control scheme are described and preliminary results on stabilization are provided. In the second part, advanced control methods for two applications coming from the world high energy physics are presented.

The notion of equivalence and lexical cohesion in the translation of political speeches

Abstract This dissertation investigates the notion of equivalence with particular reference to lexical cohesion in the translation of political speeches. Lexical cohesion poses a particular challenge to the translators of political speeches and thus preserving lexical cohesion elements as one of the major elements of cohesion is undoubtedly crucial to their translation equivalence. We rely on Halliday’s (1994) classification of lexical cohesion which comprises: repetition, synonymy, antonymy, meronymy and hyponymy. Other traditional models of lexical cohesion are examined. We include Grammatical Parallelism for its role in creating textual semantic unity which is what cohesion is all about. The study shed light on the function of lexical cohesion elements as rhetorical device. The study also deals with lexical problems resulting from the transfer of lexical cohesion elements from the SL into the TL, which is often beset by many problems that most often result from the differences between languages. Three key issues are identified as being fundamental to equivalence and lexical cohesion in the translation of political speeches: sociosemiotic approach, register analysis, rhetoric, and poetic function. The study also investigates the lexical cohesion elements in the translation of political speeches from English into Arabic, Italian and French in relation to ideology, and its control, through bias and distortion. The findings are discussed, implications examined and topics for further research suggested.

The problems of equivalence in advertising translation: examples from English and Russian

Abstract The academic environment has recently recognized the importance and benefits that an extensive research on the translation of advertising can have for translation studies. Despite the growing interest and increasing research activity in the field it is still difficult to speak about a theory of advertising translation in general. There is a need for further study encompassing different languages and both heterogeneous and homogenous cultures that will give the possibility to receive a more complete map of what the translation of advertising is and should be. Previous studies have been concentrated, for the most part, on Western European language pairs. This study is a research into perfume and cosmetics print advertisements translated from English into Russian where both visual and verbal elements are considered. Three broad translation approaches have been identified in what concerns the verbal message: Translated message, parallel translation, recreated adverts, and three approaches in dealing with the image: similar images, modified images, completely different images. The thesis shows that where Russian advertisements for perfume products tend to have a message, or create one, this is often lacking in the English copy. The article ends by suggesting that perfume advertisements favor the standardization approach when entering Russian market. The attempts to localize the advert have also been noticed although they are obviously less numerous in perfume adverts and are rather instances of adaptation - a mix between the localization and standardization approaches since they keep drawing on the same globally accepted universals about female beauty and concern for ‘woman’s identity’ (we focused our analysis on products designed for female consumers). This study, complementing previous studies, aims to be a contribution to the description of laws and strategies that guide the translation of advertising texts into Russian.