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Showing 1 to 8 of 8 for “"Thermodynamic Formalism"”.
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Maps of intervals with indifferent fixed points: thermodynamic formalism and phase transitions
We develop the thermodynamic formalism for a large class of maps of the interval with indifferent fixed points. For such systems the formalism yields one-dimensional systems with many-body infinite range interactions for which the thermodynamics is well defined while the Gibbs states are not. …
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Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type
… the cosh family. We shall build a version of thermodynamic formalism for functions in H and we shall show among others, the existence and uniqueness of a conformal measure. Then we prove a Bowen's type formula, i.e. we show that the Hausdorff dimension of the set of returning points, is the …
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An Irreversible Thermodynamic Formalism of the Electronic Contribution to the Entropy in Metals
We have applied an irreversible thermodynamic formalism to quantify the electronic contribution to the entropy in metals and alloys. We demonstrate the utility in our proposed approach by rationalizing the entropy of phase transitions in metal-insulator, order-disorder, and allotropic transitions …
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Equilibrium Measures for Symbolic Spaces Using Dimension Theory
The theory of thermodynamic formalism is well developed for subshifts of finite type. However, less is known about equilibrium measures for more general shift spaces beyond existence and, in some cases, uniqueness. Rather than constructing equilibrium measures as a limit of a sequence of measures …
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Quantization Dimension for Probability Definitions
… measures. This framework uses the theory of thermodynamic formalism and the multifractal spectrum. It is shown that at least in certain cases the quantization dimension function D(r)=Dr is a transform of the temperature function b(q), which is already known to be the Legendre transform of the …
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Accurate FE-simulation of three-dimensional microstructures
… differential equations and are derived by a thermodynamic formalism. Besides a FE-formulation for thermal problems we give a <br>more general presentation also comprising coupled <br>thermo-electro-mechanical multi-layered plate problems which for MEMS make <br>great demands on the …
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d-bar continuity beyond subshifts of finite type
The main result of this thesis is that for a mixing countable state Markov shift, the map taking a strongly positive recurrent potential to its Ruelle-Perron-Frobenius (RPF) measure is continuous in the $\overline{d}$-metric on the space of measures and the metric coming from the Hölder norm on the …
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Physics and Chemistry Based Constitutive Framework for Thermo-Chemo-Mechanical Responses of Polymeric Materials
… develop predictive physics- and chemistry-based, thermodynamically consistent constitutive frameworks to evaluate their response under extreme environmental condition. A series of interconnected experimental, theoretical, and numerical studies were developed regarding the chemical, morphological, …