A Liv\v{s}ic-type theorem and some regularity properties for nonadditive sequences of potentials

We study some notions of cohomology for asymptotically additive sequences and prove a Liv\v{s}ic-type result for almost additive sequences of potentials. As a consequence, we are able to characterize almost additive sequences based on their equilibrium measures and also show the existence of almost (and asymptotically) additive sequences of H\"older continuous functions satisfying the bounded variation condition (with a unique equilibrium measure) and which are not physically equivalent to any additive sequence generated by a H\"older continuous function. None of these examples were previously known, even in the case of full shifts of finite type. Moreover, we also use our main result to suggest a classification of almost additive sequences based on physical equivalence relations with respect to the classical additive setup.Comment: 36 page

Nonadditive families of potentials: physical equivalence and some regularity relations

We show that additive and asymptotically additive families of continuous functions with respect to suspension flows are physically equivalent. In particular, the equivalence result holds for hyperbolic flows and some classes of expansive flows in general. Moreover, we show how this equivalence result can be used to extend the nonadditive thermodynamic formalism and multifractal analysis. In the second part of this work, we obtain a Liv\v{s}ic-like result for nonadditive families of potentials and also address the H\"older and Bowen regularity problem for the physical equivalence relations with respect to hyperbolic symbolic flows.Comment: This material is a substantial upgrade on the previous submission "Asymptotically additive families of functions and a physical equivalence problem for flows" (68 pages

Hyperbolicity and Recurrence in Dynamical Systems: A Survey of Recent ResuIts

We discuss selected topics of current research interest in the theory of dynamical systems, with emphasis on dimension theory, multifractal analysis, and quantitative recurrence

Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres

The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, $\Delta s$, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), $s_\text{ex}$, and the pair-correlation contribution, $s_2$. Thus, the RMPE represents the net contribution to $s_\text{ex}$ due to spatial correlations involving three, four, or more particles. A heuristic `ordering' criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension $1<d<3$ has been proposed [Santos, A.; L\'opez de Haro, M. \emph{Phys. Rev. E} \textbf{2016}, \emph{93}, 062126]. The aim of this work is to use this approach to evaluate the RMPE as a function of both $d$ and the packing fraction $\phi$. It is observed that, for any given dimensionality $d$, the RMPE takes negative values for small densities, reaches a negative minimum $\Delta s_{\text{min}}$ at a packing fraction $\phi_{\text{min}}$, and then rapidly increases, becoming positive beyond a certain packing fraction $\phi_0$. Interestingly, while both $\phi_{\text{min}}$ and $\phi_0$ monotonically decrease as dimensionality increases, the value of $\Delta s_{\text{min}}$ exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality $d\simeq 2.38$. A plot of the scaled RMPE $\Delta s/|\Delta s_{\text{min}}|$ shows a quasiuniversal behavior in the region $-0.14\lesssim\phi-\phi_0\lesssim 0.02$.Comment: 10 pages, 3 figures; v2: minor change

The Nonadditive Generalization of Klimontovich's S-Theorem for Open Systems and Boltzmann's Orthodes

We show that the nonadditive open systems can be studied in a consistent manner by using a generalized version of S-theorem. This new generalized S-theorem can further be considered as an indication of self-organization in nonadditive open systems as prescribed by Haken. The nonadditive S-theorem is then illustrated by using the modified Van der Pol oscillator. Finally, Tsallis entropy as an equilibrium entropy is studied by using Boltzmann's method of orthodes. This part of dissertation shows that Tsallis ensemble is on equal footing with the microcanonical, canonical and grand canonical ensembles. However, the associated entropy turns out to be Renyi entropy

Network Topology in Water Nanoconfined between Phospholipid Membranes

Water provides the driving force for the assembly and stability of many cellular components. Despite its impact on biological functions, a nanoscale understanding of the relationship between its structure and dynamics under soft confinement has remained elusive. As expected, water in contact with biological membranes recovers its bulk density and dynamics at ∼1 nm from phospholipid headgroups but surprisingly enhances its intermediate range order (IRO) over a distance, at least, twice as large. Here, we explore how the IRO is related to the water’s hydrogen-bond network (HBN) and its coordination defects. We characterize the increased IRO by an alteration of the HBN up to more than eight coordination shells of hydration water. The HBN analysis emphasizes the existence of a bound–unbound water interface at ∼0.8 nm from the membrane. The unbound water has a distribution of defects intermediate between bound and bulk water, but with density and dynamics similar to bulk, while bound water has reduced thermal energy and many more HBN defects than low-temperature water. This observation could be fundamental for developing nanoscale models of biological interactions and for understanding how alteration of the water structure and topology, for example, due to changes in extracellular ions concentration, could affect diseases and signaling. More generally, it gives us a different perspective to study nanoconfined water

Fabrications and Applications of Micro/nanofluidics in Oil and Gas Recovery: A Comprehensive Review

Understanding fluid flow characteristics in porous medium, which determines the development of oil and gas oilfields, has been a significant research subject for decades. Although using core samples is still essential, micro/nanofluidics have been attracting increasing attention in oil recovery fields since it offers direct visualization and quantification of fluid flow at the pore level. This work provides the latest techniques and development history of micro/nanofluidics in oil and gas recovery by summarizing and discussing the fabrication methods, materials and corresponding applications. Compared with other reviews of micro/nanofluidics, this comprehensive review is in the perspective of solving specific issues in oil and gas industry, including fluid characterization, multiphase fluid flow, enhanced oil recovery mechanisms, and fluid flow in nano-scale porous media of unconventional reservoirs, by covering most of the representative visible studies using micro/nanomodels. Finally, we present the challenges of applying micro/nanomodels and future research directions based on the work