Phase transitions for suspension flows

This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function to be real analytic or to exhibit a phase transition. We also construct an example of a potential for which the pressure has countably many phase transitions.Comment: Example 5.2 expanded. Typos corrected. Section 6.1 superced the note "Thermodynamic formalism for the positive geodesic flow on the modular surface" arXiv:1009.462

Emulsifiers as Additives in Fats: Effect on Polymorphic Transformations and Crystal Properties of Fatty Acids and Triglycerides

The role of emulsifiers in polymorphic transformations of fats and fatty acids is treated in this paper. Their effect as crystal modifiers in solution-mediated transformations (in fatty acids) is compared to that of a dynamic controller of polymorphic transformations in triglycerides. The importance of chemical structure both in the hydrophilic and in the hydrophobic moieties of the emulsifier for an inhibitory effect on phase transitions has been emphasized. The emulsifier solubility and crystallization behavior in different solvents are probably the main factors affecting its ability to interfere with the kinetics of solution-mediated transformations. On the other hand, certain requirements for a specific chemical structure of the emulsifier which provides good structure compatibility, must be met in order to affect the kinetics and mechanism of solid-solid or melt-mediated transformations. A mechanism of emulsifier incorporation in the fat and its effect in delaying the polymorphic transformation of tristearin is proposed. It has been concluded that the presence of the emulsifier does not dictate the formation of any preferred polymorph but rather controls the mobility of the molecules and their facility to undergo polymorphic transformations. The relationship between polymorphism in fats and presence of additives plays a major role in the food industry, because of the serious quality implications involved in phase transitions

Apatite - Cholesterol Agglomerates in Human Atherosclerotic Lesions

The purpose of this study was to examine the ultrastructural relationships of cholesterol crystals and apatite deposits in human atherosclerotic lesions. Segments of human aortic atherosclerotic lesions were obtained at autopsy , fixed in glutaraldehyde and dehydrated without using any organic solvents. The aortic segments were coated with carbon and subjected to various scanning electron microscope analyses. These included secondary electron imaging, back scattering of primary electrons, energy dispersive X-ray analysis of selected spots followed by area mapping of calcium and phosphorus , and cathodoluminescence. The information gathered from scanning of selected areas in the lesions by all the techniques showed that cholesterol crystals and apatite deposits are close to each other, within 10 μm distance or less. Cholesterol crystals are often surrounded by or adjacent to apatite. The results indicate that cholesterol and apatite crystals form closely linked agglomerates in human atherosclerotic lesions. Further studies are needed to determine whether precipitation of calcium and cholesterol are somehow linked during atherosclerotic lesion development

Secondary dentin formation mechanism: The effect of attrition

Human dentin consists of a primary layer produced during tooth formation in early child-hood and a second layer which first forms upon tooth eruption and continues throughout life, termed secondary dentin (SD). The effect of attrition on SD formation was considered to be confined to the area subjacent to attrition facets. However, due to a lack of three‐dimensional methodologies to demonstrate the structure of the SD, this association could not be determined. Therefore, in the current study, we aimed to explore the thickening pattern of the SD in relation to the amount of occlusal and interproximal attrition. A total of 30 premolars (50–60 years of age) with varying attrition rates were evaluated using micro‐computerized tomography. The results revealed thickening of the SD below the cementoenamel junction (CEJ), mostly in the mesial and distal aspects of the root (p < 0.05). The pattern of thickening under the tooth cervix, rather than in proximity to attrition facets, was consistent regardless of the attrition level. The amount of SD thickening mildly corre-lated with occlusal attrition (r = 0.577, p < 0.05) and not with interproximal attrition. The thickening of the SD below the CEJ coincided with previous finite element models, suggesting that this area is mostly subjected to stress due to occlusal loadings. Therefore, we suggest that the SD formation might serve as a compensatory mechanism aimed to strengthen tooth structure against deflection caused by mechanical loading. Our study suggests that occlusal forces may play a significant role in SD formation

The Analyticity of a Generalized Ruelle's Operator

In this work we propose a generalization of the concept of Ruelle operator for one dimensional lattices used in thermodynamic formalism and ergodic optimization, which we call generalized Ruelle operator, that generalizes both the Ruelle operator proposed in [BCLMS] and the Perron Frobenius operator defined in [Bowen]. We suppose the alphabet is given by a compact metric space, and consider a general a-priori measure to define the operator. We also consider the case where the set of symbols that can follow a given symbol of the alphabet depends on such symbol, which is an extension of the original concept of transition matrices from the theory of subshifts of finite type. We prove the analyticity of the Ruelle operator and present some examples

Equilibrium states for potentials with \sup\phi - \inf\phi < \htop(f)

In the context of smooth interval maps, we study an inducing scheme approach to prove existence and uniqueness of equilibrium states for potentials $\phi$ with he `bounded range' condition \sup \phi - \inf \phi < \htop, first used by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of Perron-Frobenius operators. We demonstrate that this `bounded range' condition on the potential is important even if the potential is H\"older continuous. We also prove analyticity of the pressure in this context.Comment: Added Lemma 6 to deal with the disparity between leading eigenvalues and operator norms. Added extra references and corrected some typo

Pushing the envelope in tissue engineering: Ex vivo production of thick vascularized cardiac extracellular matrix constructs

Functional vascularization is a prerequisite for cardiac tissue engineering of constructs with physiological thicknesses. We previously reported the successful preservation of main vascular conduits in isolated thick acellular porcine cardiac ventricular ECM (pcECM). We now unveil this scaffold's potential in supporting human cardiomyocytes and promoting new blood vessel development ex vivo, providing long-term cell support in the construct bulk. A custom-designed perfusion bioreactor was developed to remodel such vascularization ex vivo, demonstrating, for the first time, functional angiogenesis in vitro with various stages of vessel maturation supporting up to 1.7 mm thick constructs. A robust methodology was developed to assess the pcECM maximal cell capacity, which resembled the human heart cell density. Taken together these results demonstrate feasibility of producing physiological-like constructs such as the thick pcECM suggested here as a prospective treatment for end-stage heart failure. Methodologies reported herein may also benefit other tissues, offering a valuable in vitro setting for "thick-tissue" engineering strategies toward large animal in vivo studies.Israeli Science Foundation/1563/10Singapore National Research Foundatio

Moment inversion problem for piecewise D-finite functions

We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation with polynomial coefficients on each continuity interval. Therefore, they may be specified by a finite amount of information. This reconstruction problem has practical importance in Signal Processing and other applications. It is somewhat of a ``folklore'' that the sequence of the moments of such ``piecewise D-finite''functions satisfies a linear recurrence relation of bounded order and degree. We derive this recurrence relation explicitly. It turns out that the coefficients of the differential operator which annihilates every piece of the function, as well as the locations of the discontinuities, appear in this recurrence in a precisely controlled manner. This leads to the formulation of a generic algorithm for reconstructing a piecewise D-finite function from its moments. We investigate the conditions for solvability of the resulting linear systems in the general case, as well as analyze a few particular examples. We provide results of numerical simulations for several types of signals, which test the sensitivity of the proposed algorithm to noise

Operator renewal theory and mixing rates for dynamical systems with infinite measure

We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer operator. This was previously an intractable problem. Examples of systems covered by our results include (i) parabolic rational maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly expanding interval maps with indifferent fixed points. In addition, we give a particularly simple proof of pointwise dual ergodicity (asymptotic behaviour of $\sum_{j=1}^nL^j$) for the class of systems under consideration. In certain situations, including Pomeau-Manneville intermittency maps, we obtain higher order expansions for $L^n$ and rates of mixing. Also, we obtain error estimates in the associated Dynkin-Lamperti arcsine laws.Comment: Preprint, August 2010. Revised August 2011. After publication, a minor error was pointed out by Kautzsch et al, arXiv:1404.5857. The updated version includes minor corrections in Sections 10 and 11, and corresponding modifications of certain statements in Section 1. All main results are unaffected. In particular, Sections 2-9 are unchanged from the published versio