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169
result(s) for
"Phase rule and equilibrium"
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Brownian regularity for the Airy line ensemble, and multi-polymer watermelons in Brownian last passage percolation
The Airy line ensemble is a positive-integer indexed system of random continuous curves whose finite dimensional distributions are
given by the multi-line Airy process. It is a natural object in the KPZ universality class: for example, its highest curve, the
Airy
In this paper, we employ the Brownian Gibbs property to make a close
comparison between the Airy line ensemble’s curves after affine shift and Brownian bridge, proving the finiteness of a superpolynomially
growing moment bound on Radon-Nikodym derivatives.
We also determine the value of a natural exponent describing in Brownian last
passage percolation the decay in probability for the existence of several near geodesics that are disjoint except for their common
endpoints, where the notion of ‘near’ refers to a small deficit in scaled geodesic energy, with the parameter specifying this nearness
tending to zero.
To prove both results, we introduce a technique that may be useful elsewhere for finding upper bounds on
probabilities of events concerning random systems of curves enjoying the Brownian Gibbs property.
Several results in this article
play a fundamental role in a further study of Brownian last passage percolation in three companion papers (Hammond 2017a,b,c), in which
geodesic coalescence and geodesic energy profiles are investigated in scaled coordinates.
eBook
MAX phases : properties of machinable ternary carbides and nitrides
In this comprehensive yet compact monograph, Michel W. Barsoum, one of the pioneers in the field and the leading figure in MAX phase research, summarizes and explains, from both an experimental and a theoretical viewpoint, all the features that are necessary to understand and apply these new materials. The book covers elastic, electrical, thermal, chemical and mechanical properties in different temperature regimes. By bringing together, in a unifi ed, self-contained manner, all the information on MAX phases hitherto only found scattered in the journal literature, this one-stop resource offers researchers and developers alike an insight into these fascinating materials.
eBook
CRC Handbook of Phase Equilibria and Thermodynamic Data of Polymer Solutions at Elevated Pressures
Thermodynamic data of polymer solutions are paramount for industrial and laboratory processes. These data also serve to understand the physical behavior of polymer solutions, study intermolecular interactions, and gain insights into the molecular nature of mixtures. Nearly a decade has passed since the release of a similar CRC Handbook and since then a large amount of new experimental data have been published, which is now compiled in this book. This book features nearly 500 newly published references containing approximately 175 new vapor-liquid equilibrium data sets, 25 new liquid-liquid equilibrium data sets, 540 new high-pressure fluid phase equilibrium data sets, 60 new data sets describing PVT properties of polymers, and 20 new data sets with densities or excess volumes.The book is a valuable resource for researchers, specialists, and engineers working in the fields of polymer science, physical chemistry, chemical engineering, materials science, biological science and technology, and those developing computerized predictive packages.
eBook
IP-x,y/I Equilibrium Data of the Binary Systems of 2-Propanol, 1-Butanol and 2-Butanol with Carbon Dioxide at 313.15 K and 333.15 K
The ability to predict the behaviour of high-pressure mixtures of carbon dioxide and alcohol is important for industrial purposes. The equilibrium composition of three binary carbon dioxide-alcohol systems was measured at temperatures of 313.15 K and 333.15 K and at pressures of up to 100 bar for carbon dioxide-2-propanol, up to 160 bar for carbon dioxide-1-butanol and up to 150 bar for carbon dioxide-2-butanol. Different equilibrium compositions of carbon dioxide in alcohols were observed despite their similar molecular weight (M[sub.2-propanol] = 60.100 g mol[sup.−1] , M[sub.1-butanol] = 74.121 g mol[sup.−1] and M[sub.2-butanol] = 74.122 g mol[sup.−1] ) and place in the functional hydroxyl group (first or second carbon molecule). It is assumed that the differences in the phase equilibria are due to different vapor pressures, polarities and solute-solute interactions.
Journal Article
Spectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows
In this work we study strong spectral properties of Ruelle transfer operators related to a large family of Gibbs measures for contact
Anosov flows. The ultimate aim is to establish exponential decay of correlations for Hölder observables with respect to a very general
class of Gibbs measures. The approach invented in 1997 by Dolgopyat in “On decay of correlations in Anosov flows” and further developed
in Stoyanov (2011) is substantially refined here, allowing to deal with much more general situations than before, although we still
restrict ourselves to the uniformly hyperbolic case. A rather general procedure is established which produces the desired estimates
whenever the Gibbs measure admits a Pesin set with exponentially small tails, that is a Pesin set whose preimages along the flow have
measures decaying exponentially fast. We call such Gibbs measures regular. Recent results in Gouëzel and Stoyanov (2019) prove existence
of such Pesin sets for hyperbolic diffeomorphisms and flows for a large variety of Gibbs measures determined by Hölder continuous
potentials. The strong spectral estimates for Ruelle operators and well-established techniques lead to exponential decay of correlations
for Hölder continuous observables, as well as to some other consequences such as: (a) existence of a non-zero analytic continuation of
the Ruelle zeta function with a pole at the entropy in a vertical strip containing the entropy in its interior; (b) a Prime Orbit
Theorem with an exponentially small error.
eBook
Non–cooperative equilibria of Fermi systems with long range interactions
The authors define a Banach space $\\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and make explicit the structure of (generalised) equilibrium states for any $\\mathfrak{m}\\in \\mathcal{M}_{1}$. In particular, the authors give a first answer to an old open problem in mathematical physics--first addressed by Ginibre in 1968 within a different context - about the validity of the so-called Bogoliubov approximation on the level of states. Depending on the model $\\mathfrak{m}\\in \\mathcal{M}_{1}$, the authors' method provides a systematic way to study all its correlation functions at equilibrium and can thus be used to analyse the physics of long range interactions. Furthermore, the authors show that the thermodynamics of long range models $\\mathfrak{m}\\in \\mathcal{M}_{1}$ is governed by the non-cooperative equilibria of a zero-sum game, called here thermodynamic game.
eBook
The Mother Body Phase Transition in the Normal Matrix Model
The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to
several other topics as quadrature domains, inverse potential problems and the Laplacian growth.
In this present paper we
consider the normal matrix model with cubic plus linear potential. In order to regularize the model, we follow Elbau & Felder and
introduce a cut-off. In the large size limit, the eigenvalues of the model accumulate uniformly within a certain domain
We also study in detail the mother body problem associated to
To construct the mother body measure, we define a quadratic differential
Following previous works of Bleher & Kuijlaars
and Kuijlaars & López, we consider multiple orthogonal polynomials associated with the normal matrix model. Applying the Deift-Zhou
nonlinear steepest descent method to the associated Riemann-Hilbert problem, we obtain strong asymptotic formulas for these polynomials.
Due to the presence of the linear term in the potential, there are no rotational symmetries in the model. This makes the construction of
the associated
eBook
Experimental Study of the Phase Relations in the Ternary Gold-Palladium-Titanium and Gold-Rhodium-Titanium Systems at 1000°C
The isothermal section of the ternary systems gold-palladium-titanium and gold-rhodium-titanium at 1000°C was studied using the diffusion couple technique. These alloying systems are relevant for various technical applications, as functional materials for example high temperature shape memory alloys (HTSMAs), brazing filler metals, luxury items or biomedical implants. The research presents, for the first time, a comprehensive determination of phase relations and tie-triangles in these systems, identifying solid solubility of the various intermetallic compounds (IMC). The binary IMC of gold and palladium with titanium show a large solubility of the third alloying element, where gold and palladium replace each other at fixed titanium content. A complete solid solubility was observed between TiAu 2 and α-Pd 2 Ti. The binary phases with B2 structure form a large single phase field with (β-titanium) that surrounds the phase field of Ti 3 Au. Moreover, this research sets the groundwork for further investigations into these alloys, recommending specific sample compositions for future studies to refine understanding of phase boundary definitions.
Journal Article
Phase Equilibria, Diffusion and Structure in the Epoxypolycaprolactone System
Currently, there is no quantitative approach for the phase structure of cured thermoplastic systems modified with thermoplastic predicting. To solve this problem, we carried out the first stage of the study on a model polycaprolactone–epoxy oligomer (PCL–DGEBA) system. Using differential scanning calorimetry (DSC), refractometry and optical interferometry, a phase diagram for PCL–DGEBA mixtures was constructed, and the Flory–Huggins interaction parameters of PCL–DGEBA mixtures were calculated. The structure of PCL–DGEBA mixtures with different PCL content was analyzed by optical microscopy. The change in the structure formation mechanism with increasing PCL concentration was shown. The diffusion coefficients are calculated by the Motano–Boltzmann method. The values of the apparent activation energy of the viscous flow PCL and of self-diffusion of DGEBA are determined. The obtained data will be used for the in situ curing kinetics and phase equilibria in the diffusion zone investigations in order to develop a quantitative method for predicting the phase structure of cured systems.
Journal Article