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  • 02.50  (1)
  • Hard spheres  (1)
  • Ising model  (1)
  • Phase equilibria, phase transitions, critical points of specific substances  (1)
  • argon–krypton mixture  (1)
  • coexistence region  (1)
  • critical phenomena  (1)
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Keywords
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Il nuovo cimento della Società Italiana di Fisica 12 (1990), S. 419-426 
    ISSN: 0392-6737
    Keywords: Classical, semiclassical, quantum theories of liquid structure ; Phase equilibria, phase transitions, critical points of specific substances
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Description / Table of Contents: Riassunto Nel presente articolo si sviluppa una teoria della crescita delle correlazioni nella regione critica di un fluido semplice. Se la descrizione della struttura a breve distanza é basata su un'approssimazione del tipo «optimized random phase», le equazioni mostrano il tipico grado di accuratezza di una buona teoria dello stato liquido fuori dalla regione critica e, allo stesso tempo, un comportamento critico non classico. In questo modo otteniamo una teoria dello stato fluido in cui é possibile calcolare sia le quantità universali che quelle non universali per un modello realistico di fluido. Il caso di interazione Lennard Jones é analizzato in dettaglio per temperature superiori alla temperatura critica e i risultati sono confrontati con esperimenti e simulazioni numeriche.
    Abstract: Резюме Развивается теория для учета дальнодействующих корреляций в жидкостях. Эта теория подтверждается посредством реалистического описания короткодействующей структуры, основанной на оптимизированном приближении случайных фаз. Предложенный подход обнаруживает типичную точность для хорошей теории жидкого состояния вдали от критической точки, наряду с истинным неклассическим критическим поведением. Таким образом, мы получаем всесторонную теорию жидкостей, в которой можно исследовать универсальные и неуниверсальные характеристики реалистической модели жидкости. Подробно анализируется случай взаимодействия Леннарда-Джонса выше критической температуры. Проводится сравнение с экспериментальными данными и результатами численного моделирования.
    Notes: Summary A theory for the build-up of long-range correlations in fluids is developed. When it is supported by a realistic description of the short-range structure, based on the optimized random phase approximation, it shows the typical accuracy of a good liquid-state theory far from the critical point together with a genuine nonclassical critical behaviour. In this way we obtain a comprehensive theory of fluids in which both universal and nonuniversal quantities can be studied for a realistic model of a liquid. The case of the Lennard-Jones interaction is analyzed in detail above the critical temperature and is compared to experiments and numerical simulations.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of low temperature physics 93 (1993), S. 879-892 
    ISSN: 1573-7357
    Keywords: 67.40 ; 02.50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The excitation spectrum of superfluid 4 He is discussed on the basis of a shadow wave function. The potential and kinetic energies of the excitations are computed at different densities. The theory has been extended at finite temperature and we obtain the roton contribution to the radial distribution function, to the depletion of the condensate and to the dynamical structure factor S(q,ω). We present also the first realistic microscopic computation of the roton energy at finite T. Possible role of thermally excited vortices on rotons is considered. With a simple model we show that some discrepancies between the linewidth of the roton response in neutron and in Raman scattering can be resolved.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 100 (2000), S. 13-38 
    ISSN: 1572-9613
    Keywords: binary mixtures ; fluctuations ; phase diagram ; critical points ; argon–krypton mixture ; neon–krypton mixture ; symmetric mixture
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The hierarchical reference theory of fluids (HRT) is applied to the study of the phase diagram of binary mixtures of simple fluids. This approach implements the renormalization group machinery into a liquid-state theory in order to systematically deal with the effect of long-range correlations which play a crucial role in the onset of criticality and phase separation. The effect of fluctuations is embodied in a partial differential equation (PDE) for the free energy of the mixture. Recently, a robust numerical algorithm has been developed which enabled us to integrate this PDE on a substantial density mesh even at low temperature, when the coexistence region spreads over most of the density– concentration plane.We have considered a model mixture of spherical particles interacting via a hard-core plus attractive tail potential, and adjusted the particle diameters σ 1, σ 2 and the strengths of the attractive interactions ε 11, ε 22, ε 12 so as to mimic mixtures of simple fluids such as argon–krypton or neon–krypton. In the latter case the theory reproduces the occurrence of a minimum in the critical temperature (the so-called critical double point) and of immiscibility at high pressure. We have also studied the phase diagram of a symmetric mixture such that σ 1=σ 2 and ε 11=ε 22 as the ratio δ=ε 12/ε 11 is varied. In particular, we find that, in agreement with the mean-field picture, by decreasing δ, a critical endpoint occurring at equal species concentration is turned into a tricritical point. An interesting feature of the HRT is that, whenever phase coexistence occurs, the conditions of phase equilibria are implemented by the theory itself, without any need of enforcing them a posteriori. This allows one to straightforwardly map the phase diagram and the critical lines of the mixture.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 64 (1991), S. 481-500 
    ISSN: 1572-9613
    Keywords: Hard spheres ; pair correlation function ; triplet correlation function ; Percus-Yevick
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new representation is obtained for the isothermal density derivative ofg(r). It explicitly exhibits the contributions of potential energy terms that are not pairwise additive. Consideration of a previously known result shows that one has to be rather cautious when using it to obtain information on the triplet correlation function from the well-known relation between this function andδg/δρ, due to large cancellations which take place at high density. By integrating with respect to density the new representation forδg/δρ, after a suitable closure has been introduced, we obtain an augmented Percus-Yevick equation for hard spheres which has full thermodynamic consistency. The equation of state and the cavity functiony(r) are very accurate at low density and considerably improve PY at medium density, so that this appears to be a useful new approach to the theory of fluids, but it is necessary to improve the closure in order to treat a dense fluid.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 72 (1993), S. 1179-1201 
    ISSN: 1572-9613
    Keywords: Ising model ; direct correlation function ; critical behavior ; coexistence region
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The hierarchical reference theory (HRT) of fluids is applied to the three-dimensional Ising model on a simple cubic lattice with nearest-neighbor ferromagnetic interaction via the equivalence with the lattice-gas model. The hierarchy is truncated to the first equation and closed with an Ornstein-Zernike ansatz for the direct correlation function embodying both thermodynamic consistency and on-site repulsion between lattice particles. The resulting equations are integrated numerically above and below the critical temperature and the results are compared with those obtained by closed-form approximants. We show that HRT yields nontrivial critical exponents with the correct scaling regime and a value of the critical temperature in very close agreement with the true one. At the same time it retains all the information about the short-range behavior of the system, and so gives a very accurate description also away from the critical point. Below the critical temperature as long as long-wavelength fluctuations are included in the system the van der Waals loop is suppressed and is replaced by a region where the compressibility is infinite, namely the coexistence region.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    International journal of thermophysics 10 (1989), S. 345-356 
    ISSN: 1572-9567
    Keywords: critical phenomena ; critical point ; liquid state theory ; rare gases
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We show that the hierarchical reference theory is an accurate global theory of fluids at least above the critical temperatureT c. The hierarchy is truncated at the first equation, the one connecting the free energy to the pair correlation function, with an Ornstein-Zernike ansatz. In this approximation the theory can be considered as a sophisticated generalization of the optimized random phase approximation which has genuine nonclassical critical exponents and for which scaling is satisfied. We study the system of hard spheres plus the Lennard-Jones attractive well and find a good agreement with measuredPVT, specific heat, correlation length, and structure factor in rare gases. The accuracy of the theory remains very good up to freezing density.
    Type of Medium: Electronic Resource
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