1,657 research outputs found
Infinite compressibility states in the Hierarchical Reference Theory of fluids. II. Numerical evidence
Continuing our investigation into the Hierarchical Reference Theory of fluids
for thermodynamic states of infinite isothermal compressibility kappa[T] we now
turn to the available numerical evidence to elucidate the character of the
partial differential equation: Of the three scenarios identified previously,
only the assumption of the equations turning stiff when building up the
divergence of kappa[T] allows for a satisfactory interpretation of the data. In
addition to the asymptotic regime where the arguments of part I
(cond-mat/0308467) directly apply, a similar mechanism is identified that gives
rise to transient stiffness at intermediate cutoff for low enough temperature.
Heuristic arguments point to a connection between the form of the Fourier
transform of the perturbational part of the interaction potential and the
cutoff where finite difference approximations of the differential equation
cease to be applicable, and they highlight the rather special standing of the
hard-core Yukawa potential as regards the severity of the computational
difficulties.Comment: J. Stat. Phys., in press. Minor changes to match published versio
Phase diagram of symmetric binary mixtures at equimolar and non-equimolar concentrations: a systematic investigation
We consider symmetric binary mixtures consisting of spherical particles with
equal diameters interacting via a hard-core plus attractive tail potential with
strengths epsilon_{ij}, i,j=1,2, such that epsilon_{11} = epsilon_{22} >
epsilon_{12}. The phase diagram of the system at all densities and
concentrations is investigated as a function of the unlike-to-like interaction
ratio delta = epsilon_{12}/epsilon_{11} by means of the hierarchical reference
theory (HRT). The results are related to those of previous investigations
performed at equimolar concentration, as well as to the topology of the
mean-field critical lines. As delta is increased in the interval 0 < delta < 1,
we find first a regime where the phase diagram at equal species concentration
displays a tricritical point, then one where both a tricritical and a
liquid-vapor critical point are present. We did not find any clear evidence of
the critical endpoint topology predicted by mean-field theory as delta
approaches 1, at least up to delta=0.8, which is the largest value of delta
investigated here. Particular attention was paid to the description of the
critical-plus-tricritical point regime in the whole density-concentration
plane. In this situation, the phase diagram shows, in a certain temperature
interval, a coexistence region that encloses an island of homogeneous,
one-phase fluid.Comment: 27 pages + 20 figure
Implementation of the Hierarchical Reference Theory for simple one-component fluids
Combining renormalization group theoretical ideas with the integral equation
approach to fluid structure and thermodynamics, the Hierarchical Reference
Theory is known to be successful even in the vicinity of the critical point and
for sub-critical temperatures. We here present a software package independent
of earlier programs for the application of this theory to simple fluids
composed of particles interacting via spherically symmetrical pair potentials,
restricting ourselves to hard sphere reference systems. Using the hard-core
Yukawa potential with z=1.8/sigma for illustration, we discuss our
implementation and the results it yields, paying special attention to the core
condition and emphasizing the decoupling assumption's role.Comment: RevTeX, 16 pages, 2 figures. Minor changes, published versio
Recent developments of the Hierarchical Reference Theory of Fluids and its relation to the Renormalization Group
The Hierarchical Reference Theory (HRT) of fluids is a general framework for
the description of phase transitions in microscopic models of classical and
quantum statistical physics. The foundations of HRT are briefly reviewed in a
self-consistent formulation which includes both the original sharp cut-off
procedure and the smooth cut-off implementation, which has been recently
investigated. The critical properties of HRT are summarized, together with the
behavior of the theory at first order phase transitions. However, the emphasis
of this presentation is on the close relationship between HRT and non
perturbative renormalization group methods, as well as on recent
generalizations of HRT to microscopic models of interest in soft matter and
quantum many body physics.Comment: 17 pages, 5 figures. Review paper to appear in Molecular Physic
Thermodynamics of Solitonic Matter Waves in a Toroidal Trap
We investigate the thermodynamic properties of a Bose-Einstein condensate
with negative scattering length confined in a toroidal trapping potential. By
numerically solving the coupled Gross-Pitaevskii and Bogoliubov-de Gennes
equations, we study the phase transition from the uniform state to the
symmetry-breaking state characterized by a bright-soliton condensate and a
localized thermal cloud. In the localized regime three states with a finite
condensate fraction are present: the thermodynamically stable localized state,
a metastable localized state and also a metastable uniform state. Remarkably,
the presence of the stable localized state strongly increases the critical
temperature of Bose-Einstein condensation.Comment: 4 pages, 4 figures, to be published in Physical Review A as a Rapid
Communication. Related papers can be found at
http://www.padova.infm.it/salasnich/tdqg.htm
Sustainable Recycling of Insoluble Rust Waste for the Synthesis of Iron-Containing Perovskite-Type Catalysts
Insoluble rust waste from the scraping of rusted iron-containing materials represents a cheap, eco-friendly, and available source of iron. LaFeO3 perovskite-type powders were successfully prepared by solution combustion synthesis using rust waste from an electricity transmission tower manufacturer. Solution combustion synthesis enabled introduction of this insoluble iron precursor directly into the final product, bypassing complex extraction procedures. Catalytic activity in the propylene oxidation of the waste-derived LaFeO3 with stoichiometric Fe/La ratio was almost identical to the commercial iron nitrate-derived LaFeO3 , thus demonstrating the viability of this recycling solution. The amount of waste iron precursor was varied and its effect on the powder properties was investigated. A lesser stoichiometric amount of precursor produced a LaFeO3 -La2O3 binary system, whereas a higher stoichiometric amount led to a LaFeO3 -Fe2O3 binary system. Catalytic activity of iron-rich compositions in the propylene oxidation was only slightly lower than the stoichiometric one, whereas iron-poor compositions were much less active. This eco-friendly methodology can be easily extended to other iron perovskites with different chemical compositions and to other iron-containing compounds
Exact Renormalization Group : A New Method for Blocking the Action
We consider the exact renormalization group for a non-canonical scalar field
theory in which the field is coupled to the external source in a special non
linear way. The Wilsonian action and the average effective action are then
simply related by a Legendre transformation up to a trivial quadratic form. An
exact mapping between canonical and non-canonical theories is obtained as well
as the relations between their flows. An application to the theory of liquids
is sketched
Phase transitions in simple and not so simple binary fluids
Compared to pure fluids, binary mixtures display a very diverse phase
behavior, which depends sensitively on the parameters of the microscopic
potential. Here we investigate the phase diagrams of simple model mixtures by
use of a microscopic implementation of the renormalization group technique.
First, we consider a symmetric mixture with attractive interactions, possibly
relevant for describing fluids of molecules with internal degrees of freedom.
Despite the simplicity of the model, slightly tuning the strength of the
interactions between unlike species drastically changes the topology of the
phase boundary, forcing or inhibiting demixing, and brings about several
interesting features such as double critical points, tricritical points, and
coexistence domains enclosing `islands' of homogeneous, mixed fluid.
Homogeneous phase separation in mixtures can be driven also by purely repulsive
interactions. As an example, we consider a model of soft particles which has
been adopted to describe binary polymer solutions. This is shown to display
demixing (fluid-fluid) transition at sufficiently high density. The nature and
the physical properties of the corresponding phase transition are investigated.Comment: 6 pages + 3 figures, presented at the 5th EPS Liquid Matter
Conference, Konstanz, 14-18 September 200
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