A dual resonance model as a Brownian process

A dual resonance model is formulated as a Brownian motion of strings on a flow of some material. It obeys the Mayer-Montroll equation of classical statistical mechanics which enables us to make a fugacity expansion. Certain divergences in the conventional loop expansion are absent in each term of the fugacity expansion, thus showing that the Kikkawa-Sakita-Virasoro dual amplitude is, by itself, free from these divergences, if all the diagrams are added and rearranged properly. In particular the first order term of the fugacity expansion reproduces the renormalized Neveu-Scherk one-loop amplitude, when the dimension of space-time is twelve.     

Fugacity and Density Expansion for Systems with Bound States

The fugacity expansion in different approximations for low densities and for systems with bound and scattering states is discussed. The meaning of a mixed expansion and the possibility to introduce a chemical picture for a system in which bound states dominate is proved. The possibility of a thermodynamical instability is shown.     

Instantons in cutoff theories

It is shown that the inhomogeneous saddle points of scale invariant theories make the semiclassical expansion sensitive to the choice of non-renormalizable operators. In particular, the instanton fugacity and the beta function of the two-dimensional non-linear sigmamodel depend on apparently non-renormalizable operators. This represents a non-perturbative breakdown of that concept of universality which is based on low dimensional operators.     

Low-fugacity asymptotic expansion for classical lattice dipole gases

We consider a classical dipole gas in the grand canonical ensemble. We prove that in dimensions greater than or equal to three, and for all temperatures, the free energy and the charges-dipoles correlation functions have an expansion in powers ofz, the fugacity of the system, which is asymptotic to all orders. We also give some information about the decay of correlations.on leave from Institut de Physique Théorique Université de Louvian, Belgium. Supported by N.S.F. grant No. PHY-15920.     

Surface tension for the two-component plasma at Γ=2 near an interface

The grand partition function for the two-dimensional, two-component plasma at =2 is evaluated exactly in a finite system for various interfaces: a charged hard wall (the so-called primitive electrode model), a second two-component plasma of different fugacity separated by an impermeable membrane (the ideally polarizable interface), and a metal wall separated by an impermeable barrier. For each of these models the surface tension is calculated directly from the asymptotic expansion of the grand partition function.     

Equation of State in the Fugacity Format for the Two-Dimensional Coulomb Gas

We derive the general form of the equation of state, in the fugacity format, for the two-dimensional Coulomb gas. Our results are valid in the conducting phase of the Coulomb gas, for temperatures above the Kosterlitz–Thouless transition. The derivation of the equation of state is based on the knowledge of the general form of the short-distance expansion of the correlation functions of the Coulomb gas. We explicitly compute the expansion up to order in the activity ζ. Our results are in very good agreement with Monte Carlo simulations at very low density.     

Fluids with highly directional attractive forces. I. Statistical thermodynamics

A new formulation of statistical thermodynamics is derived for classical fluids of molecules that tend to associate into dimers and possibly highers-mers due to highly directional attraction. A breakup of the pair potential into repulsive and highly directionally attractive parts is introduced into the expansion of the logarithm of the grand partition function in fugacity graphs. The bonding by the directional attraction is used to classify the graphs and to introduce a topological reduction which results in the replacement of the fugacity by two variables: singlet density and monomer density ₀. Results for the thermodynamic functions as functionals of and ₀ are given in the form of graph sums. Pair correlations are analyzed in terms of a new matrix analog of the direct correlation function. It is shown that the low-density limit is treated exactly, while major difficulties arise when the Mayer expansion, which employs onlyp, is used. The intricate resummations required for the Mayer expansion are illustrated for the case where dimers are the only association products.Supported by the NSF under Grant Nos. CHE-81-14968 and CHE-82-11236 and by the U.S. Air Force under Grant No. AFOSR 82-0016A.     

Infinite Ergodic Walks in Finite Connected Undirected Graphs

The micro-canonical, canonical, and grand canonical ensembles of walks defined in finite connected undirected graphs are considered in the thermodynamic limit of infinite walk length. As infinitely long paths are extremely sensitive to structural irregularities and defects, their properties are used to describe the degree of structural imbalance, anisotropy, and navigability in finite graphs. For the first time, we introduce entropic force and pressure describing the effect of graph defects on mobility patterns associated with the very long walks in finite graphs; navigation in graphs and navigability to the nodes by the different types of ergodic walks; as well as node’s fugacity in the course of prospective network expansion or shrinking.     

Electrostatistics of counter-ions at and between planar charged walls: From Poisson-Boltzmann to the strong-coupling theory

The Poisson-Boltzmann (PB) approach gives asymptotically exact counter-ion density profiles around macroscopic charged objects and forces between macroscopic charged objects in the weak-coupling limit of low counter-ion valency, low surface-charge density, and high temperature. In this paper we derive, using field-theoretic methods, a theory which becomes exact in the opposite limit of strong coupling (SC). Formally, it corresponds to a standard virial expansion. Long-range divergences render the virial expansion intractable for homogeneous bulk systems, giving rise to non-analyticities in the low-density expansion of the free-energy density of electrolyte solutions. We demonstrate that for the case of inhomogeneous density distribution functions at macroscopic charged bodies these divergences are renormalizable by a systematic expansion in powers of the fugacity. For a single planar charged wall, we obtain the counter-ion density profile in the SC limit, which decays exponentially, in contrast to the PB result, which predicts algebraic decay, and in agreement with previously published numerical results. Similarly and highly charged plates in the presence of multivalent counter-ions attract each other in the SC limit and form electrostatically bound states, in contrast to the PB limit, where the interaction is always repulsive. By considering next-leading corrections to both the PB and SC theories, we estimate the range of validity for both theories.     

Thermodynamic Properties of the Two-Dimensional Two-Component Plasma

The model under consideration is a two-dimensional two-component plasma, stable against collapse for the dimensionless coupling constant <2. The combination of a technique of renormalized Mayer expansion with the mapping onto the sine-Gordon theory provides the full thermodynamics of the plasma in the whole stability range of . The explicit forms of the density–fugacity relationship and of the specific heat (at constant volume) per particle are presented.     

CONSTANT FUGACITY MONTE-CARLO ENUP1ERATION METHOD FOR LINEAR AND BRANCHED POLYMERS

We extend the constant fugacity MC method of Redner et al.^[7] to study the linear and branched polymers. A constant fugacity MC enumeration method for the calculation of the canonical and grand canonical ensemble properties of the linear and branched polymers is proposed. The advantage of the present method over the conventional ones is that it is efficient and statistically bias free. Comparison of the MC results with that of the exact enumeration is made.     

Third Bose fugacity coefficient in one dimension, as a function of asymptotic quantities

In one of the very few exact quantum mechanical calculations of fugacity coefficients, [L.R. Dodd, A.M. Gibbs. J. Math. Phys. 15 (1974) 41] obtained b₂ and b₃ for a one dimensional Bose gas, subject to repulsive delta-function interactions, by direct integration of the wave functions. For b₂, we have shown [A. Amaya-Tapia, S.Y. Larsen, M. Lassaut. Mol. Phys. 103 (2005) 1301–1306. <arXiv:physics/0405150>] that Dodd and Gibbs’ result can be obtained from a phase shift formalism, if one also includes the contribution of oscillating terms, usually contributing only in one dimension. Now, we develop an exact expression for (where is the free particle fugacity coefficient) in terms of sums and differences of three-body eigenphase shifts. Further, we show that if we obtain these eigenphase shifts in a Distorted-Born approximation, then, to first order, we reproduce the leading low temperature behaviour, obtained from an expansion of the twofold integral of Dodd and Gibbs. The contributions of the oscillating terms cancel.The formalism that we propose is not limited to one dimension, but seeks to provide a general method to obtain virial coefficients, fugacity coefficients, in terms of asymptotic quantities. The exact one dimensional results allow us to confirm the validity of our approach in this domain.     

高温高压下氧逸度的就位测量与控制

 通过在样品与氧库间置入一固体氧离子导体以及在样品与氧库间外加一直流电压，氧在该电压驱动下可独立于温度、压力自样品中就位抽出或灌入样品；通过在样品腔内置入一氧传感器，样品中氧逸度及其变化可得到就位监测。高温高压下样品中氧逸度由此可独立于温度、压力进行就位控制。以镍-氧体系作为样品的实验表明，该方法非常成功。无疑，该方法对日后的高压实验研究具有重要的意义。     

Application of M?ssbauer spectroscopy to determine the redox potential of the upper mantle

The chemical composition of mineral associations in the rock of mantle xenoliths was investigated, the content of Fe²⁺ and Fe³⁺ being determined by the M?ssbauer spectroscopy technique. The crystallization conditions (temperature, pressure, and oxygen fugacity) of mantle xenoliths and the composition of the coexisting mantle fluids were assessed. The dependence of the iron oxidation state in spinels on the fugacity of oxygen in a particular system was determined.     

Oxygen fugacity stratification of a magma chamber revealed by Mössbauer spectroscopy: evidence from the 1875 Askja eruption,N. Iceland

Mössbauer spectra of volcanic glasses from the 1875 Askja eruption reveals that the dacitemagma chamber was stratified in oxygen fugacity. The eruption was triggered by basaltic magma which was intruded into the base of the chamber. The observed oxidation state falls within the range of oxygen fugacities of H₂O/CO₂ mixtures at the liquidus temperature of the magma. It is concluded that oxygen fugacity of the chamber was effected by volcanic gases. The source of the gases was the degassing of superheated dacite at the dacite/basalt interface along the bottom of the chamber.     

Numerical analysis of the “fugacity” factor in the periodic CP1 model

The “fugacity” factor occuring in the partition function of the periodic CP₁ model is numerically analyzed. It is shown to behave as expected.     

Reduced density matrices of the anisotropic Heisenberg model

The reduced density matrices of the anisotropic Heisenberg model are studied by means of a functional integral representation based on a generalized Poisson process. Integral equations, which are analogous to the classical Kirkwood-Salzburg equations, are then used to prove the existence of the infinite volume limit of the reduced density matrices, analyticity properties with respect to the fugacity (or magnetic field) and the potentials, and a cluster property, in the low fugacity (high magnetic field) region.The research reported in this paper was supported by the National Science Foundation.     

Entropy-Driven Phase Transition in a Polydisperse Hard-Rods Lattice System

We study a system of rods onℤ², with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with orientational long-range order. This is in sharp contrast with the case N = 2 (the monomer-dimer model), for which Heilmann and Lieb proved absence of phase transition at any fugacity. This is the first example of a pure hard-core system with phases displaying orientational order, but not translational order; this is a fundamental characteristic feature of liquid crystals.     

Fluids with highly directional attractive forces. III. Multiple attraction sites

We derive a reformulation of statistical thermodynamics for fluids of molecules which interact by highly directional attraction. The molecular model consists of a repulsive core and several sites of very short-ranged attraction. We explore the relationship between graph cancelation in the fugacity expansion and three types of steric incompatibility between repulsive and attractive interactions involving several molecules. The steric effects are used to best advantage in a limited regrouping of bonds. This controls the density parameters which appear when articulation points are eliminated in the graphical representation. Each density parameter is a singlet density for a species consisting of molecules with a specified set of sites bonded. The densities satisfy subsidiary conditions of internal consistency. These conditions are equivalent to a minimization of the Helmholtz free energyA. Graphical expressions forA and for the pressurep are derived. Analogs of thes-particle direct correlation functions and of the Ornstein-Zernike equation are found.Supported by the NSF under grant No. CHE-82-11236.     

In-situ control of oxygen fugacity for laboratory measurements of electrical conductivity of minerals and rocks in a multi-anvil press

In this paper,a new of oxygen fugacity controltechnique that can be widely applied to in-situ measurement of the grain interior electrical conductivities of minerals and rocks is presented for high temperature and high pressure. Inside the sample assembly,a metal and corresponding metal oxide form a solid oxygen buffer. The principle of this technique is to randomly monitor and adjust oxygen fugacity in the large-volume multi-anvil press by changing the types of solid oxygen buffer,metal shielding case and electrodes. At a pressure of up to 5.0 GPa and a temperature of up to 1423 K,the electrical conductivities of the dry peridotite are tested under the conditions of different oxygen fugacities. By virtue of this new technique,more and more reasonable and accurate laboratory electrical property data will be successfully obtained under controlled thermodynamic conditions.