Thermodynamic properties of a polydisperse system

Dynamics of self-adjusting systems with noise

We study several self-adjusting systems with noise. In our analytical and numerical studies, we find that the dynamics of the self-adjusting parameter can be accurately described with a rescaled diffusion equation. We find that adaptation to the edge of chaos, a feature previously ascribed to self-adjusting systems, is only a long-lived transient when noise is present in the system. In addition, using analytical, numerical, and experimental methods, we find that noise can cause chaotic outbreaks where the parameter reenters the chaotic regime and the system dynamics become chaotic. We find that these chaotic outbreaks have a power law distribution in length.

Correlation functions for estimating effects of the physical cluster formation

Two correlation functions for estimating effects of the physical cluster formation on features of a fluid must satisfy a system of two integral equations which is equivalent to the Ornstein-Zernike equation and the sum of the two correlation functions is equivalent to the pair correlation function. A specific effect of the physical cluster formation persuades the dependence of their sum on the distance r between particular pair particles to develop a deviation from the dependence which is expressed as the product of the reciprocal of r and a particular function given as the Taylor series due to powers of r . The use of the two correlation functions allows the formation of extremely large physical clusters to be predicted at least near the triple point. The two correlation functions can contribute to examining a feature of a fluid in a specific situation where an effect of the physical cluster formation are considerable.

Analytic solutions for Baxter’s model of sticky hard sphere fluids within closures different from the Percus–Yevick approximation

We discuss structural and thermodynamical properties of Baxter's adhesive hard sphere model within a class of closures which includes the Percus-Yevick (PY) one. The common feature of all these closures is to have a direct correlation function vanishing beyond a certain range, each closure being identified by a different approximation within the original square-well region. This allows a common analytical solution of the Ornstein-Zernike integral equation, with the cavity function playing a privileged role. A careful analytical treatment of the equation of state is reported. Numerical comparison with Monte Carlo simulations shows that the PY approximation lies between simpler closures, which may yield less accurate predictions but are easily extensible to multicomponent fluids, and more sophisticate closures which give more precise predictions but can hardly be extended to mixtures. In regimes typical for colloidal and protein solutions, however, it is found that the perturbative closures, even when limited to first order, produce satisfactory results.

Pole topology of the structure functions of continuous systems

We develop a theory of the pole topology of the Laplace transform of the structure functions of continuous N component systems based on the Wiener-Hopf technique. We classify systems according to the spectrum of the NxN matrix Q(t), with elements Q(ij)(t)=delta(ij)-2pi square root [rho(i)rho(j)]integrale(-tr)q(ij)(r)dr, associated with their factor functions q(ij)(r). For the simplest nontrivial class of systems--namely, that with only two eigenvalues of Q(t) different from one--a full and explicit analysis of the pole topology is possible. We illustrate the theory with exactly solvable examples, such as the Percus-Yevick equation for arbitrary mixtures of hard spheres (HS) and polydisperse HS and the mean spherical model for binary mixtures of adhesive spheres.