相关论文: Using Computational Intelligence for solving the O…
The Ornstein-Zernike equation is solved for the hard-sphere and square-well fluids using a diverse selection of closure relations; the attraction range of the square-well is chosen to be $\lambda=1.5.$ In particular, for both fluids we…
The Ornstein-Zernike equation is a powerful tool in liquid state theory for predicting structural and thermodynamic properties of fluids. Combined with a suitable closure, it has been shown to reproduce e.g. the static structure factor,…
A key challenge for soft materials design and coarse-graining simulations is determining interaction potentials between components that give rise to desired condensed-phase structures. In theory, the Ornstein-Zernike equation provides an…
The Ornstein-Zernike (OZ) equation is the fundamental equation for pair correlation function computations in the modern integral equation theory for liquids. In this work, machine learning models, notably physics-informed neural networks…
This thesis explores the evolution of liquid-state theories based on the Ornstein-Zernike (OZ) equation, summarizing the foundational methods developed by Baxter, Lebowitz, Wertheim, and others. A unifying feature of these approaches is…
In this paper we propose and explore a method of analysis of the scattering experimental data for uniform liquid-like systems. In our pragmatic approach we are not trying to introduce by hands an artificial small parameter to work out a…
We develop a multidensity formulation of the Ornstein-Zernike equation with Percus-Yevick closure for hard spheres with anisotropic surface adhesion of tetrahedral quadrupolar-like symmetry. An analytical solution is obtained using the…
The solution of the Ornstein-Zernike equation with various closure approximations is studied. This problem is rewritten as an integral equation that can be solved iteratively on a grid. The convergence of the fixed point iterations is…
The closure problem in fluid modeling is a well-known challenge to modelers aiming to accurately describe their system of interest. Over many years, analytic formulations in a wide range of regimes have been presented but a practical,…
Mixtures of hard hyperspheres in odd space dimensionalities are studied with an analytical approximation method. This technique is based on the so-called Rational Function Approximation and provides a procedure for evaluating equations of…
Inferring a generative model from data is a fundamental problem in machine learning. It is well-known that the Ising model is the maximum entropy model for binary variables which reproduces the sample mean and pairwise correlations.…
A first-principle multiscale modeling approach is presented, which is derived from the solution of the Ornstein-Zernike equation for the coarse-grained representation of polymer liquids. The approach is analytical, and for this reason is…
We have studied the structure and thermodynamic properties of isotropic three-dimensional core-softened fluid by using the second-order Ornstein-Zernike integral equations completed by the hypernetted chain and Percus-Yevick closures. The…
In this paper, we propose a novel formulation to extend CNNs to two-dimensional (2D) manifolds using orthogonal basis functions, called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific…
The properties of a classical simple liquid can be strongly affected by application of an external potential that supports inhomogeneity. To understand the nature of these property changes the equilibrium particle distribution functions of…
The main purpose of this manuscript is to analyze an intracranic fluid model from a mathematical point of view. By means of an iterative process we are able to prove the existence and uniqueness of a local solution and the existence and…
The molecular density functional theory of fluids provides an exact theory for computing solvation free energies in implicit solvents. One of the reasons it has not received nearly as much attention as quantum density functional theory for…
A simple "trick" is proposed, which allows to perform exactly the site-averaging procedure required when developing integral equation theories of interaction site models of macromolecular fluids. It shows that no approximation is involved…
We demonstrate several techniques to encourage practical uses of neural networks for fluid flow estimation. In the present paper, three perspectives which are remaining challenges for applications of machine learning to fluid dynamics are…
We propose the use of physics-informed neural networks for solving the shallow-water equations on the sphere in the meteorological context. Physics-informed neural networks are trained to satisfy the differential equations along with the…