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The properties of the ground state of liquid $^4$He are studied using a correlated basis function of the form $\prod_{i<j} \psi(r_{ij})$. Here, $\psi(r)$ is chosen as the exact solution of the Schr\"{o}dinger equation for two $^4$He atoms.…
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere…
In this report the radial distribution functions (RDFs) of liquid water are calculated on the basis of the classical density functional theory combined with the reference interaction site model for molecular liquids. The bridge functions,…
The interest in the description of the properties of fluids of restricted dimensionality is growing for theoretical and practical reasons. In this work, we have firstly developed an analytical expression for the Helmholtz free energy of the…
For a three-electron system with finite-strength interactions confined to a one-dimensional harmonic trap, we solve the Schroedinger equation analytically to obtain the exact solutions, from which we construct explicitly the simultaneous…
Analytical expressions for radial distribution function (RDF) are of critical importance for various applications, such as development of the perturbation theories for equilibrium properties. Theoretically, RDF expressions for…
The study of the exchange of momentum and energy between wave components of the turbulent velocity field, the so-called triad interactions, offers a unique way of visualizing and describing turbulence. Most often, this study has been…
Two rectangular models described by the one-dimensional Schroedinger equation with sharply localized potentials are suggested. The potentials have a multi-layer thin structure being composed from adjacent barriers and wells. Their peculiar…
The structural properties of square-shoulder fluids are derived from the use of the rational function approximation method. The computation of both the radial distribution function and the static structure factor involves mostly analytical…
This paper describes the results of our theoretical and numerical studies of hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls, under creeping-flow conditions. We propose a novel…
In a recent article, we described how the microscopic structure of density-density correlations in the fluid interfacial region, for systems with short-ranged forces, can be understood by considering the resonances of the local structure…
The main goal of this work is to accurately reproduce the structural properties of attractive systems modelled by hard-sphere plus square-well (HS+SW) interaction potential. Based on the optimized random phase approximation (ORPA), the…
We study the non-equilibrium steady-states of a one-dimensional ($1D1V$) fluid in a finite space region of length $L$. Particles interact among themselves by multi-particle collisions and are in contact with two thermal-wall heat…
We analyze here the energy states and associated wave functions available to a particle acted upon by a delta function potential of arbitrary strength and sign and fixed anywhere within a one-dimensional infinite well. We consider how the…
We use molecular dynamics simulations to test integral equation theory predictions for the structure of fluids of spherical particles with eight different piecewise-constant pair interaction forms comprising a hard core and a combination of…
The integral equations for the correlation functions of an inhomogeneous fluid mixture are derived using a functional Taylor expansion of the free energy around an inhomogeneous equilibrium distribution. The system of equations is closed by…
A numerical method based upon the immersed boundary technique for the fluid-solid coupling and on a soft-sphere approach for solid-solid contact is used to perform direct numerical simulation of the flow-induced motion of a thick bed of…
The correlation between inertial range velocity fluctuations and energy dissipation in fully developed turbulence is studied using high resolution direct numerical simulation. Runs with microscale Reynolds number up to ${\cal R}_{\lambda}…
The capability to accurately predict flood flows via numerical simulations is a key component of contemporary flood risk management practice. However, modern flood models lack the capacity to accurately model flow interactions with linear…
In ultrarelativistic heavy-ion collisions, the Fourier decomposition of the relative azimuthal angle, \Delta \phi, distribution of particle pairs yields a large cos(3\Delta \phi) component, extending out to large rapidity separations \Delta…