| In principle, all problems in confined fluids are relevant to one of the two system configurations: equilibrium or dynamical. Two problems of both types are considered.; The equation of state of a hard-sphere fluid at equilibrium in a narrow cylindrical pore with hard walls is studied. If the pore is so narrow that each particle can interact only with its nearest neighbors, analytical methods can be employed. Using a transfer operator formalism and expanding in low- and high-pressure regions, a simple analytical equation of state for almost the full range of pressure can be obtained. The results agree with our Monte Carlo simulations. The equation of state is analyzed in terms of an effective diameter of the particles, which may be useful for understanding dynamical properties of the system. Additionally, it is shown that a convenient analytical representation can be chosen to accurately describe the equation of state within the error of Monte Carlo simulation.; Anomalous diffusion is a very peculiar effect that occurs in a single-file (particles can not pass each other) fluid that diffuses under the influence of random forces. In this case, the mean squared particle displacement increases as the square root of time. Molecular Dynamics simulation is used to study the effect of anomalous diffusion of one-dimensional fluids. Particles of the fluid interact with inverse power potential. As the mechanism of applying a random force, a sporadic reversing of the velocity of each particle is proposed. The main conclusions are: the mobility factor increases linearly with the mean separation between the particles; the mobility factor is proportional to the square root of the temperature in the system, and inversely proportional to the square root of the velocity reversing rate. The properties of the fluid can be described by an effective diameter of the particle, which depends on the interaction potential and the temperature of the system, but does not depend on the reversal rate. The results are compared with the results of analytical study of one-dimensional hard core fluids and found to be consistent. |
