Dynamics of hard rods in one dimension

We examine a system consisting ofN classical, Newtonian, perfectly elastic hard rods constrained to move on a line. The mass and length of each rod are arbitrary. We develop an algorithm which gives, after any given possible sequence of collisions, the new velocities of theN rods and a necessary condition for any given pair of rods to be involved in the next collision, all in terms of the initial velocities of the rods. These results are then used to prove that for the case where there are exactly three rods on the line, the maximum possible number of collisions among them is the largest integern such that , wherem ₂ is the mass of the central particle and ₁₂ and ₂₃ are the reduced masses of the left and right particle pairs. We further derive for this three-particle case a condition on the initial velocities which is necessary and sufficient fork collisions, 1<kn, to occur, as well as explicit expressions for the velocities after each collision in terms of the initial velocities.     

Nematic ordering of rigid rods in a gravitational field

The isotropic-to-nematic transition in an athermal solution of long rigid rods subject to a gravitational (or centrifugal) field is theoretically considered in the Onsager approximation. The new feature emerging in the presence of gravity is a concentration gradient that coupled with the nematic ordering. For rodlike molecules this effect becomes noticeable at centrifugal acceleration g approximately 10(3)-10(4) m/s(2), while for biological rodlike objects, such as tobacco mosaic virus, the effect is important even for normal gravitational acceleration conditions. Rods are concentrated near the bottom of the vessel, which sometimes leads to gravity induced nematic ordering. The concentration range corresponding to phase separation increases with increasing g. In the region of phase separation the local rod concentration, as well as the order parameter, follow a step function with height.     

Surface ordering transitions at a liquid crystal-solid interface above the isotropic smectic-A transition

The degree of orientational order induced by confining cylindrical surfaces is monitored via deuteron nuclear magnetic resonance linesplitting and linewidth above the smectic-A to isotropic phase transition. The orientational order strongly depends on the length of the surfactant coupling molecule, on the surface coverage, and on the liquid crystal. Continuous and stepwise growth of orientational order and surface-induced orientational order transitions found in the isotropic phase are explained in terms of a simplified model of surface-induced layering and molecular self-diffusion.     

On the diffusion of clusters of hard rods

It is shown that the diffusion coefficient of clusters of hard rods in one dimension is exactly independent of the number of rods comprising the cluster. An expression for the autocorrelation function of the velocity of the cluster centre of mass is obtained from a simple stochastic model, and asymptotically for large clusters from the exact autocorrelation function. Neither approximate nor exact velocity autocorrelation function decays exponentially for any size of cluster.     

Ergodic properties of a semi-infinite hard rods system

A semi-infinite hard rods system in thermodynamic equilibrium is proved to be aK-system.     

Ground-state properties of a one-dimensional system of hard rods

A quantum Monte Carlo simulation of a system of bosonic hard rods in one dimension is presented and discussed. The calculation is exact since the analytical form of the wave function is known and is in excellent agreement with predictions obtained from asymptotic expansions valid at large distances. The analysis of the static structure factor and the pair distribution function indicates that a solidlike and a gaslike phases exist at high and low densities, respectively. The one-body density matrix decays following a power law at large distances and produces a divergence in the low density momentum distribution at k=0 which can be identified as a quasicondensate.     

Hexagonal order in crystalline and columnar phases of hard rods

We report a study of colloidal suspensions of highly monodisperse semiflexible chiral rodlike viruses, denoted fd, in the range of high concentrations. Small angle x-ray scattering experiments reveal the existence of two hexagonal phases: the first one is crystalline and the second one is hexatic columnar, as shown by its short-range positional order. The suspension of rodlike viruses is the first experimental system showing the whole phase sequence with increasing particle concentration theoretically predicted for systems of hard rods, ranging from the chiral nematic via the smectic to columnar and crystalline phases.     

On the kinetic equations of a system of one-dimensional hard rods

The hydrodynamical approximation to an infinite system of one-dimensional identical hard rods interacting through elastic collisions, is shown to be an integrable system possessing a one-parameter family of nonlinear Hamiltonian structures.     

Approach to field-induced stationary state in a gas of hard rods

The Boltzmann equation describing one-dimensional motion of a charged hard rod in a neutral hard rod gas at temperatureT = 0 is solved. Under the action of a constant and uniform field the charged particle attains a stationary state. In the long time limit the velocity autocorrelation function decays via damped oscillations. In the reference system moving with the mean particle velocity the decay of fluctuations in the position space is governed (in the hydrodynamic limit) by the diffusion equation. Both the stationary current and the diffusion coefficient are proportional to the square root of the field. It is conjectured that this result also holds forT > 0 in a strong field limit.On leave from the Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-081 Warsaw, Poland.     

The classical fluid of associating hard rods in an external field

Two models of one-dimensional fluids of associating hard rods in an arbitrary external field are investigated. In the first model particles can only form dimers, while in the second model, which has been solved previously by Percus, aggregates of any size coexist. In both cases the grand canonical potential and the external potential are found exactly as functionals of the density. It is shown that Wertheim's thermodynamic perturbation theory of polymerization provides a straightforward route to the exact solution by expanding the functional space to include more density parameters. This suggests that Wertheim's theory should be used also for studying the structure (and not only the thermo-dynamics) of real associating fluids.     

A ray model for hard parallel noise barriers in high-rise cities

A ray model is developed and validated for prediction of the insertion loss of hard parallel noise barriers placed in an urban environment either in front of a row of tall buildings or in a street canyon. The model is based on the theory of geometrical acoustics for sound diffraction at the edge of a barrier and multiple reflections by the ground, barrier and fa?ade surfaces. It is crucial to include the diffraction and multiple reflection effects in the ray model as they play important roles in determining the overall sound pressure levels for receivers located between the fa?ade and the near-side barrier. Comparisons of the ray model with a wave-based boundary element formulation show reasonably good agreement over a broad frequency range. Results of scale model experimental studies are also presented. It is demonstrated that the ray model agrees tolerably well with the scale model experimental data.     

Microcanonical ensemble study of a classical fluid of hard rods under gravity

The study of a system of hard rods in a box of finite length in the presence of a uniform gravitational field is made by means of the microcanonical ensemble. Explicit expressions are derived for the phase volume and the density of states, the primary functions of this ensemble. Related statistical quantities are reported, such as the entropy, the temperature, the heat capacity and the forces exerted on the fluid by the bottom and top walls. The microcanonical number density and higher order molecular distribution functions are also derived. Received: 7 April 1998 / Received in final form: 20 July 1998 / Accepted: 28 July 1998     

Kinetics of a finite one-dimensional mixture of hard rods with different masses

A one-dimensional binary mixture of impenetrable (hard core) particles with different mass ratios,m ₂/m ₁=1, 1.05, 1.2, 2, 3, and 4, was simulated to evolve in a computer by the molecular dynamics method. The systems withm ₂>m ₁ and initial velocity distribution ±v ₀ show a clear tendency to the equipartition of energy and relaxation toward a Maxwellian velocity distribution unlike the nonergodic system withm ₂=m ₁. Several quantities have been monitored during the evolution to investigate its dependence on the mass ratiom ₂/m ₁.