We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various initial conditions of the system. The method employs an effective approach for defining the phase-space distance appropriate for systems with periodic boundary and allows for an unambiguous test-orbit rescaling in the phase space required to calculate the Lyapunov exponents. We elucidate our technique by applying it to investigate the chaotic dynamics of a one-dimensional plasma with periodic boundary. Exact analytic expressions are derived for the electric field and potential using Ewald sums thereby making it possible to follow the time-evolution of the plasma in simulation without any special treatment of the boundary. By employing a set of event-driven algorithms, we calculate the largest Lyapunov exponent, the radial distribution function and the pressure by following the evolution of the system in phase space without resorting to numerical manipulation of the equations of motion. Simulation results are presented and analyzed for the one-dimensional plasma with a view to examining the dynamical and chaotic behavior exhibited by small and large versions of the system.

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We study the thermodynamic properties of a one-dimensional gas with one-dimensional gravitational interactions. Periodic boundary conditions are implemented as a modification of the potential consisting of a sum over mirror images (Ewald sum), regularized with an exponential cutoff. As a consequence, each particle carries with it its own background density. Using mean-field theory, we show that the system has a phase transition at a critical temperature. Above the critical temperature the gas density is uniform, while below the critical point the system becomes inhomogeneous. Numerical simulations of the model, which include the caloric curve, the equation of state, the radial distribution function, and the largest Lyapunov exponent, confirm the existence of the phase transition, and they are in good agreement with the theoretical predictions.

Measurement of lung volume may be useful in determining the degree of lung disease and for optimizing an infant's mechanical ventilator settings. A chest radiograph (CXR) is often used to estimate lung volume, because direct measurement, e.g., functional residual capacity (FRC), is neither practical nor possible in the neonatal intensive care unit. In supinely positioned infants, good correlation was found between lung area determined by CXR and lung volume, e.g., functional residual capacity (FRC). Whether this is true for the prone position is unknown. Since positioning may affect oxygenation and pulmonary function, we studied the relationship between lung area measured from CXR and FRC during both supine and prone positioning in 14 mechanically ventilated preterm infants. Lung area was determined from CXRs using computed radiography and FRCs obtained by helium dilution at end-expiration in both supine and prone positions. Reproducibility of lung area measurements was demonstrated by high correlations between two observers (R2 = 0.92 and 0.99 for supine and prone, respectively). When supine, lung area was 15.4 +/- 3.1 cm2, and FRC was 19.5 +/- 7.3 ml. In prone position, lung area was 16.7 +/- 4.2 cm2, and FRC 23.0 +/- 9.4 ml. There was a moderate to strong positive correlation between lung area and FRC for both positions (supine: r = 0.57, P < 0.03; prone: r = 0.63, P < 0.02). Lung area measured by computed radiography is a reproducible and practical method for estimating lung volume from routine chest X-rays in both supine and prone positions in mechanically ventilated preterm infants.

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