Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

The role of Mittag-Leffler functions in anomalous relaxation

The inertia-corrected Debye model of rotational Brownian motion of polar molecules was generalized by Coffey et al. [Phys. Rev. E, 65, 32 102 (2002)] to describe fractional dynamics and anomalous rotational diffusion. The linear- response theory of the normalized complex susceptibility was given in terms of a Laplace transform and as a function of frequency. The angular-velocity correlation function was parametrized via fractal Mittag-Leffler functions. Here we apply the latter method and complex-contour integral- representation methods to determine the original time-dependent amplitude as an inverse Laplace transform using both analytical and numerical approaches, as appropriate. (C) 2004 Elsevier B.V. All rights reserved.

Path-integral study of a two-dimensional Lennard-Jones glass

The glass transition in a quantum Lennard-Jones mixture is investigated by constant-volume path-integral simulations. Particles are assumed to be distinguishable, and the strength of quantum effects is varied by changing h from zero (the classical case) to one (corresponding to a highly quantum-mechanical regime). Quantum delocalization and zero point energy drastically reduce the sensitivity of structural and thermodynamic properties to the glass transition. Nevertheless, the glass transition temperature T-g can be determined by analyzing the phase space mobility of path-integral centroids. At constant volume, the T-g of the simulated model increases monotonically with increasing h. Low temperature tunneling centers are identified, and the quantum versus thermal character of each center is analyzed. The relation between these centers and soft quasilocalized harmonic vibrations is investigated. Periodic minimizations of the potential energy with respect to the positions of the particles are performed to determine the inherent structure of classical and quantum glassy samples. The geometries corresponding to these energy minima are found to be qualitatively similar in all cases. Systematic comparisons for ordered and disordered structures, harmonic and anharmonic dynamics, classical and quantum systems show that disorder, anharmonicity, and quantum effects are closely interlinked.

Integral completeness of locally convex spaces

A locally convex space X is said to be integrally complete if each continuous mapping f: [0, 1] --> X is Riemann integrable. A criterion for integral completeness is established. Readily verifiable sufficient conditions of integral completeness are proved.

Comparative repeatability of two handheld fractional exhaled nitric oxide monitors.

Background The use of portable fractional exhaled nitric oxide (FENO) devices is increasingly common in the diagnosis and management of allergic airways inflammation. Methods We tested two handheld FENO devices, to determine (a) if there was adequate intradevice repeatability to allow the use of single breath testing, and (b) if the devices could be used interchangeably. In a mixed pediatric population, including normal, asthmatic, and children with peanut allergies, 858 paired values were collected from the NIOX-MINO® and/or the NObreath® devices. Results The NIOX-MINO® showed excellent repeatability (mean difference of 0.1 with 95% limits of agreement between -7.93 to 7.72?ppb), while the NObreath® showed good repeatability (mean difference of -1.61 with 95% limits of agreement between -14.1 and 10.8?ppb). Intradevice repeatability was good but not adequate and the NIOX-MINO® systematically produced higher results than the NObreath® [mean difference of 7.8?ppb with 95% limits of agreement from -11.55 to 27.52?ppb (-33% to 290%)]. Conclusions Our results support the manufacturer's advice that single breath testing is appropriate for the NIOX-MINO®. NObreath® results indicate that the mean of more than one breath should be utilized. The devices cannot be used interchangeably. Pediatr Pulmonol. © 2011 Wiley Periodicals, Inc.