Generalized Langevin equation with tempered memory kernel

We study a generalized Langevin equation for a free particle in presence of a truncated power-law and Mittag-Leffler memory kernel. It is shown that in presence of truncation, the particle from subdiffusive behavior in the short time limit, turns to normal diffusion in the long time limit. The case of harmonic oscillator is considered as well, and the relaxation functions and the normalized displacement correlation function are represented in an exact form. By considering external time-dependent periodic force we obtain resonant behavior even in case of a free particle due to the influence of the environment on the particle movement. Additionally, the double-peak phenomenon in the imaginary part of the complex susceptibility is observed. It is obtained that the truncation parameter has a huge influence on the behavior of these quantities, and it is shown how the truncation parameter changes the critical frequencies. The normalized displacement correlation function for a fractional generalized Langevin equation is investigated as well. All the results are exact and given in terms of the three parameter Mittag-Leffler function and the Prabhakar generalized integral operator, which in the kernel contains a three parameter Mittag-Leffler function. Such kind of truncated Langevin equation motion can be of high relevance for the description of lateral diffusion of lipids and proteins in cell membranes. (C) 2016 Elsevier B.V. All rights reserved

Analysis of light scattered by turbid media in cylindrical geometry

The angle dependence of the transmitted light through a cylindrical turbid sample (latex suspension, developing milk gel, draining/coarsening milk, and protein foams) in a standard light scattering setup was analyzed in terms of the transport mean free path length or scattering length l* (a measure for the turbidity) and the absorption length labs. By variation of the concentration of an absorbing dye, the independence of l* and labs was demonstrated. The resulting value of the specific extinction coefficient of the dye was found to be in fair agreement with direct spectroscopic determination and practically identical in milk and latex suspensions. The validity of this technique for obtaining l* was demonstrated by monitoring the acid-induced gelation of milk. The possibility to simultaneously determine l* and labs was used to follow the time development of a draining and coarsening protein foam which contained an absorbing dye. It was shown that labs can be used as a measure for the volume fraction of air in the foam. This method of monitoring the transmission of multiple light scattering provides an easy way to determine l* and, specifically for foams, quantitative data dominated by the bulk of the foam

Generalized Langevin equation with tempered memory kernel

We study a generalized Langevin equation for a free particle in presence of a truncated power-law and Mittag-Leffler memory kernel. It is shown that in presence of truncation, the particle from subdiffusive behavior in the short time limit, turns to normal diffusion in the long time limit. The case of harmonic oscillator is considered as well, and the relaxation functions and the normalized displacement correlation function are represented in an exact form. By considering external time-dependent periodic force we obtain resonant behavior even in case of a free particle due to the influence of the environment on the particle movement. Additionally, the double-peak phenomenon in the imaginary part of the complex susceptibility is observed. It is obtained that the truncation parameter has a huge influence on the behavior of these quantities, and it is shown how the truncation parameter changes the critical frequencies. The normalized displacement correlation function for a fractional generalized Langevin equation is investigated as well. All the results are exact and given in terms of the three parameter Mittag-Leffler function and the Prabhakar generalized integral operator, which in the kernel contains a three parameter Mittag-Leffler function. Such kind of truncated Langevin equation motion can be of high relevance for the description of lateral diffusion of lipids and proteins in cell membranes. (C) 2016 Elsevier B.V. All rights reserved

Near infrared light scattering changes following acute brain injury

Acute brain injury (ABI) is associated with changes in near infrared light absorption reflecting haemodynamic and metabolic status via changes in cerebral oxygenation (haemoglobin oxygenation and cytochrome-c-oxidase oxidation). Light scattering has not been comprehensively investigated following ABI and may be an important confounding factor in the assessment of chromophore concentration changes, and/or a novel non-invasive optical marker of brain tissue morphology, cytostructure, hence metabolic status. The aim of this study is to characterize light scattering following adult ABI. Time resolved spectroscopy was performed as a component of multimodal neuromonitoring in critically ill brain injured patients. The scattering coefficient absorption coefficient and cerebral haemoglobin oxygen saturation (SO) were derived by fitting the time resolved data. Cerebral infarction was subsequently defined on routine clinical imaging. In total, 21 patients with ABI were studied. Ten patients suffered a unilateral frontal infarction, and mean μ′ was lower over infarcted compared to non-infarcted cortex (injured 6.9/cm, non-injured 8.2/cm p = 0.002). SO did not differ significantly between the two sides (injured 69.3%, non-injured 69.0% p = 0.7). Cerebral infarction is associated with changes in μ′ which might be a novel marker of cerebral injury and will interfere with quantification of haemoglobin/cytochrome c oxidase concentration. Although further work combining optical and physiological analysis is required to elucidate the significance of. these results, μ′ may be uniquely placed as a non-invasive biomarker of cerebral energy failure as well as gross tissue changes