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.

Time operator for diffusion

Volume: 11 Issue: 4 Pages: 465-477 Published: MAR 2000 Times Cited: 9 References: 15 Citation MapCitation Map beta Abstract: We extend the concept of time operator for general semigroups and construct a non-self-adjoint time operator for the diffusion equation which is intertwined with the unilateral shift. We obtain the spectral resolution, the age eigenstates and a new shift representation of the solution of the diffusion equation. Based on previous work we obtain similarly a self-adjoint time operator for Relativistic Diffusion. (C) 2000 Elsevier Science Ltd. All rights reserved.

Microscopic models for dielectric relaxation in disordered systems

It is shown how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to yield the empirical Havriliak-Negami (HN) equation of anomalous dielectric relaxation from a microscopic model based on a kinetic equation just as in the Debye model. This kinetic equation is obtained by means of a generalization of the noninertial Fokker-Planck equation of conventional Brownian motion (generally known as the Smoluchowski equation) to fractional kinetics governed by the HN relaxation mechanism. For the simple case of noninteracting dipoles it may be solved by Fourier transform techniques to yield the Green function and the complex dielectric susceptibility corresponding to the HN anomalous relaxation mechanism.

Fokker-Planck equation for a test-particle weakly coupled to a magnetized plasma

We consider the derivation of a kinetic equation for a charged test particle weakly interacting with an electrostatic plasma in thermal equilibrium, subject to a uniform external magnetic field. The Liouville equation leads to a generalized master equation to second order in the `weak' interaction; a Fokker-Planck-type equation then follows as a `Markovian' approximation. It is shown that such an equation does not preserve the positivity of the distribution function f(x,v;t). By applying techniques developed in the theory of open systems, a correct Fokker-Planck equation is derived. Explicit expressions for the diffusion and drift coefficients, depending on the magnetic field, are obtained.

Finite difference time domain modeling of phase grating diffusion

In this paper, a method for modeling diffusion caused by non-smooth boundary surfaces in simulations of room acoustics using finite difference time domain (FDTD) technique is investigated. The proposed approach adopts the well-known theory of phase grating diffusers to efficiently model sound scattering from rough surfaces. The variation of diffuser well-depths is attained by nesting allpass filters within the reflection filters from which the digital impedance filters used in the boundary implementation are obtained. The presented technique is appropriate for modeling diffusion at high frequencies caused by small surface roughness and generally diffusers that have narrow wells and infinitely thin separators. The diffusion coefficient was measured with numerical experiments for a range of fractional Brownian diffusers.

Transport Properties Investigation of Aqueous Protic Ionic Liquid Solutions through Conductivity, Viscosity, and NMR Self-Diffusion Measurements

We present a study on the transport properties through conductivity (s), viscosity (?), and self-diffusion coefficient (D) measurements of two pure protic ionic liquids—pyrrolidinium hydrogen sulfate, [Pyrr][HSO4], and pyrrolidinium trifluoroacetate, [Pyrr][CF3COO]—and their mixtures with water over the whole composition range at 298.15 K and atmospheric pressure. Based on these experimental results, transport mobilities of ions have been then investigated in each case through the Stokes–Einstein equation. From this, the proton conduction in these PILs follows a combination of Grotthuss and vehicle-type mechanisms, which depends also on the water composition in solution. In each case, the displacement of the NMR peak attributed to the labile proton on the pyrrolidinium cation with the PILs concentration in aqueous solution indicates that this proton is located between the cation and the anion for a water weight fraction lower than 8%. In other words, for such compositions, it appears that this labile proton is not solvated by water molecules. However, for higher water content, the labile protons are in solution as H3O+. This water weight fraction appears to be the solvation limit of the H+ ions by water molecules in these two PILs solutions. However, [Pyrr][HSO4] and [Pyrr][CF3COO] PILs present opposed comportment in aqueous solution. In the case of [Pyrr][CF3COO], ?, s, D, and the attractive potential, Epot, between ions indicate clearly that the diffusion of each ion is similar. In other words, these ions are tightly bound together as ion pairs, reflecting in fact the importance of the hydrophobicity of the trifluoroacetate anion, whereas, in the case of the [Pyrr][HSO4], the strong H-bond between the HSO4– anion and water promotes a drastic change in the viscosity of the aqueous solution, as well as on the conductivity which is up to 187 mS·cm–1 for water weight fraction close to 60% at 298 K.

White matter fractional anisotrophy predicts balance performance in older adults

Aging is characterized by brain structural changes that may compromise motor functions. In the context of postural control, white matter integrity is crucial for the efficient transfer of visual, proprioceptive and vestibular feedback in the brain. To determine the role of age-related white matter decline as a function of the sensory feedback necessary to correct posture, we acquired diffusion weighted images in young and old subjects. A force platform was used to measure changes in body posture under conditions of compromised proprioceptive and/or visual feedback. In the young group, no significant brain structure-balance relations were found. In the elderly however, the integrity of a cluster in the frontal forceps explained 21% of the variance in postural control when proprioceptive information was compromised. Additionally, when only the vestibular system supplied reliable information, the occipital forceps was the best predictor of balance performance (42%). Age-related white matter decline may thus be predictive of balance performance in the elderly when sensory systems start to degrade.

Score for neonatal acute physiology-II and neonatal pain predict corticospinal tract development in premature newborns

Premature infants are at risk for adverse motor outcomes, including cerebral palsy and developmental coordination disorder. The purpose of this study was to examine the relationship of antenatal, perinatal, and postnatal risk factors for abnormal development of the corticospinal tract, the major voluntary motor pathway, during the neonatal period. In a prospective cohort study, 126 premature neonates (24-32 weeks' gestational age) underwent serial brain imaging near birth and at term-equivalent age. With diffusion tensor tractography, mean diffusivity and fractional anisotropy of the corticospinal tract were measured to reflect microstructural development. Generalized estimating equation models examined associations of risk factors on corticospinal tract development. The perinatal risk factor of greater early illness severity (as measured by the Score for Neonatal Acute Physiology-II [SNAP-II]) was associated with a slower rise in fractional anisotropy of the corticospinal tract (P = 0.02), even after correcting for gestational age at birth and postnatal risk factors (P = 0.009). Consistent with previous findings, neonatal pain adjusted for morphine and postnatal infection were also associated with a slower rise in fractional anisotropy of the corticospinal tract (P = 0.03 and 0.02, respectively). Lessening illness severity in the first hours of life might offer potential to improve motor pathway development in premature newborns.

Procedural pain and brain development in premature newborns

Objective: Preterm infants are exposed to multiple painful procedures in the neonatal intensive care unit (NICU) during a period of rapid brain development. Our aim was to examine relationships between procedural pain in the NICU and early brain development in very preterm infants.

Methods: Infants born very preterm (N ¼ 86; 24–32 weeks gestational age) were followed prospectively from birth, and studied with magnetic resonance imaging, 3-dimensional magnetic resonance spectroscopic imaging, and diffusion tensor imaging: scan 1 early in life (median, 32.1 weeks) and scan 2 at term-equivalent age (median, 40 weeks). We calculated N-acetylaspartate to choline ratios (NAA/choline), lactate to choline ratios, average diffusivity, and white matter fractional anisotropy (FA) from up to 7 white and 4 subcortical gray matter regions of interest. Procedural pain was quantified as the number of skin-breaking events from birth to term or scan 2. Data were
analyzed using generalized estimating equation modeling adjusting for clinical confounders such as illness severity, morphine exposure, brain injury, and surgery.

Results: After comprehensively adjusting for multiple clinical factors, greater neonatal procedural pain was associated with reduced white matter FA (b ¼ 0.0002, p ¼ 0.028) and reduced subcortical gray matter NAA/choline (b ¼ 0.0006, p ¼ 0.004). Reduced FA was predicted by early pain (before scan 1), whereas lower NAA/choline was predicted by pain exposure throughout the neonatal course, suggesting a primary and early effect on subcortical structures with secondary white matter changes.

Interpretation: Early procedural pain in very preterm infants may contribute to impaired brain development.

Comparative study on transport properties for LiFAP and LiPF6 in alkyl-carbonates as electrolytes through conductivity, viscosity and NMR self-diffusion measurements

We present in this work a comparative study on density and transport properties, such as the conductivity (sigma), viscosity (eta) and self-diffusion coefficients (D), for electrolytes based on the lithium hexafluorophosphate, LiPF6; or on the lithium tris(pentafluoroethane)-trifluorophosphate, LiFAP dissolved in a binary mixture of ethylene carbonate (EC) and dimethylcarbonate (DMC) (50:50 wt%). For each electrolyte, the temperature dependence on transport properties over a temperature range from 10 to 80 degrees C and 20 to 70 degrees C for viscosity and conductivity, respectively, exhibits a non-Arrhenius behavior. However, this dependence is correctly correlated by using the Vogel-Tamman-Fulcher (VTF) type fitting equation. In each case, the best-fit parameters, such as the pseudo activation energy and ideal glass transition temperature were then extracted. The self-diffusion coefficients (D) of the Li+ cation and PF6- or FAP(-) anions species, in each studied electrolyte, were then independently determined by observing Li-3, F-19 and P-31 nuclei with the pulsed-gradient spin-echo (PGSE) NMR technique over the same temperature range from 20 to 80 degrees C. Results show that even if the diffusion of the lithium cation is quite similar in both electrolytes, the anions diffusion differs notably. In the case of the LiPF6-based electrolyte, for example at T approximate to 75 degrees C (high temperature), the self-diffusion coefficients of Li+ cations in solution (D (Li+)approximate to 5 x 10(-19) m(2) s(-1)) is 1.6 times smaller than that of PF6- anions (D (PF6-) = 8.5 x 10(-19) m(2) s(-1)), whereas in the case of the LiFAP-based electrolyte, FAP(-) anions diffuse at same rate as the Li+ cations (D (FAP(-)) = 5 x 10(-1) m(2) s(-1)). Based on these experimental results, the transport mobility of ions were then investigated through Stokes-Einstein and Nernst-Einstein equations to determine the transport number of lithium t(Li)(+), effective radius of solvated Li+ and of PF6- and FAP(-) anions, and the degree of dissociation of these lithium salts in the selected EC/DMC (50:50 wt%) mixture over a the temperature range from 20 to 80 degrees C. This study demonstrates the conflicting nature of the requirements and the advantage of the well-balanced properties as ionic mobility and dissociation constant of the selected electrolytes. (C) 2013 Elsevier Ltd. All rights reserved.

MRI diffusion tractography study in individuals with schizotypal features: A pilot study

Diffusion tensor imaging (DTI) studies have identified changes in white matter tracts in schizophrenia patients and those at high risk of transition. Schizotypal samples represent a group on the schizophrenia continuum that share some aetiological risk factors but without the confounds of illness. The aim of the current study was to compare tract microstructural coherence as measured by
fractional anisotropy (FA) between 12 psychometrically defined schizotypes and controls. We investigated bilaterally the uncinate and arcuate fasciculi (UF and AF) via a probabilistic tractography algorithm (PICo), with FA values compared between groups. Partial correlations were also examined between measures of subclinical hallucinatory/delusional experiences and FA values. High schizotypes
were found to have significantly higher FA values in bilateral UF only, but failed to reach significance in each hemisphere. In the whole sample there was a positive correlation between increasing FA values and measures of hallucinatory experience in the right AF. These findings suggest subtle changes in microstructural coherence are present in schizotypes. Correlations between mild hallucinatory experience and increasing FA values could indicate increasing coherence could be associated with symptom formation.