scholarly journals On the Theory of Electron Diffusion in Electrostatic Fields in Gases

1974 ◽  
Vol 27 (2) ◽  
pp. 195 ◽  
Author(s):  
HR Skullerud
Keyword(s):  
Diffusion Coefficient ◽  
Boltzmann Equation ◽  
Diffusion Equation ◽  
Diffusion Tensor ◽  
Lateral Diffusion ◽  
Mean Square ◽  
Electrostatic Fields ◽  
The Mean ◽  
Lateral Diffusion Coefficient

The motion of electrons in a gas in the presence of large electron density gradients has been studied theoretically, starting from the two-term expansion of the Boltzmann equation. The effects of material boundaries have not been considered. An electron swarm released as a b-function in space and with an equilibrium energy distribution is found initially to develop as a spheroid with dimensions determined by the lateral diffusion coefficient. It subsequently passes through a stage involving a slowly decaying pear-shaped deformation, before ultimately becoming an ellipsoid with dimensions determined by the longitudinal and lateral components of the diffusion tensor. Numerical values cited in the literature for the long-term deviations from the mean square widths predicted by the diffusion equation have been found to be in error by factors of 10 or more.

scholarly journals Turbulent pair dispersion as a ballistic cascade phenomenology

2015 ◽  
Vol 772 ◽  
pp. 678-704 ◽  
Author(s):  
Mickaël Bourgoin
Keyword(s):  
Diffusion Coefficient ◽  
Turbulent Flows ◽  
Relative Dispersion ◽  
Mean Square ◽  
Short Term ◽  
Third Order ◽  
Temporal Asymmetry ◽  
Diffusive Regime ◽  
The Mean

Since the pioneering work of Richardson in 1926, later refined by Batchelor and Obukhov in 1950, it is predicted that the rate of separation of pairs of fluid elements in turbulent flows with initial separation at inertial scales, grows ballistically first (Batchelor regime), before undergoing a transition towards a super-diffusive regime where the mean-square separation grows as $t^{3}$ (Richardson regime). Richardson empirically interpreted this super-diffusive regime in terms of a non-Fickian process with a scale-dependent diffusion coefficient (the celebrated Richardson’s ‘$4/3$rd’ law). However, the actual physical mechanism at the origin of such a scale dependent diffusion coefficient remains unclear. The present article proposes a simple physical phenomenology for the time evolution of the mean-square relative separation in turbulent flows, based on a scale-dependent ballistic scenario rather than a scale-dependent diffusive. It is shown that this phenomenology accurately retrieves most of the known features of relative dispersion for particles mean-square separation, among others: (i) it is quantitatively consistent with most recent numerical simulations and experiments for mean-square separation between particles (both for the short-term Batchelor regime and the long-term Richardson regime, and for all initial separations at inertial scales); (ii) it gives a simple physical explanation of the origin of the super-diffusive $t^{3}$ Richardson regime which naturally builds itself as an iterative process of elementary short-term scale-dependent ballistic steps; (iii) it shows that the Richardson constant is directly related to the Kolmogorov constant (and eventually to a ballistic persistence parameter); and (iv) in a further extension of the phenomenology, taking into account third-order corrections, it robustly describes the temporal asymmetry between forward and backward dispersion, with an explicit connection to the cascade of energy flux across scales. An important aspect of this phenomenology is that it simply and robustly connects long-term super-diffusive features to elementary short-term mechanisms, and at the same time it connects basic Lagrangian features of turbulent relative dispersion (both at short and long times) to basic Eulerian features of the turbulent field: second-order Eulerian statistics control the growth of separation (both at short and long times) while third-order Eulerian statistics control the temporal asymmetry of the dispersion process, which can then be directly identified as the signature of the energy cascade and associated to well-known exact results as the Karman–Howarth–Monin relation.

Centerband-only-detection-of-exchange 31P nuclear magnetic resonance and phospholipid lateral diffusion: theory, simulation and experiment

2015 ◽  
Vol 17 (38) ◽  
pp. 25160-25171 ◽  
Author(s):  
Angel Lai ◽  
Qasim Saleem ◽  
Peter M. Macdonald
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Diffusion Coefficient ◽  
Magnetic Resonance ◽  
Liquid Crystalline ◽  
Diffusion Theory ◽  
Lateral Diffusion ◽  
Liquid Crystalline Phases ◽  
Simulation And Experiment ◽  
Spherical Vesicles ◽  
Lateral Diffusion Coefficient

Theory of CODEX 31P NMR lateral diffusion coefficient measurements on phospholipids in spherical vesicles is described and used to simulate experimental results on DMPC in both the gel and liquid-crystalline phases.

Optical studies on the turbulent motion of solid particles in a pipe flow

1991 ◽  
Vol 231 ◽  
pp. 665-688 ◽  
Author(s):  
James B. Young ◽  
Thomas J. Hanratty
Keyword(s):  
Diffusion Coefficient ◽  
Particle Velocity ◽  
Turbulent Diffusion ◽  
Slip Velocity ◽  
Rate Of Change ◽  
Solid Particles ◽  
Mean Square ◽  
Turbulent Diffusion Coefficient ◽  
Fluid Turbulence ◽  
The Mean

An extension of an axial viewing optical technique (first used by Lee, Adrian & Hanratty) is described which allows the determination of the turbulence characteristics of solid particles being transported by water in a pipe. Measurements are presented of the mean radial velocity, the mean rate of change radial velocity, the mean-square of the radial and circumferential fluctuations, the Eulerian turbulent diffusion coefficient, and the Lagrangian turbulent diffusion coefficient. A particular focus is to explore the influence of slip velocity for particles which have small time constants. It is found that with increasing slip velocity the magnitude of the turbulent velocity fluctuations remains unchanged but that the turbulent diffusivity decreases. The measurements of the average rate of change of particle velocity are consistent with the notion that particles move from regions of high fluid turbulence to regions of low fluid turbulence. Measurements of the root-mean-square of the fluctuations of the rate of change of particle velocity allow an estimation of the average magnitude of the particle slip in a highly turbulent flow, which needs to be known to analyse the motion of particles not experiencing a Stokes drag.

scholarly journals Formulation of the Boltzmann Equation as a Multi-Mode Drift-Diffusion Equation

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 539-544
Author(s):  
K. Banoo ◽  
F. Assad ◽  
M. S. Lundstrom
Keyword(s):  
Diffusion Coefficient ◽  
Boltzmann Equation ◽  
Diffusion Equation ◽  
Momentum Space ◽  
Bulk Silicon ◽  
Rigorous Solution ◽  
Drift Diffusion ◽  
The Boltzmann Equation ◽  
And Diffusion ◽  
Multi Mode

We present a multi-mode drift-diffusion equation as reformulation of the Boltzmann equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.

scholarly journals Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Long Shi
Keyword(s):  
Random Walk ◽  
Diffusion Equation ◽  
Power Law ◽  
Continuous Time ◽  
Continuum Limit ◽  
Waiting Times ◽  
Mean Square Displacement ◽  
Continuous Time Random Walk ◽  
Mean Square ◽  
The Mean

In this work, a generalization of continuous time random walk is considered, where the waiting times among the subsequent jumps are power-law correlated with kernel function M(t)=tρ(ρ>-1). In a continuum limit, the correlated continuous time random walk converges in distribution a subordinated process. The mean square displacement of the proposed process is computed, which is of the form 〈x2(t)〉∝tH=t1/(1+ρ+1/α). The anomy exponent H varies from α to α/(1+α) when -1<ρ<0 and from α/(1+α) to 0 when ρ>0. The generalized diffusion equation of the process is also derived, which has a unified form for the above two cases.

scholarly journals Supratentorial cavernous malformations adjacent to the corticospinal tract: surgical outcomes and predictive value of diffusion tensor imaging findings

2018 ◽  
Vol 128 (2) ◽  
pp. 541-552 ◽  
Author(s):  
Yuanxiang Lin ◽  
Fuxin Lin ◽  
Dezhi Kang ◽  
Yuming Jiao ◽  
Yong Cao ◽  
...  
Keyword(s):  
Surgical Outcomes ◽  
Predictive Value ◽  
Diffusion Tensor ◽  
Motor Deficits ◽  
Short Term ◽  
Cavernous Malformations ◽  
Scale Scores ◽  
The Mean ◽  
Deep Location

OBJECTIVEDiffusion tensor imaging (DTI) findings may facilitate clinical decision making in patients with supratentorial cavernous malformations adjacent to the corticospinal tract (CST-CMs). The objective of this study was to determine the predictive value of preoperative DTI findings for surgical outcomes in patients with CST-CMs.METHODSA prospectively maintained database of patients with CM referred to the authors' hospital between September 2012 and October 2015 was reviewed to identify all consecutive surgically treated patients with CST-CM. All patients had undergone sagittal T1-weighted anatomical imaging and DTI before surgery. Both DTI findings and clinical characteristics of the patients and lesions were analyzed with respect to surgery-related motor deficits. DTI findings included lesion-to-CST distance (LCD) and the alteration (i.e., deviation, interruption, or degeneration due to the CM) of CST on preoperative DTI images. Surgery-related motor deficits at 1 week and the last clinic visit (≥ 3 months) after surgery were defined as short-term and long-term deficits, respectively. Preoperative and final modified Rankin Scale scores were also analyzed to identify the surgical outcomes in these patients.RESULTSA total of 56 patients with 56 CST-CMs were included in this study. The mean LCD was 3.9 ± 3.2 mm, and alterations of the CST were detected in 20 (36.7%) patients. One week after surgery, 21 (37.5%) patients had short-term surgery-related motor deficits, but only 14 (25.0%) patients had long term deficits at the last clinical visit. The mean patient follow-up was 14.7 ± 10.1 months. The difference between preoperative and final modified Rankin Scale scores was not statistically significant (p = 0.490). Multivariate analysis showed that both short-term (p < 0.001) and long-term (p = 0.002) surgery-related motor deficits were significantly associated with LCD. Receiver operating characteristic (ROC) curve results were as follows: for short-term surgery-related motor deficits, the area under the ROC curve (AUC) was 0.860, and the cutoff point was LCD = 2.55 mm; for long-term deficits, the AUC was 0.894, and the cutoff point was LCD = 2.30 mm. Both univariate (p = 0.012) and multivariate (p = 0.049) analyses revealed that CST alteration on preoperative DTI was significantly correlated with short-term surgery-related motor deficits. On univariate analysis, deep location of the CST-CMs was significantly correlated with long-term motor deficits (p = 0.016). Deep location of the CST-CMs had a trend toward significance with long-term motor deficits on the multivariate analysis (p = 0.060).CONCLUSIONSTo facilitate clinical practice, the authors propose that 3.00 mm (2.55 to ∼3.00 mm) may be the safe LCD for surgery in patients with CST-CMs. A CST alteration on preoperative DTI and a deep location of the CST-CM may be risk factors for short- and long-term surgery-related motor deficits, respectively. A randomized controlled trial is needed to demonstrate the predictive value of preoperative DTI findings on surgical outcomes in patients with CST-CMs in future studies.

The Impact of Parameterized Lateral Mixing on the Antarctic Circumpolar Current in a Coupled Climate Model

2020 ◽  
Vol 50 (4) ◽  
pp. 965-982 ◽  
Author(s):  
Sarah Ragen ◽  
Marie-Aude Pradal ◽  
Anand Gnanadesikan
Keyword(s):  
Diffusion Coefficient ◽  
Wind Stress ◽  
Antarctic Circumpolar Current ◽  
Climate Model ◽  
Lateral Diffusion ◽  
Intermediate Waters ◽  
Circumpolar Current ◽  
The Antarctic ◽  
The Impact ◽  
Lateral Diffusion Coefficient

AbstractThis study examines the impact of changing the lateral diffusion coefficient ARedi on the transport of the Antarctic Circumpolar Current (ACC). The lateral diffusion coefficient ARedi is poorly constrained, with values ranging across an order of magnitude in climate models. The ACC is difficult to accurately simulate, and there is a large spread in eastward transport in the Southern Ocean (SO) in these models. This paper examines how much of that spread can be attributed to different eddy parameterization coefficients. A coarse-resolution, fully coupled model suite was run with ARedi = 400, 800, 1200, and 2400 m2 s−1. Additionally, two simulations were run with two-dimensional representations of the mixing coefficient based on satellite altimetry. Relative to the 400 m2 s−1 case, the 2400 m2 s−1 case exhibits 1) an 11% decrease in average wind stress from 50° to 65°S, 2) a 20% decrease in zonally averaged eastward transport in the SO, and 3) a 14% weaker transport through the Drake Passage. The decrease in transport is well explained by changes in the thermal current shear, largely due to increases in ocean density occurring on the northern side of the ACC. In intermediate waters these increases are associated with changes in the formation of intermediate waters in the North Pacific. We hypothesize that the deep increases are associated with changes in the wind stress curl allowing Antarctic Bottom Water to escape and flow northward.

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