Transverse Diffusion Coefficient Research Articles

Development of a Monte Carlo tool for simulating electron transport in noble liquids

This study presents a Monte Carlo simulation tool for modeling the transportation processes of thermal electrons in noble liquids, specifically focusing on liquid argon and liquid xenon. The study aims to elucidate the microscopical mechanisms governing the drift and diffusion of electrons within the context of time projection chambers (TPCs), with detailed considerations of coherent electron-atom scattering and electric field force. The simulation tool is implemented in the Geant4 framework, allowing for the exploration of electron transport parameters, including drift velocity, longitudinal diffusion coefficient, and transverse diffusion coefficient. The simulation is validated by comparing its results for drift velocity and diffusion coefficients with experimental measurements, revealing reasonable agreement in the low to moderate electric field ranges. Discrepancies between the simulation and experimental measurements are discussed, emphasizing the necessity for enhanced cross-section calculations and high-precision sampling. Despite certain limitations, the simulation tool provides valuable insights into electron transport in noble liquids, establishing a foundation for future enhancements and applications in various research areas

Electron scattering and transport in simple liquid mixtures

The theory for electron transport in simple liquids developed by Cohen and Lekner (1967 Phys. Rev. 158 305), is extended to simple liquid mixtures. The focus is on developing benchmark models for binary mixtures of hard-spheres, using the Percus-Yevick model (Lebowitz 1964 Phys. Rev. A 133 895, Hiroike 1969 J. Phys. Soc. Japan 27 1415) to represent the density structure effects. A multi-term solution of Boltzmann’s equation is employed to investigate the effect of the binary mixture structure on hard-sphere electron scattering cross-sections and transport properties, including the drift velocity, mean energy, longitudinal and transverse diffusion coefficients. Benchmark calculations are established for electrons driven out of equilibrium by a range of reduced electric field strengths ( 0.1−100 Td).

Study of turbulent transport in magnetized plasmas with flow using symplectic maps

Turbulent transport in a magnetized plasma of the kind found in tokamaks is modeled by a 2D wave spectrum that allows reduction to a symplectic map. The properties of particle transport when chaos sets in are analyzed in various circumstances including finite Larmor radius (FLR) effects and a background plasma flow. For large wave amplitudes, regular particle orbits become chaotic, which represents a type of Lagrangian turbulence. When chaos becomes global, it leads to the loss of particle confinement. Poloidal flows tend to decrease the chaos in some regions, and they can give rise to the formation of transport barriers. FLR effects not only reduce chaos but also give rise to non-local behavior. Thus, when the particles have a thermal distribution of Larmor radii, a non-Gaussian particle distribution function in space is obtained. However, the transport preserves its diffusive scaling when there is no flow. Previous results about the dependence of the diffusion coefficient with amplitude are re-derived analytically and numerically taking into account FLR effects. In the presence of general poloidal flows, the transport has to be described by a two-step map. They modify the nature of transport in the direction of the flow from diffusive to ballistic to super-ballistic, depending on the type of flow. The transverse transport, in turn, shows suppression of the oscillations with wave amplitude that are present in the absence of flow. When the plasma flow varies linearly with radius, the transport can be studied with a similar single-step map, and the transverse diffusion coefficient is reduced while parallel transport can become super-ballistic. For non-monotonic flows, there are accelerating modes that can produce ballistic-like particles while the bulk of the particles behaves diffusively.

Permeable Cornified Envelope Layer Regulates the Solute Transport in Human Stratum Corneum

To unravel the diffusion mechanisms of percutaneous drug delivery, suitable numerical analysis of stratum corneum structure is essential. In this research paper, we accounted for the permeable envelope layer in the brick-and-mortar finite element models of human stratum corneum. Both penetration and desorption experiments for tritiated water were simulated by transient finite element analysis. Rivet-shaped corneodesmosomes were included in the brick and mortar model. Results showed that cornified lipid permeability (Penv) is a determinant in desorption of the solute, while lipid transverse diffusion coefficient (Dlip-trans) is prominent during penetration. These two major unknowns (Penv and Dlip-trans) were obtained by extensive fitting of the finite element model to the experimental water data. Penv and Dlip-trans were determined to be 1×10−2 cm/s and 5.7×10−10 cm2/s, respectively.

Monte Carlo model for ion mobility and diffusion for characteristic electric fields in nanodosimetry

The quantification of the effects of space radiation for manned spaceflight can be approximated by nanodosimetric measurements. For the development of nanodosimetric detectors, a Monte Carlo model for ion mobility and diffusion for characteristic electric fields is presented.This model can be used to describe the interactions of ions in their parent gas based solely on commonly known input parameters, such as the ionization potential, kinetic diameter, molar mass, and polarizability of the gas. A model for approximating the resonant charge exchange cross section has been proposed, requiring only the ionization energy and mass of the parent gas as input parameters. The method proposed in this work was tested against experimental drift velocity data for a wide range of gases (helium, neon, nitrogen, argon, krypton, carbon monoxide, carbon dioxide, oxygen, propane). The transverse diffusion coefficients were compared to experimental values for helium, nitrogen, neon, argon, and propane gas.With the Monte Carlo code and resonant charge exchange cross section approximation model presented in this work, it is now possible to calculate an estimate of the drift velocities, transverse diffusion, and thus the ion mobility of ions in their parent gas. This is essential for further nanodosimetric detector development, as those parameters are often not well known for the gas mixtures used in nanodosimetry.

Understanding the QCD medium by the diffusion of charm quarks using a color string percolation model

We study the drag and diffusion coefficients of the charm quark in the deconfined matter produced in the ultra-relativistic collisions by taking the Color String Percolation Model (CSPM) approach. CSPM, being a QCD-inspired model, can give us essential information about the hot and dense system produced in ultra-relativistic collisions. With the information on initial percolation temperature and percolation density, we estimate the relaxation time ($\tau_{c}$), drag coefficient ($\gamma$), transverse momentum diffusion coefficient ($B_{0}$), and spatial diffusion coefficient ($D_{s}$) of charm quark inside a deconfined medium. Finally, we compare the obtained results with lattice QCD and with various other theoretical models. A good agreement can be observed between the results obtained from CSPM and lattice QCD.

Evaluation of a random displacement model for scalar mixing in ecological channels partially covered with vegetation.

The flow structure in natural rivers may change due to the disturbance of vegetation, further affecting the transport of pollutants and sediment (Liu et al. 2020). In this paper, the random displacement model (RDM) is presented to study the material transport in the emergent vegetated flow by predicting the longitudinal dispersion coefficient (LDC), which plays an important role in the longitudinal transport of pollutants in natural rivers covered by emergent vegetation. RDM can be applied for the analysis of the vegetated flow provided that the velocity distribution and the turbulent diffusion coefficient distribution remain known. According to the experimental data on velocity and Reynolds stress, the flow field was divided into four sub-zones along the cross-sectional area where the transverse distribution of the longitudinal velocity and also transverse turbulent diffusion coefficient were determined. Moreover, the simulated results of the longitudinal dispersion coefficient were verified by using the previously measured data. In addition, the sensitivity analysis of RDM parameters was carried out. In comparison with the shear layer width and the velocity difference, the impact of vegetation zone width on the longitudinal dispersion coefficient was greater, but the model was fundamentally stable, further confirming that the analytical model can be reliable for predicting the longitudinal dispersion coefficient in the vegetated open-channel flow. Accurately estimating the longitudinal dispersion coefficient is useful for understanding the transport and fate of pollutants in river channels and, thereby, for exploring the sustainable development of the river ecological environment, as well as optimizing the planning and design of river course.

Phase-field model of grain boundary diffusion in nanocrystalline solids: Anisotropic fluctuations, anomalous diffusion, and precipitation

The anisotropic phase-filed model of grain boundary diffusion and precipitation of solute in nanocrystalline solids has been developed. In this model, the Cahn–Hilliard equation is generalized for the anisotropic phase-field diffusion of solute and anisotropic compositional fluctuations. It is found that dynamics of solute concentration profile demonstrates the anomalous diffusion behavior with scaling parameters depending on the mobility ratio and microstructure of a solid solution. It is noteworthy that the increase in source concentration can slow down the concentration front propagation due to uphill diffusion or formation of a new phase. Parameters of grain boundary diffusion control the precipitation dynamics. In particular, a decrease in transverse diffusion coefficient is responsible for longer incubation time, and lower rates of nucleation and nuclei growth in comparison with the case of isotropic solute transport near grain boundaries. Transport properties of boundary and bulk are responsible for the formation of the bimodal size distribution function of second phase particles and specific kinetics of average radius and number density.

Statistical physics of inhomogeneous transport: Unification of diffusion laws and inference from first-passage statistics.

Characterization of composite materials, whose properties vary in space over microscopic scales, has become a problem of broad interdisciplinary interest. In particular, estimation of the inhomogeneous transport coefficients, e.g., the diffusion coefficient or the heat conductivity, which shape important processes in biology and engineering, is a challenging task. The analysis of such systems is further complicated because two alternative formulations of the inhomogeneous transport equationsexist in the literature-the Smoluchowski and Fokker-Planck equations, which are also related to the so-called Ito-Stratonovich dilemma. Using the theory of statistical physics, we show that the two formulations, usually regarded as distinct models, are physically equivalent. From this result we develop efficient estimates for the transverse space-dependent diffusion coefficient in fluids near a phase boundary. Our method requires only measurements of escape probabilities and mean exit times of molecules leaving a narrow spatial region. We test our estimates in three case studies: (i) a Langevin model of a Büttikker-Landauer ratchet; atomistic molecular-dynamics simulations of liquid-water molecules in contact with (ii) vapor, and (iii) soap (surfactant) film which has promising applications in physical chemistry. Our analysis reveals that near the surfactant monolayer the mobility of water molecules is slowed down almost twice with respect to the bulk liquid. Moreover, the diffusion coefficient of water correlates with the transition from hydrophilic to hydrophobic parts of the film.

Heavy quark dynamics in a strongly magnetized quark-gluon plasma

We present a calculation of the heavy quark momentum diffusion coefficients in a quark-gluon plasma under the presence of a strong external magnetic field, within the Lowest Landau Level (LLL) approximation. In particular, we apply the Hard Thermal Loop (HTL) technique for the resummed effective gluon propagator, generalized for a hot and magnetized medium. Using the derived effective HTL gluon propagator and the LLL quark propagator we analytically derive the full results for the longitudinal and transverse momentum diffusion coefficients as well as the energy losses for charm and bottom quarks beyond the static limit. We also show numerical results for these coefficients in two special cases where the heavy quark is moving either parallel or perpendicular to the external magnetic field.

Anisotropic behaviors of moisture absorption and hygroscopic swelling of unidirectional flax fiber reinforced composites

This work aims to study the anisotropic moisture absorption characteristics of unidirectional flax fiber reinforced composites (FFRCs) and evaluate the variations of the internal stress caused by the hygroscopic deformation, which might lead to the deterioration of the mechanical properties of the composites. FFRCs were prepared using vacuum-assisted resin infusion molding (VARIM) technology. Moisture absorption tests were designed by sealing the designated surfaces with a polyurethane waterproof coating to keep the moisture absorption of FFRCs only in the desired directions. The deformation caused by moisture absorption in the width direction was also monitored. It confirms that the moisture absorption of FFRCs conformed to the 3D Fick's law, and the influence of moisture absorption in the width direction cannot be ignored, especially for the unidirectional transverse tensile test specimen (UTFRC). The hygroscopic deformation of the unidirectional FFRCs showed that the material expands perpendicular to the fiber direction but shrinks along the fiber direction. The modified 3D Fick’s law based on heat conduction equation was performed to reveal the mechanism of the above moisture absorption and hygroscopic deformation. According to the finite element inversion, it was found that the axial diffusion coefficient along flax fiber bundles was much larger than the transverse diffusion coefficient perpendicular to the fiber bundle direction due to the existence of the unique lumen structure inside flax fibers. In addition, the high internal stress caused by the mismatched swelling properties between the fiber and the matrix was the main reason for the damage of the FFRCs, especially at the interface, which may seriously affect the service life of the composites. The outcome of this study can be used to accurately analyze the hydro-elastic behaviors of plant fiber reinforced composites, which is a prerequisite for predicting the mechanical properties affected by moisture absorption.

Numerical study of the transverse diffusion coefficient for a one component model of plasma.

In this paper, we discuss the results of some molecular dynamics simulations of a magnetized one component plasma, targeted to estimate the diffusion coefficient D⊥ in the plane orthogonal to the magnetic field lines. We find that there exists a threshold with respect to the magnetic field strength |B→|: for weak magnetic field, the diffusion coefficients scale as 1/|B→|2, while a slower decay appears at high field strength. The relation of this transition with the different mixing properties of the microscopic dynamics is investigated by looking at the behavior of the velocity autocorrelation.

Influence of transverse carrier diffusion on two-dimensional optical rogue waves in broad-area semiconductor lasers with a saturable absorber

The statistics and dynamics of two-dimensional rogue waves in a broad-area semiconductor laser with an intracavity saturable absorber are numerically investigated under the effect of transverse carrier diffusion. We show that lateral diffusion of carriers alters the statistics of rogue waves by enhancing their formation in smaller ratios of carrier lifetimes in active and passive materials while suppressing them when the ratio is larger. The temporal dynamics of the emitted rogue waves is also studied and show that the finite nonzero transverse carrier diffusion coefficient gives them a longer duration. To further approach a realistic experimental situation, we also investigate the statistics and dynamics of rogue waves by simulating a circular disk-shape pump which replaces the flat pump profile typically used in numerical simulations of broad-area lasers. We show that a finite pump shape reduces the number of emitted rogue waves per unit area both below and above the laser threshold for every carrier lifetime ratio. The temporal width of the emitted rogue waves is also shown to decrease as a consequence of removing the nonphysical effects of the infinite flat pump on carrier dynamics.

Heavy quark dynamics in a strongly magnetized medium

We present a calculation of the heavy quark momentum diffusion coefficients in a strongly magnetized medium, within the Lowest Landau Level (LLL) approximation. In particular, we use the Hard Thermal Loop (HTL) resummed effective gluon propagator, generalized for a hot and magnetized medium. Using this effective HTL gluon propagator along with the LLL quark propagator we analytically derive the full results for the longitudinal and transverse momentum diffusion coefficients for charm and bottom quarks beyond the static limit. Going beyond the static limit of the heavy quark, we also show numerical results for these coefficients in two special cases where the heavy quark is moving either parallel or perpendicular to the external magnetic field.

On the properties of a negative-ion TPC prototype with GridPix readout

The performance of a GridPix detector to read out a negative ion TPC was studied using a module with four GridPix chips that are based on the Timepix3 pixelated readout ASIC. The quad module dimensions are 39.6mm×28.38mm, and the maximum drift distance is 40mm. The TPC is operated using a 93.6/5.0/1.4 gas mixture (by volume) of Ar/iC4H10/CS2 with a small amount of oxygen and water vapour at a pressure of 1030mbar and a temperature of 297K. Tracks were produced by a pulsed N2 laser. The GridPix chips are sensitive to single drift ions, and allow for the determination of the drift distance using the velocities of the different ion species. The 1.56ns time resolution of the Timepix3 chips allows for a precise determination of the drift properties in the longitudinal direction. The measured mobility of majority ion charge carriers is (1.391±0003) cm2/V/s. Using the high granularity pixel readout, the transverse and longitudinal diffusion coefficients were measured to correspond to an effective thermal diffusion temperature of 314 K and 384 K respectively. For 429 detected ions, the precision on the absolute drift distance is expected to be 1.33mm for a mean drift distance of 20mm.

Effect of CO2-brine-rock reactions on pore architecture and permeability in dolostone: Implications for CO2 storage and EOR

Geologic carbon sequestration (GCS) is considered a feasible technology for storing substantive volumes of greenhouse gases in subsurface geological formations. In the reservoir, far from carbon dioxide (CO2) injection wells or in post-injection scenarios, diffusion dominates over advection. This condition conjoins with spatially distributed geochemical reactions to induce heterogeneous changes in pore architecture, i.e. pore body and throat sizes or surface roughness. These changes can affect CO2 transport properties and storage capacity. In this work, we investigated mineral dissolution and precipitation in dolomite samples saturated with a CO2-saturated brine at 93 °C and 34.5 MPa, aged without flow. Two rock types samples, i.e. intergranular- and vuggy-dominant, were selected to investigate changes in pore size, porosity and permeability under reactive conditions. Mineral dissolution and precipitation were characterized using scanning electron microscopy. Changes in pore size were quantified via time-domain nuclear magnetic resonance (TD-NMR) transverse relaxation time (T2) and diffusion coefficient (D) distributions. We show that mineral dissolution likely occurs in highly permeable pathways. These observations are confirmed through analysis of (T2) and diffusion coefficient (D) distributions. In contrast to results during CO2-enriched brine continuous injection, mineral precipitation was observed in micropores. The leftward shift of the T2 peaks, corresponding to micropores, also evidenced mineral precipitation in low-permeability zones. However, microscale alterations resulted only in a subtle increase in porosity and permeability. Results in this study shed light on effects of geochemical reactions on alteration of rock properties in diffusion-dominated regions during CO2 storage.

A numerical study of field strength and clay morphology impact on NMR transverse relaxation in sandstones

Nuclear magnetic resonance (NMR) relaxometry is a common technique for the petrophysical characterization of sedimentary rocks. The standard interpretation of NMR transverse relaxation responses is based on the assumptions of the fast diffusion limit, dominant surface relaxation, and weak coupling between pores, allowing an interpretation of the NMR response as pore size distribution. In general, three asymptotic relaxation regimes can be defined by comparing dephasing, structural and diffusion length scales. The shortest length scale defines the dominating relaxation regime, which is either the free diffusion, motional averaging, or localization regime. Complex mineralogy and morphology of rocks, especially due to clay minerals, may lead to the co-existence and coupling of multiple relaxation regimes in the presence of surface relaxivity heterogeneity and internal gradient effects.In this work the relationship between morphology of rocks, strength of applied magnetic field, resulting relaxation regimes and observed NMR relaxation responses is studied numerically. Limitations in the discretization of clays typical for micro-CT images are addressed by introducing a fine-scale kaolinite model based on SEM images. The model is utilized to evaluate the field-dependent mean transverse relaxation time and effective diffusion coefficient of clay regions. These effective parameters are incorporated into random-walk simulations on micro-CT images. Relaxation regimes are analysed spatially for three different types of sandstone as function of external magnetic field strength. Increase of paramagnetic clay content, field strength and echo-time increases the fraction of spins relaxing in the localization regime within macro-pores, typically being localised in the regions neighbouring clay pockets and grain surfaces. We demonstrate that a significant contribution of the localization regime to relaxation may lead to incorrect predictions of pore-size distributions and fluid typing. The prefactor of permeability correlations varies significantly due to clay effects. Accounting for these effects should enable more robust petrophysical interpretations.

Relaxation and diffusion of water protons in BDDE cross-linked hyaluronic acid hydrogels investigated by NMR spectroscopy—Comparison with physicochemical properties

Cross-linked hyaluronic acid (HA) hydrogels are used in many biomedical applications but their characterization in order to distinguish between physicochemical properties is challenging. Longitudinal (T1) and transverse (T2) relaxation times and diffusion coefficient (D) of water protons in diepoxide 1,4-butanediol diglycidyl ether (BDDE)-cross-linked HA hydrogels were analyzed by high-field NMR spectroscopy to distinguish between different physicochemical properties. Hydrogels of different degrees of modification and cross-linking, representing a range of gel content, swelling ability, elastic and viscous behavior were studied, as well as solutions of native HA of different molecular weights. T1, T2 and D were measured for several concentrations of HA and as a function of temperature. D and T1 showed a weak concentration dependence, but did not differ between the hydrogels. T2, dominated by chemical exchange between water protons and exchangeable protons of HA, varied significantly between the different hydrogels and the temperature profiles changed dramatically between different concentrations.

New and rapid pulse sequences for two-dimensional D-T1 correlation measurements

Longitudinal relaxation time (T1), transverse relaxation time (T2) and diffusion coefficient (D) values have been widely used for the characterizations of materials using low field Time Domain Nuclear Magnetic Resonance (TD-NMR). Each parameter can be determined using one-dimensional techniques or their values and correlations by multi-dimensional experiments such as T1-T2, D-T2, and T1-D-T2. In this work, we studied four D-T1 sequences for TD-NMR combining Stejskal-Tanner Pulse Gradient Spin Echo (PGSE) diffusion measurement with Inversion-Recovery (IR), Saturation-Recovery (SR), Small-Angle Continuous Wave Free Precession (CWFP-T1) and Small-Angle Flip-Flop (SAFF) for T1 measurement. The results show that rapid D-T1 measurements can be obtained with single shot CWFP-T1 and SAFF sequences. The two sequences were two and eight time fast than sequences based on SR and IR, respectively. Although the two fast sequences yield low signal-to-noise ratio signal, they can be as fast as the traditional D-T2 experiment, or even faster, because it is not necessary to wait a recycle delay of 5 T1. Another advantage of the CWFP-T1 and SAFF methods, when compared to the one based on SR or CPMG (for D-T2) are the low specific absorption rate (SAR) of these sequences due the low flip angles in the sequences, that reduces the sample heating problem. These sequences were initially studied using phantom samples. They also were used to study plant tissues to observe the anisotropic diffusion in asparagus. Therefore, they can be useful methods for practical application in TD-NMR.

Drift Characteristics of Metal Ions in Helium in an External Electric Field

The results of Monte Carlo calculations of the drift characteristics of metal ions (Li, Be, Al, Fe, Cu, W, Hg, and Au) in a constant uniform electric field 1 < E/N < 1000 Td in helium are presented. The dependences of the mobility, longitudinal and transverse diffusion coefficients, and mean kinetic energy of ions, as well as their longitudinal and transverse temperatures, on the electric field strength are given.