Longitudinal Diffusion Coefficient Research Articles

$\mathcal{R}^2$ curvature-squared corrections on Langevin diffusion coefficients

Abstract The effect of finite coupling corrections to the Langevin diffusion coefficients on a moving heavy quark in the Super Yang-Mills plasma is investigated. 
These corrections are related to curvature squared corrections in the corresponding gravity sector. 
We compare the results of both longitudinal and perpendicular Langevin diffusion coefficients with those in $\mathcal{N}$=4 Super Yang-Mills plasma. It is observed that the curvature-squared corrections influence the Langevin diffusion coefficients, and the corrections for both Langevin diffusion coefficients demonstrate the dependence on the velocity of the moving heavy quark and the specifics of the higher derivative correction.
In addition, we conduct calculations for the Langevin diffusion coefficients of a moving heavy quark within the Gauss-Bonnet background. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

Diffusion and mobility measurements for propane gas with a nanodosimetric detector

For the operation of nanodosimetric detectors with propane gas, it is essential to know the gas properties at room temperature, such as drift velocity, ion mobility, longitudinal and transversal diffusion coefficients. For propane gas there is only limited experimental data available for the ion mobility and transverse diffusion coefficients. In this work, the drift velocities and ion mobilities for propane were obtained over the reduced electric field range E/N from 24 to 212 Td (1 Td = 10−17 Vcm2) based on arrival time measurements. The reduced ion mobility K0 for propane was determined to be (0.71±0.09) cm2/Vs. The longitudinal diffusion coefficients were determined from the widths of the experimental arrival time spectra and found to be NDL = (3.7 ± 0.5)⋅1019 1/ms in the low field limit below 30 Td.The results presented in this work extend the range of available experimental data for propane, as well as introduce first experimental measurements of the longitudinal diffusion coefficient of propane.

Two-Dimensional Time Fractional River-Pollution Model and Its Remediation by Unsteady Aeration

This study contains a mathematical model for river pollution and its remediation for an unsteady state and investigates the effect of aeration on the degradation of pollutants. The governing equation is a pair of nonlinear time-fractional two-dimensional advection-diffusion equations for pollutant and dissolved oxygen (DO) concentration. The coupling of these equations arises due to the chemical interactions between oxygen and pollutants, forming harmless chemicals. The Fractional Reduced Differential Transform Method (FRDTM) is applied to provide approximate solutions for the given model. Also, the convergence of solutions is checked for efficacy and accuracy. The effect of longitudinal and transverse diffusion coefficients of pollutant and DO on the concentration of pollutant and DO is analyzed numerically and graphically. Also, we checked the effect of change in the river’s longitudinal and transverse seepage velocity on pollutant and DO concentration numerically and graphically. We analyzed the comparison of change in the value of half-saturated oxygen demand concentration for pollutant decay on pollutant and DO concentration numerically and graphically. Also, numerical and graphical analysis examined the effect of fractional parameters on pollution levels.

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

Heavy quark diffusion coefficients in magnetized quark-gluon plasma

We evaluate the heavy quark momentum diffusion coefficients in a hot magnetized medium for the most general scenario of any arbitrary values of the external magnetic field. We choose to work with the systematic way of incorporating the effect of the magnetic field, by using the effective gluon and quark propagators, generalized for a hot and magnetized medium. To get gauge independent analytic form factors valid through all Landau levels, we apply the hard thermal loop technique for the resummed effective gluon propagator. The derived effective hard thermal loop gluon propagator and the generalized version of Schwinger quark propagator subsequently allow us to analytically evaluate the longitudinal and transverse momentum diffusion coefficients for charm and bottom quarks beyond the static limit. Within the static limit we also explore another way of incorporating the effect of the magnetic field, i.e. through the magnetized medium modified Debye mass and compare the results to justify the need for structural changes. Published by the American Physical Society 2024

Numerical simulation of velocity distribution and pollution transport in a two-stage channel with vegetation on a floodplain

Compound cross-sections are common forms of river cross-sections in nature. Due to their more complex structure, it is more difficult to study their hydrodynamic and pollutant transport characteristics. How to establish effective models to simulate such conditions has recently become a hot topic of attention. The work presented in this article establishes a numerical model to simulate the flow velocity and pollutant transport in a compound cross-section channel using the lattice Boltzmann method and random displacement method to study the hydrodynamic and pollutant transport characteristics under flexible vegetation cover. The model can effectively generalize the vegetation drag force on the floodplain of the compound cross-section and provide the distribution pattern of flow velocity under uneven vegetation cover. At the same time, the lateral diffusion coefficients of pollutants on the main channel and floodplain are provided separately. These have higher accuracy than those determined by traditional methods that rely on simple longitudinal diffusion coefficients. This study can provide a theoretical reference for optimizing vegetation planting in compound cross-section channels.

Heavy quark diffusion coefficient in heavy-ion collisions via kinetic theory

We compute the heavy quark momentum diffusion coefficient κ using QCD kinetic theory for a system going through bottom-up isotropization in the initial stages of a heavy ion collision. We find that the values of κ are within 30% from a thermal system at the same energy density. When matching for other quantities we observe considerably larger deviations. We also observe that the diffusion coefficient in the transverse direction is larger at high occupation numbers, whereas for an underoccupied system the longitudinal diffusion coefficient dominates. The behavior of the diffusion coefficient can be understood on a qualitative level based on the Debye mass mD and the effective temperature of soft modes T*. Our findings for the kinetic evolution of κ in different directions can be used in phenomenological descriptions of heavy quark diffusion and quarkonium dynamics to include the impact of preequilibrium stages. Published by the American Physical Society 2024

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).

Heavy quark momentum diffusion coefficient during hydrodynamization via effective kinetic theory

In these proceedings, we compute the heavy quark momentum diffusion coefficient using QCD effective kinetic theory for a plasma going through the bottom-up thermalization scenario until approximate hydrodynamization. This transport coefficient describes heavy quark momentum diffusion in the quark-gluon plasma and is used in many phenomenological frameworks, e.g. in the open quantum systems approach. Our extracted nonthermal diffusion coefficient matches the thermal one for the same energy density within 30%. At large occupation numbers in the earliest stage, the transverse diffusion coefficient dominates, while the longitudinal diffusion coefficient is larger for the underoccupied system in the later stage of hydrodynamization.

Two- and three-body attachment, electron transport and ionisation in water-air mixtures

Three-body electron attachment in the mixtures of H2O and dry air have been measured over a wide range of the density-reduced electric field, E/N, from 3–130 Td and gas pressures, for mixture combinations ranging from 1% to 50% of H2O. We have measured the regions of three-body attachment (3–30 Td) and two-body dissociative attachment (40–130 Td). Besides, the increasing amount of H2O in the mixture causes an increase in the three-body reaction rates of up to two orders of magnitude in comparison with that measured for dry air. On the other hand, the three-body attachment coefficients exceed the two-body ones (dissociative attachment) at high pressures. Good agreement has been found with previous measurements of H2O-dry air mixtures with H2O concentrations of up to 2%. We know of no previous work for higher H2O concentrations. Values of the effective ionisation coefficients and longitudinal diffusion coefficients derived from the same measurements are also presented.

Micro-scale simulation of adsorption-diffusion behaviors of nanoparticles onto mobile oil/water interface

A novel, hybrid pore-scale simulation method using Lattice-Boltzmann (LB) coupled with Langevin-Dynamics (LD) is proposed to investigate the physics of nanoparticles onto oil/water interface. Based on the LB method, the high-resolution characterization of oil-water interface is established. Then, in a fashion of discrete LB forcing source distribution, the LD method is introduced to characterize the effects of Brownian motion, thermal fluctuation-dissipation, multi-body hydrodynamics, and particle-particle interactions. By the means of the new LB-LD coupling model, the adsorption and diffusion characterization of nanoparticles onto oil/water interface are investigated. Moreover, by introducing the interference coefficient and non-equilibrium time, a modified Langmuir adsorption equation is first established by more accurately quantifying the adsorption characterization of nanoparticles and the consequent impacts onto the oil/water interfacial force (IFT), which cannot be accurately described by the classical Langmuir model. For the example of SiO2 nanoparticles adsorption, it is observed that small-size nanofluids with high concentration could accelerate the adsorption of nanoparticles. In addition, both the lateral and longitudinal diffusion coefficients of nanoparticles in the water phase and onto interface are obtained, and of which the underlying mechanisms are explained by introducing residual oil. The proposed simulation method provides valuable insights into how nanoparticles adsorb and diffuse onto oil/water interface and how oil/water IFT can be reduced.

Electron-neutral collision cross sections for H2O: II. Anisotropic scattering and assessment of the validity of the two-term approximation

This work proposes a complete and consistent set of cross sections (CS) for electron collisions with water gas molecules to be published in the IST-Lisbon database on LXCat. The set is validated by the electron swarm analysis technique. The anisotropic angular distribution of electrons in rotational collisions is considered by means of the Born approximation in a two-term Boltzmann solver (LisbOn KInetics two-term Boltzmann solver (LoKI-B)) and a Monte Carlo simulations code (LoKI-MC), both freely available as open-source codes. The inclusion of electron anisotropic scattering in rotational collisions significantly improves the agreement between calculations and measurements of the electron drift velocity, reduced mobility, characteristic energy, reduced Townsend ionisation coefficient, reduced effective Townsend coefficient and reduced attachment coefficient. The MC simulations are deemed more accurate and shown to yield similar results as LoKI-B with the proposed set. The use of LoKI-MC also validates the set of CSs against parameters that cannot be obtained by LoKI-B, such as the longitudinal diffusion coefficient or the bulk transport coefficients.

Data-driven discovery of electron continuity equations in electron swarm map for determining electron transport coefficients in argon

In this study, we develop a novel method for determining electron transport coefficients from electron swarm maps measured by a scanning drift-tube experiment. In our method, two types of electron continuity equations that describe either the spatial or the temporal evolution of an electron swarm are discovered in the electron swarm map. The electron transport coefficients can be determined from the coefficients in the discovered equations. Therefore, we can determine the Townsend ionization coefficient, ionization rate coefficient, center-of-mass drift velocity, mean arrival-time drift velocity, longitudinal diffusion coefficient, and longitudinal third-order transport coefficient. These transport coefficients in argon are determined over a wide range of reduced electric fields, E/N, from 29.7 to 1351.6 Td (1 Td = 10−21 Vm2) using our method. We establish that the consideration of high-order transport coefficients, which have been systematically ignored so far, is important for the proper determination of low-order transport coefficients, specifically the electron drift velocity and longitudinal diffusion coefficient, in the presence of ionization growth.

A predictive model for early therapeutic efficacy of colorectal liver metastases using multimodal MRI data.

Liver metastases is a pivotal factor of death in patients with colorectal cancer. The longitudinal data of colorectal liver metastases (CRLM) during treatment can monitor and reflect treatment efficacy and outcomes. The objective of this study is to establish a radiomic model based on longitudinal magnetic resonance imaging (MRI) to predict chemotherapy response in patients with CRLM. This study retrospectively enrolled longitudinal MRI data of five modalities on 100 patients. According to Response Evaluation Criteria in Solid Tumors (RECIST 1.1), 42 and 58 patients were identified as responders and non-responders, respectively. First, radiomic features were computed from different modalities of image data acquired pre-treatment and early-treatment, as well as their differences (Δ). Next, the features were screened by a two-sample t-test, max-relevance and min-redundancy (mRMR), and least absolute shrinkage and selection operator (LASSO). Then, several ensemble radiomic models that integrate support vector machine (SVM), k-nearest neighbor (KNN), gradient boost decision tree (GBDT) and multi-layer perceptron (MLP) were established based on voting method to predict chemotherapy response. Data samples were divided into training and verification queues using a ratio of 8:2. Finally, we used the area under ROC curve (AUC) to evaluate model performance. Using the ensemble model developed using featue differences (Δ) computed from the longitudinal apparent diffusion coefficient (ADC) images, AUC is 0.9007±0.0436 for the training cohort. Applying to the testing cohort, AUC is 0.8958 and overall accuracy is 0.9. Study results demonstrate advantages and high performance of the ensemble radiomic model based on the radiomics feature difference of the longitudinal ADC images in predicting chemotherapy response, which has potential to assist treatment decision-making and improve clinical outcome.

Driven particle in a two-dimensional periodic substrate: Nonmonotonic dependence of drift velocity on temperature.

Motion of a driven particle in a two-dimensional (2D) periodic potential of square symmetry is studied by means of Brownian dynamics simulations. The average drift velocity and long time diffusion coefficients are obtained as a function of driving force and temperature. For driving forces above the critical depinning force, a reduction of drift velocity is observed as temperature is increased. The drift velocity reaches a minimum for temperatures at which k_{B}T is of the order of the barrier height of the substrate potential and then increases and saturates to the value of drift velocity for the substrate free case. Depending on the driving force, the drop in drift velocity can be as large as 36% of its value at low temperatures. While this phenomenon is observed in 2D for different types of substrate potentials studied and for various drive directions, studies using the exact result show no such dip in drift velocity in one dimension (1D). As in the case of 1D, a peak is observed in the longitudinal diffusion coefficient as the driving force is varied at a fixed temperature. But unlike in 1D, the location of the peak is temperature dependent. Approximate analytical expressions for the average drift velocity and the longitudinal diffusion coefficient are formulated using the exact results in 1D by finding a temperature dependent effective 1D potential to model the motion in the presence of a 2D substrate. This approximate analysis is successful in qualitatively predicting the observations.

Scanning drift tube measurements and kinetic studies of electron transport in CO

We present scanning drift tube measurements of electron swarm transport coefficients in CO as a function of the reduced electric field at room temperature under time-of-flight conditions. The measurements are compared to modeling results and other available experimental data on swarm transport over the broad range of from 2 Td to 1603 Td. The modeling results are obtained in Monte Carlo simulations and by solving the electron Boltzmann equation using a multi-term approach and the density gradient expansion procedure. We find generally good agreement between the measured and calculated transport coefficients. We propose a strategy to improve the cross-section set used to explain certain discrepancies at lower values. Measurements and calculations of electron transport coefficients under hydrodynamic conditions are complemented by Monte Carlo simulations of electron transport in an idealized steady-state Townsend (SST) setup. The ionization coefficient is calculated as a function of from the spatial density profiles of the electrons and compared to the corresponding values evaluated from the knowledge of the effective ionization frequency, drift velocity and longitudinal diffusion coefficient. Contrary to the traditional views, according to which the spatial relaxation of the mean energy and other transport properties for electrons in molecular gases is most commonly monotonic or quasi-monotonic, we find a ‘window’ of where the SST transport properties of the electrons exhibit oscillatory behavior as they relax towards the equilibrium state far downstream from the electron emitting boundary.

Pulsed Townsend measurements with mixtures of C4F7N and C5F10O up to 1800 Td

Effective ionization rate, bulk drift velocity and bulk longitudinal diffusion coefficient for electron swarms in mixtures consisting of either C4F7N or C5F10O in atmospheric gases—CO2, N2 and O2 are measured using a Pulsed Townsend setup. Measurements are carried out between 100 Td and 1800 Td.

Cross section sets and transport parameters for Ar+ ions in CF4 gas

Understanding plasma distribution, characteristics and phenomena is important for the development and optimization of semiconductor device manufacturing plasma equipment, such as etching and deposition tools. For this reason, plasma simulation is currently being utilized at every stage of equipment design, development and improvement. The cross section sets obtained by applying Denpoh-Nanbu theory to Ar+ on CF4 collisions were found to be in general qualitative and in part quantitative agreement with data from the literature. The Monte Carlo technique was applied to perform calculations of transport parameters. Calculated cross sections can be used to obtain transport coefficients, specially drift velocity, characteristic energy, reduced mobility, longitudinal diffusion and rate coefficients for low and moderate reduced electric fields E/N (E-electric field strength; N-gas density) and accounting for the non-conservative collisions.

Measurement of the molecular diffusion coefficient and the effective longitudinal diffusion under supercritical fluid chromatography conditions in packed bed columns

The improvement of supercritical fluid chromatography (SFC) instrumentation enhanced its reliability and utility over the past decade. The further development of high speed and high resolution separations is however obstructed by the lack of accurate models for axial dispersion in SFC. This work is a first step to tackle this by developing more reliable methods to measure molecular (Dmol) and longitudinal diffusion (Deff) in SFC, as these affect all aspects of separation efficiency. In the present contribution, we report on an improved method, to enable more flexible, reliable and accurate measurements of Dmol in SFC using commercial instrumentation. A two-column variant of the stopped-flow experiment is proposed as an adapted set-up for measuring the effective longitudinal diffusion coefficient Deff in SFC-conditions. Using the set-ups for a number of test-compounds, it has been found that Deff, and the coefficients describing its constituent sub-processes (cf. particle diffusion Dpart and surface diffusion γsDs), all vary in a linearly proportional way with the bulk diffusion coefficient Dmol within a high degree of accuracy. It has also been found that Deff decreases much more sharply with increasing retention factor compared to LC. By applying the effective medium theory, it was found that the relative surface diffusion coefficient γsDs/Dmol decreases strongly with retention factor for the investigated solutes and column, in contrary to what is typically observed in reversed phase liquid chromatography. Results indicate that this might be related to a change in retention behavior of the analytes. Obviously, more analytes and conditions need to be explored to complete this picture and the extend range of applicability of these observations.

Viscosity reduction mechanism of functionalized silica nanoparticles in heavy oil-water system

The in-depth study of the viscosity reduction mechanism of nanoparticles (NPs) is especially important for the extraction of heavy oil resources. In this work, molecular dynamics (MD) simulation was used to investigate the effect of the difference in hydrophilicity/hydrophobicity of the grafted molecules on the viscosity reduction process of functionalized SiO2 NPs in heavy oil. First, we investigated the distribution of various molecules in the oil-water system, and it was found that the asphaltene and resin components in heavy oil were adsorbed on the surface of the functionalized SiO2 NPs. And with the increase of the surface lipophilicity or grafting density of the surface of the NPs, the more obvious this adsorption phenomenon is. Then, we also found that the ability to adsorb asphaltene and reduce interfacial tension between oil and water was significantly enhanced with the increase of lipophilicity on the surface of the nanoparticle viscosity reducers. And the GLA-K-SiO2 nanoparticle viscosity reducer can reduce the interfacial tension from 51.102 mN/m to 41.956 mN/m, showing the best ability to reduce interfacial tension. In addition, the amphiphilic NPs have both high longitudinal and lateral diffusion coefficients, so they diffuse more easily into the oil phase system and more favorable for adsorption of oil-phase components. Finally, by comparing the adsorption structures of asphaltene on the surface of different functionalized SiO2 NPs, two adsorption configurations were obtained: vertical or large inclined adsorption and parallel or slightly inclined adsorption. Most importantly, it was found that functionalized SiO2 NPs could disassemble the asphaltene large accumulation structure into small asphaltene clusters, which reducing the viscosity of the heavy oil. This work is of great significance to the design and study of grafted nanoparticle viscosity reducers.