Constant Diffusion Coefficient Research Articles

Quantification of the asynchronous gas diffusivity in macro-/micropores using a Nelder-Mead simplex algorithm and its application on predicting desorption-based indexes

Accurate and intelligent calculation of diffusion coefficient not only helps reduce greenhouse gas emissions, but also conduces to CO2 geological storage and CH4 displacement in coal seams. In this study, a kind of object-oriented software for conveniently and quickly obtaining bidisperse (i.e., macro-pore and micro-pore) diffusion coefficients and grasping main controlling factors of macroscopic desorption curves was designed based on the Nelder-Mead simplex algorithm. Furthermore, the gas desorption characteristics under different pressures were analyzed by performing conventional desorption experiments. The results show that the apparent diffusion coefficient obtained by the bulk technique displays three different trends as the pressure rises, namely a rising, falling and constant diffusion coefficient respectively. The three variation trends mainly result from the difference in deformation caused by adsorption swelling and mechanical compression. As desorption continues, the gas diffusion coefficient values in the macro-pores and micro-pores fluctuate for a short time, but increase in the long term. This is because the early stage corresponds to intense mechanical expansion and a flow boundary effect, while the later stage corresponds to an increasingly intense effect of desorption-induced shrinkage. Moreover, the time-dependent contribution law of macro-pore diffusion and micro-pore diffusion affects the reliability of outburst risk index, making △h2 more stable than K1. The conclusions provide theoretical guidance for the selection of rational gas drainage methods for diffusion-controlled coal seams.

CO2 solubility and diffusivity in 1-ethyl-3-methylimidazolium cation-based ionic liquids; isochoric pressure drop approach

In this study, an experimental approach based on the isochoric pressure drop principle was implemented to measure (at low equilibrium pressure, 1.3–3.6 bar) the solubility and binary diffusivity of CO2 (constant and variable) in four imidazolium-based room-temperature ionic liquids (RTILs), namely, 1-ethyl-3-methylimidazolium acetate ([emim][Ac]), 1-ethyl-3-methylimidazolium dicyanamide ([emim][DCA]), 1-ethyl-3-methylimidazolium methyl sulfate ([emim][MeSO4]) and 1-ethyl-3-methylimidazolium ethyl sulfate ([emim][EtSO4]). The molar fraction of the dissolved CO2 and Henry's law constant were measured from experimental data. Constant binary diffusion coefficients were measured from the transient thin-film and semi-infinite volume models. In the original approach, the variable diffusivity coefficient model was used to measure the concentration-based variable diffusion coefficient. Anion interaction of the RTILs was found to have a strong influence on the CO2 solubility, and Henry's law constant and the studied anions were ranked as [Ac]− >> [EtSO4]− > [DCA]− > [MeSO4]−. Increasing temperature is not likely for CO2 solubility while it favors CO2 diffusivity. Thin-film model diffusivity measurements were found to be more suitable for [emim][MeSO4] and [emim][EtSO4], while semi-infinite volume model was suitable for [emim][Ac] and [emim][DCA]. Variable diffusion coefficients were found not to be a monotonous function of time, which increased in early stages and decreased after a certain time. Gibbs free energy, enthalpy, and entropy values indicate the strength of the favorable interaction between CO2 and RTILs, mildly exothermic in nature and falling in the range of physisorption.

Transverse liquid composite moulding processes for advanced composites material manufacturing

ABSTRACT The hydrodynamic compaction behaviour in transverse (through-thickness) impregnation variants of Liquid Composite Moulding (LCM) results in a non-homogeneous fibre volume fraction distribution. A fully coupled simulation model of the entire family of transverse resin infusion/compression processes is presented, which simulates the hydrodynamic compaction behaviour and predicts the process time, fluid pressure, effective stress, and fibre volume fraction distribution. The model is applied to the compression of a saturated preform stack, resin injection into a dry preform, and Compression Resin Transfer Moulding. The simulations are verified using analytic solutions and validated against experimental results from the literature. Special forms of the constitutive equations are constructed to lead to a constant diffusion coefficient, and the resulting model is solved semi-analytically. The results are used to verify the full non-linear simulation model. Additionally, it is shown that assumptions of quasi-steady flow and uniform deformation introduce significant errors in processes involving direct piston compaction of the fibre preform.

Modeling of diffusion kinetics during gas adsorption in a coal seam with a dimensionless inversion method

Modeling gas diffusion kinetics in a coal seam plays an essential role in predicting performance of both coalbed methane production and its enhanced recovery. Throughout the diffusion period, not only does there exist a large deviation between the analytical solution of the classical Fickian unipore diffusion model (UDM) and experimental measurements, but also constant diffusion coefficients calculated with the inversion of the simplified empirical/semi-empirical correlations are still not accurate enough. In this paper, we proposed a free gas density gradient model (FGDGM) to characterize the gas adsorption and transport properties in a coal seam. Experimentally, isothermal experiments were performed using a high-temperature and high-pressure gas adsorption analyzer with methane gas. Theoretically, a Langmuir gas concentration was derived and improved as a function of free gas density, and then we correlated a numerical inversion model to determine the effective diffusion coefficients by combining dimensionless variables and empirical correlations. Finally, the developed models were validated with the measured gas adsorption isotherms. The numerical solution curves based on the FGDGM are found to be basically consistent with the measured data in the entire time scale, while the developed inversion method is accurate as well as efficient in computational expenses. On the basis of the ideal gas assumption, the actual density gradient and diffusion coefficient will be underestimated and overestimated, respectively. By incorporating real gas behaviour into the improved FGDGM, both gas mass flux and effective diffusion coefficient can be determined more accurately to model gas diffusion kinetics and gas flow patterns in a coal seam.

Convergence in Total Variation of the Euler--Maruyama Scheme Applied to Diffusion Processes with Measurable Drift Coefficient and Additive Noise

We are interested in the Euler-Maruyama discretization of a stochastic differential equation in dimension $d$ with constant diffusion coefficient and bounded measurable drift coefficient. In the scheme, a randomization of the time variable is used to get rid of any regularity assumption of the drift in this variable. We prove weak convergence with order $1/2$ in total variation distance. When the drift has a spatial divergence in the sense of distributions with $\rho$-th power integrable with respect to the Lebesgue measure in space uniformly in time for some $\rho \ge d$, the order of convergence at the terminal time improves to $1$ up to some logarithmic factor. In dimension $d=1$, this result is preserved when the spatial derivative of the drift is a measure in space with total mass bounded uniformly in time. We confirm our theoretical analysis by numerical experiments.

Robust Interior Penalty Discontinuous Galerkin Methods

A new variant of the IPDG method is presented, involving carefully constructed weighted averages of the gradient of the approximate solution. The method is shown to be robust even for the most extreme simultaneous local mesh, polynomial degree and diffusion coefficient variation scenarios, without resulting into unreasonably large penalization. The new IPDG method, henceforth termed as robust IPDG (RIPDG), offers typically significantly better error behaviour and conditioning than the standard IPDG method when applied to scenarios with strong mesh/polynomial degree/diffusion local variation, especially when the underlying approximation space does not contain a sufficiently rich conforming subspace. The latter is of particular importance in the context of IPDG methods on polygonal/polyhedral meshes. On the other hand, when using uniform meshes, constant polynomial degree for problems with constant diffusion coefficients the RIPDG method is identical to the classical IPDG. Numerical experiments indicate the favourable performance of the new RIPDG method over the classical version in terms of conditioning and error.

The truncated Euler–Maruyama method for CIR model driven by fractional Brownian motion

Recently, Hong et al. (2020) established the strong convergence rate of the backward Euler scheme for the Cox–Ingersoll–Ross (CIR) model driven by fractional Brownian motion with Hurst parameter H∈(1/2,1), which may effect the efficiency of computation. Taking advantage of being explicit and easily implementable, a positivity preserving explicit scheme is proposed in this paper. For overcoming the difficulties caused by the unbounded diffusion coefficient, an auxiliary equation with a constant diffusion coefficient obtained by proper Lamperti transformation is used. By means of Malliavin calculus, we show that the truncated Euler–Maruyama scheme applied to this auxiliary equation not only ensures the positivity of the numerical solution, but also has the H-order rate of the root mean square error over a finite time interval. Furthermore, by transforming back, an explicit scheme for the original CIR model is obtained and has the same convergence order. Finally, some numerical experiments are provided to illustrate the theoretical results.

An Efficient MultiModes Monte Carlo Homogenization Method for Random Materials

In this paper, we propose and analyze a new stochastic homogenization method for diffusion equations with random and fast oscillatory coefficients. In the proposed method, the homogenized solutions are sought through a two-stage procedure. In the first stage, the original oscillatory diffusion equation is approximated, for each fixed random sample $\omega$, by a spatially homogenized diffusion equation with piecewise constant coefficients, resulting in a random diffusion equation. In the second stage, the resulting random diffusion equation is approximated and computed by using an efficient multimodes Monte Carlo method which only requires solving a diffusion equation with a constant diffusion coefficient and a random right-hand side. The main advantage of the proposed method is that it separates the computational difficulty caused by the spatial fast oscillation of the solution and caused by the randomness of the solution, so they can be overcome separately using different strategies. The convergence of the solution of the spatially homogenized equation (from the first stage) to the solution of the original random diffusion equation is established, and the optimal rate of convergence is also obtained for the proposed multimodes Monte Carlo method. Numerical experiments on some benchmark test problems for random composite materials are also presented to gauge the efficiency and accuracy of the proposed two-stage stochastic homogenization method.

Dynamics and optimal control of a spatial diffusion HIV/AIDS model with antiretrovial therapy and pre‐exposure prophylaxis treatments

In this paper, to investigate the synthetic effect of PrEP (pre‐exposure prophylaxis) and ART (antiretrovial therapy) on HIV transmission among MSM (men who have sex with men) in heterogenous environment, a realistic HIV epidemic model with spatial diffusion is established. Here, HIV infectious people are divided into three immunity based compartments, that is, CD4+ T cell count less than 350, between 350 and 500, and more than 500, respectively. The basic reproduction number is established and proved as a threshold parameter: The global asymptotic stability of the disease‐free steady state holds for , and the disease will be present if . Considering the substantial advantages of PrEP and ART in controlling HIV transmissions among MSM, the optimal control problem is presented for the case of positive constant diffusion coefficients, which minimize the total population of susceptible individual and HIV infected individual, the cost of PrEP and ART therapy. As an illustration of our theoretical results, we conduct numerical simulations. We also conduct an optimal control case study where model parameters are estimated from the demographic and epidemiological data from China. This work suggests the following: (1) Spatial factors cannot be ignored during the HIV intervention; (2)taking the PrEP intervention measure for HIV transmissions among MSM as early as possible will help to improve the control efficiency and reduces its cost; (3) reducing the PrEP drug costs will promote the efficiency of PrEP treatment in preventing the spread of HIV among MSM.

Spatiotemporal measurement of concentration-dependent diffusion coefficient

We introduce a method to measure the concentration-dependent diffusion coefficient from a sequence of images of molecules diffusing from a source toward a sink. Generally, approaches measuring the diffusion coefficient, such as fluorescence recovery after photobleaching (FRAP), assume that the diffusion coefficient is constant. Hence, these methods cannot capture the concentration dependence of the diffusion coefficient if present. Other approaches measure the concentration-dependent diffusion coefficient from an instantaneous concentration profile and lose the temporal information. These methods make unrealistic assumptions, are not robust, and lead to 100% error. We introduce an image analysis framework that utilizes spatial and temporal information in a sequence of concentration images and numerically solves the general form of Fick's second law using radial basis functions (RBF) to measure the concentration-dependent diffusion coefficient. We term this approach as concentration image diffusimetry (CID). Our method makes no assumptions about the sink and source size and the diffusion dependence on concentration. CID is superior to existing methods in estimating spatiotemporal changes and concentration-dependent diffusion. CID also provides a statistical uncertainty quantification on the measurements using a bootstrapping approach, improving the reliability of the diffusion measurement. We assessed CID's performance using synthetically generated images. Our analysis suggests that CID accurately measures the diffusion coefficient with less than 2% error for most cases. We validated CID with FRAP experimental images and showed that CID agrees with established FRAP algorithms for samples with a constant diffusion coefficient. Finally, we demonstrate the application of CID to experimental datasets of a concentration gradient-driven protein diffusion into a tissue replicate. In conclusion, this work presents an image-based methodology that uses the spatial and temporal changes of concentration fields to measure the concentration-dependent diffusion coefficient.

Nonlinear diffusion of gluons

It is proposed to consider the fast thermalization of gluons in relativistic heavy-ion collisions as a diffusion process in momentum space. Closed-form analytical solutions of a nonlinear boson diffusion equation (NBDE) with constant drift and diffusion coefficients v, D and boundary conditions at the singularity are derived. The time evolution towards local central temperatures T≲600MeV through inelastic gluon scatterings in heavy-ion collisions is calculated for under- and overoccupied systems in the full momentum range. The results are consistent with QCD-based numerical calculations for gluon thermalization via inelastic gluon collisions.

Predictions for Gravity-mode Periods and Surface Abundances in Intermediate-mass Dwarfs from Shear Mixing and Radiative Levitation

Abstract The treatment of chemical mixing in the radiative envelopes of intermediate-mass stars has hardly been calibrated so far. Recent asteroseismic studies demonstrated that a constant diffusion coefficient in the radiative envelope is not able to explain the periods of trapped gravity modes in the oscillation spectra of γ Doradus pulsators. We present a new generation of MESA stellar models with two major improvements. First, we present a new implementation for computing radiative accelerations and Rosseland mean opacities that requires significantly less CPU time. Second, the inclusion of shear mixing based on rotation profiles computed with the 2D stellar structure code ESTER is considered. We show predictions for the mode periods of these models covering stellar masses from 1.4 to 3.0 M ⊙ across the main sequence, computed for different metallicities. The morphology of the chemical mixing profile resulting from shear mixing in combination with atomic diffusion and radiative levitation does allow for mode trapping, while the diffusion coefficient in the outer envelope is large (>106 cm2 s−1). Furthermore, we make predictions for the evolution of surface abundances for which radiative accelerations can be computed. We find that the N/C and C/O abundance ratios correlate with stellar age. We predict that these correlations are observable with precisions ≲ 0.1 dex on these ratios, given that a precise age estimate can be made.

Magnetic Resonance Imaging Features on Deep Learning Algorithm for the Diagnosis of Nasopharyngeal Carcinoma.

The objective of this research was to investigate the application values of magnetic resonance imaging (MRI) features of the deep learning-based image super-resolution reconstruction algorithm optimized convolutional neural network (OPCNN) algorithm in nasopharyngeal carcinoma (NPC) lesion diagnosis. A total of 54 patients with NPC were selected as research objects. Based on the traditional CNN structure, OPCNN was proposed. Besides, MRI processed by the traditional CNN model and the U-net network model was introduced to be analyzed and compared with its algorithm. The used assessment parameters included volume transfer constant (Ktrans), rate constant (Kep), volume fraction (Ve), and apparent diffusion coefficient (ADC). The results showed that the values of Dice coefficient, peak signal-to-noise ratio (PSNR), and structural similarity (SSIM) of the OPCNN algorithm were significantly higher than those of the traditional CNN model and the U-net network model. Meanwhile, the difference was statistically significant (P < 0.05). Ktrans, Kep, and Ve in tumor lesions were significantly higher than those in the healthy side, while the ADC was significantly lower than that in the healthy side (P < 0.05). The sensitivity, specificity, and accuracy of dynamic contrast-enhancement magnetic resonance imaging (DCE-MRI) in the diagnosis of nasopharyngeal carcinoma staging were slightly higher than those in T2-weighted imaging (T2WI) and diffusion-weighted imaging (DWI). The diagnostic sensitivity of DCE-MRI was more than 85%, its diagnostic specificity was more than 75%, and its diagnostic accuracy was more than 90%. The AUC area of NPC diagnosed by combination of the three was significantly different from that diagnosed by single T2WI, DWI, and DCE-MRI (P < 0.05). The diagnostic accuracy of MRI based on the OPCNN algorithm for nasopharyngeal carcinoma (93.2%) was significantly higher than that of single MRI (76.4%). In summary, the OPCNN algorithm proposed in this study could improve the quality of MRI images, and the effect was better than the traditional deep learning model, which had the value of clinical promotion. The application value of DCE-MRI in the diagnosis of pathogenic lesions of nasopharyngeal carcinoma was better than conventional MRI. The combined application of T2WI, DWI, and DCE-MRI in the screening of nasopharyngeal carcinoma lesions could greatly improve the diagnostic accuracy of nasopharyngeal carcinoma.

Effect of Amount of Fibre and Damage Level on Service Life of SFR Recycled Concrete in Aggressive Environment

The paper presents a numerical calculation of the service life of concrete structures considering the effect of chlorides in the case of the material properties of structural lightweight waste aggregate concrete. Different amounts of fibres (0.0%, 1.0%, and 1.5%) and different values of compressive preloading (0%, 50%, and 100% of the ultimate strength capacity-USC) were considered. The subject of the research was the comparison of the influence of the constant diffusion coefficient and the time-dependent diffusion coefficient regarding the service life of the selected structure. Nine groups of material characteristics in combination with two numerical models are compared. A time-dependent diffusion coefficient and maturation coefficient, which were determined based on long-term monitoring (up to 461 days), were accepted for the numerical modelling. Thanks to time-dependent parameters, it is possible to observe the results of the theoretical service life of the structure and the influence of the mentioned factors. The analysed structure can be considered as the upper layer of an industrial floor in a chemical plant. It is important to determine the theoretical service life at which the structure shall be inspected or replaced. The results, in general, show that a higher amount of fibres reduces the service life as well as the preloading of the structure. An exception was a mixture with 1% of fibre loaded to 50% USC, which shows a lower diffusion coefficient than the specimens without preloading.

All-at-once multigrid approaches for one-dimensional space-fractional diffusion equations

We focus on a time-dependent one-dimensional space-fractional diffusion equation with constant diffusion coefficients. An all-at-once rephrasing of the discretized problem, obtained by considering the time as an additional dimension, yields a large block linear system and paves the way for parallelization. In particular, in case of uniform space–time meshes, the coefficient matrix shows a two-level Toeplitz structure, and such structure can be leveraged to build ad-hoc iterative solvers that aim at ensuring an overall computational cost independent of time. In this direction, we study the behavior of certain multigrid strategies with both semi- and full-coarsening that properly take into account the sources of anisotropy of the problem caused by the grid choice and the diffusion coefficients. The performances of the aforementioned multigrid methods reveal sensitive to the choice of the time discretization scheme. Many tests show that Crank–Nicolson prevents the multigrid to yield good convergence results, while second-order backward-difference scheme is shown to be unconditionally stable and that it allows good convergence under certain conditions on the grid and the diffusion coefficients. The effectiveness of our proposal is numerically confirmed in the case of variable coefficients too and a two-dimensional example is given.

Generalized diffusion equation with nonlocality of space-time: Analytical and numerical analysis

We present a general approach for obtaining the generalized transport equations for weakly nonequilibrium processes with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and the Zubarev nonequilibrium statistical operator method. A generalized diffusion equation for a system of classical particles in fractional derivatives is obtained for weakly nonequilibrium processes. Based on the non-Markov diffusion equation, taking into account the spatial nonlocality and modeling the generalized coefficient of particle diffusion Dαα′(r,r′;t,t′)=W(t,t′)D̄αα′(r,r′) using fractional calculus, the generalized Cattaneo–Maxwell-type diffusion equation in fractional time and space derivatives is obtained. In the case of a constant diffusion coefficient, analytical and numerical studies of the frequency spectrum for the Cattaneo–Maxwell diffusion equation in fractional time and space derivatives are performed. Numerical calculations of the phase and group velocities with a change in values of characteristic relaxation time, diffusion coefficient, and indices of temporal ξ and spatial α nonlocality are carried out.

Drying Characteristics and Quality Attributes Affected by a Fluidized-Bed Drying Assisted with Swirling Compressed-Air for Preparing Instant Red Jasmine Rice

A new process for the production of instant red jasmine rice was investigated using fluidized bed drying with the aid of swirling compressed air. Drying characteristics were evaluated using the operating parameters of fluidizing air temperature (90–120 °C) and pressure of swirling compressed air (4–6 bar). Appropriate air pressure was determined based on the highest value of model parameters from the semi-empirical Page equation and effective diffusivity. Influences of supply time of swirling compressed air (2–10 min) and drying temperature of 90–120 °C were investigated and optimized based on the quality attributes using response surface methodology. Drying at 120 °C and compressed air pressure of 6 bar gave the highest rate constant and effective diffusion coefficient. Drying at 120 °C combined with injecting swirling air for 2 min was the most suitable approach, while drying at 90 °C and supplying compressed air for 10 min was the best choice to preserve antioxidant properties. Air temperature of 98.5 °C with 2 min supply of swirling compressed air suitably provided high physical and rehydration properties and retained high health benefits of antioxidant compounds. Finally, after rehydration in warm water at 70 °C for 10 min, the textural properties of the rehydrated rice sample were comparable to conventionally cooked rice.

Selfsimilar diffusions

This paper addresses symmetric Ito diffusions, with general position-dependent velocities and diffusion coefficients, that run over the real line. The paper establishes an explicit characterization of diffusions that are selfsimilar processes with arbitrary Hurst exponents. Specifically, for a given diffusion, the paper asserts that the four following statements are equivalent: (i) the diffusion’s trajectories are selfsimilar; (ii) the diffusion’s positions display a certain scaling property; (iii) the diffusion’s first-passage times (FTPs) to the origin display a certain scaling property; (iv) the diffusion’s velocities and diffusion coefficients admit certain power-law forms. For diffusions with constant diffusion coefficients, the paper further asserts that: selfsimilarity holds if and only if the underpinning potential is logarithmic, in which case the Hurst exponent is . The positions of selfsimilar diffusions are shown to have non-Gaussian statistics with the following features: densities that are either unimodal and explosive, or unimodal, or bimodal; and tails that are either ‘light’, or Gamma, or ‘heavy’. The FTPs to the origin of selfsimilar diffusions are shown to have inverse-Gamma statistics with infinite means and infinite moments. The results presented in this paper unveil a class of Markovian diffusions, whose trajectories are fractal objects, and whose non-Gaussian statistics can be custom designed via three parameters: a velocity parameter, a diffusion parameter, and a Hurst exponent.

Experimental study on microwave irradiation enhancing gas desorption in shale

Microwave irradiation (MI) is a new method to enhance desorption of shale gas. It is very important to explore the desorption law and influencing factors of shale samples under MI to improve energy utilization efficiency and optimize microwave stimulation effect. The gas desorption properties of shale sample under different MI time (off-line group) and power (on-line group) conditions were discussed by using an independently developed microwave treatment device. At the same time, the dynamics law of shale desorption was studied by using the traditional desorption model and the dynamics desorption model, which revealed the mechanism of shale desorption enhanced by MI. The experimental results show that MI can significantly improve the desorption rate of shale and the diffusivity of adsorbed gas. The shale temperature finally reached 580.15 K at microwave power 1800W, and the desorption amount in the MI stage is about 2.5 times than that of the natural desorption stage. Under MI, the diffusion rate of shale at desorption equilibrium is above 0.8, and increases gradually with the microwave power. The constant diffusion coefficient Dw and initial diffusion coefficient Dw0 have a threshold effect with the change of microwave power. Only when the microwave power is greater than 1200 W, the shale diffusion coefficient and the gas desorption rate would increase rapidly. The permeability model has a better fitting adaptability on MI desorption stage, followed by the empirical model and the diffusion model. The C-D model has a poor fitting suitability on the natural desorption stage. In comparison, the D-D-C model has the best fitting effect for the whole shale desorption curve, especially for the later stage. In general, D-D-C model and permeability model have better fitting effect than other models.

Interface retaining coarsening of multiphase flows

Multiphase flows are characterized by sharp moving interfaces, separating different fluids or phases. In many cases, the dynamics of the interface determines the behavior of the flow. In a coarse, or reduced order model, it may, therefore, be important to retain a sharp interface for the resolved scales. Here, a process to coarsen or filter fully resolved numerical solutions for incompressible multiphase flows while retaining a sharp interface is examined. The different phases are identified by an index function that takes different values in each phase and is coarsened by solving a constant coefficient diffusion equation, while tracking the interface contour. Small flow scales of one phase, left behind when the interface is moved, are embedded in the other phase by solving another diffusion equation with a modified diffusion coefficient that is zero at the interface location to prevent diffusion across the interface, plus a pressure-like equation to enforce incompressibility of the coarse velocity field. Examples of different levels of coarsening are shown. A simulation of a coarse model, where small scales are treated as a homogeneous mixture, results in a solution that is similar to the filtered fully resolved field for the early time Rayleigh–Taylor instability.