Time-dependent Diffusion Research Articles

Millisecond-resolved gas sorption kinetics and time-dependent diffusivity of coal

Millisecond-resolved gas sorption kinetics and time-dependent diffusivity of coal

Similarity analysis of chloride transport behavior in fly ash concrete under different environments aiding by machine learning method

To forecast chloride transport in site by applying accelerated test results, it is necessary to investigate the similarity of chloride diffusivity under different environments. However, limited by test period and cost expenses, a large amount of tests in field and simulated environment are hard to conduct, and a limit test data will make prediction on chloride diffusivity of concrete less precise. To solve this problem, machine learning methods are explored to predict chloride transport. Based on the existing chloride concentration test data of fly ash concrete in natural and accelerated simulated environment, this paper establishes a chloride concentration predictive model based on the one-dimensional convolutional neural network (1D-CNN) method at first, and verifies the stability and accuracy of the established model. Second, similarity models for concentration ratio and diffusion time ratio based on multivariate nonlinear model and based on theoretical Fick’s second law are constructed, and the model accuracy is also tested. Finally, the chloride concentration data predicted by the 1D-CNN model is applied to the constructed similarity models respectively, and the application results are compared and analyzed to determine the optimal similarity model. Results indicate that the concentration predicted by the 1D-CNN method has a strong robustness and a small prediction error. Besides, based on multivariate nonlinear model, the error of concentration predicted by the similarity models for concentration ratio and diffusion time ratio is less than 16 % and 30 %, respectively. Similarly, according to the theoretical model based on Fick’s second law, the error of concentration predicted by the similarity models for concentration ratio based on the time dependent chloride diffusion coefficient and time dependent peak chloride concentration is less than 21 % and 36 %, respectively. The similarity model for concentration ratio based on multivariate nonlinear model has the best prediction effect.

Time-dependent concrete chloride diffusion coupled with nonlinear chloride binding: An analytical study

Both the temporal dependence of chloride diffusion coefficient and the effect of nonlinear chloride binding substantially affect the behavior of concrete chloride diffusion. This study develops an exact chloride diffusion solution that accommodates the above two factors by introducing a simplified but reasonably realistic nonlinear chloride binding isotherm. The introduction of this isotherm makes it possible to achieve an analytical solution to a highly nonlinear chloride diffusion equation that involves a free chloride concentration dependent dimensionless factor which reflects the effect of chloride binding. First, a time-dependent chloride diffusion model incorporating the introduced isotherm is established with the corresponding exact solution derived. The proposed solution is successfully validated against two existing analytical solutions and a numerical solution. Parametric study is conducted using the proposed solution to investigate how the parameters regarding chloride ingress influence the corrosion initiation time, and results show that the increase of the initial effective chloride diffusivity or the before-ingress age decreases the corrosion initiation time bringing an acceleration of a different level to chloride diffusion while the increase of the age factor prolongs the corrosion initiation time decelerating chloride diffusion to some extent, and as each of the three nonlinear chloride binding associated parameters (i.e., the deflection-point concentration, the former slope and the latter slope) increases, the corrosion initiation time rises and the retardation effect on chloride diffusion is enhanced to a various extent. Lastly, to demonstrate the practical validity of the proposed solution, the solution is applied to reproducing a reported chloride diffusion test, and it turns out that our solution reproduces the diffusion test reasonably well, justifying its practical validity.

Fully discrete Galerkin scheme for a semilinear subdiffusion equation with nonsmooth data and time-dependent coefficient

We couple the L1 discretization of the Caputo fractional derivative in time with the Galerkin scheme to devise a linear numerical method for the semilinear subdiffusion equation. Two important points that we make are nonsmooth initial data and time-dependent diffusion coefficient. We prove the stability and convergence of the method under weak assumptions concerning regularity of the diffusivity. We find optimal pointwise in space and global in time errors, which are verified with several numerical experiments.

Diffusing Wave Microrheology in Polymeric Fluids.

Recently, there has been interest in determining the viscoelastic properties of polymeric liquids and other complex fluids by means of Diffusing Wave Spectroscopy (DWS). In this technique, light-scattering spectroscopy is applied to highly turbid fluids containing optical probe particles. The DWS spectrum is used to infer the time-dependent mean-square displacement and time-dependent diffusion coefficient D of the probes. From D, values for the storage modulus G'(ω) and the loss modulus G''(ω) are obtained. This paper is primarily concerned with the inference of the mean-square displacement from a DWS spectrum. However, in much of the literature, central to the inference that is said to yield D is an invocation g(1)(t)=exp(-2q2X(t)2¯) of the Gaussian Approximation for the field correlation function g(1)(t) of the scattered light in terms of the mean-square displacement X(t)2¯ of a probe particle during time t. Experiment and simulation both show that the Gaussian approximation is invalid for probes in polymeric liquids and other complex fluids. In this paper, we obtain corrections to the Gaussian approximation that will assist in interpreting DWS spectra of probes in polymeric liquids. The corrections reveal that these DWS spectra receive contributions from higher moments X(t)2n¯, n>1, of the probe displacement distribution function.

284: Time-dependent diffusion MRI for tumor characterization in biologically adapted radiotherapy

284: Time-dependent diffusion MRI for tumor characterization in biologically adapted radiotherapy

Time-dependent reliability assessment and optimal design of corroded reinforced concrete beams

It remains a significant challenge to quantitatively describe the corrosion of reinforced concrete (RC) structures under chloride penetration. Moreover, when considering uncertainties throughout the life cycle of corroded RC structures for assessing their safety, reliability, and optimal design, the complexity of the problem intensifies. To address these issues, this paper studies the time-dependent reliability analysis and optimal design of corroded RC beams. At first, the time-dependent reliability of beams is investigated by considering both the serviceability limit state (SLS), which corresponds to the corrosion initiation of the reinforced steel, and the ultimate limit state (ULS), associated with the bending failure of the beam. This analysis takes into account the time-dependent chloride diffusion coefficient and incorporates a stochastic process. The reliability is evaluated using the Monte Carlo Simulation (MCS) method and the cumulative distribution function (CDF) method. Subsequently, a time-dependent reliability-based design optimization (TRBDO) problem is formulated, and the PSO-MCS, a methodology incorporating a particle swarm optimization (PSO) algorithm and MCS is adopted to solve it. After optimization, the initial cost of the specific RC beam is reduced from 1351.879€ to 1247.075€, while the time-dependent reliability within [0, 100] years is improved from 0.6057 to 0.6508. The effectiveness of the CDF, MCS and PSO-MCS methods are demonstrated through reliability analysis and design examples of corroded RC beams.

Anomalous non-Gaussian diffusion of scaled Brownian motion in a quenched disorder environment

Abstract This paper aims to investigate particle dynamics in a random environment, subjected to power-law time-dependent temperature. To this end, the scaled Brownian motion (SBM), a stochastic process described by a diffusion equation with time-dependent diffusivity, has been studied numerically in quenched disordered systems (QDLs). Here, QDLs have been modeled by spatial correlated Gaussian random potential with an exponential normalized correlation function. Results show nonergodic non-Gaussian subdiffusion for subdiffusive SBM. While a crossover from non-Gaussian Brownian diffusion to long-time Gaussian superdiffusion has been observed for the superdiffusive SBM scenario. Furthermore, the first passage time to an object significantly depends on the governing SBM regime and its scale parameter, where the first passage time becomes faster with the increasing scale parameter. The mechanism underlying these behaviors has been uncovered numerically.

Anomalous heat transport and universality in macroscopic diffusion models

Anomalous diffusion is ubiquitous in nature and relevant for a wide range of applications, including energy transport, especially in bio- and nano-technologies. Numerous approaches have been developed to describe it from a microscopic point of view, and recently, it has been framed within universality classes, characterized by the behaviour of the moments and auto-correlation functions of the transported quantities. It is important to investigate whether such universality applies to macroscopic models. Here, the spectrum of the moments of the solutions of the transport equations is investigated for three continuous PDE models featuring anomalous diffusion. In particular, we consider the transport described by: (i) a generalized diffusion equation with time-dependent diffusion coefficient; (ii) the Porous Medium Equation and (iii) the Telegrapher Equation. For each model, the key features of the source-type solution as well as the analytical results for the moment analysis are revisited and extended via both analytical and numerical approaches. Equivalence of the asymptotic behaviour of the corresponding heat transport is confirmed within the realm of weak anomalous diffusion.

Effectiveness of Biological Mortars with Bacterial Glycocalyx on Service Life of Concrete Structures Exposed to Salt Attack

This study investigated the effectiveness and limitations of newly developed biological mortars regarding chloride ion diffusion resistance. Through several tests on the glycocalyx production capacity and growth potentials of bacteria cells under marine environments, Bacillus licheniformis was isolated and immobilized in the expanded vermiculites together with a bacterial culture medium for producing biological mortars. The chloride ion diffusion coefficient of the mortars up to 91 days was determined through natural diffusion cell tests. Subsequently, the service life of RC structure repaired with biological mortars under chloride attack was evaluated considering multilayer theory and time-dependent diffusion. The addition of expanded vermiculites immobilizing Bacillus licheniformis significantly reduced the chloride ion diffusion coefficient. When its addition increased from 10 to 30%, the chloride ion diffusion coefficient decreased by 50–90% compared to that of mortars without bacteria. The service life of reinforced concrete structures repaired with biological mortars containing 30% expanded vermiculite concentration and thickness of 50 mm was evaluated to be six times longer than that of repaired with conventional mortar. Overall, this novel approach holds significant potential in addressing the salt-induced deterioration challenges faced by RC structures.

Extraordinary optical and transport properties of disordered stealthy hyperuniform two-phase media

Disordered stealthy hyperuniform two-phase media are a special subset of hyperuniform structures with novel physical properties due to their hybrid crystal-liquid nature. We have previously shown that the rapidly converging strong-contrast expansion of a linear fractional form of the effective dynamic dielectric constant εek1,ω (Torquato and Kim 2021 Phys. Rev. X 11 021002) leads to accurate approximations for both hyperuniform and nonhyperuniform two-phase composite media when truncated at the two-point level for distinctly different types of microstructural symmetries in three dimensions. In this paper, we further elucidate the extraordinary optical and transport properties of disordered stealthy hyperuniform media. Among other results, we provide detailed proofs that stealthy hyperuniform layered and transversely isotropic media are perfectly transparent (i.e. no Anderson localization, in principle) within finite wavenumber intervals through the third-order terms. Remarkably, these results imply that there can be no Anderson localization within the predicted perfect transparency interval in stealthy hyperuniform layered and transversely isotropic media in practice because the localization length (associated with only possibly negligibly small higher-order contributions) should be very large compared to any practically large sample size. We further contrast and compare the extraordinary physical properties of stealthy hyperuniform two-phase layered, transversely isotropic media, and fully three-dimensional isotropic media to other model nonstealthy microstructures, including their attenuation characteristics, as measured by the imaginary part of εek1,ω , and transport properties, as measured by the time-dependent diffusion spreadability S(t) . We demonstrate that there are cross-property relations between them, namely, we quantify how the imaginary parts of εek1,ω and the spreadability at long times are positively correlated as the structures span from nonhyperuniform, nonstealthy hyperuniform, and stealthy hyperuniform media. It will also be useful to establish cross-property relations for stealthy hyperuniform media for other wave phenomena (e.g. elastodynamics) as well as other transport properties. Cross-property relations are generally useful because they enable one to estimate one property, given a measurement of another property.

Streamwise dispersion of soluble matter in solvent flowing through a tube

For the dispersion of soluble matter in solvent flowing through a tube as investigated originally by G.I. Taylor, a streamwise dispersion theory is developed from a Lagrangian perspective for the whole process with multi-scale effects. By means of a convected coordinate system to decouple convection from diffusion, a diffusion-type governing equation is presented to reflect superposable diffusion processes with a multi-scale time-dependent anisotropic diffusivity tensor. A short-time benchmark, complementing the existing Taylor–Aris solution, is obtained to reveal novel statistical and physical features of mean concentration for an initial phase with isotropic molecular diffusion. For long times, effective streamwise diffusion prevails asymptotically corresponding to the overall enhanced diffusion in Taylor's classical theory. By inverse integral expansions of local concentration moments, a general streamwise dispersion model is devised to match the short- and long-time asymptotic solutions. Analytical solutions are provided for most typical cases of point and area sources in a Poiseuille tube flow, predicting persistent long tails and skewed platforms. The theoretical findings are substantiated through Monte Carlo simulations, from the initial release to the Taylor dispersion regime. Asymmetries of concentration distribution in a circular tube are certified as originated from (a) initial non-uniformity, (b) unidirectional flow convection, and (c) non-penetration boundary effect. Peculiar peaks in the concentration cloud, enhanced streamwise dispersivity and asymmetric collective phenomena of concentration distributions are illustrated heuristically and characterised to depict the non-equilibrium dispersion. The streamwise perspective could advance our understanding of macro-transport processes of both passive solutes and active suspensions.

Thermodynamic description of active brownian particle driven by fractional gaussian noise

As a natural extension of the recent results on the thermodynamics of an active Brownian particle (self-propelled), we study the thermodynamics of an active Brownian particle (ABP) driven by fractional Gaussian noise (FGN). To serve as a prelude of the main results, we start from the conventional Markov process but with time dependent diffusion coefficient, where deviation in integral fluctuation relation (IFR) for total entropy production requires a general definition of the temperature, following the same case for a Brownian particle. In other words, the general temperature definition for this case is independent to the statistics of the rotational motion. We then proceed with the main problem of the paper, which is an active Brownian particle driven by fractional Gaussian noise. Under the assumption that self-propulsion is even under time-reversal, temperature is defined as well as the distance on how far the IFR for total entropy production deviates from the standard definition by adopting the standard definition of trajectory-level entropy and the joint probability of ABP. Furthermore, second law-like concept based on the found deviation is derived, as well as a generalized Clausius inequality. Lastly, magnitude of this deviation diminishes in the case of pure white noise.

Anodic dissolution model with diffusion–migration transport for simulating localized corrosion

A one-dimensional model for simulating localized corrosion is developed, incorporating a time-dependent diffusion–migration transport and a moving interface. The model is applied to iron with the Butler–Volmer formula as the dissolution law, and both crevice and pit configurations are simulated. The mathematical procedure for solving this strongly coupled differential equations system and the numerical development for simulations are detailed. A finite-difference ALE scheme is used for the numerical computation of the solutions of this free boundary problem. The results show that the dissolution rate increases with chloride concentration and metal potential, and migration plays, most of the time, a significant role in species transport for both crevice and pit configurations. The evolution of the repassivation potential with pit depth is computed and is in good agreement with experimental results. The time-dependent model under consideration provides more accurate quantitative results for concentration profile and crevice depth than stationary models.

An Overview of the mechanism-based thermomechanical fatigue method (DTMF) in the design of automotive components

The DTMF damage Parameter described in the paper is the generalization of the creep fatigue parameter (DCF) proposed by Riedel, which quantifies the amount of damage produced by a non-isothermal loading cycle. The entire design methodology is outlined in the text, starting with the calibration of Chaboche's viscoplastic model and then the determination of the thermomechanical fatigue (TMF) parameters. Chaboche is generally a good choice for its ability to describe well both kinematic and isotropic hardening behaviors, also enabling stress relaxation and strain rate dependency to be considered. The DTMF method is based on the fracture mechanics concept of cyclic crack tip opening displacement (ΔCTOD) where the effective stress range takes the crack closure effect into account. This method is typically used to describe the thermomechanical low cycle fatigue behavior of cast irons, cast steels, stainless steels, Inconel, HiSiMo and nickel-based alloys. These materials are used in components that need to withstand high temperatures (higher than half of the melting point) in service as exhaust manifolds, cylinder heads, valves, turbochargers and disk brakes. Three failure mechanisms are detailed here: oxidation, creep and fatigue. Oxidation is a complex phenomenon that may occur when the material is hot under tensile in-phase loading or hot under compressive out-of-phase loading. Creep is a time and temperature dependent diffusion process which is incorporated into the DTMF parameter as a multiplicative factor. In this context fatigue life is defined as the number of cycles to propagate an existent microcrack up to an arbitrary size that is defined on a case-by-case basis.

A kinetic non-steady state analysis of immobilized enzyme systems with external mass transfer resistance

<abstract><p>The goal of this paper is to utilize the homotopy perturbation method (HPM) and Laplace transform to provide an approximate analytical expression to the non-linear time-dependent reaction diffusion equation arising in a mathematical model of an immobilized enzyme system with external mass transfer resistance. This mathematical model is a non-steady, non-linear reaction diffusion equation based on Michaelis–Menten kinetics. Approximate analytical expressions are also provided for various geometries of the enzyme catalytic pellets, namely, planar, cylindrical, and spherical. Obtained semi-analytical expressions are proven to fit for all the parameters appearing in the system and for all the geometries of enzyme catalytic pellets. When comparing the numerical and approximate analytical solutions, satisfactory results are obtained. Also, approximate analytical expressions of the effectiveness factor (EF) of the immobilized system are presented, and the effect of parameters on the EF is also analyzed.</p></abstract>

TDKI-Net: A Joint q-t Space Learning Network for Diffusion-Time-Dependent Kurtosis Imaging.

Time-dependent diffusion magnetic resonance imaging (TDDMRI) is useful for the non-invasive characterization of tissue microstructure. These models require both densely sampled q-t space data for microstructural fitting, leading to very time-consuming acquisition protocols. To overcome this problem, we present a joint q-t space model-tDKI-Net to estimate diffusion-time dependent kurtosis and the transmembrane exchange, using downsampled q-t space data. The tDKI-Net is composed of several q-Encoders and a t-Encoder, designed based on the extragradient mechanism, each integrated with their respective mapping networks. In the tDKI-Net, two types of encoders along with their mapping networks are employed sequentially to generate kurtosis at individual diffusion times and to fit the transmembrane exchange time ( τm) using the time-dependent kurtosis according the Kärger's model. Meanwhile, we proposed a three-stage training strategy, including physics-informed self-supervised pretraining, DKI warm-up, and joint training, to match the network structure. Our results demonstrated that the proposed tDKI-Net could effectively accelerate tDKI scans, resulting in lower estimation error compared with other methods. Our proposed three-stage training strategy demonstrated superior results than those training from scratch, e.g., the normalized root mean square error (NRMSE) of τm decreased by up to 1.4%. We also investigated the training data size effects and found that although we used one-subject training, the network achieved lower NRMSEs for Kavg, K0 and τm (2.50%, 3.04%, 10.86%) than previous work that used three-subject training (3.8%, 9.5%, 12.1%). tDKI-Net can considerably reduce the scan time by 10.5- fold by joint downsampling the q-t space data without compromising the estimation accuracy.

Enhanced diffusion in thin-film Cu-Zr nanoglasses

Tracer measurements with both radioactive, 55Fe, as well as natural, mainly 56Fe, isotopes are used to investigate Fe diffusion in a Cu-Zr nanoglass in comparison to their diffusion rates in a homogeneous amorphous counterpart. The columnar-structured nanoglass and the homogeneous amorphous films are synthesized using radio-frequency magnetron sputtering. Ion beam sputtering (with the 55Fe radioisotope) and time-of-flight secondary ion mass spectroscopy (with natural Fe) are used for the diffusion experiments. Remarkably, faster Fe diffusion is observed in the columnar nanoglasses, supporting the concept of glass–glass interfaces. The relative diffusion enhancement is explained within the excess free volume concept that is supported by structural investigations using transmission electron microscopy. For the first time, the relaxation dynamics in a nanoglass as well as in a homogeneous thin-film glass of identical composition are evaluated via time-dependent diffusion measurements.

Exact higher-order moments for linear non-homogeneous stochastic differential equation

This paper investigates the moments of a stochastic process that satisfies the one-dimensional linear stochastic differential equation (SDE) with nonlinear time-dependent drift and diffusion coefficients. The goal is to derive formulas for the nth exact moment, that instead of seeking the transition density function by solving the Fokker-Plank equations or moment-generating functions, which can be difficult to solve in closed form. We will appropriately apply Itô’s formula and the properties of the Wiener process with a constant drift and diffusion term, which is a Gaussian process to obtain the exact higher-order moments.

Lower-Dimensional Model of the Flow and Transport Processes in Thin Domains by Numerical Averaging Technique

In this work, we present a lower-dimensional model for flow and transport problems in thin domains with rough walls. The full-order model is given for a fully resolved geometry, wherein we consider Stokes flow and a time-dependent diffusion–convection equation with inlet and outlet boundary conditions and zero-flux boundary conditions for both the flow and transport problems on domain walls. Generally, discretizations of a full-order model by classical numerical schemes result in very large discrete problems, which are computationally expensive given that sufficiently fine grids are needed for the approximation. To construct a computationally efficient numerical method, we propose a model-order-reduction numerical technique to reduce the full-order model to a lower-dimensional model. The construction of the lower-dimensional model for the flow and the transport problem is based on the finite volume method and the concept of numerical averaging. Numerical results are presented for three test geometries with varying roughness of walls and thickness of the two-dimensional domain to show the accuracy and applicability of the proposed scheme. In our numerical simulations, we use solutions obtained from the finite element method on a fine grid that can resolve the complex geometry at the grid level as the reference solution to the problem.