Transient Diffusion Research Articles

Aggregation of adult parasitic nematodes in sex-mixed groups analysed by transient anomalous diffusion formalism.

Intestinal parasitic worms are widespread throughout the world, causing chronic infections in humans and animals. However, very little is known about the locomotion of the worms in the host gut. We studied the movement of Heligmosomoides bakeri, naturally infecting mice, and used as an animal model for roundworm infections. We investigated the locomotion of H. bakeri in simplified environments mimicking key physical features of the intestinal lumen, i.e. medium viscosity and intestinal villi topology. We found that the motion sequence of these nematodes is non-periodic, but the migration could be described by transient anomalous diffusion. Aggregation as a result of biased, enhanced-diffusive locomotion of nematodes in sex-mixed groups was detected. This locomotion is probably stimulated by mating and reproduction, while single nematodes move randomly (diffusive). Natural physical obstacles such as high mucus-like viscosity or villi topology slowed down but did not entirely prevent nematode aggregation. Additionally, the mean displacement rate of nematodes in sex-mixed groups of 3.0 × 10-3 mm s-1 in a mucus-like medium is in good agreement with estimates of migration velocities of 10-4 to 10-3 mm s-1 in the gut. Our data indicate H. bakeri motion to be non-periodic and their migration random (diffusive-like), but triggerable by the presence of kin.

Transient thermal convective and radiative diffusion–reaction of magneto‐metallic Brinkman‐type nanofluid flow with isothermal and ramped temperature impacts

AbstractFluid‐containing nanoparticle research is well‐known for its heat transmission properties due to real‐world applications in various thermal systems. This demonstration shows how time‐dependent magneto‐hydrodynamic (MHD) Brinkman‐type nanofluid can flow through a vertical oscillating absorbent plate immersed in a porous environment. The governing dimensional partial differential system of equations is translated into a non‐dimensional partial differential system with applicable scaling variables. The transient equations governing nanofluid flow's momentum, thermal and mass are solved using the finite semi‐discretization difference line method. The obtained outcomes are validated by comparing them with previous works. Graphical resolutions for momentum, heat, and mass distribution fields are presented to examine essential physical terms with the isothermal and ramped temperature impacts. It was found that magnifying the Brinkman parameter and magnetic parameter brings in a decrement in fluid velocity. In contrast, reversal deportment is exposed with an enlargement of permeability parameters and thermal and solute buoyancy effects. Reynold's number has shown a declining impact in the fluid velocity, but time progress unveiled a contrary tendency. The sprouting radiation parameter deepens the fluid temperature, whereas the rising heat absorption parameter curtails the fluid temperature. The fluid concentration deflates for growing Schmidt number and chemical reactive agent. The wall friction increased with the porosity parameter but has shown a reverse trend with magnetic and Brinkman parameters. Increasing the Prandtl number and heat‐consumption parameter helps to raise the temperature gradient. The concentration gradient lessened on augmentation of chemical reaction and Schmidt number.

Heat-dependent properties of methane diffusion in coal: an experimental study and mechanistic analysis.

Coalbed methane thermodynamic extraction, as an emerging ECBM recovery method, can effectively improve gas recovery rates. And clarifying methane diffusion and migration law in coal under thermal stimulation is crucial for the selection of its process parameters. Based on laboratory methane adsorption-release experiments, the evolution law of methane diffusion characteristics with temperature and pressure was studied, and the control mechanism of heat-dependent methane diffusion behavior was explored. The results show that both thermal stimulation and high adsorption pressure accelerated the methane diffusion rate in coal. Adsorption pressure had little effect on methane diffusion percentage, but thermal stimulation promoted a significant increase in diffusion percentage and improved the net methane yield. The influence mechanisms of adsorption pressure and thermal stimulation on methane diffusion characteristics are elucidated in relation to the amount and proportion of methane-activated molecules in the diffusion process. The constant diffusion coefficient of methane is heat-dependent, based on which a diffusion model is derived to accurately predict the methane release process in coal. Additionally, temperature has a more important effect on transient diffusion coefficient than pressure. Thermal stimulation leads to a net increase rather than a decrease in diffusion coefficient in the early diffusion stages and can also accelerate the attenuation of diffusion coefficient, with this intensifying effect becoming more pronounced at higher temperatures. The research results can provide some reference for the determination of coal seam gas content and the selection of heat injection process parameters.

Model-free chemomechanical interfaces: History-dependent damage under transient mass diffusion

This paper presents a data-driven framework based on distance functional for chemo-mechanical cohesive interfaces to capture transient diffusion and resulting interfacial damage evolution. The framework eliminates reliance on complex constitutive models and phenomenological assumptions, especially avoiding the coupling tangent terms with a given material database. The interfacial chemical potential and its jumps are used to expand the phase space for describing the chemical states of interfaces. Subsequently, a novel chemo-mechanical distance norm, including traction-separation pair, interfacial chemical potential-concentration pair and corresponding chemical potential jump-flux pair, is presented. Momentum conservation law for interfacial tractions and mass conservation law for interfacial concentration are enforced via Lagrange multipliers. For tracking the history-dependent state of the interface damage, an internal variable, termed interface integrity, is introduced to condition the interfacial database and manage the subsets mapping strategies, following physically motivated evolution constraints. Numerical examples are conducted to investigate the efficiency and capability of the present framework. A monotonic loading test validates a good numerical convergence relative to the number of data points. Subsequent cyclic loading simulations, compared with the reference solutions, show that the algorithm is well suitable to predict the history-dependent interface damage evolution under complex loading paths. Finally, the chemo-mechanically coupled examples capture phenomena such as interfacial swelling and interface degradation induced by transient diffusion and stress-driven diffusion. The current work provides a promising tool for understanding chemo-mechanical behaviors of interfaces within heterogeneous composites.

Random walk algorithms for solving nonlinear chemotaxis problems

Abstract Random walk based stochastic simulation methods for solving a nonlinear system of coupled transient diffusion and drift-diffusion equations governing a two-component chemotaxis process are developed. The nonlinear system is solved by linearization, the system is evolved in time, by small time steps, where on each step a linear system of equations is solved by using the solution from the previous time step. Three different stochastic algorithms are suggested, (1) the global random walk on grid (GRWG), (2) a randomized vector algorithm (RVA) based on a special transformation of the original matrix to a stochastic matrix, and (3) a stochastic projection algorithm (SPA). To get high precision results, these methods are combined with an iterative refinement method.

Numerical study of transient diffusion behavior of SF6 and He in a nuclear power plant condenser

Numerical study of transient diffusion behavior of SF6 and He in a nuclear power plant condenser

ML-GLE: A machine learning enhanced Generalized Langevin equation framework for transient anomalous diffusion in polymer dynamics

In this work we introduce ML-GLE, a machine learning framework to generate long-term single-polymer dynamics by exploiting short-term trajectories from molecular dynamics (MD) simulations of polymer melts. Even with current advances in machine learning for MD, these polymeric materials remain difficult to simulate and characterize due to prohibitive computational costs when long relaxation timescales are involved. Our method relies on a 3D neural auto-regressive model for single polymer lower dimensional collective variables, called normal modes. This enhances the Generalized Langevin Equation (GLE) capabilities in modelling diffusion phenomena. We exploit a particular GLE solution which is known to reproduce the mean square displacement curve relative to transient anomalous diffusion and connect it with the normal modes collective variables. ML-GLE is capable of emulating the single polymer statistical properties in the long-term, predicting the diffusion coefficient. As a consequence, this results in an enormous acceleration in terms of simulation time with respect to the full-size simulation. Moreover, this approach is also scalable with system size.

Vertical matrix advection dominates transient anomalous diffusion within fracture-matrix systems using a modified diffusion model

Pollutant transport in fractured media has been well analyzed using process-based diffusion models and concise, time-nonlocal models like the tempered fractional derivative (TFD) model. While traditional diffusion models are limited to specific transport processes, TFD model parameters lack hydrogeological meaning. In addressing these knowledge gaps, a modified diffusion model is proposed to augment the traditional diffusion model and offer hydrogeological interpretations for TFD parameters. This modified diffusion model incorporates transverse advection in low-permeability matrices, allowing for the quantification of transient anomalous diffusion in a single fracture-matrix system. This model offers a semi-analytical solution, systematically validated for its applicability. Memory function analysis establishes a quantitative connection between the modified diffusion model and the TFD model, uncovering a pivotal discovery in this study. Parameter sensitivity analysis further shows that the matrix characteristic rate defined as a function of (Vm)2/(4Dm), where Vm is the transverse matrix velocity and Dm is the transverse matrix diffusion coefficient, controls the temporal evolution of anomalous sub-diffusion in the fracture. Applications are performed to check the feasibility of the modified diffusion model. The developed modified diffusion model sheds light on quantifying complex transport in fracture-matrix systems and enhances the predictability of nonlocal transport models.

Hierarchically Coupled Ornstein–Uhlenbeck Processes for Transient Anomalous Diffusion

The nonlinear dependence of the mean-squared displacement (MSD) on time is a common characteristic of particle transport in complex environments. Frequently, this anomalous behavior only occurs transiently before the particle reaches a terminal Fickian diffusion. This study shows that a system of hierarchically coupled Ornstein–Uhlenbeck equations is able to describe both transient subdiffusion and transient superdiffusion dynamics, as well as their sequential combinations. To validate the model, five distinct experimental, molecular dynamics simulation, and theoretical studies are successfully described by the model. The comparison includes the transport of particles in random optical fields, supercooled liquids, bedrock, soft colloidal suspensions, and phonons in solids. The model’s broad applicability makes it a convenient tool for interpreting the MSD profiles of particles exhibiting transient anomalous diffusion.

Modeling pulsed dye laser treatment of psoriatic plaques by combining numerical methods and image-derived lesion morphologies.

Knowledge of the physical effects of pulsed dye laser (PDL) treatment of psoriatic lesions is essential in unraveling the remedial mechanisms of this treatment and hence also in maximizing in its disease-modifying potential. Therefore, the main objective of this study was to provide estimates of these physical effects (for laser wavelengths of 585and 595 nm), with the aim of identifying pathogenic processes that may be affected by these conditions. We modeled the laser light propagation and subsequent photothermal heating by numerically solving the transient diffusion and heat equations simultaneously. To this end, we used the finite element method in conjunction with an image-derived psoriatic lesion morphology (which was defined by segmenting blood vessels from a confocal microscopy image of a fluorescently labeled section of a 3 mm punch biopsy of a psoriatic lesion). The resulting predictions of the generated temperature field within the lesion were then used to assess the possibility of stalling or arresting some suspected pathogenic processes. According to our results, it is conceivable that perivascular nerves are thermally denatured, as almost all locations that reach 60°C were found to be within 18 µm (at 585 nm) and 11 µm (at 595 nm) of a blood vessel wall. Furthermore, activation of TRPV1 and TRPV2 channels in perivascular neuronal and immune cells is highly likely, since a critical temperature of 43°C is generated at locations within up to 350 µm of a vessel wall (at both wavelengths) and sustained for up to 700 ms (at 585 nm) and 40 ms (at 595 nm), while a critical temperature of 52°C is reached by locations within 80 µm (at 585 nm) and 30 µm (at 595 nm) of a vessel wall and sustained for up to 100 ms (at 585 nm) and 30 ms (at 595 nm). Finally, we found that the blood vessel coagulation-inducing temperature of 70°C is sustained in the vascular epithelium for up to 19and 5 ms at 585and 595 nm, respectively, rendering partial or total loss of vascular functionality a distinct possibility. The presented approach constitutes a useful tool to provide realistic estimates of the photothermal effects of PDLtreatment of psoriatic plaques (as well as other selective photothermolysis-based treatments), yielding information that is essential in guiding future experimental studies towardunraveling the remedial mechanisms of these treatments.

Directional enrichment functions for finite element solutions of transient anisotropic diffusion

The present study proposes a novel approach for efficiently solving an anisotropic transient diffusion problem using an enriched finite element method. We develop directional enrichment for the finite elements in the spatial discretization and a fully implicit scheme for the temporal discretization of the governing equations. Within this comprehensive framework, the proposed class of exponential functions as enrichment enhance the approximation of the finite element method by capturing the directional based behaviour of the solution. The incorporation of these enrichment functions leverages a priori knowledge about the anisotropic problem using the partition of unity technique, resulting in significantly improved approximation efficiency while retaining all the advantages of the standard finite element method. Consequently, the proposed approach yields accurate numerical solutions even on coarse meshes and with significantly fewer degrees of freedom compared to the standard finite element methods. Moreover, the choice of mesh coarseness remains independent of the anisotropy in the problem, enabling the use of the same mesh regardless of changes in the anisotropy. Using extensive numerical experiments, we consistently demonstrate the efficiency of the proposed method in attaining the desired levels of accuracy. Our approach not only provides reliable and precise solutions but also extends the capabilities of the finite element method to effectively address aspects of the heterogeneous anisotropic transient diffusion problems that were previously considered ineffective when using this method.

Assessment of Local Radial Basis Function Collocation Method for Diffusion Problems Structured with Multiquadrics and Polyharmonic Splines

This paper aims to systematically assess the local radial basis function collocation method, structured with multiquadrics (MQs) and polyharmonic splines (PHSs), for solving steady and transient diffusion problems. The boundary value test involves a rectangle with Dirichlet, Neuman, and Robin boundary conditions, and the initial value test is associated with the Dirichlet jump problem on a square. The spectra of the free parameters of the method, i.e., node density, timestep, shape parameter, etc., are analyzed in terms of the average error. It is found that the use of MQs is less stable compared to PHSs for irregular node arrangements. For MQs, the most suitable shape parameter is determined for multiple cases. The relationship of the shape parameter with the total number of nodes, average error, node scattering factor, and the number of nodes in the local subdomain is also provided. For regular node arrangements, MQs produce slightly more accurate results, while for irregular node arrangements, PHSs provide higher accuracy than MQs. PHSs are recommended for use in diffusion problems that require irregular node spacing.

Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional‐Derivative Equation

AbstractHydrologically mediated hot moments (HM‐HMs) of transient anomalous diffusion (TAD) denote abrupt shifts in hydraulic conditions that can profoundly influence the dynamics of anomalous diffusion for pollutants within heterogeneous aquifers. How to efficiently model these complex dynamics remains a significant challenge. To bridge this knowledge gap, we propose an innovative model termed “the impulsive, tempered fractional advection‐dispersion equation” (IT‐fADE) to simulate HM‐HMs of TAD. The model is approximated using an L1‐based finite difference solver with unconditional stability and an efficient convergence rate. Application results demonstrate that the IT‐fADE model and its solver successfully capture TAD induced by hydrologically trigged hot phenomena (including hot moments and hot spots) across three distinct aquifers: (a) transient sub‐diffusion arising from sudden shifts in hydraulic gradient within a regional‐scale alluvial aquifer, (b) transient sub‐ or super‐diffusion due to convergent or push‐pull tracer experiments within a local‐scale fractured aquifer, and (c) transient sub‐diffusion likely attributed to multiple‐conduit flow within an intermediate‐scale karst aquifer. The impulsive terms and fractional differential operator integrated into the IT‐fADE aptly capture the ephemeral nature and evolving memory of HM‐HMs of TAD by incorporating multiple stress periods into the model. The sequential HM‐HM model also characterizes breakthrough curves of pollutants as they encounter hydrologically mediated, parallel hot spots. Furthermore, we delve into discussions concerning model parameters, extensions, and comparisons, as well as impulse signals and the propagation of memory within the context of employing IT‐fADE to capture hot phenomena of TAD in aquatic systems.

Order-of-Magnitude Increase in Carbon Nanotube Yield Based on Modeling Transient Diffusion and Outgassing of Water From Reactor Walls

Abstract While reactor wall preconditioning was previously shown to influence the yield in chemical vapor deposition (CVD), especially for the growth of carbon nanotubes (CNTs), it was limited to studying accumulating carbonaceous deposits over a number of runs. However, the effects of temperature and duration as the reactor walls are exposed to hot humidity for extended periods between growth runs were not previously studied systematically. Here, we combine experimental measurements with a mathematical model to elucidate how the thermochemical history of reactor walls impacts growth yield, especially knowing that only a specific range of humidity promotes growth. Importantly, we demonstrate a one-order-of-magnitude higher CNT yield by increasing the interim, i.e., the time between runs. We explain the results based on previously unexplored process sensitivity to trace amounts of oxygen-containing species in the reactor. In particular, we model the effect of small amounts of water vapor being desorbed from reactor walls during growth. Our results reveal the outgassing dynamics and show the underlying mechanism of generating growth-promoting molecules. By installing a humidity sensor in our custom-designed multizone rapid thermal CVD reactor, we are able to uniquely correlate the amount of moisture within the reactor to real-time measurements of growth kinetics, as well as ex situ characterization of CNT alignment and atomic defects. Our findings enable a scientifically grounded approach toward both boosting growth yield and improving its consistency by reducing run-to-run variations. Accordingly, engineered dynamics recipes with added preprocessing steps can be envisioned to leverage this phenomenon for improving manufacturing process scalability and robustness.

Behavior of Stiffened Rafts Resting on Expansive Soil and Subjected to Column Loads of Lightweight-Reinforced Concrete Structures

An approach to estimate the behavior of stiffened rafts under column loads of a lightweight-reinforced concrete structure resting on expansive soils is presented in this paper. The analysis was conducted using the computer program SLAB97, which estimates the 3D distorted mound shape using the finite difference method by solving the transient suction diffusion equation in 3D and computing the corresponding soil movements. The interaction between the stiffened rafts and the 3D distorted mound shape is then analyzed using the finite element method. The SLAB97 program has been validated by comparing its results with the results of others that were shown to be valid. The goal of the study is to make the expansive soil structure interaction models that the previous researchers proposed more logical. Assuming the worst initial 3D distorted mound shapes of the two cases of edge heave and edge shrinkage, an upper-bound solution is obtained. Using the two scenarios of edge shrinkage and edge heave, the program was utilized in a parametric investigation to examine the impact of various parameters on the behavior of stiffened rafts on expansive soils. These parameters include the stiffening beam depth, the maximum differential movement of the distortion mound shape, and the raft dimensions. The behavior of the stiffened rafts subjected to concentrated column loads is concluded to be similar to that of the stiffened rafts subjected to uniform and perimeter line loads in both cases of distortion modes, with regard to the shape of raft deformation and distribution of the bending moments; however, the values of the design parameters such as maximum deflection, maximum differential deflection, and maximum moments are entirely different in these two situations.

Effect of bonding temperature on microstructure and properties of TLP joined Q355 steel with Cu interlayer

Abstract Q355 steel with Cu interlayer was bonded by transient liquid phase diffusion bonding (TLP-DB) at different bonding temperatures, and good bonding joints were obtained. The joints were characterized by optical microscopy, scanning electron microscopy and mechanical properties. The results show that there is a bending phenomenon caused by the difference of element diffusion at the bonding interface at the bonding temperature of 1050 °C. With the increase of the bonding temperature, the diffusion of Cu element plays a role in refining the grain, but with the increase of the bonding temperature, it will also lead to the overgrowth of the grain; At the bonding temperature of 1050 °C, there are obvious mutations in the diffusion of Cu and Fe elements, but the increase of the bonding temperature has a good effect on the interdiffusion of the elements. The mechanical properties test showed that with the increase of the bonding temperature, the hardness, shear strength, and impact toughness at the center of the joint increased first and then decreased, and all reached the maximum at 1100 °C. The electrochemical performance test showed that with the increase of temperature, the corrosion resistance of the joint also increased first and then decreased.

The influence of holding time on the microstructure and properties of TLP joints of Q355 steel

Using BNi as the interlayer material, transient liquid phase diffusion welding experiments were conducted on Q355 steel at a welding temperature of 1050 °C under different holding times (10, 15, 20, 25 min). The welded joint microstructure, element diffusion migration, and phase composition were analyzed by using modern analytical testing instruments such as optical microscope (OM), scanning electron microscope (SEM), and energy dispersive spectrometer (EDS). The mechanical properties of the joint were tested and analyzed by using a microhardness tester, universal testing machine, and impact testing machine. The electrochemical corrosion property of the welded joint was analyzed and studied by using an electrochemical workstation. The results showed that under the conditions of 1050 °C and 6 MPa pressure, the Q355 steel TLP welded joint with better property could be obtained with a 20-min holding time. With the increase of holding time, the width of the bonding interface layer increased first and then decreased, and the microstructure tended to be more uniform. The shear strength gradually increased, reaching a maximum of 496.7 MPa (25 min), but the impact toughness increased first and then decreased, with a maximum of 250.61 J/cm2 (20 min). The corrosion resistance of the joint also improved first and then weakened.

Atomic force microscopy observation of surface morphologies and measurements of local contact potential differences of amorphous solid water samples deposited at 15 and 100 K.

We use an ultra-high vacuum cryogenic atomic force microscope to investigate the surface morphology of amorphous solid water (ASW) prepared by oblique deposition of water vapor onto Si(111)7 × 7 substrates at temperatures of 15 and 100 K. Height-height correlation function analysis of topographic images suggests that ASW at 15 K has a columnar structure and that the typical diameter of the column is 5-10 nm. At 100 K, the typical diameter is 10-30 nm, although columnar features are less prominent. The surface roughness (i.e., deviation of the height) is greater at 15 K than at 100 K, indicating that the surface at 100 K exhibits a relatively flat morphology. This result implies that transient diffusion of deposited water molecules affects the surface morphology at 100 K. In addition, measurements of the local contact potential difference between the tip and the ASW surface suggest that the magnitude of the negative surface potential at the microscopic scale, which is attributed to spontaneous polarisation, cannot simply be scaled by the thickness of ASW as predicted in previous experiments with Kelvin probes.

Modeling large-scale bioreactors with diffusion equations. Part I: Predicting axial dispersion coefficient and mixing times.

Bioreactor scale-up is complicated by dynamic interactions between mixing, reaction, mass transfer, and biological phenomena, the effects of which are usually predicted with simple correlations or case-specific simulations. This two-part study investigated whether axial diffusion equations could be used to calculate mixing times and to model and characterize large-scale stirred bioreactors in a general and predictive manner without fitting the dispersion coefficient. In this first part, a resistances-in-series model analogous to basic heat transfer theory was developed to estimate the dispersion coefficient such that only available hydrodynamic numbers and literature data were needed in calculations. For model validation, over 800 previously published experimentally determined mixing times were predicted with the transient axial diffusion equation. The collected data covered reactor sizes up to 160 m3 , single- and multi-impeller configurations with diverse impeller types, aerated and non-aerated operation in turbulent and transition flow regimes, and various mixing time quantification methods. The model performed excellently for typical multi-impeller configurations as long as flooding conditions were avoided. Mixing times for single-impeller and few nonstandard bioreactors were not predicted equally well. The transient diffusion equation together with the developed transfer resistance analogy proved to be a convenient and predictive model of mixing in typical large-scale bioreactors.

Coherent Spatial Control of Wave Packet Dynamics on Quantum Lattices.

Quantum lattices are pivotal in the burgeoning fields of quantum materials and information science. Novel experimental techniques allow the preparation and monitoring of wave packet dynamics on quantum lattices with high spatiotemporal resolution. We present an analytical study of wave packet diffusivity and diffusion length on tight-binding quantum lattices subject to stochastic noise. Our analysis reveals the crucial role of spatial coherence and predicts a set of novel phenomena: (1) noise can enhance the transient diffusivity and diffusion length of spatially extended initial states; (2) standing or traveling initial states, with large momentum, spread faster than a localized initial state and exhibit a noise-induced peak in the transient diffusivity; (3) the differences in the diffusivity or diffusion length of extended and localized initial states have a universal dependence on initial width. These predictions suggest the possibility of controlling the wave packet dynamics by spatial manipulations, which will have implications for materials science and quantum technologies.