Diffusion Process Research Articles

Low-frequency approximations to the finite-length Warburg diffusion impedance: The reflexive case

A study on the influence of the characteristic parameters of the finite-length diffusion processes on the galvanostatic dynamic response of electrochemical systems described by the reflexive Warburg impedance, is presented. The characteristic frequencies of the reflexive diffusion impedance, originally including those of the purely diffusive behaviour, are identified. The galvanostatic charge/discharge cycle is interpreted from the truncated series obtained from the development into partial fractions of the impedance. The low-frequency behaviour is also compared to the impedance obtained from the development into continued fractions with an only characteristic frequency. Interesting results associated to the transition between the capacitive and diffusive behaviours, emerge from the use of a hybrid methodology dealing with frequency and time domains. A simple electric circuit physically based on the series developments of the reflexive Warburg impedance with an only relaxation time, is used to interpret the galvanostatic charge curve of a commercial supercapacitor and to validate the theoretical study.

Improving the superconducting properties of 100 m class MgB2 wire with 18+1 filaments produced via an internal Mg diffusion process

Internal Mg diffusion (IMD) technology reveals the expansive prospects of MgB2 superconducting wires. To facilitate the practical application of IMD, a series of 100 m class MgB2 wires with 18 + 1 filaments were prepared in this study. Based on the optical micrographs and performance analyses, the annealing temperature, B powder type and diameter of wires were refined. The results indicated that introducing C-coated B powder into wires would accelerate the diffusion of Mg melt and enhance the J e and layer J c significantly, while shrinking the wire diameter would further improve the wire transport capability. The optimal J e and layer J c of wire with an 0.8 mm diameter reached 1.2 × 104 and 1.1 × 105 A cm−2, respectively at 4.2 K and 8 T, which contained C-coated B powder and was annealed at 650 °C. These improved wires were eligible for magnet use in terms of performances, integrity, length and uniformity.

Parameter sharing fault data generation method based on diffusion model under imbalance data

Abstract Rotating machinery will inevitably fail under long-term heavy load working conditions. Obtaining enough data to train the deep learning model can enable managers to detect and deal with related failures in time, which greatly improves the safety of equipment operation. Mechanical fault samples are often much smaller than healthy samples. Traditional data enhancement methods mostly change the original data, but cannot improve the diversity of its features, so that the number of fault samples becomes larger, but the features remain unchanged. Aiming at the above problems, a diffusion model based on parameter sharing and inverted bottleneck residual structure (DDPM) is proposed. Firstly, the diffusion process gradually covers the original data with Gaussian noise, to learn the corresponding fault characteristics of the original data. In the diffusion process, the parameter sharing attention mechanism is embedded in the learning process of the diffusion process. Then, the feature extraction module is constructed by using the inverted bottleneck residual structure to enhance the learning ability of the network. After obtaining the fault characteristics of the original data, the reverse process of the results restores the Gaussian noise to data with different fault characteristics through the same steps as the diffusion process. By comparing the results of various generation models and analysing the characteristics of the generated data, the feasibility and universality of the proposed method in data augmentation tasks are verified.

Three-Dimensional Modeling of Polygonal Ridges in Salt Playas.

In this work, we investigate the formation of the curious polygonal salt ridges that tessellate salt playas worldwide using suitable three-dimensional modeling and simulation of the dynamical processes that are responsible for their formation. We employ the principles of fracture mechanics under cyclic wetting and drying, fluid and mass transport in fracture channels, and processes of crystallization and self-organization to finally replicate the almost Voronoidal pattern of salt ridge mosaics observed in playas. The model is generic and applicable to playas having different salt compositions, as the effect of the salt diffusion coefficient and critical salinity for crystallization are factored in. The final pattern of polygonal salt ridges obtained by simulation visually resembles the geometry of the salt ridges reported in the literature. A single equation describing the time of first crystallization of salt in terms of evaporation suction pressure P, diffusion coefficient D of salt, and relative salinity Δc with respect to critical salinity at saturation, has been proposed. The saturation of crystal growth rate is shown to be a dynamic equilibrium between advection and diffusion processes. We show that the stable polygonal geometry of the salt playas is an effort toward the total minimization of system energy.

A closed-form solution for spot volatility from options under limited data

In this article, the closed-form solution for spot volatility from European options is investigated. The price of the underlying asset follows a diffusion process with stochastic volatility. This approach requires only four European option contracts, making it applicable within limited data constraints. Numerical simulations are presented to prove the effectiveness and robustness.

Self-assembled polysilane artificial solid electrolyte interphase layer towards highly reversible zinc electrochemistry

Commercial applications of aqueous Zn batteries primarily encounter challenges related to surface corrosion and dendrite formation. In this study, a hydrophobic polysilane layer functionalized with −CF3 groups (CF3-PSiOX) is tailored for Zn anode through a two-step process involving self-assembly and condensation. The CF3-PSiOX layer functions as a protective barrier, effectively isolating water and inhibiting corrosion. Moreover, the primary interactions between −CF3 and Zn2+ guides the diffusion and deposition processes of Zn2+ while optimizing the de-solvation process, ultimately resulting in dendrite inhibition. Hence, cells with CF3-PSiOX layer boasts a high Coulombic efficiency (∼99.8 % after 1500 cycles), a long lifespan (over 2400 h), and optimized capacity retention (73.3 % over 1000 cycles). The self-assembled polysilane layer with customizable groups offers a novel approach for tuning the interface properties of Zn anodes and establishes a general principle for interface adjustment applicable to alternative metallic electrodes.

A supersymmetric quantum perspective on the explicit large deviations for reversible Markov jump processes, with applications to pure and random spin chains

The large deviations at various levels that are explicit for Markov jump processes satisfying detailed balance are revisited in terms of the supersymmetric quantum Hamiltonian H that can be obtained from the Markov generator via a similarity transformation. We first focus on the large deviations at level 2 for the empirical density p^(C) of the configurations C seen during a trajectory over the large time window [0,T] , and rewrite the explicit Donsker–Varadhan rate function as the matrix element I[2][p^(.)]=⟨p^|H|p^⟩ involving the square-root ket |p^⟩ . (The analog formula is also discussed for reversible diffusion processes as a comparison.) We then consider the explicit rate functions at higher levels, in particular for the joint probability of the empirical density p^(C) and the empirical local activities a^(C,C′) characterizing the density of jumps between two configurations (C,C′) . Finally, the explicit rate function for the joint probability of the empirical density p^(C) and of the empirical total activity A^ that represents the total density of jumps of a long trajectory is written in terms of the two matrix elements ⟨p^|H|p^⟩ and ⟨p^|Hoff|p^⟩ , where Hoff represents the off-diagonal part of the supersymmetric Hamiltonian H. This general framework is then applied to pure or random spin chains with single-spin-flip or two-spin-flip transition rates, where the supersymmetric Hamiltonian H corresponds to quantum spin chains with local interactions involving Pauli matrices of two or three neighboring sites. It is then useful to introduce the quantum density matrix ρ^=|p^⟩⟨p^| associated with the empirical density p^(.) in order to rewrite the various rate functions in terms of reduced density matrices involving only two or three neighboring sites.

A study using a semi-analytical approach to the reaction kinetics that describes the behavior of heterogeneous reaction–diffusion process with a glyoxyl-agarose immobilized enzyme (penicillin G acylase) in a batch reactor

This research article examines the reaction–diffusion process in a batch reactor by means of immobilized penicillin G acylase (PGA) with a glyoxyl-agarose matrix support. This study employs the Akbari-Ganji’s Method (AGM) when the system is under the internal (intra-particle) diffusional restrictions, and the external (film) diffusional restrictions is negligible. The semi-analytical approximations by the AGM technique are employed for computing the dimensionless steady-state solutions for a system of nonlinear differential equations to examine the impact of internal diffusional restrictions (IDR) as a function of catalyst enzyme loading and particle size. The model entails highly nonlinear components that adhere to the standard Michaelis-Menten kinetics. In addition to the proposed model, the dynamics for the mean integrated effectiveness factor (MIEF) of the dimensionless substrate concentration phenylglycine methyl ester (PGME) is presented. In light of this, there is a satisfactory level of agreement on the comparison of the semi-analytical result with the simulated numerical results across the whole concentration range where the dimensionless initial substrate and product concentrations are S1b=30,S2b=15, and P1b=60,P2b=100. The behavior of concentration profiles under the steady/unsteady state conditions for the effect of IDR on the overall reaction rates by immobilized biocatalyst PGA were examined. A sensitivity analysis is carried out to identify the effective parameter which can influence the diffusional restrictions on MIEF. An error analysis is performed on the dimensionless concentration equations to assess the amount of accuracy and the convergence of a solution.

Comparative simulations of methanol steam reforming on PdZn alloy using kinetic Monte Carlo and mean-field microkinetic model.

Methanol steam reforming (MSR) is an attractive route for producing clean energy hydrogen. PdZn alloys are extensively studied as potential MSR catalysts for their stability and high CO2 selectivity. Here, we investigated the reaction mechanism using density functional calculations, mean-field microkinetic modeling (MF-MKM), and kinetic Monte Carlo (kMC) simulations. To overcome the over-underestimation of CO2 selectivity by log-kMC, an ads-kMC algorithm is proposed in which the adsorption/desorption rate constants were reduced under certain requirements and the diffusion process was treated by redistributing surface species each time an event occured. The simulations show that the dominant pathway to CO2 at low temperatures is CH3OH → CH3O → CH2O → H2COOH → H2COO → HCOO → CO2. The ads-kMC predicted OH coverage is 2-3 times that of MF-MKM, while they produce similar coverage for other species. Analyses indicate that surface OH promotes the dehydrogenation of CH3OH, CH3O, and H2COOH significantly and plays a key role in the MSR process. The dissociation of water/methanol is the most important rate-limiting/rate-inhibiting step. The CO2 selectivity obtained by the two methods is close to each other and consistent with the experimental trend with temperature. Generally, the ads-kMC results agree with the MF-MKM ones, supporting the previous finding that kMC and MF-MKM predict similar results if the diffusion is very fast and adsorbate interactions are neglected. The present study sheds light on the MSR process on PdZn alloys, and the proposed scheme to overcome the stiff problems in kMC simulations is worthy of being extended to other systems.

Exploring the chaotic structure and soliton solutions for (3 + 1)-dimensional generalized Kadomtsev–Petviashvili model

The study of the Kadomtsev–Petviashvili (KP) model is widely used for simulating several scientific phenomena, including the evolution of water wave surfaces, the processes of soliton diffusion, and the electromagnetic field of transmission. In current study, we explore some multiple soliton solutions of the (3+1)-dimensional generalized KP model via applying modified Sardar sub-equation approach (MSSEA). By extracting the novel soliton solutions, we can effectively obtain singular, dark, combo, periodic and plane wave solutions through a multiple physical regions. We also investigate the chaotic structure of governing model using the chaos theory. The behavior of the collected solutions is visually depicted to demonstrate the physical properties of the proposed model. The solutions obtained in this paper can expand the existing solutions of the (3+1)-dimensional KP model and enhance our understanding of the nonlinear dynamic behaviors. This approach allows for consistent and effective treatment of the computation process for nonlinear KP model.

Adsorption and Diffusion Properties of Gas in Nanopores of Kerogen: Insights from Grand Canonical Monte Carlo and Molecular Dynamics Simulations

Investigating the adsorption and diffusion processes of shale gas within the nanopores of kerogen is essential for comprehending the presence of shale gas in organic matter of shale. In this study, an organic nanoporous structure was constructed based on the unit structure of Longmaxi shale kerogen. Grand canonical Monte Carlo and molecular dynamics simulation methods were employed to explore the adsorption and diffusion mechanisms of pure CH4, CO2, and N2, as well as their binary mixtures with varying mole fractions. The results revealed that the physical adsorption characteristics of CH4, CO2, and N2 gases on kerogen adhered to the Langmuir adsorption law. The quantity of adsorbed gas molecules increased with rising pressure but decreased with increasing temperature. The variation in the heat of adsorption was also analyzed. Under identical temperature and pressure conditions, the adsorption of CH4 increased with higher mole fractions of CH4, whereas it decreased with greater mole fractions of CO2 and N2. Notably, CO2 molecules exhibited a robust interaction with kerogen molecules compared to the adsorption properties of CH4 and N2. Furthermore, the self-diffusion coefficient of gas within kerogen nanopores gradually decreased with increasing pressure or decreasing temperature. The diffusion capacity of gas molecules followed the descending order N2 > CH4 > CO2 under the same pressure and temperature conditions.

Comparison of the adsorption dynamics of leucyl-leucine enantiomers and glycyl-glycine on Chirobiotic R and Chirobiotic V columns

The adsorption dynamics of the LL- and DD-enantiomers of Leu-Leu and Gly-Gly on a Chirobiotic V column packed with a CSP bearing glycopeptide antibiotic vancomycin was studied and compared with the adsorption dynamics of the same dipeptides on a Chirobiotic R column packed with a CSP with bonded antibiotic ristocetin A. The column efficiencies were essentially different. The heights equivalent to a theoretical plate (HETP) on Chirobiotic R were 2-4 times larger than on Chirobiotic V, and the shape of van Deemter plots, strongly convex-upwards on the former column, demonstrated minor (Leu-Leu) or lacking (Gly-Gly) convexity on the latter column. This difference is attributed to differences in the binding kinetics of dipeptides to the antibiotics, fast for vancomycin and slow for ristocetin A. Since the kinetic C term of the van Deemter equation cannot explain such a large discrepancy in HETP for the same analyte on two columns, and since the A and B terms for the Chirobiotic R column were essentially larger than for the Chirobiotic V column, it is suggested that binding kinetics influences eddy and longitudinal diffusion processes associated with those terms. It is also hypothesized that unusually high values of van Deemter B coefficients occasionally found in chiral chromatography are not experimental artifacts but the manifestation of coupling the effects of slow adsorption kinetics and longitudinal diffusion.

ReF-DDPM: A novel DDPM-based data augmentation method for imbalanced rolling bearing fault diagnosis

Effective bearing fault diagnosis is crucial to ensure the safety and reliability of mechanical systems. Due to the complex and harsh working environment, mechanical data often comes from imbalanced datasets, which is a pressing problem in diagnosis applications. However, currently proposed data augmentation methods mainly based on generative adversarial networks, remain challenging in balancing the quality and diversity of the generation samples. To solve it, this paper proposes a new data enhancement method called the reparameterized residual denoising diffusion probability model (ReF-DDPM) and applies it to fault diagnosis. The proposed architecture includes a forward diffusion process and a reverse denoising process, where Gaussian noise and original samples are transformed by Markov chains. To improve the quality of generation samples, the noise prediction network is modified for better feature representation by enhancing intra-level and inter-level features. Furthermore, signal labels are added to the model as conditional information to direct the generation of relevant category samples during the sampling process. The study provides a new data augmentation method for bearing imbalanced data, and generation data can be further used for fault diagnosis tasks. Verification experiments demonstrate the effectiveness and good generalization of the method, and improve the accuracy of imbalance fault diagnosis.

Learning Joint 2-D and 3-D Graph Diffusion Models for Complete Molecule Generation.

Designing new molecules is essential for drug discovery and material science. Recently, deep generative models that aim to model molecule distribution have made promising progress in narrowing down the chemical research space and generating high-fidelity molecules. However, current generative models only focus on modeling 2-D bonding graphs or 3-D geometries, which are two complementary descriptors for molecules. The lack of ability to jointly model them limits the improvement of generation quality and further downstream applications. In this article, we propose a joint 2-D and 3-D graph diffusion model (JODO) that generates geometric graphs representing complete molecules with atom types, formal charges, bond information, and 3-D coordinates. To capture the correlation between 2-D molecular graphs and 3-D geometries in the diffusion process, we develop a diffusion graph transformer (DGT) to parameterize the data prediction model that recovers the original data from noisy data. The DGT uses a relational attention mechanism that enhances the interaction between node and edge representations. This mechanism operates concurrently with the propagation and update of scalar attributes and geometric vectors. Our model can also be extended for inverse molecular design targeting single or multiple quantum properties. In our comprehensive evaluation pipeline for unconditional joint generation, the experimental results show that JODO remarkably outperforms the baselines on the QM9 and GEOM-Drugs datasets. Furthermore, our model excels in few-step fast sampling, as well as in inverse molecule design and molecular graph generation. Our code is provided in https://github.com/GRAPH-0/JODO.

Guidelines for oncologic surveillance in a patient with established cirrhosis

Cirrhosis is a chronic, diffuse disease process characterized by fibrosis and remodeling of the organ's normal architectonics into regenerative nodules. It is also one of the risk factors for cancers of the organ. One of the most common is hepatocellular carcinoma (HCC). The etiologic agent of HCC, which usually also causes cirrhosis, can be determined in more than 90% of patients. The annual risk of developing HCC ranges from 1% to 8%. It is estimated that about 1/3 of cirrhotic patients will develop HCC. By preventing cirrhosis and controlling its course, we reduce the risk of hepatocellular carcinoma [1].

Large-Scale Analysis on Accelerated Aging of Pentaerythritol Tetranitrate (PETN) Powders in Detonators.

Pentaerythritol tetranitrate (PETN) has been used extensively in commercial detonators and other explosive applications for many decades. Here, we show the results of a comprehensive 1.5 year aging study of PETN in commercial detonators, addressing batch-to-batch variations, surface area changes, and comparisons of aged loose powders side-by-side with identically aged detonators. Function time analysis of the aged detonators has also been provided and discussed in the context of powder aging. This large-scale, statistically relevant study addresses long-standing questions on PETN aging without the complications from making comparisons between multiple batches of material. We have evaluated the aging time required to reach the maximum measured amount of PETN coarsening and estimated an activation barrier of ∼123 kJ mol-1, which is higher than literature values reported by Gee et al. It is possible that this discrepancy is due to the fact that that this study cannot quantify the relative contributions of surface diffusion versus sublimation processes. At the lower temperatures of 50 and 60 °C, we assume that surface diffusion dominates over sublimation processes, even at longer aging times. At the higher temperature of 75 °C, we assume that both surface diffusion and sublimation contribute at the early time points, which are included in the Arrhenius analysis for coarsening.

Unraveling relationship between complex lifetimes and microscopic diffusion in deep eutectic solvents.

Aqueous mixtures of deep eutectic solvents (DESs) have emerged as a subject of interest in recent years for their tailored physicochemical properties. However, a comprehensive understanding of water's multifaceted influence on the microscopic dynamics, including its impact on improved transport properties of the DES, remains elusive. Additionally, the diffusion mechanisms within DESs manifest heterogeneous behavior, intricately tied to the formation and dissociation kinetics of complexes and hydrogen bonds. Therefore, it is imperative to explore the intricate interplay between bond kinetics, diffusion mechanism, and dynamical heterogeneity. This work employs water as an agent to explore their relationships by studying various relaxation phenomena in a DES based on acetamide and lithium perchlorate over a wide range of water concentrations. Notably, acetamide exhibits Fickian yet non-Gaussian diffusion across all water concentrations with Fickian (τf) and Gaussian (τg) timescales following a power-law relationship, τg∝τfγ, γ ∼ 1.4. The strength of coupling between bond kinetics and different diffusion timescales is estimated through various power-law relationships. Notably, acetamide-water hydrogen bond lifetime is linked to diffusive timescales through a single power-law over the entire water concentration studied. However, the relationship between diffusive timescales and the lifetime of acetamide-lithium complexes shows a sharp transition in behavior at 20 wt. % water, reflecting a change from vehicular diffusion below this concentration to structural diffusion above it. Our findings emphasize the critical importance of understanding bond dynamics within DESs, as they closely correlate with and regulate the molecular diffusion processes within these systems.

Efficient and scalable prediction of stochastic reaction–diffusion processes using graph neural networks

The dynamics of locally interacting particles that are distributed in space give rise to a multitude of complex behaviours. However the simulation of reaction–diffusion processes which model such systems is highly computationally expensive, the cost increasing rapidly with the size of space. Here, we devise a graph neural network based approach that uses cheap Monte Carlo simulations of reaction–diffusion processes in a small space to cast predictions of the dynamics of the same processes in a much larger and complex space, including spaces modelled by networks with heterogeneous topology. By applying the method to two biological examples, we show that it leads to accurate results in a small fraction of the computation time of standard stochastic simulation methods. The scalability and accuracy of the method suggest it is a promising approach for studying reaction–diffusion processes in complex spatial domains such as those modelling biochemical reactions, population evolution and epidemic spreading.

LAS-on-edge: A real-time laser absorption spectroscopic water vapor sensor on edge computing platforms

Real-time and in situ water vapor (H2O) sensors are increasingly demanded to indicate thermochemical parameters of energy systems. As an accurate, fast and non-intrusive sensing technology, laser absorption spectroscopy (LAS) enables simultaneous measurement of gas concentration and temperature. Due to the complex spectral computation, real-time and rapid LAS signal processing are still challenging. Most state-of-the-art LAS sensors utilize high-level computing units to post-process laser measurements in real time, hindering their portable deployment in harsh industrial environments. To address the above challenge, we developed an online LAS gas sensor on edging computing platforms, named as LAS-on-Edge. The developed sensor achieves an online monitoring rate up to 62.5 Hz by deploying a spectral-informed neural network on an embedded device. Simultaneously, it reserves the raw kilo-Hz measurements offline for underlying dynamics understanding. The LAS-on-Edge sensor’s compactness also enables its flexible and in situ integration. The sensor is firstly used to monitor a slow mist diffusion and accumulation process, exhibiting a high measurement accuracy with low spectra recovery residuals below 0.01. It is further applied to online monitor the H2O concentration and temperature variation during a lab-scale propane combustion process. It demonstrates a minimal temperature deviation of 1.86 % compared to the thermocouple reference in the flame. The sensor also successfully detects the fundamental flame pulsation at 5.65 Hz as well as high-frequency pulsations exceeding 200 Hz, thereby effectively reveals underlying flame dynamic behaviors.

Effect of continuous gradient Al on high-temperature oxidation of Ni-Cr-Co based superalloys via a high-throughput method

This study focuses on the effect of the main antioxidation element Al on the high-temperature oxidation resistance of Ni-Cr-Co based superalloys. A novel “3D printing-high temperature diffusion” high-throughput method was used to accurately determine the critical Al content to form continuous Al2O3 film. Results show that Al2O3 film significantly affects the element diffusion process during oxidation, and the critical Al content to form continuous Al2O3 film is 0.8 wt%. This conclusion was further confirmed by the corresponding discrete samples. It was also found that Ni-Cr-Co based superalloys exhibit “oxidation weight loss” and “Kp-antioxidation positive correlation” phenomena in high humidity condition.