Model Of Diffusion Process Research Articles

A novel prognostic method for degrading devices with nonlinear degradation processes indexed by both continuous and discrete time scales

Remaining useful life (RUL) prediction techniques based on degradation modeling to ensure the safety and reliability of stochastic degraded devices are of critical value. However, although the performance degradation of various devices in engineering practice is affected by multi-timescales, there are few RUL prediction methods for stochastic degraded devices with dual time scales in the existing literature. The research of prediction methods considering continuous and discrete time scales is blank. Toward this end, this paper proposes a novel prognostic method for nonlinear degradation devices based on the continuous-discrete dual time scales. First, the performance degradation with a discrete timescale is determined with a compound Poisson process and integrated into the diffusion process model to establish a nonlinear dual-timescale degradation model. Subsequently, the joint expression of the dual-timescale RUL distribution of the device in the first hitting time sense solves with threshold transformation. Finally, the effectiveness and superiority of the proposed method are verified through a numerical simulation and a gyroscope example. The experimental results show that the proposed method can provide more comprehensive information about the life distribution and effectively improve the accuracy of the RUL prediction.

An experimental study of the thermal-hydraulics of a spent nuclear fuel pool under loss-of-cooling accident conditions. Part II: a first interpretation of the MIDI tests

This article provides a first interpretation of the MIDI tests that were conducted in the frame of the IRSN’s DENOPI project. A first-level phenomenological analysis is detailed here. It is shown that the actual phenomenology mostly complies with the one that was envisioned by the community right after the Fukushima-Daiichi nuclear accident. Next, the diverse modes of water vaporization that may come into play during a spent nuclear fuel pool loss-of-cooling accident are quantified for each achieved test, by means of a proposed analytical model of the vapor diffusion process taking place on top of the liquid pool free surface. Then, a so-called vaporization regimes map is reconstructed on the basis of the test data. This map allows predicting the most likely dominant vaporization mode, given the pool level and total heat power. At last, the obtained data is reduced through the form of a set of dimensionless correlations, involving some of the classical numbers in heat and mass transfers. In doing so, the free surface evaporation, degassing of dissolved gaseous species and bubbles release processes are all modeled by means of a simple mathematical formulation.

Generalized Linear Driving Force Formulas for Diffusion and Reaction in Porous Catalysts

Approximate models are a fast and most often precise tool for determining the effectiveness factor for heterogeneous catalysis processes that are realized in the real world. They are also frequently applied as robust transient models describing the work of a single catalyst pellet or as a part of a more complex model, for example, a reactor model, where mass balances for the gas phase and solid phase are necessary. So far, approximate models for diffusion and reaction processes have been presented for processes described by a single balance equation. In the present work, approximate models without the mentioned limitation are presented and discussed. In addition, simple rules are shown for the development of other complex approximate models without tedious derivation in the complex domain. The formulas considered in this work are typical long-time approximations of the transient process. The accuracy is good, especially in the range of small and intermediate Thiele modulus values.

Numerical analysis of field aging in asphalt pavements via coupling of diffusion process and kinetics aging model

The asphalt aging model is a crucial module in the Mechanistic-Empirical (ME) pavement design programme for asphalt pavement performance prediction. In this study, an analytical aging model that couples diffusion and kinetics aging model (CDKAM) is improved to analyze and predict the field aging of asphalt pavements. The complex modulus (E*) of field cores was used as the aging property to illustrate the derivation of explicit expressions of time-averaged thermal source term ( TST ¯ ( t ) ) and time-averaged diffusion coefficient ( D ¯ ( t ) ). The value of the material-related parameter (M) in TST ¯ ( t ) model differs among different mixtures, which could assess the mixture’s susceptibility to thermal oxidation. The CDKAM with TST ¯ ( t ) and D ¯ ( t ) was used to predict E* of field aging for asphalt pavements in Texas after 22-month service life. The calibrated CDKAM could reasonably quantify the aging extent over time and the aging gradient over depth for studied asphalt pavements.

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. II

Modeling of the impurity diffusion process in a layer under the action of a system of random point sources is carried out. Mass sources of different power are uniformly distributed in a certain internal interval, that may also coincide with the entire region of the layer. The statistics of random sources is given. The solution of the initial-boundary value problem is found as the sum of the homogeneous problem solution and the convolution of the Green's function with the system of the random point sources. Averaging of the solution is performed on the internal subinterval and in the entire body region. The formulas for the variance, correlation function of the concentration field and coefficient of correlation are expressed in terms of the second moment of random mass sources. Software modules are developed for simulating the behavior of the averaged concentration, variance and correlation function. Their numerical analysis also is performed. General properties of the considered function are determined depending on the problem parameters.

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. I

The model of the impurity diffusion process in the layer where a system of random point mass sources acts, is proposed. Mass sources of various power are uniformly distributed in a certain internal interval of the body. Statistics of random sources are given. The solution of the initial-boundary value problem is constructed as a sum of the homogeneous problem solution and the convolution of the Green's function and the system of the random point mass sources. The solution is averaged over both certain internal subinterval and the entire body region. Simulation units are designed for modeling of the behavior of the averaged concentration function with acting system of point mass sources of various power. On this basis, the averaged concentration field is investigated depending on the internal interval length, power and number of sources in the system as well as the concentration values at the layer boundaries.

Концепция верификации работы клеточных автоматов при вариации геометрических решёток для модели диффузионного процесса

The methodology of cellular automata occupies one of the key positions in the discrete dynamic simulations. The adequacy of the results of solving applied problems is largely determined by the choice of the type of geometric lattice of the cellular automaton. The article presents a formalization and numerical verification of the concept of verification of the operation of a cellular automata model of the classical diffusion process for a set of basic two-dimensional geometric lattices. The approach is based on a direct comparison of the space-time solution of the diffusion equation obtained by the finite element method with the solution of a discrete analogue of this equation based on the operation of a cellular automata algorithm. The software implementation of the cell-automation was performed with the C+ using the Unity platform while the finite element solution of the evolutionary problem of mathematical physics was carried out using the Matlab tools. Cellular automaton lattices were constructed using various cell geometric primitives traditionally used in diffusion modeling applications. Obtained findings indicate that the hexagonal cellular automaton demonstrates the minimum error in the numerical implementation.

Physics-informed neural network for first-passage reliability assessment of structural dynamic systems

The first-passage failure of structural dynamic systems is a typical failure mode in engineering. Most of the existing methods use ordinary or partial differential equations (ODEs/PDEs) to describe the dynamic systems, and transform the first-passage reliability assessment into the solution of differential equations. Thus, the efficient solution of ODEs/PDEs is the main difficulty of the first-passage problems, especially for the structures with multi-degree-of-freedom and unknown parameters. For addressing this issue, a novel first-passage reliability assessment method based on physics-informed neural network (PINN) is proposed. In this paper, we firstly use ODEs/PDEs to describe the dynamic properties of the two classical first-passage models: Poisson process model and Markov diffusion process model. Then, the ODEs/PDEs are used to construct loss functions of the neural network, and the PINN evaluation model of the first-passage reliability is obtained finally. The effectiveness and accuracy of the proposed method are verified by several examples, and the potential value of the deep learning framework combined with physical properties and sample data in the field of dynamic reliability analysis is proved.

Stability Remarks on Discretized Multi-dimensional Diffusion Process Models and its Application to Model Reduction

Stability Remarks on Discretized Multi-dimensional Diffusion Process Models and its Application to Model Reduction

Local asymptotic normality for ergodic jump-diffusion processes via transition density approximation

We show local asymptotic normality (LAN) for a statistical model of discretely observed ergodic jump-diffusion processes, where the drift coefficient, diffusion coefficient, and jump structure are parametrized. Under the LAN property, we can discuss the asymptotic efficiency of regular estimators, and the quasi-maximum-likelihood and Bayes-type estimators proposed in Shimizu and Yoshida (Stat. Inference Stoch. Process. 9 (2006) 227–277) and Ogihara and Yoshida (Stat. Inference Stoch. Process. 14 (2011) 189–229) are shown to be asymptotically efficient in this model. Moreover, we can construct asymptotically uniformly most powerful tests for the parameters. Unlike with a model for diffusion processes, Aronson-type estimates of the transition density functions do not hold, which makes it difficult to prove LAN. Therefore, instead of Aronson-type estimates, we employ the idea of Theorem 1 in Jeganathan (Sankhyā Ser. A 44 (1982) 173–212) and use the L2 regularity condition. Moreover, we show that local asymptotic mixed normality of a statistical model is implied from that for a model generated by approximated transition density functions under suitable conditions. Together with density approximation by means of thresholding techniques, the LAN property for the jump-diffusion processes is proved.

Arrhenius-model-based degradable oligourethane hydrogels for controlled growth factor release.

Biodegradable hydrogels are growing in demand to enable the delivery of biomolecules (e.g. growth factors) for regenerative medicine. This research investigated the resorption of an oligourethane/polyacrylic acid hydrogel, a biodegradable hydrogel which supports tissue regeneration. The Arrhenius model was used to characterize the resorption of the polymeric gels in relevant in vitro conditions, and the Flory-Rehner equation was used to correlate the volumetric swelling ratio with the extent of degradation. The study found that the swelling rate of the hydrogel follows the Arrhenius model at elevated temperatures, estimating degradation time in saline solution at 37°C to be between 5 and 13 months, serving as a preliminary approximation of degradation in vivo. The degradation products had low cytotoxicity towards endothelial cells, and the hydrogel supported stromal cell proliferation. Additionally, the hydrogels were able to release growth factors and maintain the biomolecules' bioactivity towards cell proliferation. The study of the vascular endothelial growth factor (VEGF) release from the hydrogel used a diffusion process model, showing that the electrostatic attraction between VEGF and the anionic hydrogel allowed for controlled and sustained VEGF release over three weeks. In a rat subcutaneous implant model, a selected hydrogel with desired degradation rates exhibited minimal foreign body response and supported M2a macrophage phenotype, and vascularization. The low M1 and high M2a macrophage phenotypes within the implants were associated with tissue integration. This research supports the use of oligourethane/polyacrylic acid hydrogels as a promising material for delivering growth factors and supporting tissue regeneration. STATEMENT OF SIGNIFICANCE: There is a need for degradable elastomeric hydrogels that can support the formation of soft tissues and minimize long-term foreign body responses. An Arrhenius model was used to estimate the relative breakdown of hydrogels, in-vitro. The results demonstrate that hydrogels made from a combination of poly(acrylic acid) and oligo-urethane diacrylates can be designed to resorb over defined periods ranging from months to years depending on the chemical formulation prescribed by the model. The hydrogel formulations also provided for different release profiles of growth factors, relevant to tissue regeneration. In-vivo, these hydrogels had minimal inflammatory effects and showed evidence of integration into the surrounding tissue. The hydrogel approach can help the field design a broader range of biomaterials for tissue regeneration.

A copula approach in the probabilistic evaluation of chloride ingress process for coastal concrete structures

One of the most prevalent causes of reinforced concrete (RC) structural deterioration is chloride-induced corrosion. This paper is concerned with a novel approach to assess the chloride ingress process for coastal concrete structures under consideration of environmental effects. Firstly, the chloride diffusion process model for one-dimensional (1-D) and two-dimensional (2-D) concrete and the copula theory are introduced. Secondly, the climate data from the National Meteorological Center of China are investigated. Dependencies between temperature and humidity are described with a dedicated copula. Meanwhile, the results are analyzed regarding the geographical variations along the coastline. The critical environmental factors governing the diffusion process are identified and discussed. Finally, the feature of adopting the copula in modeling the environmental characteristics is highlighted. The work could significantly improve the durability design of coastal structures in China. A copula approach is developed to capture dependencies that are difficult to quantify from a physical perspective, including their uncertainties. Comparison to traditional methods shows the advantages clearly.

A reduced order model for fission gas diffusion in columnar grains

In fast reactors, restructuring of the fuel micro-structure driven by high temperature and high temperature gradient can cause the formation of columnar grains. The non-spheroidal shape and the non-uniform temperature field in such columnar grains implies that standard models for fission gas diffusion can not be applied. To tackle this issue, we present a reduced order model for the fission gas diffusion process which is applicable in different geometries and with non-uniform temperature fields, maintaining a computational requirement in line with its application in fuel performance codes. This innovative application of reduced order models as meso-scale tools within fuel performance codes represents a first-of-a-kind achievement that can be extended beyond fission gas behaviour.

Incorporating hybrid networks into urban transportation infrastructures for improved COVID-19 transmission forecasting

In this study, we focus on exploring the propagation characteristics of particle swarms in social networks and analyze the diffusion process of viruses among populations based on system dynamics. The article mainly discusses three propagation influence mechanisms, including individual attributes, group attributes, and particle swarm attributes, and delves into the modeling of diffusion processes based on network structures. Firstly, we adopt the main roads in the transportation network (hub nodes) as the initial network backbone. On this basis, by introducing branch networks with small-world characteristics and scale-free characteristics, we construct a transportation network that integrates multiple properties. Using this network, we conducted a detailed simulation and analysis of the COVID-19 transmission process and compared and verified it with the infection dynamic data of COVID-19 in Shanghai from March to September 2022. The verification results reveal that our proposed model can significantly improve prediction accuracy. Compared with other existing dynamic models, our model demonstrates excellent performance, possessing high practical application value. This study provides robust theoretical support for the propagation characteristics of particle swarms in social networks and lays the foundation for further research and application in related fields.

Modeling diffusion processes in a two-phase strip with randomly distributed spherical inclusions located near boundaries of the body. II. Quantitative analysis

Modeling diffusion processes in a two-phase strip with randomly distributed spherical inclusions located near boundaries of the body. II. Quantitative analysis

Correlation of the Diffusion Parameters and the Biological Activities in the Formulation of Pinus halepensis Essential Oil in Phosphogypsum Material

The use of natural biopesticides, specifically essential oils, is being explored as an alternative solution to protect stored foodstuffs. This study focuses on a formulation of phosphogypsum–Pinus halepensis essential oil as a pesticidal product. First, the essential oil chemical composition was determined using gas chromatography with mass spectrometry (GC-MS), while the phosphogypsum (waste from the phosphate mining industry) was analyzed using scanning electron microscopy, X-ray fluorescence, X-ray diffraction, Fourier-transform infrared spectroscopy, and thermogravimetric–differential thermal analysis; thus, physico-chemical properties and heavy metal contents were determined. In a second step, the preparation of the formulation consists in grafting the essential oil on the phosphogypsum (adsorption) in a cylindrical geometric shape adapted to the models applied in the bioprocesses of storage. The study of essential oil transfers in the material in the case of desorption along the axis (Oz) was carried out using analytical and numerical models of the Fickian diffusion process to understand the behavior of the oil and determine physicochemical parameters such as diffusivity (D) and evaporation flux (F). By using statistical methods such as experimental design and principal component analysis, these parameters can help explain the mechanisms involved in the insecticidal activities against the primary pest of lentils (Bruchus signaticornis) and in the parameters of lentil seed germination.

Signed networks - The role of negative links for the diffusion of innovation

We study the effects of negative links for the innovation diffusion process. To do so we employ an agent-based simulation model of a threshold diffusion process. Our results reveal that negative relationships can have a negative but also positive impact on the innovation diffusion. If network actors simply weigh the positive/negative signals coming from peers that have adopted the innovation, already few negative links will have a significant negative impact on the diffusion performance. If, however, network actors additionally consider the signals coming from peers that have not adopted the innovation, networks with a medium to high number of negative links create a ‘double-negative’ effect which drives the diffusion. Finally, an empirical network shows that our results hold also for real world network data. Our results emphasize the need to better understand how negative relationships, foe effects, and non-adopter effects can hinder or support the diffusion of innovations, potentially explaining why key innovations fail to spread and others succeed. The implications of this research are relevant for the discussion on the diffusion of innovation but also for the diffusion of information, opinions etc. It offers insights for researchers, companies, and policymakers wishing to scale and diffuse innovations more quickly.

Bayesian MRI reconstruction with joint uncertainty estimation using diffusion models.

We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction. Samples are drawn from the posterior distribution given the measured k-space using the Markov chain Monte Carlo (MCMC) method, different from conventional deep learning-based MRI reconstruction techniques. In addition to the maximum a posteriori estimate for the image, which can be obtained by maximizing the log-likelihood indirectly or directly, the minimum mean square error estimate and uncertainty maps can also be computed from those drawn samples. The data-driven Markov chains are constructed with the score-based generative model learned from a given image database and are independent of the forward operator that is used to model the k-space measurement. We numerically investigate the framework from these perspectives: (1)the interpretation of the uncertainty of the image reconstructed from undersampled k-space; (2) the effect of the number of noise scales used to train the generative models; (3) using a burn-in phase in MCMC sampling to reduce computation; (4) the comparison to conventional -wavelet regularized reconstruction; (5) the transferability of learned information; and (6) the comparison to fastMRI challenge. A framework is described that connects the diffusion process and advanced generative models with Markov chains. We demonstrate its flexibility in terms of contrasts and sampling patterns using advanced generative priors and the benefits of also quantifying the uncertainty for every pixel.

Rubidium and potassium isotopic variations in chondrites and Mars: Accretion signatures and planetary overprints

As moderately volatile elements, isotopes of Rb and K can trace volatilization processes in planetary bodies. Rubidium isotopic data are however very scarce, especially for non-carbonaceous meteorites. Here, we report combined Rb and K isotopic data (δ87/85Rb and δ41/39Κ) for 7 ordinary, 6 enstatite, and 4 Martian meteorite falls to understand the causes for the variations in volatile abundances and isotopic compositions. Bulk Rb and K isotopic compositions of planetary bodies are estimated to be (Table 1): Mars +0.10 ± 0.03 ‰ for Rb and −0.26 ± 0.05 ‰ for K, bulk OCs -0.12-0.24+0.15 ‰ for Rb and -0.72-0.41+0.28 ‰ for K, bulk ECs +0.02-0.26+0.29 ‰ for Rb and -0.33-0.23+0.37 ‰ for K. The bulk K isotopic compositions of subgroup OCs are estimated to be -0.72-0.55+0.26 ‰ for H chondrites, -0.71-0.39+0.23 ‰ for L chondrites, and -0.77-0.30+0.63 ‰ for LL chondrites. A broad correlation between the Rb and K isotopic compositions of planetary bodies is observed. The correlation follows a slope that is consistent with kinetic evaporation and condensation processes, suggesting volatility-controlled mass-dependent isotope fractionation (as opposed to nucleosynthetic anomalies).Individual ordinary and enstatite chondrites show large Rb and K isotopic variations (−1.02 to +0.29 ‰ for Rb and −0.91 to −0.15 ‰ for K). Samples of lower metamorphic grades display correlated elemental and isotopic fractionations between Rb and K, while samples of higher metamorphic grades show great scatter, suggesting that chondrite parent-body processes have decoupled the two elements and their isotopes at the sample scale. Several processes could have contributed to the observed isotopic variations of Rb and K, including (i) chondrule “nugget effect”, (ii) volatilization during parent-body thermal metamorphism (heat-induced vaporization and gas transport within parent bodies), (iii) thermal diffusion during parent-body metamorphism, and (iv) impact/shock heating. Quantitative modeling of the first two processes suggests that neither of them could produce isotopic variations large enough to explain the observed isotopic variations. Volatilization during parent-body thermal metamorphism [the scenario (ii)], which has been commonly invoked to explain the isotopic variations of volatile elements, is gas transport-limited and its effect on isotopic fractionations of moderately volatile elements should be negligible. Modeling of diffusion processes suggests that (iii) could produce K isotopic variation comparable to the observed variation. The large isotopic variations in non-carbonaceous meteorites are thus most likely due to diffusive redistribution of K and Rb during metamorphism and/or shock-induced heating and vaporization.

METHODS OF MATHEMATICAL SIMULATION AND MACHINE IDENTIFICATION OF ANOMALOUS DIFFUSION PROCESSES

For the class of anomalous diffusion processes, the mathematical models of which are formalized in the form of variational inequalities in partial derivatives, a method of mathematical modeling based on the optimization procedure is proposed. The method is considered in relation to the generalized mathematical model of the studied class of anomalous diffusion processes. Which made it possible to ensure the principle of unification and typification in the application of this method, as well as the correctness of using the generalized mathematical model in applied problems of mathematical modeling of known industrial and practically important natural cases of anomalous diffusion processes. At the same time, the task of implementing mathematical models of anomalous diffusion processes based on the proposed method is reduced to finding the maximum of the Hamiltonian function defined in the state space of the processes under consideration. A method of parametric identification of mathematical models of anomalous diffusion processes in the formulation of the problem of optimal control is also proposed. The method is reduced to the use of the optimization procedure of the gradient projection method. The possibility of solving the problem of parametric identification in cases of both linear and non-linear mathematical models of anomalous diffusion processes is proved. Moreover, the nonlinear formulation of the parametric identification problem does not lead to computational implementation complications, since the solution is based only on finding the gradient projection of the state function of the anomalous diffusion process. The proposed methods are presented in strict compliance with the provisions of functional analysis, which ensures their correctness and adequacy in solving a wide range of applied problems.