Search results for: low temperature diffusion

Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

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The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: closed surfaces, high-order approachs, numerical solutions, reaction-diffusion systems

Procedia PDF Downloads 339

Authors: Poonam Yadav, Dong Bok Lee

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Isothermal oxidation at 800°C for 50h and Cyclic oxidation at 600°C and 800°C for 40h of Pure Ti and Ti64 were performed in a muffle furnace. In Cyclic oxidation, massive scale spallation occurred, and the oxide scale cracks and peels off were observed at high temperature, it represents oxide scale that formed during cyclic oxidation was spalled out owing to stresses due to thermal shock generated during repetitive oxidation and subsequent cooling. The thickness of scale is larger in cyclic oxidation than the isothermal case. This is due to inward diffusion of oxygen through oxide scales and/or pores and cracks in cyclic oxidation.

Keywords: cyclic, diffusion, isothermal, cyclic

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Authors: Torchane Lazhar

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In this work, our task consists in optimizing the nitriding treatment at low-temperature of the steel 32CrMoV13 by the way of the mixtures of ammonia gas, nitrogen and hydrogen to improve the mechanical properties of the surface (good wear resistance, friction and corrosion), and of the diffusion layer of the nitrogen (good resistance to fatigue and good tenacity with heart). By limiting our work to the pure iron and to the alloys iron-chromium and iron-chrome-carbon, we have studied the various parameters which manage the nitriding: flow rate and composition of the gaseous phase, the interaction chromium-nitrogen and chromium-carbon by the help of experiments of nitriding realized in the laboratory by thermogravimetry. The acquired knowledge have been applied by the mastery of the growth of the combination layer on the diffusion layer in the case of the industrial steel 32CrMoV13.

Keywords: diffusion of nitrogen, gaseous nitriding, layer growth kinetic, steel

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Authors: R. Whalley

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The heat transfer modelling for a diffusion process will be considered. Difficulties in computing the time-distance dynamics of the representation will be addressed. Incomplete and irrational Laplace function will be identified as the computational issue. Alternative approaches to the response evaluation process will be provided. An illustration application problem will be presented. Graphical results confirming the theoretical procedures employed will be provided.

Keywords: heat, transfer, diffusion, modelling, computation

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Authors: Gkolfo I. Smani, Vasileios Megalooikonomou

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Social influence and influence diffusion have been studied in social networks. However, most existing tasks on this subject focus on static networks. In this paper, the problem of maximizing influence diffusion in dynamic social networks, i.e., the case of networks that change over time, is studied. The DM algorithm is an extension of the MATI algorithm and solves the influence maximization (IM) problem in dynamic networks and is proposed under the linear threshold (LT) and independent cascade (IC) models. Experimental results show that our proposed algorithm achieves a diffusion performance better by 1.5 times than several state-of-the-art algorithms and comparable results in diffusion scale with the Greedy algorithm. Also, the proposed algorithm is 2.4 times faster than previous methods.

Keywords: influence maximization, dynamic social networks, diffusion, social influence, graphs

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Authors: Sheldon Liu, Gordon Wang, Lei Liu, Xuefeng Liu

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Anomaly detection, also referred to as one-class classification, plays a crucial role in identifying product images that deviate from the expected distribution. This study introduces Data-centric Anomaly Detection with Diffusion Models (DCADDM), presenting a systematic strategy for data collection and further diversifying the data with image generation via diffusion models. The algorithm addresses data collection challenges in real-world scenarios and points toward data augmentation with the integration of generative AI capabilities. The paper explores the generation of normal images using diffusion models. The experiments demonstrate that with 30% of the original normal image size, modeling in an unsupervised setting with state-of-the-art approaches can achieve equivalent performances. With the addition of generated images via diffusion models (10% equivalence of the original dataset size), the proposed algorithm achieves better or equivalent anomaly localization performance.

Keywords: diffusion models, anomaly detection, data-centric, generative AI

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Authors: Dong Bok Lee, Min Jung Kim

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The commercially available titanium alloy, Ti-6Al-4V, was oxynitrided in the deoxygenated nitrogen gas at high temperatures followed by cooling in oxygen-containing nitrogen in order to analyze the influence of oxynitriding parameters on the phase modification, hardness, and the microstructural evolution of the oxynitrided coating. The surface microhardness of the oxynitrided alloy increased due to the strengthening effect of the formed titanium oxynitrides, TiN_xO_y. The maximum microhardness was obtained, when TiN_xO_y had near equiatomic composition of nitrogen and oxygen. It could be attained under the optimum oxygen partial pressure and temperature-time condition.

Keywords: titanium alloy, oxynitriding, gas diffusion, surface treatment

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Authors: Ayobami Solomon Popoola

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Yam is majorly a carbohydrate food grown in most parts of the world. It could be boiled, fried or roasted for consumption in a variety of ways. Blanching is an established heat pre-treatment given to fruits and vegetables prior to further processing such as dehydration, canning, freezing etc. Losses of soluble solids during blanching has been a great problem because a reasonable quantity of the water-soluble nutrients are inevitably leached into the blanching water. Without blanching, the high residual levels of reducing sugars after extended storage produce a dark, bitter-tasting product because of the Maillard reactions of reducing sugars at frying temperature. Measurement and prediction of such losses are necessary for economic efficiency in production and to establish the level of effluent treatment of the blanching water. This paper aims at resolving this problem by investigating the effects of cube size and temperature on the rate of diffusional losses of reducing sugars and total sugars during hot water blanching of water-yam. The study was carried out using four temperature levels (65, 70, 80 and 90 °C) and two cubes sizes (0.02 m³ and 0.03 m³) at 4 times intervals (5, 10, 15 and 20 mins) respectively. Obtained data were fitted into Fick’s non-steady equation from which diffusion coefficients (Da) were obtained. The Da values were subsequently fitted into Arrhenius plot to obtain activation energies (Ea-values) for diffusional losses. The diffusion co-efficient were independent of cube size and time but highly temperature dependent. The diffusion coefficients were ≥ 1.0 ×10⁻⁹ m²s⁻¹ for reducing sugars and ≥ 5.0 × 10⁻⁹ m²s⁻¹ for total sugars. The Ea values ranged between 68.2 to 73.9 KJmol⁻¹ and 7.2 to 14.30 KJmol⁻¹ for reducing sugars and total sugars losses respectively. Predictive equations for estimating amount of reducing sugars and total sugars with blanching time of water-yam at various temperatures were also presented. The equation could be valuable in process design and optimization. However, amount of other soluble solids that might have leached into the water along with reducing and total sugars during blanching was not investigated in the study.

Keywords: blanching, kinetics, sugar losses, water yam

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Authors: M. Abdoos, A. Amadeh, M. Adabi

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In recent decades, the use of titanium and its alloys due to their high mechanical properties, light weight and their corrosion resistance has increased in military and industry applications. However, the poor surface properties can limit their widely usage. Many researches were carried out to improve their surface properties. The most effective technique is based on solid-state diffusion of elements that can form intermetallic compounds with the substrate. In the present work, inter-diffusion of nickel and titanium and formation of Ni-Ti intermetallic compounds in nickel-coated Ti-6Al-4V alloy have been studied. Initially, nickel was electrodeposited on the alloy using Watts bath at a current density of 20 mA/cm2 for 1 hour. The coated specimens were then heat treated in a tubular furnace under argon atmosphere at different temperatures near Ti β-transus to maximize the diffusion rate for various durations in order to improve the surface properties of the Ti-6Al-4V alloy. The effect of temperature and time on the thickness of diffusion layer and characteristics of intermetallic phases was studied by means of scanning electron microscope (SEM) equipped with energy dispersive X-ray spectrometer (EDS) and microhardness test. The results showed that a multilayer structure was formed after heat treatment: an outer layer of remaining nickel, an area of intermetallic layers with different compositions and solid solution of Ni-Ti. Three intermetallic layers was detected by EDS analysis, namely an outer layer with about 75 at.% Ni (Ni3Ti), an intermediate layer with 50 at.% Ni (NiTi) and finally an inner layer with 36 at.% Ni (NiTi2). It was also observed that the increase in time or temperature led to the formation of thicker intermetallic layers. Meanwhile, the microhardness of heat treated samples increased with formation of Ni-Ti intermetallics; however, its value depended on heat treatment parameters.

Keywords: heat treatment, microhardness, Ni coating, Ti-6Al-4V

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Authors: Douglas Yeboah, Jai Singh

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It has been experimentally demonstrated that exciton diffusion length in organic solids can be improved by fine-tuning the material parameters that govern exciton transfer. Here, a theoretical study is carried out to support this finding. We have therefore derived expressions for the exciton diffusion length and diffusion coefficient of singlet and triplet excitons using Förster resonance energy transfer and Dexter carrier transfer mechanisms and are plotted as a function of photoluminescence (PL) quantum yield, spectral overlap integral, refractive index and dipole moment of the photoactive material. We found that singlet exciton diffusion length increases with PL quantum yield and spectral overlap integral, and decreases with increase in refractive index. Likewise, the triplet exciton diffusion length increases when PL quantum yield increases and dipole moment decreases. The calculated diffusion lengths in different organic materials are compared with existing experimental values and found to be in reasonable agreement. The results are expected to provide insight in developing new organic materials for fabricating bulk heterojunction (BHJ) organic solar cells (OSCs) with better photoconversion efficiency.

Keywords: Dexter carrier transfer, diffusion coefficient, exciton diffusion length, Föster resonance energy transfer, photoactive materials, photophysical parameters

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Authors: N. I. Kargin, G. K. Safaraliev, A. S. Gusev, A. O. Sultanov, N. V. Siglovaya, S. M. Ryndya, A. A. Timofeev

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In this paper, an experimental and theoretical study of the processes of mesoporous silicon carbonization during the formation of buffer layers for the subsequent epitaxy of 3C-SiC films and related wide-band-gap semiconductors is performed. Experimental samples were obtained by the method of chemical vapor deposition and investigated by scanning electron microscopy. Analytic expressions were obtained for the effective diffusion factor and carbon atoms diffusion length in a porous system. The proposed model takes into account the processes of Knudsen diffusion, coagulation and overgrowing of pores during the formation of a silicon carbide layer.

Keywords: silicon carbide, porous silicon, carbonization, electrochemical etching, diffusion

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Authors: Pavlo Selyshchev, Samuel Akintunde

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A theoretical approach to consider formation of chemical compound layer at the interface between initial substances A and B due to the interfacial interaction and diffusion is developed. It is considered situation when speed of interfacial interaction is large enough and diffusion of A-atoms through AB-layer is much more then diffusion of B-atoms. Atoms from A-layer diffuse toward B-atoms and form AB-atoms on the surface of B-layer. B-atoms are assumed to be immobile. The growth kinetics of the AB-layer is described by two differential equations with non-linear coupling, producing a good fit to the experimental data. It is shown that growth of the thickness of the AB-layer determines by dependence of chemical reaction rate on reactants concentration. In special case the thickness of the AB-layer can grow linearly or parabolically depending on that which of processes (interaction or the diffusion) controls the growth. The thickness of AB-layer as function of time is obtained. The moment of time (transition point) at which the linear growth are changed by parabolic is found.

Keywords: phase formation, binary systems, interfacial reaction, diffusion, compound layers, growth kinetics

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Authors: Sachin Kumar

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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: Md. Abud Darda

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Different options for natural gas production in wide geographic areas may be described through diffusion of innovation models. This type of modeling approach provides an indirect estimate of an ultimately recoverable resource, URR, capture the quantitative effects of observed strategic interventions, and allow ex-ante assessments of future scenarios over time. In order to ensure a sustainable energy policy, it is important to forecast the availability of this natural resource. Considering a finite life cycle, in this paper we try to investigate the natural gas production of Myanmar and Algeria, two important natural gas provider in the world energy market. A number of homogeneous and heterogeneous diffusion models, with convenient extensions, have been used. Models validation has also been performed in terms of prediction capability.

Keywords: diffusion models, energy forecast, natural gas, nonlinear production

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Authors: S. Chikh, S. Boulifa

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The present study addresses the problem of ammonia evaporation during filling of a vertical cylindrical tank and the influence of various external factors on the stability of storage by determining the conditions for minimum evaporation. Numerical simulation is carried out by solving the governing equations namely, continuity, momentum, energy, and diffusion of species. The effect of temperature of surrounding air, the filling speed of the reservoir and the temperature of the filling liquid ammonia on the evaporation rate is investigated. Results show that the temperature of the filling liquid has little effect on the liquid ammonia for a short period, which, in fact, is function of the filling speed. The evaporation rate along the free surface of the liquid is non-uniform. The inlet temperature affects the vapor ammonia temperature because of pressure increase. The temperature of the surrounding air affects the temperature of the vapor phase rather than the liquid phase. The maximum of evaporation is reached at the final step of filling. In order to minimize loss of ammonia vapors automatically causing losses in quantity of the liquid stored, it is suggested to ensure the proper insulation for the walls and roof of the reservoir and to increase the filling speed.

Keywords: evaporation, liquid ammonia, storage tank, numerical simulation

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Authors: Michele Aleandri, Matteo Colangeli, Davide Gabrielli

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We study a generalization to a continuous setting of the classical Markov chain tree theorem. In particular, we consider an irreducible diffusion process on a metric graph. The unique invariant measure has an atomic component on the vertices and an absolutely continuous part on the edges. We show that the corresponding density at x can be represented by a normalized superposition of the weights associated to metric arborescences oriented toward the point x. A metric arborescence is a metric tree oriented towards its root. The weight of each oriented metric arborescence is obtained by the product of the exponential of integrals of the form ∫a/b², where b is the drift and σ² is the diffusion coefficient, along the oriented edges, for a weight for each node determined by the local orientation of the arborescence around the node and for the inverse of the diffusion coefficient at x. The metric arborescences are obtained by cutting the original metric graph along some edges.

Keywords: diffusion processes, metric graphs, invariant measure, reversibility

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Authors: Amartya Hatua, Trung Nguyen, Andrew Sung

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In this paper, we study the information diffusion process on Twitter as a multivariate time series problem. Our model concerns three measures (volume, network influence, and sentiment of tweets) based on 10 features, and we collected 27 million tweets to build our information diffusion time series dataset for analysis. Then, different time series clustering techniques with Dynamic Time Warping (DTW) distance were used to identify different patterns of information diffusion. Finally, we built the information diffusion prediction models for new hashtags which comprise two phrases: The first phrase is recognizing the pattern using k-NN with DTW distance; the second phrase is building the forecasting model using the traditional Autoregressive Integrated Moving Average (ARIMA) model and the non-linear recurrent neural network of Long Short-Term Memory (LSTM). Preliminary results of performance evaluation between different forecasting models show that LSTM with clustering information notably outperforms other models. Therefore, our approach can be applied in real-world applications to analyze and predict the information diffusion characteristics of selected topics or memes (hashtags) in Twitter.

Keywords: ARIMA, DTW, information diffusion, LSTM, RNN, time series clustering, time series forecasting, Twitter

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Authors: Yildiray Keskin, Omer Acan, Murat Akkus

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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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Authors: E. Obreque-Slier, V. Contreras-Cortez, R. López-Solís

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Astringency is a drying, roughing, and sometimes puckering sensation that is experienced on the various oral surfaces during or immediately after tasting foods. This sensation has been closely related to the interaction and precipitation between salivary proteins and polyphenols, specifically flavanols or proanthocyanidins. In addition, the type and concentration of proanthocyanidin influences significantly the intensity of the astringency and consequently the protein/proanthocyanidin interaction. However, most of the studies are based on the interaction between saliva and highly complex polyphenols, without considering the effect of monomeric proanthoancyanidins present in different foods. The aim of this study was to evaluate the effect of different monomeric proanthocyanidins on the diffusion and precipitation of salivary proteins. Thus, solutions of catechin, epicatechin, epigallocatechin and gallocatechin (0, 2.0, 4.0, 6.0, 8.0 and 10 mg/mL) were mixed with human saliva (1: 1 v/v). After incubation for 5 min at room temperature, 15 µL aliquots of each mix were dotted on a cellulose membrane and allowed to dry spontaneously at room temperature. The membrane was fixed, rinsed and stained for proteins with Coomassie blue. After exhaustive washing in 7% acetic acid, the membrane was rinsed once in distilled water and dried under a heat lamp. Both diffusion area and stain intensity of the protein spots were semiqualitative estimates for protein-tannin interaction (diffusion test). The rest of the whole saliva-phenol solution mixtures of the diffusion assay were centrifuged, and 15-μL aliquots from each of the supernatants were dotted on a cellulose membrane. The membrane was processed for protein staining as indicated above. The blue-stained area of protein distribution corresponding to each of the extract dilution-saliva mixtures was quantified by Image J 1.45 software. Each of the assays was performed at least three times. Initially, salivary proteins display a biphasic distribution on cellulose membranes, that is, when aliquots of saliva are placed on absorbing cellulose membranes, and free diffusion of saliva is allowed to occur, a non-diffusible protein fraction becomes surrounded by highly diffusible salivary proteins. In effect, once diffusion has ended, a protein-binding dye shows an intense blue-stained roughly circular area close to the spotting site (non-diffusible fraction) (NDF) which becomes surrounded by a weaker blue-stained outer band (diffusible fraction) (DF). Likewise, the diffusion test showed that epicatechin caused the complete disappearance of DF from saliva with 2 mg/mL. Also, epigallocatechin and gallocatechin caused a similar effect with 4 mg/mL, while catechin generated the same effect at 8 mg/mL. In the precipitation test, the use of epicatechin and gallocatechin generated evident precipitates at the bottom of the Eppendorf tubes. In summary, the flavanol type differentially affects the diffusion and precipitation of saliva, which would affect the sensation of astringency perceived by consumers.

Keywords: astringency, polyphenols, tannins, tannin-protein interaction

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Authors: Muhammad Asif ShakoorI, Maogang He, Aamir Shahzad

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Dusty (complex) plasmas contained micro-sized charged dust particles in addition to ions, electrons, and neutrals. It is typically low-temperature plasma and exists in a wide variety of physical systems. In this work, the effects of an external electric field on the diffusion coefficient and share viscosity are investigated through equilibrium molecular dynamics (EMD) simulations in three-dimensional (3D) strongly coupled (SC) dusty plasmas (DPs). The effects of constant and varying normalized electric field strength (E*) have been computed along with different combinations of plasma states on the diffusion of dust particles using EMD simulations. Diffusion coefficient (D) and share viscosity (η) along with varied system sizes, in the limit of varying E* values, is accounted for an appropriate range of plasma coupling (Γ) and screening strength (κ) parameters. At varying E* values, it is revealed that the 3D diffusion coefficient increases with increasing E* and κ; however, it decreases with an increase of Γ but within statistical limits. The share viscosity increases with increasing E*and Γ and decreases with increasing κ. New simulation results are outstanding that the combined effects of electric field and screening strengths give well-matched values of Dandη at low-intermediate to large Γ with varying small-intermediate to large N. The current EMD simulation outcomes under varying electric field strengths are in satisfactory well-matched with previous known simulation data of EMD simulations of the SC-DPs. It has been shown that the present EMD simulation data enlarged the range of E* strength up to 0.1 ≤ E*≤ 1.0 in order to find the linear range of the DPs system and to demonstrate the fundamental nature of electric field linearity of 3D SC-DPs.

Keywords: strongly coupled dusty plasma, diffusion coefficient, share viscosity, molecular dynamics simulation, electric field strength

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Authors: A. M. Tahsini

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Computational study of two dimensional supersonic reacting hydrogen-air flows is performed to investigate the nitrogen effects on ignition delay time for premixed and diffusion flames. Chemical reaction is treated using detail kinetics and the advection upstream splitting method is used to calculate the numerical inviscid fluxes. The results show that only in the stoichiometric condition for both premixed and diffusion flames, there is monotone dependency of the ignition delay time to the nitrogen addition. In other situations, the optimal condition from ignition viewpoint should be found using numerical investigations.

Keywords: diffusion flame, ignition delay time, mixing layer, numerical simulation, premixed flame, supersonic flow

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Authors: Jang kyun Cho, Jeong-dong Lee

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The advent of the Internet, mobile communications, and social network services has stimulated social interactions among consumers, allowing people to affect one another’s innovation adoptions by exchanging information more frequently and more quickly. Previous diffusion models, such as the Bass model, however, face limitations in reflecting such recent phenomena in society. These models are weak in their ability to model interactions between agents; they model aggregated-level behaviors only. The agent based model, which is an alternative to the aggregate model, is good for individual modeling, but it is still not based on an economic perspective of social interactions so far. This study assumes the presence of social utility from other consumers in the adoption of innovation and investigates the effect of individual interactions on innovation diffusion by developing a new model called the interaction-based diffusion model. By comparing this model with previous diffusion models, the study also examines how the proposed model explains innovation diffusion from the perspective of economics. In addition, the study recommends the use of a small-world network topology instead of cellular automata to describe innovation diffusion. This study develops a model based on individual preference and heterogeneous social interactions using utility specification, which is expandable and, thus, able to encompass various issues in diffusion research, such as reservation price. Furthermore, the study proposes a new framework to forecast aggregated-level market demand from individual level modeling. The model also exhibits a good fit to real market data. It is expected that the study will contribute to our understanding of the innovation diffusion process through its microeconomic theoretical approach.

Keywords: innovation diffusion, agent based model, small-world network, demand forecasting

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Authors: Ali Safdari-Vaighani

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Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method.

Keywords: basket option, jump diffusion, ‎radial basis function, RBF-PUM

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Authors: Maria Boile, Eirini Sifaki

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This study, based on desktop research and the analysis of questionnaires completed by a representative sample of museums, adopts the Diffusion of Innovation (DOI) theory of Everett Rogers as a theoretical basis to figure out the perceived benefits that occur for any organization after the adoption of an official website, and identify the factors that affect its diffusion process. The most important conclusion is that Greek archaeological museums are far away from involving such technologies in their strategies, mainly because of the bureaucracy, the lack of necessary funds, and the lack of personnel.

Keywords: dDiffusion of innovation, websites, archaeological museums, economic crisis

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Authors: Meng Su

Abstract:

High-dimensional data analysis often presents challenges in capturing the complex, nonlinear relationships and manifold structures inherent to the data. This article presents a novel approach that leverages the strengths of two powerful techniques, Diffusion Maps and Diffusion Probabilistic Models (DPMs), to address these challenges. By integrating the dimensionality reduction capability of Diffusion Maps with the data modeling ability of DPMs, the proposed method aims to provide a comprehensive solution for analyzing and generating high-dimensional data. The Diffusion Map technique preserves the nonlinear relationships and manifold structure of the data by mapping it to a lower-dimensional space using the eigenvectors of the graph Laplacian matrix. Meanwhile, DPMs capture the dependencies within the data, enabling effective modeling and generation of new data points in the low-dimensional space. The generated data points can then be mapped back to the original high-dimensional space, ensuring consistency with the underlying manifold structure. Through a detailed example implementation, the article demonstrates the potential of the proposed hybrid approach to achieve more accurate and effective modeling and generation of complex, high-dimensional data. Furthermore, it discusses possible applications in various domains, such as image synthesis, time-series forecasting, and anomaly detection, and outlines future research directions for enhancing the scalability, performance, and integration with other machine learning techniques. By combining the strengths of Diffusion Maps and DPMs, this work paves the way for more advanced and robust data analysis methods.

Keywords: diffusion maps, diffusion probabilistic models (DPMs), manifold learning, high-dimensional data analysis

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Authors: Yanqin Chen, Chao Jiang, Chongdu Cho

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This research presents the three-dimensional mechanical characteristics of a commercial gas diffusion layer by experiment and simulation results. Although the mechanical performance of gas diffusion layers has attracted much attention, its reliability and accuracy are still a major challenge. With the help of simulation analysis methods, it is beneficial to the gas diffusion layer’s extensive commercial development and the overall stress analysis of proton electrolyte membrane fuel cells during its pre-production design period. Therefore, in this paper, a three-dimensional constitutive model of a commercial gas diffusion layer, including its material stiffness matrix parameters, is developed and coded, in the user-defined material model of a commercial finite element method software for simulation. Then, the model is validated by comparing experimental results as well as simulation outcomes. As a result, both the experimental data and simulation results show a good agreement with each other, with high accuracy.

Keywords: gas diffusion layer, proton electrolyte membrane fuel cell, stiffness matrix, three-dimensional mechanical characteristics, user-defined material model

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Authors: Bekir Turedi

Abstract:

Exploiting the potential of perovskite single-crystal solar cells in optoelectronic applications necessitates overcoming a significant challenge: the low charge collection efficiency at increased thickness, which has restricted their deployment in radiation detectors and nuclear batteries. Our research details a promising approach to this problem, wherein we have successfully fabricated single-crystal MAPbI3 solar cells employing a space-limited inverse temperature crystallization (ITC) methodology. Remarkably, these cells, up to 400-fold thicker than current-generation perovskite polycrystalline films, maintain a high charge collection efficiency even without external bias. The crux of this achievement lies in the long electron diffusion length within these cells, estimated to be around 0.45 mm. This extended diffusion length ensures the conservation of high charge collection and power conversion efficiencies, even as the thickness of the cells increases. Fabricated cells at 110, 214, and 290 µm thickness manifested power conversion efficiencies (PCEs) of 20.0, 18.4, and 14.7% respectively. The single crystals demonstrated nearly optimal charge collection, even when their thickness exceeded 200 µm. Devices of thickness 108, 214, and 290 µm maintained 98.6, 94.3, and 80.4% of charge collection efficiency relative to their maximum theoretical short-circuit current value, respectively. Additionally, we have proposed an innovative, self-consistent technique for ascertaining the electron-diffusion length in perovskite single crystals under operational conditions. The computed electron-diffusion length approximated 446 µm, significantly surpassing previously reported values for this material. In conclusion, our findings underscore the feasibility of fabricating halide perovskite single-crystal solar cells of hundreds of micrometers in thickness while preserving high charge extraction efficiency and PCE. This advancement paves the way for developing perovskite-based optoelectronics necessitating thicker active layers, such as X-ray detectors and nuclear batteries.

Keywords: perovskite, solar cell, single crystal, diffusion length

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Authors: Kunpeng Wang, Hongchun, Wu, Liangzhi Cao, Chuanqi Zhao

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The distributions of homogeneous neutron flux within a node were expanded into a set of analytic basis functions which satisfy the diffusion equation at any point in a triangular-z node for each energy group, and nodes were coupled with each other with both the zero- and first-order partial neutron current moments across all the interfaces of the triangular prism at the same time. Based this method, a code TABFEN has been developed and applied to solve the neutron diffusion equation in a complicated geometry. In addition, after a series of numerical derivation, one can get the neutron adjoint diffusion equations in matrix form which is the same with the neutron diffusion equation; therefore, it can be solved by TABFEN, and the low-high scan strategy is adopted to improve the efficiency. Four benchmark problems are tested by this method to verify its feasibility, the results show good agreement with the references which demonstrates the efficiency and feasibility of this method.

Keywords: analytic basis function expansion method, arbitrary triangular-z node, adjoint neutron flux, complicated geometry

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Authors: Said Algarni

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The purpose of this study was to investigate selected numerical methods that demonstrate good performance in solving PDEs. We adapted alternative method that involve rational polynomials. Padé time stepping (PTS) method, which is highly stable for the purposes of the present application and is associated with lower computational costs, was applied. Furthermore, PTS was modified for our study which focused on diffusion equations. Numerical runs were conducted to obtain the optimal local error control threshold.

Keywords: Padé time stepping, finite difference, reaction diffusion equation, PDEs

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Authors: Yohanes Chekol Malede

Abstract:

σ-phase has negative effects on the corrosion responses and the mechanical properties of steels. The growth of σ-phase in the austenite matrix of AISI 347H FG steel was simulated using DICTRA software using CALPHAD method. The simulation work included the influence of both volume diffusion and grain boundary diffusion. The simulation results showed a good agreement with the experimental findings. The simulation results revealed a Cr-depleted and a Ni-enriched σ-phase/austenite interface. Effects of temperature, grain size, and composition of alloying elements on the growth kinetics of σ-phase were assessed. The simulated results were fitted to the JMAK equation and a good correlation was obtained.

Keywords: AISI 347H FG austenitic steel, CALPHAD, sigma phase, microstructure evolution

Procedia PDF Downloads 124