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Journal articles on the topic '1D diffusion model'

Author: Grafiati

Published: 8 June 2024

Last updated: 31 July 2025

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1

Kim, Hongchul, and Seon-Gyu Kim. "SATURATION ASSUMPTIONS FOR A 1D CONVECTION-DIFFUSION MODEL." Korean Journal of Mathematics 22, no. 4 (2014): 599–609. http://dx.doi.org/10.11568/kjm.2014.22.4.599.

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Baro, M., N. Ben Abdallah, P. Degond, and A. El Ayyadi. "A 1D coupled Schrödinger drift-diffusion model including collisions." Journal of Computational Physics 203, no. 1 (2005): 129–53. http://dx.doi.org/10.1016/j.jcp.2004.08.009.

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3

Xu, Yinsheng, Yuhao Xu, Xue Han, Shengping Wang, and Jingxian Yu. "From 1D to 1D–2D–1D: new insights into Li⁺ diffusion behavior in optimized MnO₂ with the cooperative effect of tunnel and interface." Journal of Materials Chemistry A 9, no. 43 (2021): 24397–405. http://dx.doi.org/10.1039/d1ta05108c.

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Larsson, Henrik, and Lars Höglund. "Multiphase diffusion simulations in 1D using the DICTRA homogenization model." Calphad 33, no. 3 (2009): 495–501. http://dx.doi.org/10.1016/j.calphad.2009.06.004.

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Tchedre, Esso-Ehanam, Boubacar Soro, Guy Serge Tchouadep, Mahamadi Savadogo, Issa Zerbo, and Martial Zoungrana. "Impact of Simulation Model and Grain Size on the Bifacial Gain of a Silicon Solar Cell." Advances in Image and Video Processing 12, no. 5 (2024): 194–203. https://doi.org/10.14738/aivp.125.17604.

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The characterisation of the performance of a bifacial silicon cell in a simulation study is carried out through different simulation models. These are the one-dimensional (1D) model, the classical three-dimensional model using constant diffusion parameters and the empirical 3D model which uses diffusion parameters varying with grain size. For each of these models, by comparing the electrical parameters of the solar cell subjected to front side illumination and then to double illumination, the different bifacial gains are obtained and then compared to each other. This study revealed a tendency

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Elhareef, Mohamed, Zeyun Wu, and Massimiliano Fratoni. "A Consistent One-Dimensional Multigroup Diffusion Model for Molten Salt Reactor Neutronics Calculations." Journal of Nuclear Engineering 4, no. 4 (2023): 654–67. http://dx.doi.org/10.3390/jne4040041.

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Molten Salt Reactors (MSRs) have recently gained resurged research and development interest in the advanced reactor community. Several computational tools are being developed to capture the strong neutronics/thermal-hydraulics coupling effect in this special reactor configuration. This paper presents a consistent one-dimensional (1D) multigroup neutron diffusion model for MSR analysis, with the primary aim for fast and accurate calculations for long transients, as well as sensitivity and uncertainty analysis of the reactor. A fictitious radial leakage cross section is introduced in the model t

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Voges, Jannik, Iryna Smokovych, Fabian Duvigneau, Michael Scheffler, and Daniel Juhre. "Modeling the oxidation of a polymer-derived ceramic with chemo-mechanical coupling and large deformations." Acta Mechanica 233, no. 2 (2022): 701–23. http://dx.doi.org/10.1007/s00707-021-03142-x.

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AbstractTo get a better insight into the coating behavior of a polymer-derived ceramic material, we model and simulate the diffusion, oxidation and reaction-induced volume expansion of a specimen without outer mechanical loads. In this macroscale approach, we use an oxidation state variable which determines the composition of the starting material and the oxide material. The model contains a reaction rate which is based on the change of the free energy due to a change of the concentrations of the starting material, the oxide material and a diffusing gaseous material. Using this, we model a gro

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Navalho, J. E. P., J. M. C. Pereira, and J. C. F. Pereira. "Multi-Scale Modeling of Internal Mass Diffusion Limitations in CO Oxidation Catalysts." Defect and Diffusion Forum 364 (June 2015): 92–103. http://dx.doi.org/10.4028/www.scientific.net/ddf.364.92.

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This work applies a 3D multi-scale bottom-up approach for modeling the processes of diffusion and reaction-diffusion in porous catalyst layers. The performance of the random pore model to predict effective transport coefficients are compared with the results of the multi-scale diffusion model. The results of the 3D multi-scale diffusion model are employed in a 1D pseudo-homogeneous reaction-diffusion model with a relative good agreement with the 3D multi-scale reaction-diffusion model. Furthermore, the former multi-scale model was coupled to a full-scale reactor model with good results and hig

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Herrero-Durá, Iván, Alejandro Cebrecos, Rubén Picó, Vicente Romero-García, Luis Miguel García-Raffi, and Víctor José Sánchez-Morcillo. "Sound Absorption and Diffusion by 2D Arrays of Helmholtz Resonators." Applied Sciences 10, no. 5 (2020): 1690. http://dx.doi.org/10.3390/app10051690.

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We report a theoretical and experimental study of an array of Helmholtz resonators optimized to achieve both efficient sound absorption and diffusion. The analysis starts with a simplified 1D model where the plane wave approximation is used to design an array of resonators showing perfect absorption for a targeted range of frequencies. The absorption is optimized by tuning the geometry of the resonators, i.e., by tuning the viscothermal losses of each element. Experiments with the 1D array were performed in an impedance tube. The designed system is extended to 2D by periodically replicating th

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10

Holmas, H., T. Sira, M. Nordsveen, H. P. Langtangen, and R. Schulkes. "Analysis of a 1D incompressible two-fluid model including artificial diffusion." IMA Journal of Applied Mathematics 73, no. 4 (2007): 651–67. http://dx.doi.org/10.1093/imamat/hxm066.

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11

Cheng, Hu, Sophia Vinci-Booher, Jian Wang, et al. "Denoising diffusion weighted imaging data using convolutional neural networks." PLOS ONE 17, no. 9 (2022): e0274396. http://dx.doi.org/10.1371/journal.pone.0274396.

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Diffusion weighted imaging (DWI) with multiple, high b-values is critical for extracting tissue microstructure measurements; however, high b-value DWI images contain high noise levels that can overwhelm the signal of interest and bias microstructural measurements. Here, we propose a simple denoising method that can be applied to any dataset, provided a low-noise, single-subject dataset is acquired using the same DWI sequence. The denoising method uses a one-dimensional convolutional neural network (1D-CNN) and deep learning to learn from a low-noise dataset, voxel-by-voxel. The trained model c

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12

KASSEBAUM, PAUL G., and GERMANO S. IANNACCHIONE. "EMERGENT 1D ISING BEHAVIOR IN AN ELEMENTARY CELLULAR AUTOMATON MODEL." International Journal of Modern Physics C 20, no. 01 (2009): 133–45. http://dx.doi.org/10.1142/s0129183109013510.

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The fundamental nature of an evolving one-dimensional (1D) Ising model is investigated with an elementary cellular automaton (CA) simulation. The emergent CA simulation employs an ensemble of cells in one spatial dimension, each cell capable of two microstates interacting with simple nearest-neighbor rules and incorporating an external field. The behavior of the CA model provides insight into the dynamics of coupled two-state systems not expressible by exact analytical solutions. For instance, state progression graphs show the causal dynamics of a system through time in relation to the system'

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13

ROHDE, CHRISTIAN, and FENG XIE. "DECAY RATES TO VISCOUS CONTACT WAVES FOR A 1D COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL." Mathematical Models and Methods in Applied Sciences 23, no. 03 (2013): 441–69. http://dx.doi.org/10.1142/s0218202512500522.

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We are concerned with the nonlinear stability of contact waves subject to general perturbations of initial datum in the Cauchy problem for a radiating gas model. The model is represented mathematically as a one-dimensional hyperbolic–elliptic system. It is known that general perturbations of contact discontinuities may generate diffusion waves which evolve and interact with the contact wave. In order to quantify the decay to the contact waves exactly, we need to construct the corresponding diffusion waves explicitly depending on the perturbation of the initial datum. Then, the constructed diff

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14

Lin, Meng, Ibadillah A. Digdaya, and Chengxiang Xiang. "Modeling the electrochemical behavior and interfacial junction profiles of bipolar membranes at solar flux relevant operating current densities." Sustainable Energy & Fuels 5, no. 7 (2021): 2149–58. http://dx.doi.org/10.1039/d1se00201e.

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A 1D, multi-physics model that accounts for the migration and diffusion of species, electrostatics, and chemical reactions, in particular water dissociation, at BPM interfaces was developed to study the electrochemical behavior.

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15

Ma, Wen Cui, Xue Yi You, Xin Xin Wang, and Yu Chen. "Numerical Simulation of Migration and Transformation of Petroleum Hydrocarbons in Soils." Advanced Materials Research 1073-1076 (December 2014): 653–56. http://dx.doi.org/10.4028/www.scientific.net/amr.1073-1076.653.

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Considering the diffusion, adsorption or desorption, and microbial degradation of petroleum hydrocarbons (PHs) in the soil–water system, the numerical model describing the migration and transportation of PHs is estabilished and it is simulated by HYDRUS-1D model. The degradation effect of time and depth variation of PHs is gained by numerical simulation. The results show that the degradation ability of indigenous microbial of PHs is poor. The HYDRUS-1D software is feasible in simulating and predicting the migration and transformation of PHs in soils.

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16

SHIBUTANI, Yoko, Masamitsu KUROIWA, and Yuhei MATSUBARA. "Shoreline Change Model due to Beach Nourishment using 1D Advection Diffusion Equation." PROCEEDINGS OF COASTAL ENGINEERING, JSCE 54 (2007): 646–50. http://dx.doi.org/10.2208/proce1989.54.646.

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17

Morrison, Hugh, Mikael Witte, George H. Bryan, Jerry Y. Harrington, and Zachary J. Lebo. "Broadening of Modeled Cloud Droplet Spectra Using Bin Microphysics in an Eulerian Spatial Domain." Journal of the Atmospheric Sciences 75, no. 11 (2018): 4005–30. http://dx.doi.org/10.1175/jas-d-18-0055.1.

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Abstract This study investigates droplet size distribution (DSD) characteristics from condensational growth and transport in Eulerian dynamical models with bin microphysics. A hierarchy of modeling frameworks is utilized, including parcel, one-dimensional (1D), and three-dimensional large-eddy simulation (LES). The bin DSDs from the 1D model, which includes only vertical advection and condensational growth, are nearly as broad as those from the LES and in line with observed DSD widths for stratocumulus clouds. These DSDs are much broader than those from Lagrangian microphysical calculations wi

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18

Wu, Junxiao, and Qingyun Liu. "Simulation-Aided PEM Fuel Cell Design and Performance Evaluation." Journal of Fuel Cell Science and Technology 2, no. 1 (2004): 20–28. http://dx.doi.org/10.1115/1.1840819.

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A multi-resolution fuel cell simulation strategy has been employed to simulate and evaluate the design and performance of hydrogen PEM fuel cells with different flow channels. A full 3D model is employed for the gas diffusion layer and a 1D+2D model is applied to the catalyst layer. Further, a quasi-1D method is used to model the flow channels. The cathode half-cell simulation was performed for three types of flow channels: serpentine, parallel, and interdigitated. Simulations utilized the same overall operating conditions. Comparisons of results indicate that the interdigitated flow channel i

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19

Taulamet, Maria Jose, Osvaldo Miguel Martinez, Guillermo Fernando Barreto, and Nestor Javier Mariani. "INFLUENCE OF NON-ISOTROPIC DIFFUSION ON EFFECTIVE REACTION RATES IN CATALYST PARTICLES." Latin American Applied Research - An international journal 53, no. 1 (2023): 59–64. http://dx.doi.org/10.52292/j.laar.2023.1077.

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The non-isotropic diffusion and reaction problem in cylindrical particles of different cross-sections is analyzed in this contribution employing the one-dimensional Generalized Cylinder Model (1D-GCG). Such a model presents a single parameter of straightforward calculation from the geometrical magnitudes of the catalyst particles. Different but uniform values of axial and transversal effective diffusivities are assumed. The performance of the 1D-GCG model for the effectiveness factor estimation is assessed for a variety of particle shapes and a set of kinetic expressions. Maximum errors in the

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20

LHOUSSAINE, EL MEZOUARY, KABBAJ SAMIR, and EL MANSOURI BOUABID. "ANALYTICAL MODEL SOLUTION OF THE GROUNDWATER FLOW EQUATION." Seybold Report 16, no. 02 (2021): 36–57. https://doi.org/10.5281/zenodo.6552448.

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<strong>Abstract</strong> This paper presents an analytical model solution for the prediction of the one-dimensional (1D) time-dependent groundwater flow profile in an unconfined system. Groundwater level can be estimated by using the proposed solution with several input data, such as permeability layer thicknesses, specific yield. This hydraulic charge prediction problem is modeled as a boundary value problem governed by the classic heat diffusion equations. The solution technique employs the separation of variables method and the result are compared to the 2 implicit numerical solutions of C

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21

Napitupulu, Gandhi, Achmad Nagi, Mutiara Rachmat Putri, and Ivonne Milichristi Radjawane. "The One-Dimensional (1D) Numerical Model: An Application to Oxygen Diffusion in Mitochondria Cell." ComTech: Computer, Mathematics and Engineering Applications 14, no. 2 (2023): 101–18. http://dx.doi.org/10.21512/comtech.v14i2.9705.

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The first model of oxygen transport was formulated by August Krogh. However, the investigations conducted have yet to yield a complete analytical model and a widely applicable solution for One-Dimensional (1D) network construction. The research sought to provide numerical and analytical solutions for the oxygen transfer model in mitochondrial cells to enable researchers to estimate the molecular dynamics and diffusion characteristics in mitochondrial cells. The oxygen diffusion process in mitochondria was modeled with ID numerical models. The numerical models used to solve the equations were e

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22

Wang, Ke, Mobin Salasi, and Mariano Iannuzzi. "(Digital Presentation) Progress Towards the Key Factors Governing Pit Stability." ECS Meeting Abstracts MA2022-02, no. 11 (2022): 708. http://dx.doi.org/10.1149/ma2022-0211708mtgabs.

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The pit stability product—defined as the product of pit depth and dissolution current density (x·i)—was first introduced by Galvele as the criterion indicating the conditions that sustain a critically acidic solution within the pit. The one-dimensional (1D) electrode is the most commonly used experimental configuration for determining the pit solution chemistry and pit stability product. In our current works, a ‘sandwich’ like 1D pit electrode was developed, which enabled the in-situ and ex-situ visualization of pit depth. A methodology that avoids lacy cover formation was proposed to pre-diss

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23

Furtak-Cole, Eden, and Aleksey S. Telyakovskiy. "A 3D Numerical Study of Interface Effects Influencing Viscous Gravity Currents in a Parabolic Fissure, with Implications for Modeling with 1D Nonlinear Diffusion Equations." Fluids 4, no. 2 (2019): 97. http://dx.doi.org/10.3390/fluids4020097.

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Although one-dimensional non-linear diffusion equations are commonly used to model flow dynamics in aquifers and fissures, they disregard multiple effects of real-life flows. Similarity analysis may allow further analytical reduction of these equations, but it is often difficult to provide applicable initial and boundary conditions in practice, or know the magnitude of effects neglected by the 1D model. Furthermore, when multiple simplifying assumptions are made, the sources of discrepancy between modeled and observed data are difficult to identify. We derive one such model of viscous flow in

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24

Faccanoni, Gloria, and Cédric Galusinski. "Influence of a nonlinear degenerate diffusion on an advection-diffusion equation in a diffuse interface framework." ESAIM: Proceedings and Surveys 72 (2023): 143–62. http://dx.doi.org/10.1051/proc/202372143.

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This work is motivated by the modelling a liquid-vapour flows with phase transition describing the evolution of the coolant within an heat exchanger (e.g. the core of a Pressurized Water Reactor). We investigate an advection-diffusion equation with a degenerate and nonlinear diffusion coefficient. The degeneracy corresponds to a liquid-vapor mixture in the original model whereas the diffusion coefficient is non-degenerate in the pure phase cases. We focus on the influence of the diffusion coefficient on a simple 1D configuration for which some analytical computations can be done, leading to a

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Magdalena, Ikha, Vivianne Kusnowo, Moh Ivan Azis, and Widowati. "1D–2D Numerical Model for Wave Attenuation by Mangroves as a Porous Structure." Computation 9, no. 6 (2021): 66. http://dx.doi.org/10.3390/computation9060066.

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In this paper, we investigate wave attenuation caused by mangroves as a porous media. A 1-D mathematical model is derived by modifying the shallow water equations (SWEs). Two approaches are used to involve the existing of mangrove: friction term and diffusion term. The model will be solved analytically using the separation of variables method and numerically using a staggered finite volume method. From both methods, wave transmission coefficient will be obtained and used to observe the damping effect induced by the porous media. Several comparisons are shown to examine the accuracy and robustn

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SHIK, ALEXANDER, HARRY E. RUDA, and SLAVA V. ROTKIN. "ELECTROSTATICS OF NANOWIRES AND NANOTUBES: APPLICATION FOR FIELD–EFFECT DEVICES." International Journal of High Speed Electronics and Systems 16, no. 04 (2006): 937–58. http://dx.doi.org/10.1142/s0129156406004090.

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We present a quantum and classical theory of electronic devices with one–dimensional (1D) channels made of a single carbon nanotube or a semiconductor nanowire. An essential component of the device theory is a self–consistent model for electrostatics of 1D systems. It is demonstrated that specific screening properties of 1D wires result in a charge distribution in the channel different from that in bulk devices. The drift–diffusion model has been applied for studying transport in a long channel 1D field–effect transistor. A unified self–consistent description is given for both a semiconductor

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27

ZHDANOV, VLADIMIR P., and BENGT KASEMO. "KINETICS OF ELECTROCHEMICAL REACTIONS ON MODEL SUPPORTED CATALYSTS: READSORPTION AND MASS TRANSPORT." Surface Review and Letters 15, no. 06 (2008): 745–51. http://dx.doi.org/10.1142/s0218625x08011962.

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To bridge the structure gap, electrochemical reactions can be studied in flow cells with nm-sized catalyst particles deposited or fabricated on the cell walls. The understanding of the role of mass transport in such cells is now limited. To clarify the likely effects in this field, we analyze the simplest reaction scheme including intermediate desorption, readsorption, and subsequent reaction and show how the net rate of the formation of intermediate can be influenced by its diffusion in the liquid phase. With certain approximations, we derive analytical results describing reaction and diffusi

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28

Cordiner, Stefano, Vincenzo Mulone, and Fabio Romanelli. "Thermal-Fluid-Dynamic Simulation of a Proton Exchange Membrane Fuel Cell Using a Hierarchical 3D-1D Approach." Journal of Fuel Cell Science and Technology 4, no. 3 (2006): 317–27. http://dx.doi.org/10.1115/1.2744052.

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The use of proton exchange membrane fuel cells (PEFC) based power trains and stationary systems has been technically demonstrated but is still far from commercial application. Technical development is still required to reach cost and durability targets, and to this aim, modeling and simulation are useful tools to obtain both better understanding of the fundamental occurring processes and to shorten design-associated costs and time. In this paper, a hierarchical 3D-1D approach is proposed, to overcome the deficiencies of a full 1D approach and the characteristic computational costs of a full 3D

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Tanaka, Hiroaki, Rei Utata, Keiko Tsuganezawa, Sachiko Takahashi, and Akiko Tanaka. "Through Diffusion Measurements of Molecules to a Numerical Model for Protein Crystallization in Viscous Polyethylene Glycol Solution." Crystals 12, no. 7 (2022): 881. http://dx.doi.org/10.3390/cryst12070881.

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Protein crystallography has become a popular method for biochemists, but obtaining high-quality protein crystals for precise structural analysis and larger ones for neutron analysis requires further technical progress. Many studies have noted the importance of solvent viscosity for the probability of crystal nucleation and for mass transportation; therefore, in this paper, we have reported on experimental results and simulation studies regarding the use of viscous polyethylene glycol (PEG) solvents for protein crystals. We investigated the diffusion rates of proteins, peptides, and small molec

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30

Del Sarto, Gianmarco, Jochen Bröcker, Franco Flandoli, and Tobias Kuna. "Variational techniques for a one-dimensional energy balance model." Nonlinear Processes in Geophysics 31, no. 1 (2024): 137–50. http://dx.doi.org/10.5194/npg-31-137-2024.

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Abstract. A one-dimensional climate energy balance model (1D EBM) is a simplified climate model for the zonally averaged global temperature profile, based on the Earth's energy budget. We examine a class of 1D EBMs which emerges as the parabolic equation corresponding to the Euler–Lagrange equations of an associated variational problem, covering spatially inhomogeneous models such as with latitude-dependent albedo. Sufficient conditions are provided for the existence of at least three steady-state solutions in the form of two local minima and one saddle, that is, of coexisting “cold”, “warm” a

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31

Pan, Yuwei, Haijun Ruan, Yagya N. Regmi, Billy Wu, Huizhi Wang, and Nigel Brandon. "A Machine Learning Accelerated Hierarchical 3D+1D Model for Proton Exchange Membrane Fuel Cells." ECS Meeting Abstracts MA2023-02, no. 37 (2023): 1706. http://dx.doi.org/10.1149/ma2023-02371706mtgabs.

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Physics-based continuum models for proton exchange membrane fuel cells (PEMFCs) are an essential tool for fuel cell design and management. To date, many continuum models, ranging from 1D to 3D, have been developed for PEMFCs. Although computationally efficient, 1D models do not account for heterogeneity in flow fields, which negatively impact their accuracy. In contrast, 2D and 3D models are usually more representative of actual operating conditions but computationally intensive due to the coupled partial differential equations and large number of mesh elements involved. To overcome these issu

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Lukaševičs, Edmunds, and Ilmārs Kangro. "MATHEMATICAL MODELING OF DIFFUSION BOUNDARY PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS USING MATLAB AND C++ FOR NUMERICAL AND ANALYTICAL SOLUTIONS." HUMAN. ENVIRONMENT. TECHNOLOGIES. Proceedings of the Students International Scientific and Practical Conference, no. 27 (October 30, 2023): 19–27. http://dx.doi.org/10.17770/het2023.27.7373.

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The article examines a second-order parabolic partial differential equation of a three-dimensional (3D) non-stationary boundary problem with constant diffusion coefficients and periodic boundary conditions in the x and y directions. The method for reducing the (3D) non-stationary boundary problem to the corresponding one-dimensional (1D) non-stationary boundary problem using periodic boundary conditions in the x and y directions is discussed. The stationary (analytical) solution of the obtained (1D) stationary boundary problem is also obtained. The numerical solutions of the 1D boundary proble

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Liu, Qingyun, and Junxiao Wu. "Multi-Resolution PEM Fuel Cell Model Validation and Accuracy Analysis." Journal of Fuel Cell Science and Technology 3, no. 1 (2005): 51–61. http://dx.doi.org/10.1115/1.2134737.

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A multi-resolution simulation method was developed for the polymer electrolyte membrane (PEM) fuel cell simulation: a full 3D model was employed for the membrane and diffusion layer; a 1D+2D model was applied to the catalyst layer, that is, at each location of the fuel cell plate, the governing equations were integrated only in the direction perpendicular to the fuel cell plate; and a quasi-1D model with high numerical efficiency and reasonable accuracy was employed for the flow channels. The simulation accuracy was assessed in terms of the fuel cell polarization curves and membrane Ohmic over

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Hariri, I., A. Radid, and K. Rhofir. "Physics-informed neural networks for the reaction-diffusion Brusselator model." Mathematical Modeling and Computing 11, no. 2 (2024): 448–54. http://dx.doi.org/10.23939/mmc2024.02.448.

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In this work, we are interesting in solving the 1D and 2D nonlinear stiff reaction-diffusion Brusselator system using a machine learning technique called Physics-Informed Neural Networks (PINNs). PINN has been successful in a variety of science and engineering disciplines due to its ability of encoding physical laws, given by the PDE, into the neural network loss function in a way where the network must not only conform to the measurements, initial and boundary conditions, but also satisfy the governing equations. The utilization of PINN for Brusselator system is still in its infancy, with man

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35

Seminara, S. A., M. I. Troparevsky, M. A. Fabio, and G. La Mura. "Anomalous Diffusion with Caputo-Fabrizio Time Derivative: an Inverse Problem." Trends in Computational and Applied Mathematics 23, no. 3 (2022): 515–29. http://dx.doi.org/10.5540/tcam.2022.023.03.00515.

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In this work we approximate the source for a non homogeneous fractionaldiffusion equation in 1D, from measurements of the concentration at a finite number ofpoints. We use Caputo-Fabrizio time fractional derivative to model anomalous diffusion.Separating variables, we arrive to a linear system which provides approximate values forthe Fourier coefficients of the unknown source. Numerical examples show the efficiency ofthe method, as well as some of its practical limitations.

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Braun, Elishan Christian, Gabriella Bretti, and Roberto Natalini. "Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips." Mathematics 9, no. 6 (2021): 688. http://dx.doi.org/10.3390/math9060688.

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The present work is inspired by the recent developments in laboratory experiments made on chips, where the culturing of multiple cell species was possible. The model is based on coupled reaction-diffusion-transport equations with chemotaxis and takes into account the interactions among cell populations and the possibility of drug administration for drug testing effects. Our effort is devoted to the development of a simulation tool that is able to reproduce the chemotactic movement and the interactions between different cell species (immune and cancer cells) living in a microfluidic chip enviro

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Mao, Huaqing, Paul Woodward, Falk Herwig, et al. "3D Hydrodynamic Simulations of Massive Main-sequence Stars. III. The Effect of Radiation Pressure and Diffusion Leading to a 1D Equilibrium Model." Astrophysical Journal 975, no. 2 (2024): 271. http://dx.doi.org/10.3847/1538-4357/ad6c4f.

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Abstract We present 3D hydrodynamical simulations of core convection with a stably stratified envelope of a 25 M ⊙ star in the early phase of the main sequence. We use the explicit gas-dynamics code PPMstar, which tracks two fluids and includes radiation pressure and radiative diffusion. Multiple series of simulations with different luminosities and radiative thermal conductivities are presented. The entrainment rate at the convective boundary, internal gravity waves in and above the boundary region, and the approach to dynamical equilibrium shortly after a few convective turnovers are investi

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Xu, Yanan, Ming Hui, and Haozhe Qu. "Design of a 3D Platform for the Evaluation of Water Quality in Urban Rivers Based on a Digital Twin Model." Water 16, no. 24 (2024): 3668. https://doi.org/10.3390/w16243668.

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To improve the informatization construction and intelligent decision-making level of river and lake basin management, the water quality of a digital twin basin was considered as the starting point and a water quality evaluation platform for Chuancheng River and Baihe River in Nanyang City, Henan Province was established. Based on digital twin technology, the platform establishes a virtual space city model, uses the long short-term memory algorithm to establish a water quality prediction model, draws the distribution of water pollution factors in two dimensions based on Kriging interpolation, s

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Lazar, Arne L., Swantje C. Konradt, and Hermann Rottengruber. "Open-Source Dynamic Matlab/Simulink 1D Proton Exchange Membrane Fuel Cell Model." Energies 12, no. 18 (2019): 3478. http://dx.doi.org/10.3390/en12183478.

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This work presents an open-source, dynamic, 1D, proton exchange membrane fuel cell model suitable for real-time applications. It estimates the cell voltage based on activation, ohmic and concentration overpotentials and considers water transport through the membrane by means of osmosis, diffusion and hydraulic permeation. Simplified equations reduce the computational load to make it viable for real-time analysis, quick parameter studies and usage in complex systems like complete vehicle models. Two modes of operation for use with or without reference polarization curves allow for a flexible ap

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Skolotneva, Ekaterina, Marc Cretin, and Semyon Mareev. "A Simple 1D Convection-Diffusion Model of Oxalic Acid Oxidation Using Reactive Electrochemical Membrane." Membranes 11, no. 6 (2021): 431. http://dx.doi.org/10.3390/membranes11060431.

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In recent years, electrochemical methods utilizing reactive electrochemical membranes (REM) have been recognized as the most promising technologies for the removal of organic pollutants from water. In this paper, we propose a 1D convection-diffusion-reaction model concerning the transport and oxidation of oxalic acid (OA) and oxygen evolution in the flow-through electrochemical oxidation system with REM. It allows the determination of unknown parameters of the system by treatment of experimental data and predicts the behavior of the electrolysis setup. There is a good agreement in calculated a

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Derrida, Bernard, Vincent Hakim, and Vincent Pasquier. "Exact First-Passage Exponents of 1D Domain Growth: Relation to a Reaction-Diffusion Model." Physical Review Letters 75, no. 4 (1995): 751–54. http://dx.doi.org/10.1103/physrevlett.75.751.

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Ismail, Mohammed, Derek Ingham, Kevin J. Hughes, Lin Ma, and Mohamed Pourkashanian. "The effects of shape on the performance of cathode catalyst agglomerates in polymer electrolyte fuel cells." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 3/4 (2016): 1145–56. http://dx.doi.org/10.1108/hff-10-2015-0416.

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Purpose – The purpose of this paper is to numerically investigate the effects of the shape on the performance of the cathode catalyst agglomerate used in polymer electrolyte fuel cells (PEFCs). The shapes investigated are slabs, cylinders and spheres. Design/methodology/approach – Three 1D models are developed to represent the slab like, cylindrical and spherical agglomerates, respectively. The models are solved for the concentration of the dissolved oxygen using a finite element software, COMSOL Multiphysics®. “1D” and “1D axisymmetric” schemes are used to model the slab like and cylindrical

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Mensah, Prince Romeo. "Vanishing centre-of-mass limit of the 2D-1D corotational Oldroyd-B polymeric fluid-structure interaction problem." Nonlinearity 38, no. 3 (2025): 035027. https://doi.org/10.1088/1361-6544/adb9b0.

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Abstract We consider the Oldroyd-B model for a two-dimensional dilute corotational polymer fluid with centre-of-mass diffusion that is interacting with a one-dimensional viscoelastic shell. We show that any family of strong solutions of the system described above that is parametrized by the centre-of-mass diffusion coefficient converges, as the coefficient goes to zero, to a weak solution of a corotational polymer fluid-structure interaction system without centre-of-mass diffusion but with essentially bounded polymer number density and extra stress tensor. As a consequence, we also obtain a we

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Zhou, Jingquan, Xinhe Yang, and Zhu Ren. "SCConv-Denoising Diffusion Probabilistic Model Anomaly Detection Based on TimesNet." Electronics 14, no. 4 (2025): 746. https://doi.org/10.3390/electronics14040746.

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Time series anomaly detection is a significant challenge due to the inherent complexity and diversity of time series data. Traditional methods for time series anomaly detection (TAD) often struggle to effectively address the intricate nature of a complex time series and the composite characteristics of diverse anomalies. In this paper, we propose SCConv-Denoising Diffusion Probabilistic Model Anomaly Detection Based on TimesNet (SDADT), a novel framework that integrates the Spatial and Channel Reconstruction Convolution (SCConv) module and Denoising Diffusion Probabilistic Models (DDPMs) to ad

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Kregar, Ambroz, Matej Prijatelj, and Tomaž Katrašnik. "1D Spatially Resolved Model of Alloyed Catalyst Degradation in LT-PEMFC." ECS Meeting Abstracts MA2023-02, no. 37 (2023): 1777. http://dx.doi.org/10.1149/ma2023-02371777mtgabs.

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Low-temperature fuel cells with proton exchange membrane (LT-PEMFC) are among the most promising energy devices for future decarbonizaion of heavy-duty long-distance transport. Fuel cells use hydrogen as the energy source and air as oxidizer to produce electricity in catalyzed electrochemical process, with only side-products being heat and water. Despite some clear advantages over other energy sources, i.e. batteries, their adoption is still somewhat limited by some prominent factors such as high price and limited durability. Both of these factors are closely related to the use of specific cat

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Rivero, Joanna R., Grigorios Panagakos, Austin Lieber, and Katherine Hornbostel. "Hollow Fiber Membrane Contactors for Post-Combustion Carbon Capture: A Review of Modeling Approaches." Membranes 10, no. 12 (2020): 382. http://dx.doi.org/10.3390/membranes10120382.

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Hollow fiber membrane contactors (HFMCs) can effectively separate CO2 from post-combustion flue gas by providing a high contact surface area between the flue gas and a liquid solvent. Accurate models of carbon capture HFMCs are necessary to understand the underlying transport processes and optimize HFMC designs. There are various methods for modeling HFMCs in 1D, 2D, or 3D. These methods include (but are not limited to): resistance-in-series, solution-diffusion, pore flow, Happel’s free surface model, and porous media modeling. This review paper discusses the state-of-the-art methods for model

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Lugon Junior, Jader, João Flávio Vieira Vasconcellos, Diego Campos Knupp, Gisele Moraes Marinho, Luiz Bevilacqua, and Antônio José da Silva Neto. "Solution of Fourth Order Diffusion Equations and Analysis Using the Second Moment." Defect and Diffusion Forum 399 (February 2020): 10–20. http://dx.doi.org/10.4028/www.scientific.net/ddf.399.10.

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The classical concept of diffusion characterized by Fick’s law is well suited for describing a wide class of practical problems of interest. Nevertheless, it has been observed that it is not enough to properly represent other relevant applications of practical interest. When in a system of particles their spreading is slower or faster than predicted by the classical diffusion model, such a phenomenon is referred to as anomalous diffusion. Time fractional, space fractional and even space-time fractional equations are widely used to model phenomena such as solute transport in porous media, finan

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Bajwa, Ali I., and Martin J. Blunt. "Early-Time 1D Analysis of Shale-Oil and -Gas Flow." SPE Journal 21, no. 04 (2016): 1254–62. http://dx.doi.org/10.2118/179742-pa.

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Summary We present a new semianalytic method to solve the nonlinear pressure-diffusion equation at early time, before reservoir boundaries are encountered, and under constant bottomhole pressure (BHP), applicable to the analysis of unconventional reservoirs. We assume that the flow rate is inversely proportional to the square root of time since the beginning of production. The method is an extension of the semianalytic solution proposed by Schmid et al. (2011) for spontaneous imbibition; we replace the solution for saturation with one for pressure, while extending the functional form of the go

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Mykhailenko, Viacheslav, and Pavol Bobik. "Statistical Error for Cosmic Rays Modulation Evaluated by SDE Backward in Time Method for 1D Model." Fluids 7, no. 2 (2022): 46. http://dx.doi.org/10.3390/fluids7020046.

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The propagation of cosmic rays through the heliosphere has been solved for more than half a century by stochastic methods based on Ito’s lemma. This work presents the estimation of statistical error of solution of Fokker–Planck equation by the 1D backward in time stochastic differential equations method. The error dependence on simulation statistics and energy is presented for different combinations of input parameters. The 1% precision criterion in mean value units of intensity standard deviation is defined as a function of solar wind velocity and diffusion coefficient value.

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L. Schultheiß, Annika, Ravi A. Patel, and Frank Dehn. "Probabilistic service life prediction of cracked concrete using numerical and engineering models." ce/papers 6, no. 6 (2023): 1524–33. http://dx.doi.org/10.1002/cepa.2958.

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AbstractChloride ingress induced depassivation of reinforcing steel leading to corrosion is a major durability concern for concrete structures. The influence of the presence of cracks commonly occurring in concrete structures on chloride ingress should be accounted to improve the accuracy of service life predictions. This study investigates the depassivation probability of the reinforcement in both cracked and uncracked concrete using both analytical and 1D numerical models. The probabilistic service life prediction is realized using the Monte Carlo simulation to incorporate the uncertainty an

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