Journal articles on the topic '1D diffusion model'
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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 (December 30, 2014): 599–609. http://dx.doi.org/10.11568/kjm.2014.22.4.599.
2
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 (February 2005): 129–53. http://dx.doi.org/10.1016/j.jcp.2004.08.009.
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.
4
Larsson, Henrik, and Lars Höglund. "Multiphase diffusion simulations in 1D using the DICTRA homogenization model." Calphad 33, no. 3 (September 2009): 495–501. http://dx.doi.org/10.1016/j.calphad.2009.06.004.
5
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 (October 6, 2023): 654–67. http://dx.doi.org/10.3390/jne4040041.
Abstract:
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 to properly account for the radial leakage effects of the reactor. The leakage cross section and other consistent neutronics parameters are generated with the Monte Carlo code Serpent using high-fidelity three-dimensional (3D) models. The accuracy of the 1D consistent model is verified by the reference solution from the Monte Carlo model on the Molten Salt Reactor Experiment (MSRE) configuration. The 1D consistent model successfully reproduced the integrated flux from the 3D model and the reactor multiplication factor keff with the error in the range of 95 to 397 pcm (per cent mille), depending on discretized energy group structures. The developed model is also extended to estimate the reactivity loss due to fuel circulation in MSRE. The estimate of reactivity loss in dynamics analysis is in great agreement with the experimental data. This model functions as the first step in the development of a 1D fully neutronics/thermal-hydraulics coupled model for short- and long-term MSRE transient analysis.
6
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 (January 28, 2022): 701–23. http://dx.doi.org/10.1007/s00707-021-03142-x.
Abstract:
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 growing oxide layer in a perhydropolysilazane (PHPS)-based polymer-derived ceramic (PDC), containing silicon filler particles. Within the mechanical part of the modeling, we use the Neo-Hookean material law which allows for the consideration of volume expansion and the diffusion kinematics in terms of finite deformations. We derive this continuum formulation in 3D and reduce it later to 1D, as we show that a 1D formulation is sufficient for thin oxide layers in our consideration. In such a case, the reaction-induced volume expansion is mostly limited to strains orthogonal to the oxide layer, as the bulk material hinders transversal deformation. Both formulations, i.e., 1D and 3D, are implemented in the finite element software FEAP. We perform a parameter study and fit the results with experimental data. We investigate the diffusion kinematics in the presence of volume expansion. Additionally, we discuss the influence of the elastic energy on the reaction rate.
7
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.
Abstract:
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 high advantages in terms of computational time savings.
8
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 (November 17, 2007): 651–67. http://dx.doi.org/10.1093/imamat/hxm066.
9
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 (March 2, 2020): 1690. http://dx.doi.org/10.3390/app10051690.
Abstract:
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 the 1D array. The 2D system has been numerically modeled and experimentally tested in an anechoic chamber. It preserves the absorption properties of the 1D system and introduces efficient diffusion at higher frequencies due to the joint effect of resonances and multiple scattering inside the discrete 2D structure. The combined effect of sound absorption at low frequencies and sound diffusion at higher frequencies, may play a relevant role in the design of noise reduction systems for different applications.
10
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.
Abstract:
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, financial modelling and cancer tumor behavior. Considering the effects of partial and temporary retention in dispersion processes a new analytical formulation was derived to simulate anomalous diffusion. The new approach leads to a fourth-order partial differential equation (PDE) and assumes the existence of two concomitant fluxes. This work investigates the behavior of the bi-flux approach in one dimensional (1D) medium evaluating the mean square displacement for different cases in order to classify the diffusion process in normal, sub-diffusive or super-diffusive.
11
Cheng, Hu, Sophia Vinci-Booher, Jian Wang, Bradley Caron, Qiuting Wen, Sharlene Newman, and Franco Pestilli. "Denoising diffusion weighted imaging data using convolutional neural networks." PLOS ONE 17, no. 9 (September 15, 2022): e0274396. http://dx.doi.org/10.1371/journal.pone.0274396.
Abstract:
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 can then be applied to high-noise datasets from other subjects. We validated the 1D-CNN denoising method by first demonstrating that 1D-CNN denoising resulted in DWI images that were more similar to the noise-free ground truth than comparable denoising methods, e.g., MP-PCA, using simulated DWI data. Using the same DWI acquisition but reconstructed with two common reconstruction methods, i.e. SENSE1 and sum-of-square, to generate a pair of low-noise and high-noise datasets, we then demonstrated that 1D-CNN denoising of high-noise DWI data collected from human subjects showed promising results in three domains: DWI images, diffusion metrics, and tractography. In particular, the denoised images were very similar to a low-noise reference image of that subject, more than the similarity between repeated low-noise images (i.e. computational reproducibility). Finally, we demonstrated the use of the 1D-CNN method in two practical examples to reduce noise from parallel imaging and simultaneous multi-slice acquisition. We conclude that the 1D-CNN denoising method is a simple, effective denoising method for DWI images that overcomes some of the limitations of current state-of-the-art denoising methods, such as the need for a large number of training subjects and the need to account for the rectified noise floor.
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 (January 2009): 133–45. http://dx.doi.org/10.1142/s0129183109013510.
Abstract:
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's entropy. Unique graphical analysis techniques are introduced through difference patterns, diffusion patterns, and state progression graphs of the 1D ensemble visualizing the evolution. All analyses are consistent with the known behavior of the 1D Ising system. The CA simulation and new pattern recognition techniques are scalable (in both dimension, complexity, and size) and have many potential applications such as complex design of materials, control of agent systems, and evolutionary mechanism design.
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 (January 14, 2013): 441–69. http://dx.doi.org/10.1142/s0218202512500522.
Abstract:
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 diffusion waves can be added to the viscous contact wave to form a new combined wave pattern. In this paper, we will show that the new combined wave pattern is nonlinear stable provided that the general perturbation of the initial datum and the strength of the contact wave are suitably small. In particular we give detailed convergence rates using anti-derivative methods and elaborated energy estimates. The work extends the results of Huang, Xin and Yang in [Contact discontinuity with general perturbations for gas motions, Adv. Math. 219 (2008) 1246–1297] for compressible Navier–Stokes equations to a system with much weaker dissipation mechanism.
14
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.
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.
Abstract:
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.
16
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.
Abstract:
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.
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 (October 31, 2018): 4005–30. http://dx.doi.org/10.1175/jas-d-18-0055.1.
Abstract:
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 within a parcel framework that serve as a numerical benchmark for the 1D tests. In contrast, the bin-modeled DSDs are similar to the Lagrangian microphysical benchmark for a rising parcel in which Eulerian transport is not considered. These results indicate that numerical diffusion associated with vertical advection is a key contributor to broadening DSDs in the 1D model and LES. This DSD broadening from vertical numerical diffusion is unphysical, in contrast to the physical mixing processes that previous studies have indicated broaden DSDs in real clouds. It is proposed that artificial DSD broadening from vertical numerical diffusion compensates for underrepresented horizontal variability and mixing of different droplet populations in typical LES configurations with bin microphysics, or the neglect of other mechanisms that broaden DSDs such as growth of giant cloud condensation nuclei. These results call into question the ability of Eulerian dynamical models with bin microphysics to investigate the physical mechanisms for DSD broadening, even though they may reasonably simulate overall DSD characteristics.
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 (September 29, 2004): 20–28. http://dx.doi.org/10.1115/1.1840819.
Abstract:
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 is the optimal design under the specified operating conditions.
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 (January 1, 2023): 59–64. http://dx.doi.org/10.52292/j.laar.2023.1077.
Abstract:
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 predictions, varying a Thiele modulus and the axial-to-transversal diffusivities ratio, are below 6% for the first order reaction and rise up to around of 9% and 11% for a LHHW (Langmuir-Hinshelwood-Hougen-Watson) expression at the verge of the appearance of multiple steady states, in the case of Raschig rings and solid circular cylinders, respectively.
20
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 (May 28, 2019): 97. http://dx.doi.org/10.3390/fluids4020097.
Abstract:
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 a parabolic fissure from first principals. The parabolic fissure is formed by extruding an upward opening parabola in a horizontal direction. In this setting, permeability is a power law function of height, resulting in a generalized Boussinesq equation. To gauge the effects neglected by this model, 3D Navier-Stokes multiphase flow simulations are conducted for the same geometry. Parameter variations are performed to assess the nature of errors induced by applying the 1D model to a realistic scenario, where the initial and boundary conditions can not be matched exactly. Numerical simulations reveal an undercutting effect observed in laboratory experiments, but not modeled when the Dupuit-Forchheimer assumption is applied. By selectively controlling the effects placed on the free surface in 3D simulations, we are able to demonstrate that free surface slope is the primary driver of the undercutting effect. A consistent lag and overshoot flow regime is observed in the 3D simulations as compared to the 1D model, based on the choice of initial condition. This implies that the undercutting effect is partially induced by the initial condition. Additionally, the presented numerical evidence shows that some of the flow behavior unaccounted for in the 1D model scales with the 1D model parameters.
21
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 (June 7, 2021): 66. http://dx.doi.org/10.3390/computation9060066.
Abstract:
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 robustness of the derived numerical scheme. The results show that the friction coefficient, diffusion coefficient and vegetation’s length have a significant effect on the transmission coefficient. Moreover, numerical observation is extended to a 2-D SWEs, where we conduct a numerical simulation over a real bathymetry profile. The results from the 2-D numerical scheme will be validated using the data obtained from the field measurement which took place in Demak, Central Java, Indonesia. The results from this research will be beneficial to determine the characteristics of porous structures used for coastal protection.
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 (October 9, 2022): 708. http://dx.doi.org/10.1149/ma2022-0211708mtgabs.
Abstract:
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-dissolve a Type 316L stainless steel (SS) 1D electrode to specific depths. Based on the new methodology and mathematical models, it was found that 1D Fick’s law of diffusion could not be used to estimate the pit stability product under a salt film because electro-migration had a measurable contribution (i.e., 67%) to the dissolution current. Although the diffusion coefficient of metal cations decreased with an increasing concentration inside the pit, it could be replaced by a constant diffusion coefficient to estimate the pit stability product, defined as an equivalent diffusion coefficient in our work. Later, a more comprehensive mathematical model, which included hydrolysis reactions and activity, was built to predict the local chemistry within the pit cavity. Recently, a galvanostatic method was developed to estimate the critical pit stability product of Type 316L SS, which was between 0.8 and 0.9 A/m in 0.6 M NaCl at 25°C, findings that were also confirmed by mass transport modelling. Here, we will present the proposed improved theoretical framework and discuss the next steps in modelling the propagation of pits in stainless steels.
23
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.
Abstract:
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 surprising behavior of the phase transition with respect to the diffusion.
24
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 (December 2008): 745–51. http://dx.doi.org/10.1142/s0218625x08011962.
Abstract:
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 diffusion near catalyst particles and in more remote regions in the simplest 1D case and more complex 2D and 3D situations.
25
Milosevic, Miljan, Dusica Stojanovic, Vladimir Simic, Bogdan Milicevic, Andjela Radisavljevic, Petar Uskokovic, and Milos Kojic. "A Computational Model for Drug Release from PLGA Implant." Materials 11, no. 12 (November 29, 2018): 2416. http://dx.doi.org/10.3390/ma11122416.
Abstract:
Due to the relative ease of producing nanofibers with a core–shell structure, emulsion electrospinning has been investigated intensively in making nanofibrous drug delivery systems for controlled and sustained release. Predictions of drug release rates from the poly (d,l-lactic-co-glycolic acid) (PLGA) produced via emulsion electrospinning can be a very difficult task due to the complexity of the system. A computational finite element methodology was used to calculate the diffusion mass transport of Rhodamine B (fluorescent drug model). Degradation effects and hydrophobicity (partitioning phenomenon) at the fiber/surrounding interface were included in the models. The results are validated by experiments where electrospun PLGA nanofiber mats with different contents were used. A new approach to three-dimensional (3D) modeling of nanofibers is presented in this work. The authors have introduced two original models for diffusive drug release from nanofibers to the 3D surrounding medium discretized by continuum 3D finite elements: (1) A model with simple radial one-dimensional (1D) finite elements, and (2) a model consisting of composite smeared finite elements (CSFEs). Numerical solutions, compared to experiments, demonstrate that both computational models provide accurate predictions of the diffusion process and can therefore serve as efficient tools for describing transport inside a polymer fiber network and drug release to the surrounding porous medium.
26
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 (December 2006): 937–58. http://dx.doi.org/10.1142/s0129156406004090.
Abstract:
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 nanowire and a single–wall nanotube. Within this basic model we analytically calculate equilibrium (at zero current) and quasi–equilibrium (at small current) charge distributions in the channel. Numerical results are presented for arbitrary values of the driving current. General analytic expressions, found for basic device characteristic, differ from equations for a standard bulk three–dimensional field–effect device. The device characteristics are shown to be sensitive to the gate and leads geometry and are analyzed separately for bulk, planar and quasi–1D contacts. The basic model is generalized to take into account external charges which can be polarized and/or moving near the channel. These charges change the self–consistent potential profile in the channel and may show up in device properties, for instance, a hysteresis may develop which can have a memory application.
27
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 (March 8, 2024): 137–50. http://dx.doi.org/10.5194/npg-31-137-2024.
Abstract:
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” and unstable “intermediate” climates. We also give an interpretation of minimizers as “typical” or “likely” solutions of time-dependent and stochastic 1D EBMs. We then examine connections between the value function, which represents the minimum value (across all temperature profiles) of the objective functional, regarded as a function of greenhouse gas concentration, and the global mean temperature (also as a function of greenhouse gas concentration, i.e. the bifurcation diagram). Specifically, the global mean temperature varies continuously as long as there is a unique minimizing temperature profile, but coexisting minimizers must have different global mean temperatures. Furthermore, global mean temperature is non-decreasing with respect to greenhouse gas concentration, and its jumps must necessarily be upward. Applicability of our findings to more general spatially heterogeneous reaction–diffusion models is also discussed, as are physical interpretations of our results.
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 (August 31, 2006): 317–27. http://dx.doi.org/10.1115/1.2744052.
Abstract:
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 approach. The polymeric membrane and catalyst layers are represented by a local 1D model, while channels, gas diffusion layers, and solid electrodes are modeled by a full 3D approach. The model capabilities are first investigated with respect to experimental data by means of a full fuel cell simulation; the main chemical, fluid dynamic, and thermal fields are then analyzed in a straight channel configuration. The proposed 3D/1D model is able to accurately represent PEFC specific phenomena and their physical coupling. It could be then successfully applied to both design and development.
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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 (December 22, 2023): 1706. http://dx.doi.org/10.1149/ma2023-02371706mtgabs.
Abstract:
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 issues, a hierarchical approach that combines a 2D/3D description of flow fields, gas diffusion layers (GDLs) and a simplified microporous layer (MPL)/catalyst layer (CL)/membrane sub-model has been proposed in the literature. However, studies based on this method often use a simplified or 0D MPL/CL/membrane sub-model, whose results may deviate from a full 1D description due to the neglected nonlinearity, especially at higher loads. In this study, we present a computationally efficient 3D+1D hierarchical model for PEMFCs accelerated by machine learning. The 3D model, which captures the two-phase flow in the gas channels and GDLs, is coupled with a full 1D description of the MPLs, membrane, CLs, and CL agglomerates by exchanging boundary values and fluxes, as shown in the figure. To avoid the high computing cost increase associated with the full 1D description, we develop a physics-informed neural network to replace the 1D sub-model for coupling with the 3D model, while maintaining the full description of fuel cell internal states. Large synthetic datasets are generated using the 1D model for training the neural network, ensuring the accuracy of the model. The proposed 3D+1D model is validated against experimentally obtained polarization curves and high frequency resistances under different relative humidities. The proposed model is then used to study the nonlinear distribution of the internal states along the thickness direction of the membrane electrode assembly as well as in the 3D flow field. The model is also highly effective in elucidating the dominant voltage loss factor under different operating conditions. Our developed model offers high accuracy at low computing cost under a wide range of operating conditions, potentially aiding the rapid optimization of both the membrane electrode assembly and the gas channel geometry and advance the water and thermal management of existing fuel cell designs. Figure 1
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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 (June 21, 2022): 881. http://dx.doi.org/10.3390/cryst12070881.
Abstract:
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 molecules in viscous PEG solvents using fluorescence correlation spectroscopy. In high-molecular-weight PEG solutions (molecular weights: 10,000 and 20,000), solute diffusion showed deviations, with a faster diffusion than that estimated by the Stokes–Einstein equation. We showed that the extent of the deviation depends on the difference between the molecular sizes of the solute and PEG solvent, and succeeded in creating equations to predict diffusion coefficients in viscous PEG solutions. Using these equations, we have developed a new numerical model of 1D diffusion processes of proteins and precipitants in a counter-diffusion chamber during crystallization processes. Examples of the application of anomalous diffusion in counter-diffusion crystallization are shown by the growth of lysozyme crystals.
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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 (August 2, 2005): 51–61. http://dx.doi.org/10.1115/1.2134737.
Abstract:
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 overpotential. Overall, good agreements between the simulated results and the experimental data were obtained. However, at large current densities, with high relative humidity reactant inputs, the simulation under-predicted the fuel cell performance due to the single-phase assumption; the simulation slightly over-predicted the fuel cell performance for a dry cathode input, possibly due to the nonlinearity of the membrane properties in dehydration case. Further, a parameter study was performed under both fully humidified and relatively dry conditions for the parameters related to the cathode catalyst layer and the gas diffusion layer (GDL). It is found that the effects of liquid water in both the GDL and catalyst layer on the cell performance, and the accurate identification of the cathode catalyst layer parameters such as the cathodic transfer coefficient should be focused for future studies in order to further improve the model accuracy.
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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.
Abstract:
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 problem are obtained using the Matlab package "pdepe" and the C++ programming language. As a practical application of the developed mathematical model, the article discusses calculating the concentration of heavy metal Ca in a peat layer based on the obtained experimental data (measurements).
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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 (June 7, 2021): 431. http://dx.doi.org/10.3390/membranes11060431.
Abstract:
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 and experimental data at different transmembrane pressures and initial concentrations of OA. The model provides an understanding of the processes occurring in the system and gives the concentration, current density, potential, and overpotential distributions in REM. The dispersion coefficient was determined as a fitting parameter and it is in good agreement with literary data for similar REMs. It is shown that the oxygen evolution reaction plays an important role in the process even under the kinetic limit, and its contribution decreases with increasing total organic carbon flux through the REM.
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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 (July 24, 1995): 751–54. http://dx.doi.org/10.1103/physrevlett.75.751.
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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 (March 23, 2021): 688. http://dx.doi.org/10.3390/math9060688.
Abstract:
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 environment. The main issues faced in this work are the introduction of mass-preserving and positivity-preserving conditions, involving the balancing of incoming and outgoing fluxes passing through interfaces between 2D and 1D domains of the chip and the development of mass-preserving and positivity preserving numerical conditions at the external boundaries and at the interfaces between 2D and 1D domains.
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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 (September 12, 2022): 515–29. http://dx.doi.org/10.5540/tcam.2022.023.03.00515.
Abstract:
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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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 (September 9, 2019): 3478. http://dx.doi.org/10.3390/en12183478.
Abstract:
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 application even without information about cell parameters. The program code is written in MATLAB and provided under the terms and conditions of the Creative Commons Attribution License (CC BY). It is designed to be used inside of a Simulink model, which allows this fuel cell model to be used in a wide variety of 1D simulation platforms by exporting the code as C/C++.
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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 (May 3, 2016): 1145–56. http://dx.doi.org/10.1108/hff-10-2015-0416.
Abstract:
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 agglomerates, respectively. There is no one-dimensional scheme available in COMSOL Multiphysics® for spherical coordinate systems. To resolve this, the governing equation in “1D” scheme is mathematically modified to match that of the spherical coordinate system. Findings – For a given length of the diffusion path, the variation in the performances of the investigated agglomerates is dependent on the operational overpotential. Under low magnitudes of the overpotentials, where the performance is mainly limited by reaction, the slab-like agglomerate outperforms the spherical and cylindrical agglomerates. In contrast, under high magnitudes of the overpotentials where the agglomerate performance is mainly limited by diffusion, the spherical and cylindrical agglomerates outperform the slab-like agglomerate. Practical implications – The current advances in the nano-fabrication technology gives more flexibility in designing the catalyst layers in PEFCs to the desired structures. If the design of the agglomerate catalyst is to be assessed, the current micro-scale modelling offers an efficient and rapid way forward. Originality/value – The current micro-scale modelling is an efficient alternative to developing a full (or half) fuel cell model to evaluate the effects of the agglomerate structure.
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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 (December 22, 2023): 1777. http://dx.doi.org/10.1149/ma2023-02371777mtgabs.
Abstract:
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 catalyst materials needed to ensure high efficiency and power density of hydrogen fuel cells. Due to its high catalytic activity, Pt is traditionally used as a catalyst material, dispersed in form of nanoparticles on a highly porous carbon matrix ensuring good accessibility of hydrogen and air to the catalyst surface and efficient removal of water. Due to harsh local conditions in the catalyst layer, i.e. high temperatures of up to 80° C, high humidity and high electric potentials, catalyst nanoparticles are exposed to various degradation processes. Electrochemical corrosion of carbon support can result in detachment of particles and their consequent agglomeration, which results in a decrease of specific area suitable for electrochemical reactions. Despite high redox potential of Pt (1.115 V vs. SHE), high electric potential in fuel cell cathode can also lead to electrochemical dissolution of catalyst particles, which is additionally accelerated by their small size. Dissolved catalyst can either redeposit to larger particles, resulting in net growth of catalyst particles (so-called Ostwald ripening), or diffuse in proton exchange membrane, where it is reduced by crossover hydrogen. Both processes result in a loss of electrochemically active surface area in the catalyst layer. To reduce the amount of Pt used and thus lower the price, new types of catalyst materials are being developed, using alloys of Pt with other metals, such as Co, Cu or Ni, which also increases the specific electrochemical activity of the material. [1] Since alloying metals have lower redox potential compared to Pt, alloyed catalyst are more susceptible to dissolution, which represents a significant challenge in their wider adoption. Degradation is somewhat mitigated by preconditioning of catalyst nanoparticles during which Pt shell is formed around alloy particle core, resulting in higher stability of core-shell catalysts. Despite clear advantages, the use of alloyed catalyst might introduce some new risks in terms of fuel cell durability. Dissolution of alloying metal introduces ions of transition metals into the membrane, where they could serve as a catalyst in chemical reactions leading to the chemical degradation of the membrane [2]. Metal ions can also block the active sites in proton exchange membrane and thus reduce its proton conductivity, while diffusion from cathode to anode catalyst layer and deposition on catalyst surface can present a risk of anode catalyst surface passivization [3]. To improve the understanding of aforementioned processes, we propose a 1-dimensional spatially and temporally resolved degradation model of alloyed catalyst degradation in the membrane-electrode assembly (MEA). The model describes the changes of cathode core-shell catalyst structure as a redistribution of particle core sizes and shell thicknesses due to electrochemical surface oxidation, dissolution and redeposition. To provide realistic internal states of the fuel cell during operation, the degradation model is coupled with advanced spatially and temporally resolved model of the fuel cell operation [4]. Dissolution model represents a source of Pt and alloying ions in the catalyst layer, which is coupled to 1D model of ion diffusion in the catalyst layer and the membrane, taking into account the specifics of transport in different MEA components. The transport model is further coupled with potential ion sinks, such as reduction in the presence of hydrogen, interaction with the proton exchange membrane and redeposition on the anode. Preliminary results indicate that Pt ions diffusion results in spatial inhomogeneities of catalyst layer degradation. The location and mechanism of metal ion deposition depends on the redox potential of metal and can occur in either membrane or anode catalyst layer. The model shows great promise in developing a better understanding of degradation processes of alloyed catalyst materials and could in future guide a development of better operation strategies for fuel cell use, mitigating their degradation and improving their lifetime. [1] E. Antolini et al., J. Power Sources. 160 (2006) 957–968. [2] M. Strlič et al., Acta Chim. Slov. 50 (2003) 619–632. [3] A. Han et al., Int. J. Hydrogen Energy. 45 (2020) 25276–25285. [4] A. Kregar et al., Appl. Energy. 263 (2020) 114547
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Pratt, F. L., F. Lang, S. J. Blundell, W. Steinhardt, S. Haravifard, S. Mañas-Valero, E. Coronado, B. M. Huddart, and T. Lancaster. "Studying spin diffusion and quantum entanglement with LF-µSR." Journal of Physics: Conference Series 2462, no. 1 (March 1, 2023): 012038. http://dx.doi.org/10.1088/1742-6596/2462/1/012038.
Abstract:
Abstract LF-µSR studies have previously been used to study the diffusive 1D motion of solitons and polarons in conducting polymers. This type of study was also applied to investigating the diffusive motion of spinons in spin-1/2 antiferromagnetic chains. Recently the method has been extended to examples of 2D layered triangular spin lattices which can support quantum spin liquid states, such as 1T-TaS2 and YbZnGaO4. These systems are found to show spin dynamics that matches well to 2D spin diffusion, such a model being found to provide a much better fit to the data than previously proposed models for spin correlations in such systems. In YbZnGaO4 the diffusion rate shows a clear crossover between classical and quantum regimes as T falls below the exchange coupling J. That the spin diffusion approach works well in the high T classical region might be expected, but it is found that it also works equally well in the low T quantum region where quantum entanglement controls the spin dynamics. Measurement of the diffusion rate allows a T dependent length scale to be derived from the data that can be assigned to a quantum entanglement length ξ E. Another entanglement measure, the Quantum Fisher Information F Q can also be obtained from the data and its T dependence is compared to that of ξ E.
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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 (November 30, 2020): 382. http://dx.doi.org/10.3390/membranes10120382.
Abstract:
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 modeling carbon capture HFMCs in 1D, 2D, and 3D. State-of-the-art 1D, 2D, and 3D carbon capture HFMC models are then compared in depth, based on their underlying assumptions. Numerical methods are also discussed, along with modeling to scale up HFMCs from the lab scale to the commercial scale.
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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 (August 15, 2016): 1254–62. http://dx.doi.org/10.2118/179742-pa.
Abstract:
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 governing diffusion equation. The solution can accommodate arbitrary pressure-dependent nonlinear rock and fluid properties as well as production caused by desorption. The mathematical formulation is presented for a general nonlinear case and tested by use of synthetic data. Field production from the Barnett Shale is then used to estimate effective matrix permeability. The model can be used to predict production if the rock and fluid properties are known, or can be used to constrain reservoir properties from production data. It is a complement to traditional pressure- or rate-transient analysis; if the response of a well for constant-pressure production can be determined, our method can be used to determine reservoir properties, without any approximations inherent in linearizing the flow equations.
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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 (January 19, 2022): 46. http://dx.doi.org/10.3390/fluids7020046.
Abstract:
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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AUBRY, S. "KAM TORI AND ABSENCE OF DIFFUSION OF A WAVE-PACKET IN THE 1D RANDOM DNLS MODEL." International Journal of Bifurcation and Chaos 21, no. 08 (August 2011): 2125–45. http://dx.doi.org/10.1142/s0218127411029677.
Abstract:
When nonlinearity is added to an infinite system with purely discrete linear spectrum, Anderson modes become coupled with one another by terms of higher order than linear, allowing energy exchange between them. It is generally believed, on the basis of numerical simulations in such systems, that any initial wave-packet with finite energy spreads down chaotically to zero amplitude with second moment diverging as a power law of time, slower than standard diffusion (subdiffusion). We present results which suggest that the interpretation of spreading cannot be described as initially believed and that new questions arise and still remain opened. We show that an initially localized wave-packet with finite norm may generate two kinds of trajectories both obtained with nonvanishing probability.The first kind consists of KAM trajectories which are recurrent and do not spread. Empirical investigations suggest that KAM theory may still hold in infinite systems under two conditions: (1) the linearized spectrum is purely discrete, (2) the considered solutions are square summable and not too large in amplitude. We check numerically that in appropriate regions of the parameter space, indeed many initial conditions can be found with finite probability that generate (nonspreading) infinite dimension tori (almost periodic solutions) in a fat Cantor set in (projected) phase space.The second kind consists of trajectories which look initially chaotic and often spread over long times. We first rigorously prove that initial chaos does not necessarily imply complete spreading e.g. for large norm initial wave-packet. Otherwise, in some modified models, no spreading at all is proven to be possible, despite the presence of initial chaos in contradiction with early beliefs. The nature of the limit state is still unknown.However, we attempt to present empirical arguments suggesting that if a trajectory starts chaotically spreading, there will necessarily exist (generally large) critical spreading distances that depend on the disorder realization where the trajectory will be sticking to a dense set of KAM tori. This effect should induce drastic slowing down of the spreading which could be viewed as "inverse Arnold diffusion" since the trajectory approaches KAM tori regions instead of leaving them. We suggest that this effect should self-organize the chaotic behavior and that at long time, the wave-packet might not be spread down to zero, but could have a limit profile with marginal chaos (with singular continuous spectrum), despite a long spatial tail. Further analytical and numerical investigations are required.
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Hu, Yongsheng. "3D Model Encryption Algorithm by Parallel Bidirectional Diffusion and 1D Map with Sin and Logistic Coupling." Computer Systems Science and Engineering 47, no. 2 (2023): 1819–38. http://dx.doi.org/10.32604/csse.2023.040729.
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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 (December 2023): 1524–33. http://dx.doi.org/10.1002/cepa.2958.
Abstract:
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 and variability in the input variables. For uncracked concrete the result of the numerical model agreed well with the fib chloride model. For cracked concrete, the numerical simulation suggests that the optimal engineering approach to account for cracks in a service life analysis is the adaptation of crack depth. Although, the approach could lead to an overestimation of chloride concentration because the 1D numerical simulation did not consider lateral diffusion in cracked concrete.
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Shang, Zhi, Jing Lou, and Hongying Li. "A New Multidimensional Drift Flux Mixture Model for Gas–Liquid Droplet Two-Phase Flow." International Journal of Computational Methods 12, no. 04 (August 2015): 1540001. http://dx.doi.org/10.1142/s0219876215400010.
Abstract:
A new multidimensional drift flux mixture model was developed to simulate gas–liquid droplet two-phase flows. The new drift flux model was modified by considering the centrifugal force on the liquid-droplets. Therefore the traditional 1D drift flux model was upgraded to multidimension, 2D and 3D. The slip velocities between the continual phase (gas) and the dispersed phase (liquid droplets) were able to calculate through the multidimensional diffusion flux velocities based on the new modified drift flux model. Through the numerical simulations comparing with the experiments and the simulations of other models on the backward-facing step and the water mist spray two-phase flows, the new model was validated.
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Mukherjee, Debasmita, Lakshmi Narayan Guin, and Santabrata Chakravarty. "Dynamical behavior of a mathematical model of early atherosclerosis." International Journal of Modeling, Simulation, and Scientific Computing 11, no. 01 (February 2020): 2050006. http://dx.doi.org/10.1142/s1793962320500063.
Abstract:
Atherosclerosis, a continual inflammatory disease occurring due to plaque cumulation in the arterial intima, is one of the main reasons behind deaths from diverse cardiovascular diseases. The basic interactions between oxidized low density lipoprotein (LDL) and macrophages in the formation of atherosclerotic plaque are modeled here in terms of a reaction–diffusion system in one-dimensional (1D) space under Neumann boundary conditions. Two simple mathematical models are considered which differ by the influx term only in the case of the interaction of oxidized LDL. Both the spatial and nonspatial systems are simply analyzed theoretically and numerically. Numerical bifurcation analysis confirms the existence of Hopf bifurcation concerning four significant model parameters. Examining the gravity of the model offered in this investigation, an obvious insight into this inflammatory response can be achieved both qualitatively and quantitatively.
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Salomoni, Valentina Anna Lia, and Nico De Marchi. "Numerical Solutions of Space-Fractional Advection–Diffusion–Reaction Equations." Fractal and Fractional 6, no. 1 (December 31, 2021): 21. http://dx.doi.org/10.3390/fractalfract6010021.
Abstract:
Background: solute transport in highly heterogeneous media and even neutron diffusion in nuclear environments are among the numerous applications of fractional differential equations (FDEs), being demonstrated by field experiments that solute concentration profiles exhibit anomalous non-Fickian growth rates and so-called “heavy tails”. Methods: a nonlinear-coupled 3D fractional hydro-mechanical model accounting for anomalous diffusion (FD) and advection–dispersion (FAD) for solute flux is described, accounting for a Riesz derivative treated through the Grünwald–Letnikow definition. Results: a long-tailed solute contaminant distribution is displayed due to the variation of flow velocity in both time and distance. Conclusions: a finite difference approximation is proposed to solve the problem in 1D domains, and subsequently, two scenarios are considered for numerical computations.
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Rendall, Joseph, Fernando Karg Bulnes, Kyle Gluesenkamp, Ahmad Abu-Heiba, William Worek, and Kashif Nawaz. "A Flow Rate Dependent 1D Model for Thermally Stratified Hot-Water Energy Storage." Energies 14, no. 9 (May 2, 2021): 2611. http://dx.doi.org/10.3390/en14092611.
Abstract:
Stratified tank models are used to simulate thermal storage in applications such as residential or commercial hot-water storage tanks, chilled-water storage tanks, and solar thermal systems. The energy efficiency of these applications relates to the system components and the level of stratification maintained during various flow events in the tank. One-dimensional (1D) models are used in building energy simulations because of the short computation time but often do not include flow-rate dependent mixing. The accuracy of 1D models for plug flow, plug flow with axial conduction, and two convection eddy-diffusivity models were compared with experimental data sets for discharging a 50-gal residential tank and recharging the tank with hot water from an external hot-water source. A minimum and maximum relationship for the eddy diffusivity factor were found at Re <2100 and >10,000 for recirculation of hot water to the top of the tank and vertical tubes inletting cold water at the bottom. The root mean square error decreased from >4 °C to near 2 °C when considering flow-based mixing models during heating, while the exponential decay of the eddy diffusion results in a root mean square error reduction of 1 °C for cone-shaped diffusers that begin to relaminarize flow at the inlet.