Anomalous Grain Boundary Diffusion: Fractional Calculus Approach by Renat T. Sibatov

“…Interpreting experimental data with the use of the classical Fisher model sometimes encounters contradictions that can be related to violation of Fick’s law. …”
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Laws of Gas Diffusion in Coal Particles: A Study Based on Experiment and Numerical Simulation by Yongjiang Hao, Xiaofeng Ji, Jiewen Pang

“…The cumulative methane desorption quantity (CMDQ) with time increasing was obtained to show that the reciprocal of CMDQ was in linear relation with the reciprocal of the square root of time, and the correlation coefficients were all above 0.99, on basis of which an empirical formula of CMDQ was established. Then, according to Fick diffusion law and Darcy percolation law, the mathematical models of methane emission from the spherical coal particles were created, respectively, and the corresponding calculating software was programmed by the finite difference method to obtain the simulated CMDQ of each sample under different conditions. …”
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Production Analysis for Fractured Vertical Well in Coal Seam Reservoirs with Stimulated Reservoir Volume by Chen Li

“…Based on the dual-porosity flowing mechanism, combined with the Langmuir adsorb equation, Fick diffusion law, and Darcy law, a mathematical model considering diffusion in matrix and transport in natural fracture system is established, using spherical matrix to describe the transient steady-state sorption, and using cubic matrix to describe the pseudosteady-state sorption. …”
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Semianalytical Solutions to the Axisymmetric Free Strain Consolidation Problem of Unsaturated Soils under the Homogeneous and Mixed Boundary Conditions by Yuanchun Huang, Lei Wang, Sidong Shen

“…The boundary condition is the main factor affecting the consolidation process with the determined consolidation model and related parameters. In this paper, the governing equations of water and air in the polar coordinate were given according to two stress state variables theory of unsaturated soils, Darcy’s law, and Fick’s law under the axisymmetric condition. …”
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Uptake of Photosensitizer 2-Devinyl-2-(1-methoxylethyl) Chlorin f in Human Breast Cancer Cells: A Diffusion Kinetics Study by Ping Chen, Feng Zhang, Lei Zhang, Song-Cheng Mao, Lie Lin, Hua Bai, Guo-Qing Tang, Jian-Zhong Yao, Jun-Hong Yang, Yun-Feng Ma

“…Subcellular distribution study revealed that CPD4 was primarily localized on the mitochondria and membranes, supporting that the mode of transmembrane transport was diffusion. A kinetics model describing CPD4 passing through the plasma membrane of MCF-7 cells was proposed based on Fick's first law of diffusion. …”
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Yttria stabilized zirconia membrane stability in molten fluoride fluxes for low-carbon magnesium production by the SOM process by Milshtein J., Gratz E., Pati S., Powell A.C., Pal U.

“…The diffusion process was modeled using a numerical approach with an analytic solution to Fick’s second law. …”
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Mass Transfer during Atmospheric and Vacuum Frying of Chorizo by Piedad Margarita Montero Castillo, Lesly Torres Díaz, Sandy Torres Díaz, Diofanor Acevedo Correa, Raúl J. Martelo Gómez

“…The kinetics of moisture loss during atmospheric and vacuum frying was studied from the analytical solution of Fick’s second law for cylinder geometry. Oil absorption was also determined using a first-order kinetic model. …”
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Large-scale Cosmic-ray Anisotropies with 19 yr of Data from the Pierre Auger Observatory by A. Abdul Halim, P. Abreu, M. Aglietta, I. Allekotte, K. Almeida Cheminant, A. Almela, R. Aloisio, J. Alvarez-Muñiz, A. Ambrosone, J. Ammerman Yebra, G. A. Anastasi, L. Anchordoqui, B. Andrada, L. Andrade Dourado, S. Andringa, L. Apollonio, C. Aramo, P. R. Araújo Ferreira, E. Arnone, J. C. Arteaga Velázquez, P. Assis, G. Avila, E. Avocone, A. Bakalova, F. Barbato, A. Bartz Mocellin, J. A. Bellido, C. Berat, M. E. Bertaina, G. Bhatta, M. Bianciotto, P. L. Biermann, V. Binet, K. Bismark, T. Bister, J. Biteau, J. Blazek, C. Bleve, J. Blümer, M. Boháčová, D. Boncioli, C. Bonifazi, L. Bonneau Arbeletche, N. Borodai, J. Brack, P. G. Brichetto Orchera, F. L. Briechle, A. Bueno, S. Buitink, M. Buscemi, M. Büsken, A. Bwembya, K. S. Caballero-Mora, S. Cabana-Freire, L. Caccianiga, F. Campuzano, R. Caruso, A. Castellina, F. Catalani, G. Cataldi, L. Cazon, M. Cerda, B. Čermáková, A. Cermenati, J. A. Chinellato, J. Chudoba, L. Chytka, R. W. Clay, A. C. Cobos Cerutti, R. Colalillo, R. Conceição, A. Condorelli, G. Consolati, M. Conte, F. Convenga, D. Correia dos Santos, P. J. Costa, C. E. Covault, M. Cristinziani, C. S. Cruz Sanchez, S. Dasso, K. Daumiller, B. R. Dawson, R. M. de Almeida, B. de Errico, J. de Jesús, S. J. de Jong, J. R. T. de Mello Neto, I. De Mitri, J. de Oliveira, D. de Oliveira Franco, F. de Palma, V. de Souza, E. De Vito, A. Del Popolo, O. Deligny, N. Denner, L. Deval, A. di Matteo, C. Dobrigkeit, J. C. D’Olivo, L. M. Domingues Mendes, Q. Dorosti, J. C. dos Anjos, R. C. dos Anjos, J. Ebr, F. Ellwanger, M. Emam, R. Engel, I. Epicoco, M. Erdmann, A. Etchegoyen, C. Evoli, H. Falcke, G. Farrar, A. C. Fauth, T. Fehler, F. Feldbusch, A. Fernandes, B. Fick, J. M. Figueira, P. Filip, A. Filipčič, T. Fitoussi, B. Flaggs, T. Fodran, M. Freitas, T. Fujii, A. Fuster, C. Galea, B. García, C. Gaudu, P. L. Ghia, U. Giaccari, F. Gobbi, F. Gollan, G. Golup, M. Gómez Berisso, P. F. Gómez Vitale, J. P. Gongora, J. M. González, N. González, D. Góra, A. Gorgi, M. Gottowik, F. Guarino, G. P. Guedes, E. Guido, L. Gülzow, S. Hahn, P. Hamal, M. R. Hampel, P. Hansen, V. M. Harvey, A. Haungs, T. Hebbeker, C. Hojvat, J. R. Hörandel, P. Horvath, M. Hrabovský, T. Huege, A. Insolia, P. G. Isar, P. Janecek, V. Jilek, J. Jurysek, K.-H. Kampert, B. Keilhauer, A. Khakurdikar, V. V. Kizakke Covilakam, H. O. Klages, M. Kleifges, F. Knapp, J. Köhler, F. Krieger, M. Kubatova, N. Kunka, B. L. Lago, N. Langner, M. A. Leigui de Oliveira, Y. Lema-Capeans, A. Letessier-Selvon, I. Lhenry-Yvon, L. Lopes, J. P. Lundquist, A. Machado Payeras, D. Mandat, B. C. Manning, P. Mantsch, F. M. Mariani, A. G. Mariazzi, I. C. Mariş, G. Marsella, D. Martello, S. Martinelli, O. Martínez Bravo, M. A. Martins, H.-J. Mathes, J. Matthews, G. Matthiae, E. Mayotte, S. Mayotte, P. O. Mazur, G. Medina-Tanco, J. Meinert, D. Melo, A. Menshikov, C. Merx, S. Michal, M. I. Micheletti, L. Miramonti, S. Mollerach, F. Montanet, L. Morejon, K. Mulrey, R. Mussa, W. M. Namasaka, S. Negi, L. Nellen, K. Nguyen, G. Nicora, M. Niechciol, D. Nitz, D. Nosek, V. Novotny, L. Nožka, A. Nucita, L. A. Núñez, C. Oliveira, M. Palatka, J. Pallotta, S. Panja, G. Parente, T. Paulsen, J. Pawlowsky, M. Pech, J. Pȩkala, R. Pelayo, V. Pelgrims, L. A. S. Pereira, E. E. Pereira Martins, C. Pérez Bertolli, L. Perrone, S. Petrera, C. Petrucci, T. Pierog, M. Pimenta, M. Platino, B. Pont, M. Pothast, M. Pourmohammad Shahvar, P. Privitera, M. Prouza, S. Querchfeld, J. Rautenberg, D. Ravignani, J. V. Reginatto Akim, A. Reuzki, J. Ridky, F. Riehn, M. Risse, V. Rizi, E. Rodriguez, J. Rodriguez Rojo, M. J. Roncoroni, S. Rossoni, M. Roth, E. Roulet, A. C. Rovero, A. Saftoiu, M. Saharan, F. Salamida, H. Salazar, G. Salina, P. Sampathkumar, J. D. Sanabria Gomez, F. Sánchez, E. M. Santos, E. Santos, F. Sarazin, R. Sarmento, R. Sato, C. M. Schäfer, V. Scherini, H. Schieler, M. Schimassek, M. Schimp, D. Schmidt, O. Scholten, H. Schoorlemmer, P. Schovánek, F. G. Schröder, J. Schulte, T. Schulz, S. J. Sciutto, M. Scornavacche, A. Sedoski, A. Segreto, S. Sehgal, S. U. Shivashankara, G. Sigl, K. Simkova, F. Simon, R. Šmída, P. Sommers, R. Squartini, M. Stadelmaier, S. Stanič, J. Stasielak, P. Stassi, S. Strähnz, M. Straub, T. Suomijärvi, A. D. Supanitsky, Z. Svozilikova, Z. Szadkowski, F. Tairli, A. Tapia, C. Taricco, C. Timmermans, O. Tkachenko, P. Tobiska, C. J. Todero Peixoto, B. Tomé, Z. Torrès, A. Travaini, P. Travnicek, M. Tueros, M. Unger, R. Uzeiroska, L. Vaclavek, M. Vacula, J. F. Valdés Galicia, L. Valore, E. Varela, V. Vašíčková, A. Vásquez-Ramírez, D. Veberič, I. D. Vergara Quispe, V. Verzi, J. Vicha, J. Vink, S. Vorobiov, C. Watanabe, A. A. Watson, A. Weindl, M. Weitz, L. Wiencke, H. Wilczyński, D. Wittkowski, B. Wundheiler, B. Yue, A. Yushkov, O. Zapparrata, E. Zas, D. Zavrtanik, M. Zavrtanik, The Pierre Auger Collaboration

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