Articles citing this paper
General Method of Exact Solution of the Concentration?Dependent Diffusion Equation
JR Philip
13(1) pp.1 - 12
101 articles found in Crossref database.
Determination of the Size and Shape of Protein Molecules (1961)
Analysis of capillary water imbibition in sandstone via a combination of nuclear magnetic resonance imaging and numerical DEM modeling
Fu Teng-Fei,
Xu Tao,
Heap Michael J.,
Meredith Philip G.,
Yang Tian-hong,
Mitchell Thomas M., Nara Yoshitaka
Engineering Geology. 2021 285 p.106070
A nonlinear supercooled Stefan problem
Briozzo Adriana C., Natale Maria F.
Zeitschrift für angewandte Mathematik und Physik. 2017 68(2).
Some exact solutions for nonlinear desorptive diffusion
Brutsaert Wilfried
Zeitschrift für angewandte Mathematik und Physik. 1982 33(4). p.540
Conditionally integrable PDEs, non-classical symmetries and applications
Broadbridge Philip,
Bradshaw-Hajek Bronwyn H., Hutchinson Ashleigh J.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2023 479(2276).
Hydrology (1979)
Boundary value problems for strongly degenerate parabolic equations
Lavrentiev Jr. M.,
Broadbridge P., Belov V.
Communications in Partial Differential Equations. 1997 22(1-2). p.17
Nonlinear Formulation of Multicomponent Reactive Transport With Species‐Specific Dispersion Properties
Pérez‐Illanes Rodrigo,
Saaltink Maarten W., Fernàndez‐Garcia Daniel
Water Resources Research. 2024 60(3).
Numerical method to evaluate the influence of organic solvent absorption on the conductivity of polymeric composites
Carrillo Antonio,
Martı́n-Domı́nguez Ignacio R,
Rosas Armando, Márquez Alfredo
Polymer. 2002 43(23). p.6307
Concentration dependence of hydrogen diffusion in Armco iron
Govindan Namboodhiri T.K, Nanis Leonard
Acta Metallurgica. 1973 21(5). p.663
An efficient analytical model for horizontal infiltration in soils
Hayek Mohamed
Journal of Hydrology. 2018 564 p.1120
Pseudospectral methods provide fast and accurate solutions for the horizontal infiltration equation
Mathias Simon A., Sander Graham C.
Journal of Hydrology. 2021 598 p.126407
Flood frequency estimation by a derived distribution procedure
Loukas Athanasios
Journal of Hydrology. 2002 255(1-4). p.69
Analytical solution of transient radial air flow to an extraction well
Guo Weixing
Journal of Hydrology. 1997 194(1-4). p.1
The numerical solution of problems of planar growth where the diffusion coefficient is concentration dependent
Atkinson C
Acta Metallurgica. 1968 16(8). p.1019
Computational Methods in Water Resources Vol.1 Modeling Surface and Sub-Surface Flows, Proceedings of the VII International Conference, Proceedings of the VII International Conference (1988)
(1967)
Solution for 4th-order nonlinear axisymmetric surface diffusion by inverse method
Gallage Dilruk,
Triadis Dimetre,
Broadbridge Philip, Cesana Pierluigi
Physica D: Nonlinear Phenomena. 2020 405 p.132288
Derivation of flood frequency curves in poorly gauged Mediterranean catchments using a simple stochastic hydrological rainfall-runoff model
Aronica G.T., Candela A.
Journal of Hydrology. 2007 347(1-2). p.132
On the importance of accurate depiction of infiltration processes on modelled soil moisture and vegetation water stress
Manfreda Salvatore,
Scanlon Todd M., Caylor Kelly K.
Ecohydrology. 2010 3(2). p.155
The shear-driven Rayleigh problem for generalised Newtonian fluids
Duffy Brian R.,
Pritchard David, Wilson Stephen K.
Journal of Non-Newtonian Fluid Mechanics. 2014 206 p.11
Some explicit solutions to the non-linear diffusion equation
Tuck B
Journal of Physics D: Applied Physics. 1976 9(11). p.1559
New approach to model rehydration of dry food particulates utilizing principles of liquid transport in porous media
Sam Saguy I.,
Marabi Alejandro, Wallach Rony
Trends in Food Science & Technology. 2005 16(11). p.495
THEORETICAL SOLUTION OF THE UNSTEADY UNSATURATED FLOW PROBLEMS IN SOILS
LIAKOPOULOS ARISTIDES C.
International Association of Scientific Hydrology. Bulletin. 1965 10(1). p.5
Self similar solution of plasma equations
Lonngren K E
Proceedings of the Indian Academy of Sciences - Section A. 1977 86(2). p.125
Nonlinear Partial Differential Equations in Engineering (1965)
Concentration dependence of D in the growth or dissolution of precipitates
Atkinson C
Acta Metallurgica. 1967 15(7). p.1207
The Theory of Transformations in Metals and Alloys (2002)
Точні розв'язки з узагальненим відокремленням змінних рівняння нелінійної теплопровідності з джерелом
Barannyk A.,
Barannyk T., Yuryk I.
Ukrains’kyi Matematychnyi Zhurnal. 2024 76(2). p.179
Macroscopic analysis of the behavior of colloidal suspensions
Philip J.R., Smiles D.E.
Advances in Colloid and Interface Science. 1982 17(1). p.83
Estimation of Soil Moisture Profile and Diffusivity Using Simple Laboratory Procedures
Evangelides Chris,
Arampatzis George, Tzimopoulos Christos
Soil Science. 2010 175(3). p.118
Nonlinear diffusion and particle production in relativistic systems
Wolschin Georg
Nuclear Physics A. 2009 820(1-4). p.295c
The concise formulation of diffusive sorption of water in a dry soil
Brutsaert Wilfried
Water Resources Research. 1976 12(6). p.1118
Diffusion of small molecules in polymers
Frisch H. L., Stern S. Alexander
Critical Reviews in Solid State and Materials Sciences. 1983 11(2). p.123
ACE Guided-Transformation Method for Estimation of the Coefficient of Soil-Water Diffusivity
De Veaux Richard D., Steele J. Michael
Technometrics. 1989 31(1). p.91
Mass-time and space-time fractional partial differential equations of water movement in soils: Theoretical framework and application to infiltration
Su Ninghu
Journal of Hydrology. 2014 519 p.1792
Soil water diffusivity obtained from visual inspection experiment and comparison with γ-ray measurements
Evangelides C.,
Arampatzis G., Tzimopoulos C.
Desalination and Water Treatment. 2017 86 p.327
Patterns and scaling properties of surface soil moisture in an agricultural landscape: An ecohydrological modeling study
Korres W.,
Reichenau T.G., Schneider K.
Journal of Hydrology. 2013 498 p.89
Analytical solutions of the linearized Richards equation for discrete arbitrary initial and boundary conditions
Menziani Marilena,
Pugnaghi Sergio, Vincenzi Sergio
Journal of Hydrology. 2007 332(1-2). p.214
Predictions of rainfall-runoff response and soil moisture dynamics in a microscale catchment using the CREW model
Lee H.,
Zehe E., Sivapalan M.
Hydrology and Earth System Sciences. 2007 11(2). p.819
Supercooled Stefan problem with a Neumann type boundary condition
Briozzo Adriana C.
Electronic Journal of Differential Equations. 2020 2020(01-132).
A method for estimating soil water diffusivity from moisture profiles and its application across an experimental catchment
Espejo A.,
Giráldez J.V.,
Vanderlinden K.,
Taguas E.V., Pedrera A.
Journal of Hydrology. 2014 516 p.161
Handbook of Nonlinear Partial Differential Equations (2003)
Analytical solution of Fick's second law when the diffusion coefficient varies directly as concentration
Pelton A.D., Etsell T.H.
Acta Metallurgica. 1972 20(11). p.1269
Analytical solutions to the transient, unsaturated transport of water and contaminants through horizontal porous media
Sander G.C., Braddock R.D.
Advances in Water Resources. 2005 28(10). p.1102
A unified theory of the self-similar supersonic Marshak wave problem
Krief Menahem, McClarren Ryan G.
Physics of Fluids. 2024 36(5).
Nonlinear Ordinary Differential Equations in Transport Processes (1968)
Watershed modeling applications with a modular physically-based and spatially-distributed watershed educational toolbox
Huning Laurie S., Margulis Steven A.
Environmental Modelling & Software. 2015 68 p.55
Thin-source concentration-dependent diffusion: A full solution
Eng Genghmun
Physical Review B. 1989 39(3). p.1518
A simple method for modeling the concentration-dependent water sorption in reinforced polymeric materials
Joannès S.,
Mazé L., Bunsell A.R.
Composites Part B: Engineering. 2014 57 p.219
Explicit Approximate Analytical Solution of the Horizontal Diffusion Equation
Tzimopoulos Christos,
Evangelides Chris, Arampatzis George
Soil Science. 2015 180(2). p.47
Exact solutions for concentration dependent diffusion and the inverse complementary error function
Shampine L.F.
Journal of the Franklin Institute. 1973 295(3). p.239
Two-zone model for solid—liquid separation by filtration and expression
Buttersack Christoph
Chemical Engineering Science. 1994 49(8). p.1145
Estimation of Flood Frequencies for Ungaged Catchments
Raines Timothy H., Valdés Juan B.
Journal of Hydraulic Engineering. 1993 119(10). p.1138
Investigation of the Flux–Concentration Relation for Horizontal Flow in Soils
Kargas George,
Londra Paraskevi, Kerkides Petros
Water. 2019 11(12). p.2442
Random fractional partial differential equations and solutions for water movement in soils: Theory and applications
Su Ninghu
Hydrological Processes. 2023 37(3).
SOIL WATER DIFFUSIVITY DETERMINATION BY GENERAL SIMILARITY THEORY1
Shao Mingan, Horton Robert
Soil Science. 1996 161(11). p.727
Fundamentals of Transport Phenomena in Porous Media (1972)
Determination of water permeability for a moisture transport model with minimized batch effect
Zhang Zhidong, Scherer George
Construction and Building Materials. 2018 191 p.193
A physically based stochastic-deterministic procedure for the estimation of flood frequency
Loukas Athanasios,
Quick Michael C., Russell Samuel O.
Water Resources Management. 1996 10(6). p.415
A simplified stochastic model for infiltration into a heterogeneous soil forced by random precipitation
Castelli Fabio
Advances in Water Resources. 1996 19(3). p.133
Free boundary problems with nonlinear diffusion
Broadbridge P.,
Tritscher P., Avagliano A.
Mathematical and Computer Modelling. 1993 18(10). p.15
New approximate solutions of horizontal confined–unconfined flow
Wang Xu-Sheng,
Wan Li, Hu Bill
Journal of Hydrology. 2009 376(3-4). p.417
Exact Solutions with Generalized Separation of Variables in the Nonlinear Heat Equation
Barannyk A. F.,
Barannyk T. A., Yuryk I. I.
Ukrainian Mathematical Journal. 2022 74(3). p.330
Diffusion Phenomena (2001)
HE HYDROLOGY OF OVERLAND FLOW IN WETLANDS
KADLEC ROBERT H.,
HAMMER DAVID E.,
NAM IN-SIK, WILKES JAMES O.
Chemical Engineering Communications. 1981 9(1-6). p.331
Etude expérimentale du transfert hydrique dans un sol initialement non saturé
Zadjaoui Abdeldjalil,
Bekkouche Abdelmalek,
Magnan Jean-Pierre, Reiffsteck Philippe
European Journal of Environmental and Civil Engineering. 2009 13(10). p.1221
Diffusional formation of ferrite in iron and its alloys
Bhadeshia H.K.D.H.
Progress in Materials Science. 1985 29(4). p.321
Magnetic viscosity in a UPtAl single crystal
Musbnikov N.V.,
Andreev A.V.,
Korolyov A.V., Shiokawa Y.
Journal of Alloys and Compounds. 2000 305(1-2). p.188
Kinetic diffusion in polymer gels
Lightfoot Edwin J.
Physica A: Statistical Mechanics and its Applications. 1990 169(2). p.191
Similarity solutions for nonlinear diffusion ? a new integration procedure
Hill J. M.
Journal of Engineering Mathematics. 1989 23(2). p.141
Exact solutions to radially symmetric two-phase flow for an arbitrary diffusivity
Sander G.C.,
Parlange J.-Y.,
Lisle I.G., Weeks S.W.
Advances in Water Resources. 2005 28(10). p.1112
A class of similar solutions of the non-linear diffusion equation
Pert G J
Journal of Physics A: Mathematical and General. 1977 10(4). p.583
History of the Kohlrausch (stretched exponential) function: Pioneering work in luminescence
Berberan‐Santos M.,
Bodunov E.N., Valeur B.
Annalen der Physik. 2008 520(7). p.460
Validation of an analytical method for determining soil hydraulic properties of stony soils using experimental data
Ma DongHao,
Shao MingAn,
Zhang JiaBao, Wang QuanJiu
Geoderma. 2010 159(3-4). p.262
Storm‐coverage effect on dynamic flood‐frequency analysis: empirical data analysis
Moon Jangwon,
Kim Joong‐Hoon, Yoo Chulsang
Hydrological Processes. 2004 18(1). p.159
A perturbation solution for a nonlinear diffusion equation
Liu Philip L.‐F.
Water Resources Research. 1976 12(6). p.1235
Surface-concentration-dependent nonlinear diffusion
King J. R.
European Journal of Applied Mathematics. 1992 3(1). p.1
Explicit solutions to the one-phase Stefan problem with temperature-dependent thermal conductivity and a convective term
Natale Marı́a F., Tarzia Domingo A.
International Journal of Engineering Science. 2003 41(15). p.1685
THEORETICAL APPROACH TO THE SOLUTION OF THE INFILTRATION PROBLEM
LIAKOPOULOS A. C.
International Association of Scientific Hydrology. Bulletin. 1966 11(1). p.69
Method of determining the diffusion profile for a concentration dependent diffusion coefficient
Litovskii M. A., Malkovich R. Sh.
Physica Status Solidi (a). 1976 36(2). p.K145
Agricultural Physics (1966)
(1969)
Transient gas flow around boreholes
Chan Derek Y. C.,
Hughes Barry D., Paterson Lincoln
Transport in Porous Media. 1993 10(2). p.137
On a non-linear moving boundary problem for a diffusion–convection equation
Briozzo A.C., Natale M.F.
International Journal of Non-Linear Mechanics. 2012 47(6). p.712
On a weighted residual method for absorption
Lockington D. A.
Transport in Porous Media. 1994 16(3). p.299
Effect of solute concentration on the diffusivity of carbon dioxide in water
Tang Y.P., Himmelblau D.M.
Chemical Engineering Science. 1965 20(1). p.7
Unified Testing Method for Measuring Diffusion Coefficients for Unsaturated Soil Drying and Wetting in Laboratory
Mabirizi Daniel, Bulut Rifat
Transportation Research Record: Journal of the Transportation Research Board. 2010 2170(1). p.109
Improved analytical expressions for transient specific yield in shallow groundwater drainage
Xiao Xue,
Xu Xu, Huang Guanhua
Journal of Hydrology. 2021 597 p.126186
Development and testing of a large, transportable rainfall simulator for plot-scale runoff and parameter estimation
Wilson T. G.,
Cortis C.,
Montaldo N., Albertson J. D.
Hydrology and Earth System Sciences. 2014 18(10). p.4169
Generalisation of various hydrological and environmental transport models using the Fokker–Planck equation
Su Ninghu
Environmental Modelling & Software. 2004 19(4). p.345
The numerical solution of non-linear partial differential equations by the method of lines
Graney L., Richardson A.A.
Journal of Computational and Applied Mathematics. 1981 7(4). p.229
On exact solutions of the nonlinear heat equation
Barannyk A.F.,
Barannyk T.A. , Yuryk I.I.
Reports of the National Academy of Sciences of Ukraine. 2019 5 p.11
Exact solvability of the Mullins nonlinear diffusion model of groove development
Broadbridge P.
Journal of Mathematical Physics. 1989 30(7). p.1648
Infiltration from supply at constant water content: an integrable model
Broadbridge P.,
Triadis D., Hill J. M.
Journal of Engineering Mathematics. 2009 64(2). p.193
Theoretical and Applied Mechanics (1973)
Regional Assessment of Global Change Impacts (2016)
Modelling of soil nitrogen dynamics within the decision support system DANUBIA
Klar C.W.,
Fiener P.,
Neuhaus P.,
Lenz-Wiedemann V.I.S., Schneider K.
Ecological Modelling. 2008 217(1-2). p.181
Handbook on Plasma Instabilities (1982)
Modeling moisture and thermal transport in unsaturated porous media
Yeh Gour-Tsyh, Luxmoore Robert J.
Journal of Hydrology. 1983 64(1-4). p.299
Efficient Approach to Solving Transient Unsaturated Flow Problems. I: Analytical Solutions
Cavalcante André Luís Brasil, Zornberg Jorge Gabriel
International Journal of Geomechanics. 2017 17(7).
