Publikationen

Renormalisation on Sierpinski-type Fractals
R. Hilfer, A. Blumen
Journal of Physics A: Mathematical and General 17, L573-L545 (1984)
10.1088/0305-4470/17/10/004
Renormalisation on Symmetric Fractals
R. Hilfer, A. Blumen
J.Phys.A: Math. Gen. 17, L783 (1984)
https://doi.org/10.1088/0305-4470/17/14/011
Stochastic Models for Corporate Planning
R. Hilfer
GBI — Verlag, München, 1985
ISBN-10: 3890030157, ISBN-13: 978-3890030159
Renormalisation Group Approach in the Theory of Disordered Systems
R. Hilfer
Verlag Harri Deutsch, Frankfurt, 1986
ISBN-10: 3871449792, ISBN-13: 978-3871449796
On Finitely Ramified Fractals and Their Extensions
R. Hilfer, A. Blumen
in: Fractals in Physics
edited by: L. Pietronero and E. Tosatti
Elsevier Publishing Co., Amsterdam, 33 (1986)
Fluctuation-Dissipation on Fractals: A Probabilistic Approach
R. Hilfer, A. Blumen
in: Time Dependent Effects in Disordered Materials
edited by: R.Pynn and T. Riste
Plenum Press, New York, 217 (1987)
On Dense Branching Phase Separation
R. Hilfer, S. Alexander, R. Bruinsma
in: Time Dependent Effects in Disordered Materials
edited by: R.Pynn and T. Riste
Plenum Press, New York, 417 (1987)
https://doi.org/10.1007/978-1-4684-7476-3_43
ISBN 978-1-4684-7478-7, ISBN 978-1-4684-7476-3
Probabilistic Interpretation of the Einstein Relation
R. Hilfer, A. Blumen
Physical Review A 37, 578 (1988)
10.1103/PhysRevA.37.578
Phase Separation by Coupled Single-Crystal Growth and Polycrystalline Fingering in Al/Ge: Theory
S. Alexander, R. Bruinsma, R. Hilfer, G. Deutscher, Y. Lereah
Physical Review Letters 60, 1514 (1988)
10.1103/PhysRevLett.60.1514
Continuous Time Random Walk Approach to Dynamic Percolation
R. Hilfer, R. Orbach
Chemical Physics 128, 275 (1988)
https://doi.org/10.1016/0301-0104(88)85076-6
Pattern Formation at Liquid Interfaces
B. Heidel, C. Knobler, R. Hilfer, R. Bruinsma
Physical Review Letters 60, 2492 (1988)
10.1103/PhysRevLett.60.2492
Theoretical Aspects of Polycrystalline Pattern Growth in Al/Ge Films
R. Hilfer
in: Fluctuation Phenomena and Pattern Growth
edited by: H.E. Stanley and N. Ostrowsky
Kluwer Academic Publishing, Dordrecht, 127 (1988)
https://doi.org/10.1007/978-94-009-2653-0_23
ISBN 978-94-009-2653-0, ISBN 978-0-7923-0073-1
Correlated Random Walks in Dynamically Disordered Systems
R. Hilfer, R. Orbach
in: Dynamical Processes in Condensed Molecular Systems
edited by: J. Klafter and J. Jortner and A. Blumen
World Scientific Publ.Co., Singapore, 175 (1989)
https://doi.org/10.1142/9789814434379_0009
ISBN: 978-981-4434-37-9
The Continuum Limit for Selfsimilar Laplacians and the Greens Function Localization Exponent
R. Hilfer
UCLA-Report 982051, Los Angeles, 1989
Theoretical Aspects of Realistic Spin Glass Models
R. Hilfer
in: New Trends in Magnetism
edited by: M.D. Coutinho-Filho and S.M. Rezende
World Scientific Publ.Co., Singapore, 32 (1989)
Correlation Effects on Hopping Transport in a Disordered Medium
R. Hilfer
in: Dynamical Processes in Condensed Molecular Systems
edited by: A. Blumen and J. Klafter and D. Haarer
World Scientific Publ.Co., Singapore, 302 (1990)
https://doi.org/10.1142/9789814540261
ISBN: 978-981-4540-26-1
Frequency Dependent Response and Dynamic Disorder
R. Hilfer
Journal of Non-Crystalline Solids 131–133, 213 (1991)
https://doi.org/10.1016/0022-3093(91)90303-N
Correlated Hopping in a Disordered Medium
R. Hilfer
Physical Review B 44, 628 (1991)
10.1103/PhysRevB.44.628
Random Walks with Short Memory in a Disordered Environment
R. Hilfer
Physical Review B 44, 638 (1991)
10.1103/PhysRevB.44.638
Geometric and Dielectric Characterization of Porous Media
R. Hilfer
Physical Review B 44, 60 (1991)
https://doi.org/10.1103/PhysRevB.44.60
Analysis of Multilayer Adsorption Models without Screening
R. Hilfer, J.-S. Wang
Journal of Physics A: Mathematical and General 24, L389 (1991)
10.1088/0305-4470/24/7/013
Thermodynamic Scaling Derived via Analytic Continuation from the Classification of Ehrenfest
R. Hilfer
Physica Scripta 44, 321 (1991)
10.1088/0031-8949/44/4/002
Local Porosity Theory for Flow in Porous Media
R. Hilfer
Physical Review B 45, 7115 (1992)
https://doi.org/10.1103/PhysRevB.45.7115
Geometry, Dielectric Response and Scaling in Porous Media
R. Hilfer
Physica Scripta T44, 51 (1992)
10.1088/0031-8949/1992/t44/007
Orientational Ordering in Lipid Monolayers: A Two-dimensional Model of Rigid Rods Grafted onto a Lattice
M. Scheringer, R. Hilfer, K. Binder
Journal of Chemical Physics 96, 2269 (1992)
https://doi.org/10.1063/1.462077
Multiscaling and the Classification of Continuous Phase Transitions
R. Hilfer
Physical Review Letters 68, 190 (1992)
10.1103/PhysRevLett.68.190
Grain Size Distribution for Competitive Growth with Nucleation
R. Hilfer, P. Meakin
Zeitschrift für Physik B 88, 223 (1992)
https://doi.org/10.1007/BF01323576
Microstructural Sensitivity of Local Porosity Distributions
F. Boger, J. Feder, R. Hilfer, T. Jøssang
Physica A 187, 55 (1992)
https://doi.org/10.1016/0378-4371(92)90408-I
Scaling Theory and the Classification of Phase Transitions
R. Hilfer
Mod. Phys. Lett. B 6, 773 (1992)
https://doi.org/10.1142/S0217984992000855
Dynamic and geometric correlation effects in disordered systems
R. Hilfer
Habilitationsschrift, Universität Mainz, 1992
Modeling of Orientational Ordering in Lipid Monolayers
M.Kreer, M.Scheringer, K.Binder, K.Kremer, R.Hilfer
in: Computer Simulation Studies in Condensed Matter Physics IV
edited by: D.P. Landau and K.K. Mon and H.B. Schüttler
Springer Verlag, Berlin, 159 (1993)
https://doi.org/10.1007/978-3-642-84878-0_13
ISBN 978-3-642-84878-0
Local Porosity Theory for Electrical and Hydrodynamical Transport through Porous Media
R. Hilfer
Physica A 194, 406 (1993)
https://doi.org/10.1016/0378-4371(93)90372-B
Dielectric Dispersion Measurements of Salt Water Saturated Porous Glass Compared with Local Porosity Theory
B.D. Hansen, E. Haslund, R. Hilfer, B. Nøst
Materials Research Society Proceedings 290, 185 (1993)
https://doi.org/10.1557/PROC-290-185
Classification Theory for Phase Transitions
R. Hilfer
International Journal of Modern Physics B 7, 4371 (1993)
https://doi.org/10.1142/S0217979293003711
Classification Theory for Anequilibrium Phase Transitions
R. Hilfer
Physical Review E 48, 2466 (1993)
10.1103/PhysRevE.48.2466
Fractal Behaviour of CO_2 Pits
T. Johnsen, Th. Walmann, R. Hilfer, P. Meakin, T. Jøssang, J. Feder
Fracton A/S, Oslo, 1993
On a New Class of Phase Transitions
R. Hilfer
in: Random Magnetism and High-Temperature Superconductivity
edited by: W.P. Beyermann and N.L. Huang-Liu and D.E. MacLaughlin
World Scientific Publ. Co., Singapore, 85 (1994)
https://doi.org/10.1142/2378
978-981-4550-80-2
Two Phase Flow and Relative Permeabilities
R. Hilfer, P.E. Øren
Statoil Publication Nr. F&U-LoU-94001, Trondheim, 1993
Thermal Field Theory
R. Hilfer
UR.Nr. 451/92 Weirich, Ingelheim, 1992
Local Porosity Theory for the Frequency Dependent Dielectric Function of Porous Rocks and Polymer Blends
R. Hilfer, B.Nøst, E.Haslund, Th.Kautzsch, B.Virgin, B.D.Hansen
Physica A 207, 19 (1994)
https://doi.org/10.1016/0378-4371(94)90350-6
Dimensional Analysis of Pore Scale and Field Scale Immiscible Displacement
R. Hilfer, P.E. Øren
Transport in Porous Media 22, 53 (1996)
https://doi.org/10.1007/BF00974311
Absence of Hyperscaling Violations for Phase Transitions with Positive Specific Heat Exponent
R. Hilfer
Zeitschrift für Physik B: Condensed Matter 96, 63 (1994)
https://doi.org/10.1007/BF01313016
Are Critical Finite Size Scaling Functions Calculable From Knowledge of an Appropriate Critical Exponent ?
R. Hilfer, N.B.Wilding
J. Phys. A: Math. Gen. 28, L281 (1995)
10.1088/0305-4470/28/10/001
Measurement of Local Porosities and Dielectric Dispersion for a Water Saturated Porous Medium
E. Haslund, B.D. Hansen, R. Hilfer, B. Nøst
Journal of Applied Physics 76, 5473 (1994)
https://doi.org/10.1063/1.357205
Continuum Monte-Carlo Simulations of Phase Transitions in Rodlike Molecules at Surfaces
R. Hilfer, F.M. Haas, K. Binder
Il Nuovo Cimento D 16, 1297-1303 (1994)
https://doi.org/10.1007/BF02458816
Layers of Semiflexible Chain Molecules Endgrafted at Interfaces: An Off-Lattice Monte Carlo Simulation
F.M. Haas, R. Hilfer, K. Binder
Journal of Chemical Physics 102, 2960-2969 (1995)
https://doi.org/10.1063/1.468604
Fractional Master Equations and Fractal Time Random Walks
R. Hilfer, L. Anton
Physical Review E, Rapid Communication 51, R848 (1995)
https://doi.org/10.1103/PhysRevE.51.R848
Exact Solutions for a Class of Fractal Time Random Walks
R. Hilfer
Fractals 3(1), 211-216 (1995)
https://doi.org/10.1142/S0218348X95000163
Fractional Dynamics, Irreversibility and Ergodicity Breaking
R. Hilfer
Chaos, Solitons and Fractals 5, 1475 (1995)
https://doi.org/10.1016/0960-0779(95)00027-2
Transport and Relaxation Phenomena in Porous Media
R. Hilfer
Advances in Chemical Physics XCII, 299 (1996)
ISBN: 978-0-470-14204-2
Foundations of Fractional Dynamics
R. Hilfer
Fractals 3, 549 (1995)
https://doi.org/10.1142/S0218348X95000485
An Extension of the Dynamical Foundation for the Statistical Equilibrium Concept
R. Hilfer
Physica A 221, 89-96 (1995)
https://doi.org/10.1016/0378-4371(95)00240-8
Probabilistic Methods, Upscaling and Fractal Statistics in Porous Media
R. Hilfer
Zentralblatt für Geologie und Paläontologie, Teil I 11/12, 1035 (1997)
Local Porosity Theory for the Transition from Microscales to Macroscales in Porous Media
R. Hilfer, B. Virgin, T. Rage
ERCOFTAC Bull. 28, 6 (1996)
Rescaling Relations between Two- and Three Dimensional Local Porosity Distributions for Natural and Artificial Porous Media
B. Virgin, E. Haslund, R. Hilfer
Physica A 232, 1-10 (1996)
https://doi.org/10.1016/0378-4371(96)00131-8
Continuum Monte Carlo Simulation at Constant Pressure of Stiff Chain Molecules at Surfaces
F. M. Haas, R. Hilfer
Journal of Chemical Physics 105, 3859 (1996)
https://doi.org/10.1063/1.472206
Phase Transitions in Dense Lipid Monolayers Grafted to a Surface: Monte Carlo Investigation of a Coarse-Grained Off-Lattice Model
F. M. Haas, R. Hilfer, K. Binder
The Journal of Physical Chemistry 100 (37), 15290-15300 (1996)
DOI: 10.1021/jp9610980
Local Percolation Probabilities for a Natural Sandstone
R. Hilfer, T. Rage, B. Virgin
Physica A 241, 105 (1997)
https://doi.org/10.1016/S0378-4371(97)00067-8
Local Entropy Characterization of Correlated Random Microstructures
C. Andraud, A. Beghdadi, E. Haslund, R. Hilfer, J. Lafait, B. Virgin
Physica A 235, 307 (1997)
https://doi.org/10.1016/S0378-4371(96)00354-8
Scaling of Multiphase Flow
R. Hilfer, P.E. Øren
Statoil Publication Nr. F&U-LoU-96015, Trondheim, 1996
Statistical Prediction of Corrosion Front Penetration
T. Johnsen, R. Hilfer
Phys.Rev. E 55, 5433 (1997)
https://doi.org/10.1103/PhysRevE.55.5433
Fractional Derivatives in Static and Dynamic Scaling
R. Hilfer
in: Scale Invariance and Beyond
edited by: B. Dubrulle and F. Graner and D. Sornette
Springer, Berlin, 53 (1997)
10.1007/978-3-662-09799-1
978-3-540-64000-4
Threedimensional Local Porosity Analysis of Porous Media
B. Biswal, C. Manwart, R. Hilfer
Physica A 255, 221 (1998)
https://doi.org/10.1016/S0378-4371(98)00111-3
Macroscopic Equations of Motion for Two Phase Flow in Porous Media
R. Hilfer
Physical Review E 58, 2090 (1998)
https://doi.org/10.1103/PhysRevE.58.2090
On Fractional Diffusion and its Relation with Continuous Time Random Walks
R. Hilfer
in: Anomalous Diffusion: From Basis to Applications
edited by: R. Kutner, A. Pekalski and K. Sznajd-Weron
Lecture Notes in Physics, vol. 519,Springer, Berlin, 77 (1999)
10.1007/BFb0106828
978-3-662-14242-4
Microstructure Analysis of Reconstructed Porous Media
B. Biswal, R. Hilfer
Physica A 266, 307 (1999)
https://doi.org/10.1016/S0378-4371(98)00607-4
Applications of Fractional Calculus in Physics
R. Hilfer
World Scientific Publ. Co., Singapore, 2000
https://doi.org/10.1142/3779
ISBN: 978-981-02-3457-7
Trapping and Mobilization of Residual Fluid During Capillary Desaturation in Porous Media
L. Anton, R. Hilfer
Physical Review E 59, 6819 (1999)
https://doi.org/10.1103/PhysRevE.59.6819
Reconstruction of Random Media Using Monte Carlo Methods
C. Manwart, R. Hilfer
Physical Review E 59, 5596 (1999)
https://doi.org/10.1103/PhysRevE.59.5596
Quantitative Prediction of Effective Material Properties of Heterogeneous Media
J. Widjajakusuma, B. Biswal, R. Hilfer
Computational Materials Science 16, 70 (1999)
https://doi.org/10.1016/S0927-0256(99)00047-6
Exact and Approximate Calculations for Conductivity of Sandstones
J. Widjajakusuma, C. Manwart, B. Biswal, R. Hilfer
Physica A 270, 325 (1999)
https://doi.org/10.1016/S0378-4371(99)00141-7
Macroscopic Dielectric Constant for Microstructures of Sedimentary Rocks
R. Hilfer, J. Widjajakusuma, B. Biswal
Granular Matter 2, 137 (1999)
https://doi.org/10.1007/s100359900035
Quantitative Analysis of Experimental and Synthetic Microstructures for Sedimentary Rock
B. Biswal, C. Manwart, R. Hilfer, S. Bakke, P.E. Øren
Physica A 273, 452 (1999)
https://doi.org/10.1016/S0378-4371(99)00248-4
Old Problems and New Solutions for Multiphase Flow in Porous Media
R. Hilfer, H. Besserer
in: Porous Media: Physics, Mo\-dels, Simulation
edited by: A. Dmitrievsky and M. Panfilov
World Scientific Publ. Co., Singapore, 133-144 (2000)
https://doi.org/10.1142/9789812817617_0008
ISBN: 978-981-02-4126-1
Macroscopic Two Phase Flow in Porous Media
R. Hilfer, H. Besserer
Physica B 279, 125 (2000)
https://doi.org/10.1016/S0921-4526(99)00694-8
On the Analysis of Spatial Binary Images
C. Lang, J. Ohser, R. Hilfer
Journal of Microscopy 203, 303 (2001)
https://doi.org/10.1046/j.1365-2818.2001.00899.x
Macroscopic equations for twophase flow
R. Hilfer
Statoil Publication Nr. F&U-LoU-9901x, Trondheim, 1999
Fractional Time Evolution
R. Hilfer
in: Applications of Fractional Calculus in Physics
edited by: R. Hilfer
World Scientific, Singapore, 87-130 (2000)
https://doi.org/10.1142/3779
ISBN: 978-981-02-3457-7
Fractional Calculus and Regular Variation in Thermodynamics
R. Hilfer
in: Applications of Fractional Calculus in Physics
edited by: R. Hilfer
World Scientific, Singapore, 429-463 (2000)
https://doi.org/10.1142/3779
ISBN: 978-981-02-3457-7
Fractional Evolution Equations and Irreversibility
R. Hilfer
in: Traffic and Granular Flow’99
edited by: D. Helbing and H. Herrmann and M. Schreckenberg and D. Wolf
Springer, Berlin, 215 (2000)
10.1007/978-3-642-59751-0
ISBN: 978-3-642-64109-1
Local Porosity Theory and Stochastic Reconstruction for Porous Media
R. Hilfer
in: Räumliche Statistik und Statistische Physik
edited by: D. Stoyan and K. Mecke
Springer, Berlin, 203 (2000)
10.1007/3-540-45043-2
ISBN: 978-3-642-08725-7
Fractional Diffusion based on Riemann-Liouville Fractional Derivatives
R. Hilfer
The Journal of Physical Chemistry B 104, 3914-3917 (2000)
DOI: 10.1021/jp9936289
Erosion-Dilation Analysis for Experimental and Synthetic Microstructures of Sedimentary Rock
A. Tscheschel, D. Stoyan, R. Hilfer
Physica A 284, 46 (2000)
https://doi.org/10.1016/S0378-4371(00)00116-3
Stochastic Reconstruction of Sandstones
C. Manwart, S. Torquato, R. Hilfer
Physical Review E 62, 893 (2000)
https://doi.org/10.1103/PhysRevE.62.893
Physics on fast computers: What are computer experiments good for?
R. Hilfer, S. Schwarzer, F. Gähler, J. Roth
Stuttgarter Uni Kurier 86 2/2000, 53 (2000)
Effective Physical Properties of Sandstones
J. Widjajakusuma, R. Hilfer
in: IUTAM Symposium on Theoretical and Numerical Methods in Continuum Mechanics of Porous Materials
edited by: W. Ehlers
Solid Mechanics and Its Applications, vol. 87,Kluwer, Dordrecht, 113 (2001)
10.1007/0-306-46953-7
ISBN: 978-0-7923-6766-6
Review on Scale Dependent Characterization of the Microstructure of Porous Media
R. Hilfer
Transport in Porous Media 46, 373 (2002)
https://doi.org/10.1023/A:1015014302642
Permeability and Conductivity for Reconstruction Models of Porous Media
R. Hilfer, C. Manwart
Physical Review E 64, 21304 (2001)
https://doi.org/10.1103/PhysRevE.64.021304
Analytical representations for relaxation functions of glasses
R. Hilfer
Journal of Non-Crystalline Solids 305, 122 (2002)
https://doi.org/10.1016/S0022-3093(02)01088-8
H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems
R. Hilfer
Physical Review E 65, 061510 (2002)
https://doi.org/10.1103/PhysRevE.65.061510
Physics on the Computer
R. Hilfer
ICP, Stuttgart, 2002
Fitting the excess wing in the dielectric alpha-relaxation of propylene carbonate
R. Hilfer
Journal of Physics: Condensed Matter 14, 2297 (2002)
https://doi.org/10.1088/0953-8984/14/9/318
Lattice-Boltzmann and finite-difference simulations for the permeability of three-dimensional porous media
C. Manwart, U. Aaltosalmi, A. Koponen, R. Hilfer, J. Timonen
Physical Review E 66, 016702 (2002)
https://doi.org/10.1103/PhysRevE.66.016702
Experimental Evidence for Fractional Time Evolution in Glass Forming Materials
R. Hilfer
Chem.Phys. 284, 399 (2002)
https://doi.org/10.1016/S0301-0104(02)00670-5
Strange Kinetics
R. Hilfer, R. Metzler, A. Blumen, J. Klafter(eds)
Chemical Physics 284, 1 (2002)
https://doi.org/10.1016/S0301-0104(02)00801-7
Numerical Simulation of Creeping Fluid Flow in Reconstruction Models of Porous Media
C. Manwart, R. Hilfer
Physica A 314, 706 (2002)
https://doi.org/10.1016/S0378-4371(02)01193-7
On Fractional Relaxation
R. Hilfer
in: Scaling and Disordered Systems
edited by: F. Family and M. Daoud and H. Herrmann and H.E. Stanley
World Scientific, Singapore, 251 (2002)
https://doi.org/10.1142/9789812778109_0026
ISBN: 978-981-02-4838-3
On Fractional Relaxation
R. Hilfer
Fractals 11, 251 (2003)
https://doi.org/10.1142/S0218348X03001914
Quantitative comparison of meanfield mixing laws for conductivity and dielectric constant of porous media
R. Hilfer, J. Widjajakusuma, B. Biswal
Physica A 318, 319 (2003)
https://doi.org/10.1016/S0378-4371(02)01197-4
Thermodynamic potentials for the infinite range Ising model with strong coupling
R. Hilfer
Physica A 320, 429 (2003)
https://doi.org/10.1016/S0378-4371(02)01585-6
Remarks on Fractional Time
R. Hilfer
in: Time, Quantum and Information
edited by: L. Castell and O. Ischebeck
Springer, Berlin, 235 (2003)
10.1007/978-3-662-10557-3
ISBN: 978-3-540-44033-8
On fractional diffusion and continuous time random walks
R. Hilfer
Physica A 329, 35 (2003)
https://doi.org/10.1016/S0378-4371(03)00583-1
Numerical Results for the Generalized Mittag-Leffler Function
H.J. Seybold, R. Hilfer
Fractional Calculus and Applied Analysis 8, 127 (2005)
Multicanonical Monte-Carlo Study and Analysis of Tails for the Order-Parameter Distribution of the Two-Dimensional Ising Model
R. Hilfer, B. Biswal, H.G. Mattutis, W. Janke
Physical Review E 68, 046123 (2003)
https://doi.org/10.1103/PhysRevE.68.046123
Dimensional analysis and upscaling of two-phase flow in porous media with piecewise constant heterogeneities
R. Hilfer, R. Helmig
Advances in Water Resources 27, 1033 (2004)
https://doi.org/10.1016/j.advwatres.2004.07.003
Multicanonical Simulations of the Tails of the Order-Parameter Distribution of the two-dimensional Ising Model
R. Hilfer, B. Biswal, H.G. Mattutis, W. Janke
Computer Physics Communications 169, 230 (2005)
https://doi.org/10.1016/j.cpc.2005.03.053
Characterization of Porous Media by Local Porosities, Minkowski- and Non-Minkowski Functionals
R. Hilfer
Microscopy and Microanalysis 10, 72 (2004)
DOI: 10.1017/S1431927604884472
Computation of the Generalized Mittag-Leffler Function and its Inverse in the Complex Plane
R. Hilfer, H.J. Seybold
Integral Transforms and Special Functions 17, 637 (2006)
https://doi.org/10.1080/10652460600725341
Simulating the Saturation Front Using a Fractional Diffusion Model
E. Gerolymatou, I. Vardoulakis, R. Hilfer
in: Proceedings of the GRACM05 International Congress on Computational Mechanics, Limassol 2005
edited by: G. Georgiou, P. Papanastasiou, M. Papadrakakis
GRACM, Athens, 653 (2005)
Capillary Pressure, Hysteresis and Residual Saturation in Porous Media
R. Hilfer
Physica A 359, 119 (2006)
https://doi.org/10.1016/j.physa.2005.05.086
Modeling Infiltration by Means of a Nonlinear Fractional Diffusion Model
E. Gerolymatou, I. Vardoulakis, R. Hilfer
Journal of Physics D: Applied Physics 39, 4104 (2006)
Macroscopic Capillarity and Hysteresis for Flow in Porous Media
R. Hilfer
Physical Review E 73, 016307 (2006)
https://doi.org/10.1103/PhysRevE.73.016307
Macroscopic capillarity without a constitutive capillary pressure function
R. Hilfer
Physica A 371, 209 (2006)
https://doi.org/10.1016/j.physa.2006.04.051
Stochastic Multiscale Model for Carbonate Rocks
B. Biswal, P.E. Øren, R. Held, S. Bakke, R. Hilfer
Physical Review E 75, 061303 (2007)
https://doi.org/10.1103/PhysRevE.75.061303
Pore Scale Modeling of Carbonate Rocks
R. Hilfer
Statoil Publication 4500523922, Trondheim, 2007
Transubstantiation
R. Hilfer
Forum Katholische Theologie 33, 304–318 (2017)
Katechon
R. Hilfer
Forum Katholische Theologie 38, 161–173 (2022)
Dimensional Analysis of Two-phase Flow Including a Rate-dependent Capillary Pressure-Saturation Relationship
S. Manthey, M. Hassanizadeh, R. Helmig, R. Hilfer
Advances in Water Resources 31, 1137 (2008)
https://doi.org/10.1016/j.advwatres.2008.01.021
Some Bounds for Alternating Mathieu Type Series
Z. Tomovski, R. Hilfer
Journal of Mathematical Inequalities 2, 17 (2008)
dx.doi.org/10.7153/jmi-02-03
Threefold Introduction to Fractional Derivatives
R. Hilfer
in: Anomalous Transport: Foundations and Applications
edited by: R. Klages and G. Radons and I. Sokolov
Wiley-VCH, Weinheim, 17-74 (2008)
ISBN: 978-3-527-40722-4
Numerical Algorithm for Calculating the Generalized Mittag-Leffler Function
H.J. Seybold, R. Hilfer
SIAM Journal on Numerical Analysis 47, 69 (2008)
https://doi.org/10.1137/070700280
Numerical Modeling of Fluid Flow in Porous Media and in Driven Colloidal Suspensions
J. Harting, T. Zauner, R. Weber, R. Hilfer
in: High Performance Computing in Science and Engineering ’08
edited by: W. Nagel and D. Kröner and M. Resch
Springer, Berlin, 349 (2009)
10.1007/978-3-540-88303-6
ISBN: 978-3-540-88301-2
Modeling and simulation of macrocapillarity
R. Hilfer
in: CP1091, Modeling and Simulation of Materials
edited by: P. Garrido and P. Hurtado and J. Marro
American Institute of Physics, New York, 141 (2009)
https://doi.org/10.1063/1.3082273
Modeling of Multiscale Porous Media
B. Biswal, P.E. Øren, R.J. Held, S. Bakke, R. Hilfer
Image Analysis and Stereology 28, 23-34 (2009)
DOI: 10.5566/ias.v28.p23-34
Percolation as a basic concept for macroscopic capillarity
R. Hilfer, F. Doster
Transport in Porous Media 82, 507 (2010)
https://doi.org/10.1007/s11242-009-9395-0
Operational Method for the Solution of Fractional Differential Equations with Generalized Riemann-Liouville Fractional Derivatives
R. Hilfer, Y. Luchko, Z. Tomovski
Fractional Calculus and Applied Analysis 12, 299 (2009)
Towards precise prediction of transport properties from synthetic computer tomography of reconstructed porous media
B. Biswal, R.J. Held, V. Khanna, J. Wang, R. Hilfer
Physical Review E 80, 041301 (2009)
https://doi.org/10.1103/PhysRevE.80.041301
Continuum reconstruction of the pore scale microstructure for Fontainebleau sandstone
F. Latief, B. Biswal, U. Fauzi, R. Hilfer
Physica A 389, 1607 (2010)
https://doi.org/10.1016/j.physa.2009.12.006
Numerical solutions of a generalized theory for macroscopic capillarity
F. Doster, P. Zegeling, R. Hilfer
Physical Review E 81, 036307 (2010)
https://doi.org/10.1103/PhysRevE.81.036307
Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations
A. Narvaez, Th. Zauner, F. Raischel, R. Hilfer, J. Harting
Journal of Statistical Mechanics 2010, P11026 (2010)
https://doi.org/10.1088/1742-5468/2010/11/P11026
Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions
Z. Tomovski, R. Hilfer, H.M. Srivastava
Integral Transforms and Special Functions 21, 797 (2010)
https://doi.org/10.1080/10652461003675737
Erratum on ”Some Bounds for Alternating Mathieu Type Series”
R. Hilfer
J.Math.Inequalities 4, 615 (2010)
dx.doi.org/10.7153/jmi-04-56
Particle-based Rendering for Porous Media
S. Grottel, G. Reina, T. Zauner, R. Hilfer, T. Ertl
in: Proceedings of SIGRAD 2010: Content aggregation and visualization
edited by: K. Jää-Aro and T. Larsson
Linköping Electronic Conference Proceedings, vol. 52,Linköping University Electronic Press, Linköping, 45 (2010)
Continuum-based rock model of a reservoir dolostone with four orders of magnitude in pore sizes
S. Roth, B. Biswal, G. Afshar, R. Held, P. Øren, L. Berge, R. Hilfer
AAPG Bulletin 95, 925 (2011)
DOI:10.1306/12031010092
Foundations of Fractional Dynamics: A Short Account
R. Hilfer
in: Fractional Dynamics: Recent Advances
edited by: J. Klafter and S. Lim and R. Metzler
World Scientific, Singapore, 207 (2011)
https://doi.org/10.1142/8087
ISBN: 978-981-4340-58-8
High precision synthetic computed tomography of reconstructed porous media
R. Hilfer, T. Zauner
Physical Review E 84, 062301 (2011)
https://doi.org/10.1103/PhysRevE.84.062301
Generalized Buckley-Leverett theory for two phase flow in porous media
F. Doster, R. Hilfer
New Journal of Physics 13, 123030 (2011)
https://doi.org/10.1088/1367-2630/13/12/123030
Horizontal flows and capillarity driven redistribution
F. Doster, O. Hönig, R. Hilfer
Physical Review E 86, 016317 (2012)
https://doi.org/10.1103/PhysRevE.86.016317
Nonmonotone Saturation Profiles for Hydrostatic Equilibrium in Homogeneous Media
R. Hilfer, F. Doster, P. Zegeling
Vadose Zone Journal 11, vzj2012.0021 (2012)
doi:10.2136/vzj2012.0021
Applications and Implications of Fractional Dynamics for Dielectric Relaxation
R. Hilfer
in: Recent Advances in Broadband Dielectric Spectroscopy
edited by: Y. Kalmykov
Springer, Berlin, 123 (2012)
10.1007/978-94-007-5012-8
978-94-007-5011-1
Travelling Wave Solutions in a Generalized Theory for Macroscopic Capillarity
O. Hönig, F. Doster, R. Hilfer
Transport in Porous Media 99, 467 (2013)
https://doi.org/10.1007/s11242-013-0196-0
A comparison between simulation and experiment for hysteretic phenomena during two phase immiscible displacement
F. Doster, R. Hilfer
Water Resources Research 50, 681-686 (2014)
https://doi.org/10.1002/2013WR014619
Saturation overshoot and hysteresis for twophase flow in porous media
R. Hilfer, R. Steinle
The European Physical Journal ST 223, 2323-2338 (2014)
https://doi.org/10.1140/epjst/e2014-02267-x
Excess wings in broadband dielectric spectroscopy
S. Candelaresi, R. Hilfer
AIP Conference Proceedings 1637, 1283 (2014)
https://doi.org/10.1063/1.4907293
Parallel domain decomposition method with non-blocking communication for flow through porous media
A. Lemmer, R. Hilfer
Journal of Computational Physics 281, 970-981 (2015)
https://doi.org/10.1016/j.jcp.2014.08.032
Experimental Implications of Bochner-Levy-Riesz Diffusion
R. Hilfer
Fractional Calculus and Applied Analysis 18, 333-341 (2015)
https://doi.org/10.1515/fca-2015-0022
Differential porosimetry and permeametry for random porous media
R. Hilfer, A. Lemmer
Physical Review E 92, 013305 (2015)
https://doi.org/10.1103/PhysRevE.92.013305
Capillary saturation and desaturation
R. Hilfer, R. Armstrong, S. Berg, A. Georgiadis, H. Ott
Physical Review E 92, 063023 (2015)
https://doi.org/10.1103/PhysRevE.92.063023
Time Automorphisms on C*-Algebras
R. Hilfer
Mathematics 3, 623-643 (2015)
https://doi.org/10.3390/math3030626
Influence of Initial Conditions on Propagation, Growth and Decay of Saturation Overshoot
R. Steinle, R. Hilfer
Transport in Porous Media 111, 369-380 (2016)
https://doi.org/10.1007/s11242-015-0598-2
Non-monotonic Travelling Wave Fronts in a System of Fractional Flow Equations from Porous Media
O. Hönig, P. Zegeling, F. Doster, R. Hilfer
Transport in Porous Media 114, 309-340 (2016)
https://doi.org/10.1007/s11242-015-0618-2
Mathematical analysis of time flow
R. Hilfer
Analysis 36, 49-64 (2016)
https://doi.org/10.1515/anly-2015-5005
Pore-scale displacement mechanisms as a source of hysteresis for two-phase flow in porous media
S. Schlüter, S. Berg, M. Rücker, R. Armstrong, H.-J. Vogel, R. Hilfer, D. Wildenschild
Water Resources Research 52, 2194-2205 (2016)
https://doi.org/10.1002/2015WR018254
Hysteresis in relative permeabilities suffices for propagation of saturation overshoot: A quantitative comparison with experiment
R. Steinle, R. Hilfer
Physical Review E 95, 043112 (2017)
https://doi.org/10.1103/PhysRevE.95.043112
Ground state collapse at strong coupling
R. Hilfer
Journal MESA 8, 307-310 (2017)
Composite Continuous Time Random Walks
R. Hilfer
Eur.Phys.J. B 90, 233 (2017)
https://doi.org/10.1140/epjb/e2017-80369-y
Stable Propagation of Saturation Overshoots for Two-Phase Flow in Porous Media
M. Schneider, T. Köppl, R. Helmig, R. Steinle, R. Hilfer
Transport in Porous Media 121, 621-641 (2018)
https://doi.org/10.1007/s11242-017-0977-y
On Local Equilibrium and Ergodicity
R. Hilfer
Acta Physica Polonica B 49, 859 (2018)
DOI: 10.5506/APhysPolB.49.859
Multiscale local porosity theory, weak limits, and dielectric response in composite and porous media
R. Hilfer
Journal of Mathematical Physics 59, 103511 (2018)
https://doi.org/10.1063/1.5063466
Desiderata for Fractional Derivatives and Integrals
R. Hilfer, Yu. Luchko
Mathematics 7, 149 (2019)
https://doi.org/10.3390/math7020149
Mathematical and physical interpretations of fractional derivatives and integrals
R. Hilfer
in: Handbook of Fractional Calculus with Applications: Basic Theory, Vol. 1
edited by: A. Kochubei and Y. Luchko
Walter de Gruyter GmbH, Berlin, 47-86 (2019)
https://doi.org/10.1515/9783110571622
ISBN: 9783110571622
Convolution Operators on Weighted Spaces of Continuous Functions and Supremal Convolution
T. Kleiner, R. Hilfer
Annali di Matematica Pura ed Applicata 199, 1547-1569 (2020)
https://doi.org/10.1007/s10231-019-00931-z
Weyl Integrals on Weighted Spaces
T. Kleiner, R. Hilfer
Fractional Calculus and Applied Analysis 22, 1225-1248 (2019)
DOI: 10.1515/fca-2019-0065
Excess wing physics and nearly constant loss in glasses
R. Hilfer
Journal of Statistical Mechanics: Theory and Experiment 2019, 104007 (2019)
https://doi.org/10.1088/1742-5468/ab38bc
Maximal Domains for Fractional Derivatives and Integrals
R. Hilfer, T. Kleiner
Mathematics 8, 1107 (2020)
https://doi.org/10.3390/math8071107
A Critical Review of Capillary Number and its Application in Enhanced Oil Recovery
H. Guo, K. Song, R. Hilfer
SPE Conference Proceedings 2020, SPE-200419-MS (2020)
https://doi.org/10.2118/200419-MS
Capillary number correlations for two-phase flow in porous media
R. Hilfer
Physical Review E 102, 053103 (2020)
https://doi.org/10.1103/PhysRevE.102.053103
Fractional glassy relaxation and convolution modules of distributions
T. Kleiner, R. Hilfer
Analysis and Mathematical Physics 11, 130 (2021)
https://doi.org/10.1007/s13324-021-00504-5
On extremal domains and codomains for convolution of distributions and fractional calculus
T. Kleiner, R. Hilfer
Monatshefte für Mathematik 198, 122-152 (2022)
https://doi.org/10.1007/s00605-021-01646-1
Percolativity of Porous Media
R. Hilfer, J. Hauskrecht
Transport in Porous Media 145, 1-12 (2022)
https://doi.org/10.1007/s11242-021-01735-7
Foundations of statistical mechanics for unstable interactions
R. Hilfer
Physical Review E 105, 024142 (2022)
https://doi.org/10.1103/PhysRevE.105.024142
A Brief Review of Capillary Number and its Use in Capillary Desaturation Curves
H. Guo, K. Song, R. Hilfer
Transport in Porous Media 144, 3-31 (2022)
https://doi.org/10.1007/s11242-021-01743-7
Sequential generalized Riemann–Liouville derivatives based on distributional convolution
T. Kleiner, R. Hilfer
Fractional Calculus and Applied Analysis 25, 267-298 (2022)
https://doi.org/10.1007/s13540-021-00012-0
Existence and Uniqueness of Nonmonotone Solutions in Porous Media Flow
R. Steinle, T. Kleiner, P. Kumar, R. Hilfer
Axioms 11, 327 (2022)
https://doi.org/10.3390/axioms11070327
Effective transport coefficients of anisotropic disordered materials
R. Hilfer, J. Hauskrecht
European Physical Journal B 95, 117 (2022)
https://doi.org/10.1140/epjb/s10051-022-00338-5
Convolution on Distribution Spaces Characterized by Regularization
T. Kleiner, R. Hilfer
Mathematische Nachrichten 296, 1938-1963 (2023)
https://doi.org/10.1002/mana.202100330