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Publications

Complete list (PDF)

Invited and summary papers


PDF D. S. Grebenkov, Surveying Diffusion in Complex Geometries. An Essay (Research summary for defending Habilitation for Research Supervision (HDR), 2009).

PDF D. S. Grebenkov, Partially Reflected Brownian Motion: A Stochastic Approach to Transport Phenomena, in "Focus on Probability Theory", Ed. L. R. Velle, pp. 135-169 (Nova Science Publishers, 2006).

Peer reviewed journals


2012


PDF T. Calandre, O. Bénichou, D. S. Grebenkov, and R. Voituriez, The interfacial territory covered by surface-mediated diffusion, accepted to Phys. Rev. E.

PDF A. Rozanova-Pierrat, D. S. Grebenkov, and B. Sapoval, Faster Diffusion across an Irregular Boundary, accepted to Phys. Rev. Lett.

PDF A. L. Delitsyn, B.-T. Nguyen, and D. S. Grebenkov, Trapped modes in finite quantum waveguides, accepted to Eur. Phys. J. B.



2011


PDF J. S. Gill, C. M. Salafia, D. S. Grebenkov, D. D. Vvedensky, Modelling oxygen transport in human terminal villi, J. Theor. Biol. 291, 33-41 (2011).

PDF D. S. Grebenkov, Probability Distribution of the Time-Averaged Mean-Square Displacement of a Gaussian Process, Phys. Rev. E 84, 031124 (2011).

PDF D. S. Grebenkov, Time-Averaged Quadratic Functionals of a Gaussian Process, Phys. Rev. E 83, 061117 (2011). [Erratum]

PDF O. Benichou, D. S. Grebenkov, P. Levitz, C. Loverdo, R. Voituriez, Mean first-passage time of surface-mediated diffusion in spherical domains, J. Stat. Phys. 142, 657-685 (2011).

PDF D. S. Grebenkov, A fast random walk algorithm for computing the pulsed-gradient spin-echo signal in multiscale porous media, J. Magn. Reson. 208, 243-255 (2011).



2010


PDF D. S. Grebenkov, Searching for partially reactive sites: Analytical results for spherical targets, J. Chem. Phys. 132, 034104 (2010).

PDF D. S. Grebenkov, Subdiffusion in a bounded domain with a partially absorbing-reflecting boundary, Phys. Rev. E 81, 021128 (2010).

PDF D. S. Grebenkov, Use, Misuse and Abuse of Apparent Diffusion Coefficients, Conc. Magn. Reson. A36, 24-35 (2010).

PDF D. S. Grebenkov, Pulsed-gradient spin-echo monitoring of restricted diffusion in multilayered structures, J. Magn. Reson. 205, 181-195 (2010).

PDF O. Benichou, D. S. Grebenkov, P. Levitz, C. Loverdo, R. Voituriez, Optimal Reaction Time for Surface-Mediated Diffusion, Phys. Rev. Lett. 105, 150606 (2010).

PDF B. T. Nguyen, D. S. Grebenkov, A Spectral Approach to Survival Probability in Porous Media, J. Stat. Phys. 141, 532-554 (2010).



2009


PDF D. S. Grebenkov, Y. A. Goddard, G. Diakova, J.-P. Korb, and R. G. Bryant, Dimensionality of Diffusive Exploration at the Protein Interface in Solution, J. Phys. Chem. B 113, 13347-13356 (2009).

PDF D. S. Grebenkov, Laplacian Eigenfunctions in NMR. II Theoretical Advances, Conc. Magn. Reson. 34A, 264-296 (2009).



2008


PDF D. S. Grebenkov, Laplacian Eigenfunctions in NMR I. A Numerical Tool, Conc. Magn. Reson. 32A, 277-301 (2008).

PDF M. Filoche, D. S. Grebenkov, J. S. Andrade Jr., B. Sapoval, Passivation of Irregular Surfaces Accessed by Diffusion, Proc. Natl. Acad. Sci. 105, 7636-7640 (2008).

PDF D. S. Grebenkov, M. Pica Ciamarra, A. Coniglio, M. Nicodemi, Flow, Ordering and Jamming of Sheared Granular Suspensions, Phys. Rev. Lett. 100, 078001 (2008).

PDF D. S. Grebenkov, Analytical solution for restricted diffusion in circular and spherical layers under inhomogeneous magnetic fields, J. Chem. Phys. 128, 134702 (2008). [Erratum]

PDF D. Habib, D. S. Grebenkov, G. Guillot, Gas diffusion in a pulmonary acinus model: experiments with hyperpolarized helium-3, Magn. Reson. Imaging 26, 1101-1113 (2008).

PDF M. Filoche, D. S. Grebenkov, The toposcopy, a new tool to probe the geometry of an irregular interface by measuring its transfer impedance, Eur. Phys. Lett. 81, 40008 (2008).



2007


PDF D. S. Grebenkov, NMR Survey of Reflected Brownian Motion, Rev. Mod. Phys. 79, 1077-1137 (2007). [Erratum]

PDF D. S. Grebenkov, Residence times and other functionals of reflected Brownian motion, Phys. Rev. E 76, 041139 (2007). [Erratum]

PDF D. S. Grebenkov, Multiple Correlation Function Approach: Rigorous Results for Simple Geometries, Diff. Fundam. 5, 1-34 (2007).

PDF D. S. Grebenkov, G. Guillot, B. Sapoval, Restricted Diffusion in a Model Acinar Labyrinth by NMR. Theoretical and Numerical Results, J. Magn. Reson. 184, 143-156 (2007).

PDF D. S. Grebenkov, NMR Restricted Diffusion between Parallel Planes in a Cosine Magnetic Field: An Exactly Solvable Model, J. Chem. Phys. 126, 104706 (2007).

PDF D. S. Grebenkov, M. Filoche, B. Sapoval, A Simplified Analytical Model for Laplacian Transfer Across Deterministic Prefractal Interfaces, Fractals 15, 27-39 (2007).

PDF D. S. Grebenkov, Multiple correlation function approach to study the restricted diffusion under arbitrary magnetic field, Magn. Reson. Imag. 25, 559 (2007).

PDF D. S. Grebenkov, G. Guillot, NMR of diffusion in porous media: branched or disordered structure?, Magn. Reson. Imag. 25, 560 (2007).

PDF D. Habib, D. S. Grebenkov, G. Guillot, Probing a model pulmonary acinus by NMR gas diffusion, Magn. Reson. Imag. 25, 560 (2007).




2006


PDF P. Levitz, D. S. Grebenkov, M. Zinsmeister, K. Kolwankar, B. Sapoval, Brownian flights over a fractal nest and first passage statistics on irregular surfaces, Phys. Rev. Lett. 96, 180601 (2006).

PDF D. S. Grebenkov, M. Filoche, B. Sapoval, Mathematical Basis for a General Theory of Laplacian Transport towards Irregular Interfaces, Phys. Rev. E 73, 021103 (2006).

PDF D. S. Grebenkov, Multiexponential attenuation of the CPMG spin echoes due to a geometrical confinement, J. Magn. Reson. 180, 118-126 (2006).

PDF D. S. Grebenkov, Scaling Properties of the Spread Harmonic Measures, Fractals 14 (3), 231-243 (2006).




2005


PDF D. S. Grebenkov, What Makes a Boundary Less Accessible, Phys. Rev. Lett. 95, 200602 (2005).

PDF D. S. Grebenkov, M. Filoche, B. Sapoval, M. Felici, Diffusion-Reaction in Branched Structures: Theory and Application to the Lung Acinus, Phys. Rev. Lett. 94, 050602 (2005).

PDF D. S. Grebenkov, A. A. Lebedev, M. Filoche, B. Sapoval, Multifractal Properties of the Harmonic Measure on Koch Boundaries in Two and Three Dimensions, Phys. Rev. E 71, 056121 (2005).

PDF B. Sapoval, J. S. Andrade Jr, A. Baldassari, A. Desolneux, F. Devreux, M. Filoche, D. S. Grebenkov, S. Russ, New Simple Properties of a Few Irregular Systems, Physica A 357, 1-17 (2005).

PDF D. S. Grebenkov, G. Guillot, Numerical MRI of the translational diffusion in branching three-dimensional labyrinths of a model pulmonary acinus, MAGMA 18, S128 (2005).


2003


PDF D. S. Grebenkov, M. Filoche, B. Sapoval, Spectral Properties of the Brownian Self-Transport Operator, Eur. Phys. J. B 36 (2), 221-231 (2003).

PDF A. P. Grinin, D. S. Grebenkov, Study of Relaxation in Micellar Solution by the Numerical Experiment , Colloid Journal 65 (5), 552-561 [pages 603-613 in the Russian version] (2003).


2002


PDF D. S. Grebenkov, Parametric Equations of the Theory of Formation of Spherical Micelles, J. Coll. Int. Sci. 249, 162-171 (2002).


2001


PDF D. S. Grebenkov, A. P. Grinin, Numerical simulation of transitive processes of micellization, Vestnik Sankt-Peterburgskogo Universiteta, Series 4, 4 (28), 3-12 (2001).


1999


D. S. Grebenkov, A. P. Grinin, F. M. Kuni, Numerical verification of the accuracy of some analytical results in the nucleation theory, Vestnik Sankt-Peterburgskogo Universiteta, Series 4, 2 (11), 3-10 (1999).



Peer reviewed conference proceedings


PDF D. S. Grebenkov, An exactly solvable model for restricted diffusion in NMR, Proceedings of the XXIII IUPAP International Conference on Statistical Physics, p. 174 (Genoa, Italy, 2007).

PDF D. S. Grebenkov, Multiple correlation function approach to study the restricted diffusion under arbitrary magnetic field, Proceedings of the 8th International Bologna Conference on Magnetic Resonance in Porous Media, p. 54 (Bologna, Italy, 2006).

PDF D. S. Grebenkov, G. Guillot, NMR of diffusion in porous media: branched or disordered structure?, Proceedings of the 8th International Bologna Conference on Magnetic Resonance in Porous Media, p. 55 (Bologna, Italy, 2006).

PDF D. Habib, D. S. Grebenkov, G. Guillot, Probing a model pulmonary acinus by NMR gas diffusion, Proceedings of the 8th International Bologna Conference on Magnetic Resonance in Porous Media, p. 55 (Bologna, Italy, 2006).

PDF D. S. Grebenkov, G. Guillot, Localization regime of restricted diffusion in a model pulmonary acinus, Proceedings of the Fourteenth ISMRM Meeting, # 1624 (Seattle, USA, 2006).

PDF D. Habib, D. S. Grebenkov, X. Maitre, L. De Rochefort, E. Durand, G. Guillot, Experimental study of gas diffusion in a pulmonary acinus model, Proceedings of the Fourteenth ISMRM Meeting, # 1323 (Seattle, USA, 2006).

PDF D. S. Grebenkov, G. Guillot, Numerical MRI of the translational diffusion in branching three-dimensional labyrinths of a model pulmonary acinus, Proceedings of the 22th Annual Meeting of ESMRMB, # 219 (Basle, Switzerland, 2005).

PDF D. S. Grebenkov, E. Chassaing, M. Filoche, B. Sapoval, Rôle de l'irrégularité géométrique d'une électrode : approche théorique et vérification expérimentale, Proceedings of the 17th Forum of Electrochemical Impedances, pp. 183-192 (Paris, France, 2005).

PDF D. S. Grebenkov, Numerical Study of the Multifractal Properties of the Harmonic Measure on a Cubic Koch Surface, Proceedings of Europhysics Conference on Computational Physics, Ed. G. Ciccotti, p. 121 (Genua, Italy, 2004).

PDF D. S. Grebenkov, Approximate Distribution of Hitting Probabilities for a Regular Surface with Compact Support in 2D, Proceedings of European Summer School 2001 "Asymptotic Combinatorics with Application to Mathematical Physics", 221-242 (2002).



Other publications


I. S. Siparov, D. S. Grebenkov, Numerical simulation of the relaxation process of micellar solution, Proceedings of the student conference (Saint Petersburg, Russia, 2000).

PDF D. S. Grebenkov, Explicit Construction of the Brownian Self-Transport Operator, math.PR/0204215 (electronic version only)

PDF D. S. Grebenkov, Propriétés de l'opérateur d'auto-transport brownien, Rapport de stage à l'Ecole Polytechnique (France, 2000). [Here you can download the figures]
Your appreciation can be sent to denis.grebenkov@polytechnique.edu
Last modified 30/04/2012

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