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Publications

Complete list (PDF)


Invited and summary papers


PDF D. S. Grebenkov, B. Helffer, and N. Moutal, On the spectral properties of the Bloch-Torrey equation in infinite periodically perforated domains, Chapter 10 in "Partial Differential Equations, Spectral Theory, and Mathematical Physics: The Ari Laptev Anniversary Volume", Eds. P. Exner, R. L. Frank, F. Gesztesy, H. Holden and T. Weidl, EMS Series of Congress Reports Vol. 18 (EMS Press, Berlin, 2021) pp. 177-195. [DOI 10.4171/ECR/18]

PDF D. S. Grebenkov, Imperfect Diffusion-Controlled Reactions, in "Chemical Kinetics: Beyond the Textbook", Eds. K. Lindenberg, R. Metzler, G. Oshanin (World Scientific, New Jersey, 2019), pp. 191-219 [DOI: 10.1142/q0209].

PDF D. S. Grebenkov, From the microstructure to diffusion NMR, and back, in "Diffusion NMR of confined systems", Eds. R. Valiullin (RSC Publishing, Cambridge, 2016).

PDF D. S. Grebenkov, Efficient Monte Carlo methods for simulating diffusion-reaction processes in complex systems, in "First-Passage Phenomena and Their Applications", Eds. R. Metzler, G. Oshanin, S. Redner (World Scientific Press, Singapore, 2014).

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, New York, 2006).


Preprints


PDF Y. Almog, D. S. Grebenkov, and B. Helffer, On a Schrödinger operator with a purely imaginary potential in the semiclassical limit, ArXiv 1703.07733 (2017).

PDF D. S. Grebenkov and B. Helffer, On spectral properties of the Bloch-Torrey operator in two dimensions, ArXiv 1608.01925v1 (2016).

PDF D. S. Grebenkov, B. Helffer, and R. Henry, The complex Airy operator with a semi-permeable barrier, ArXiv 1603.06992v1 (2016).




Peer reviewed journals


2022


PDF A. Delitsyn and D. S. Grebenkov, Resonance scattering in a waveguide with identical thick perforated barriers, Appl. Math. Comput. 412, 126592 (2022).



2021


PDF D. S. Grebenkov, R. Metzler, and G. Oshanin, A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes, New J. Phys. 23, 093004 (2021).

PDF M. Reva, D. A. DiGregorio, and D. S. Grebenkov, A first-passage approach to diffusion-influenced reversible binding: insights into nanoscale signaling at the presynapse, Sci. Rep. 11, 5377 (2021).

PDF D. S. Grebenkov, A physicist’s guide to explicit summation formulas involving zeros of Bessel functions and related spectral sums, Rev. Math. Phys. 33, 2130002 (2021) [Erratum].

PDF D. S. Grebenkov, V. Sposini, R. Metzler, G. Oshanin, and F. Seno, Exact distributions of the maximum and range of random diffusivity processes, New J. Phys. 23, 023014 (2021).

PDF D. S. Grebenkov, V. Sposini, R. Metzler, G. Oshanin, and F. Seno, Exact first-passage time distributions for three random diffusivity models, J. Phys. A: Math. Theor. 54, 04LT01 (2021).

PDF D. S. Grebenkov, Statistics of boundary encounters by a particle diffusing outside a compact planar domain, J. Phys. A.: Math. Theor. 54, 015003 (2021).



2020


PDF D. S. Grebenkov and A. T. Skvortsov, Mean first-passage time to a small absorbing target in an elongated planar domain, New J. Phys. 22, 113024 (2020).

PDF D. S. Grebenkov, Joint distribution of multiple boundary local times and related first-passage time problems with multiple targets, J. Stat. Mech. 103205 (2020).

PDF N. Moutal and D. S. Grebenkov, The localization regime in a nutshell, J. Magn. Reson. 320, 106836 (2020).

PDF D. S. Grebenkov, R. Metzler, and G. Oshanin, From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of N random walkers, New J. Phys. 22, 103004 (2020).

PDF G. Berthelot, L. Tupikina, M.-Y. Kang, B. Sapoval, and D. S. Grebenkov, Pseuso-Darwinian evolution of physical flows in complex networks, Sci. Rep. 10, 15477 (2020).

PDF D. S. Grebenkov, Surface Hopping Propagator: An Alternative Approach to Diffusion-Influenced Reactions, Phys. Rev. E 102, 032125 (2020) [Erratum].

PDF F. Le Vot, S. B. Yuste, E. Abad, and D. S. Grebenkov, First-encounter time of two diffusing particles in confinement, Phys. Rev. E 102, 032118 (2020).

PDF D. S. Grebenkov, Paradigm Shift in Diffusion-Mediated Surface Phenomena, Phys. Rev. Lett. 125, 078102 (2020) [SM].

PDF N. Moutal, A. Moutal, and D. S. Grebenkov, Diffusion NMR in periodic media: efficient computation and spectral properties, J. Phys. A: Math. Theor. 53, 325201 (2020).

PDF V. Sposini, D. S. Grebenkov, R. Metzler, G. Oshanin, and F. Seno, Universal spectral features of different classes of random diffusivity processes, New J. Phys. 22, 063056 (2020).

PDF D. S. Grebenkov, Diffusion toward non-overlapping partially reactive spherical traps: fresh insights onto classic problems, J. Chem. Phys. 152, 244108 (2020).

PDF D. S. Grebenkov, D. Holcman, and R. Metzler, New trends in first-passage methods and applications in the life sciences and engineering, J. Phys. A: Math. Theor. 53, 190301 (2020).

PDF J. Guillot, B. Roussière, S. Tusseau-Nenez, D. S. Grebenkov, and M. Ignacio, Influence of density and release properties of UCx targets on the fission product yields at ALTO, Nucl. Inst. Meth. Phys. Res. B 468, 1-7 (2020).



2019


PDF D. S. Grebenkov, R. Metzler, and G. Oshanin, Full distribution of first exit times in the narrow escape problem, New J. Phys. 21, 122001 (2019).

PDF N. Moutal and D. S. Grebenkov, Diffusion across semi-permeable barriers: spectral properties, efficient computation, and applications, J. Scient. Comp. 81, 1630-1654 (2019) [SM].

PDF D. S. Grebenkov, Probability distribution of the boundary local time of reflected Brownian motion in Euclidean domains, Phys. Rev. E 100, 062110 (2019).

PDF F. Piazza and D. S. Grebenkov, Diffusion-controlled reaction rate on non-spherical partially absorbing axisymmetric surfaces, Phys. Chem. Chem. Phys. 21, 25896-25906 (2019).

PDF N. Moutal, I. Maximov, and D. S. Grebenkov, Probing surface-to-volume ratio of an anisotropic medium by diffusion NMR with general gradient encoding, IEEE Trans. Med. Imag. 38, 2507-2522 (2019).

PDF D. S. Grebenkov, Reversible reactions controlled by surface diffusion on a sphere, J. Chem. Phys. 151, 154103 (2019).

PDF D. S. Grebenkov, Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces, J. Chem. Phys. 151, 104108 (2019).

PDF Y. Almog, D. S. Grebenkov, and B. Helffer, On a Schrödinger operator with a purely imaginary potential in the semiclassical limit, Comm. Part. Diff. Eq. 44, 1542-1604 (2019).

PDF P. Witzel, M. Götz, Y. Lanoiselée, T. Franosch, D. S. Grebenkov, and D. Heinrich, Heterogeneities Shape Passive Intracellular Transport, Biophys. J. 117, 203-213 (2019).

PDF N. Moutal, K. Demberg, D. S. Grebenkov, and T. A. Kuder, Localization regime in diffusion NMR: theory and experiments, J. Magn. Reson. 305, 162-174 (2019).

PDF Y. Lanoiselée and D. S. Grebenkov, Non-Gaussian diffusion of mixed origins, J. Phys. A 52, 304001 (2019).

PDF M.-Y. Kang, G. Berthelot, L. Tupikina, C. Nicolaides, J.-F. Colonna, B. Sapoval, and D. S. Grebenkov, Morphological organization of point-to-point transport in complex networks, Sci. Rep. 9, 8322 (2019).

PDF D. S. Grebenkov, R. Metzler, G. Oshanin, L. Dagdug, A. M. Berezhkovskii, and A. T. Skvortsov, Trapping of diffusing particles by periodic absorbing rings on a cylindrical tube, J. Chem. Phys. 150, 206101 (2019).

PDF L. Tupikina and D. S. Grebenkov, Structural and temporal heterogeneities on networks, Appl. Net. Sci. 4, 16 (2019).

PDF S. Valeyre, D. S. Grebenkov, and S. Aboura, Emergence of correlations between securities at short time scales, Physica A 526, 121026 (2019).

PDF D. S. Grebenkov, A unifying approach to first-passage time distributions in diffusing diffusivity and switching diffusion models, J. Phys. A 52, 174001 (2019).

PDF S. Valeyre, D. S. Grebenkov, and S. Aboura, The Reactive Beta Model, J. Finan. Res. 42, 71-113 (2019).

PDF D. S. Grebenkov, Time-averaged mean square displacement for switching diffusion, Phys. Rev. E 99, 032133 (2019).

PDF J. R. Diaz Simões, D. S. Grebenkov, P. Bourgine, and N. Peyriéras, Brownian-like deviation of neighboring cells in the early embryogenesis of the zebrafish, Phys. Biol. 16, 024001 (2019).

PDF J. Guillot, B. Roussière, S. Tusseau-Nenez, D. S. Grebenkov, N. Barré-Boscher, E. Borg, and J. Martin, Development of radioactive beam at ALTO: Part 2. Influence of the UCx target microstructure on the release properties of fission products, Nucl. Inst. Meth. Phys. Res. B 440, 1-10 (2019).

PDF D. S. Grebenkov and S. Traytak, Semi-analytical computation of Laplacian Green functions in three-dimensional domains with disconnected spherical boundaries, J. Comput. Phys. 379, 91–117 (2019).



2018


PDF Y. Lanoiselée, D. S. Grebenkov, G. Sikora, A. Grzesiek, and A. Wylomanska, Optimal parameters for anomalous diffusion exponent estimation from noisy data, Phys. Rev. E 98, 062139 (2018).

PDF D. S. Grebenkov, R. Metzler, and G. Oshanin, Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control, Commun. Chem. 1, 96 (2018).

PDF Y. Lanoiselée, G. Briand, O. Dauchot, and D. S. Grebenkov, Statistical analysis of random trajectories of vibrated disks: towards a macroscopic realization of Brownian motion, Phys. Rev. E 98, 062112 (2018).

PDF A. Delitsyn and D. S. Grebenkov, Mode matching methods in spectral and scattering problems, Quart. J. Mech. Appl. Math. 71, 537–580 (2018).

PDF Y. Lanoiselée, N. Moutal, and D. S. Grebenkov, Diffusion-limited reactions in dynamic heterogeneous media, Nature Commun. 9, 4398 (2018).

PDF N. Moutal, M. Nilsson, D. Topgaard, and D. S. Grebenkov, The Kärger vs bi-exponential model: theoretical insights and experimental validations, J. Magn. Reson. 296, 72-78 (2018).

PDF D. S. Grebenkov and D. Krapf, Steady-state reaction rate of diffusion-controlled reactions in sheets, J. Chem. Phys 149, 064117 (2018) [Erratum].

PDF D. S. Grebenkov, Diffusion MRI/NMR at high gradients: challenges and perspectives, Micro. Meso. Mater. 269, 79-82 (2018).

PDF D. S. Grebenkov, R. Metzler, and G. Oshanin, Towards a full quantitative description of single-molecule reaction kinetics in biological cells, Phys. Chem. Chem. Phys. 20, 16393-16401 (2018) [SI].

PDF Y. Almog, D. S. Grebenkov, and B. Helffer, Spectral semi-classical analysis of a complex Schrodinger operator in exterior domains, J. Math. Phys. 59, 041501 (2018).

PDF Y. Lanoiselée and D. S. Grebenkov, A model of non-Gaussian diffusion in heterogeneous media, J. Phys. A 51, 145602 (2018) [Erratum]

PDF D. S. Grebenkov and B. Helffer, On the spectral properties of the Bloch-Torrey operator in two dimensions, SIAM J. Math. Anal. 50, 622-676 (2018).

PDF D. S. Grebenkov and L. Tupikina, Heterogeneous continuous-time random walks, Phys. Rev. E 97, 012148 (2018).

PDF S. D. Traytak and D. S. Grebenkov, Diffusion-influenced reaction rates for active “sphere-prolate spheroid” pairs and Janus dimers, J. Chem. Phys. 148, 024107 (2018).



2017


PDF D. S. Grebenkov and D. Beliaev, How anisotropy beats fractality in two-dimensional on-lattice DLA growth, Phys. Rev. E 96, 042159 (2017).

PDF D. S. Grebenkov, R. Metzler, and G. Oshanin, Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains, New J. Phys. 19, 103025 (2017).

PDF D. S. Grebenkov, Y. Lanoiselée, and S. N. Majumdar, Mean perimeter and mean area of the convex hull over planar random walks, J. Stat. Mech. 103203 (2017).

PDF D. S. Grebenkov, First passage times for multiple particles with reversible target-binding kinetics, J. Chem. Phys. 147, 134112 (2017).

PDF Y. Lanoiselée and D. S. Grebenkov, Unravelling intermittent features in single particle trajectories by a local convex hull method, Phys. Rev. E 96, 022144 (2017).

PDF G. Sikora, M. Teuerle, A. Wylomanska, and D. S. Grebenkov, Statistical properties of the anomalous scaling exponent estimator based on time averaged mean square displacement, Phys. Rev. E 96, 022132 (2017).

PDF M.-Y. Kang, D. S. Grebenkov, H. Guénard, I. Katz, and B. Sapoval, The Roughton-Forster equation for DLCO and DLNO re-examined, Respir. Physiol. Neurobiol. 241, 62-71 (2017).

PDF D. S. Grebenkov, B. Helffer, and R. Henry, The complex Airy operator on the line with a semi-permeable barrier, SIAM J. Math. Anal. 49, 1844-1894 (2017).

PDF I. Seroussi, D. S. Grebenkov, O. Pasternak, and N. Sochen, Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance, J. Magn. Reson. 277, 95-103 (2017).

PDF D. S. Grebenkov and J.-F. Rupprecht, The escape problem for mortal walkers, J. Chem. Phys. 146, 084106 (2017).

PDF D. S. Grebenkov and G. Oshanin, Diffusive escape through a narrow opening: new insights into a classic problem, Phys. Chem. Chem. Phys. 19, 2723-2739 (2017) [SM]



2016


PDF D. S. Grebenkov, Universal formula for the mean first passage time in planar domains, Phys. Rev. Lett. 117, 260201 (2016) [SM]

PDF Y. Lanoiselée and D. S. Grebenkov, Revealing nonergodic dynamics in living cells from a single particle trajectory, Phys. Rev. E 93, 052146 (2016).

PDF D. S. Grebenkov, Anomalous growth of aging populations, J. Stat. Phys. 163, 440-455 (2016).

PDF S. K. Ghosh, A. G. Cherstvy, D. S. Grebenkov, and R. Metzler, Anomalous, non-Gaussian tracer diffusion in heterogeneously crowded environments, New J. Phys. 18, 013027 (2016).

PDF A. S. Serov, C. Salafia, D. S. Grebenkov, and M. Filoche, The Role of Morphology in Mathematical Models of Placental Gas Exchange, J. Appl. Physiol. 120, 17-28 (2016).

PDF D. S. Grebenkov, D. Belyaev, and P. W. Jones, A multiscale guide to Brownian motion, J. Phys. A 49, 043001 (2016).

PDF C. Bardos, D. S. Grebenkov, and A. Rozanova-Pierrat, Heat content asymptotics in compact domains with discontinuous transmission boundary conditions, Models Methods Appl. Sci. 26, 59-110 (2016).



2015


PDF D. S. Grebenkov, Analytical representations of the spread harmonic measure, Phys. Rev. E 91, 052108 (2015).

PDF D. S. Grebenkov and J. Serror, Optimal Allocation of Trend Following Strategies, Physica A 433, 107-125 (2015).

PDF O. Benichou, D. S. Grebenkov, L. Hillairet, L. Phun, R. Voituriez, and M. Zinsmeister, Mean exit time for surface-mediated diffusion: spectral analysis and asymptotic behavior, Anal. Math. Phys. 5, 321-362 (2015).

PDF H. T. Nguyen, D. S. Grebenkov, D. V. Nguyen, C. Poupon, D. Le Bihan, and J.-R. Li, Parameter estimation using macroscopic dMRI signal models, Phys. Med. Biol. 60, 3389-3413 (2015).

PDF D. V. Nguyen, J.-R. Li, D. S. Grebenkov, and D. Le Bihan, Numerical study of a cylinder model of the diffusion MRI signal for neuronal dendrite trees, J. Magn. Reson. 252, 103-113 (2015).

PDF A. S. Serov, C. Salafia, M. Filoche, and D. S. Grebenkov, Analytical theory of oxygen transfer in the human placenta, J. Theor. Biol. 368, 133-144 (2015).

PDF M. Sarracanie, D. S. Grebenkov, J. Sandeau, S. Coulibaly, A. R. Martin, K. Hill, J. M. Perez Sanchez, R. Fodil, L. Martin, E. Durand, G. Caillibotte, D. Isabey, L. Darrasse, J. Bittoun, and X. Maitre, Phase-contrast helium-3 MRI of aerosol deposition in human airways, NMR Biomed. 28, 180-187 (2015).

PDF J.-F. Rupprecht, O. Benichou, D. S. Grebenkov, and R. Voituriez, Exit time distribution in spherically symmetric two-dimensional domains, J. Stat. Phys. 158, 192-230 (2015).

PDF E. Fodor, D. S. Grebenkov, P. Visco, and F. van Wijland, Generalized Langevin Equation with Hydrodynamic Interactions: Equilibrium Properties, Physica A 422, 107-112 (2015).

PDF D. S. Grebenkov, First Exit Times of Harmonically Trapped Particles: A Didactic Review, J. Phys. A: Math. Theor. 48, 013001 (2015).

PDF A. Serov, C. Salafia, P. Brownbill, D. S. Grebenkov, and M. Filoche, Optimal villous density for maximal oxygen uptake in the human placenta, J. Theor. Biol. 364, 383-396 (2015).



2014


PDF B.-T. Nguyen, D. S. Grebenkov, and A. L. Delitsyn, On the Exponential Decay of Laplacian Eigenfunctions in Planar Domains with Branches, Contemp. Math. 630, 337-348 (2014).

PDF D. S. Grebenkov, Exploring diffusion across permeable barriers at high gradients. II. Localization regime, J. Magn. Reson. 248, 164-176 (2014) [SM].

PDF D. S. Grebenkov, D. V. Nguyen, and J.-R. Li, Exploring diffusion across permeable barriers at high gradients. I. Narrow pulse approximation, J. Magn. Reson. 248, 153-163 (2014).

PDF F. Cadiz, P. Barate, D. Paget, D. S. Grebenkov, J.-P. Korb, A. C. H. Rowe, T. Amand, S. Arscott, and E. Peytavit, All optical method for investigation of spin and charge transport in semiconductors: combination of spatially- and time-resolved luminescence, J. Appl. Phys. 116, 023711 (2014).

PDF H. T. Nguyen, J.-R. Li, D. S. Grebenkov, D. Le Bihan, and C. Poupon, Parameters estimation from the diffusion MRI signal using a macroscopic model, J. Phys.: Conf. Ser. 490, 012117 (2014).

PDF D. V. Nguyen, J.-R. Li, D. S. Grebenkov, and D. Le Bihan, Modeling the diffusion magnetic resonance imaging signal inside neurons, J. Phys.: Conf. Ser. 490, 012013 (2014).

PDF M. V. Tamm, V. I. Stadnichuk, A. M. Ilyina, and D. S. Grebenkov, Overlap of two Brownian trajectories: exact results for scaling functions, Phys. Rev. E 89, 042137 (2014).

PDF D. V. Nguyen, J.-R. Li, D. S. Grebenkov, and D. Le Bihan, A finite elements method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging, J. Comput. Phys. 263, 283-302 (2014).

PDF T. Calandre, O. Bénichou, D. S. Grebenkov, and R. Voituriez, Splitting probabilities and interfacial territory covered by 2D and 3D surface-mediated diffusion, Phys. Rev. E 89, 012149 (2014).

PDF D. S. Grebenkov and M. Vahabi, Analytical solution of the generalized Langevin equation with hydrodynamic interactions: subdiffusion of heavy tracers, Phys. Rev. E 89, 012130 (2014).

PDF D. S. Grebenkov and J. Serror, Following a Trend with an Exponential Moving Average: Analytical Results for a Gaussian Model, Physica A 394, 288-303 (2014).



2013


PDF D. S. Grebenkov and B.-T. Nguyen, Geometrical structure of Laplacian eigenfunctions, SIAM Reviews 55, 601-667 (2013). [Erratum]

PDF D. S. Grebenkov, M. Vahabi, E. Bertseva, L. Forro, and S. Jeney, Hydrodynamic and subdiffusive motion of tracers in a viscoelastic medium, Phys. Rev. E 88, 040701(R) (2013).

PDF D. S. Grebenkov, Optimal and sub-optimal quadratic forms for non-centered Gaussian processes, Phys. Rev. E 88, 032140 (2013).

PDF B.-T. Nguyen and D. S. Grebenkov, Localization of Laplacian eigenfunctions in circular, spherical and elliptical domains, SIAM J. Appl. Math. 73, 780-803 (2013).

PDF D. S. Grebenkov, H. T. Nguyen, and J.-R. Li, A fast random walk algorithm for computing diffusion-weighted NMR signals in multi-scale porous media: a feasibility study for a Menger sponge, Micropor. Mesopor. Mater. 178, 56-59 (2013).

PDF M. Nordin, D. S. Grebenkov, M. N. Jacobi, and M. Nyden, An efficient eigenfunction approach to calculate spin-echo signals, Micropor. Mesopor. Mater. 178, 7-10 (2013).

PDF D. V. Nguyen, D. S. Grebenkov, C. Poupon, D. Le Bihan, and J.-R. Li, Effective diffusion tensor computed by homogenization, Diff. Fundam. 18 (9), 1-6 (2013).

PDF S. Valeyre, D. S. Grebenkov, S. Aboura, and Q. Liu, The Reactive Volatility Model, Quant. Finance 13, 1697-1706 (2013).



2012


PDF A. L. Delitsyn, B.-T. Nguyen, and D. S. Grebenkov, Exponential decay of Laplacian eigenfunctions in domains with branches of variable cross-sectional profiles, Eur. Phys. J. B 85, 371 (2012).

PDF J.-F. Rupprecht, O. Bénichou, D. S. Grebenkov, and R. Voituriez, Exact mean exit time for surface-mediated diffusion, Phys. Rev. E 86, 041135 (2012).

PDF E. Bertseva, D. S. Grebenkov, P. Schmidhauser, S. Gribkova, S. Jeney, and L. Forro, Optical Trapping Microrheology in Cultured Human Cells, Eur. Phys. J. E 35, 63 (2012).

PDF A. Andreanov and D. S. Grebenkov, Time-averaged MSD of Brownian motion, J. Stat. Mech. P07001 (2012).

PDF J.-F. Rupprecht, O. Bénichou, D. S. Grebenkov, and R. Voituriez, Kinetics of active surface-mediated diffusion in spherically symmetric domains, J. Stat. Phys. 147, 891-918 (2012).

PDF T. Calandre, O. Bénichou, D. S. Grebenkov, and R. Voituriez, The interfacial territory covered by surface-mediated diffusion, Phys. Rev. E. 85, 051111 (2012).

PDF A. Rozanova-Pierrat, D. S. Grebenkov, and B. Sapoval, Faster Diffusion across an Irregular Boundary, Phys. Rev. Lett. 108, 240602 (2012).

PDF A. L. Delitsyn, B.-T. Nguyen, and D. S. Grebenkov, Trapped modes in finite quantum waveguides, Eur. Phys. J. B. 85, 176 (2012).



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) [Erratum].



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]

DISCLAIMER: All provided pdf files on this site are intended only for non-profitable educational purposes! Any item will be removed upon the first request from the copyright holder.
Your appreciation can be sent to denis.grebenkov@polytechnique.edu
Last modified 30/07/2020

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