Publications

Articles in scientific journals

• Linkov, A. M. (2011) Speed Equation and Its Application for Solving Ill-Posed Problems of Hydraulic Fracturing. Doklady Physics, Vol.56, No.8, pp 436-438. Pleiades Publishing, Ltd. 2011: Linkov-SpeedEqn-English.pdf, Linkov-SpeedEqn-Russian.pdf
• Vellender, A., Mishuris, G. and Movchan, A. (2011) Weight Function in a Bimaterial Strip Containing an Interfacial Crack and an Imperfect Interface. Application to Bloch.Floquet Analysis in a Thin Inhomogeneous Structure with Cracks. Multiscale Modeling and Simulution, 9, 1327-1349. DOI: 10.1137/110824838
• Piccolroaz, A., Mishuris, G., Movchan, A., and Movchan, N. (2012) Mode III crack propagation in a bimaterial plane driven by a channel of small line defects. Computational Materials Science, 64, 239-243. doi: 10.1016/j.commatsci.2012.02.037
• Piccolroaz, A., Mishuris, G., Movchan, A., and Movchan, N. (2012) Perturbation analysis of Mode III interfacial cracks advancing in a dilute heterogeneous material. International Journal of Solids and Structures, 49, 244-255. doi: 10.1016/j.ijsolstr.2011.10.006
• Mishuris, G., Movchan, A., Movchan, N. and Piccolroaz, A. (2012) Interaction of an interfacial crack with linear small defects under out-of-plane shear loading. Computational Materials Science, 52, 226-230. DOI: 10.1016/j.commatsci.2011.01.023
• Mishuris, G., Wrobel, M., Linkov., (2012) On Modelling Hydraulic Fracture in Proper Variables: Stiffness, Accuracy, Sensitivity. International Journal of Engineering Science, 61, 10–23. doi: 10.1016/j.ijengsci.2012.06.005
• Piccolroaz, A., Mishuris, G. and Radi, E. (2012) Mode III interfacial crack in the presence of couple stress elastic materials. Engineering Fracture Mechanics, 80, 60-71. doi: 10.1016/j.engfracmech.2011.03.001
• Vellender, A. and Mishuris, G. (2012) Eigenfrequency correction of Bloch-Floquet waves in a thin periodic bi-material strip with cracks lying on perfect and imperfect interfaces. Wave Motion, 49, 258-270. vellender_mishuris_2012.pdf
• Linkov, A. M. (2012) On efficient simulation of hydraulic fracturing in terms of particle velocity. Int. J. Eng. Sci., 2012, 52, 77-88. doi: 10.1016/j.ijengsci.2011.11.009
• Piccolroaz, A. and Mishuris, G. (2013) Integral identities for a semi-infinite interfacial crack in 2D and 3D elasticity. Journal of Elasticity, 110, 117-140. DOI: 10.1007/s10659-012-9385-2
• Kilbas, A.A., Koroleva, A.A., Rogosin, S. (2013) Multi-parametric Mittag-Leffler functions and their extension. Fractional Calculus and Applied Analysis, 16, 2, 378-404. DOI: 10.2478/s13540-013-0024-9
• Rivero, M., Rogosin, S., Tenreiro Machado, J., Trujillo, J. (2013) Stability of Fractional Order Systems. Mathematical Problems in Engineering, Volume 2013, Article ID 356215, 14 pages. Doi: 10.1155/2013/356215
• Gryshchuk, S., Rogosin, S. (2013) Effective Conductivity of 2D Disk - Ring Composite Material. Mathematical Modelling and Analysis, 18, 3, 386-394. DOI:10.3846/13926292.2013.804890
• Ilchukov, A., Rogosin, S. (2013) Boundary value problems in spaces defined by modulus of continuity. Siauliai Math. Sem., 8 (16), 71-82. Ilchukov_Rogosin_2013.pdf
• Vellender, A., Mishuris, G.S., Piccolroaz, A. (2013) Perturbation analysis for an imperfect interface crack problem using weight function techniques. International Journal of Solids and Structures, 50, 4098-4107. doi:10.1016/j.ijsolstr.2013.08.023
• Lavrov, A. (2013) Redirection and channelization of power-law fluid flow in a rough-walled fracture. Chemical Engineering Science, 99: 81-88. http://dx.doi.org/10.1016/j.ces.2013.05.045
• Lavrov, A. (2013) Numerical modeling of steady-state flow of a non-Newtonian power-law fluid in a rough-walled fracture. Computers and Geotechnics, 50: 101-109. http://dx.doi.org/10.1016/j.compgeo.2013.01.004
• Jones, S. A., Dollet, B., Méheust, Y., Cox, S. J., Cantat, I. (2013) Structure-dependent mobility of a dry aqueous foam flowing along two parallel channels. Phys. Fluids 25, 063101. Doi: 10.1063/1.4811178
• Satomi, R., Grassia, P., Cox, S.J., Mishuris, G., Lue, L. (2013) Diffusion of curvature on a sheared semi-infinite film, Proc. Roy. Soc A. 469, 20130359.DOI: 10.1098/rspa.2013.0359
• Kusmierczyk, P., Mishuris, G., Wrobel, M. (2013) Remarks on application of different variables for the PKN model of hydrofracturing: various fluid-flow regimes. Int. Journal of Fracture, 184(1), 185-213 Doi: 10.1007/s10704-013-9867-7
• Wrobel, M., Mishuris, G. (2013) Efficient pseudo-spectral solvers for the PKN model of hydrofracturing. Int. Journal of Fracture, 184, pp 151-170. <Doi: 10.1007/s10704-013-9847-y
• Ferguson, D.J., Cox, S.J. (2013) The motion of a foam lamella traversing an idealised bi-conical pore with a rounded central region, Coll. Surf. A, 438, 56-62. doi: 10.1016/j.colsurfa.2013.02.015
• Grassia, P., Hernandez, E., Shokri, N., Cox, S.J., Mishuris, G., Rossen, B. (2014) Analysis of a model for foam improved oil recovery. Journal of Fluid Mechanics, 751, pp 346-405. doi:10.1017/jfm.2014.287
• Mishuris, G., Rogosin, S. (2014) An asymptotic method of factorization of a class of matrix functions. Proc. Royal Soc. A, 2014, 470, 20140109. Doi: 10.1098/rspa.2014.0109
• Rejwer, E., Rybarska-Rusinek, L., Linkov, A. (2014) The complex variable fast multipole boundary element method for the analysis of strongly inhomogeneous media. Engineering Analysis with Boundary Elements, 43, 105–116. DOI: 10.1016/j.enganabound.2014.04.001
• Jaworski, D., Linkov, A., Rybarska-Rusinek, L. (2014) A note on evaluation of temporal derivative of hypersingular integrals over open surface with propagating contour. Journal of Elasticity. Doi: 10.1007/s10659-014-9499-9.
• Linkov, A. (2014) On comparison of thinning fluids used for hydraulic fracturing. International Journal of Engineering Science, 77, 14-23. doi:10.1016/j.ijengsci.2013.12.005
• Mishuris G., Piccolroaz A., Vellender A. (2014) Boundary integral formulation for cracks at imperfect interfaces. The Quarterly Journal of Mechanics and Applied Mathematics, 67, 363-387. doi: 10.1093/qjmam/hbu010
• Kuzkin V.A., Krivtsov, A.M., Linkov, A.M (2014) Computer simulation of effective viscosity of fluid-proppant mixture used in hydraulic fracturing. Journal of Mining Science, 50, 1-9. DOI: 10.1134/S1062739114010013
• Durand, M., Kraynik, A.M., van Swol, F., Kafer, J., Quilliet, C., Cox, S.J., Talebi, S.A., Graner, F. (2014) Statistical Mechanics of Two-Dimensional Shuffled Foams, part II: Geometry - Topology Correlation in Small or Large Disorder Limits. Phys. Rev. E. 89, 062309. DOI: 10.1103/PhysRevE.89.062309
• Lavrov, A. (2014) Radial flow of non-Newtonian power-law fluid in a rough-walled fracture: Effect of fluid rheology. Transport in Porous Media. Doi: 10.1007/s11242-014-0384-6
• Mainardi F., Rogosin S. (2014) George William Scott Blair – the pioneer of fractional calculus in rheology. Comm. in Applied and Industrial Math., v. 6, no. 1. – e481. doi:10.1685/journal.caim.481 Rogosin_Mainardi_2014.pdf
• Pryce, L., Vellender A., Zagnetko, A. (2014) Integral identities for interfacial cracks in an anisotropic bimaterial with an imperfect interface (submitted).
• Rybarska-Rusinek, L., Jaworski, D., Linkov, A. (2014) On efficient evaluation of integrals entering boundary equations of 3D potential and elasticity theory. Journal of Mathematics and Applications, 37, 85-96. jma-37-25-Rybarska_Jaworski_Linkov_2014.pdf
• Mishuris, G., Rogosin, S., Wrobel, M. (2014) Hele-Shaw flow with a small obstacle. Meccanica, 49, 2037–2047 Doi: 10.1007/s11012-014-9919-8.
• Cox, S.J. (2015) Simulations of bubble division in the flow of a foam past an obstacle in a narrow channel. Colloids and Surfaces A: Physicochem. Eng. Aspects, 473, 104–108. doi:10.1016/j.colsurfa.2014.10.038
• Whittaker, R.J., Cox, S. (2015) Stability Of A Helicoidal Surface Inside A Cylinder With Pinned Diameters. Q J Mechanics Appl Math, 68 (1), 23-52. Doi: 10.1093/qjmam/hbu026
• Mishuris, G., Rogosin, S., Wrobel, M. (2015) Moving Stone in the Hele-Shaw Flow. Mathematika, 61 (2), 457- 474. Doi: 10.1112/S0025579314000461
• Linkov, A. (2015) Particle velocity, speed equation and universal asymptotics for efficient modeling hydraulic fractures. Appl. Math. Mech., 79 (1), 54-63. doi:10.1016/j.jappmathmech.2015.04.018
• Dalla Riva M., Musolino P., Rogosin S. (2015) Series expansions for the solution of the Dirichlet problem in a planar domain with a small hole. Asymptotic Analysis, 92, 339-361. DOI: 10.3233/ASY-151283
• Wrobel M., Mishuris G. (2015) Hydraulic fracture revisited: Particle velocity based simulation. International Journal of Engineering Science, 94, 23-58. Doi: 10.1016/j.ijengsci.2015.04.003
• Peck D., Mishuris G., Rogosin S., Wrobel M. (2015) Simulating the Hele-Shaw flow in the presence of various obstacles and moving particles. Meccanica, 09, 1-15. DOI: 10.1007/s11012-015-0271-4
• Perkowska M., Wrobel M., Mishuris G. (2015) Universal hydrofracturing algorithm for shear-thinning fluids: particle velocity based simulation. Computers and Geotechnics, 71, 310-337. DOI: 10.1016/j.compgeo.2015.10.005.
• Wrobel, M., Mishuris, G., Piccolroaz, A. (2016) Energy Release Rate in hydraulic fracture: can we neglect an impact of the hydraulically induced shear stress? (in press) International Journal of Engineering Sciences. DOI: 10.1016/j.ijengsci.2016.09.01 (see arxiv preprint)

Books and book chapters

• Rogosin, S. (2012) 2D Free Boundary Value Problems. In book "Advances in Applied Analysis", ed. S. Rogosin, A. Koroleva, Chapter 6, pp.225-253. DOI: 10.1007/978-3-0348-0417-2_6
• Linkov, A.M., Mishuris, G. (2013) Modified Formulation, ε-Regularization and the Efficient Solution of Hydraulic Fracture Problems. In book "Effective and Sustainable Hydraulic Fracturing", ed. A.P. Bunger, J. McLennan and R. Jeffrey, Chapter 31, pp 641-657. Doi: 10.5772/56218
• Linkov, A.M., Mishuris, G., Rybarska-Rusinek, L. (2014) Selected topics of mathematics for engineers. Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszów 2014, ISBN 978-83-7199-933-X, 186 pages.
  More information can be found here.

Articles in refereed conference proceeding journals

• Linkov, A. M. (2011) On Numerical Simulation of Hydraulic Fracturing. Proceedings of The International Summer School-Conference “Advanced Problems in Mechanics”, St. Petersburg: Linkov-On-Numer-Simul-Hydraulic-Frac-Proc-APM-2011-p291-296.pdf
• Dobroskok A., Linkov A. M. (2011) Numerical Approach to Interpretation of Acoustic Emission Occurring at Different Scales. Proceedings of The International Summer School-Conference “Advanced Problems in Mechanics”, St. Petersburg: DobroskokLinkov_APM2011-1.pdf
• Jaworski, D., Linkov, A. M., Rybarska-Rusinek, L., (2012) Evaluation of Temporal Derivative for Propagating Front of Hydraulic Fracture. Proceedings of 40 Summer-School Conference "Advanced Problems in Mechanics", 2012. Jaworski_Linkov_Rybarska.pdf
• Linkov, A. M., (2012) Numerical Modelling of Hydraulic Fractures: State of art and New Results. Proceedings of 40 Summer-School Conference "Advanced Problems in Mechanics", 2012. Linkov_APM2012.pdf
• Rejwer, E., Rybarska-Rusinek, L., Linkov, A. M., (2012) Complex Variable Fast Multipole Method for Modelling Hydraulic Fracturing in Inhomogeneous Media. Proceedings of 40 Summer-School Conference "Advanced Problems in Mechanics", 2012. Rejwer_Rybarska_Linkov.pdf
• Nonnekes, L.E., Cox, S.J., Rossen, W.R. (2012) Effect of Gas Diffusion on Mobility of foam for EOR. SPE Annual Technical Conference and Exhibition, San Antonio, Texas, U.S.A., 8-10 Oct. 2012 DOI: 10.2118/159817-MS
• Nonnekes, L.E., Cox, S.J., Rossen, W.R. (2012) A 2D Model for the Effect of Gas Diffusion on Mobility of Foam for EOR. Proc. ECMOR XIII - 13th European Conference on the Mathematics of Oil Recovery, Biarritz. DOI: 10.3997/2214-4609.20143207
• Kuzkin, V.A., Krivtsov, A.M., Linkov, A.M. (2013) Proppant transport in hydraulic fractures: computer simulation of effective properties and movement of the suspension. Proceedings of 41 Summer-School Conference "Advanced Problems in Mechanics", 2013, pp 321-336.
• Linkov, A. M. (2013) Using Modified Formulation for Hydraulic Fractures Driven by Thinning Fluids Proceedings of 41 Summer-School Conference "Advanced Problems in Mechanics", pp 349-358.
• Lavrov, A. (2013) Non-Newtonian fluid flow in rough-walled fractures: a review. In: Proceedings of the 3rd ISRM Symposium on Rock Mechanics SINOROCK 2013. Taylor & Francis Group, pp.363-368. ISBN 978-1-13-800057-5.
• Linkov, A.M. (2013) Numerical modeling of seismicity: theory and applications. Proceedings of 8-th International Symposium on Rockbursts and Seismicity in Mines. Saint Petersburg-Moscow, Russia; 1 - 8 September 2013, pp 197-219.
• Rybarska-Rusinek, L., Rejwer, E., Jaworski, D. (2013) Evaluation of stresses in strongly inhomogeneous rock with multiple cracks, openings and pillars. Proceedings of 8-th International Symposium on Rockbursts and Seismicity in Mines. Saint Petersburg-Moscow, Russia; 1 - 8 September 2013, pp 249-259.
• Dubatovskaya, M., Rogosin, S. (2014) On effective conductivity formula for bounded symmetric composite material. Complex Analysis and Potential Theory and Applications (Editors: T. Aliev Azerogly, A. Golberg, S. Rogosin), 53-62. - Proceedings of two sessions of The 9th ISAAC Congress, Krakow, Poland, 5-9 August 2013.
• Koroleva, A., Mishuris, G., Rogosin, S. (2014) Description of the contact zone by using the Wright function. Complex Analysis and Potential Theory and Applications (Editors: T. Aliev Azerogly, A. Golberg, S. Rogosin), 133-138. - Proceedings of two sessions of The 9th ISAAC Congress, Krakow, Poland, 5-9 August 2013.

Preprints

• Linkov, A. M., Use of a speed equation for numerical simulation of hydraulic fractures. arXiv:1108.6146. http://arxiv.org/abs/1108.6146
• Piccolroaz A., Mishuris G., Movchan A., Movchan N., Perturbation analysis of Mode III interfacial cracks advancing in a dilute heterogeneous material. arXiv: 1105.3497. http://arxiv.org/abs/1105.3497
• Vellender A., Mishuris G., Movchan A., Weight Function In a Bimaterial Strip Containing an Interfacial Crack and an Imperfect Interface. Application to Bloch-Floquet Analysis In a Thin Inhomogeneous Structure With Cracks. arXiv: 1107.5690v1. http://arxiv.org/abs/1107.5690
• Vellender A., Mishuris G., Eigenfrequency correction of Bloch-Floquet waves in a thin periodic bi-material strip with cracks lying on perfect and imperfect interfaces. arXiv: 1107.5948. http://arxiv.org/abs/1107.5948
• Mishuris G., Wrobel M., Linkov A., On modeling hydraulic fracture in proper variables: stiffness, accuracy, sensitivity. arXiv: 1203.5691 http://arxiv.org/abs/1203.5691.
• Piccolroaz, A., Mishuris, G., Movchan, A., Movchan, N. Mode III crack propagation in a bimaterial plane driven by a channel of small line defects. http://arxiv.org/abs/1110.5836
• Piccolroaz, A., Mishuris, G. Integral identities for a semi-infinite interfacial crack in 2D and 3D elasticity. http://arxiv.org/abs/1110.3612.
• Piccolroaz, A., Mishuris, G., Movchan, A., Movchan, N. Perturbation analysis of Mode III interfacial cracks advancing in a dilute heterogeneous material. http://arxiv.org/abs/1105.3497.
• Mishuris, G., Movchan, A., Movchan, N., Piccolroaz, A. Interaction of an interfacial crack with linear small defects under out-of-plane shear loading. http://arxiv.org/abs/1010.6223.
• Piccolroaz, A., Mishuris, G., Radi, E. Mode III interfacial crack in the presence of couple stress elastic materials. http://arxiv.org/abs/1010.1822.
• Wrobel, M., Mishuris, G. Efficient pseudo-spectral solvers for the PKN model of hydrofracturing, http://arxiv.org/abs/1302.1209.
• Mishuris G., Piccolroaz A., Vellender A. Boundary integral formulation for cracks at imperfect interfaces. http://arxiv.org/abs/1312.2582
• Jones, S. A., Dollet, B., Méheust, Y., Cox, S. J., Cantat, I. Structure-dependent mobility of a dry aqueous foam flowing along two parallel channels. arXiv:1309.2481
• Kusmierczyk, P., Mishuris, G., Wrobel, M. Remarks on application of different variables for the PKN model of hydrofracturing. Various fluid-flow regimes, http://arxiv.org/abs/1211.6474.
• Satomi, R., Grassia, P., Cox, S.J., Mishuris, G., Lue, L. Diffusion of curvature on a sheared semi-infinite film, http://users.aber.ac.uk/sxc/WORK/sheared_film.pdf.
• Mishuris, G., Rogosin, S. An asymptotic method of factorization of a class of matrix functions, http://arxiv.org/abs/1402.2120.
• Mainardi, F., Rogosin, S. George William Scott Blair - the pioneer of fractional calculus in rheology. , http://arxiv.org/abs/1404.3295.
• Mishuris, G., Rogosin, S., Wrobel, M. Moving Stone in the Hele-Shaw Flow , http://arxiv.org/abs/1404.3547.
• Perkowska M., Wrobel M., Mishuris G. Universal hydrofracturing algorithm for shear-thinning fluids: particle velocity based simulation, http://arxiv.org/abs/1506.08310.
• Wrobel M., Mishuris G. Particle velocity based universal algorithm for numerical simulation of hydraulic fractures, http://arxiv.org/abs/1412.5529.
• Wrobel, M., Mishuris, G., Piccolroaz, A. Energy Release Rate in hydraulic fracture: can we neglect an impact of the hydraulically induced shear stress? https://arxiv.org/pdf/1610.07881v1.pdf