Research

Mathematical modeling of wave propagation in heterogeneous media;

Multiscale modeling of flow through porous media;

Multiscale modeling of thermo-viscoelastic properties of composites;

Mathematical modeling of dynamical systems with applications to biology

2024    Savatorova, V.L., Talonov, A.V. (2024) Differential equations for modeling pathways leading to diabetes onset CODEE Journal: Vol. 18, Article 1., 

            https://scholarship.claremont.edu/codee/vol18/iss1/1

2023     Savatorova, V. (2023) Exploring Parameter Sensitivity Analysis in Mathematical Modeling with Ordinary Differential Equations, CODEE Journal:   

              Vol. 16, Article 4., https://scholarship.claremont.edu/codee/vol16/iss1/4

2023     Savatorova V.L., Talonov A.V., Teaching differential equations through modelling: hot water heater. International Lournal of Mathematical 

              Educationin Science and Technology, DOI: 10.1080/0020739X.2023.2249899

2023      Savatorova V.L., Talonov A.V., Mathematical modeling of wave propagation in  materials with multi-periodic hierarchical structure of heterogeneities.

              Composites:  Mechanics, Computations, Applications. An International Journal.-14(3), p.45-72, 2023

               DOI: 10.1615/CompMechComputApplIntJ.2023047434.

2023     Vlasov, A.N., Volkov-Bogorodsky, D.B., Savatorova, V.L.,Using Asymptotic homogenization in parametric space to determine effective thermo-   

              viscoelastic  properties of fibrous composites. In: Altenbach, H., Kaplunov, J., Lu, H., Nakada, M.  (eds) Advances in Mechanics of Time-Dependent

               Materials. Advanced Structured Materials, vol 188. Springer, Cham.(2023)  https://doi.org/10.1007/978-3-031-22401-0_10

2022      Vlasov A.N., Volkov-Bogorodsky D.B., Savatorova V.L., Using asymptotic homogenization in parametric space to determine effective thermo-

              viscoelastic properties of fibrous composites (submitted for publication as a chapter in the book Advances in Mechanics of Time-dependent Materials 

               Eds. Holm Altenbach, Julius Kaplunov, Hongbing Lu, Masayuki Nakada, to be published by Springer)

2022      Vlasov A.N., Volkov-Bogorodsky D.B., Savatorova V.L., Using asymptotic homogenization to determine effective thermo-viscoelastic properties 

              of fibrous composites with interphase layer. Mathematics and Mechanics of Solids. https://journals.sagepub.com/doi/10.1177/10812865221140526

2021       Talonov A.V., Savatorova V.L., Heat transfer in a composite material with structural hierarchy. Composites: Mechanics, Computations, 

               Applications. An International Journal.-12(2), p.45-59, 2021. DOI: 10.1615/CompMechComputApplIntJ.2021038886

2021      Vlasov A.N., Volkov-Bogorodsky D.B., Savatorova V.L. Calculation of the effective  properties of thermo-viscoelastic composites using asymptotic 

               homogenization in parametric space. Mech Time Depend Mater (2021).  https://doi.org/10.1007/s11043-021-09501-4

2020      Savatorova V.L. Talonov A.V. Acoustic waves propagation in saturated cracked  porous media under compression.  Composites: Mechanics, 

              Computations, Applications. An International Journal. –11(1), 57-75. http://dx.doi.org/10.1615/CompMechComputApplIntJ.2020033386

2019      Savatorova V.L., Talonov A.V., Mathematical modeling of gas transport in porous geological media with contrast of properties and irregular 

              distribution of pores, ZAMM Z.Angew.Math. Mech, https://doi.org/10.1002/zamm.201800217. 

2017     Talonov A.V., Savatorova V.L., Vlasov A.N. High-frequency approximation of plane wave propagation in an elastic medium with periodic distribution of cracks, Composites: Mechanics, Computations, Applications. An International Journal. –8(4), p.339-354.

2017      Savatorova V.L., Talonov A.V., Vlasov A.N. Low-frequency wave propagation in geological media with isolated cracks, Composites: Mechanics, Computations, Applications. An International Journal. –8(2), p.85-107.

2017      Talonov A.V., Kossovich E.L., Savatorova V.L.  Elastic waves in fractured rocks under periodic compression, International Journal of Mechanical and Materials Engineering.- 12: 13. doi:10.1186/s40712-017-0080-8

2016      Savatorova V.L., Talonov A.V., Vlasov A.N. Upscaling of dual-porosity models for gas transport in organic-rich shales, Composites: Mechanics, Computations, Applications. An International Journal. -7(3), p. 233-259.

2016      Savatorova V.L., Talonov A.V., Vlasov A.N., Volkov-Bogorodsky D.B. Multiscale modeling of gas flow through organic-rich shale matrix, Composites: Mechanics, Computations, Applications. An International Journal. -7(1), p. 45-70.

2015      Brown D.L., Efendiev Y., Li G., Savatorova V. Homogenization of high contrast Brinkman flows, SIAM Multiscale Model. Simul. - 13(2),p. 472–490.     

2015      Savatorova V.L., Talonov A.V., Vlasov A.N., Volkov-Bogorodsky D.B.  Brinkman’s filtration of fluid in rigid porous media: multiscale analysis and investigation of effective permeability, Composites: Mechanics, Computations, Applications. An International Journal. -6(3), p. 239-264.

2015      Akkutlu I.Y., Efendiev Y., Savatorova V. Multi-scale Asymptotic Analysis of Gas Transport in Shale Matrix, Transport in Porous Media.-v. 107(1), p. 235-260.

2014      Savatorova, V.L., Talonov A.V., Vlasov A.N., Volkov-Bogorodsky D.B.  Averaging of the non-stationary equations of viscous substance filtration through a rigid porous medium, Composites: Mechanics, Computations, Applications. An International Journal. -5(1), p.35-61.        

2013      Brown D., Efendiev Y, Li G., Popov P., Savatorova V. Multiscale Modeling of High Contrast Brinkman Equations with Applications to Deformable Porous Media, Poromechanics V, p. 1991-1996, ASCE.        

2013      Savatorova V.L., Talonov A.V., Vlasov A.N., Volkov-Bogorodsky D.B.  Averaging of time-dependent equations of viscous fluid filtration in non-deformable porous medium, Composite mechanics and design. - v.19.- N4.- p.535-555.

2013      Savatorova V.L., Vlasov A.N. Modeling of viscous fluid filtration in porous media with cylindrical symmetry, Composites: Mechanics, Computations, Applications. An International Journal. - 4(1), p.1–20.

2013      Kudryashov N.A., Kochanov M.B., Savatorova V.L. Approximate self-similar solutions for the boundary value problem arising in modeling of gas flow in porous media with pressure dependent permeability, Applied Mathematical Modeling -v.37, issue 7, p.5563-5573.

2012      Savatorova V.L., Talonov A.V., Vlasov A.N. Homogenization of thermoelasticity processes in composite materials with periodic structure of heterogeneities, ZAMM Z.Angew.Math. Mech.-1-22(2012) DOI 10.1002/zamm.201200032.

2012      Savatorova V.L., Talonov A.V., Vlasov A.N., Volkov-Bogorodsky D.B. Multiscale modelling of thermoelastic properties of composites with periodic structure of heterogeneities, Material’s Physics and Mechanics.- v.13, p.130-142.

2011      Savatorova V.L., Talonov A.V., Vlasov A.N., Volkov-Bogorodsky D.B. Homogenization of nonlinear heat conductivity equation for modeling of conductive heat transfer in layered materials, Composite mechanics and design (special issue: Proceedings of All-Russian Conference “Mechanics of nano- structured materials and systems ”, Moscow, December 13-15).- v.2.- p.77-88.

2011      Savatorova V.L., Rajagopal K.R. Homogenization of a generalization of Brinkman’s equation for the flow of a fluid with pressure dependent viscosity through a rigid porous solid, ZAMM Z.Angew.Math. Mech. - v.91, N8, p.630-648.

2010      Savatorova V.L., Talonov A.V., Vlasov A.N. Averaging of Brinkman’s filtration equations in layered porous media, Composite mechanics and design.- v.16.- N4.- p. 483-502.

2010      Savatorova V.L.  Solution of coupled problems of heat conductivity and filtration in layered heterogeneous medium, Scientific-technical journal of the St.Petersburg State Polytechnical University. - №4 (109). – p. 76-86.

2010      Savatorova V.L., Talonov A.V., Vlasov A.N., Volkov-Bogorodsky D.B. Mathematical simulation of heat transfer in a periodic medium with cylindrical inclusions separated from the matrix by a thin contact layer, Herald of the Nizhny Novgorod University named after N.I. Lobachevsky. - №6.- p.178-185.

2010      Savatorova V.L., Talonov A.V., Shirochin D.L. Propagation of melting front in structurally heterogeneous media having phase transitions of inhomogeneities, ZAMM Z.Angew.Math. Mech. -  v.90, N4, p.309-322.

2010      Savatorova V.L., Vlasov A.N., Talonov A.V. Averaging of the heat conduction equations with account for the convective mechanism of heat transfer, Composites: Mechanics, Computations, Applications. An International Journal. -v.1, N2, p.1-21.

2009      Savatorova V.L., Balueva M.A., Blohin D.I., Talonov A.V., Sheinin V.I. The modeling of influence of micro cracks in loaded geological materials on variations in temperature, Journal of Mining Science. - № 6, p.55-60. 

2009      Savatorova V.L., Vlasov A.N., Talonov A.V. Homogenization of heat transfer equations, considering convective mechanism of heat transfer, Composite mechanics and design. - v.15. -№1. -p.17-31. 

2010      Savatorova, V.L., Beliy, A.A. Mathematical modeling of heat transfer in heterogeneous media with periodic structure. Mining Informational and Analytical Newsletter, №9, 98pp.

2010      Savatorova, V.L. Mathematical modeling of the filtration of fluid through porous medium with periodic structure. Mining Informational and Analytical Newsletter, №8, 61pp. 

2009      Savatorova, V.L., Vlasov, A.N., Talonov, A.V. The modeling of physical processes in media with heterogeneities of structure. Peoples’ Friendship University of Russia, Moscow, 258 pp.

2023    Savatorova V.L., Talonov A.V. “Models described using differential equations: First steps in the study of parameter sensitivity analysis”, Proceedings of 

            the MAA MathFest 2023, Tampa, FL, August 2-5, 2023.

2023     Savatorova V.L. “Differential equations for modeling long-term development  of diabetes: stability analysis”. Proceedings of the Joint Mathematic

   Meetings, Boston, MA, January 4-7, 2023.

2023    Savatorova V.L., Talonov A.V., “Mathematical modeling of wave propagation in materials with multi-periodic hierarchical structure of heterogeneities”. 

            Proceedings of the Joint Mathematics Meetings, Boston,MA, January 4-7,  2023.

2022    Savatorova V.L. “Differential equations for modeling blood glucose dynamics and detecting diabetes”, Proceedings of the MAA MathFest 2022,   

            Philadelphia, PA, August 3-6, 2022. 

2022    Savatorova V.L. “Modeling nonlinear oscillations in the plane: from Van der Pol oscillator to mathematics of heartbeat and nerve impulse transmission”. 

            Proceedings of the Joint Mathematics Meetings, virtual meetings,  April 6-9,   2022.

2022    Savatorova V.L., Talonov A.V. “Using software to manipulate equations and visualize solutions”. Proceedings (and video recording) of the 34th 

            International Conference  on  Technology in Collegiate Mathematics (ICTCM), Whole > Σ parts, Virtual event, March 14, 2022.

2022    Savatorova V.L., Talonov A.V. “Teaching differential equations through modeling: hot water heater”. SIMIODE EXPO 2022, February 10-13, 2022.

2021    Savatorova V.L., Talonov A.V. “Melting ice in northern seas due to the global warming: self-similar solution for Stefan’s problem”. Virtual 2021 

            MathFest, 4-7 August 2021.

2021    Savatorova V.L., Talonov A.V.“Using technology in remote teaching of ODEs  and  Linear Algebra”. Proceedings (and video recording) of the 33rd 

            International Conference on Technology in Collegiate Mathematics (ICTCM),  Reimagined. Virtual Conference,  March 12, June 11, October 8, 2021.

2021    Savatorova V.L. Tools of the trade or how to encourage student’s engageme in remote ODE class. Proceedings of the Joint Mathematics Meetings, 

            virtual meetings,  January 6-9, 2021.

2020    Talonov A.V., Savatorova V.L. Modeling of heat transfer in heterogeneo materials with a complex hierarchical structure. Proceedings of the 10th

            Conference on Mechanics of  Composite Materials and Structures (MCMS 2020), Online, November 17-19, 2020. 

2020    Savatorova V.L., Talonov A.V. Mathematical modeling of wave propagation in pre-loaded elastic materials with multiscale structure. Proceedings (and 

            video recording) of  XLVIII International Summer School-Conference Advanced Problems in Mechanics  (APM 2020), Online, June 21-26, 2020.

2020   Savatorova V.L., Talonov A.V., Cox K. “Web-based Audience Response Systems for Student’s Engagement in the Math Classroom”. Proceedings (and 

           video recording) of the 32nd International Conference on Technology in  Collegiate Mathematics (ICTCM), Virtual Conference, May 2020.

2020   Savatorova V.L., Talonov A.V. Above and beyond traditional instruction through integrating research projects into Calculus classroom. Proceedings of 

           the Joint  Mathematics Meetings, Denver, CO, January 15-18, 2020.

2020    Talonov A.V., Savatorova V.L. Transformative Teaching Redesign:  Development of  High-Impact Strategies to Maximize Learning and Minimize 

           Failure in Introductory Courses of Mathematics. Proceedings of the Joint Mathematics Meetings, Denver, CO, January 15-18, 2020.

2019    Talonov A.V., Cox K., Savatorova V.L., Strategies to maximize learning and  minimize failure in precalculus classes. Proceedings of the MAA Southern 

            California -Nevada Section Fall 2019, University of Nevada Las Vegas, Las Vegas, NV, October 6-7, 2019.

2019    Savatorova V.L., Talonov A.V. Acoustic Waves Propagation in Fractured Porous Materials: High and Low Frequency Approximation. Proceedings of

            the SIAM Geosciences 2019, Houston, TX, March 11-14, 2019.

2019    Savatorova V.L., Talonov A.V. High-frequency homogenization for modeling acoustic wave propagation in multi-scale periodic media. Proceedings of

            the Joint Mathematics Meetings, Baltimore, MD, January 16-19, 2019.

2019    Savatorova V.L., Talonov A.V. Undergraduate ODEs and Linear Algebra for engineering  majors: studying the foundations and learning by doing. 

            Proceedings of the Joint  Mathematics Meetings, Baltimore, MD, January 16- 19, 2019.

2018    Savatorova V.L. A multiscale coupled model for shale gas transport in porous geological media with contrast of properties. Proceedings of the II 

            International conference  Multiscale Methods and Large-scale Scientific Computing, Moscow, August 15-17,  2018. 

2018    Savatorova V.L., Talonov A.V. Gas transport in porous geological media with contract of  properties, and irregular distribution of pores. Proceedings of

            the InterPore 10th Annual Meeting and Jubilee, New Orleans, USA, May 14-17, 2018.

2018     Savatorova V.L., Talonov A.V. Multi-scale modeling of high frequency wave propagation in heterogeneous medium with cracks. Proceedings of the

             Joint Mathematics Meetings, San Diego, CA, January 10-13,2018.

2017    Savatorova V.L., Talonov A.V. Small amplitude wave propagation in heterogeneous media with pores and cracks: high- and low frequency

            approximations. Proceedings of the SIAM, Conference on Analysis of Partial Differential Equations, Baltimore, Maryland, December 9-12, 2017. 

2017    Savatorova V.L., Talonov A.V., Vlasov A.N. Modeling of gas filtration processes in geomaterials of organic origin with a structure close to periodic.

           Proceedings of the    conference Mechanics of composite materials and   structures, complex and heterogeneous media, Institute of Applied Mechanics of

            Russian Academy of Sciences, Moscow, Russia, November 21-23, 2017.

2017   Savatorova V.L., Talonov A.V. Wave propagation in heterogeneous media with cracks: high- and low frequency approximations. Proceedings of the Fall 2017 AMS Western Sectional Meeting, University of California, Riverside, November 4-5, 2017.

2017    Savatorova V.L., Talonov A.V, Kossovich E.L. Dispersion and anisotropy of waves propagating in fractured porous media. Proceedings of the 6th International conference “The problems of mathematical physics and mathematical modeling”, National Research Nuclear University MEPhI, Moscow, Russia, May 25-27, 2017. 

2016    Savatorova V.L., Vlasov A.N., Talonov A.V, Kossovich E.L. Modeling of acoustic waves propagation in pre-loaded media with penny shaped cracks and pores. Proceedings of the conference “Mechanics of composite materials and structures, complex and heterogeneous media”, Institute of Applied Mechanics of RAS, Moscow, Russia, November 16-18, 2016.

2016    Savatorova V.L., Talonov A.V. Modeling of gas transport in organic-rich shales with irregular distribution of pores. Proceedings of the Fall 2016 AMS Western Sectional Meeting, University of Denver, Denver, October 8-9, p. 90, 2016.

2016    Savatorova V.L., Talonov A.V. Wave propagation in heterogeneous geological media with cracks. Proceedings of the 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 1 - July 5, Orlando, Florida, 2016.

2016    Savatorova V.L., Talonov A.V. Fluid transport through the porous media with irregular distribution of heterogeneities. Proceedings of the 8th International Conference on Porous Media, Cincinnati, Ohio, May 9 -12, 2016.

2016    Savatorova V., Talonov A., Kossovich E. The Multiscale Modelling for wave propagation in heterogeneous media. Proceedings of the 5th international conference “Problems of Mathematical and Theoretical Physics and Mathematical Modeling, National Research Nuclear University “MEPhI”, Moscow, Russia, April 5-7, 2016.

2016    Savatorova V., Talonov A. Homogenization of PDEs arising in Dual-Porosity Models for Fluid Flow in Organic-Rich Shales. Proceedings of AMS conference. Spring Southeastern Sectional Meeting, University of Georgia, Athens, March 5-6, 2016.

2015    Savatorova V., Talonov A., Vlasov A., Volkov-Bogorodsky D. Multi scale averaging of equations describing transport of gas phase in a porous medium. Proceedings of the Conference “Mechanics of composite materials and structures, complex and heterogeneous media”. Moscow, Institute of Applied Mechanics of Russian Academy of Sciences, December 15-17, p.544-545, 2015.

2015    Savatorova V.L., Kossovich E.L., Talonov A.V.  A Multi-scale Approach to Modeling of Gas Transport in Shales. Proceedings of the SIAM Conference on Mathematics & Computational Issues in the Geosciences, Stanford, California USA, June 29- July 2, p.89, 2015.

2015    Kossovich E.L., Talonov A.V., Savatorova V.L.  Multi-scale Asymptotic Analysis of Gas Transport in Porous Media. Proceedings of the 7th International Conference on Porous Media, Padova, May 18-21, 2015.

2015    Savatorova V. L., Efendiev Y., Akkutlu I.Y. Modeling of gas transport in organic-rich recourse shales. Proceedings of AMS conference. Spring Western Sectional Meeting, University of Nevada Las Vegas, April 18-19, p. 87, 2015.

2015    SavatorovaV.L. Moscow school of mathematics: history of the origin, the heyday and the disintegration of the legendary Luzitania. Proceedings of AMS conference. Spring Western Sectional Meeting, University of Nevada Las Vegas, April 18-19, p. 60, 2015.

2015    Kossovich E., Talonov A., Savatorova V. Modeling of gas transport in nano- and microporous heterogeneous media. Proceedings of the 4th Conference ” Methods of mathematical physics and mathematical modeling of physical processes”, Scientific Session of the NRNU ‘MEPhI’, February, 18-21, 2015.

2015    Savatorova V., Talonov A., Vlasov A. Rheology of shales: Three-scale model of gas phase transport in a porous media. Proceedings of the Conference “Mechanics of nano- structured materials and heterogeneous systems”, Moscow, Institute of Applied Mechanics of Russian Academy of Sciences, p.8-17, 2015.

2014    Savatorova V.L. “Modeling of gas transport in kerogene nanopores”, 6th International Conference on Porous Media, University of Wisconsin, Milwaukee, Wisconsin, USA, May 27-30, 2014.

2013    Savatorova V.L., Talonov A.V., Vlasov A.N., Volkov-Bogorodsky D.B. Rheology of shales: transport of gas phase in kerogen nanopores. Proceedings of the 2nd Conference “Mechanics of nano- structured materials and systems,” Moscow, Institute of Applied Mechanics of Russian Academy of Sciences, December 17-19, 2013.

2013    Brown D., Li G., Efendiev Y., Savatorova V. “Multiscale modeling of High Contrast Brinkman Equations with Applications to Deformable Porous Media.” Proceedings of the 5th Biot Conference on Poromechanics, July 10-12, Vienna, 2013.

2013    Savatorova V.L., Talonov A.V., Vlasov A.N. Homogenization in case of transient motion of a fluid through a porous medium. Proceedings of the SIAM Conference on Mathematics & Computational Issues in the Geosciences, Department of Mathematics University of Padova, Italy, June 17-20, p.79, 2013.

2013    Brown D., Li G., Efendiev Y., Savatorova V. Homogenization of High-Contrast Brinkman Flows. Proceedings of the 5th International Conference on Porous Media, Czech Technical University in Prague, May 22-24, 2013.

2013    Savatorova V.L., Talonov A.V., Vlasov A.N., Volkov-Bogorodsky D.B. Upscaling in case of transient motion of a compressible fluid through a porous medium. Proceedings of the 5th International Conference on Porous Media, Czech Technical University in Prague, May 22-24, 2013.

2012    Savatorova V.L., Talonov A.V., Vlasov A.N. Transient flow in rigid porous material. Proceedings of the 4th All-Russian symposium “Composite mechanics and design.” Moscow, Institute of Applied Mechanics of Russian Academy of Sciences, December 4-6, p.81, 2012.

2012   “Upscaling of filtration in rigid porous media. Investigation of effective permeability of periodic granular medium.” 4th International Conference on Porous Media, Purdue University, May 14-16, 2012.

2011    Savatorova V.L., Talonov A.V., Vlasov A.N., Volkov-Bogorodsky D.B. Homogenization of nonlinear heat conductivity equation for modeling of conductive heat transfer in layered materials. Proceedings of the Conference “Mechanics of nano- structured materials and systems”, Moscow, Institute of Applied Mechanics of Russian Academy of Sciences, December 13-15, p.89, 2011.

2011    Savatorova V.L., Talonov A.V., Vlasov A.N., Volkov-Bogorodsky D.B. Multi scale modeling of thermo-mechanical properties of composites with

            periodic structure of heterogeneities. Proceedings of the 14th International Workshop on New Approaches to High-Tech: Nano-Design, Technology, 

            Computer Simulations (NDTCS-2011), Espoo, Finland, August 22-26, p.63, 2011.

2011    Savatorova V.L. “Homogenization of filtration process through rigid porous medium on the base of Brinkman’s equation”, 3rd International Conference

             on Porous Media, Bordeaux, March 29-31, 2011.

2011      Savatorova V.L. Multi-scale Modeling of Brinkman’s Filtration in Layered Porous Media. Proceedings of the SIAM Conference on Mathematics & Computational Issues in the Geosciences, Long Beach, California USA, March 21-24, p.89, 2011.

2009    Vlasov A.N., Savatorova V.L., Talonov A.V. Thermo mechanical behavior of composed materials with layered structure with taking into consideration the effects of nonlinear thermo conductivity. Mechanics and nano mechanics of heterogeneous media. Proceedings of the Conference, devoted to 20th anniversary of Institute of Applied Mechanics of Russian Academy of Sciences, Moscow, p.30, 2009.

2009      Savatorova V.L.,Talonov A.V., Shirochin D.L. The solution of heat conductivity problem in heterogeneous medium, considering the dependence of heat conductivity coefficient on temperature. Proceedings of the X Russian Symposium on Applied and Industrial Mathematics (fall session), Sochi - Dagomis, October 1-8, 2009.

2009      Vlasov A.N., Markelov P.E., Savatorova V.L. Analysis of deformation behavior of  the system: “matrix-layer-inclusion”. Proceedings of the X Russian Symposium on Applied and Industrial Mathematics (fall session), Sochi - Dagomis, October 1-8, 2009.

2009      Vlasov A.N., Nikitina E.A., Savatorova V.L., Talonov A.V. The modeling of the strength properties of media, considering nano characteristics of the layer in the system carbon particles – organic polymer. Proceedings of the Second Conference “Multiscale modeling of the processes and structures in nanotechnology”, Moscow, MEPHI, p.403-404, 2009.