THE UNIVERSITY OF BIRMINGHAM

THE SCHOOL OF MATHEMATICS

THE APPLIED MATHEMATICS GROUP

N.B.PETROVSKAYA

Refereed papers

  E.Forbes, M.Back, A.Brooks, N.Petrovskaya, S.Petrovskii, T.Pope, and K.F.A.Walters.   Stability of Patches of Higher Population Density Within the Heterogeneous Distribution of the Grey Field Slug (Deroceras reticulatum) in Arable Fields in the UK.   Insects, 2021, 12, 9; https://dx.doi.org/10.3390/insects12010009

  J.R.Ellis, N.B.Petrovskaya, E.Forbes, K.F.A.Walters and S.V.Petrovskii.   Patterns of Individual Movement of the Grey Field Slug (Deroceras reticulatum) in an Arable Field.   Scientific Reports, 2020, 10:17970 https://doi.org/10.1038/s41598-020-74643-3

  J.R.Ellis, N.B.Petrovskaya.   A Computational Study of Density-Dependent Individual Movement and the Formation of Population Clusters in Two-Dimensional Spatial Domains.   Journal of Theoretical Biology, 2020, 505: 110421; https://doi.org/10.1016/j.jtbi.2020.11042

  E.Forbes, M.Back, A.Brooks, N.Petrovskaya, S.Petrovskii, T.Pope, and K.F.A.Walters.   Locomotor Behaviour and the Discontinuous Distribution of Slugs in a Commercial Winter Wheat Field: Tracking the Movement of Deroceras Reticulatum Above and Below the Soil Surface Using Radio Frequency Identification Tags.   Pest Management Science, 2020,   https://doi.org/10.1002/ps.5895

  N.B.Petrovskaya, J.R.Ellis, E.Forbes, and K.F.A. Walters.   Modelling a Targeted Use of Pesticide Procedure for Pest Populations with Heterogeneous Spatial Distributions.   Ecological Modelling, 2020, 427: 109059   https://doi.org/10.1016/j.ecolmodel.2020.109059

  N.B.Petrovskaya, W. Zhang.   When Seeing is not Believing: Comparative Study of Various Spatial Distributions of Invasive Species.   Journal of Theoretical Biology, 2020, 488: 110141   https://doi.org/10.1016/j.jtbi.2019.110141

  J.R.Ellis, N.B.Petrovskaya, S.V.Petrovskii.   Effect of Density-Dependent Individual Movement on Emerging Spatial Population Distribution: Brownian Motion vs Levy Flights.   Journal of Theoretical Biology 2019, vol.464, pp. 159–178,   doi:10.1016/j.jtbi.2018.12.016

  N.B.Petrovskaya, E. Forbes, S.V.Petrovskii, K.F.A. Walters.   Towards the Development of a More Accurate Monitoring Procedure for Invertebrate Populations, in the Presence of Unknown Spatial Pattern of Population Distribution in the Field.   Insects 2018, vol. 9, 29;   doi:10.3390/insects9010029   abstract ,   pdf file

  N.B.Petrovskaya, S.V.Petrovskii, W.Zhang.   Patchy, not Patchy, or How Much Patchy? Classification of Spatial Patterns Appearing in a Model of Biological Invasion. Math. Model. Nat. Phenom. 2017, vol.12, pp. 208-225   doi: https://doi.org/10.1051/mmnp/2017065   abstract ,   pdf file

  N.B.Petrovskaya   `Catch Me If You Can': Evaluating the Population Size in the Presence of a Spatial Pattern. Ecol. Complex., 2017, doi: 10.1016/j.ecocom.2017.03.003   abstract ,   pdf file

  N.B.Petrovskaya, S.V.Petrovskii.   Catching Ghosts with a Coarse Net: Use and Abuse of Spatial Sampling Data in Detecting Synchronization. J. R. Soc. Interface, 2017, 14: 20160855,   doi: 10.1098/rsif.2016.0855   abstract ,   pdf file

  L.A.D. Rodrigues, D.C.Mistro, E.R.Cara, N.B.Petrovskaya, S.V.Petrovskii.   Patchy Invasion of Stage-Structured Alien Species with Short-Distance and Long-Distance Dispersal.   Bulletin of Mathematical Biology, 2015, vol.77, pp. 1583–1619,   doi: 10.1007/s11538-015-0097-1   abstract ,   pdf file

  D. Bearup, N.B.Petrovskaya, S.V.Petrovskii.   Some Analytical and Numerical Approaches to Understanding Trap Counts Resulting from Pest Insect Immigration.   Mathematical Biosciences, 2015, vol.263, pp.143-160,   doi: http://dx.doi.org/10.1016/j.mbs.2015.02.008   abstract ,   pdf file

  N.L.Embleton, N.B.Petrovskaya.   On the Accuracy of Estimating Pest Insect Abundance from Data with Random Error.   Ecol. Complex., 2015, vol.21, pp.185-198,   doi: 10.1016/j.ecocom.2014.05.006   abstract ,   pdf file

  N.L.Embleton, N.B.Petrovskaya.   A Novel Approach to Evaluation of Pest Insect Abundance in the Presence of Noise.   Bulletin of Mathematical Biology, 2014, vol.76, pp.718-743,   doi: 10.1007/s11538-014-9940-z   abstract ,   pdf file

  S.V.Petrovskii, N.B.Petrovskaya, D.Bearup.   Multiscale Ecology of Agroecosystems is an Emerging Research Field That Can Provide a Stronger Theoretical Background for the Integrated Pest Management. (Reply to Comments on the Review "Multiscale Approach to Pest Insect Monitoring: Random Walks, Pattern Formation, Synchronization, and Networks." by S.V.Petrovskii et al.) Phys Life Rev, 2014, vol.11, pp.536-539,   doi: 10.1016/j.plrev.2014.07.001   pdf file

  S.V.Petrovskii, N.B.Petrovskaya, D.Bearup.   Multiscale Approach to Pest Insect Monitoring: Random Walks, Pattern Formation, Synchronization, and Networks. Phys Life Rev, 2014, vol.11, pp.467-525,   doi: 10.1016/j.plrev.2014.02.001   abstract ,   pdf file

  N.B.Petrovskaya, N.L.Embleton.   Evaluation of Peak Functions on Ultra-Coarse Grids.   Proc. R. Soc. A, 2013, 469:20120665, doi: 10.1098/rspa.2012.0665   abstract   pdf file

  N.L.Embleton, N.B.Petrovskaya.   On Numerical Uncertainty in Evaluation of Pest Population Size.   Ecol. Complex., 2013, vol.14(2), pp.117-131, doi: 10.1016/j.ecocom.2012.11.004   abstract   pdf file

  S.V.Petrovskii, N.B.Petrovskaya.   Computational Ecology as an Emerging Science.   J.R.Soc. Interface Focus, 2012, vol.2(2), pp.241-254, doi:10.1098/rsfs.2011.0083   abstract   pdf file

  N.B.Petrovskaya, S.V.Petrovskii, A.K.Murchie.   Challenges of Ecological Monitoring: Estimating Population Abundance From Sparse Trap Counts.   J.R.Soc.Interface, 2012, vol.9(68), pp.420-435, doi:10.1098/rsif.2011.0386   abstract ,   pdf file

  N.B.Petrovskaya, E.Venturino.   Numerical Integration of Sparsely Sampled Data.   Simulat. Modell. Pract. Theory, 2011, vol.19(9), pp.1860–1872, doi:10.1016/j.simpat.2011.05.003   abstract ,   pdf file

  A. V. Wolkov, Ch. Hirsch, N.B.Petrovskaya.   Application of a Higher Order Discontinuous Galerkin Method in Computational Aerodynamics.   Mathematical Modeling of Natural Phenomena, 2011, vol.6(3) (invited issue on computational aerodynamics), pp.237-263, doi:10.1051/mmnp/20116310   abstract ,   pdf file

  N.B.Petrovskaya.   Data Dependent Weights in Discontinuous Weighted Least-Squares Approximation with Anisotropic Support.   Calcolo, 2011, vol.48(1), pp.127-143, doi: 10.1007/s10092-010-0032-7   abstract ,   pdf file

  N.B.Petrovskaya, S. V. Petrovskii.   The Coarse-Grid Problem in Ecological Monitoring.   Proc. R. Soc. A, 2010, vol.466, pp. 2933-2953, doi: 10.1098/rspa.2010.0023.   abstract ,   pdf file

  A.V.Wolkov, N.B.Petrovskaya.   Higher Order Discontinuous Galerkin Method for Acoustic Pulse Problem.   Comput. Phys. Commun., 2010, vol.181, pp. 1186–1194.   abstract ,   pdf file

  N.B.Petrovskaya, A.V.Wolkov.   The Impact of Grid Geometry on the Accuracy of Higher Order Finite-Volume and Finite Element Schemes.   J. Math. Mod., 2010, vol.22(3), pp.145-160, in Russian.   abstract ,   pdf file

  N.B.Petrovskaya.   Quadratic Least-Squares Solution Reconstruction in a Boundary Layer Region.   Commun. Numer.Meth. Engng., 2010, vol.26(12), pp.1721-1735, doi: 10.1002/cnm.1259.   abstract ,   pdf file

  N.B.Petrovskaya.   Discontinuous Weighted Least-Squares Approximation on Irregular Grids.   CMES: Computer Modeling in Engineering & Sciences, 2008, vol.32(2), pp.69-84, doi: 10.3970/cmes.2008.032.069   abstract ,   pdf file

  N.B.Petrovskaya.   The Accuracy of Least-Squares Approximation on Highly Stretched Meshes. Int. J. Comput. Methods, 2008, vol.5(3), pp.449 - 462.   abstract   pdf file

  N.B.Petrovskaya, A.V.Wolkov, S.V.Lyapunov.   Modification of Basis Functions in High Order Discontinuous Galerkin Schemes for Advection Equation. Appl. Math. Model., 2008, vol.32(5), pp.826-835.   abstract ,   pdf file

  N.B.Petrovskaya, A.V.Wolkov.   The Issues of Solution Approximation in Higher Order Schemes on Distorted Grids. Int. J. Comput. Methods, 2007, vol.4(2), pp.367-382.   abstract ,   pdf file

  N.B.Petrovskaya.   On Oscillations in Discontinuous Galerkin Discretization Schemes for Steady State Problems. SIAM J. Sci. Comput., 2006, vol.27(4), pp.1329-1346.   abstract ,   pdf file

  N.B.Petrovskaya, S.V. Petrovskii, B.-L. Li.   Biodiversity Measures Revisited. Ecol. Complex., 2006, vol.3, pp.13-22.   abstract ,   pdf file

  N.B.Petrovskaya.   Two Types of Solution Overshoots in Discontinuous Galerkin Discretization Schemes.   Comm. Math. Sci., 2005, vol.3(2), pp.235-249.   abstract ,   pdf file

  N.B.Petrovskaya.   Implementation of Newton's Method in High Order Schemes for Steady State Problems.   Comput. Tech., 2005, vol.10(2), pp.106-113, in Russian.   abstract ,   pdf file

  N.B.Petrovskaya.   Approximation of Discontinuous Solutions in High Order Discontinuous Galerkin Schemes.   J. Math. Mod., 2005, vol.17(1), pp.79 - 92, in Russian.   abstract ,   pdf file

  N.B.Petrovskaya.   The Analysis of the Grid Refinement Procedure for Vector Functions.  Comput. Tech., 2004, vol.9(4), pp.3-14.   abstract ,   pdf file

  N.B.Petrovskaya.  The Choice of Weight Coefficients for the Least-Squares Gradient Approximation.   J. Math. Mod., 2004, vol.16(5), pp.83-93, in Russian.   abstract ,   pdf file

  N.B.Petrovskaya.  Modification of a Finite Volume Scheme for Laplace's Equation.   SIAM J. Sci. Comput., 2001, vol.23(3), pp.891-909.   abstract ,   pdf file

  K.V.Brushlinskii, M.S. Mikhailova, A.I.Morozov, N.B.Petrovskaya, V.D.Pustovitov, N.M. Zueva.  Computer Simulation of "Galatea -Stellarator",  Problems of Atomic Science and Technology (ser. Plasma Phys.), 1999, vol.2(2), pp.24-29.

  K.V.Brushlinskii, A.I.Morozov, N.B.Petrovskaya.   Numerical Simulation of Equilibrium Helical Configuration with Plasma on the Separatrix.  J. Math. Mod., 1998, vol.10(11), pp.29-36, in Russian (transl. Eng.)

  K.V.Brushlinskii, N.M.Zueva, M.S.Mikhaylova, N.B.Petrovskaya. Mathematical Model of "Stellarator - Galateya" and Boundary Value Problems with the Grad-Shafranov Equation. Proceedings of European Physical Society (Controlled Fusion and Plasma Physics), Kiev, Ukraine, 1996, pp.119-126.

  K.V.Brushlinskii, N.M.Zueva, M.S.Mikhaylova, N.B.Petrovskaya.   On Uniqueness and Stability of Solutions to 2-D Plasmastatics Problems.  J. Math. Mod., 1995, vol.7(4), pp.73-86, in Russian (transl. Eng.)

  K.V.Brushlinskii, N.M.Zueva, M.S.Mikhaylova, N.B.Petrovskaya.  Dependence of Properties of Helical Plasma Sheaths on Helix Lead.   Plasma Phys. Rep., 1995, vol.21(3), pp.211-225.

  K.V.Brushlinskii, N.M.Zueva, M.S.Mikhaylova, A.I.Morozov, V.D.Pustovitov, N.B.Tuzova (Petrovskaya).  Numerical Simulation of Straight Helical Sheaths with Conductors Immersed in Plasma.   Plasma Phys. Rep., 1994, vol.20(3), pp.284-294.

  K.V.Brushlinskii, V.S.Ryaben'ky, N.B.Tuzova (Petrovskaya).  The Transfer of Boundary Conditions Across a Vacuum in Axisymmetric Problems.  J. Comput. Math. and Math. Phys., 1992, vol.32(12), pp.1757-1767.

  K.V.Brushlinskii, A.I.Morozov, T.A.Ratnikova, N.B.Tuzova(Petrovskaya).  Dissipative Evolution of the Magnetic Configuration of an Autonomic Probe ("Microgalatea").  Sov. J. Plasma Phys., 1992, vol.18(8), pp.1047-1058, in Russian (transl. Eng.)

  K.V.Brushlinskii, T.A.Ratnikova, N.B.Tuzova(Petrovskaya).  Calculation of the Evolution of the Magnetic Field and Temperature in a Conducting Hoop with Current in an Applied Uniform Field.  J.Math. Mod., 1991, vol.2(11), pp.45-54, in Russian (transl. Eng.)

Refereed book chapters

  N.B.Petrovskaya, W. Zhang.   Accurate Recognition of Spatial Patterns Arising in Spatio-Temporal Dynamics of Invasive Species.   in: M.Aguiar, C.Braumann, B.Kooi, A.Pugliese, N.Stollenwerk, E.Venturino (eds.), Current Trends in Dynamical Systems in Biology and Natural Sciences, SEMA-SIMAI Springer Series 21, 2020, pp.19-43,   https://doi.org/10.1007/978-3-030-41120-6_2

  E. Forbes, M. Back, A. Brooks, N. Petrovskaya, S.Petrovskii, T.Pope, and K.F.A.Walters.   Sustainable Management of Slugs in Commercial Fields: Assessing the Potential for Targeting Control Measures   in: R.Hull, G.Jellis, M.May, P.Miller, S.Moss, C.Nicholls, J.Orson (eds.), Aspects of Applied Biology 134, 2017, pp.89-96.   abstract ,   pdf file

  N.B.Petrovskaya.   Algorithms of Solution Reconstruction on Unstructured Grids in Computational Aerodynamics : Impact on Aircraft Design at The Boeing Company.   in: Ph. Aston, T. Mulholland, K. Tant (eds.), UK Success Stories in Industrial Mathematics, Springer-Verlag Berlin Heidelberg, 2016, pp. 137-143.   abstract ,   pdf file

  N.B.Petrovskaya, N.L.Embleton.   Computational Methods for Accurate Evaluation of Pest Insect Population Size.   W.A.C. Godoy and C.P. Ferreira (eds.), Ecological Modelling Applied to Entomology, Springer-Verlag Berlin Heidelberg, 2014, pp.171-218.   abstract ,   pdf file

  N.B.Petrovskaya, N.L.Embleton, S.V.Petrovskii.   Numerical Study of Pest Population Size at Various Diffusion Rates.   M.A. Lewis et al. (eds.), Dispersal, Individual Movement and Spatial Ecology, Lecture Notes in Mathematics, vol.2071, Springer-Verlag Berlin Heidelberg, 2013, pp. 355-386, doi: http://dx.doi.org/10.1007/978-3-642-35497-7_13   abstract ,   pdf file

  N.B.Petrovskaya.   Solution Limiters and Flux Limiters for High Order Discontinuous Galerkin Schemes.   T. Boyanov et al (eds.),   Lecture Notes in Computer Science, vol.4310, Springer-Verlag Berlin Heidelberg, 2007, pp. 668-677.   abstract ,   pdf file

Other publications

  N.B.Petrovskaya.   Preface.   Mathematical Modeling of Natural Phenomena, 2011, vol.6(3) (invited issue on computational aerodynamics), pp.1-1.   pdf file

  N.B.Petrovskaya.   Some Issues of Implementation of Higher Order Schemes in Computational Aerodynamics.   Boeing technical report 66-ZB-B001-10A-533,  The Boeing Company,   Seattle, WA, 2007.

  N.B.Petrovskaya.   A Least-Squares Approximation Problem on "Bad" Grids.   Boeing technical report 104AE, Boeing Operations International, Inc., Moscow, 2003.

  N.B.Petrovskaya.   Non-oscillating Discontinuous Galerkin Schemes for Steady State Problems.   Boeing technical report 104AE, Boeing Operations International, Inc., Moscow, 2003.

    N.B.Petrovskaya.   The Impact of Grid Cell Geometry on the Least - Squares Gradient Reconstruction.   preprint N21, Inst. Appl. Math., Rus.Ac.Sci., 2003.

  N.B.Petrovskaya.   A Modified Discontinuous Galerkin Discretization Scheme for One - Dimensional Conservation Laws.   Boeing technical report 104Z, Boeing Operations International, Inc., Moscow, 2002.

  N.B.Petrovskaya.   Treatment of a Shock for the Discontinuous Galerkin Discretization Scheme.   Boeing technical report 104Z, Boeing Operations International, Inc., Moscow, 2002.

  N.B.Petrovskaya.   The Choice of Grid Adaptation Strategy for Vector Functions.   Boeing technical report 104Y, Boeing Operations International, Inc., Moscow, 2001.

  N.B.Petrovskaya.   Measuring Adaptive Grid Information.   Boeing technical report 104Y, Boeing   Operations International, Inc., Moscow, 2001.

  N.B.Petrovskaya.   Error Indicators and Analysis of Refinement Technology for Vector Functions.   Boeing technical report 104W, Boeing Operations International, Inc., Moscow, 2000.

  N.B.Petrovskaya.  Positive Finite Volume Scheme for Laplace's Equation on Arbitrary 2-D Unstructured Meshes.   In Proceedings of 16-th IMACS World Congress 2000, Lausanne, Switzerland, August 21-25, 2000.

  N.B.Petrovskaya.   Large Angles Tolerant Discretization.   Boeing technical report 104R, Boeing Operations International, Inc., Moscow, 1999.

  N.B.Petrovskaya.   A Modified Finite Volume Scheme for Laplace's Equation.   Boeing technical report 104R, Boeing Operations International, Inc., Moscow, 1999.

  S.K.Godunov, O.B.Feodoritova,A.V.Gusev, D.S.Kamenetskii, M.V.Mikchailuk, I.L.Petrouchenkov, N.B.Petrovskaya, V.T. Zhukov.   Grid Generation System. User's guide.   Boeing technical report 104L, Boeing Operations International,Inc., Moscow, 1997

  N.B.Petrovskaya.   A Surface Grid Generation Problem in the Presence of Singular Points.   Boeing technical report 104G, Boeing Operations International, Inc., Moscow, 1996

  N.B.Petrovskaya.   A Bifurcation Model for Solutions to a One-Dimensional Plasmastatics Problem.   preprint N61, Inst. Appl. Math., Rus.Ac.Sci., 1994, in Russian.