Education and Employment Honors and Awards Research Projects and Grants Publications Graduate Students Curriculum Vitæ UT Arlington Faculty Profile Home

RESEARCH INTERESTS Numerical Analysis Numerical Solution of Ordinary and Partial Differential Equations/Systems: Nonstandard Finite Difference Methods Mathematical Biology Modeling and Analysis of Complex Biological Systems: Biofilms, Predator-Prey Systems, and Other Systems in Aquatic Ecology Fluid Mechanics Flows in Porous Media Scientific Computation     My main scientific research can be divided into the following two broad categories: numerical analysis and mathematical biology. It is strongly motivated and oriented toward applications. I am primarily interested in the formulation, analysis and implementation of new, stable and efficient numerical methods for nonlinear ordinary and partial differential equations/systems. I am also interested in the accurate mathematical modeling and theoretical analysis of biological phenomena, in particular the modeling of microbial populations, biofilms, and general competition dynamics in porous media and in flow reactors. EDUCATIONAL HISTORY Ph.D. (Applied Mathematics), 1998 Department of Mathematics, University of Wyoming, U.S.A. M.S. (Mathematics), 1994 Faculty of Mathematics and Informatics, Sofia University "St. Kliment Ohridski", Bulgaria M.S. (Secondary Mathematics Education), 1994 Faculty of Mathematics and Informatics, Sofia University "St. Kliment Ohridski", Bulgaria EMPLOYMENT HISTORY Associate Professor, Department of Mathematics, University of Texas at Arlington, U.S.A., 9/2006-Present Assistant Professor, Department of Mathematics, University of Texas at Arlington, U.S.A., 9/2000-8/2006 Visiting Assistant Professor, Department of Biology, University of Texas at Arlington, U.S.A., 9/2001-8/2002 Visiting Assistant Professor, Department of Mathematics, Arizona State University, U.S.A., 9/1998-5/2000 PROFESSIONAL AFFILIATIONS (UT ARLINGTON) Bioscience & Bioengineering Center Center for Numerical Simulation and Modeling Ecology Group UT Arlington's student chapter of the MAA RECENT HONORS AND AWARDS 2009; Travel/Professional Development Award, Office of the Provost and Vice President for Academic Affairs, University of Texas at Arlington 2008; Travel/Professional Development Award, Office of the Provost and Vice President for Academic Affairs, University of Texas at Arlington 2007; Research Excellence Award, Office of the Provost and Vice President for Academic Affairs, University of Texas at Arlington 2007; Travel/Professional Development Award, Office of the Provost and Vice President for Academic Affairs, University of Texas at Arlington 2007; Who's Who of Emerging Leaders, The 1-st Edition of Marquis Who's Who of Emerging Leaders 2006; Research Excellence Award, Office of the Provost and Vice President for Academic Affairs, University of Texas at Arlington 2006; Travel/Professional Development Award, Office of the Provost and Vice President for Academic Affairs, University of Texas at Arlington 2006; Faculty Travel Supplement Program Award, Office of the Dean of the Graduate School, University of Texas at Arlington 2006-2007; Who's Who in Science and Engineering, The 9-th Edition of Marquis Who's Who in Science and Engineering 2006-2007; Who's Who in American Education, The 7-th Edition of Marquis Who's Who in American Education 2006; Who's Who in America, The 60-th Diamond Anniversary Edition of Marquis Who's Who in America 2005; Professor of the Year, Mathematical Association of America, UTA Student Chapter, University of Texas at Arlington 2005; Research Excellence Award, Office of the Provost and Vice President for Academic Affairs, University of Texas at Arlington 2005; Travel/Professional Development Award, Office of the Provost and Vice President for Academic Affairs, University of Texas at Arlington 2005; Who's Who in America, The 59-th Edition of Marquis Who's Who in America CURRENT RESEARCH PROJECTS ``Mathematical Modeling and Numerical Simulation of Neutrophils-Biofilm Interactions on Biomedical Implants'' (in collaboration with Dr. Liping Tang, Department of Bioengineering and Dr. B. Chen-Charpentier, Department of Mathematics, University of Texas at Arlington) ``Mathematical Modeling and Numerical Simulation of Biofilms in Unsaturated Media'' (in collaboration with Dr. W.-S. Chang, Department of Biology and Dr. B. Chen-Charpentier, Department of Mathematics, University of Texas at Arlington) ``Nonstandard Finite-Difference Methods for Dynamical Systems with Applications in Mathematical Biology'' (in collaboration with Dr. D. Dimitrov, Fred Hutchinson Cancer Research Center; and Dr. R. Anguelov, University of Pretoria, South Africa). ``Realistic Mathematical Models for Interacting Microbial Populations'' (in collaboration with Dr. J. Grover, Department of Biology, University of Texas at Arlington; and Dr. I. Martines, Mathematics Program, Western State College of Colorado). ``Modeling and Evaluation of Subsurface Biobarrier Formation and Persistence in Saturated Porous Media'' (in collaboration with Dr. B. Chen-Charpentier, Department of Mathematics, University of Texas at Arlington and Dr. Al Cunningham, Montana State's Center for Biofilm Engineering). RESEARCH, EDUCATION, AND TRAVEL GRANTS:      AWARDED RESEARCH AND EDUCATION GRANTS: ``Tensor-SUMMA Grant: Strengthening Underrepresented Minority Mathematics Achievement'' (Co-PI; D. Grantcharov, PI), Mathematical Association of America (8/2009-5/2010, Total Amt.: $6,000.00). ``UBM-Institutional: Undergraduate Training in Theoretical Ecology Research (UTTER)'' (PI; J. Grover, D.L. Hawkins, C. Kribs Zaleta, L. Mydlarz, Co-PIs; L. Gough, FA), National Science Foundation, Ref: DUE-0827136 (9/2008-8/2013, Total Amt.: $780,946.00). ``Scholarships for Undergraduates to Reach Goals in Education (SURGE)'' (Co-PI; J. Zhu, PI; T. Aktosun, R. Gornet, B. Shipman, Co-PIs), National Science Foundation, Ref: DUE-0807110 (6/2008-5/2012, Total Amt.: $483,000.00) ``Interdisciplinary Grants in the Mathematical Sciences: Modeling Microbial Populations, Biofilms and Competition Dynamics in a General Gradostat'' (PI; J. Grover, N. Smatresk, Co-PIs), National Science Foundation, Ref: DMS-0107439 (09/2001-08/2002, Total Amt.: $99,998.00). ``Mathematical and Computational Methods for Modeling of Subsurface Biobarrier Persistence in the Presence of Protozoa'' (PI), UT Arlington, Ref: REP-14748717 (9/2001-8/2002, Total Amt.: $8,200.00).      AWARDED TRAVEL GRANTS: 2007 AMS-MAA Joint Mathematics Meeting: ``Diversity Initiative Grant'', The Mathematical Association of America - Committee on Student Activities and Chapters (12/2006, Total Amt.: $500.00). AMS Conference: ``Mathematical Challenges of the 21-st Century'', American Mathematical Society - National Science Foundation (8/2000, Total Amt.: $1,000.00). IMA Workshop: ``Confinement and Remediation of Environmental Hazards'', Institute for Mathematics and its Applications - National Science Foundation (1/2000, Total Amt.: $1,500.00). ``Grant-in-Aid for Foreign Studies'', National Science Foundation ``Eureka'', Bulgaria (1/1995). PUBLISHED WORK      REFEREED PUBLICATIONS: Anguelov, R. and H.V. Kojouharov, "Continuous Age-Structured Model for Bovine Tuberculosis in African Buffalo", AIP Conference Proceedings, 1186:1 (2009) 443-450. Martines, I.P., H.V. Kojouharov and J.P. Grover, "A Chemostat Model of Resource Competition and Allelopathy", Applied Mathematics and Computation, 215:2 (2009) 573-582. Chen-Charpentier, B.M., Dimitrov, D.T., and H.V. Kojouharov, "Numerical Simulation of Multispecies Biofilms in Porous Media for Different Kinetics", Mathematics and Computers in Simulation, 79:6 (2009) 1846-1861. H.V. Kojouharov and D.T. Dimitrov, "Compatible Discretizations for Continuous Dynamical Systems", AIP Conference Proceedings, 1067:1 (2008) 28-37. Chen-Charpentier, B.M. and H.V. Kojouharov, "Mathematical Modeling of Bioremediation of Trichloroethylene in Aquifers", Computers & Mathematics with Applications, 56:3 (2008) 645-656. Dimitrov, D.T. and H.V. Kojouharov, "Nonstandard Finite Difference Methods for Predator-Prey Models with General Functional Response", Mathematics and Computers in Simulation, 78:1 (2008) 1-11. Dimitrov, D.T. and H.V. Kojouharov, " Nonstandard numerical methods for a class of predator-prey models with predator interference", Electronic Journal of Differential Equations, 15 (2007) 67-75. Dimitrov, D.T. and H.V. Kojouharov, "Stability-Preserving Finite-Difference Methods for General Multi-Dimensional Autonomous Dynamical Systems", International Journal of Numerical Analysis and Modeling, 4:2 (2007) 282-292. Chen-Charpentier, B.M., D.T. Dimitrov, H.V. Kojouharov, "Combined Nonstandard Numerical Methods for ODEs with Polynomial Right-Hand Sides", Mathematics and Computers in Simulation, 73:1-4 (2006) 105-113. Dimitrov, D.T. and H.V. Kojouharov, "Positive and elementary stable nonstandard numerical methods with applications to predator-prey systems", Journal of Computational and Applied Mathematics, 189:1-2 (2006) 98-108. Dimitrov, D.T. and H.V. Kojouharov, ``Analysis and Numerical Simulation of Phytoplankton-Nutrient Systems with Nutrient Loss'', Mathematics and Computers in Simulation, 70:1 (2005) 33-43. Dimitrov, D.T. and H.V. Kojouharov, "Nonstandard finite-difference schemes for general two-dimensional autonomous dynamical systems", Applied Mathematics Letters, 18:7 (2005) 769-774. Dimitrov, D.T. and H.V. Kojouharov, "Complete mathematical analysis of predator-prey models with linear prey growth and Beddington-DeAngelis functional response", Applied Mathematics and Computation, 162:2 (2005) 523-538. Kojouharov, H.V. and B.M. Chen, "Nonstandard Eulerian-Lagrangian methods for multi-dimensional reactive transport problems", Applied Numerical Mathematics, 49:2 (2004) 225-243. Kojouharov, H.V. and B.D. Welfert, "Generalized Nonstandard Numerical Methods for Nonlinear Advection-Diffusion-Reaction Equations", Lecture Notes in Computer Science 2907, Large-Scale Scientific Computing, pp. 465 - 472 (Lirkov et al., Eds.), Springer-Verlag Berlin Heidelberg, 2004. Chen, B.M. and H.V. Kojouharov, "Numerical simulation of dual-species biofilms in porous media", Applied Numerical Mathematics, 47:3-4 (2003) 377-389. Jones, D., H.V. Kojouharov, D. Le and H. Smith, "The Freter model: A simple model of biofilm formation", Journal of Mathematical Biology, 47:2 (2003) 137-152. Kojouharov, H.V. and B.D. Welfert, "A Nonstandard Euler Scheme for y"+g(y)y'+f(y)y=0", Journal of Computational and Applied Mathematics, 151:2 (2003) 335-353. Jones, D., H.V. Kojouharov, D. Le and H. Smith, "Microbial Competition for Nutrient in a Flow Reactor", Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications and Algorithms, 10:1 (2003) 57-68. Jones, D., H.V. Kojouharov, D. Le and H. Smith, "Bacterial Wall Attachment in a Flow Reactor", SIAM Journal on Applied Mathematics, 62:5 (2002) 1728-1771. B.M. Chen-Charpentier and H.V. Kojouharov, "Simulation of Biobarrier-Protozoa Interaction in Porous Media", Contemporary Mathematics 295, Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment, pp. 105-113 (Z. Chen and R.E. Ewing, Eds.), American Mathematical Society, Providence, RI, 2002. Jones, D., H.V. Kojouharov, D. Le and H. Smith, "Bacterial Wall Attachment in a Flow Reactor: Mixed Culture", Canadian Applied Mathematics Quarterly, 10:1 (2002) 111-138. B.M. Chen-Charpentier and H.V. Kojouharov, "Numerical Simulation of Biofilm-Forming Bacteria and Other Microbes in Porous Media", Developments in Water Science 47, Computational Methods in Water Resources, Vol. 1, pp. 819-827 (S.M. Hassanizadeh et al., Eds.), Elsevier Science B.V., Amsterdam, The Netherlands, 2002. Kojouharov, H.V. and B.D. Welfert, "A New Numerical Approach for the Solution of Scalar Nonlinear Advection-Reaction Equations", International Journal of Applied Science and Computations, 8:2 (2001) 119-126. B. Chen and H. Kojouharov, "Metodos No Estandard Para Ecuaciones Diferenciales", (review article) Terceras Jornadas de Investigacion y Fomento de la Multidisciplinariedad, pp. 17-27 (eds. C. Coll, R. Esteban, A. Martinez and L. Jodar), Editorial U.P.V., Valencia, Spain, 2001. Chen, B.M. and H.V. Kojouharov, "Modeling of Subsurface Biobarrier Formation", Journal of Hazardous Substance Research, 3:1 (2001) 1-13. Kojouharov, H.V. and B.M. Chen, "Nonstandard Methods for the Convective-Dispersive Transport Equation with Nonlinear Reactions", Numerical Methods for Partial Differential Equations, 15:6 (1999) 617-624. Chen, B.M. and H.V. Kojouharov, "Nonstandard Numerical Methods Applied to Subsurface Biobarrier Formation Models in Porous Media", Bulletin of Mathematical Biology, 61:4 (1999) 779-798. Kojouharov, H.V. and B.M. Chen, "Nonstandard Methods for the Convective Transport Equation with Nonlinear Reactions", Numerical Methods for Partial Differential Equations, 14:4 (1998) 467-485. Liu, B., M.B. Allen, H. Kojouharov, and B. Chen, "Finite-Element Solution of Reaction-Diffusion Equations with Advection", Computational Methods in Water Resources XI, Computational Methods in Subsurface Flow and Transport Problems, Vol. 1, pp. 3-12 (A.A. Aldama et al., Eds.), Computational Mechanics Publications, WIT Press, Southampton, UK, 1996.      CHAPTERS IN BOOKS: Chen-Charpentier, B.M. and Kojouharov, H.V., ``Biofilms in Porous Media: Mathematical Modeling and Numerical Simulation'', pp. 481-511, Environmental Bioremediation Technologies, (Singh, S.N. and Tripathi, R.D.; Eds.), Springer-Verlag Berlin Heidelberg New York, 2007. Dimitrov, D.T., Kojouharov, H.V., B.M. Chen, ``Reliable Finite Difference Schemes with Applications in Mathematical Ecology'', pp. 249-286, Advances in the Applications of the Nonstandard Finite Difference Schemes, (R.E. Mickens, Editor), World Scientific Publishing, River Edge, NJ, 2005. Kojouharov, H.V. and B.M. Chen, ``Nonstandard Eulerian-Lagrangian Methods for Advection-Diffusion-Reaction Equations'', pp. 55-108, Applications of Nonstandard Finite Difference Schemes, (R.E. Mickens, Editor), World Scientific Publishing, River Edge, NJ, 2000.      NON-REFEREED CONFERENCE PROCEEDINGS: Chen, B.M. and H.V. Kojouharov, ``Modeling of Subsurface Biobarrier Formation'', Proceedings of the 2000 Conference on Hazardous Waste Research: Environmental Challenges and Solutions to Resource Development, Production, and Use, pp. 228-237 (Larry E. Erickson, Ed.), Great Plains/Rocky Mountain Hazardous Substance Research Center, Manhattan, KS, 2001. Kojouharov, H.V. and B.D. Welfert, ``A New Numerical Approach for the Solution of Nonlinear Advection-Reaction Equations'', Proceedings of the International Conference on Scientific Computing & Mathematical Modeling, pp. 124-127 (D. Shultz, B. Wade, J. Vigo-Aguiar, and S.K. Dey, Eds.), Institute of Applied Science and Computations, Milwaukee, WI, 2000. Chen, B.M. and H.V. Kojouharov, ``Accurate Numerical Simulation of Biobarrier Formation in Porous Media'', Proceedings of the 1998 Conference on Hazardous Waste Research: Bridging Gaps in Technology and Culture, pp. 224-240 (Larry E. Erickson and Mary M. Rarkin, Eds.), Great Plains/Rocky Mountain Hazardous Substance Research Center, Manhattan, KS, 1999. Kojouharov, H.V., ``Non-standard Methods for Reaction-Dispersion Equations with Convection'', Proceedings of the Seventeenth Annual American Geophysical Union Hydrology Days, pp. 183-191 (Hubert J. Morel-Seytoux, Ed.), Hydrology Days Publications, Atherton, California, 1997. GRADUATE STUDENT SUPERVISIONS      CURRENT PH.D. STUDENTS: Alicia Prieto Langarica, Ph.D. Student, UT Arlington Research Project: ``Mathematical Modeling and Numerical Simulation of Neutrophils-Biofilm Interactions on Biomedical Implants'' Xiaoyang Dong, Ph.D. Student, UT Arlington Research Project: ``Realistic Mathematical Models for Interacting Microbial Populations''      PH.D. DISSERTATIONS DIRECTED: Ian P. Martines, Ph.D., UT Arlington, 4/2008 Dissertation Title: ``Mathematical Analysis of Allelopathy and Resource Competition Models'' Current Position: Assistant Professor, Mathematics Department, St. Mary's University, San Antonio, TX Dobromir T. Dimitrov, Ph.D., UT Arlington, 4/2005 Dissertation Title: ``Nonstandard Finite-Difference Methods for Dynamical Systems with Applications in Mathematical Biology'' Current Position: Staff Scientist, Vaccine and Infectious Disease Institute, Fred Hutchinson Cancer Research Center, Seattle, WA Hilaire M. Kadjo, Ph.D., UT Arlington, 4/2004 Dissertation Title: ``An Age-Structured Population Model: Interactions Between Nutrients and Phytoplankton'' Current Position: Software Engineer FCS GSI, Network Centric Systems, Raytheon Company, Plano, TX      M.S. SPECIAL PROJECTS / THESES DIRECTED: Darren Sheets, M.S., UT Arlington, 4/2009 ``Multiple Linear Regression Model of Visceral Leishmaniasis in Bihar, India'' Nithin Rahul, M.S., UT Arlington, 11/2005 ``Interpolation of an Economic Model using the Newton's Method and the Cubic Spline Method'' Yonael Gebreyohannes, M.S., UT Arlington, 4/2005 ``Numerical Simulation of Multi-Lane Traffic Flow'' Sompoom Meechowna, M.S., UT Arlington, 11/2004 ``Numerical Methods for a System of Partial Differential Equations for Traffic Flow'' Dobromir T. Dimitrov, M.S., UT Arlington, 7/2003 ``Complete Mathematical Analysis of a Predator-Prey Model with a Beddington-DeAngelis Functional Response''