Curriculum Vitae



Curriculum Vitae

Yuri A. Melnikov, PhD, DrSc

Professor of Mathematics

Mailing Address: Department of Mathematical Sciences

Middle Tennessee State University

P.O. Box 34

Murfreesboro, TN, 37132, USA

Phone: (Office) 615 898-2844, (Home) 615 896-2580

E-mail address: ymelniko@mtsu.edu

URL:

Home Address: 519 Brandywine Dr., Murfreesboro, TN 37129

Professional Preparation:

• DrSc in Computational Mechanics (Dissertation: A Basis for Computing Thermal and Stress-Strain Fields in Bodies of Complex Configuration) – Moscow Civil Engineering Institute, USSR, 1982

• PhD in Differential and Integral Equations (Dissertation: Boundary Integral Equation Method for Problems in Applied Mechanics) – Dnepropetrovsk State University, USSR, 1971

• Masters in Mechanical Engineering – Dnepropetrovsk State University, USSR, 1964

Area of Expertise:

Construction of Green’s functions for applied partial differential equations and implementation of Green’s function-based methods for boundary value problems that simulate phenomena and processes in engineering and science.

Appointments:

1992 – Present: Professor, Department of Mathematical Sciences, Middle Tennessee State University, USA

2008 - 2008: Visiting Senior Research Fellow, City University of Hong Kong, Hong Kong

1999 – 1999: Special Visiting Professor, Department of Civil Engineering, Nagoya Institute of Technology, Japan

1992 – 1992: Visiting Professor, Department of Mechanical Engineering, Vanderbilt University, USA

1982 – 1992: Professor and Chair, Department of Computational Mathematics, Dnepropetrovsk State University, USSR

1971 – 1982: Assistant Professor, Associate Professor, Department of Applied Mathematics, Dnepropetrovsk State University, USSR

1975 – 1976: Visiting Scholar, Department of Aerospace and Applied Mechanics, Brooklyn Polytechnic Institute, USA

1976 – 1976: Visiting Scholar, Technological Institute, Northwestern University, Evanston, USA

Awards:

• Honorary Doctor Degree, Dnepropetrovsk State University, Ukraine, 2008

• Senior Fellow, City University of Hong Kong, 2008

• Fellow, Wessex Institute of Great Britain, 2003

• Distinguished Research Award, MTSU Foundation, 2001

• Research Fellow, Nagoya Institute of Technology, Japan, 1999

• Outstanding Research Award, MTSU Foundation, 1995

• All-Nation Distinguished Teacher Award, Ministry of Higher Education of the USSR, 1989

• Distinguished Research and Teaching Award, Dnepropetrovsk State University, USSR, 1987

Recent (since at MTSU) Publications:

The total number of research publications from 1969 till present is over 200. All the works published in the field of development and implementation of the Green’s function method. Most of the works published prior to the year 1992 are in Russian. What follows is the list of recent works published after joining MTSU in 1992.

Research Books:

1. Yu.A. Melnikov, Green’s Functions in Applied Mechanics, Computational Mechanics Publications, Southampton – Boston, 1995 (267pp.)

2. Yuri A. Melnikov, Influence Functions and Matrices, Marcel Dekker, New York – Basel, 1999 (469pp.)

3. Yuri A. Melnikov, Influence Function Approach. Selected Topics of Structural Mechanics, WITPress, Southampton - Boston, 2008 (365pp.)

4. Yuri A. Melnikov, Green's Functions and Infinite Products, Springer-Birkhauser, New York - London, 2011 (165pp.)

5. Yuri A. Melnikov and Max Y. Melnikov, Green's Functions. Construction and Applications, DeGruyter, Berlin-Boston, 2012 (440pp.)

6. Yuri A. Melnikov and Volodymyr N. Borodin, Green's Functions. Potential Fields on Surfaces, Springer International Publishing AG, 2017 (200pp.)

Peer-reviewed Papers:

• Yu.A. Melnikov and S.A. Titarenko, A new approach to 2-D eigenvalue shape design, Int. J. of Numerical Methods in Engineering, 36, 12, 2017-2030, 1993

• Yu.A. Melnikov and V.V. Shubenko, Green’s function attacks geometric nonlinearity in bending of plates, Boundary Element Method-XV (eds: C.A. Brebbia and J.J. Rencis), 135-147, 1993

• Yu.A. Melnikov and V.A. Koshnaryova, Green’s matrices and two-dimensional elasto-potentials for external problems, Applied Mathematical Modeling, 18, 3, 161-167, 1994

• Yu.A. Melnikov, Green’s function approach to some nonlinear problems in applied mechanics, Boundary Element Technology-IX (eds: C.A. Brebbia and A.J. Kassab), 271-278, 1994

• Yu.A. Melnikov, K.L. Shirley and A.J. Worsey, Computing potential fields of a point source on joint surfaces, Boundary Element Technology-IX (eds: C.A. Brebbia and A.J. Kassab), 279-286, 1994

• Yu.A. Melnikov and K.L. Shirley, Matrix of Green’s type for potential equation on a cylindrical surface joined to a hemi-sphere, Applied Mathematics and Computation, 65, 3, 241-252, 1994

• Yu.A. Melnikov, Computing influence functions for compound regions of complex configuration, IABEM Symposium, 2654-2658, Hawaii, 1995

• Yu.A. Melnikov, A.A. Bobylyov and V.V. Shubenko, Green’s function approach to the nonlinear bending of closely-spaced parallel plates, Int. J. of Solids and Structures, 34, 12, 1771-1791, 1995

• Yu.A. Melnikov and S.A. Titarenko, Green’s function boundary element method for optimal shape design, Engineering Analysis with Boundary Elements, 15, 1, 1-10, 1995

• Yu.A. Melnikov, S. Hughes and S. McDaniel, Boundary element approach based on Green’s functions, Boundary Element Technology-XI (eds: R.C. Ertekin, C.A. Brebbia, M. Tanaka and R. Shaw), 307-316, 1996

• Yu.A. Melnikov, Influence functions for 2-D compound regions of complex configuration, Computational Mechanics, 17, 5, 297-305, 1996

• Yu.A. Melnikov and Ye.A. Bobylyov, Green’s function method solution of the Reissner plate problems, Engineering Analysis with Boundary Elements, 17, 4, 255-262, 1996

• Yu.A. Melnikov, V.V. Loboda and V.B. Govorukha, Field of potential in a compound rectangle containing a linear inclusion, Quarterly of Applied Mathematics, 55, 2, 299-311, 1997

• Yu.A. Melnikov and J.O. Powell, A Green’s function method for detection of a cavity from a boundary measurement, Boundary Element Technology-XII (eds: J.I. Frankel, C.A. Brebbia and A.M.H. Aliabadi), 121-130, 1997

• Yu.A. Melnikov and M.T. Hall, Influence matrices for systems of equations posed on graphs, Boundary Element Technology-XII (eds: J.I. Frankel, C.A. Brebbia and A.M.H. Aliabadi), 289-298, 1997

• Yu.A. Melnikov, Green’s function formalism extended to systems of applied differential equations posed on graphs, Journal of Engineering Mathematics, 34, 4, 369-386, 1998

• Yu.A. Melnikov, Elastic equilibrium of a semi-strip undergoing a point body force, Boundary Element Technology-XIII (eds: C.S. Chen, C.A. Brebbia and D.W. Pepper), 505-514, 1999

• Yu.A. Melnikov and J.O. Powell, Green’s function numerical method for some inverse boundary value problems, J. of the Chinese Institute of Engineering, 22, 6, 813-820, 1999

• Yu.A. Melnikov and V.D. Sheremet, Some new Green’s functions for a circular Poisson-Kirchhoff plate, Annual Meeting of the Japanese Computational Mechanics Society, Tokyo, 1-15, 1999

• Yu.A. Melnikov, An alternative construction of Green’s functions for the 2-dimensional heat equation, Engineering Analysis with Boundary Elements, 24, 6, 467-475, 2000

• Yu.A. Melnikov and V.D. Sheremet, Some new results on the bending of a circular plate subject to point forces, Mathematics and Mechanics of Solids, 6, 1, 29-46, 2001

• Yu.A. Melnikov, Green’s functions of a thin circular plate with supported edge, Engineering Analysis with Boundary Elements, 25, 669-676, 2001

• Yu.A. Melnikov and M.Yu. Melnikov, Accurate computation of Green’s functions in regions of complex configuration, Boundary Element Technology-XIV (eds: A. Kassab and C.A. Brebbia), 219-228, 2001

• Yu.A. Melnikov and A.A. Arman, The field of potential generated by a point source in the ring-shaped region, Mathematical Engineering in Industry, 8, 3, 223-238, 2001

• Yu.A. Melnikov, Matrices of Green’s type for steady-state heat conduction in multiply-connected piecewise homogeneous regions, Engineering Analysis with Boundary Elements, 27, 779-787, 2003

• Yu.A. Melnikov, Computable representations of influence functions for multiply-connected Kirchhoff plates, in: Boundary Element Technology XV, WIT Press, Southampton, Boston, 95-104, 2003

• Yu.A. Melnikov, Influence functions of a point force for Kirchhoff plates with inclusions, Journal of Mechanics, 20, 4, 449-456, 2004

• Yu.A. Melnikov, Influence functions of a point source for perforated compound plates with facial convection, Journal of Engineering Mathematics, 49, 3, 253-270, 2004

• Yu.A. Melnikov, Influence functions of a point force for multiply-connected Kirchhoff plates, Mathematics and Mechanics of Solids, 9, 4, 419-437, 2004

• Yu.A. Melnikov and M.Yu. Melnikov, Stress-strain state provoked by displacement of inclusions in thin plates, Advances in Boundary Element Technology VI (editors: A.P.S. Selvadurai, C.L. Tan, M.H. Aliabadi), EC-Ltd, Montreal, 115-122, 2005

• M.Y. Melnikov and Yu.A. Melnikov, Design of test settings for BEM algorithms, in: Boundary Elements XXVII (editors: A. Kassab, C.A. Brebbia, E. Divo and D. Poljak), WIT Press, Southampton, Boston, 297-306, 2005

• Yu.A. Melnikov and M.Y. Melnikov, Computability of series representation of Green’s functions in a rectangle, Engineering Analysis with Boundary Elements, 30, 1, 774-780, 2006

• Yu.A. Melnikov, Green’s function for mixed problems in compound regions of irregular shape, E. J. of Boundary Elements, 4, 3, 82-104, 2006

• I.K. Lifanov, Yu.A. Melnikov and S.A. Nenashev, The Green’s functions for domains of irregular shape and singular integral equations, Doklady of the Russian Academy of Sciences, 74, 2, 668-773, 2006 (in Russian)

• I.K. Lifanov, Yu.A. Melnikov and S.A. Nenashev, Computing of point source-generated potential in multiply-connected regions of irregular shape, Advances in Computational and Experimental Engineering and Sciences, Proceedings of ICCES’07, Miami, FL, USA, 555-560, 2007

• Yu.A. Melnikov, Potential fields generated by point sources in regions with apertures and foreign inclusions, Engineering Analysis with Boundary Elements, 31, pp.1003-1012, 2007

• M.Yu. Melnikov and Yu.A. Melnikov, Construction of Green’s functions for the Black-Scholes equation, E. Journal of Differential Equations, 153, pp.1-14, 2007

• G.S. Chandekar, J.D. Richardson, Y.A. Melnikov and S.J. Pardue, Green’s function analysis of an axisymmetric cavity near a rigid wall, E. Journal of Boundary Elements, 5, 2, pp.69-83, 2007

• Y.A. Melnikov, New infinite product representations of some elementary functions, Journal of Applied Mathematical Sciences, 2, 2, pp.81-97, 2008

• Yu.A. Melnikov, A new approach to the representation of trigonometric and hyperbolic functions by infinite products, Journal of Mathematical Analysis and Applications, 344, pp.521-534, 2008

• Yuri Melnikov, A surprising outcome of a routine procedure for the construction of Green’s functions for Laplace equation, The Third International Conference on Modeling, Simulation and Applied Optimization, Proceedings of ICMSAO’09, Sharjah, UAE, 1-5, 2009

• Yu.A. Melnikov, Efficient representations of Green’s functions for some elliptic equations with piecewise-constant coefficients, Central European Journal of Mathematics, 8, 1, pp.53-72, 2010

• Y.C. Hon, M. Li, and Y.A. Melnikov, Inverse source identification by Green's function, Eng. Anal. with Boundary Elements, 34, pp.352-358, 2010

• Yu.A. Melnikov, Construction of Green's functions for the two-dimensional static Klein-Gordon equation, Journal of Partial Differential Equations, 24, 2, pp.114-139, 2011

• Yu.A. Melnikov, Green's function-based approach to the representation of elementary functions by infinite products, 1074th AMS Regional Meeting, Lincoln, Nebraska, pp.97-98, 2011

• Yuri A. Melnikov, Alternative forms of Green’s functions as a source for infinite product representation of elementary functions, Advances in Boundary Element and Meshless Techniques, pp. 171-177, 2012

• V.N. Borodin and Y.A. Melnikov, Matrices of Green’s type for sets of Laplace equations posed on joint surfaces weakened with apertures, The International Conference on Applied Mathematics, Modeling, and Computational Science, Waterloo, Canada, p. 367, 2013

• Y.A. Melnikov and V. Reshniak, An Efficient meshless approach to 2-D heat conduction problems in regions of irregular shape, Applied Problems of Fluid Dynamics and Heat and Mass Transfer, Dnipropetrovsk, Ukraine, pp. 116-118, 2014

• Y.A. Melnikov and V. Reshniak, A semi-analytical approach to Green’s functions for heat equation in regions of irregular shape, Engineering Analysis with Boundary Elements, 46, pp. 108-115, 2014

• Yuri A. Melnikov, To the efficiency of a Green’s function modification of the method of functional equations, Journal of Applied and Computational Mathematics, 3, 3, pp. 1-7, 2014

• Yuri A. Melnikov, Green’s functions for boundary-value problems simulating potential fields in regions of irregular configuration on surfaces of revolution, 1107 Regional AMS Meeting, Georgetown University, Washington, DC, p. 106, 2015

• Y.A. Melnikov and V.N. Borodin, Recover of missing data for boundary-value problems simulating potential fields in thin shell structures, 1113 Regional AMS Meeting, University of Memphis, Memphis, Tennessee, p. 69, 2015

• Y.A. Melnikov, M.Y. Melnikov, and V.N. Borodin, Green's function method as an instrumental tool in applied mathematics, International Conference on Applied Mathematics and Mechanics, Dnepropetrovsk National University, Ukraine, 2016

• Y.A. Melnikov and B.N. Borodin, Green’s functions for problems simulating potential fields in thin-walled assemblies of irregular configuration, The 6th Eurasian Conference on Mathematical Sciences and Applications, Budapest, pp. 188-189, 2017

• Y.A. Melnikov and V.N. Borodin, Further expansion of computing horizons of the Green's function method, Transactions of Azerbaijan Academy of Sciences, Applied Mechanics, Baku, Azerbaijan, 2017

• Y.A. Melnikov and V.N. Borodin, Green’s functions for problems that simulate potential fields induced in thin-walled structures of irregular configuration, Journal of Engineering Mathematics, 112, pp. 75-93, 2018

• Y.A. Melnikov, Computational Green’s Function Approach to Boundary Value Problems Arising in Applied Mechanics, Plenary Talk at the SCON Int. Convention on Astro Physics and Particle Physics, May 23-24, Amsterdam, Netherlands, 2019

Presentations:

Since 1992, numerous presentations have been made to professional meetings at International, National and Regional level. A number of Keynote Lectures have been delivered, the most recent of those are: Symposium Inverse Problems in Engineering, Tuscaloosa, Alabama, 2003; International Conference Integral Equation and Modeling of Applied Problems, Moldova, Chisinau, 2005; Fourth International Conference of Applied Mathematics and Computing, Plovdiv, Bulgaria, 2007, the International Conferences on the Memory of prof. Mossakovsky, Dnepropetrovsk, Ukraine, 2009 and 2019; Azerbaijan National Academy of Sciences, 2016; ADA University, Baku, 2016; and Plenary talk delivered to the SCON Int. Convention on Astro Physics and Particle Physics, Amsterdam, Netherlands, 2019

Invited Seminars:

• Stanford University: April 1992, March 1994

• Vanderbilt University: 1994, 1995, and 2007

• Kentucky University: March 1993

• Wessex Institute of Technology, Great Britain: May 1997

• Haifa Institute of Technology, Israel: May 1998

• Society of Computational Mechanics, Japan, September 1999

• Shinshu University, Japan: September 1999

• Nagoya Institute of Technology, Japan: October 1999

• Kyoto University, Japan: October 1999

• Tohoku University, Japan: November 1999

• University of Central Florida, Orlando: May 2000

• University of Alabama, Tuscaloosa: June 2003

• University of Nebraska, Lincoln: November 2004

• State University of Moldova, Chisinau: June 2005

• Akron University, Ohio: October 2005

• University of Mississippi, Oxford: March 2006

• University of Southern Mississippi: April 2007

• City University of Hong Kong: March 2008

• Dnepropetrovsk State University: 2008, 2010, 2016

• American University of Sharjah, UAE: January 2009

• Baylor University: October 2009

• Oak Ridge National Laboratory, USA: June 2014

• ADA University, Baku, Azerbaijan 2016

• Institute of Mathematics, ANAS, 2016

Editorial Responsibilities

• Guest Editor for the Special Issue “Modern Applications of Green’s Functions in Mechanics and Related Fields” of the Journal of Engineering Mathematics, (Vol. 49, No.3, 2004)

• Member, Board of Referees of the J. of Eng. Mathematics

• Referee of the J. of Eng. Analysis with Boundary Elements

• Referee of the International Journal of Solids and Structures

• Referee of the Journal Mathematics and Mechanics of Solids

• Referee of the Journal of Computational Mechanics

Conferences Organized

• Advisory Committee member, International Conference Boundary Element Technology-XI, 1996, Hawaii, USA

• Key-Note Speaker, Symposium on Inverse Problems in Engineering, Tuscaloosa, Alabama, 2003

• Co-chairman and Key-Note Speaker, International Conference Integral Equations and Modeling of Applied Problems, 2005, Cishineu, Moldova

• Advisory Committee member, International Conference Boundary Element Method-29, 2007, New Forest, UK

• Section Organizer, Applied Partial Differential Equations, Southeastern Regional Conference of the American Mathematical Society, 2007, Murfreesboro, USA

• Advisory Committee member, International Conferences dedicated to the memory of Professor V. I. Mossakovski, Dnepropetrovsk, Ukraine, 2009 and 2019

Research Collaboration

Published:

Dr. V.V. Loboda, Dnepropetrovsk State University, (1997)

Dr. J.Q. Powell, Middle Tennessee State University (1997, 1999)

Dr. Z. Sinkala, Middle Tennessee State University (1994)

Dr. A. Worsey, Middle Tennessee State University (1994)

Dr. S.A. Titarenko, St-Petersburg Civil Engineering Institute, Russian Federation (1993, 1995)

Dr. V.A. Koshnaryova, Dnepropetrovsk State University, (1994)

Dr. K.L. Shirley, Middle Tennessee State University (1995)

Dr. A.A. Bobylyov, Dnepropetrovsk State University, (1995)

Dr. V.V. Shubenko, Dnepropetrovsk State University, Ukraine (1990, 1993, 1995)

Dr. E.A. Bobylyov, Dnepropetrovsk State University, (1996)

Dr.V.B. Govorukha, Dnepropetrovsk State University, (1997)

Dr. T.V.Rydvanskaya, Dnepropetrovsk State University, Ukraine (1983, 1984)

Dr. R.D. Krasnikova, Dnepropetrovsk State University, (1981)

Dr. A.V. Krasnikov, Ukrainian Academy of Science, (1978)

Dr. V.G. Boborykin, Dnepropetrovsk State University, (1985)

Dr. I.M. Dolgova, Dnepropetrovsk State University, (1978, 1983)

Dr. V.L. Voloshko, Dnepropetrovsk State University, (1987)

Dr. G.A. Larionov, Dnepropetrovsk State University, (1986)

Dr. E.T. Tsadikova, Dnepropetrovsk State University, (1985)

Dr. V.D. Sheremet, Moldova State University, Republic of Moldova (1999, 2001)

Dr. M.Y. Melnikov, Cumberland University, Tennessee, (2001, 2005, 2006, 2007)

Dr. I.K. Lifanov, Moscow State University, Russia (2006, 2007)

Dr. S.A. Nenashev, Zhukovsky Air Force Academy, Russian Federation (2006, 2007)

Mr. A.S.Arman, Middle Tennessee State University (2001)

Mr. P.L. Roubides, Middle Tennessee State University (1998)

Mr. M.T. Hall, Middle Tennessee State University (1997)

Mr. S. Hughes, Middle Tennessee State University (1996)

Mr. S. McDaniel, Middle Tennessee State University (1996)

Dr.Sc. Thesis

Supported

Dr. V.V. Loboda, 1993 (Dnepropetrovsk State University)

Dr. N.V. Polyakov, 1994 (Dnepropetrovsk State University)

Dr. E.M. Kiselyova, 1995 (Dnepropetrovsk State University)

Dr. S.A. Smirnov, 1996 (Dnepropetrovsk State University)

PhD Thesis

Supervised

Krasnikov A.V., 1978 (Dnepropetrovsk State University)

Dolgova I.M., 1980 (Dnepropetrovsk State University)

Titarenko S.A., 1984 (Dnepropetrovsk State University)

Boborykin V.G., 1985 (Dnepropetrovsk State University)

Koshnaryova V.A., 1986 (Dnepropetrovsk State University)

Voloshko V.L., 1988 (Dnepropetrovsk State University)

Rydvanskaya T.V., 1988 (Dnepropetrovsk State University)

Larionov G.A., 1989 (Dnepropetrovsk State University)

Tsadikova E.T., 1989 (Dnepropetrovsk State University)

Shubenko V.V., 1990 (Dnepropetrovsk State University)

Govorukha V.B., 1996 (Dnepropetrovsk State University)

Borodin, V.N., 2014 (Middle Tennessee State University)

Reshniak, V., 2016 (Middle Tennessee State University)

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