Professor Konstantin Z. Markov, PhD., Dr.  Sci
Faculty of Mathematics and Informatics
"St. Kliment Ohridski'' University of Sofia
5 blvd J. Bourchier, POB 48, BG-1164 Sofia
BULGARIA

L I S T
of publications of  K. Z. MARKOV


Tensor functions
Microstructure elasticity
Composites
Random media
80ies|90ies| 00ies
Varia
Books and collections
Conference presentations


Tensor functions

K. Z. Markov.
Anisotropic creep of two-dimensional media (in Russian), Vestnik Leningradskogo Universiteta 1972, No 1, pp. 111-115.

K. Z. Markov.
A note on isomers (in Russian), Vestnik Leningradskogo Universiteta 1973, No 1, pp. 49-51.
(see Engl. transl. of Vestnik LGU 6, 1979, pp. 59-62).
A. A. Vakulenko and K. Z. Markov.
On the bases of the space of second-order tensors. Bull. Acad. Polon. sci., ser. sci. techn. 24, 1976, pp. 283-291.
A. A. Vakulenko and K. Z. Markov.
On the representation for tensor functions. Bull. Acad. Polon. sci., ser. sci. techn. 29, 1981, pp. 43-50.
K. Z. Markov.
On the class of symmetry groups of tensors and tensor functions, Annuaire Univ. Sofia, Fac. Math. Méc., Livre 2, 76/1982, 1986, pp. 131-139.
K. Z. Markov.
Condition for nondegeneracy for a second-order symmetric tensor, Annuaire Univ. Sofia, Fac. Math. Méc., Livre 2, 81/1987, 1993, pp. 71-73.     Abstract     Full text (75 KB)

Microstructure theories of elasticity

K. Z. Markov.
On the theory of elasticity of media with independent dilatation of particles (in Russian), Theor. Appl. Mechanics, Bulg. Acad. Sci., 5, 1974, No 1, pp. 93-99.

K. Z. Markov.
A note on microelasticity, Bull. Acad. Polon. sci., ser. sci. techn., 24, 1976, pp. 275 - 282.
K. Z. Markov.
On the inhomogeneity problem in micropolar elasticity, Theoretical and Applied Mechanics. Bulgarian Academy of Sciences, Sofia, 1979, Year X, No. 3, pp. 52 - 59.     Abstract     Full text (130 KB)
K. Z. Markov.
Nonlocality and size effect in composite mechanics, C. R. Acad. Bulg. Sci. 30, No 2, 1977, pp. 195-188.
K. Z. Markov.
Inhomogeneity problem in micropolar elasticity, Annuaire Univ. Sofia, Fac. Math. Méc., Livre 2, 75/1981, 1985, pp. 75-93.      Abstract
K. Z. Markov.
On the dilatation theory of elasticity, ZAMM 61, 1981, pp. 349-358.
V. S. Mechandjieva and K. Z. Markov.
Stress concentration around a hole in a micropolar solid with voids, Annuaire Univ. Sofia, Fac. Math. Méc., Livre 2, 81/1987, 1993, pp. 85-104.      Abstract     Full text (215 KB)
E. Inan and K. Z. Markov.
On a Lamé problem in the micromorphic theory of anisotropic damage. Bulletin of Technical University of Istanbul, special issue, dedicated to Prof. E. Suhubi, 47, No 3, 1994, pp. 365-377.     Abstract     Full text (140 KB)
K. Z. Markov.
On a microstructural model of damage in solids, Int. J. Engng Sci., 33, No. 1, pp. 139-150, 1995.     Abstract      full text (161 KB)

Composites

K. Z. Markov.
A study of the yield criterion for perforated metal plates, Annuaire Univ. Sofia, Fac. Math. Méc., Livre 2, 75/1981, 1985, pp. 93-106.

K. Z. Markov.
On the yield locus for porous solids, Bull. Acad. Polon. sci., ser. sci. techn. 29, 1981, pp. 57-66. [Compressed PCX images of the text (757 KB)]
K. Z. Markov.
Yield surface for two-phase composite materials, C. R. Acad. Bulg. Sci. 34, No 5, 1981, pp. 631-634.
K. Z. Markov.
An anisotropic yield criterion for perforated metal plates, Res Mechanica Letters 1, 1981, pp. 315-318.
K. Z. Markov.
Problems of the plasticity theory of perforated plates (in Russian), Advances in Mechanics (Warsaw) 6, 1983, No 3/4, pp. 31-67.
K. Z. Markov.
On the viscoelastic behaviour of particulate composites, Theor. Appl. Mechanics, Bulg. Acad. Sci. 14, 1983, No 4, pp. 45-54.
K. Z. Markov.
Justification of an effective field method in elasto-static of heterogeneous solids, Journal of the Mechanics and Physics of Solids, 49, Issue 11, November 2001, Pages 2621-2634.     Abstract     Full text (158 KB) (Preprint NI0001-SMM, Isaac Newton Institute of Mathematical Studies, University of Cambridge,  Cambridge, UK, January 2000. [download (PREP-INI.DVI 60 KB)]

Random media (1984 - 1990)

K. Z. Markov.
An application of Volterra-Wiener series in mechanics of composite materials, Theor. Appl. Mechanics, Bulg. Acad. Sci., 15, 1984, No 1, pp. 41-50.

C. I. Christov and K. Z. Markov.
Stochastic functional expansion for random media with perfectly disordered constitution, SIAM J. Appl. Math. 45, 1985, pp. 289-311.
C. I. Christov and K. Z. Markov.
Stochastic functional expansion in elasticity of heterogeneous solids, Int. J. Solids and Structures 21, 1985,
pp. 1197-1211.
K. Z. Markov.
Application of Volterra-Wiener series for bounding the overall properties of heterogeneous media. Part I. General procedure. Part. II. Suspensions of equi-sized spheres. SIAM J. Appl. Math. 47, 1987, pp. 831-849, 850-870.
K. Z. Markov.
Bounds on the effective transverse conductivity of fibre materials, Annuaire Univ. Sofia, Fac. Math. Méc., Livre 2, 79/1985, 1988, pp. 113-124.
C. I. Christov and K. Z. Markov.
Stochastic functional expansion for heat conductivity of polydisperse perfectly disordered suspensions, Annuaire Univ. Sofia, Fac. Math. Méc., Livre 2, 79/1985, 1988, pp. 191-207.
K. Z. Markov.
Bounds on the effective transverse conductivity of fibre materials, Annuaire Univ. Sofia, Fac. Math. Méc., Livre 2, 79/1985, 1988, pp. 113-124.
K. Z. Markov and K. D. Zvyatkov.
On the bounds for the effective properties of random suspensions of spheres, C. R. Acad. bulg. Sci. 40, No 3, 1987, pp.17-20.
K. Z. Markov and K. D. Zvyatkov.
c2-bounds on the elastic moduli of a random dispersion of spheres, C. R. Acad. bulg. Sci., 41, No 7, 1988, pp. 21-24.
K. Z. Markov and K. D. Zvyatkov
On the effective behaviour of a nonlinear dispersion of spheres materials, Annuaire Univ. Sofia, Fac. Math. Méc., Livre 2, 82/1988, 1992, pp. 179-192.     Abstract      Full text (172 KB)
K. Z. Markov and K. D. Zvyatkov.
On the optimal third-order bounds on the effective conductivity of random dispersions of spheres, Theor. Applied Mech., Bulg. Acad. Sci. 22, No 3, 1991, pp. 107-116.     Abstract
K. Z. Markov and K. D. Zvyatkov.
On the optimal third-order bounds on the effective elastic moduli of random dispersions of spheres, Annuaire Univ. Sofia, Fac. Math. Méc., Livre 2 83/1989, 1992, pp. 37-64.
K. Z. Markov.
On the heat propagation problem for random dispersions of spheres, Math. Balkanica (New Series) 3, 1989, pp. 399-417.     Abstract     Full text (133 KB)

Random media (1990 - 1999)

K. Z. Markov.
On the factorial functional series and their application to random media, SIAM J. Appl. Math. 51, 1991, No 1, 172-186.    Abstract      Full text (133 KB)
K. Z. Markov and K. D. Zvyatkov.
Optimal third-order bounds on the effective properties of some composite media, and related problems, Advances in Mechanics (Warsaw) 14, No 4, 1991, pp. 3-46.
K. Z. Markov and C. I. Christov.
On the problem of heat conduction for random dispersions of spheres allowed to overlap, Mathematical Models and Methods in Applied Sciences 2, 1992, pp. 249-269.      Abstract     Full text (204 KB)
K. Z. Markov and K. S. Ilieva.
A note on the c2-term of the effective conductivity for random dispersions, Annuaire Univ. Sofia, Fac. Math. Méc., Livre 2, 84/1990, 1993, pp. 123-137.      Abstract     Full text (178 KB)
K. Z. Markov and K. D. Zvyatkov.
Functional series and Hashin-Shtrikman's type bounds on the effective properties of random media. In: Recent Advances in Mathematical Modelling of Composite Materials, K. Z. Markov., ed., World Sci., 1994, 59-106.  Abstract     Full text (336 KB)   
M. K. Kolev and K. Z. Markov.
On the absorption coefficient of random dispersions, Annuaire Univ. Sofia, Fac. Math. Inf.,  86/1992, Livre 2, Mécanique, Sofia, 1994, 17-29.    Abstract     Full text (122 KB)
K. Z. Markov and M. K. Kolev.
A variational treatment of an absorption problem in random media, Int. J. Engng Sci., 32, 1994, 1859-1875.
    Abstract     Full text PDF (177 KB)
K. Z. Markov and M. K. Kolev.
On the absorption problem for random dispersions, Mathematical Models and Methods in Applied Sciences, 4, 1994, 755-722.    Abstract     Full text
K. Z. Markov and K. D. Zvyatkov.
Functional series and Hashin-Shtrikman's type bounds on the effective conductivity of random media. European Journal of Applied Mathematics, 6, No 6, 1995, 611-629.     Abstract     Full text (210 KB)
K. Z. Markov. D.R.S. Talbot and J. R. Willis.
On stationary diffusion in heterogeneous media, IMA J. Applied Mathematics, 56, 1996, 133-144.     Abstract     Full text (150 KB)
K. Z. Markov.
On the "triangular" inequality in the theory of two-phase random media, Annuaire Univ. Sofia, Fac. Math. Inf., L. 1, Mat. et Méc. , 89(1995), 159-167, 1998.     full text (172 KB)
K. Z. Markov.
On the cluster bounds on the effective properties of microcracked solids, Journal of the Mechanics and Physics of Solids, 46, No 2, pp. 357-388, 1998.     Abstract     Full text (243 KB)
K. Z. Markov and J. R. Willis.
On the two-point correlation function for dispersions of nonoverlapping spheres, Mathematical Models and Methods in Applied Sciences, 8, 1998, 359-377.      Abstract     Full text (215 KB)
K. Z. Markov.
On the two-point correlation functions in random arrays of nonoverlapping spheres, Annuaire Univ. Sofia, Fac. Math. Inf., L. 2, Mat. Appl. et Inf., 91 (1997), 1999,151 - 175.       Abstract        full text   (163 KB)]
K. S. Ilieva and K. Z. Markov.
On the field fluctuations in a random dispersion, Annuaire Univ. Sofia, Fac. Math. Inf., L. 2, Mat. Appl. et Inf., 91 (1998), 1999, 203-214.      full text (147 KB)
K. Z. Markov.
On the correlation functions of two-phase random media and related problems, Proc. Roy. Soc. London A, 455, 1999, 1069-1087.      full text (240 KB)
K. Z. Markov and K. S. Ilieva.
Field fluctuations and the effective behaviour of micro-inhomogeneous solids, Annuaire Univ. Sofia, Fac. Math. Inf., L. 1, Mat. et Méc., 92 (1999), 2000, 135-144. full text (140 KB)

Random media (1999 -> )

M. K. Kolev and K. Z. Markov.
A note on the bulk modulus of a binary elastic mixture. Annuaire Univ. Sofia, Fac. Math. Inf., L. 1, Mat. et Méc., 92 (1999), 2000, 145 - 150.     Abstract     full text (100 KB)

M. K. Kolev and K. Z. Markov.
A note on the shear modulus of a binary elastic mixture. Annuaire Univ. Sofia, Fac. Math. Inf., L. 1, Mat. et Méc., 93 (2000), 2001, 109 - 120.     Abstract     full text (100 KB)
K. Z. Markov.
Elementary micromechanis of heterogeneous media, In: heterogeneous Media, Modelling and Simulation, Chapter 1, eds. K.Z. Markov and L. Preziosi, Birkhauser Boston, 2000,    pp. 1 - 162.      full text  (765 KB)    compressed post-script (340 KB)
K. Z. Markov.
A new bound on the absorption coefficient of a two-phase medium. Annuaire Univ. Sofia, Fac. Math. Inf., 94/2000, Sofia, 2001, 123-131.    Abstract        full text (146 KB)
K. Z. Markov.
On the sink strength and permeability of microcracked arrays. Proc. R. Soc. Lond. A (2003) 459, 1035–1051.       Abstract       full text
K. Z. Markov, K. S. Ilieva.
Generalization of the Voigt-Reuss bounds for a binary medium. Annuaire de L'Université de Sofia "St. Kliment Ohridski", Faculté de Mathématiques et Informatique, 95(2001), Sofia, 2002, in press.    Abstract      full text
K. Z. Markov.
Estimates for the sedimentaion speed. Proc. Roy. Soc. London A, submitted  19.02.2003    Abstract       full text
K. Z. Markov.
Sedimentation in a dilute dispersion of spheres. The functional series approach. Proc. Roy. Soc. London A, submitted   14.05.2003   Abstract       full text

Varia

A. A. Vakulenko and K. Z. Markov.
Some problems of the continuum theory of dislocations (in Russian), Vestnik Leningradskogo Universiteta, 1970, No 7, pp. 74-87.
K. Z. Markov and S. Yu. Rotfel'd.
Classes of compact operators in Hilbert scales (in Russian), Vestnik Leningradskogo Universiteta, 1971, No 7, pp. 150-151.
K. Z. Markov.
On the rheology of porous solids (in Russian), Theor. Appl. Mechanics, Bulg. Acad. Sci. 7 1976, No 4, pp. 51-58.
R. A. Arutyunyan and K. Z. Markov.
Loozening and fracture of plastic solids, Lett. Appl. Engng Sci., 5, 1977, pp. 187-193.
R. A. Arutyunyan and K. Z. Markov.
Modification of Coffin's low cycle fracture criterion, Theor. Appl. Mechanics, Bulg. Acad. Sci. 9, 1978, No 1, pp. 128-131.
N. Mankov and K. Z. Markov.
Dynamic model of starting processes in rubber belt conveyors, C. R. Acad. Bulg. Sci., 32, No 7, 1979,
pp. 883-885.
K. Z. Markov.
A note on the shape of yield surface in the space of invariants, ZAMM, 65, 1985, pp. 179-180.

Books and collections

K. Z. Markov, Editor.
Recent Advances in Mathematical Modelling of Composite Materials. World Sci. Publishing Co., 1996.
K. Z. Markov, Editor.
Continuum Models of Discrete Systems, Proceedings of the 8th Int. Symposium (Varna, 1995), World Sci. Publishing Co., 1996.
E. Inan and K. Z. Markov, Editors.
Continuum Models of Discrete Systems, Proceedings of the 9th Int. Symposium (Istanbul, 1998), World Sci. Publishing Co., 1999.
K. Z. Markov and L. Preziosi, Editors.
Heterogeneous Media: Micromechanics Modeling Methods and Simulation, Birkhauser Boston, 2000. [Contents, Preface, Contributors]
K. Z. Markov.
Mathematical Modelling. "St. Kliment Ohridski'' University Press, Sofia, 2002, 235 p. (in Bulgarian with English contents and summary)     Предговор - BG,     Съдържание - BG
K. Z. Markov.
Continuum Mechanics (in press). "St. Kliment Ohridski'' University Press, Sofia, 2003, 251 p. (in Bulgarian with English table of contents) (Съдържание - Bg)
K. Z. Markov.
Ръководство по аналитична механика. (Analtyical Mechanics - a textbook). "St. Kliment Ohridski'' University Press, Sofia, 1995, 2001, 204 p. (in Bulgarian)

Selected conference presentations

K. Z. Markov and M. M. Mihovsky.
Application of ultrasonic bell-shaped impulses for measuring damping coefficient (in Bulgarian), Defectoscopija 77, Proc. 2nd Nat. Conference (Varna, June 1977), Sofia, pp. 67-78.

K. Z. Markov and A. A. Vakulenko.
On the structure of anisotropic tensor functions in continua, In: Comportment Mécanique des Solides Anisotropes, J. P. Boehler, ed., Editions du CNRS, Paris, 1982, pp. 34-46.
K. Z. Markov.
A study of yielding and fracture for anisotropic composite materials, In: Comportment Plastique des Solides Anisotropes, J. P. Boehler, ed., Editions du CNRS, Paris, 1984, pp. 181-193. [Compressed PCX images of the text (890 KB)]
K. Z. Markov.
Dilatation theories of elasticity, In: New Problems in Mechanics of Continua, O. Brulin, R. Hsieh, eds, Univ. Waterloo Press, Waterloo, Ontario, 1983, pp. 129-138.
K. Z. Markov.
"One-particle" approximations in mechanics of composite materials, In: Continuum Models and Discrete Systems, O. Brulin, R. Hsieh, eds, North-Holland, 1981, pp. 441-448.
K. Z. Markov.
A virial stochastic solution for a random suspension of spheres, In: Continuum Models of Discrete Systems, A. J. M. Spencer, ed., Balkema, Rotterdam, 1987, pp. 97-105.
K. Z. Markov.
Micromorphic models for damaged solids, In: Yielding, Damage, and Failure of Anisotropic Solids, J. P. Boehler, ed., Mech. Engng Publ., London, 1989, pp. 665-677.
K. Z. Markov.
Analysis of random particulate media via factorial functional expansions, In: Continuum Models and Discrete Systems, G. A. Maugin, ed., Longman, London, 1991, vol. 2, pp. 169-176. Abstract
M. K. Kolev and K. Z. Markov.
Bounds on the effective absorption coefficient of random media, In: Continuum Models and Discrete Systems, K.-H. Anthony and H.-J. Wagner, eds., Trans Tech Publications, Switzerland, 1993, pp. 315-320. Full text (107 KB)
K. Z. Markov.
On a statistical parameter in the theory of random dispersions of spheres, In: Continuum Models of Discrete Systems, Proc. 8th Int. Symposium (Varna, 1995), ed. K.Z. Markov. World Sci., 1996, pp. 241-249. Full text (136KB)
G. M. Draganova and K. Z. Markov.
On a model of damage in polymer materials. In: Continuum Models of Discrete Systems, Proc. 8th Int. Symposium (Varna, 1995), ed. K. Z. Markov. World Sci., 1996, pp. 615-622.     Abstract     Full text (115 KB)
K. Z. Markov.
On a two-point correlation function in random dispersions and an application. In: Continuum Models and Discrete Systems, Proc. 9th Int. Symposium (Istanbul, 1998), eds. E. Inan and K. Z. Markov, World Sci., 1998, pp. 206-215.      Full text (170 KB)

January, 2003