Book

 Fractional Dynamics on Networks and Lattices

ISBN : 9781786301581

Publication Date : March 2019

Hardcover 330 pp

Publications à comité de lecture

 B.V. Librovitch, AF Nowakowski, FCGA Nicolleau, TM Michelitsch, Non-equilibrium evaporation/condensation model, Int. Journal of Applied Mechanics Vol. 9, No. 8 (2017) 1750111, DOI: 10.1142/S1758825117501113 

 Michelitsch TM, Collet B, Nowakowski AF, Nicolleau FCGA, Lattice fractional Laplacian and continuum limit kernels on the finite cyclic chain, Chaos, Solitons & Fractals 82 (2016) 3847, doi: http://dx.doi.org/10.1016/j.chaos.2015.10.035

 T.M. Michelitsch, B. Collet, A.Perez Riascos, A.F. Nowakowski, F.C.G.A. Nicolleau, A fractional generalization of the classical lattice dynamics approach, Chaos, Solitons & Fractalsc92 (2016) 4350. DOI: http://dx.doi.org/10.1016/j.chaos.2016.09.009

  Michelitsch T.M., Collet B, Nowakowski A.F.,Nicolleau F.C.G.A., (2015) Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit. Journal of Physics A: Mathematical and Theoretical 48 (2015) 295202. doi:10.1088/1751-8113/48/29/295202

 Challamel N., Picandet V., Collet B., Michelitsch T., Elishakoff I., Wang C.M., (2015) Revisiting finite difference and finite element methods applied to structural mechanics within enriched continua. European Journal of Mechanics A/Solids 53 (2015) 107-120.http://dx.doi.org/10.1016/j.euromechsol.2015.03.003

Challamel N., Zhang Z., Wang C. M., Reddy J. N., Wang Q., Michelitsch T., Collet B., (2014)
On nonconservativeness of Eringen’s nonlocal elasticity in beam mechanics: correction from a
discrete-based approach.Archive of Applied Mechanics, 2014. 84(911): p. 12751292.

Michelitsch T. M., Collet B., and Wang X., (2014) Nonlocal constitutive laws generated by
matrix functions: Lattice dynamics models and their continuum limits. International Journal of
Engineering Science, 2014. 80: p. 106-123.

Michelitsch T. M., Maugin G. A., Derogar S., Rahman M., (2014) A regularized representa-
tion of the fractional Laplacian in n dimensions and its relation to Weierstrass-Mandelbrot-type
fractal functions. IMA Journal of Applied Mathematics, 2014. 79(5): p. 753-777.

Michelitsch T. M., Collet B., (2014) A nonlocal constitutive model generated by matrix func-
tions for polyatomic periodic linear chains. Archive of Applied Mechanics, 2014. 84(911):
p. 1477-1500.

Michelitsch T.M., Maugin G.A., Nowakowski A.F., Nicolleau F.C.G.A, Rahman M. (2013),
The Fractional Laplacian as a limiting case of a selfsimilar spring model and applications to
n-dimensional anomalous diffusion. Fractional Calculus & Applied Analysis, Vol. 16, No
4 (2013), pp. 827859; DOI: 10.2478/s1354001300525

 Michelitsch T.M., Maugin G.A., Rahman M., Derogar S., Nowakowski A.F., Nicolleau
F.C.G.A., (2012), A continuum theory for one-dimensional self-similar elasticity and appli-
cations to wave propagation and diffusion. European. Journal. of Appl. Mathematics vol.
23, pp. 709735. December 2012, doi:10.1017/S095679251200023X

Michelitsch, T.M., Maugin, G.A., Rahman, M., Derogar, S., Nowakowski, A.F., Nicolleau,
F.C.G.A, (2012), An approach to generalized one-dimensional self-similar elasticity. Int.
Journal of Engineering Science 61, issue , pp. 103 111 ,
http://dx.doi.org/10.1016/j.ijengsci.2012.06.014

Michelitsch, T.M. (2011),
The self-similar field and its application to a diffusion
problem, Journal of Physics A: Math. Theor. 44 ,465206 (13pp) doi:10.1088/1751-
8113/44/46/465206, Online at stacks.iop.org/JPhysA/44/465206

Nicolleau F.C.G.A., Nowakowski A.F., Michelitsch T.M. (2011), Synthetic turbulence pre-
diction in non-Kolmogorov turbulence, 2011, Journal of Physics: Conf. Ser. 318 042009
(2011) doi:10.1088/1742-6596/318/4/042009

Thomas M. Michelitsch, Gérard A. Maugin, Franck C.G.A. Nicolleau, Andrzej F. Nowakowski, Shahram Derogar, (2009). "DISPERSION RELATIONS AND WAVE OPERATORS IN SELF-SIMILAR QUASI-CONTINUOUS LINEAR CHAINS" Physical Review E 80, 011135

T. M. Michelitsch, Gérard A. Maugin, Andrzej F. Nowakowski, Franck C.G.A. Nicolleau,(2009). "ANALYSIS OF THE VIBRATIONAL MODE SPECTRUM OF A LINEAR CHAIN WITH SPATIALLY EXPONENTIAL PROPERTIES" International Journal of Engineering Science 4, 2 pages 209-220 DOI: 10.1016/j.ijengsci.2008.08.011

Michelitsch T.M., Gitman I.M., Askes H., 2007. Critical wave lengths and instabilities in gradient enriched continuum theories, Mechanics Research Communications 34, 515-521.

Rahman M., Michelitsch T.M., 2007. The reciprocal theorem and rigid sperical inclusions vis a vis certain point singularities, Phil. Mag. 87(32), 5129-5142.

Rahman M., Michelitsch T.M., 2007. A General Procedure for Solving Boundary Value Problems of Elastostatics for a Spherical Geometry Based Love's Approach, The Quarterly J. of Mech. and Appl. Math. 60(2), 139-160.

 Rahman M, Michelitsch T.M. 2006., A Note on the Formula for the Rayleigh wave speed, Wave Motion 43, 272-276.

Michelitsch T.M., Wang J., Gao H., Levin V.M., 2005. On the retarded potentials of inhomogeneous ellipsoids and sources of arbitrary shapes in the three-dimensional infinite space, Int. J. Solids Structures, 42, 51-67.

 Wang J., Michelitsch T.M., Gao H. and Levin V.M., 2005. On the solution of the dynamic Eshelby problem for inclusions of various shapes, Int. J. Solids Structures, Micromechanics of Materials, Special Issue, M. Kachanov, guest ed., Vol. 42(2), 353-363.

Michelitsch T.M., Gao H., Levin V.M., 2003. Dynamic Eshelby Tensors and Potentials for Ellipsoidal Inclusions, Proceedings of the Royal Society of London A, 459, 863-890.

Michelitsch T.M., V.M. Levin and Gao H., 2002. Dynamic Green's Functions of a Quasiplane Piezoelectric Medium With Inclusion. Proceedings of the Royal Society of London A, 458, 2393-2415.
Michelitsch T.M. Gao, H. Levin V.M., 2003. On the Dynamic Potentials of Ellipsoidal Shells Quarterly J. Mech. Appl. Math. 56(4), 629-648.

Levin V.M., Michelitsch T.M., Gao H., 2002. Propagation of electroacoustic waves in the transversely isotropic piezoelectric medium reinforced by randomly distributed cylindrical inhomogeneities, Int. J. Solids Structures, 39, 5013-5015.

Wang J., Michelitsch T.M., Gao H., 2003. Dynamic Fiber Inclusions with Ellipsoidal and Arbitrary Cross-Sections and Related Retarded Potentials in a Quasi-Plane Piezoelectric Medium. Int. J. Solids Structures, 40, 6307-6333.

Kuhn R., Michelitsch T., Levin V.M., Vakulenko A.A., 2002. The analogue of the Eshelby tensor for a piezoelectric spheroidal inclusion in the hexagonal electroelastic medium. Z. Angew. Math. Phys. 53, 584-602.

Michelitsch, T.M., Gao H., 2003. Dynamic Eshelby Inclusion Problem of a Quasiplane Transversely Isotropic Piezoelectric Medium, in: Chin. J. Mech. A 19 (1) (Birthday Volume in honor of the 70th birthday of Prof. T.C.T. Ting), 113-118.

 Michelitsch T., Levin V.M., 2001. Green's function for the in¯nite two-dimensional orthotropic medium Int. J. Fracture 107(2), L33-L38.

Levin V.M., Michelitsch T., 2001. Scattering of acoustoelectric waves on a cylindrical inhomogeneity in a transversely isotropic piezoelectric medium. Mech. Compos. Mater: 37(1), 47-54.

Diebels S., Ehlers W., and Michelitsch T., 2001. Particle simulation as a microscopic approach to a Cosserat continuum. J. Phys. IV , 11, 5203-5210.

Ehlers W., Diebels S., Michelitsch T., 2001. Microscopic investigation of cosserat continua. Z. Angew. Math. Mech. 81, 335-336.

Levin V.M., Michelitsch T., Sevostianov I., 2000. Spheroidal inhomogeneity in a transversely isotropic piezoelectric medium Arch. Appl. Mech. 70(10), 673-693.

Michelitsch T., Levin V.M., 2000. Inclusions and inhomogeneities in electroelastic media with hexagonal symmetry Eur. Phys J. B 14(3), 527-533.

Michelitsch T., Levin V.M., 1999. Inclusion and inhomogeneity problems in the hexagonal electroelastic medium. Phys. Stat. Sol. B 215(2), R13-R14.

Michelitsch T, Kreher WS 1998. A simple model for the nonlinear material behavior of ferroelectrics. Acta Mater: 46(14), 5085-5094.

 Michelitsch T., 1997. Calculation of the electroelastic Green's function of the hexagonal infinite medium. Z. Physik B 104(3), 497-503.

Michelitsch T., 1997. Theory of small-angle x-ray scattering caused by incompatibilities in elastic anisotropic media and the application to dislocations in H.C.P. crystals. Phys. Stat. Sol. B 203(1), 3-16.

Michelitsch T, Wunderlin A., 1996.Fundamental solution of the incompatibility problem in three- dimensional infinite anisotropic elasticity theory Acta Mech. 119, 25-34.

 Michelitsch T, Wunderlin A., 1996. On the theory of Huang X-ray scattering caused by point defects in hexagonal crystals Phys. Stat. Sol. B 198(2), 615-620.

Michelitsch T, Wunderlin A., 1996. Continuum theory of the volume efect caused by point defects in hexagonal media Z. Physik B 101(1), 61-72.

Michelitsch T, Wunderlin A., 1996. Solution of the incompatibility problem in linear three-dimensional anisotropic media for an isotropic incompatibility tensor. Phys. Stat. Sol.B 195, 119-122.

Michelitsch T, Wunderlin A., 1996. Stress functions and internal stresses in linear three-dimensional anisotropic elasticity. Z. Physik B 100(1), 53-56.

Michelitsch T., Michelitsch M. 1992. A Novel Mandelbrot Set and Its Julia Sets. Machine GRAPHICS & VISION 1(4), 634-635.

Michelitsch T. 1994. A Quasi Julia-Set generated by a nonanalytic Trigonometric Function. Machine GRAPHICS & VISION 3(4), 677-679.

Michelitsch T., Michelitsch M., 1995. A Mandelbrot set of the transcendental mapping c cos z with special initial conditions. Machine GRAPHICS & VISION 4 (1/2), 125-130.

Actes de congrues avec comité - chapitres d'ouvrages

Michelitsch, T.M., Niccoleau F.C.G.A, Nowakowski A.F., Derogar S., sous presse (parution prévu pour 2010) "KS input spectrum, some fundamental works on the vibration spectrum
of a self-similar linear chain"" in ERCOFTAC Series, Series Editors: Oliemans, René, Rodi, Wolfgang ISSN: 1382-4309 , (Proceedings of the ERCOFTAC/SIG 42,4thWorkshop on Synthetic
Turbulence Models, 11th-12th December 2008, Nancy).
 Michelitsch T.M. Allan L., A.F.L. Hyde, 2006. Macroscopic Balance Equations For Granular Materials. TC35 Conference, Geomechanics and Geotechnics of Particulate Media, Yamaguchi University, Yamaguchi, Japan, September 12-14, 2006.
 Askes H., Gitman I.M., Michelitsch T.M., 2006. Critical Wave Lengths and Instabilities in Gradient Enriched Continuum Theories, Proceedings, The Fourth International Conference on Mathematical Modeling and Computer Simulation of Materials Technologies, MMT-2006, Ariel, Israel, September 11 - 15, 2006.
 Michelitsch T.M., Askes H., Wang J., Levin V.M., 2005. Solutions of dynamic Variants of Eshelby Inclusion problem, in: Vibration Problems in Physics ICOVP 2005, Series: Springer Proceedings in Physics, Inan, Esin; Kiris Ahmed (Eds.), ISBN-10: 1-4020-5400-9.
 Michelitsch T.M., Wang J., Gao H., Levin V.M., 2003. Solution of the inhomogeneous Helmholtz- and Wave Equation for Ellipsoidal Sources. Continuum models an discrete systems. Proceedings of the NATO Advanced. Research Workshop, Shoresh, Israel, July 2003.
 V.M. Levin, T.M. Michelitsch, Gao H., 2002. Modelling of the E®ective Dynamic Characteristics of Reinforced Transversely Isotropic Piezoelectric Materials. Proceedings of the SPIE, Smart Structure and Materials San Diego 2002 Active Materials (C. Lynch Ed.) Paper no. 4699-14.
Ehlers W, Diebels S., Michelitsch T., 2001. Microscopic modelling of granular materials taking into account particle rotations, In P. A. Vermeer et al. (eds.): Continous and Discontinous Modelling of Cohesive-Frictional Materials { Lecture Notes in Physics, Springer-Verlag, 259-274.
Diebels S., Ehlers W., and Michelitsch T., 2001. From discontinuous to continuous modelling of materials. In N. Bicanic, Editor, Proceeding of ICADD-4, 251-260. University of Glasgow, Scotland, UK, 2001.
 Levin, V.M., Michelitsch T., 2001. Scattering of Accoustoelectric Waves on a Cylindrical Inhomogeneity in the Transversely Isotropic Piezoelectric Medium. Proceedings of SPIE, Smart Structures and Materials, Newport Beach 2001. Active Materials (C. Lynch Ed.) Paper no. 4333-51.
Michelitsch T, Levin V.M., 2000. Construction of the Electroelastic Green's Function of the Hexagonal Infinite Medium and Its Application to Inclusion Problems. Proceedings of SPIE, Smart Structures and Materials Newport Beach 2000. Active Materials (C. Lynch Ed.) 3992, 341-352.
Levin, V.M., Michelitsch T., 1999, Scattering of acoustoelectric waves on a cylindrical inhomoneity in the transversely in the transversely isotropic piezoelectric medium. Annuaire de l'Université de Sofia "St. Kliment Ohridski" Facult¶e de Mathematiques et Informatique 93, 127-155.

Publications sans comité

 Wang J. Michelitsch T.M., Gao H., 2003. On the Solution of the Dynamic Eshelby Problem for Inclusions with Ellipsoidal and Arbitrary Shapes. International Conference on the Mechanical Behaviour of Materials (ICM9), Geneva May 25-29, 2003, Proceedings.
Michelitsch T. M., Gao H. Levin V.M., 2003. Solution of the inhomogeneous Helmholtz equation for an ellipsoidal source region. International Conference on the Mechanical Behaviour
of Materials (ICM9), Geneva May 25-29, 2003, Proceedings.
[ Michelitsch T.M., Derogar S., Nowakowski A.F. and Nicolleau F.C.G.A., 2008. On the lattice dynamics of a fractal gasket. In: Continuum Models and Discrete Systems, Jeulin, D., Forrest, S. (Eds.), Ecole de mines de Paris, 173-179, ISBN: 978-2-35671-000-0.
Thomas M. Michelitsch, Gérard A. Maugin, Franck C.G.A. Nicolleau, Andrzej F. Nowakowski, Shahram Derogar, (2009). "Quasi-continuous linear chains with self-similar harmonic interactions: wave operators and dispersion relations". Proceedings of ENSTA (Paris), Workshop 11
June 2009.
Thomas M. Michelitsch, Gérard A. Maugin, Franck C.G.A. Nicolleau, Andrzej F. Nowakowski, Shahram Derogar, (2009). "Relations de dispersion pour chanes linéaires comportant des interactions harmoniques auto-similaires", version franaise abrégée de l'article: Michelitsch et al., Physical Review E 80 (2009) 011135, HAL: hal-00420287, http://hal.archives-ouvertes.fr/hal-00420287/fr/
JicunWang, Thomas Michelitsch, ArneWunderlin, Ravi Mahadeva, (2009)."AGING AS A CONSEQUENCE OF MISREPAIR { A NOVEL THEORY OF AGING ", e-print server HAL:hal-00373085, http://hal.archives-ouvertes.fr/hal-00373085/fr/