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1

Duquennoy, Marc, Mohammadi Ouaftouh, Dany Devos, Frédéric Jenot, and Mohamed Ourak. "Effective elastic constants in acoustoelasticity." Applied Physics Letters 92, no. 24 (2008): 244105. http://dx.doi.org/10.1063/1.2945882.

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2

Volovik, G. E. "Fundamental constants in effective theory." Journal of Experimental and Theoretical Physics Letters 76, no. 2 (2002): 77–79. http://dx.doi.org/10.1134/1.1510061.

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3

Grimsditch, M. "Effective elastic constants of superlattices." Physical Review B 31, no. 10 (1985): 6818–19. http://dx.doi.org/10.1103/physrevb.31.6818.

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4

Kim, Jin-Yeon. "Effective elastic constants of anisotropic multilayers." Mechanics Research Communications 28, no. 1 (2001): 97–101. http://dx.doi.org/10.1016/s0093-6413(01)00149-5.

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5

Mayerhöfer, Thomas G., and Jürgen Popp. "Effective optical constants: A fundamental discrepancy." Vibrational Spectroscopy 42, no. 1 (2006): 118–23. http://dx.doi.org/10.1016/j.vibspec.2006.01.002.

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6

Bosher, S. H. B., and D. J. Dunstan. "Effective elastic constants in nonlinear elasticity." Journal of Applied Physics 97, no. 10 (2005): 103505. http://dx.doi.org/10.1063/1.1894586.

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7

Bonilla, Luis L. "Effective elastic constants of polycrystalline aggregates." Journal of the Mechanics and Physics of Solids 33, no. 3 (1985): 227–40. http://dx.doi.org/10.1016/0022-5096(85)90013-4.

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8

Afremov, Leonid L., Sergey Anisimov, and Tamara Agapova. "Effective Anisotropy Constant of Bilayer Film." Advanced Materials Research 887-888 (February 2014): 779–82. http://dx.doi.org/10.4028/www.scientific.net/amr.887-888.779.

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A reasonable composition of different kinds of magnetic anisotropy of bilayer film has been carried out. The criterium of magnetic uniaxiality of bilayer film contained the first-order and the second-order crystallographic anisotropy has been defined. It has been demonstrated that the effective constants of the first-order and the second-order magnetic anisotropy of bilayer film has a non-linear dependence on the corresponding constants of crystallographic anisotropy of the layers, angles between them and constants of interlayer exchange interaction.
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9

XU WEN-LAN. "EFFECTIVE OPTICAL CONSTANTS OF COATINGS WITH PARTICLES." Acta Physica Sinica 47, no. 9 (1998): 1555. http://dx.doi.org/10.7498/aps.47.1555.

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10

Watson, James K. G. "Directional centrifugal constants and effective vibrational frequencies." Chemical Physics 283, no. 1-2 (2002): 171–83. http://dx.doi.org/10.1016/s0301-0104(02)00506-2.

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11

Dunstan, D. J., S. H. B. Bosher, and J. R. Downes. "Effective thermodynamic elastic constants under finite deformation." Applied Physics Letters 80, no. 15 (2002): 2672–74. http://dx.doi.org/10.1063/1.1469658.

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12

Akcakaya, E., and G. W. Farnell. "Effective elastic and piezoelectric constants of superlattices." Journal of Applied Physics 64, no. 9 (1988): 4469–73. http://dx.doi.org/10.1063/1.341270.

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13

Lee, Changyol, and Xavier Gonze. "Dielectric constants and Born effective charges ofTiO2rutile." Physical Review B 49, no. 20 (1994): 14730–31. http://dx.doi.org/10.1103/physrevb.49.14730.

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14

Bulut, Osman, Necla Kadioglu, and Senol Ataoglu. "Absolute effective elastic constants of composite materials." Structural Engineering and Mechanics 57, no. 5 (2016): 897–920. http://dx.doi.org/10.12989/sem.2016.57.5.897.

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15

Meneghini, R., and L. Liao. "Effective Dielectric Constants of Mixed-Phase Hydrometeors." Journal of Atmospheric and Oceanic Technology 17, no. 5 (2000): 628–40. http://dx.doi.org/10.1175/1520-0426(2000)017<0628:edcomp>2.0.co;2.

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16

Hansen, K. "The effective temperature in microcanonical rate constants." Chemical Physics Letters 620 (January 2015): 43–45. http://dx.doi.org/10.1016/j.cplett.2014.12.016.

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17

Haija, A. J., W. Larry Freeman, and Rachel Umbel. "Effective optical constants and effective optical properties of ultrathin trilayer structures." Physica B: Condensed Matter 406, no. 2 (2011): 225–30. http://dx.doi.org/10.1016/j.physb.2010.10.048.

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18

Zhu, P. Y., A. K. Fung, and K. W. Wong. "Effective propagation constants in dense random media under effective medium approximation." Radio Science 22, no. 2 (1987): 234–50. http://dx.doi.org/10.1029/rs022i002p00234.

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19

Chwał, Małgorzata. "Numerical Evaluation of Effective Material Constants for CNT-Based Polymeric Nanocomposites." Advanced Materials Research 849 (November 2013): 88–93. http://dx.doi.org/10.4028/www.scientific.net/amr.849.88.

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The effective material constants for CNT-based polymeric composites are studied. The analysis is based on the elasticity theory involving a spatial square representative volume element and the finite element method. The transversally isotropic body having aligned and uniformly distributed long carbon nanotubes is assumed. The perfect bonding between the carbon nanotubes and the matrix are considered. For such a material the five elastic material constants is needed to completely describe the elastic behavior. Related to the calculated material constants, the results are given and compared with the other models presented in the literature. Generally, the increase of the effective material constants normalized by the matrix modulus is observed.
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20

Monecke, J. "Microstructure Dependence of Effective Material Constants of Composites." Materials Science Forum 62-64 (January 1991): 755–56. http://dx.doi.org/10.4028/www.scientific.net/msf.62-64.755.

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21

KARUBE, Daizo, Shouji KATO, and Jun'ichi KATSUYAMA. "Effective stress and soil constants of unsaturated Kaoline." Doboku Gakkai Ronbunshu, no. 370 (1986): 179–88. http://dx.doi.org/10.2208/jscej.1986.370_179.

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22

Grojean, C., J. Cline, and G. Servant. "Supergravity inspired warped compactifications and effective cosmological constants." Nuclear Physics B 578, no. 1-2 (2000): 259–76. http://dx.doi.org/10.1016/s0550-3213(00)00157-7.

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23

Sun, C. T., and Sijian Li. "Three-Dimensional Effective Elastic Constants for Thick Laminates." Journal of Composite Materials 22, no. 7 (1988): 629–39. http://dx.doi.org/10.1177/002199838802200703.

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24

Olson, Tamara, and Marco Avellaneda. "Effective dielectric and elastic constants of piezoelectric polycrystals." Journal of Applied Physics 71, no. 9 (1992): 4455–64. http://dx.doi.org/10.1063/1.350788.

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25

Knessl, Charles, and Mark W. Coffey. "An effective asymptotic formula for the Stieltjes constants." Mathematics of Computation 80, no. 273 (2010): 379–86. http://dx.doi.org/10.1090/s0025-5718-2010-02390-7.

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26

Iwanaga, Masanobu. "Effective optical constants in stratified metal-dielectric metameterial." Optics Letters 32, no. 10 (2007): 1314. http://dx.doi.org/10.1364/ol.32.001314.

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27

Levin, Valery M., and Juan M. Alvarez-Tostado. "Explicit Effective Constants for an Inhomogeneous Porothermoelastic Medium." Archive of Applied Mechanics 76, no. 3-4 (2006): 199–214. http://dx.doi.org/10.1007/s00419-006-0016-x.

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28

Reinert, Th, H. Kiewel, Hans Joachim Bunge, and L. Fritsche. "Calculation of Effective Elastic Constants for Polycrystalline Materials." Materials Science Forum 273-275 (February 1998): 617–24. http://dx.doi.org/10.4028/www.scientific.net/msf.273-275.617.

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29

Deeter, M. N., D. Sarid, C. D. England, W. R. Bennett, and Charles M. Falco. "Determination of effective optical constants of magnetic multilayers." Applied Physics Letters 54, no. 21 (1989): 2059–61. http://dx.doi.org/10.1063/1.101165.

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30

Pinghua, Zhang, and R. D. Newman. "Reduction of Effective "Spring Constants" Using Gravitational Fields." Chinese Physics Letters 9, no. 8 (1992): 397–99. http://dx.doi.org/10.1088/0256-307x/9/8/002.

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31

Grimsditch, M., and F. Nizzoli. "Effective elastic constants of superlattices of any symmetry." Physical Review B 33, no. 8 (1986): 5891–92. http://dx.doi.org/10.1103/physrevb.33.5891.

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32

Radwanski, R. J., J. J. M. Franse, and S. Sinnema. "Effective anisotropy constants in rare earth-3d intermetallics." Journal of Magnetism and Magnetic Materials 70, no. 1-3 (1987): 313–15. http://dx.doi.org/10.1016/0304-8853(87)90453-7.

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33

Leshchenko, P. V., and B. P. Maslov. "Effective constants of piezoactive composites of stochastic structure." Soviet Applied Mechanics 23, no. 3 (1987): 268–75. http://dx.doi.org/10.1007/bf00886604.

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34

Badke, R. "Effective renormalised coupling constants and the critical point." Physics Letters A 119, no. 7 (1987): 365–69. http://dx.doi.org/10.1016/0375-9601(87)90617-7.

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35

Kim, Jin O., Jan D. Achenbach, Meenam Shinn, and Scott A. Barnett. "Effective Elastic Constants of Superlattice Films Measured by Line-Focus Acoustic Microscopy." Journal of Engineering Materials and Technology 117, no. 4 (1995): 395–401. http://dx.doi.org/10.1115/1.2804732.

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The effective elastic constants of single-crystal nitride superlattice films have been determined by calculation and by measurement methods. The calculation method uses formulas to calculate the effective elastic constants of superlattices from the measured elastic constants of the constituent layers. The calculated effective elastic constants are tested by comparing the corresponding surface acoustic wave (SAW) velocities calculated for thin-film/substrate systems with the corresponding SAW velocities measured by line-focus acoustic microscopy (LFAM). The measurement method determines the effective elastic constants of the superlattices directly from the SAW velocity dispersion data measured by LFAM. Two kinds of superlattice films are considered: one has relatively flat and sharp interfaces between layers, and the other has rough interfaces with interdiffusion. The calculation method has yielded very good results for the superlattices with flat and sharp interfaces but not for the superlattices with rough interfaces. The measurement method yields results for both kinds, with the restriction that the constituent layers have similar crystal symmetries.
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36

BRINDEJONC, VINCENT, and GILLES COHEN-TANNOUDJI. "AN EFFECTIVE STRONG GRAVITY INDUCED BY QCD." Modern Physics Letters A 10, no. 23 (1995): 1711–18. http://dx.doi.org/10.1142/s0217732395001836.

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37

BUCHBINDER, I. L., S. D. ODINTSOV, and O. A. FONAREV. "THE BEHAVIOR OF THE EFFECTIVE COUPLING CONSTANTS FOR E6 GUT IN CURVED SPACE-TIME." Modern Physics Letters A 04, no. 28 (1989): 2713–17. http://dx.doi.org/10.1142/s0217732389003026.

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The one-loop renormalization group equations for effective coupling constants corresponding to parameters of nonminimal coupling of scalars and gravitational field in E6 asymptotically free grand unification theory in curved space-time are obtained. The behavior of these effective coupling constants in strong gravitational field is investigated. In strong gravitational field, these effective coupling constants infinitely rise.
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38

Dundurs, John, and Iwona Jasiuk. "Effective Elastic Moduli of Composite Materials: Reduced Parameter Dependence." Applied Mechanics Reviews 50, no. 11S (1997): S39—S43. http://dx.doi.org/10.1115/1.3101847.

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In this paper, we focus on the effective elastic constants of composite materials and pay attention to the possibility of reducing the number of independent variables. Surprisingly, this important issue has hardly been explored before. In our analysis, we rely on a new result in plane elasticity due to Cherkaev, Lurie, and Milton (1992), and use Dundurs constants (Dundurs, 1967, 1969). As an example, we consider a result for the effective elastic moduli of a composite containing a dilute concentration of perfectly-bonded circular inclusions.
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39

Kim, Jin O., Jan D. Achenbach, Meenam Shinn, and Scott A. Barnett. "Effective elastic constants and acoustic properties of single-crystal TiN/NbN superlattices." Journal of Materials Research 7, no. 8 (1992): 2248–56. http://dx.doi.org/10.1557/jmr.1992.2248.

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Using the measured elastic constants of TiN and NbN single crystals with cubic symmetry, the effective elastic constants of single-crystal TiN/NbN superlattice films with tetragonal symmetry, namely c11, c12, c13, c33, c44, and c66 have been calculated for various thickness ratios of the layers. Using a line-focus acoustic microscope, measurements of surface acoustic waves (SAWs) have been carried out on single-crystal TiN/NbN superlattice films grown on the (001) plane of cubic crystal MgO substrates. The phase velocities measured as functions of the angle of propagation display the expected anisotropic nature of cubic crystals. Dispersion curves of SAWs propagating along the symmetry axes have been obtained by measuring wave velocities for various film thicknesses and frequencies. The SAW dispersion curves calculated from the effectiveelastic constants and the effective mass density of the superlattice films show very good agreement with experimental results. The results of this paper exhibit no anomalous dependence of the elastic constants on the superlattice period of TiN/NbN superlattices.
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40

Sun, Yi, Gao Ying Kang, Ding Cui, and Jing Ran Ge. "Study on Effective Elastic Constants of Homogenization Tube Sheet." Advanced Materials Research 430-432 (January 2012): 158–63. http://dx.doi.org/10.4028/www.scientific.net/amr.430-432.158.

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The expressions of the effective elastic constants of composite material with cylindrical inclusions are derived based on M-T method, and it can be used in discussing the approximate range of effective elastic constant of air. Moreover, it is possible to homogenize tube-sheet by making use of the expression. The numerical result obtained is in good agreement with effective elastic constant adopted by the ASME code. It demonstrates that the approach is effective and accurate. At the last, the relationship between effective elastic and thickness of the tube-sheet is discussed.
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41

MOHAMMADI, A. "A special case of effective equidistribution with explicit constants." Ergodic Theory and Dynamical Systems 32, no. 1 (2011): 237–47. http://dx.doi.org/10.1017/s0143385710000799.

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AbstractAn effective equidistribution with explicit constants for the isometry group of rational forms with signature (2,1) is proved. As an application we get an effective discreteness of the Markov spectrum.
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42

O'Rourke, John P., Marc S. Ingber, and Martin W. Weiser. "The Effective Elastic Constants of Solids Containing Spherical Exclusions." Journal of Composite Materials 31, no. 9 (1997): 910–34. http://dx.doi.org/10.1177/002199839703100905.

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43

Wang, Wei, and Iwona Jasiuk. "Effective Elastic Constants of Particulate Composites with Inhomogeneous Interphases." Journal of Composite Materials 32, no. 15 (1998): 1391–424. http://dx.doi.org/10.1177/002199839803201503.

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44

Kiewel, H., L. Fritsche, and T. Reinert. "Calculation of nonlinear effective elastic constants of polycrystalline materials." Journal of Applied Physics 79, no. 8 (1996): 3963. http://dx.doi.org/10.1063/1.361823.

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45

SKALOZUB, VLADIMIR V. "EFFECTIVE COUPLING CONSTANTS IN GAUGE THEORIES AT HIGH TEMPERATURE." International Journal of Modern Physics A 11, no. 32 (1996): 5643–57. http://dx.doi.org/10.1142/s0217751x96002595.

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High temperature behavior of the effective gauge coupling constants, defined through the effective Lagrangians L(H, T) of strong magnetic field H=const, is investigated for a number of models. In spinor QED the well-known zero charge behavior is realized in the limit T≫(gH)1/2>μ, μ is subtraction point in the field. In scalar QED in addition to logarithmic term ~ln T/T0 describing the zero charge, the term ~T/(gH)1/2 appears and dominates at high temperatures. Similar terms are also present in the non-Abelian models and spoil asymptotic freedom of perturbative vacuum. In the latter models, the linear in T terms are resulted in the generation of classical homogeneous magnetic fields. At this background asymptotic freedom is restored.
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46

Gu, Guoqing. "Calculation methods for effective constants of periodic composite media." Journal of Physics D: Applied Physics 26, no. 9 (1993): 1371–77. http://dx.doi.org/10.1088/0022-3727/26/9/005.

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47

Sokolov, A. I. "Universal effective coupling constants for the generalized Heisenberg model." Physics of the Solid State 40, no. 7 (1998): 1169–74. http://dx.doi.org/10.1134/1.1130512.

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48

Srivastava, S. K. "Effective (1+1)-dimensional cosmological model and fundamental constants." Classical and Quantum Gravity 10, no. 11 (1993): 2307–15. http://dx.doi.org/10.1088/0264-9381/10/11/013.

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49

Kusumaatmaja, Halim, and Reinhard Lipowsky. "Equilibrium Morphologies and Effective Spring Constants of Capillary Bridges." Langmuir 26, no. 24 (2010): 18734–41. http://dx.doi.org/10.1021/la102206d.

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50

Drygaś, Piotr, Simon Gluzman, Vladimir Mityushev, and Wojciech Nawalaniec. "Effective elastic constants of hexagonal array of soft fibers." Computational Materials Science 139 (November 2017): 395–405. http://dx.doi.org/10.1016/j.commatsci.2017.08.009.

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