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1

Grimvall, G., and M. S�derberg. "Transport in macroscopically inhomogeneous materials." International Journal of Thermophysics 7, no. 1 (January 1986): 207–11. http://dx.doi.org/10.1007/bf00503811.

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2

Klemens, P. G. "Thermal conductivity of inhomogeneous materials." International Journal of Thermophysics 10, no. 6 (November 1989): 1213–19. http://dx.doi.org/10.1007/bf00500572.

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3

Nan, Ce-Wen. "Physics of inhomogeneous inorganic materials." Progress in Materials Science 37, no. 1 (January 1993): 1–116. http://dx.doi.org/10.1016/0079-6425(93)90004-5.

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4

Pasternak, Viktoriya, Lyudmila Samchuk, Artem Ruban, Oleksandr Chernenko, and Nataliia Morkovska. "Investigation of the Main Stages in Modeling Spherical Particles of Inhomogeneous Materials." Materials Science Forum 1068 (August 19, 2022): 207–14. http://dx.doi.org/10.4028/p-9jq543.

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Анотація:
This scientific study deals with the main issues related to the process of filling inhomogeneous materials into a rectangular hopper. The article develops an algorithm for filling particles of structurally inhomogeneous materials. A micrograph of the structure of samples of inhomogeneous materials is presented. It was found that the structure of samples of heterogeneous materials consists of three layers: external, internal and impurities of various grinding aggregates. Based on microstructural analysis, the presence of particles of various shapes and sizes was justified. On the basis of which the main initial conditions for filling the package with spherical particles were described. The basic physical and mechanical properties of structurally inhomogeneous materials were studied using the obtained results. We also constructed an approximate dependence of porosity on the particle diameter of inhomogeneous materials.
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5

Milton, Graeme W. "Analytic materials." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2195 (November 2016): 20160613. http://dx.doi.org/10.1098/rspa.2016.0613.

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Анотація:
The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer p . If p takes its maximum value, then we have a complete analytic material. Otherwise, it is incomplete analytic material of rank p . For two-dimensional materials, further progress can be made in the identification of analytic materials by using the well-known fact that a 90 ° rotation applied to a divergence-free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.
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6

Mironov, Vladimir I., Olga A. Lukashuk, and Dmitry A. Ogorelkov. "On Durability of Structurally Inhomogeneous Materials." Materials Science Forum 1031 (May 2021): 24–30. http://dx.doi.org/10.4028/www.scientific.net/msf.1031.24.

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Numerical methods used to calculate strength are based on energy approaches and minimization of functionals of one type or another. Yet the model of a material is limited to stable processes of deformation. As a result, a considerable number of deformation properties related to realization of the softening stage in materials of structural elements remains unaccounted for. To describe fracture as a new phenomenon in the behavior of structures, one needs to apply newer experimental and calculational approaches. The article cites results of modelling and experimental notions on the stage of softening in materials and its role in determining their durability. It is proposed to define the durability of a structurally inhomogeneous material as its capacity of equilibrium deformation beyond its ultimate strength under specified loading conditions. That reflects nonlocality of criteria for the failure of the material, their dependence both on its own properties and the geometry of a structural element. Complete stress-strain diagrams for structural materials of various classes and examples on how the softening stage is realized in structural materials are given.
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7

Dyakonov, O. M. "Briquetting of structurally inhomogeneous porous materials." Proceedings of the National Academy of Sciences of Belarus, Physical-Technical Series 65, no. 2 (July 7, 2020): 205–14. http://dx.doi.org/10.29235/1561-8358-2020-65-2-205-214.

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Анотація:
The work is devoted to solving the axisymmetric problem of the theory of pressing porous bodies with practical application in the form of force calculation of metallurgical processes of briquetting small fractional bulk materials: powder, chip, granulated and other metalworking wastes. For such materials, the shape of the particles (structural elements) is not geometrically correct or generally definable. This was the basis for the decision to be based on the continual model of a porous body. As a result of bringing this model to a two-dimensional spatial model, a closed analytical solution was obtained by the method of jointly solving differential equilibrium equations and the Guber–Mises energy condition of plasticity. The following assumptions were adopted as working hypotheses: the normal radial stress is equal to the tangential one, the lateral pressure coefficient is equal to the relative density of the compact. Due to the fact that the problem is solved in a general form and in a general formulation, the solution itself should be considered as methodological for any axisymmetric loading scheme. The transcendental equations of the deformation compaction of a porous body are obtained both for an ideal pressing process and taking into account contact friction forces. As a result of the development of a method for solving these equations, the formulas for calculating the local characteristics of the stressed state of the pressing, as well as the integral parameters of the pressing process are derived: pressure, stress, and deformation work.
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8

Alshits, V. I., and H. O. K. Kirchner. "Cylindrically anisotropic, radially inhomogeneous elastic materials." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 457, no. 2007 (March 8, 2001): 671–93. http://dx.doi.org/10.1098/rspa.2000.0687.

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9

Zhou, Q., Z. Bian, and A. Shakouri. "Pulsed cooling of inhomogeneous thermoelectric materials." Journal of Physics D: Applied Physics 40, no. 14 (June 29, 2007): 4376–81. http://dx.doi.org/10.1088/0022-3727/40/14/037.

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10

HIGUCHI, Masahiro, Kyohei TAKEO, Harunobu NAGINO, Takuya MORIMOTO, and Yoshinobu TANIGAWA. "OS0121 Plate Theories of inhomogeneous materials." Proceedings of the Materials and Mechanics Conference 2009 (2009): 305–7. http://dx.doi.org/10.1299/jsmemm.2009.305.

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11

Zhu, S. B., J. Lee, and G. W. Robinson. "Kinetic energy imbalance in inhomogeneous materials." Chemical Physics Letters 161, no. 3 (September 1989): 249–52. http://dx.doi.org/10.1016/s0009-2614(89)87069-1.

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12

Hoff, Heinrich. "Asymmetrical heat conduction in inhomogeneous materials." Physica A: Statistical Mechanics and its Applications 131, no. 2 (June 1985): 449–64. http://dx.doi.org/10.1016/0378-4371(85)90008-1.

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13

Kayuk, Ya F., and M. K. Shekera. "Reduced mechanical characteristics of inhomogeneous materials." Soviet Applied Mechanics 27, no. 5 (May 1991): 501–7. http://dx.doi.org/10.1007/bf00887776.

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14

Khmelevskaya, V. S., and V. G. Malynkin. "Radiation-induced inhomogeneous state of materials." Metal Science and Heat Treatment 42, no. 8 (August 2000): 331–34. http://dx.doi.org/10.1007/bf02471310.

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15

Kumar, Kuldeep, and Rajesh Kumar. "On Inhomogeneous Deformations in ES Materials." International Journal of Engineering Science 48, no. 4 (April 2010): 405–16. http://dx.doi.org/10.1016/j.ijengsci.2009.10.005.

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16

Kharevych, Lily, Patrick Mullen, Houman Owhadi, and Mathieu Desbrun. "Numerical coarsening of inhomogeneous elastic materials." ACM Transactions on Graphics 28, no. 3 (July 27, 2009): 1–8. http://dx.doi.org/10.1145/1531326.1531357.

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17

Svenson, O. M. "Nondestructive testing of highly inhomogeneous materials." Materials Science 32, no. 4 (July 1996): 491–504. http://dx.doi.org/10.1007/bf02538978.

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18

Axell, Jörgen, Johan Helsing, and Göran Grimvall. "Joule heat distribution in inhomogeneous materials." Physica A: Statistical Mechanics and its Applications 157, no. 1 (May 1989): 618. http://dx.doi.org/10.1016/0378-4371(89)90371-3.

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19

Brice, David K. "Ion implantation distributions in inhomogeneous materials." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 17, no. 4 (November 1986): 289–99. http://dx.doi.org/10.1016/0168-583x(86)90114-x.

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20

Gondzik, J., and H. Stachowiak. "Positron lifetime in inhomogeneous metallic materials." Crystal Research and Technology 22, no. 12 (December 1987): 1511–14. http://dx.doi.org/10.1002/crat.2170221216.

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21

Erokhin, Sergey, and Victor Levin. "Inhomogeneous creep equation for viscoelastic materials." E3S Web of Conferences 410 (2023): 03002. http://dx.doi.org/10.1051/e3sconf/202341003002.

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Анотація:
The paper consider an inhomogeneous creep equation arising from a generalized Voigt model containing a Riemann-Liouville fractional derivative of the order 0 < β < 1. The Laplace transform is used for the numerical solution. The obtained solutions are compared with experimental data of polymer concrete samples. On the basis of this comparison the conclusion about the adequacy of the numerical solution method is made, and estimates of the model parameters are given.
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22

Tao, Xiang Hua, Jing Qing Huang, and Ying Chun Cai. "Inverse Analysis for Inhomogeneous Dielectric Coefficient of Pavement Material Based on Genetic Algorithm." Applied Mechanics and Materials 438-439 (October 2013): 430–35. http://dx.doi.org/10.4028/www.scientific.net/amm.438-439.430.

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Анотація:
The key of ground penetrating radars application lies in the calculation of dielectric coefficient. The pavement materials are inhomogeneous medium in fact, the particle surface can induce the scatter and diffraction of electromagnetic wave. The inhomogeneous dielectricity can change the characteristics of reflected wave. It may even cause background noise of reflected signal, which will lead to mistakes in signal interpretation. Therefore it is necessary to analyze the inhomogeneous dielectric coefficients by GPR. This paper proposes the solutions of inverse analysis for inhomogeneous dielectric coefficients of pavement materials used GPR data. Two examples are given to assess the validity of genetic algorithms in inversion of pavement materials inhomogeneous dielectricity. The results show that genetic algorithm can converge into true solutions well. The backcalculated inhomogeneous dielectric coefficients can help to evaluate pavement properties further.
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23

Budanov, V. E., N. L. Yevich, and N. N. Suslov. "Permittivity Measurement Technique for Inhomogeneous Dielectric Materials." Telecommunications and Radio Engineering 65, no. 15 (2006): 1439–51. http://dx.doi.org/10.1615/telecomradeng.v65.i15.80.

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24

Roganova, N. A., and G. Z. Sharafutdinov. "Identification of mechanical properties of inhomogeneous materials." Mechanics of Solids 47, no. 4 (July 2012): 448–53. http://dx.doi.org/10.3103/s0025654412040097.

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25

Wang, Xu, Dongxing Mao, Wuzhou Yu, and Zaixiu Jiang. "Sound barriers from materials of inhomogeneous impedance." Journal of the Acoustical Society of America 137, no. 6 (June 2015): 3190–97. http://dx.doi.org/10.1121/1.4921279.

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26

Elmaimouni, L., J. E. Lefebvre, A. Raherison, and F. E. Ratolojanahary. "Acoustical Guided Waves in Inhomogeneous Cylindrical Materials." Ferroelectrics 372, no. 1 (November 14, 2008): 115–23. http://dx.doi.org/10.1080/00150190802382074.

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27

Crocker, John C., M. T. Valentine, Eric R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, and D. A. Weitz. "Two-Point Microrheology of Inhomogeneous Soft Materials." Physical Review Letters 85, no. 4 (July 24, 2000): 888–91. http://dx.doi.org/10.1103/physrevlett.85.888.

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28

Vislov, I. S., S. N. Kladiev, S. M. Slobodyan, and A. M. Bogdan. "A Batch Feeder for Inhomogeneous Bulk Materials." IOP Conference Series: Materials Science and Engineering 124 (April 2016): 012033. http://dx.doi.org/10.1088/1757-899x/124/1/012033.

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29

Haddi, A., and D. Weichert. "Elastic-plastic J-integral in inhomogeneous materials." Computational Materials Science 8, no. 3 (July 1997): 251–60. http://dx.doi.org/10.1016/s0927-0256(97)00008-6.

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30

Bernabei, D., F. Ganovelli, N. Pietroni, P. Cignoni, S. Pattanaik, and R. Scopigno. "Real-time single scattering inside inhomogeneous materials." Visual Computer 26, no. 6-8 (April 21, 2010): 583–93. http://dx.doi.org/10.1007/s00371-010-0449-7.

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31

Scibetta, M. "Master Curve analysis of potentially inhomogeneous materials." Engineering Fracture Mechanics 94 (November 2012): 56–70. http://dx.doi.org/10.1016/j.engfracmech.2012.07.012.

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32

Kichigin, A. F., A. E. Kolosov, V. V. Klyavlin, and V. G. Sidyachenko. "Probabilistic-geometric model of structurally inhomogeneous materials." Soviet Mining Science 24, no. 2 (March 1988): 87–94. http://dx.doi.org/10.1007/bf02497828.

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33

Meister, J. J. "Ultrasonic methods in evaluation of inhomogeneous materials." Signal Processing 14, no. 3 (April 1988): 306. http://dx.doi.org/10.1016/0165-1684(88)90086-2.

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34

Zhu, S. B., J. Lee, and G. W. Robinson. "Non-Maxwell velocity distributions in inhomogeneous materials." Journal of Fusion Energy 9, no. 4 (December 1990): 465–67. http://dx.doi.org/10.1007/bf01588279.

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35

Maugin, Gérard A., Marcelo Epstein, and Carmine Trimarco. "Pseudomomentum and material forces in inhomogeneous materials." International Journal of Solids and Structures 29, no. 14-15 (1992): 1889–900. http://dx.doi.org/10.1016/0020-7683(92)90180-2.

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36

Furukawa, Akira, and Hajime Tanaka. "Inhomogeneous flow and fracture of glassy materials." Nature Materials 8, no. 7 (June 14, 2009): 601–9. http://dx.doi.org/10.1038/nmat2468.

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37

Kubicki, B. "About endurance limit of ductile inhomogeneous materials." Journal of Materials Science 31, no. 9 (1996): 2475–79. http://dx.doi.org/10.1007/bf01152964.

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38

Maekawa, S., and J. Inoue. "Giant magneto-transport phenomena in inhomogeneous materials." Materials Science and Engineering: B 31, no. 1-2 (April 1995): 11–16. http://dx.doi.org/10.1016/0921-5107(94)08024-0.

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39

Goldsmid, H. J., and J. W. Sharp. "The thermal conductivity of inhomogeneous thermoelectric materials." physica status solidi (b) 241, no. 11 (September 2004): 2571–74. http://dx.doi.org/10.1002/pssb.200402048.

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40

Qi, Yao, Duo Chen, Chao Sun, Qingyu Hai, and Xiaopeng Zhao. "The Influence of Electroluminescent Inhomogeneous Phase Addition on Enhancing MgB2 Superconducting Performance and Magnetic Flux Pinning." Materials 17, no. 8 (April 19, 2024): 1903. http://dx.doi.org/10.3390/ma17081903.

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Анотація:
As a highly regarded superconducting material with a concise layered structure, MgB2 has attracted significant scientific attention and holds vast potential for applications. However, its limited current-carrying capacity under high magnetic fields has greatly hindered its practical use. To address this issue, we have enhanced the superconducting performance of MgB2 by incorporating inhomogeneous phase nanostructures of p-n junctions with electroluminescent properties. Through temperature-dependent measurements of magnetization, electronic specific heat, and Hall coefficient under various magnetic fields, we have confirmed the crucial role of inhomogeneous phase electroluminescent nanostructures in improving the properties of MgB2. Experimental results demonstrate that the introduction of electroluminescent inhomogeneous phases effectively enhances the superconducting performance of MgB2. Moreover, by controlling the size of the electroluminescent inhomogeneous phases and optimizing grain connectivity, density, and microstructural uniformity, we can further improve the critical temperature (TC) and flux-pinning capability of MgB2 superconducting materials. Comprehensive studies on the physical properties of MgB2 superconducting structures added with p-n junction electroluminescent inhomogeneous phases also confirm the general effectiveness of electroluminescent inhomogeneous phases in enhancing the performance of superconducting materials.
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41

Kolednik, O., J. Predan, G. X. Shan, N. K. Simha, and F. D. Fischer. "On the fracture behavior of inhomogeneous materials––A case study for elastically inhomogeneous bimaterials." International Journal of Solids and Structures 42, no. 2 (January 2005): 605–20. http://dx.doi.org/10.1016/j.ijsolstr.2004.06.064.

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42

Wapenaar, Kees, and Evert Slob. "Reciprocity and Representations for Wave Fields in 3D Inhomogeneous Parity-Time Symmetric Materials." Symmetry 14, no. 11 (October 25, 2022): 2236. http://dx.doi.org/10.3390/sym14112236.

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Анотація:
Inspired by recent developments in wave propagation and scattering experiments with parity-time (PT) symmetric materials, we discuss reciprocity and representation theorems for 3D inhomogeneous PT-symmetric materials and indicate some applications. We start with a unified matrix-vector wave equation which accounts for acoustic, quantum-mechanical, electromagnetic, elastodynamic, poroelastodynamic, piezoelectric and seismoelectric waves. Based on the symmetry properties of the operator matrix in this equation, we derive unified reciprocity theorems for wave fields in 3D arbitrary inhomogeneous media and 3D inhomogeneous media with PT-symmetry. These theorems form the basis for deriving unified wave field representations and relations between reflection and transmission responses in such media. Among the potential applications are interferometric Green’s matrix retrieval and Marchenko-type Green’s matrix retrieval in PT-symmetric materials.
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43

Zhao, Jing, Fei Zhu, Liyou Xu, Yong Tang, and Sheng Li. "A homogenization method for nonlinear inhomogeneous elastic materials." Virtual Reality & Intelligent Hardware 3, no. 2 (April 2021): 156–70. http://dx.doi.org/10.1016/j.vrih.2021.01.002.

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44

Molchanov, I. S., S. N. Chiu, and S. A. Zuyev. "Design of inhomogeneous materials with given structural properties." Physical Review E 62, no. 4 (October 1, 2000): 4544–52. http://dx.doi.org/10.1103/physreve.62.4544.

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45

Arzamaskova, L. M., E. E. Evdokimov, and O. V. Konovalov. "Research of Construction Elements of Structure-inhomogeneous Materials." IOP Conference Series: Materials Science and Engineering 463 (December 31, 2018): 032074. http://dx.doi.org/10.1088/1757-899x/463/3/032074.

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46

Jiang, Hai, Robert Penno, Krishna M. Pasala, Leo Kempel, and Stephan Schneider. "Broadband Microstrip Leaky Wave Antenna With Inhomogeneous Materials." IEEE Transactions on Antennas and Propagation 57, no. 5 (May 2009): 1558–62. http://dx.doi.org/10.1109/tap.2009.2016785.

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47

Takamatsu, Hiroyuki, Shingo Sumie, Tsutomu Morimoto, Yutaka Kawata, Yoshiro Nishimoto, Takefumi Horiuchi, Hiroshi Nakayama, Takashi Kita, and Taneo Nishino. "Theoretical Analysis of Photoacoustic Displacement for Inhomogeneous Materials." Japanese Journal of Applied Physics 33, Part 1, No. 10 (October 15, 1994): 6032–38. http://dx.doi.org/10.1143/jjap.33.6032.

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48

Nan, Ce-Wen, and G. J. Weng. "Theoretical approach to effective electrostriction in inhomogeneous materials." Physical Review B 61, no. 1 (January 1, 2000): 258–65. http://dx.doi.org/10.1103/physrevb.61.258.

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49

Kadigrobov, A., R. I. Shekhter, and M. Jonson. "Triplet superconducting proximity effect in inhomogeneous magnetic materials." Low Temperature Physics 27, no. 9 (September 2001): 760–66. http://dx.doi.org/10.1063/1.1401185.

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50

Tosaki, Mitsuo, Daisuke Ohsawa, and Yasuhito Isozumi. "Experimental energy straggling of protons in inhomogeneous materials." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 219-220 (June 2004): 241–45. http://dx.doi.org/10.1016/j.nimb.2004.01.061.

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