An integration model for two different ethnic groups

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June 2014, 3(2): 277-286. doi: 10.3934/eect.2014.3.277

An integration model for two different ethnic groups

Mauro Fabrizio ^1, and Jaime Munõz Rivera ^2,

1.	Department of Mathematics, University of Bologna, Italy
2.	LNCC, Petropolis, Brazil

Received October 2013 Revised February 2014 Published May 2014

Abstract
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For the purpose of studying the integration of two different ethnic populations, we compare their evolution with that of a mixture of two fluids. For this model we consider the concentration of only one species, whose evolution will be described by a Cahn-Hilliard equation. Instead, the separation between the two phases will be controlled by the educational levels of two components. Finally, we assume that the homogenization phase occurs when the mean of the cultural levels is greater then a critical value.

Keywords: Cahn-Hilliard equation, phase transitions, thermodynamics., Integration-separation, life science.

Mathematics Subject Classification: Primary: 92D25, 92H10; Secondary: 923.

Citation: Mauro Fabrizio, Jaime Munõz Rivera. An integration model for two different ethnic groups. Evolution Equations and Control Theory, 2014, 3 (2) : 277-286. doi: 10.3934/eect.2014.3.277

References:

[1]	C. Argyris and D. Schon, Organizational Learning: A Theory of Action Perspective 22, Park: Addison-Wesley, 1978.
[2]	J. W. Barrett and J. F. Blowey, Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility, Math. Comp., 68 (1999), 487-517. doi: 10.1090/S0025-5718-99-01015-7.
[3]	A. Berti and I. Bochicchio, A mathematical model for phase separation: A generalized Cahn-Hilliard equation, Math. Meth. Appl. Sci., 34 (2011), 1193-1201. doi: 10.1002/mma.1432.
[4]	L. Bevilacqua, A. C. Galeão, F. Pietrobon-Costa and S. L. Monteiro, Knowledge diffusion paths in a research chain, Mecânica Computacional, 24 (2010), 2061-2069.
[5]	H. P. Boswijk and P. H. Franses, On the econometrics of the bass diffusion model, Journal of Business & Economic Statistics, 23 (2005), 255-268. doi: 10.1198/073500104000000604.
[6]	V. Berti, M. Fabrizio and C. Giorgi, Well-posedness for solid-liquid phase transitions with a fourth-order nonlinearity, Physica D, 236 (2007), 13-21. doi: 10.1016/j.physd.2007.07.009.
[7]	J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial energy, J. Chem. Phys, 28 (1958), 258-267. doi: 10.1063/1.1744102.
[8]	J. W. Cahn, C. M. Elliott and A. Novik-Cohen, The Cahn-Hilliard equation with a concentration dependent mobility: Motion of minus Laplacian of the mean curvature, European J. Appl. Math., 7 (1996), 287-301. doi: 10.1017/S0956792500002369.
[9]	L. L. Cavalli-Sforza and M. Feldman, Cultural Transmission and Evolution, Princeton University Press, Princeton, 1981.
[10]	E. Collett, Immigrant Integration in Europe in a Time of Austerity, Migration Policy Institute, Washington, 2011.
[11]	M. Fabrizio, C. Giorgi and A. Morro, A continuum theory for first-order phase transitions based on the balance of structure order, Math. Meth. Appl. Sci., 31 (2008), 627-653. doi: 10.1002/mma.930.
[12]	M. Fabrizio, C. Giorgi and A. Morro, Phase separation in quasi-incompressible Cahn-Hilliard fluids, European Journal of Mechanics B/Fluids, 30 (2011), 281-287. doi: 10.1016/j.euromechflu.2010.12.003.
[13]	M. Fabrizio, B. Lazzari and R. Nibbi, Thermodynamics of non-local materials: Extra fluxes and internal powers, Continuum Mech. Thermodyn, 23 (2011), 509-525. doi: 10.1007/s00161-011-0193-x.
[14]	M. Gladwell, The Tipping Point. How little things can make a big difference, Little Brown and Company, London, 2000.
[15]	M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D, 92 (1996), 178-192. doi: 10.1016/0167-2789(95)00173-5.
[16]	J. He, Knowledge management and knowledge fermentation, Science of Science and Management of S.&.T., 25 (2004), 23-26.
[17]	G. Hedlund, A model of knowledge management and the N-Form corporation, Strategic Management Journal, 15 (1994), 73-90. doi: 10.1002/smj.4250151006.
[18]	Z. Li, T. Zhu and W. Lai, A Study on the knowledge diffusion of communities of practice based on the weighted small-world network, Journal of Computers, 5 (2010), 1046-1053. doi: 10.4304/jcp.5.7.1046-1053.
[19]	R. McAdam, Knowledge creation and idea generations critical quality perspective, Technovation, 24 (2004), 697-705.
[20]	I. Nonaka and N Konno, The concept of Ba: Building a foundation for knowledge creation, California Management Review, 40 (1998), 40-54. doi: 10.2307/41165942.
[21]	Z. Shaoying, The model of dynamic spread knowledge based on organizational learning, Science Research Management, 24 (2003), 67-71.

show all references

References:

[1]	C. Argyris and D. Schon, Organizational Learning: A Theory of Action Perspective 22, Park: Addison-Wesley, 1978.
[2]	J. W. Barrett and J. F. Blowey, Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility, Math. Comp., 68 (1999), 487-517. doi: 10.1090/S0025-5718-99-01015-7.
[3]	A. Berti and I. Bochicchio, A mathematical model for phase separation: A generalized Cahn-Hilliard equation, Math. Meth. Appl. Sci., 34 (2011), 1193-1201. doi: 10.1002/mma.1432.
[4]	L. Bevilacqua, A. C. Galeão, F. Pietrobon-Costa and S. L. Monteiro, Knowledge diffusion paths in a research chain, Mecânica Computacional, 24 (2010), 2061-2069.
[5]	H. P. Boswijk and P. H. Franses, On the econometrics of the bass diffusion model, Journal of Business & Economic Statistics, 23 (2005), 255-268. doi: 10.1198/073500104000000604.
[6]	V. Berti, M. Fabrizio and C. Giorgi, Well-posedness for solid-liquid phase transitions with a fourth-order nonlinearity, Physica D, 236 (2007), 13-21. doi: 10.1016/j.physd.2007.07.009.
[7]	J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial energy, J. Chem. Phys, 28 (1958), 258-267. doi: 10.1063/1.1744102.
[8]	J. W. Cahn, C. M. Elliott and A. Novik-Cohen, The Cahn-Hilliard equation with a concentration dependent mobility: Motion of minus Laplacian of the mean curvature, European J. Appl. Math., 7 (1996), 287-301. doi: 10.1017/S0956792500002369.
[9]	L. L. Cavalli-Sforza and M. Feldman, Cultural Transmission and Evolution, Princeton University Press, Princeton, 1981.
[10]	E. Collett, Immigrant Integration in Europe in a Time of Austerity, Migration Policy Institute, Washington, 2011.
[11]	M. Fabrizio, C. Giorgi and A. Morro, A continuum theory for first-order phase transitions based on the balance of structure order, Math. Meth. Appl. Sci., 31 (2008), 627-653. doi: 10.1002/mma.930.
[12]	M. Fabrizio, C. Giorgi and A. Morro, Phase separation in quasi-incompressible Cahn-Hilliard fluids, European Journal of Mechanics B/Fluids, 30 (2011), 281-287. doi: 10.1016/j.euromechflu.2010.12.003.
[13]	M. Fabrizio, B. Lazzari and R. Nibbi, Thermodynamics of non-local materials: Extra fluxes and internal powers, Continuum Mech. Thermodyn, 23 (2011), 509-525. doi: 10.1007/s00161-011-0193-x.
[14]	M. Gladwell, The Tipping Point. How little things can make a big difference, Little Brown and Company, London, 2000.
[15]	M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D, 92 (1996), 178-192. doi: 10.1016/0167-2789(95)00173-5.
[16]	J. He, Knowledge management and knowledge fermentation, Science of Science and Management of S.&.T., 25 (2004), 23-26.
[17]	G. Hedlund, A model of knowledge management and the N-Form corporation, Strategic Management Journal, 15 (1994), 73-90. doi: 10.1002/smj.4250151006.
[18]	Z. Li, T. Zhu and W. Lai, A Study on the knowledge diffusion of communities of practice based on the weighted small-world network, Journal of Computers, 5 (2010), 1046-1053. doi: 10.4304/jcp.5.7.1046-1053.
[19]	R. McAdam, Knowledge creation and idea generations critical quality perspective, Technovation, 24 (2004), 697-705.
[20]	I. Nonaka and N Konno, The concept of Ba: Building a foundation for knowledge creation, California Management Review, 40 (1998), 40-54. doi: 10.2307/41165942.
[21]	Z. Shaoying, The model of dynamic spread knowledge based on organizational learning, Science Research Management, 24 (2003), 67-71.

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