American Institute of Mathematical Sciences

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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

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 & 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). Google Scholar

[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. doi: 10.1090/S0025-5718-99-01015-7. Google Scholar

[3]

A. Berti and I. Bochicchio, A mathematical model for phase separation: A generalized Cahn-Hilliard equation,, Math. Meth. Appl. Sci., 34 (2011), 1193. doi: 10.1002/mma.1432. Google Scholar

[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. Google Scholar

[5]

H. P. Boswijk and P. H. Franses, On the econometrics of the bass diffusion model,, Journal of Business & Economic Statistics, 23 (2005), 255. doi: 10.1198/073500104000000604. Google Scholar

[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. doi: 10.1016/j.physd.2007.07.009. Google Scholar

[7]

J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial energy,, J. Chem. Phys, 28 (1958), 258. doi: 10.1063/1.1744102. Google Scholar

[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. doi: 10.1017/S0956792500002369. Google Scholar

[9]

L. L. Cavalli-Sforza and M. Feldman, Cultural Transmission and Evolution,, Princeton University Press, (1981). Google Scholar

[10]

E. Collett, Immigrant Integration in Europe in a Time of Austerity,, Migration Policy Institute, (2011). Google Scholar

[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. doi: 10.1002/mma.930. Google Scholar

[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. doi: 10.1016/j.euromechflu.2010.12.003. Google Scholar

[13]

M. Fabrizio, B. Lazzari and R. Nibbi, Thermodynamics of non-local materials: Extra fluxes and internal powers,, Continuum Mech. Thermodyn, 23 (2011), 509. doi: 10.1007/s00161-011-0193-x. Google Scholar

[14]

M. Gladwell, The Tipping Point. How little things can make a big difference,, Little Brown and Company, (2000). Google Scholar

[15]

M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance,, Physica D, 92 (1996), 178. doi: 10.1016/0167-2789(95)00173-5. Google Scholar

[16]

J. He, Knowledge management and knowledge fermentation,, Science of Science and Management of S.&.T., 25 (2004), 23. Google Scholar

[17]

G. Hedlund, A model of knowledge management and the N-Form corporation,, Strategic Management Journal, 15 (1994), 73. doi: 10.1002/smj.4250151006. Google Scholar

[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. doi: 10.4304/jcp.5.7.1046-1053. Google Scholar

[19]

R. McAdam, Knowledge creation and idea generations critical quality perspective,, Technovation, 24 (2004), 697. Google Scholar

[20]

I. Nonaka and N Konno, The concept of Ba: Building a foundation for knowledge creation,, California Management Review, 40 (1998), 40. doi: 10.2307/41165942. Google Scholar

[21]

Z. Shaoying, The model of dynamic spread knowledge based on organizational learning,, Science Research Management, 24 (2003), 67. Google Scholar

show all references

References:
[1]

C. Argyris and D. Schon, Organizational Learning: A Theory of Action Perspective 22,, Park: Addison-Wesley, (1978). Google Scholar

[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. doi: 10.1090/S0025-5718-99-01015-7. Google Scholar

[3]

A. Berti and I. Bochicchio, A mathematical model for phase separation: A generalized Cahn-Hilliard equation,, Math. Meth. Appl. Sci., 34 (2011), 1193. doi: 10.1002/mma.1432. Google Scholar

[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. Google Scholar

[5]

H. P. Boswijk and P. H. Franses, On the econometrics of the bass diffusion model,, Journal of Business & Economic Statistics, 23 (2005), 255. doi: 10.1198/073500104000000604. Google Scholar

[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. doi: 10.1016/j.physd.2007.07.009. Google Scholar

[7]

J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial energy,, J. Chem. Phys, 28 (1958), 258. doi: 10.1063/1.1744102. Google Scholar

[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. doi: 10.1017/S0956792500002369. Google Scholar

[9]

L. L. Cavalli-Sforza and M. Feldman, Cultural Transmission and Evolution,, Princeton University Press, (1981). Google Scholar

[10]

E. Collett, Immigrant Integration in Europe in a Time of Austerity,, Migration Policy Institute, (2011). Google Scholar

[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. doi: 10.1002/mma.930. Google Scholar

[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. doi: 10.1016/j.euromechflu.2010.12.003. Google Scholar

[13]

M. Fabrizio, B. Lazzari and R. Nibbi, Thermodynamics of non-local materials: Extra fluxes and internal powers,, Continuum Mech. Thermodyn, 23 (2011), 509. doi: 10.1007/s00161-011-0193-x. Google Scholar

[14]

M. Gladwell, The Tipping Point. How little things can make a big difference,, Little Brown and Company, (2000). Google Scholar

[15]

M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance,, Physica D, 92 (1996), 178. doi: 10.1016/0167-2789(95)00173-5. Google Scholar

[16]

J. He, Knowledge management and knowledge fermentation,, Science of Science and Management of S.&.T., 25 (2004), 23. Google Scholar

[17]

G. Hedlund, A model of knowledge management and the N-Form corporation,, Strategic Management Journal, 15 (1994), 73. doi: 10.1002/smj.4250151006. Google Scholar

[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. doi: 10.4304/jcp.5.7.1046-1053. Google Scholar

[19]

R. McAdam, Knowledge creation and idea generations critical quality perspective,, Technovation, 24 (2004), 697. Google Scholar

[20]

I. Nonaka and N Konno, The concept of Ba: Building a foundation for knowledge creation,, California Management Review, 40 (1998), 40. doi: 10.2307/41165942. Google Scholar

[21]

Z. Shaoying, The model of dynamic spread knowledge based on organizational learning,, Science Research Management, 24 (2003), 67. Google Scholar

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