An integration model for two different ethnic groups

Previous Article
Observability of rectangular membranes and plates on small sets
EECT Home
This Issue
Next Article
A vanishing diffusion limit in a nonstandard system of phase field equations

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
Related Papers

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.

[1]	Mauro Fabrizio, Claudio Giorgi, Angelo Morro. Phase transition and separation in compressible Cahn-Hilliard fluids. Discrete and Continuous Dynamical Systems - B, 2014, 19 (1) : 73-88. doi: 10.3934/dcdsb.2014.19.73
[2]	Desheng Li, Xuewei Ju. On dynamical behavior of viscous Cahn-Hilliard equation. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 2207-2221. doi: 10.3934/dcds.2012.32.2207
[3]	Laurence Cherfils, Alain Miranville, Sergey Zelik. On a generalized Cahn-Hilliard equation with biological applications. Discrete and Continuous Dynamical Systems - B, 2014, 19 (7) : 2013-2026. doi: 10.3934/dcdsb.2014.19.2013
[4]	Álvaro Hernández, Michał Kowalczyk. Rotationally symmetric solutions to the Cahn-Hilliard equation. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 801-827. doi: 10.3934/dcds.2017033
[5]	Pierluigi Colli, Gianni Gilardi, Danielle Hilhorst. On a Cahn-Hilliard type phase field system related to tumor growth. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2423-2442. doi: 10.3934/dcds.2015.35.2423
[6]	Tian Ma, Shouhong Wang. Cahn-Hilliard equations and phase transition dynamics for binary systems. Discrete and Continuous Dynamical Systems - B, 2009, 11 (3) : 741-784. doi: 10.3934/dcdsb.2009.11.741
[7]	Georgia Karali, Yuko Nagase. On the existence of solution for a Cahn-Hilliard/Allen-Cahn equation. Discrete and Continuous Dynamical Systems - S, 2014, 7 (1) : 127-137. doi: 10.3934/dcdss.2014.7.127
[8]	Tomáš Roubíček. Cahn-Hilliard equation with capillarity in actual deforming configurations. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 41-55. doi: 10.3934/dcdss.2020303
[9]	Dimitra Antonopoulou, Georgia Karali, Georgios T. Kossioris. Asymptotics for a generalized Cahn-Hilliard equation with forcing terms. Discrete and Continuous Dynamical Systems, 2011, 30 (4) : 1037-1054. doi: 10.3934/dcds.2011.30.1037
[10]	Annalisa Iuorio, Stefano Melchionna. Long-time behavior of a nonlocal Cahn-Hilliard equation with reaction. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 3765-3788. doi: 10.3934/dcds.2018163
[11]	Dimitra Antonopoulou, Georgia Karali. Existence of solution for a generalized stochastic Cahn-Hilliard equation on convex domains. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 31-55. doi: 10.3934/dcdsb.2011.16.31
[12]	Alain Miranville, Sergey Zelik. The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 275-310. doi: 10.3934/dcds.2010.28.275
[13]	S. Maier-Paape, Ulrich Miller. Connecting continua and curves of equilibria of the Cahn-Hilliard equation on the square. Discrete and Continuous Dynamical Systems, 2006, 15 (4) : 1137-1153. doi: 10.3934/dcds.2006.15.1137
[14]	Laurence Cherfils, Madalina Petcu, Morgan Pierre. A numerical analysis of the Cahn-Hilliard equation with dynamic boundary conditions. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1511-1533. doi: 10.3934/dcds.2010.27.1511
[15]	Hussein Fakih, Ragheb Mghames, Noura Nasreddine. On the Cahn-Hilliard equation with mass source for biological applications. Communications on Pure and Applied Analysis, 2021, 20 (2) : 495-510. doi: 10.3934/cpaa.2020277
[16]	Amy Novick-Cohen, Andrey Shishkov. Upper bounds for coarsening for the degenerate Cahn-Hilliard equation. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 251-272. doi: 10.3934/dcds.2009.25.251
[17]	Gianni Gilardi, A. Miranville, Giulio Schimperna. On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions. Communications on Pure and Applied Analysis, 2009, 8 (3) : 881-912. doi: 10.3934/cpaa.2009.8.881
[18]	Dong Li. A regularization-free approach to the Cahn-Hilliard equation with logarithmic potentials. Discrete and Continuous Dynamical Systems, 2022, 42 (5) : 2453-2460. doi: 10.3934/dcds.2021198
[19]	Matthieu Brachet, Philippe Parnaudeau, Morgan Pierre. Convergence to equilibrium for time and space discretizations of the Cahn-Hilliard equation. Discrete and Continuous Dynamical Systems - S, 2022, 15 (8) : 1987-2031. doi: 10.3934/dcdss.2022110
[20]	Keith Promislow, Qiliang Wu. Undulated bilayer interfaces in the planar functionalized Cahn-Hilliard equation. Discrete and Continuous Dynamical Systems - S, 2022, 15 (9) : 2633-2656. doi: 10.3934/dcdss.2022035

2021 Impact Factor: 1.169

Tools

Metrics

Other articles
by authors

on AIMS
Mauro Fabrizio Jaime Munõz Rivera
on Google Scholar
Mauro Fabrizio Jaime Munõz Rivera

[Back to Top]