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1. | Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, TX 75080, United States |
References:
[1] |
A. Visintin, Differential Models of Hysteresis, Springer, 1994.
doi: 10.1007/978-3-662-11557-2. |
[2] |
I. D. Mayergoyz, Mathematical Models of Hysteresis and Their Applications, Elsevier, 1993. |
[3] |
J. C. Mallison, The Foundations of Magnetic Recording, Academic Press, 2012. |
[4] | |
[5] |
M. Brokate, P. Krejci and D. Rachinskii, Some analytical properties of the multidimensional continuous Mroz model of plasticity, Control Cybernet, 27 (1998), 199-215. |
[6] |
V. Lampaert, F. Al-Bender and J. Swevers, A generalized Maxwell-slip friction model appropriate for control purposes, Physics and Control, Proceedings, International Conference, 4 (2013), 1170-1177.
doi: 10.1109/PHYCON.2003.1237071. |
[7] |
M. Ruderman, F. Hoffmann and T. Bertram, Modeling and identification of elastic robot joints with hysteresis and backlash, IEEE Tran. Ind. Electron, 56 (2009), 3840-3847.
doi: 10.1109/TIE.2009.2015752. |
[8] |
K. Kuhnen, Compensation of parameter-dependent complex hysteretic actuator nonlinearities in smart material systems, J. Intell. Mater. Syst., 19 (2008), 1411-1424.
doi: 10.1177/1045389X08089690. |
[9] |
D. Daniele, P. Krejči and C. Visone, Fully coupled modeling of magnetomechanical hysteresis through thermodynamic compatibility, Smart Mater. Struct., 22 (2013), 095009. |
[10] |
M. Eleuteri, J. Kopfova and P. Krejči, A new phase field model for material fatigue in an oscillating elastoplastic beam, Discret. Cont. Dyn. S. A, 35 (2015), 2465-2495.
doi: 10.3934/dcds.2015.35.2465. |
[11] |
J.-Y. Parlange, Capillary hysteresis and relationship between drying and wetting curves, Water Resources Res., 12 (1976), 224-228.
doi: 10.1029/WR012i002p00224. |
[12] |
A. Rahunanthan, F. Furtado, D. Marchesin and M. Piri, Hysteretic enhancemnet of carbon dioxide trapping in deep aquifers, Comput. Geosci., 18 (2014), 899-912. |
[13] |
M. Brokate, N. D. Botkin and O. A. Pykhteev, Numerical simulation for a two-phase porous medium flow problem with rate independent hysteresis, Physica B, 407 (2012), 1336-1339.
doi: 10.1016/j.physb.2011.06.048. |
[14] |
E. K. H. Salje and K. A. Dahmen, Crackling noise in disordered materials, Annual Review of Condensed Matter Physics, 5 (2014), 233-254.
doi: 10.1146/annurev-conmatphys-031113-133838. |
[15] |
M. Dimian and P. Andrei, Noise-Driven Phenomena in Hysteretic Systems, Springer, 2014.
doi: 10.1007/978-1-4614-1374-5. |
[16] |
P. L. Gurevich, W. Jaeger and A. L. Skubachevskii, On periodicity of solutions for thermocontrol problems with hysteresis-type switches, SIAM J. Math. Anal., 41 (2009), 733-752.
doi: 10.1137/080718905. |
[17] |
M. Brokate and J. Sprekels, Hysteresis and Phase Transitions, Springer, 1996.
doi: 10.1007/978-1-4612-4048-8. |
[18] |
L. Landau and E. Lifshitz, Statistical Physics, Pergamon Press, Oxford, 1969. |
[19] |
R. E. O'Malley, Singular Perturbation Methods for Ordinary Differential Equations, Springer, 1991.
doi: 10.1007/978-1-4612-0977-5. |
[20] |
A. Visintin, A Weiss-type model of ferromagnetism, Physica B, 275 (2000), 87-91.
doi: 10.1016/S0921-4526(99)00712-7. |
[21] |
J. P. O'Kane and D. Flynn, Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: A non-linear systems theory, Hydrol. Earth Syst. Sci., 11 (2007), 443-459.
doi: 10.5194/hess-11-443-2007. |
[22] |
P. Krejči, J. P. O'Kane, A. Pokrovskii and D. Rachinskii, Stability results for a soil model with singular hysteretic hydrology, J. Phys.: Conf. Ser., 268 (2011), 012016. |
[23] |
B. Athukorallage, E. Aulisa, R. Iyer and L. Zhang, Macroscopic theory for capillary pressure hysteresis, Langmuir, 31 (2015), 2390-2397.
doi: 10.1021/la504495c. |
[24] |
M. Brokate, S. MacCarthy, A. Pimenov, A. Pokrovskii and D. Rachinskii, Modelling energy dissipation due to soil-moisture hysteresis, Environ. Model. Assess., 16 (2011), 313-333.
doi: 10.1007/s10666-011-9258-2. |
[25] |
I. Rychlik, A new definition of the rainflow cycle counting method, Internat. J. Fatigue, 9 (1987), 119-121.
doi: 10.1016/0142-1123(87)90054-5. |
[26] |
P. Krejči, H. Lamba, S. Melnik and D. Rachinskii, Analytical solution for a class of network dynamics with mechanical and financial applications, Phys. Rev. E, 90 (2014), 032822. |
[27] |
R. Cross, H. McNamara, A. Pokrovskii and D. Rachinskii, A new paradigm for modelling hysteresis in macroeconomic flows, Physica B, 403 (2008), 231-236.
doi: 10.1016/j.physb.2007.08.017. |
[28] |
R. Cross, H. Hutchinson, H. Lamba and D. Strachan, Reflections on Soros: Mach, Quine, Arthur and far-from-equilibrium dynamics, J. Econ. Methodology, 20 (2014), 357-367.
doi: 10.1080/1350178X.2013.859406. |
[29] |
S. Melnik, J. A. Ward, J. P. Gleeson and M. A. Porter, Multi-stage complex contagions, Chaos, 23 (2013), 013124, 13pp.
doi: 10.1063/1.4790836. |
[30] |
C. Chiu, F. C. Hoppensteadt and W. Jäger, Analysis and computer simulation of accretion patterns in bacterial cultures, J. Math. Biol., 32 (1994), 841-855.
doi: 10.1007/BF00168801. |
[31] |
G. Friedman, S. McCarthy and D. Rachinskii, Hysteresis can grant fitness in stochastically varying environment, PLOS ONE, 9 (2014), e103241.
doi: 10.1371/journal.pone.0103241. |
[32] |
A. Pimenov, T. C. Kelly, A. Korobeinikov, M. J. A. O'Callaghan, A. V. Pokrovskii and D. Rachinskii, Memory effects in population dynamics: Spread of infectious disease as a case study, Math. Model. Nat. Phenom., 7 (2012), 204-226.
doi: 10.1051/mmnp/20127313. |
[33] |
, The Science of Hysteresis,, (eds. I. D. Mayergoyz and G. Bertotti), (2005).
|
[34] |
, Singular Perturbations and Hysteresis,, (eds. M. P. Mortell, (2005).
doi: 10.1137/1.9780898717860. |
[35] |
M. A. Krasnosel'skii and A. V. Pokrovskii, Systems with Hysteresis, Springer, 1989.
doi: 10.1007/978-3-642-61302-9. |
[36] |
P. Krejči and V. Recupero, BV solutions of rate independent differential inclusions, Math. Bohem., 139 (2014), 607-619. |
[37] |
P. Krejči, Hysteresis, Convexity and Dissipation in Hyperbolic Equations, Gakkotosho, 1996. |
[38] |
A. Mielke, R. Rossi and G. Savaré, Variational convergence of gradient flows and rate-independent evolutions in metric spaces, Milan J. Math., 80 (2012), 381-410.
doi: 10.1007/s00032-012-0190-y. |
[39] |
K. J. Aström, Oscillations in systems with relay feedback, in Adaptive Control, Filtering and Signal Processing (eds. K. Aström, G. Goodwin and P. Kumar), Springer, 74 (1995), 1-25.
doi: 10.1007/978-1-4419-8568-2_1. |
[40] |
M. Brokate, A. Pokrovskii and D. Rachinskii, Asymptotic stability of continuum sets of periodic solutions to systems with hysteresis, J. Math. Anal. Appl., 319 (2006), 94-109.
doi: 10.1016/j.jmaa.2006.02.060. |
[41] |
A. Pimenov and D. Rachinskii, Linear stability analysis of systems with Preisach memory, Discret. Contin. Dyn. S. B, 11 (2009), 997-1018.
doi: 10.3934/dcdsb.2009.11.997. |
[42] |
A. Krasnosel'skii and D. Rachinskii, Bifurcation of forced periodic oscillations for equations with Preisach hysteresis, J. Phys.: Conf. Ser., 22 (2005), 93-102.
doi: 10.1088/1742-6596/22/1/006. |
[43] |
A. Krasnosel'skii and D. Rachinskii, On a bifurcation governed by hysteresis nonlinearity, NoDEA Nonlinear Differential Equations Appl., 9 (2002), 93-115.
doi: 10.1007/s00030-002-8120-2. |
[44] |
P. Krejči, J. P. O'Kane, A. Pokrovskii and D. Rachinskii, Properties of solutions to a class of differential models incorporating Preisach hysteresis operator, Physica D, 241 (2012), 2010-2028.
doi: 10.1016/j.physd.2011.05.005. |
show all references
References:
[1] |
A. Visintin, Differential Models of Hysteresis, Springer, 1994.
doi: 10.1007/978-3-662-11557-2. |
[2] |
I. D. Mayergoyz, Mathematical Models of Hysteresis and Their Applications, Elsevier, 1993. |
[3] |
J. C. Mallison, The Foundations of Magnetic Recording, Academic Press, 2012. |
[4] | |
[5] |
M. Brokate, P. Krejci and D. Rachinskii, Some analytical properties of the multidimensional continuous Mroz model of plasticity, Control Cybernet, 27 (1998), 199-215. |
[6] |
V. Lampaert, F. Al-Bender and J. Swevers, A generalized Maxwell-slip friction model appropriate for control purposes, Physics and Control, Proceedings, International Conference, 4 (2013), 1170-1177.
doi: 10.1109/PHYCON.2003.1237071. |
[7] |
M. Ruderman, F. Hoffmann and T. Bertram, Modeling and identification of elastic robot joints with hysteresis and backlash, IEEE Tran. Ind. Electron, 56 (2009), 3840-3847.
doi: 10.1109/TIE.2009.2015752. |
[8] |
K. Kuhnen, Compensation of parameter-dependent complex hysteretic actuator nonlinearities in smart material systems, J. Intell. Mater. Syst., 19 (2008), 1411-1424.
doi: 10.1177/1045389X08089690. |
[9] |
D. Daniele, P. Krejči and C. Visone, Fully coupled modeling of magnetomechanical hysteresis through thermodynamic compatibility, Smart Mater. Struct., 22 (2013), 095009. |
[10] |
M. Eleuteri, J. Kopfova and P. Krejči, A new phase field model for material fatigue in an oscillating elastoplastic beam, Discret. Cont. Dyn. S. A, 35 (2015), 2465-2495.
doi: 10.3934/dcds.2015.35.2465. |
[11] |
J.-Y. Parlange, Capillary hysteresis and relationship between drying and wetting curves, Water Resources Res., 12 (1976), 224-228.
doi: 10.1029/WR012i002p00224. |
[12] |
A. Rahunanthan, F. Furtado, D. Marchesin and M. Piri, Hysteretic enhancemnet of carbon dioxide trapping in deep aquifers, Comput. Geosci., 18 (2014), 899-912. |
[13] |
M. Brokate, N. D. Botkin and O. A. Pykhteev, Numerical simulation for a two-phase porous medium flow problem with rate independent hysteresis, Physica B, 407 (2012), 1336-1339.
doi: 10.1016/j.physb.2011.06.048. |
[14] |
E. K. H. Salje and K. A. Dahmen, Crackling noise in disordered materials, Annual Review of Condensed Matter Physics, 5 (2014), 233-254.
doi: 10.1146/annurev-conmatphys-031113-133838. |
[15] |
M. Dimian and P. Andrei, Noise-Driven Phenomena in Hysteretic Systems, Springer, 2014.
doi: 10.1007/978-1-4614-1374-5. |
[16] |
P. L. Gurevich, W. Jaeger and A. L. Skubachevskii, On periodicity of solutions for thermocontrol problems with hysteresis-type switches, SIAM J. Math. Anal., 41 (2009), 733-752.
doi: 10.1137/080718905. |
[17] |
M. Brokate and J. Sprekels, Hysteresis and Phase Transitions, Springer, 1996.
doi: 10.1007/978-1-4612-4048-8. |
[18] |
L. Landau and E. Lifshitz, Statistical Physics, Pergamon Press, Oxford, 1969. |
[19] |
R. E. O'Malley, Singular Perturbation Methods for Ordinary Differential Equations, Springer, 1991.
doi: 10.1007/978-1-4612-0977-5. |
[20] |
A. Visintin, A Weiss-type model of ferromagnetism, Physica B, 275 (2000), 87-91.
doi: 10.1016/S0921-4526(99)00712-7. |
[21] |
J. P. O'Kane and D. Flynn, Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: A non-linear systems theory, Hydrol. Earth Syst. Sci., 11 (2007), 443-459.
doi: 10.5194/hess-11-443-2007. |
[22] |
P. Krejči, J. P. O'Kane, A. Pokrovskii and D. Rachinskii, Stability results for a soil model with singular hysteretic hydrology, J. Phys.: Conf. Ser., 268 (2011), 012016. |
[23] |
B. Athukorallage, E. Aulisa, R. Iyer and L. Zhang, Macroscopic theory for capillary pressure hysteresis, Langmuir, 31 (2015), 2390-2397.
doi: 10.1021/la504495c. |
[24] |
M. Brokate, S. MacCarthy, A. Pimenov, A. Pokrovskii and D. Rachinskii, Modelling energy dissipation due to soil-moisture hysteresis, Environ. Model. Assess., 16 (2011), 313-333.
doi: 10.1007/s10666-011-9258-2. |
[25] |
I. Rychlik, A new definition of the rainflow cycle counting method, Internat. J. Fatigue, 9 (1987), 119-121.
doi: 10.1016/0142-1123(87)90054-5. |
[26] |
P. Krejči, H. Lamba, S. Melnik and D. Rachinskii, Analytical solution for a class of network dynamics with mechanical and financial applications, Phys. Rev. E, 90 (2014), 032822. |
[27] |
R. Cross, H. McNamara, A. Pokrovskii and D. Rachinskii, A new paradigm for modelling hysteresis in macroeconomic flows, Physica B, 403 (2008), 231-236.
doi: 10.1016/j.physb.2007.08.017. |
[28] |
R. Cross, H. Hutchinson, H. Lamba and D. Strachan, Reflections on Soros: Mach, Quine, Arthur and far-from-equilibrium dynamics, J. Econ. Methodology, 20 (2014), 357-367.
doi: 10.1080/1350178X.2013.859406. |
[29] |
S. Melnik, J. A. Ward, J. P. Gleeson and M. A. Porter, Multi-stage complex contagions, Chaos, 23 (2013), 013124, 13pp.
doi: 10.1063/1.4790836. |
[30] |
C. Chiu, F. C. Hoppensteadt and W. Jäger, Analysis and computer simulation of accretion patterns in bacterial cultures, J. Math. Biol., 32 (1994), 841-855.
doi: 10.1007/BF00168801. |
[31] |
G. Friedman, S. McCarthy and D. Rachinskii, Hysteresis can grant fitness in stochastically varying environment, PLOS ONE, 9 (2014), e103241.
doi: 10.1371/journal.pone.0103241. |
[32] |
A. Pimenov, T. C. Kelly, A. Korobeinikov, M. J. A. O'Callaghan, A. V. Pokrovskii and D. Rachinskii, Memory effects in population dynamics: Spread of infectious disease as a case study, Math. Model. Nat. Phenom., 7 (2012), 204-226.
doi: 10.1051/mmnp/20127313. |
[33] |
, The Science of Hysteresis,, (eds. I. D. Mayergoyz and G. Bertotti), (2005).
|
[34] |
, Singular Perturbations and Hysteresis,, (eds. M. P. Mortell, (2005).
doi: 10.1137/1.9780898717860. |
[35] |
M. A. Krasnosel'skii and A. V. Pokrovskii, Systems with Hysteresis, Springer, 1989.
doi: 10.1007/978-3-642-61302-9. |
[36] |
P. Krejči and V. Recupero, BV solutions of rate independent differential inclusions, Math. Bohem., 139 (2014), 607-619. |
[37] |
P. Krejči, Hysteresis, Convexity and Dissipation in Hyperbolic Equations, Gakkotosho, 1996. |
[38] |
A. Mielke, R. Rossi and G. Savaré, Variational convergence of gradient flows and rate-independent evolutions in metric spaces, Milan J. Math., 80 (2012), 381-410.
doi: 10.1007/s00032-012-0190-y. |
[39] |
K. J. Aström, Oscillations in systems with relay feedback, in Adaptive Control, Filtering and Signal Processing (eds. K. Aström, G. Goodwin and P. Kumar), Springer, 74 (1995), 1-25.
doi: 10.1007/978-1-4419-8568-2_1. |
[40] |
M. Brokate, A. Pokrovskii and D. Rachinskii, Asymptotic stability of continuum sets of periodic solutions to systems with hysteresis, J. Math. Anal. Appl., 319 (2006), 94-109.
doi: 10.1016/j.jmaa.2006.02.060. |
[41] |
A. Pimenov and D. Rachinskii, Linear stability analysis of systems with Preisach memory, Discret. Contin. Dyn. S. B, 11 (2009), 997-1018.
doi: 10.3934/dcdsb.2009.11.997. |
[42] |
A. Krasnosel'skii and D. Rachinskii, Bifurcation of forced periodic oscillations for equations with Preisach hysteresis, J. Phys.: Conf. Ser., 22 (2005), 93-102.
doi: 10.1088/1742-6596/22/1/006. |
[43] |
A. Krasnosel'skii and D. Rachinskii, On a bifurcation governed by hysteresis nonlinearity, NoDEA Nonlinear Differential Equations Appl., 9 (2002), 93-115.
doi: 10.1007/s00030-002-8120-2. |
[44] |
P. Krejči, J. P. O'Kane, A. Pokrovskii and D. Rachinskii, Properties of solutions to a class of differential models incorporating Preisach hysteresis operator, Physica D, 241 (2012), 2010-2028.
doi: 10.1016/j.physd.2011.05.005. |
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