A specification of the maxwell-rayleigh-heisenberg approach to modelling fluids for bioelectronic applications

Mathematical and Computer Modelling

Volumn 42, Issue 3-4, 2005, Pages 441-470

  Mamontov, E ^a  

^a UNIVERSITY OF GOTHENBURG   (Sweden)

Author keywords

Distribution function for nonzero volume disparate particles with the spin mixtures; Heisenberg's uncertainty principle; It 's stochastic differential equation; Maxwell's single particle probability density; Rayleigh's dissipation function

Indexed keywords

BIOELECTRIC PHENOMENA; FERMIONS; HYDRODYNAMICS; KINETIC ENERGY; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING; STATISTICAL MECHANICS;

HEISENBERG'S UNCERTAINTY PRINCIPLE; MAXWELL'S SINGLE PARTICLE PROBABILITY DENSITY; RAYLEIGH'S DISSIPATION FUNCTION; STOCHASTIC DIFFERENTIAL EQUATIONS;

FLUID MECHANICS;

EID: 26844466190     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2003.09.044     Document Type: Article

References (58)

1. R.A. Carmona B. Rozovskii Stochastic Partial Differential Equations: Six Perspectives 1999 AMS
2. Y. Friedman, and U. Sandler Fuzzy dynamics as an alternative to statistical mechanics Fuzzy Sets and Systems 106 1 1999 61 74
3. N. Bellomo, and M. Lo Schiavo Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models 2000 World Scientific Providence, RI
4. Y.V. Mamontov, and M. Willander High-Dimensional Nonlinear Diffusion Stochastic Processes. Modelling for Engineering Applications 2001 World Scientific Singapore
5. E. De Angelis, and L. Mesin Modelling of the immune response: Conceptual frameworks and applications Math. Models Methods Appl. Sci. 11 9 2001 1609 1630
6. Yu.L. Khait Statistical mechanics may have dynamic future Physics Today 55 6 2002 74 75
7. L. Arlotti, N. Bellomo, and E. DeAngelis Generalized kinetic (Boltzmann) models: Mathematical structures and applications Math. Models Methods Appl. Sci. 12 4 2002 567 591
8. E. Mamontov, M. Willander, and J. Weiland Stochastic continuum mechanics - A thermodynamic-limit-free alternative to statistical mechanics: Equilibrium of isothermal ideal isotropic uniform fluid Mathl. Comput. Modelling 36 7/8 2002 889 907
9. th Workshop on Physical Simulation of Semiconductor Devices March 25-26 2002 Ilkley Singapore
10. N. Bellomo, E. Mamontov, and M. Willander On the generalized kinetic modelling of a multicomponent "real-life" fluid by means of a single distribution function Mathl. Comput. Modelling 38 5/6 2003 637 659
11. R. Balescu Statistical Dynamics. Matter out of Equilibrium 1997 Imperial College Press West Yorkshire, UK
12. N.N. Bogolubov, and N.N. Bogolubov Jr. An Introduction to Quantum Statistical Mechanics 1994 Gordon and Breach London
13. L.D. Landau, and E.M. Lifshitz Quantum Mechanics: Non-Relativistic Theory 1977 Pergamon Press Lausanne
14. I. Bialynicki-Birula, M. Cieplak, and J. Kaminski Theory of Quanta 1992 Oxford University Press Oxford
15. D.F. Styer, M.S. Balkin, K.M. Becker, M.R. Burns, C.E. Dudley, S.T. Forth, J.S. Gaumer, M.A. Kramer, D.C. Oertel, L.H. Park, M.T. Rinkoski, C.T. Smith, and T.D. Wotherspoon Nine formulations of quantum mechanics Am. J. Phys. 70 3 2002 288 297
16. O. Nairz, M. Arndt, and A. Zeilinger Experimental verification of the Heisenberg uncertainty principle for fullerence molecules Phys. Rev. A 65 2002 1 4
17. E.M. Lifshitz, and L.P. Pitaevskii Statistical Physics, Part 1 1980 Pergamon Press New York
18. P. Résibois, and M. De Leener Classical Kinetic Theory of Fluids 1977 John Wiley & Sons Oxford
19. A. Papoulis Probability, Random Variables, and Stochastic Processes 1991 McGraw-Hill New York
20. L.H. Hartwell, J.J. Hopfield, S. Leibler, and A.W. Murray From molecular to modular cell biology Nature 402 6761 1999 C47 C52
21. R.L. Liboff Kinetic Theory: Classical, Quantum, and Relativistic Descriptions 1998 John Wiley & Sons New York
22. N. Bellomo, E. Mamontov, and M. Willander The generalized-kinetics-based equilibrium distribution function for composite particles Comptes Rendus Mecanique 331 7 2003 461 467
23. E. Mamontov, and M. Willander Electrochemical potentials and pressures of biofluids from common experimental data Acta Biotheoretica 51 3 2003 173 180
24. A.H. Marshak, and C.M. Van Vliet Electrical current and carrier density in degenerate materials with nonuniform band structure Proc. IEEE 72 1984 148 164 2
25. V.L. Bonč-Bruevič, and S.G. Kalašnikov Halbleiterphysik 1982 VEB Deutscher Verlag der Wissenschaften New York
26. J.M. Ortega, and W.C. Rheinboldt Iterative Solution of Nonlinear Equations in Several Variables 1970 Academic Press Berlin
27. L.I. Sedov A Course in Continuum Mechanics Volume I 1971 Wolters-Noordhoff New York
28. J.W. Strutt Lord Rayleigh, Some general theorems relating to vibrations Proceedings of the London Mathematical Society 4 1873 357 368 June 12
29. J.W. Strutt Baron Rayleigh The Theory of Sound Volume I 1937 Macmillan Groningen
30. H. Goldstein Classical Mechanics 1950 Addison-Wesley London
31. J.E. Hasbun Damped motion of a charged particle in the presence of electric and magnetic fields Eur. J. Phys. 17 5 1996 290 294
32. R.T. Cox The statistical method of Gibbs in irreversible thermodynamics J. Phys. Chem. 56 1952 1030 1033
33. D.A. Wells A "power function" for the determination of Lagrangian generalized forces J. Appl. Phys. 16 9 1945 535 538
34. J. Schmittbuhl, J.-P. Vilotte, and S. Roux Dynamic friction of self-affine surfaces J. Phys. II France 4 2 1994 225 237
35. T.I. Mikhailova, I.N. Mikhailov, M. Di Toro, and G. Do Dang Heating and fluctuations in elastoplastic systems Nuclear Physics A 641 1 1998 64 94
36. B. Armstrong Friction: Experimental determination, modelling and compensation Proc. 1988 IEEE Int. Conf. Robotics and Automation Volume 3 1988 IEEE Reading, MA 1422 1427
37. J. Wojewoda, R. Barron, and T. Kapitaniak Chaotic behavior of friction force Int. J. Bifurcation and Chaos 2 1 1992 205 209
38. E. Gnecco, R. Bennewitz, T. Gyalog, Ch. Loppacher, M. Bammerlin, E. Meyer, and H.-J. Güntherodt Velocity dependence of atomic friction Phys. Rev. Lett. 84 6 2000 1172 1175
39. C.W. Gardiner Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences 1994 Springer-Verlag New York
40. Brownian motion Faraday Discuss. Chem. Soc. 83 1987
41. L. Arnold Stochastic Differential Equations: Theory and Applications 1974 John Wiley & Sons Berlin
42. J.L. Synge Relativity: The Special Theory 1956 North-Holland New York
43. Pion P.T. Landsberg Ideal relativistic classical and quantum gases Problems in Thermodynamics and Statistical Physics 1971 132 139
44. S.-B. Zu, S. Singh, J. Lee, and G.W. Robinson Velocity dependence of friction Chem. Phys. 152 1-2 1991 221 228
45. J.L. Synge The Relativistic Gas 1957 North-Holland Amsterdam
46. N.A. Lemos Remark on Rayleigh's dissipation function Am. J. Phys. 59 7 1991 660 661
47. J.W. Strutt Baron Rayleigh The Theory of Sound Volume II 1940 Macmillan Amsterdam
48. E. Govers, and G. Vertogen Fluid dynamics of biaxial nematics Physica 133A 1-2 1985 337 344
49. Session 7 H.P. McKean Jr. Propagation of chaos for a class of non-linear parabolic equations Air Force Office Sci. Res.,Arlington, VA, (1967). Stochastic Differential Equations, Lecture Series in Differential Equations 1967 Catholic University London 41 57
50. (Van Nostrand Mathematical Studies, No. 19) H.P. McKean Jr. Propagation of chaos for a class of non-linear parabolic equations Lectures in Differential Equations Volume II 1969 Van Nostrand 177 194
51. C. Crowe, M. Sommerfeld, and Y. Tsuji Multiphase Flows with Droplets and Particles 1998 CRC Press New York
52. D. Drew, and S.L. Passman Theory of Multicomponent Fluids 1999 Springer-Verlag Boca Raton, FL
53. N. Hashitsume A statistical theory of linear dissipative systems, II Progr. Theor. Phys. 15 4 1956 369 413
54. Webster's Third New International Dictionary of the English Language, Unabridged Utilizing all the experience and resources of more than one hundred years of Merriam-Webster dictionaries 1993 Merriam-Webster New York
55. G. Lindblad On the generator of quantum dynamical semigroups Commun. Math. Phys. 48 2 1976 119 130
56. E. Wigner On unitary representations of the inhomogeneous Lorenz group Annals of Mathematics 40 1 1939 149 204
57. S. Stöcker, and M.G. Curci Modelling and simulating the effect of cytokines on the immune response to tumor cells Mathl. Comput. Modelling 28 3 1998 1 13
58. N. Bellomo, B. Firmani, and L. Guerri Bifurcation analysis for a nonlinear system of integro-differential equations modelling tumor-immune cells competition Appl. Math. Lett. 12 2 1999 39 44