Conformal mapping of some non-harmonic functions in transport theory

Martin Z. Bazant1,2
1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
2École Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, 75231 Paris, France

Tóm tắt

Từ khóa


Tài liệu tham khảo

10.1103/PhysRevLett.89.135503

Barenblatt G. I. 1995 Scaling self-similarity and intermediate asymptotics. Cambridge University Press.

10.1103/PhysRevE.65.046144

10.1103/PhysRevE.65.045101

Batchelor G. K. 1967 An introduction to fluid dynamics. Cambridge University Press.

10.1103/PhysRevLett.91.045503

10.1088/0951-7715/7/3/004

10.1103/PhysRevA.43.5724

10.1016/0167-2789(96)00090-5

10.1063/1.870041

10.1103/RevModPhys.58.977

10.1016/S0022-0728(00)00470-8

Boussinesq M. J., 1905, Sur le pouvoir refroidissant d'un courant liquide ou gazeux, J. Math., 1, 285

10.1016/S0065-2156(08)70100-5

Carrier G. Krook M. & Pearson C. E. 1983 Functions of a complex variable. Ithaca NY: Hod Books.

10.1137/S1064827595292710

Churchill R. V. & Brown J. W. 1990 Complex variables and applications 5th edn. McGraw-Hill.

Crank J. 1975 Mathematics of diffusion 2nd edn. Oxford: Clarendon.

10.1017/S0956792599003976

10.1023/A:1016105004845

10.1017/S0022112098003188

10.1103/PhysRevA.43.6672

10.1103/PhysRevE.59.1368

10.1103/PhysRevE.62.1706

10.1098/rspa.1999.0471

10.1093/qjmam/44.4.507

Entov V. M., 1997, Viscous flows with time-dependent free boundaries in a non-planar Hele-Shaw cell, Eur. J. Appl. Math., 8, 23, 10.1017/S0956792596002938

10.1023/A:1010313106449

Galin L. A., 1945, Unsteady filtration with a free surface, Dokl. Akad. Nauk SSSR, 47, 246

Goldenfeld N. 1992 Lectures on phase transitions and the renormalization group. Reading MA: Perseus Books.

10.1090/qam/119755

10.1103/PhysRevLett.87.175502

10.1016/S0167-2789(97)00244-3

10.1149/1.2430263

10.1017/S0022112086002902

10.1017/S0956792500000802

10.1017/S0022112001007236

Ivantsov G. P., 1947, Temperature field around spherical, cylindrical and needle-shaped crystals which grow in supercooled melts, Dokl. Akad. Nauk SSSR, 58, 567

10.1103/PhysRevLett.56.889

10.1080/00018738800101379

10.1115/1.3245684

10.1103/PhysRevE.50.4650

10.1103/PhysRevLett.74.82

10.1098/rspa.1994.0141

10.1016/0142-727X(94)90029-9

Morse P. M. & Feshbach H. 1953 Methods of theoretical physics. McGraw-Hill.

10.1112/plms/s2-3.1.104

Muskhelishvili N. I. 1953 Some basic problems in the mathematical theory of elasticity. Groningen: Noordhoff.

Needham T. 1997 Visual complex analysis. Oxford: Clarendon Press.

Newman J. 1991 Electrochemical systems 2nd edn. Englewood Cliffs NJ: Prentice-Hall.

10.1103/PhysRevLett.52.1033

Polubarinova-Kochina P. Ya., 1945, On a problem of the motion of the contour of a petroleum shell, Dokl. Akad. Nauk SSSR, 47, 254

Polubarinova-Kochina P. Ya., 1945, Concerning unsteady motions in the theory of filtration, Prikl. Mat. Mech., 9, 79

10.1017/S0022112086001088

10.1098/rspa.1958.0085

10.1098/rspa.2000.0652

10.1103/PhysRevA.30.2840

10.1103/PhysRevLett.83.5523

10.1103/PhysRevE.63.061102

10.1063/1.866225

10.1098/rsta.1993.0049

Trefethen L. N. 1986 Numerical conformal mapping. Amsterdam: North-Holland.

Whitham G. B. 1974 Linear and nonlinear waves. Wiley.

10.1103/PhysRevLett.47.1400