메뉴 건너뛰기




Volumn 4, Issue 2, 2005, Pages 641-663

Construction of projection operators for nonlinear evolutionary dynamics

Author keywords

Coarse graining; Homogenization theory; Multiresolution analysis; Nonlinear evolutionary dynamics; Partial differential equations; Projection operator techniques; Renormalization group

Indexed keywords

FOURIER TRANSFORMS; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; WAVELET TRANSFORMS;

EID: 33745102798     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/040603152     Document Type: Article
Times cited : (2)

References (40)
  • 2
    • 0001898814 scopus 로고
    • The renormalization group and the ε-expansion
    • K. G. Wilson and J. Kogut, The renormalization group and the ε-expansion, Phys. Rep., 12 (1974), pp. 75-199.
    • (1974) Phys. Rep. , vol.12 , pp. 75-199
    • Wilson, K.G.1    Kogut, J.2
  • 3
    • 0024611341 scopus 로고
    • A renormalization group approach to image processing problems
    • B. Gidas, A renormalization group approach to image processing problems, IEEE Trans. Patt. Anal. Mach. Int., 11 (1989), pp. 164-180.
    • (1989) IEEE Trans. Patt. Anal. Mach. Int. , vol.11 , pp. 164-180
    • Gidas, B.1
  • 6
    • 33646342125 scopus 로고
    • Two-loop renormalization group analysis of the Burgers-Kardar-Parisi-Zhang equation
    • E. Frey and U. C. Täuber, Two-loop renormalization group analysis of the Burgers-Kardar-Parisi-Zhang equation, Phys. Rev. E, 50 (1994), pp. 1024-1045.
    • (1994) Phys. Rev. E , vol.50 , pp. 1024-1045
    • Frey, E.1    Täuber, U.C.2
  • 7
    • 0000738770 scopus 로고    scopus 로고
    • Mode-coupling and renormalization group results for the noisy Burgers equation
    • E. Frey, U. C. Täuber, and T. Hwa, Mode-coupling and renormalization group results for the noisy Burgers equation, Phys. Rev. E, 53 (1996), pp. 4424-4438.
    • (1996) Phys. Rev. E , vol.53 , pp. 4424-4438
    • Frey, E.1    Täuber, U.C.2    Hwa, T.3
  • 8
    • 0039992071 scopus 로고    scopus 로고
    • Block spins for partial differential equations
    • N. D. Goldenfeld, A. McKane, and Q. Hou, Block spins for partial differential equations, J. Statist. Phys., 93 (1998), pp. 699-714.
    • (1998) J. Statist. Phys. , vol.93 , pp. 699-714
    • Goldenfeld, N.D.1    McKane, A.2    Hou, Q.3
  • 9
    • 0035275704 scopus 로고    scopus 로고
    • Renormalization group and perfect operators for stochastic differential equations
    • Q. Hou, N. D. Goldenfeld, and A. McKane, Renormalization group and perfect operators for stochastic differential equations, Phys. Rev. E, 63 (2001), 036125.
    • (2001) Phys. Rev. E , vol.63 , pp. 036125
    • Hou, Q.1    Goldenfeld, N.D.2    McKane, A.3
  • 10
    • 0003500871 scopus 로고
    • Lectures on Phase Transitions and the Renormalization Group
    • Perseus Books, Reading, MA
    • N. D. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, Perseus Books, Reading, MA, 1992.
    • (1992)
    • Goldenfeld, N.D.1
  • 11
    • 0037172443 scopus 로고    scopus 로고
    • Renormalization group method applied to kinetic equations: Roles of initial values and time
    • Y. Hatta and T. Kunihiro, Renormalization group method applied to kinetic equations: Roles of initial values and time, Ann. Physics, 298 (2002), pp. 24-57.
    • (2002) Ann. Physics , vol.298 , pp. 24-57
    • Hatta, Y.1    Kunihiro, T.2
  • 12
    • 41349084541 scopus 로고    scopus 로고
    • Real-space renormalization-group approach to field evolution equations
    • A. Degenhard and J. Rodríguez-Laguna, Real-space renormalization-group approach to field evolution equations, Phys. Rev. E, 65 (2001), 036703.
    • (2001) Phys. Rev. E , vol.65 , pp. 036703
    • Degenhard, A.1    Rodríguez-Laguna, J.2
  • 13
    • 0141672055 scopus 로고    scopus 로고
    • Towards the evaluation of the relevant degrees of freedom in nonlinear partial differential equations
    • A. Degenhard and J. Rodríguez-Laguna, Towards the evaluation of the relevant degrees of freedom in nonlinear partial differential equations, J. Statist. Phys., 106 (2002), pp. 1093-1120.
    • (2002) J. Statist. Phys. , vol.106 , pp. 1093-1120
    • Degenhard, A.1    Rodríguez-Laguna, J.2
  • 15
    • 0034622781 scopus 로고    scopus 로고
    • A non-perturbative real-space renormalization group scheme
    • A. Degenhard, A non-perturbative real-space renormalization group scheme, J. Phys. A, 33 (2000), pp. 6173-6185.
    • (2000) J. Phys. A , vol.33 , pp. 6173-6185
    • Degenhard, A.1
  • 17
    • 0024700097 scopus 로고
    • A theory for multiresolution signal decomposition: The wavelet representation
    • S. G. Mallat, A theory for multiresolution signal decomposition: The wavelet representation, IEEE Trans. Patt. Anal. Mach. Int., 11 (1989), pp. 674-693.
    • (1989) IEEE Trans. Patt. Anal. Mach. Int. , vol.11 , pp. 674-693
    • Mallat, S.G.1
  • 18
    • 6444234121 scopus 로고    scopus 로고
    • Multiscale and Multiresolution Methods: Theory and Applications
    • eds., Springer, Berlin
    • T. J. Barth, T. Chan, and R. Haimes, eds., Multiscale and Multiresolution Methods: Theory and Applications, Lect. Notes Comput. Sci. Eng. 20, Springer, Berlin, 2002.
    • (2002) Lect. Notes Comput. Sci. Eng. 20
    • Barth, T.J.1    Chan, T.2    Haimes, R.3
  • 22
    • 84990610636 scopus 로고
    • Fast wavelet transform and numerical algorithms I
    • G. Beylkin, R. Coifman, and V. Rokhlin, Fast wavelet transform and numerical algorithms I, Comm. Pure Appl. Math., 44 (1991), pp. 141-183.
    • (1991) Comm. Pure Appl. Math. , vol.44 , pp. 141-183
    • Beylkin, G.1    Coifman, R.2    Rokhlin, V.3
  • 23
    • 0026995365 scopus 로고
    • On the representation of operators in bases of compactly supported wavelets
    • G. Beylkin, On the representation of operators in bases of compactly supported wavelets, SIAM J. Numer. Anal., 29 (1992), pp. 1716-1740.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1716-1740
    • Beylkin, G.1
  • 25
    • 0040710255 scopus 로고
    • Numerical resolution of nonlinear partial differential equations using the wavelet approach
    • Jones and Bartlett, London
    • J. Liandrat, V. Perrier, and Ph. Tchamitchian, Numerical resolution of nonlinear partial differential equations using the wavelet approach, in Wavelets and Their Applications, Jones and Bartlett, London, 1992, pp. 227-238.
    • (1992) Wavelets and Their Applications , pp. 227-238
    • Liandrat, J.1    Perrier, V.2    Tchamitchian, Ph.3
  • 26
    • 0001542801 scopus 로고
    • A multiresolution strategy for numerical homogenization
    • M. E. Brewster and G. Beylkin, A multiresolution strategy for numerical homogenization, Appl. Comput. Harmon. Anal., 2 (1995), pp. 327-349.
    • (1995) Appl. Comput. Harmon. Anal. , vol.2 , pp. 327-349
    • Brewster, M.E.1    Beylkin, G.2
  • 27
    • 33745089007 scopus 로고    scopus 로고
    • Multiresolution homogenization schemes for differential equations and applications
    • London
    • A. C. Gilbert, Multiresolution homogenization schemes for differential equations and applications, in Topics in Analysis and its Applications, World Scientific, London, 2000, pp. 153-168.
    • (2000) Topics in Analysis and Its Applications, World Scientific , pp. 153-168
    • Gilbert, A.C.1
  • 29
    • 0000007919 scopus 로고    scopus 로고
    • A comparison of multiresolution and classical one-dimensional homogenization schemes
    • A. C. Gilbert, A comparison of multiresolution and classical one-dimensional homogenization schemes, Appl. Comput. Harmon. Anal., 5 (1998), pp. 1-35.
    • (1998) Appl. Comput. Harmon. Anal. , vol.5 , pp. 1-35
    • Gilbert, A.C.1
  • 32
    • 0035443178 scopus 로고    scopus 로고
    • Homogenization and effective properties formulations for propagation in finely structured laminates - A multi-resolution approach
    • B. Z. Steinberg, Homogenization and effective properties formulations for propagation in finely structured laminates - a multi-resolution approach, Wave Motion, 34 (2001), pp. 319-337.
    • (2001) Wave Motion , vol.34 , pp. 319-337
    • Steinberg, B.Z.1
  • 33
    • 0003294834 scopus 로고    scopus 로고
    • A multiresolution strategy for reduction of elliptic PDEs and eigenvalue problems
    • G. Beylkin and N. Coult, A multiresolution strategy for reduction of elliptic PDEs and eigenvalue problems, Appl. Comput. Harmon. Anal., 5 (1998), pp. 129-155.
    • (1998) Appl. Comput. Harmon. Anal. , vol.5 , pp. 129-155
    • Beylkin, G.1    Coult, N.2
  • 34
    • 0346985377 scopus 로고    scopus 로고
    • A multiresolution method for numerical reduction and homogenization of nonlinear ODEs
    • G. Beylkin, M. E. Brewster, and A. C. Gilbert, A multiresolution method for numerical reduction and homogenization of nonlinear ODEs, Appl. Comput. Harmon. Anal., 5 (1998), pp. 450-486.
    • (1998) Appl. Comput. Harmon. Anal. , vol.5 , pp. 450-486
    • Beylkin, G.1    Brewster, M.E.2    Gilbert, A.C.3
  • 37
    • 33745089991 scopus 로고
    • The Numerical Algorithms Group Inc., NAG Fortran Library, Mark 17, Oxford, UK
    • The Numerical Algorithms Group Inc., NAG Fortran Library, Mark 17, Oxford, UK, 1995.
    • (1995)
  • 39
    • 0001592733 scopus 로고
    • Universality classes for deterministic surface growth
    • J. Krug and H. Spohn, Universality classes for deterministic surface growth, Phys. Rev. A, 38 (1988), pp. 4271-4283.
    • (1988) Phys. Rev. A , vol.38 , pp. 4271-4283
    • Krug, J.1    Spohn, H.2
  • 40
    • 0003209153 scopus 로고
    • Wavelets: A renormalization group point of view
    • Jones and Bartlett, London
    • G. Battle, Wavelets: A renormalization group point of view, in Wavelets and Their Applications, Jones and Bartlett, London, 1992, pp. 323-349.
    • (1992) Wavelets and Their Applications , pp. 323-349
    • Battle, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.