메뉴 건너뛰기




Volumn 53, Issue 7-8, 2011, Pages 1394-1409

Optimizing the principal eigenvalue of the Laplacian in a sphere with interior traps

Author keywords

Capacitance; Discrete energy; Matched asymptotic expansions; Mean first passage time; Neumann Green's function; Splitting probability

Indexed keywords

DISCRETE ENERGY; MATCHED ASYMPTOTIC EXPANSION; MEAN FIRST PASSAGE TIME; NEUMANN GREEN'S FUNCTION; SPLITTING PROBABILITY;

EID: 77958045526     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2010.02.025     Document Type: Article
Times cited : (116)

References (36)
  • 1
    • 10344243553 scopus 로고    scopus 로고
    • Escape through a small opening: receptor trafficking in a synaptic membrane
    • Holcman D., Schuss Z. Escape through a small opening: receptor trafficking in a synaptic membrane. J. Stat. Phys. 2004, 117(5-6):975-1014.
    • (2004) J. Stat. Phys. , vol.117 , Issue.5-6 , pp. 975-1014
    • Holcman, D.1    Schuss, Z.2
  • 3
    • 42549164971 scopus 로고    scopus 로고
    • Narrow escape time problem: time needed for a particle to exit a confining domain through a small window
    • Bénichou O., Voituriez R. Narrow escape time problem: time needed for a particle to exit a confining domain through a small window. Phys. Rev. Lett. 2008, 100:168105.
    • (2008) Phys. Rev. Lett. , vol.100 , pp. 168105
    • Bénichou, O.1    Voituriez, R.2
  • 4
    • 36148968483 scopus 로고    scopus 로고
    • The narrow escape problem for diffusion in cellular microdomains
    • Schuss Z., Singer A., Holcman D. The narrow escape problem for diffusion in cellular microdomains. Proc. Natl. Acad. Sci. 2007, 104(41):16098-16103.
    • (2007) Proc. Natl. Acad. Sci. , vol.104 , Issue.41 , pp. 16098-16103
    • Schuss, Z.1    Singer, A.2    Holcman, D.3
  • 5
    • 33644532542 scopus 로고    scopus 로고
    • Narrow escape, Part II: the circular disk
    • Singer A., Schuss Z., Holcman D. Narrow escape, Part II: the circular disk. J. Stat. Phys. 2006, 122(3):465-489.
    • (2006) J. Stat. Phys. , vol.122 , Issue.3 , pp. 465-489
    • Singer, A.1    Schuss, Z.2    Holcman, D.3
  • 6
    • 33644521764 scopus 로고    scopus 로고
    • Narrow escape, Part III: non-smooth domains and Riemann surfaces
    • Singer A., Schuss Z., Holcman D. Narrow escape, Part III: non-smooth domains and Riemann surfaces. J. Stat. Phys. 2006, 122(3):491-509.
    • (2006) J. Stat. Phys. , vol.122 , Issue.3 , pp. 491-509
    • Singer, A.1    Schuss, Z.2    Holcman, D.3
  • 8
    • 42649133151 scopus 로고    scopus 로고
    • Diffusion escape through a cluster of small absorbing windows
    • (15 pp.)
    • Holcman D., Schuss Z. Diffusion escape through a cluster of small absorbing windows. J. Phys. A 2008, 41:155001. (15 pp.).
    • (2008) J. Phys. A , vol.41 , pp. 155001
    • Holcman, D.1    Schuss, Z.2
  • 9
    • 77951907993 scopus 로고    scopus 로고
    • An asymptotic analysis of the mean first passage time for narrow escape problems: Part I: two-dimensional domains, SIAM Multiscale Model. Simul. (2010) 28 pages (in press).
    • S. Pillay, M.J. Ward, A. Peirce, T. Kolokolnikov, An asymptotic analysis of the mean first passage time for narrow escape problems: Part I: two-dimensional domains, SIAM Multiscale Model. Simul. (2010) 28 pages (in press).
    • Pillay, S.1    Ward, M.J.2    Peirce, A.3    Kolokolnikov, T.4
  • 10
    • 77951899892 scopus 로고    scopus 로고
    • An asymptotic analysis of the mean first passage time for narrow escape problems: Part II: the sphere, SIAM Multiscale Model
    • Simul. 32 pages (in press).
    • A. Cheviakov, M.J. Ward, R. Straube, An asymptotic analysis of the mean first passage time for narrow escape problems: Part II: the sphere, SIAM Multiscale Model. Simul. (2010) 32 pages (in press).
    • (2010)
    • Cheviakov, A.1    Ward, M.J.2    Straube, R.3
  • 11
    • 34547369831 scopus 로고    scopus 로고
    • Dwell time of a Brownian molecule in a microdomain with traps and a small hole on the boundary
    • Taflia A., Holcman D. Dwell time of a Brownian molecule in a microdomain with traps and a small hole on the boundary. J. Chem. Phys. 2007, 126(23):234107.
    • (2007) J. Chem. Phys. , vol.126 , Issue.23 , pp. 234107
    • Taflia, A.1    Holcman, D.2
  • 12
    • 0005510987 scopus 로고
    • Asymptotic variational formulae for eigenvalues
    • Swanson C.A. Asymptotic variational formulae for eigenvalues. Canad. Math. Bull. 1963, 6:15-25.
    • (1963) Canad. Math. Bull. , vol.6 , pp. 15-25
    • Swanson, C.A.1
  • 13
    • 84972569644 scopus 로고
    • Singular variation of domains and eigenvalues of the Laplacian
    • Ozawa S. Singular variation of domains and eigenvalues of the Laplacian. Duke Math. J. 1981, 48(4):767-778.
    • (1981) Duke Math. J. , vol.48 , Issue.4 , pp. 767-778
    • Ozawa, S.1
  • 14
    • 0012357461 scopus 로고
    • An asymptotic formula for the eigenvalues of the Laplacian in a three-dimensional domain with a small hole
    • Ozawa S. An asymptotic formula for the eigenvalues of the Laplacian in a three-dimensional domain with a small hole. J. Fac. Sci. Univ. Tokyo 1A 1983, 30(2):243-257.
    • (1983) J. Fac. Sci. Univ. Tokyo 1A , vol.30 , Issue.2 , pp. 243-257
    • Ozawa, S.1
  • 15
    • 84972571455 scopus 로고
    • Asymptotic property of an eigenfunction of the Laplacian under singular variation of domains-the Neumann condition
    • Ozawa S. Asymptotic property of an eigenfunction of the Laplacian under singular variation of domains-the Neumann condition. Osaka J. Math. 1985, 22(4):639-655.
    • (1985) Osaka J. Math. , vol.22 , Issue.4 , pp. 639-655
    • Ozawa, S.1
  • 16
    • 0027608991 scopus 로고
    • Strong localized perturbations of eigenvalue problems
    • Ward M.J., Keller J.B. Strong localized perturbations of eigenvalue problems. SIAM J. Appl. Math. 1993, 53(3):770-798.
    • (1993) SIAM J. Appl. Math. , vol.53 , Issue.3 , pp. 770-798
    • Ward, M.J.1    Keller, J.B.2
  • 17
    • 0027606742 scopus 로고
    • Summing logarithmic expansions for singularly perturbed eigenvalue problems
    • Ward M.J., Henshaw W.D., Keller J.B. Summing logarithmic expansions for singularly perturbed eigenvalue problems. SIAM J. Appl. Math. 1993, 53(3):799-828.
    • (1993) SIAM J. Appl. Math. , vol.53 , Issue.3 , pp. 799-828
    • Ward, M.J.1    Henshaw, W.D.2    Keller, J.B.3
  • 18
    • 0005460971 scopus 로고
    • Approximation of dirichlet eigenvalues on domains with small holes
    • Flucher M. Approximation of dirichlet eigenvalues on domains with small holes. J. Math. Anal. Appl. 1995, 193(1):169-199.
    • (1995) J. Math. Anal. Appl. , vol.193 , Issue.1 , pp. 169-199
    • Flucher, M.1
  • 19
    • 0035527623 scopus 로고    scopus 로고
    • On the placement of an obstacle or a well so as to optimize the fundamental eigenvalue
    • Harrell E.M., Kröger P., Kurata K. On the placement of an obstacle or a well so as to optimize the fundamental eigenvalue. SIAM J. Math. Anal. 2001, 33(1):240-259.
    • (2001) SIAM J. Math. Anal. , vol.33 , Issue.1 , pp. 240-259
    • Harrell, E.M.1    Kröger, P.2    Kurata, K.3
  • 20
    • 23844511916 scopus 로고    scopus 로고
    • Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps
    • Kolokolnikov T., Titcombe M.S., Ward M.J. Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps. European J. Appl. Math. 2005, 16(2):161-200.
    • (2005) European J. Appl. Math. , vol.16 , Issue.2 , pp. 161-200
    • Kolokolnikov, T.1    Titcombe, M.S.2    Ward, M.J.3
  • 21
    • 72049111861 scopus 로고    scopus 로고
    • Diffusion on a sphere with localized traps: mean first passage time, eigenvalue asymptotics, and fekete points
    • Coombs D., Straube R., Ward M.J. Diffusion on a sphere with localized traps: mean first passage time, eigenvalue asymptotics, and fekete points. SIAM J. Appl. Math. 2009, 70(1):302-332.
    • (2009) SIAM J. Appl. Math. , vol.70 , Issue.1 , pp. 302-332
    • Coombs, D.1    Straube, R.2    Ward, M.J.3
  • 22
    • 33847032231 scopus 로고    scopus 로고
    • Random walks and Brownian motion: a method of computation for first-passage times and related quantities in confined geometries
    • Condamin S., Bênichou O., Moreau M. Random walks and Brownian motion: a method of computation for first-passage times and related quantities in confined geometries. Phys. Rev. E 2007, 75:021111.
    • (2007) Phys. Rev. E , vol.75 , pp. 021111
    • Condamin, S.1    Bênichou, O.2    Moreau, M.3
  • 24
    • 0010829627 scopus 로고
    • Ueber Einige Extremalaufgaben der Potential Theorie
    • Szegö G. Ueber Einige Extremalaufgaben der Potential Theorie. Math. Z. 1930, 31:583-593.
    • (1930) Math. Z. , vol.31 , pp. 583-593
    • Szegö, G.1
  • 25
    • 0012057151 scopus 로고    scopus 로고
    • Electrostatic capacitance of two unequal overlapping spheres and the rate of diffusion-controlled absorption
    • Felderhof B.U., Palaniappan D. Electrostatic capacitance of two unequal overlapping spheres and the rate of diffusion-controlled absorption. J. Appl. Phys. 1999, 86(11):6501-6506.
    • (1999) J. Appl. Phys. , vol.86 , Issue.11 , pp. 6501-6506
    • Felderhof, B.U.1    Palaniappan, D.2
  • 27
    • 0040166463 scopus 로고
    • A note on the capacitance of two closely separated spheres
    • Love J.D. A note on the capacitance of two closely separated spheres. J. Inst. Math. Appl. 1979, 24:255-257.
    • (1979) J. Inst. Math. Appl. , vol.24 , pp. 255-257
    • Love, J.D.1
  • 28
    • 0003643982 scopus 로고
    • Springer-Verlag, Berlin, (reprinted from the first edition of 1929)
    • Kellogg O.D. Foundations of Potential Theory 1967, Springer-Verlag, Berlin, (reprinted from the first edition of 1929).
    • (1967) Foundations of Potential Theory
    • Kellogg, O.D.1
  • 29
  • 30
    • 0004032847 scopus 로고
    • Kluwer Academic Publishers, Dordrecht, Boston, R. Horst, P.M. Pardalos (Eds.)
    • Handbook of Global Optimization 1995, Kluwer Academic Publishers, Dordrecht, Boston. R. Horst, P.M. Pardalos (Eds.).
    • (1995) Handbook of Global Optimization
  • 32
    • 1842664459 scopus 로고    scopus 로고
    • The cutting angle method-a tool for constrained global optimization
    • Beliakov G. The cutting angle method-a tool for constrained global optimization. Optim. Methods Softw. 2004, 19(2):137-151.
    • (2004) Optim. Methods Softw. , vol.19 , Issue.2 , pp. 137-151
    • Beliakov, G.1
  • 33
    • 33845307114 scopus 로고    scopus 로고
    • Dynamical systems described by relational elasticities with applications to global optimization
    • Springer, New York, A. Rubinov, V. Jeyakumar (Eds.)
    • Mammadov M.A., Rubinov A., Yearwood J. Dynamical systems described by relational elasticities with applications to global optimization. Continuous Optimization: Current Trends and Modern Applications 2005, 365-385. Springer, New York. A. Rubinov, V. Jeyakumar (Eds.).
    • (2005) Continuous Optimization: Current Trends and Modern Applications , pp. 365-385
    • Mammadov, M.A.1    Rubinov, A.2    Yearwood, J.3
  • 34
    • 79951579357 scopus 로고    scopus 로고
    • GANSO Software Library: University of Ballarat, Ballarat, Victoria, Australia.
    • GANSO Software Library: University of Ballarat, Ballarat, Victoria, Australia, http://www.ballarat.edu.au/ciao.
  • 35
    • 0033746854 scopus 로고    scopus 로고
    • A periodic Green function for calculation of coulombic lattice potentials
    • Marshall S.L. A periodic Green function for calculation of coulombic lattice potentials. J. Phys.: Condens. Matter 2000, 12:4575-4601.
    • (2000) J. Phys.: Condens. Matter , vol.12 , pp. 4575-4601
    • Marshall, S.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.