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Volumn 68, Issue 3, 2007, Pages 844-868

Partially reflected diffusion

Author keywords

Markovian jump process; Reactive boundary condition; Stochastic differential equations; Wiener Hopf boundary layer equation

Indexed keywords

BIOLOGICAL APPLICATIONS; BOUNDARY LAYER ANALYSIS; BOUNDARY LAYER EQUATIONS; BOUNDARY REFLECTIONS; CONVERGENCE (MATHEMATICS); DIFFUSING PARTICLES; DIFFUSION EQUATIONS; DIFFUSION MATRICES; EULER SCHEMES; FOKKER PLANCK EQUATION (FPE); HALF SPACES; JUMP PROCESSES; MARKOVIAN; MASTER EQUATIONS; NON UNIFORM; NUMERICAL SCHEMES; OBLIQUE DIRECTION; PROBABILITY DENSITIES; REACTION CONSTANT; REACTIVE BOUNDARY; REFLECTED DIFFUSION; REFLECTION PROBABILITY; ROBIN BOUNDARY CONDITIONS;

EID: 47149106223     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/060663258     Document Type: Article
Times cited : (121)

References (39)
  • 2
    • 0025299421 scopus 로고
    • Diffusion-controlled ligand binding to spheres partially covered by receptors: An effective medium treatment
    • R. ZWANZIG, Diffusion-controlled ligand binding to spheres partially covered by receptors: An effective medium treatment, Proc. Natl. Acad. Sci. USA, 87 (1990), pp. 5856-5857.
    • (1990) Proc. Natl. Acad. Sci. USA , vol.87 , pp. 5856-5857
    • ZWANZIG, R.1
  • 3
    • 0037381791 scopus 로고    scopus 로고
    • Finite element simulations of acetylcholine diffusion in neuromuscular junctions
    • K. TAI, S. D. BOND, H. R. MACMILLAN, N. A. BAKER, M. J. HOLST, AND J. A. MCCAMMON, Finite element simulations of acetylcholine diffusion in neuromuscular junctions, Biophys. J., 84 (2003), pp. 2234-2241.
    • (2003) Biophys. J , vol.84 , pp. 2234-2241
    • TAI, K.1    BOND, S.D.2    MACMILLAN, H.R.3    BAKER, N.A.4    HOLST, M.J.5    MCCAMMON, J.A.6
  • 4
    • 0344551102 scopus 로고    scopus 로고
    • Stochastic model of autocrine and paracrine signals in cell culture assays
    • L. BATSILAS, A. M. BEREZHKOVSKII, AND S. Y. SHVARTSMAN, Stochastic model of autocrine and paracrine signals in cell culture assays, Biophys. J., 85 (2003), pp. 3659-3665.
    • (2003) Biophys. J , vol.85 , pp. 3659-3665
    • BATSILAS, L.1    BEREZHKOVSKII, A.M.2    SHVARTSMAN, S.Y.3
  • 6
    • 34547554487 scopus 로고    scopus 로고
    • Reactions on cell membranes: Comparison of continuum theory and Brownian dynamics simulations
    • M. I. MONINE AND J. M. HAUGH, Reactions on cell membranes: Comparison of continuum theory and Brownian dynamics simulations, J. Chem. Phys., 123 (2005), 074908.
    • (2005) J. Chem. Phys , vol.123 , pp. 074908
    • MONINE, M.I.1    HAUGH, J.M.2
  • 7
    • 1942519782 scopus 로고    scopus 로고
    • Finite element solution of the steady-state Smoluchowski equation for rate constant calculations
    • Y. SONG, Y. ZHANG, T. SHEN, C. L. BAJAJ, J. A. MCCAMMON, AND N. A. BAKER, Finite element solution of the steady-state Smoluchowski equation for rate constant calculations, Biophys. J., 86 (2004), pp. 2017-2029.
    • (2004) Biophys. J , vol.86 , pp. 2017-2029
    • SONG, Y.1    ZHANG, Y.2    SHEN, T.3    BAJAJ, C.L.4    MCCAMMON, J.A.5    BAKER, N.A.6
  • 8
    • 34147128541 scopus 로고    scopus 로고
    • Reactive boundary conditions for stochastic simulations of reaction-diffusion processes
    • R. ERBAN AND J. CHAPMAN, Reactive boundary conditions for stochastic simulations of reaction-diffusion processes, Phys. Biol., 4 (2007), pp. 16-28.
    • (2007) Phys. Biol , vol.4 , pp. 16-28
    • ERBAN, R.1    CHAPMAN, J.2
  • 9
    • 33748520215 scopus 로고    scopus 로고
    • Stochastic simulation of chemical reactions with spatial resolution and single molecule detail
    • S. ANDREWS AND D. BRAY, Stochastic simulation of chemical reactions with spatial resolution and single molecule detail, Phys. Biol., 1 (2004) pp. 137-151.
    • (2004) Phys. Biol , vol.1 , pp. 137-151
    • ANDREWS, S.1    BRAY, D.2
  • 10
    • 84966207705 scopus 로고
    • Diffusion processes in one dimension
    • W. FELLER, Diffusion processes in one dimension, Trans. Amer. Math. Soc., 77 (1954), pp. 1-31.
    • (1954) Trans. Amer. Math. Soc , vol.77 , pp. 1-31
    • FELLER, W.1
  • 11
    • 0001379748 scopus 로고
    • Stochastic equations for diffusion processes in a bounded region
    • A. V. SKOROKHOD, Stochastic equations for diffusion processes in a bounded region, Theory Probab. Appl., 6 (1961), pp. 264-274.
    • (1961) Theory Probab. Appl , vol.6 , pp. 264-274
    • SKOROKHOD, A.V.1
  • 12
    • 21344441885 scopus 로고
    • Discretization error in simulation of one-dimensional reflecting Brownian motion
    • S. ASMUSSEN, P. GLYNN, AND J. PITMAN, Discretization error in simulation of one-dimensional reflecting Brownian motion, Ann. Appl. Probab., 5 (1995), pp. 875-896.
    • (1995) Ann. Appl. Probab , vol.5 , pp. 875-896
    • ASMUSSEN, S.1    GLYNN, P.2    PITMAN, J.3
  • 13
    • 0000078650 scopus 로고
    • Euler scheme for reflected stochastic differential equations
    • D. LÉPINGLE, Euler scheme for reflected stochastic differential equations, Math. Comput. Simulation, 38 (1995), pp. 119-126.
    • (1995) Math. Comput. Simulation , vol.38 , pp. 119-126
    • LÉPINGLE, D.1
  • 14
    • 0031997542 scopus 로고    scopus 로고
    • Numerical approximation for functionals of reflecting diffusion processes
    • C. COSTANTINI, B. PACCHIAROTTI, AND F. SARTORETTO, Numerical approximation for functionals of reflecting diffusion processes, SIAM J. Appl. Math., 58 (1998), pp. 73-102.
    • (1998) SIAM J. Appl. Math , vol.58 , pp. 73-102
    • COSTANTINI, C.1    PACCHIAROTTI, B.2    SARTORETTO, F.3
  • 15
    • 0345850145 scopus 로고    scopus 로고
    • Path integral approach to the Schrödinger current
    • A. MARCHEWKA AND Z. SCHUSS, Path integral approach to the Schrödinger current, Phys. Rev. A, 61 (2000), 052107.
    • (2000) Phys. Rev. A , vol.61 , pp. 052107
    • MARCHEWKA, A.1    SCHUSS, Z.2
  • 16
    • 41349105786 scopus 로고    scopus 로고
    • Brownian simulations and unidirectional flux in diffusion
    • A. SINGER AND Z. SCHUSS, Brownian simulations and unidirectional flux in diffusion, Phys. Rev. E, 71 (2005), 026115.
    • (2005) Phys. Rev. E , vol.71 , pp. 026115
    • SINGER, A.1    SCHUSS, Z.2
  • 17
    • 0022360954 scopus 로고
    • An asymptotic theory of large deviations for Markov jump processes
    • C. KNESSL, B. J. MATKOWSKY, Z. SCHUSS, AND C. TIER, An asymptotic theory of large deviations for Markov jump processes, SIAM J. Appl. Math., 45 (1985), pp. 1006-1028.
    • (1985) SIAM J. Appl. Math , vol.45 , pp. 1006-1028
    • KNESSL, C.1    MATKOWSKY, B.J.2    SCHUSS, Z.3    TIER, C.4
  • 18
    • 0040915330 scopus 로고
    • A singular perturbation approach to first passage times for Markov jump processes
    • C. KNESSL, B. J. MATKOWSKY, Z. SCHUSS, AND C. TIER, A singular perturbation approach to first passage times for Markov jump processes, J. Stat. Phys., 42 (1986), pp. 169-184.
    • (1986) J. Stat. Phys , vol.42 , pp. 169-184
    • KNESSL, C.1    MATKOWSKY, B.J.2    SCHUSS, Z.3    TIER, C.4
  • 19
    • 34250124127 scopus 로고
    • Boundary behavior of diffusion approximations to Markov jump processes
    • C. KNESSL, B. J. MATKOWSKY, Z. SCHUSS, AND C. TIER, Boundary behavior of diffusion approximations to Markov jump processes, J. Stat. Phys., 45 (1986), pp. 245-266.
    • (1986) J. Stat. Phys , vol.45 , pp. 245-266
    • KNESSL, C.1    MATKOWSKY, B.J.2    SCHUSS, Z.3    TIER, C.4
  • 20
    • 84996131097 scopus 로고    scopus 로고
    • Euler schemes and half-space approximation for the simulation of diffusion in a domain
    • E. GOBET, Euler schemes and half-space approximation for the simulation of diffusion in a domain, ESAIM Probab. Stat., 5 (2001), pp. 261-297.
    • (2001) ESAIM Probab. Stat , vol.5 , pp. 261-297
    • GOBET, E.1
  • 21
    • 10244256462 scopus 로고    scopus 로고
    • A symmetrized Euler scheme for an efficient approximation of reflected diffusions
    • M. BOSSY, E. GOBET, AND D. TALAY, A symmetrized Euler scheme for an efficient approximation of reflected diffusions, J. Appl. Probab., 41 (2004), pp. 877-889.
    • (2004) J. Appl. Probab , vol.41 , pp. 877-889
    • BOSSY, M.1    GOBET, E.2    TALAY, D.3
  • 22
    • 0141902430 scopus 로고
    • Diffusion- controlled reaction rates
    • F. C. COLLINS AND G. E. KIMBALL, Diffusion- controlled reaction rates, J. Colloid Sci., 4 (1949), pp. 425-437.
    • (1949) J. Colloid Sci , vol.4 , pp. 425-437
    • COLLINS, F.C.1    KIMBALL, G.E.2
  • 23
    • 36849124850 scopus 로고
    • Random walk with semiadsorbing barrier
    • F. C. GOODRICH, Random walk with semiadsorbing barrier, J. Chem. Phys., 22 (1954), pp. 588-594.
    • (1954) J. Chem. Phys , vol.22 , pp. 588-594
    • GOODRICH, F.C.1
  • 24
    • 0001971785 scopus 로고
    • Grid free simulation of diffusion using random walk methods
    • A. F. GHONIEM AND F. S. SHERMAN, Grid free simulation of diffusion using random walk methods, J. Comput. Phys., 61 (1985), pp. 1-37.
    • (1985) J. Comput. Phys , vol.61 , pp. 1-37
    • GHONIEM, A.F.1    SHERMAN, F.S.2
  • 25
    • 36549093963 scopus 로고
    • Optimization of Brownian dynamics methods for diffusion-influenced rate constant calculations
    • S. H. NORTHRUP, M. S. CURVIN, S. A. ALLISON, AND J. A. MCCAMMON, Optimization of Brownian dynamics methods for diffusion-influenced rate constant calculations, J. Chem. Phys., 84 (1986), pp. 2196-2203.
    • (1986) J. Chem. Phys , vol.84 , pp. 2196-2203
    • NORTHRUP, S.H.1    CURVIN, M.S.2    ALLISON, S.A.3    MCCAMMON, J.A.4
  • 26
    • 42749108428 scopus 로고    scopus 로고
    • Stochastic boundary conditions to the convection-diffusion equation including chemical reactions at solid surfaces
    • P. SZYMCZAK AND A. J. C. LADD, Stochastic boundary conditions to the convection-diffusion equation including chemical reactions at solid surfaces, Phys. Rev. E, 69 (2004), 036704.
    • (2004) Phys. Rev. E , vol.69 , pp. 036704
    • SZYMCZAK, P.1    LADD, A.J.C.2
  • 27
    • 0342913644 scopus 로고
    • On the simulation of diffusion processes close to boundaries
    • N. J. B. GREEN, On the simulation of diffusion processes close to boundaries, Molec. Phys., 65 (1988), pp. 1399-1408.
    • (1988) Molec. Phys , vol.65 , pp. 1399-1408
    • GREEN, N.J.B.1
  • 28
    • 0242579352 scopus 로고    scopus 로고
    • Boundary conditions for stochastic solutions of the convection-diffusion equation
    • P. SZYMCZAK AND A. J. C. LADD, Boundary conditions for stochastic solutions of the convection-diffusion equation, Phys. Rev. E, 68 (2003), 036704.
    • (2003) Phys. Rev. E , vol.68 , pp. 036704
    • SZYMCZAK, P.1    LADD, A.J.C.2
  • 29
    • 4243465324 scopus 로고
    • Numerical solutions of first-exit-time problems
    • M. BECCARIA, G. CURCI, AND A. VICERE, Numerical solutions of first-exit-time problems, Phys. Rev. E, 48 (1993), pp. 1539-1546.
    • (1993) Phys. Rev. E , vol.48 , pp. 1539-1546
    • BECCARIA, M.1    CURCI, G.2    VICERE, A.3
  • 31
    • 0043282192 scopus 로고    scopus 로고
    • Absorbing boundaries and optimal stopping in a stochastic differential equation
    • R. MANNELLA, Absorbing boundaries and optimal stopping in a stochastic differential equation, Phys. Lett. A, 254 (1999), pp. 257-262.
    • (1999) Phys. Lett. A , vol.254 , pp. 257-262
    • MANNELLA, R.1
  • 32
    • 0036870950 scopus 로고    scopus 로고
    • Integration of stochastic differential equations on a computer
    • R. MANNELLA, Integration of stochastic differential equations on a computer, Internat. J. Modern Phys. C, 13 (2002), pp. 1177-1194.
    • (2002) Internat. J. Modern Phys. C , vol.13 , pp. 1177-1194
    • MANNELLA, R.1
  • 33
    • 0346435516 scopus 로고
    • On the simulation of the Smoluchowski boundary condition and the interpolation of Brownian paths
    • P. CLIFFORD AND N. J. B. GREEN, On the simulation of the Smoluchowski boundary condition and the interpolation of Brownian paths, Molec. Phys., 57 (1986), pp. 123-128.
    • (1986) Molec. Phys , vol.57 , pp. 123-128
    • CLIFFORD, P.1    GREEN, N.J.B.2
  • 34
    • 37649026611 scopus 로고    scopus 로고
    • Efficient Brownian dynamics simulation of particles near walls. I. Reflecting and absorbing walls
    • E. A. J. F. PETERS AND TH. M. A. O. M. BARENBRUG, Efficient Brownian dynamics simulation of particles near walls. I. Reflecting and absorbing walls, Phys. Rev. E, 66 (2002), 056701.
    • (2002) Phys. Rev. E , vol.66 , pp. 056701
    • PETERS, E.A.J.F.1    BARENBRUG, T.M.A.O.M.2
  • 36
    • 14544283338 scopus 로고
    • Note on a problem in the linear conduction of heat
    • G. H. BRYAN, Note on a problem in the linear conduction of heat, Proc. Camb. Phil. Soc., 7 (1891), pp. 246-248.
    • (1891) Proc. Camb. Phil. Soc , vol.7 , pp. 246-248
    • BRYAN, G.H.1
  • 38
    • 36549098160 scopus 로고
    • Diffusion with back reaction
    • N. AGMON, Diffusion with back reaction, J. Chem. Phys., 81 (1984), pp. 2811-2817.
    • (1984) J. Chem. Phys , vol.81 , pp. 2811-2817
    • AGMON, N.1
  • 39
    • 0001138912 scopus 로고
    • Drei Vorträge über Diffusion, Brownsche Molekular-bewegung und Koagulation von Kolloidteilchen
    • M. R. VON SMOLAN SMOLUCHOWSKI, Drei Vorträge über Diffusion, Brownsche Molekular-bewegung und Koagulation von Kolloidteilchen, Phys. Zeits., 17 (1916), p. 557-585.
    • (1916) Phys. Zeits , vol.17 , pp. 557-585
    • VON SMOLAN SMOLUCHOWSKI, M.R.1


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