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Volumn 44, Issue 5, 2008, Pages 298-320

A seamless approach towards stochastic modeling: Sparse grid collocation and data driven input models

Author keywords

Data driven models; Deterministic simulators; Microstructures; Model reduction; Random heterogeneous media; Random processes; Sparse grids; Stochastic collocation; Stochastic partial differential equations

Indexed keywords

BOUNDARY CONDITIONS; CODES (SYMBOLS); COMPUTER SOFTWARE; MICROSTRUCTURE; PARTIAL DIFFERENTIAL EQUATIONS; UNCERTAINTY ANALYSIS;

EID: 40249116821     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.finel.2007.11.015     Document Type: Article
Times cited : (17)

References (68)
  • 1
    • 40249110842 scopus 로고    scopus 로고
    • Major Aircraft Disasters, information available at: 〈http://dnausers.d-n-a.net/dnetGOJG/Disasters.htm〉.
    • Major Aircraft Disasters, information available at: 〈http://dnausers.d-n-a.net/dnetGOJG/Disasters.htm〉.
  • 2
    • 40249114196 scopus 로고    scopus 로고
    • AIM, Accelerated Insertion of Materials Program, DSO Office, DARPA, information available at: 〈http://www.darpa.mil/dso/thrust/matdev/aim.htm〉.
    • AIM, Accelerated Insertion of Materials Program, DSO Office, DARPA, information available at: 〈http://www.darpa.mil/dso/thrust/matdev/aim.htm〉.
  • 3
    • 40249109300 scopus 로고    scopus 로고
    • Prognosis, Prognosis Program, DSO Office, DARPA, information available at: 〈http://www.arpa.mil/dso/thrust/matdev/prognosis.htm〉.
    • Prognosis, Prognosis Program, DSO Office, DARPA, information available at: 〈http://www.arpa.mil/dso/thrust/matdev/prognosis.htm〉.
  • 4
    • 40249106869 scopus 로고    scopus 로고
    • National Security Assessment of the U.S. Forging Industry, Bureau of Industry and Security, U.S. Department of Commerce 〈https://www.bis.doc.gov/defenseindustrialbaseprograms/osies/〉.
    • National Security Assessment of the U.S. Forging Industry, Bureau of Industry and Security, U.S. Department of Commerce 〈https://www.bis.doc.gov/defenseindustrialbaseprograms/osies/〉.
  • 5
    • 40249116421 scopus 로고    scopus 로고
    • MAI, Metals Affordability Initiative, AFRL/ML, information available at: 〈http://www.wrs.afrl.af.mil/contract/〉.
    • MAI, Metals Affordability Initiative, AFRL/ML, information available at: 〈http://www.wrs.afrl.af.mil/contract/〉.
  • 6
    • 40249102485 scopus 로고    scopus 로고
    • The USAF/Navy Forging Supplier Initiative, information available at: 〈http://www.onr.navy.mil/sci_tech/industrial/mantech/docs/successes/metals/〉.
    • The USAF/Navy Forging Supplier Initiative, information available at: 〈http://www.onr.navy.mil/sci_tech/industrial/mantech/docs/successes/metals/〉.
  • 8
    • 0032496593 scopus 로고    scopus 로고
    • Probabilistic characterization of transport in heterogeneous porous media
    • Ghanem R. Probabilistic characterization of transport in heterogeneous porous media. Comput. Methods Appl. Mech. Eng. 158 (1998) 199-220
    • (1998) Comput. Methods Appl. Mech. Eng. , vol.158 , pp. 199-220
    • Ghanem, R.1
  • 9
    • 0037159819 scopus 로고    scopus 로고
    • Mid-frequency structural dynamics with parameter uncertainty
    • Ghanem R., and Sarkar A. Mid-frequency structural dynamics with parameter uncertainty. Comput. Methods Appl. Mech. Eng. 191 (2002) 5499-5513
    • (2002) Comput. Methods Appl. Mech. Eng. , vol.191 , pp. 5499-5513
    • Ghanem, R.1    Sarkar, A.2
  • 10
    • 0032871636 scopus 로고    scopus 로고
    • Higher order sensitivity of heat conduction problems to random data using the spectral stochastic finite element method
    • Ghanem R. Higher order sensitivity of heat conduction problems to random data using the spectral stochastic finite element method. ASME J. Heat Transfer 121 (1999) 290-299
    • (1999) ASME J. Heat Transfer , vol.121 , pp. 290-299
    • Ghanem, R.1
  • 11
    • 0037184252 scopus 로고    scopus 로고
    • Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos
    • Xiu D., and Karniadakis G.E. Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Comput. Methods Appl. Mech. Eng. 191 (2002) 4927-4948
    • (2002) Comput. Methods Appl. Mech. Eng. , vol.191 , pp. 4927-4948
    • Xiu, D.1    Karniadakis, G.E.2
  • 12
    • 0037408312 scopus 로고    scopus 로고
    • Modeling uncertainty in flow simulations via generalized polynomial chaos
    • Xiu D., and Karniadakis G.E. Modeling uncertainty in flow simulations via generalized polynomial chaos. J. Comput. Phys. 187 (2003) 137-167
    • (2003) J. Comput. Phys. , vol.187 , pp. 137-167
    • Xiu, D.1    Karniadakis, G.E.2
  • 13
    • 0141792397 scopus 로고    scopus 로고
    • A new stochastic approach to transient heat conduction modeling with uncertainty
    • Xiu D., and Karniadakis G.E. A new stochastic approach to transient heat conduction modeling with uncertainty. Int. J. Heat Mass Transfer 46 (2003) 4681-4693
    • (2003) Int. J. Heat Mass Transfer , vol.46 , pp. 4681-4693
    • Xiu, D.1    Karniadakis, G.E.2
  • 14
    • 34447293547 scopus 로고    scopus 로고
    • Sparse grid collocation schemes for stochastic natural convection problems
    • Ganapathysubramanian B., and Zabaras N. Sparse grid collocation schemes for stochastic natural convection problems. J. Comput. Phys. 225 1 (2007) 652-685
    • (2007) J. Comput. Phys. , vol.225 , Issue.1 , pp. 652-685
    • Ganapathysubramanian, B.1    Zabaras, N.2
  • 15
    • 40249102484 scopus 로고    scopus 로고
    • I. Babuska, F. Nobile, R. Tempone, A stochastic collocation method for elliptic partial differential equations with random input data, ICES Report 05-47, 2005.
    • I. Babuska, F. Nobile, R. Tempone, A stochastic collocation method for elliptic partial differential equations with random input data, ICES Report 05-47, 2005.
  • 16
    • 33646577797 scopus 로고    scopus 로고
    • High order collocation methods for the differential equation with random inputs
    • Xiu D., and Hesthaven J.S. High order collocation methods for the differential equation with random inputs. SIAM J. Sci. Comput. 27 (2005) 1118-1139
    • (2005) SIAM J. Sci. Comput. , vol.27 , pp. 1118-1139
    • Xiu, D.1    Hesthaven, J.S.2
  • 19
    • 33646514831 scopus 로고    scopus 로고
    • Maximum likelihood representation of stochastic chaos representations from experimental data
    • Desceliers C., Ghanem R., and Soize C. Maximum likelihood representation of stochastic chaos representations from experimental data. Int. J. Numer. Methods Eng. 66 (2006) 978-1001
    • (2006) Int. J. Numer. Methods Eng. , vol.66 , pp. 978-1001
    • Desceliers, C.1    Ghanem, R.2    Soize, C.3
  • 20
    • 34548420549 scopus 로고    scopus 로고
    • Modelling diffusion in random heterogeneous media: data-driven models, stochastic collocation and the variational multi-scale method
    • Ganapathysubramanian B., and Zabaras N. Modelling diffusion in random heterogeneous media: data-driven models, stochastic collocation and the variational multi-scale method. J. Comput. Phys. 226 (2007) 326-353
    • (2007) J. Comput. Phys. , vol.226 , pp. 326-353
    • Ganapathysubramanian, B.1    Zabaras, N.2
  • 21
    • 40249120616 scopus 로고    scopus 로고
    • B. Ganapathysubramanian, N. Zabaras, A non-linear dimension reduction methodology for generating data-driven stochastic input models, J. Comput. Phys., submitted for publication.
    • B. Ganapathysubramanian, N. Zabaras, A non-linear dimension reduction methodology for generating data-driven stochastic input models, J. Comput. Phys., submitted for publication.
  • 22
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • Roweis S.T., and Saul L.K. Nonlinear dimensionality reduction by locally linear embedding. Science 290 (2000) 2323-2326
    • (2000) Science , vol.290 , pp. 2323-2326
    • Roweis, S.T.1    Saul, L.K.2
  • 23
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimension reduction
    • Tenenbaum J., DeSilva V., and Langford J. A global geometric framework for nonlinear dimension reduction. Science 290 5500 (2000) 2319-2323
    • (2000) Science , vol.290 , Issue.5500 , pp. 2319-2323
    • Tenenbaum, J.1    DeSilva, V.2    Langford, J.3
  • 24
    • 84899009769 scopus 로고    scopus 로고
    • Global versus local methods in nonlinear dimensionality reduction
    • deSilva V., and Tenenbaum J.B. Global versus local methods in nonlinear dimensionality reduction. Adv. Neural Inf. Process. Syst. 15 (2003) 721-728
    • (2003) Adv. Neural Inf. Process. Syst. , vol.15 , pp. 721-728
    • deSilva, V.1    Tenenbaum, J.B.2
  • 25
    • 40249106967 scopus 로고    scopus 로고
    • M. Bernstein, V. deSilva, J.C. Langford, J.B. Tenenbaum, Graph approximations to geodesics on embedded manifolds, December 2000, Preprint may be downloaded at the URL: 〈http://isomap.stanford.edu/BdSLT.pdf〉.
    • M. Bernstein, V. deSilva, J.C. Langford, J.B. Tenenbaum, Graph approximations to geodesics on embedded manifolds, December 2000, Preprint may be downloaded at the URL: 〈http://isomap.stanford.edu/BdSLT.pdf〉.
  • 27
    • 4143048964 scopus 로고    scopus 로고
    • J.A. Costa, A.O. Hero, Entropic graphs for manifold learning, in: Proceedings of the IEEE Asilomar Conference on Signals, Systems, and Computers, Pacific Groove, CA, November 2003.
    • J.A. Costa, A.O. Hero, Entropic graphs for manifold learning, in: Proceedings of the IEEE Asilomar Conference on Signals, Systems, and Computers, Pacific Groove, CA, November 2003.
  • 28
    • 3543131272 scopus 로고    scopus 로고
    • Geodesic entropic graphs for dimension and entropy estimation in manifold learning
    • Costa J.A., and Hero A.O. Geodesic entropic graphs for dimension and entropy estimation in manifold learning. IEEE Trans. Signal Process. 52 (2004) 2210-2221
    • (2004) IEEE Trans. Signal Process. , vol.52 , pp. 2210-2221
    • Costa, J.A.1    Hero, A.O.2
  • 30
    • 40249116419 scopus 로고    scopus 로고
    • J.A. Costa, A.O. Hero, Manifold Learning with Geodesic Minimal Spanning Trees, 2003, arXiv:cs/0307038v1.
    • J.A. Costa, A.O. Hero, Manifold Learning with Geodesic Minimal Spanning Trees, 2003, arXiv:cs/0307038v1.
  • 33
    • 0036702786 scopus 로고    scopus 로고
    • Groundwater flow in heterogeneous composite aquifers
    • Winter C.L., and Tartakovsky D.M. Groundwater flow in heterogeneous composite aquifers. Water Resour. Res. 38 (2002) 23.1
    • (2002) Water Resour. Res. , vol.38
    • Winter, C.L.1    Tartakovsky, D.M.2
  • 34
    • 0036563331 scopus 로고    scopus 로고
    • Numerical solutions of moment equations for flow in heterogeneous composite aquifers
    • Winter C.L., Tartakovsky D.M., and Guadagnini A. Numerical solutions of moment equations for flow in heterogeneous composite aquifers. Water Resour. Res. 38 1 (2002) 13.1
    • (2002) Water Resour. Res. , vol.38 , Issue.1
    • Winter, C.L.1    Tartakovsky, D.M.2    Guadagnini, A.3
  • 35
    • 0037223311 scopus 로고    scopus 로고
    • Moment equations for flow in highly heterogeneous porous media
    • Winter C.L., Tartakovsky D.M., and Guadagnini A. Moment equations for flow in highly heterogeneous porous media. Surv. Geophys. 24 (2003) 81-106
    • (2003) Surv. Geophys. , vol.24 , pp. 81-106
    • Winter, C.L.1    Tartakovsky, D.M.2    Guadagnini, A.3
  • 36
    • 1142296114 scopus 로고    scopus 로고
    • Spectral polynomial chaos solutions of the stochastic advection equation
    • Jardak M., Su C.-H., and Karniadakis G.E. Spectral polynomial chaos solutions of the stochastic advection equation. J. Sci. Comput. 17 (2002) 319-338
    • (2002) J. Sci. Comput. , vol.17 , pp. 319-338
    • Jardak, M.1    Su, C.-H.2    Karniadakis, G.E.3
  • 37
    • 35048857417 scopus 로고    scopus 로고
    • D. Lucor, C.-H. Su, G.E. Karniadakis, Karhunen-Loève representation of periodic second-order autoregressive processes, in: International Conference on Computational Science, 2004, pp. 827-834.
    • D. Lucor, C.-H. Su, G.E. Karniadakis, Karhunen-Loève representation of periodic second-order autoregressive processes, in: International Conference on Computational Science, 2004, pp. 827-834.
  • 38
    • 21444449245 scopus 로고    scopus 로고
    • An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
    • Wan X., and Karniadakis G.E. An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. J. Comput. Phys. 209 (2005) 617-642
    • (2005) J. Comput. Phys. , vol.209 , pp. 617-642
    • Wan, X.1    Karniadakis, G.E.2
  • 39
    • 16244388194 scopus 로고    scopus 로고
    • Stochastic solutions for the two-dimensional advection-diffusion equation
    • Wan X., Xiu D., and Karniadakis G.E. Stochastic solutions for the two-dimensional advection-diffusion equation. SIAM J. Sci. Comput. 26 (2005) 578-590
    • (2005) SIAM J. Sci. Comput. , vol.26 , pp. 578-590
    • Wan, X.1    Xiu, D.2    Karniadakis, G.E.3
  • 40
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D., and Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24 (2002) 619-644
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 619-644
    • Xiu, D.1    Karniadakis, G.E.2
  • 41
    • 8744246329 scopus 로고    scopus 로고
    • Variational multiscale stabilized FEM formulations for transport equations: stochastic advection-diffusion and incompressible stochastic Navier-Stokes equations
    • Velamur Asokan B., and Zabaras N. Variational multiscale stabilized FEM formulations for transport equations: stochastic advection-diffusion and incompressible stochastic Navier-Stokes equations. J. Comput. Phys. 202 (2005) 94-133
    • (2005) J. Comput. Phys. , vol.202 , pp. 94-133
    • Velamur Asokan, B.1    Zabaras, N.2
  • 42
    • 0035964634 scopus 로고    scopus 로고
    • Solution of stochastic partial differential equations using the Galerkin finite element techniques
    • Deb M.K., Babuska I.K., and Oden J.T. Solution of stochastic partial differential equations using the Galerkin finite element techniques. Comput. Methods Appl. Mech. Eng. 190 (2001) 6359-6372
    • (2001) Comput. Methods Appl. Mech. Eng. , vol.190 , pp. 6359-6372
    • Deb, M.K.1    Babuska, I.K.2    Oden, J.T.3
  • 43
    • 13844314882 scopus 로고    scopus 로고
    • Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation
    • Babuska I., Tempone R., and Zouraris G.E. Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation. Comput. Methods Appl. Mech. Eng. 194 (2005) 1251-1294
    • (2005) Comput. Methods Appl. Mech. Eng. , vol.194 , pp. 1251-1294
    • Babuska, I.1    Tempone, R.2    Zouraris, G.E.3
  • 44
    • 13844319204 scopus 로고    scopus 로고
    • Galerkin finite elements approximation of stochastic finite elements
    • Babuska I., Tempone R., and Zouraris G.E. Galerkin finite elements approximation of stochastic finite elements. SIAM J. Numer. Anal. 42 (2004) 800-825
    • (2004) SIAM J. Numer. Anal. , vol.42 , pp. 800-825
    • Babuska, I.1    Tempone, R.2    Zouraris, G.E.3
  • 46
    • 40249099621 scopus 로고    scopus 로고
    • R. Tempone, Numerical complexity analysis of weak approximation of stochastic differential equations, Ph.D. Thesis, 2002.
    • R. Tempone, Numerical complexity analysis of weak approximation of stochastic differential equations, Ph.D. Thesis, 2002.
  • 47
    • 19044387138 scopus 로고    scopus 로고
    • Using stochastic analysis to capture unstable equilibrium in natural convection
    • Velamur Asokan B., and Zabaras N. Using stochastic analysis to capture unstable equilibrium in natural convection. J. Comput. Phys. 208 (2005) 134-153
    • (2005) J. Comput. Phys. , vol.208 , pp. 134-153
    • Velamur Asokan, B.1    Zabaras, N.2
  • 48
    • 0009273790 scopus 로고    scopus 로고
    • The curse of dimension and a universal method for numerical integration
    • Nurnberger G., Schmidt J.W., and Walz G. (Eds), Springer, Berlin
    • Novak E., and Ritter K. The curse of dimension and a universal method for numerical integration. In: Nurnberger G., Schmidt J.W., and Walz G. (Eds). Multivariate Approximation and Splines (1997), Springer, Berlin 177-188
    • (1997) Multivariate Approximation and Splines , pp. 177-188
    • Novak, E.1    Ritter, K.2
  • 49
    • 0242440688 scopus 로고    scopus 로고
    • Numerical integration using sparse grids
    • Gerstner T., and Griebel M. Numerical integration using sparse grids. Numer. Algorithms 18 (1998) 209-232
    • (1998) Numer. Algorithms , vol.18 , pp. 209-232
    • Gerstner, T.1    Griebel, M.2
  • 51
    • 0034381734 scopus 로고    scopus 로고
    • High dimensional polynomial interpolation on sparse grids
    • Barthelmann V., Novak E., and Ritter K. High dimensional polynomial interpolation on sparse grids. Adv. Comput. Math. 12 (2000) 273-288
    • (2000) Adv. Comput. Math. , vol.12 , pp. 273-288
    • Barthelmann, V.1    Novak, E.2    Ritter, K.3
  • 52
    • 40249120615 scopus 로고    scopus 로고
    • A. Klimke, Uncertainty modeling using fuzzy arithmetic and sparse grids, Ph.D. Thesis, Universität Stuttgart, Shaker Verlag, Aachen, 2006.
    • A. Klimke, Uncertainty modeling using fuzzy arithmetic and sparse grids, Ph.D. Thesis, Universität Stuttgart, Shaker Verlag, Aachen, 2006.
  • 54
    • 34447270699 scopus 로고    scopus 로고
    • Efficient collocational approach for parametric uncertainty analysis
    • Xiu D. Efficient collocational approach for parametric uncertainty analysis. Commun. Comput. Phys. 2 (2007) 293-309
    • (2007) Commun. Comput. Phys. , vol.2 , pp. 293-309
    • Xiu, D.1
  • 55
    • 33745213726 scopus 로고    scopus 로고
    • Algorithm 847: spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB
    • Klimke A., and Wohlmuth B. Algorithm 847: spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB. ACM Trans. Math. Software 31 (2005)
    • (2005) ACM Trans. Math. Software , vol.31
    • Klimke, A.1    Wohlmuth, B.2
  • 56
    • 40249093908 scopus 로고    scopus 로고
    • A. Klimke, Sparse grid interpolation toolbox-user's guide, IANS Report 2006/001, University of Stuttgart, 2006.
    • A. Klimke, Sparse grid interpolation toolbox-user's guide, IANS Report 2006/001, University of Stuttgart, 2006.
  • 57
    • 40249109299 scopus 로고    scopus 로고
    • 〈http://mpdc.mae.cornell.edu/Software〉.
    • 〈http://mpdc.mae.cornell.edu/Software〉.
  • 58
    • 0001235357 scopus 로고    scopus 로고
    • Turbulent convection over rough surfaces
    • Shen Y., Tong P., and Xia K.-Q. Turbulent convection over rough surfaces. Phys. Rev. Lett. 76 (1996) 908-911
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 908-911
    • Shen, Y.1    Tong, P.2    Xia, K.-Q.3
  • 59
    • 33746340259 scopus 로고    scopus 로고
    • Stochastic analysis of transport in tubes with rough walls
    • Tartakovsky D.M., and Xiu D. Stochastic analysis of transport in tubes with rough walls. J. Comput. Phys. 217 (2006) 248-259
    • (2006) J. Comput. Phys. , vol.217 , pp. 248-259
    • Tartakovsky, D.M.1    Xiu, D.2
  • 60
    • 0034592313 scopus 로고    scopus 로고
    • Recent developments in Rayleigh-Bénard convection
    • Bodenschatz E., Pesch W., and Ahlers G. Recent developments in Rayleigh-Bénard convection. Annu. Rev. Fluid Mech. 32 (2000) 709-778
    • (2000) Annu. Rev. Fluid Mech. , vol.32 , pp. 709-778
    • Bodenschatz, E.1    Pesch, W.2    Ahlers, G.3
  • 61
    • 0031250142 scopus 로고    scopus 로고
    • Natural convective heat transfer in a fluid saturated variable porosity medium
    • Nithiarasu P., Seetharamu K.N., and Sundararajan T. Natural convective heat transfer in a fluid saturated variable porosity medium. Int. J. Heat Mass Transfer 40 (1997) 3955-3967
    • (1997) Int. J. Heat Mass Transfer , vol.40 , pp. 3955-3967
    • Nithiarasu, P.1    Seetharamu, K.N.2    Sundararajan, T.3
  • 62
    • 0000777333 scopus 로고    scopus 로고
    • Reconstruction of random media using Monte Carlo methods
    • Manwart C., and Hilfer R. Reconstruction of random media using Monte Carlo methods. Phys. Rev. E 59 (1999) 5597-5600
    • (1999) Phys. Rev. E , vol.59 , pp. 5597-5600
    • Manwart, C.1    Hilfer, R.2
  • 63
    • 23844559163 scopus 로고    scopus 로고
    • Modeling melt convection in solidification processes with stabilized finite element techniques
    • Samanta D., and Zabaras N. Modeling melt convection in solidification processes with stabilized finite element techniques. Int. J. Numer. Methods Eng. 64 (2005) 1769-1799
    • (2005) Int. J. Numer. Methods Eng. , vol.64 , pp. 1769-1799
    • Samanta, D.1    Zabaras, N.2
  • 64
    • 0342305461 scopus 로고
    • Elastic properties of a tungsten-silver composite above and below the melting point of silver
    • Umekawa S., Kotfila R., and Sherby O.D. Elastic properties of a tungsten-silver composite above and below the melting point of silver. J. Mech. Phys. Solids 13 (1965) 229-230
    • (1965) J. Mech. Phys. Solids , vol.13 , pp. 229-230
    • Umekawa, S.1    Kotfila, R.2    Sherby, O.D.3
  • 66
    • 0033323222 scopus 로고    scopus 로고
    • Elastic properties of a tungsten-silver composite by reconstruction and computation
    • Roberts A.P., and Garboczi E.J. Elastic properties of a tungsten-silver composite by reconstruction and computation. J. Mech. Phys. Solids 47 (1999) 2029-2055
    • (1999) J. Mech. Phys. Solids , vol.47 , pp. 2029-2055
    • Roberts, A.P.1    Garboczi, E.J.2
  • 67
    • 0035934133 scopus 로고    scopus 로고
    • Gaussian random fields with two level-cuts-model for asymmetric microemulsions with nonzero spontaneous curvature
    • Arleth L., Marćelja S., and Zemb T. Gaussian random fields with two level-cuts-model for asymmetric microemulsions with nonzero spontaneous curvature. J. Chem. Phys. 115 8 (2001) 3923-3936
    • (2001) J. Chem. Phys. , vol.115 , Issue.8 , pp. 3923-3936
    • Arleth, L.1    Marćelja, S.2    Zemb, T.3
  • 68
    • 40249093909 scopus 로고    scopus 로고
    • 〈http://www.mathworks.com/products/matlab/〉.
    • 〈http://www.mathworks.com/products/matlab/〉.


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