DOI: 10.1098/rsta.1981.0214. A non-gaussian model for random surfaces

A non-gaussian model for random surfaces

10.1098/rsta.1981.0214

Crossref journal-article

The Royal Society

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences (175)

Abstract

The central concern of this paper is to develop for rough (two-dimensional, metallic) surfaces a model other than the Gaussian one usually used. An analysis, via the notion of ‘upcrossing characteristics’, of some new data on abraded stainless steel, as well as a new look at some old data, indicates the need for such a model. The model adopted is of a form that gives X 2 -type marginal height distributions for the surface. After the new model has been introduced and motivated, its properties are investigated in some detail. In particular, the properties of the surface and its profiles at local maxima are studied by examining, for example, the height distribution and the surface curvature at such points. Phenomena are observed that are notably, qualitatively, different to what happens in the Gaussian model. Although the model introduced here is motivated by problems in the study of metallic surfaces, we believe it to be useful in other areas. Consequently, those sections of the paper that investigate the properties of the model are written so as to be independent of the original motivation. The paper also reintroduces, in an applied setting, the idea of examining surfaces via their upcrossing characteristics.

Bibliography

A non-gaussian model for random surfaces. (1981). Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 303(1479), 433â462.

Authors 0

None

References 41 Referenced 65

Abramowitz M. & Stegun I. A. 1965 Handbook of mathematicalfunctions. New York: Dover.
Adler R. J. 1977 Biometrika 64 367-373. (10.1093/biomet/64.2.367)
Adler R .J . 1981 The geometry of randomfields. London: Wiley.
Adler R .J . 1982 Bull. int. statist.Inst. 49 (To be published.)
10.1214/aop/1176996176
Archard J. F. Hunt R. T. & Onions R. A. 1975 In Proc. IU T A M Symposium on the Mechanics of Contact between Deformable Bodies (ed. A. D. de Pater & J. J. Kalker) pp. 282-303. Delft University Press. (10.1007/978-94-011-8137-2_20)
{'key': 'p_7', 'first-page': '45', 'article-title': 'Proc. Camb. phil', 'volume': '88', 'author': 'Baddeley A.', 'year': '1980', 'journal-title': 'Soc.'} / Soc. / Proc. Camb. phil by Baddeley A. (1980)
{'key': 'p_8', 'first-page': '1', 'article-title': 'In Proc', 'volume': '2', 'author': 'Belyaev K.', 'year': '1972', 'journal-title': 'Sixth Berkeley Symp. Math. Statist. Prob.'} / Sixth Berkeley Symp. Math. Statist. Prob. / In Proc by Belyaev K. (1972)
Bowyer A. 1980 Ph.D. thesis University of London.
Bowyer A. & Cameron A. 1977 Proc. Fourth Leeds-Lyon Symp. London: Institute of Mechanical Engineers.
Cramer H. & Leadbetter M. R. 1967 Stationary and related stochastic processes. New York: Wiley.
Davenport A. G. 1967 In International Research Seminar on Wind Effects on Buildings and Structures pp. 19-82. Ottawa: University of Toronto Press.
{'key': 'p_13', 'first-page': '617', 'article-title': 'Trans metall', 'volume': '239', 'author': 'De Hoff R. T.', 'year': '1971', 'journal-title': 'Soc. A. I. M. E.'} / Soc. A. I. M. E. / Trans metall by De Hoff R. T. (1971)
{'key': 'p_14', 'first-page': '99', 'article-title': 'In Geometricprobability and biological structures (ed. R. E. Miles & J. Serra)', 'volume': '23', 'author': 'De Hoff R. T.', 'year': '1978', 'journal-title': 'Led. Notes Biomath.'} / Led. Notes Biomath. / In Geometricprobability and biological structures (ed. R. E. Miles & J. Serra) by De Hoff R. T. (1978)
10.1098/rspa.1975.0138
Gradshteyn I. S. & Ryzhik I. M. 1965 Table of integrals series and products. New York: Academic Press.
10.1098/rspa.1966.0242
{'key': 'p_18', 'first-page': '150', 'article-title': 'Aust', 'volume': '12', 'author': 'Hasofer A. M.', 'year': '1970', 'journal-title': 'J. Statist.'} / J. Statist. / Aust by Hasofer A. M. (1970)
{'key': 'p_19', 'first-page': '69', 'article-title': 'a Proc. Inst. civ', 'volume': '51', 'author': 'Hasofer A. M.', 'year': '1972', 'journal-title': 'Engrs'} / Engrs / a Proc. Inst. civ by Hasofer A. M. (1972)
{'key': 'p_20', 'first-page': '599', 'article-title': 'b Proc. Inst. civ', 'volume': '53', 'author': 'Hasofer A. M.', 'year': '1972', 'journal-title': 'Engrs'} / Engrs / b Proc. Inst. civ by Hasofer A. M. (1972)
Hasofer A. M. 1974 In Studies in probability and statistics (ed. E. J. Williams) pp. 153-159. Jerusalem: Academic Press.
Johnson K. L. 1975 In Proc. IU T A M Symposium on the Mechanics of Contact Between Deformable Bodies (ed. A. D. de Pater & J. J. Kalker) pp. 26-40. Delft University Press.
10.1098/rspa.1971.0141
{'key': 'p_24', 'first-page': '1215', 'article-title': 'Ann. math', 'volume': '30', 'author': 'Kac M.', 'year': '1959', 'journal-title': 'Statist.'} / Statist. / Ann. math by Kac M. (1959)
{'key': 'p_25', 'first-page': '195', 'article-title': 'Ark', 'volume': '10', 'author': 'Lindgren G.', 'year': '1972', 'journal-title': 'Mat.'} / Mat. / Ark by Lindgren G. (1972)
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{'key': 'p_28', 'first-page': '398', 'volume': '93', 'author': 'Nayak P. R.', 'year': '1971', 'journal-title': 'Engrs. J. Iubr. Technol.'} / Engrs. J. Iubr. Technol. by Nayak P. R. (1971)
Nayak P. R. 1973 a
Nayak P. R. 1973 ft W ear26 165-174. W ear26 305-333. (10.1016/0043-1648(73)90132-4)
Nosko V. P. 1969 Soviet Math. 10 1481-1484.
O 'Callaghan M. & Cameron M. A. 1976 Wear 36 79-97. (10.1016/0043-1648(76)90145-9)
10.1088/0022-3727/6/3/302
Santalo L. A. 1976 Integral geometry and geometric probability Addison-Wesley Encyclopaedia of mathematics series vol. 1.
Serra J. 1969 Introduction a la morphologie mathe'matique Cahiers du centre de morphologie mathimatique vol. 3. Paris: Ecoles de Mines.
{'key': 'p_36', 'first-page': '373', 'article-title': 'Adv. appl', 'volume': '10', 'author': 'Sharpe K.', 'year': '1978', 'journal-title': 'Prob.'} / Prob. / Adv. appl by Sharpe K. (1978)
Silverman B. 1980 In Asymptotic theory of statistical tests (ed. I. M. Chakravarti). London New York: Academic Press.
{'key': 'p_38', 'first-page': '123', 'article-title': 'Bull. int. statist', 'volume': '47', 'author': 'Switzer P.', 'year': '1977', 'journal-title': 'Inst.'} / Inst. / Bull. int. statist by Switzer P. (1977)
10.1098/rspa.1970.0068
Wilson R. G. & Adler R. J. 1982 Adv. appl. Probab. 14 (in the press). A SYMPOSI UM ON PLANETARY SCIENCE (10.1017/S0001867800020632)
IN CELEBRATION OF THE QUINCENTENARY OF NICOLAUS COPERNICUS 1473 TO 1543

Dates

Type	When
Created	18 years, 8 months ago (Dec. 18, 2006, 6:37 p.m.)
Deposited	4 years, 6 months ago (Feb. 18, 2021, 9:55 p.m.)
Indexed	4 months ago (April 25, 2025, 1:28 a.m.)
Issued	43 years, 8 months ago (Dec. 24, 1981)
Published	43 years, 8 months ago (Dec. 24, 1981)
Published Online	28 years, 7 months ago (Jan. 1, 1997)
Published Print	43 years, 8 months ago (Dec. 24, 1981)

Funders 0

None

BibTeX

@article{1981, volume={303}, ISSN={2054-0272}, url={http://dx.doi.org/10.1098/rsta.1981.0214}, DOI={10.1098/rsta.1981.0214}, number={1479}, journal={Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences}, publisher={The Royal Society}, year={1981}, month=dec, pages={433–462} }

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