Probability Distribution Of Height Research Articles

Statistics of branched fracture surfaces.

A statistical analysis of fracture surfaces of the polycrystalline intermetallic compound ${\mathrm{Ni}}_{3}$Al is reported. Although these surfaces contain secondary branches, a roughness exponent \ensuremath{\zeta} can be defined, and is found close to 0.8. The number of branches is shown to have nontrivial fluctuations, which exhibit a power-law increase with an exponent strongly dependent upon the dynamics of crack branching during crack propagation. Moreover, the probability distributions of both heights and averaged heights are shown to slowly decrease, i.e., like power laws, for high enough altitudes. Dynamical effects could be responsible for these ``anomalous'' statistics.

Probability distribution of wave height in Todos Santos Bay, B.C., Mexico

The significant wave height of waves recorded from August 1986 to July 1989, at a station located in Todos Santos Bay, B.C., Mexico, is analysed. The results show a seasonal variation. The maximum value (2.4 m) occurred in winter and the minimum (0.2 m) in summer. The probability distribution of significant wave height is tested with the theoretical distributions of Fisher-Tippett I, Weibull and Rayleigh. The best fit is shown by the Fisher-Tippett I probability density function. This function is also used to estimate the significant wave height of 50 and 100-year return periods, giving 3.41 and 3.76 m, respectively.

Elastic/plastic contact of surfaces considering ellipsoidal asperities of work-hardening multi-phase materials

The importance of the plasticity index for defining the degree of elastic and plastic deformation of surface asperities is described. Some experimental validation of the argument is provided and the method is extended to cover the case of ellipsoidal asperity contacts and the effect of work-hardening for a general asperity height probability distribution. It is also shown how the model may be applied to study the behaviour of multi-phase composites. The arguments are based on Hertzian contacts without tractions but may be used with reasonable confidence for contacts where the coefficient of friction is less than 0.1.

A probability distribution of breaking wave crest height based on a crest-acceleration threshold method

For the designers of offshore structures, the probability of encountering a breaking wave crest at or above a specified level above the mean may be an important question. Such a probability may be stated explicity by assuming that a breaking wave has a downward crest acceleration magnitude exceeding a certain threshold α g , as in Snyder and Kennedy [ J. phys. Oceanogr. 13, 1482–1492 (1983)] and Srokosz [ J. phys. Oceanogr. 16, 382–385 (1986)]. The resulting simple expression contains the fourth moment, m 4 , as important parameter, and this is not easily measured nor included in the oceanographic data usually published because it depends critically upon the high-frequency components of the wave spectrum. By comparing oceanographic data from a buoy and photographs from the same area and time with the theory of Snyder and Kennedy for total whitecap coverage, an empirical relation between m 4 and the significant wave parameters H s and T s is suggested. This enables m 4 to be estimated for each sea-state in an H s −T s diagram, and consequently the number of breaking wave crests above any specified value is easily calculated. The results are very dependent upon the higher sea-states in the scatter diagram and are thus quite-dependent, but the method, being very simple, could be easily applied to any other H s −T s scatter diagrams.

The Elastic—Plastic Contact of Rough Surfaces and its Relevance in the Study of Wear

In a recent paper it was shown that the limit of elastic behaviour of rough surfaces could be defined by a unique relationship between the plasticity index and the nominal pressure. Specific experimental evidence suggested that the best theoretical model was one when the asperity height probability distribution was assumed Gaussian with a truncation of 3 σ. This paper extends this argument by showing that for a given ratio of plastic-elastic area of real contact, similar unique relations exist between the plasticity index and nominal pressure. It is assumed that the maximum non-dimensional elastic deformation is given by the inverse of the square of the plasticity index, and this is supported by experimental results. It is also shown that the model proposed is in error at higher pressures, due to the interaction of the deformations of adjacent asperities.

A NONLINEAR MODEL OF IRREGULAR WAVE RUN-UP HEIGHT A D PERIOD DISTRIBUTIONS ON GENTLE SLOPES

This paper discusses the probability distributions of irregular wave run-up height and period on gentle slopes. Assuming that the long period component appeared on the run-up oscillation corresponds to the incident envelope wave period, a nonlinear model to estimate the probability distributions of run-up heights and periods is proposed. Laboratory experiments on gentle slopes of 1/15,1/30 and 1/40, and field measurements on a natural sandy beach with swash slopes of 1/6 to 1/14 were performed to examine the proposed model. The proposed model is shown to agree with the experiments.

Ocean wave studies in western Cook Strait

Ocean wave records (February 1977 ‐ January 1978) from the Maui A site (39° 33′ S, 173° 27′ E) and methods used for their analysis are described. Spectral history segments typical of pure swell and of locally generated sea are given with descriptions of the associated meteorological situations. The joint probability distribution of significant wave height and average zero‐crossing period is used to characterise the ocean wave climate of the region.

The use of laser ligth in the study of metal surfaces

Optical methods are available for evaluating the surface finish of metals. This paper covers measurements of the specular and diffuse reflection from ground and lapped surfaces using helium-neon laser light. The specular reflection gives information on the probability distribution of roughness height, while the diffuse reflection depends on the roughness slope distribution.

Coherence of human judgment in a limited probabilistic environment

The extent to which human subjects can handle a limited probabilistic task environment is studied. The basic question concerns the existence of an internal representation of probability distributions of heights of men and women, accessible through different response-modes. Forty-eight subjects estimated each probability distribution separately (1) by giving percentiles of the cumulative distribution and (2) through probability estimates on pairs of discrete height intervals. From these two sets of estimates, values were inferred for p(m) i: the probability that a person is a man, m, given the person's height, i. This probability was also (3) directly estimated. Half of the subjects participated in a fair betting game during probability estimation. All subjects were trained in the operational meaning of the probability concept. Direct estimates of p(m) i agreed well with values inferred from individual percentile estimates. Values inferred from the more difficult probability estimates on pairs of intervals, however, showed a strong central tendency effect. Significant correlations in performance among the three response-modes indicated that the latter consistently reflect individual differences in conservatism/radicalism. No effect was observed of participation in the betting game. The results are discussed in relation to the concept of subjective sampling distributions, which is sometimes used to explain accuracy variations in binomial and multinomial inference tasks. It is hypothesized that subjects, through experience and understanding, acquire an internal representation of the task environment. This representation can be put to use in some desired form only if a proper response-device is sufficiently well understood so that it makes the information accessible. The quality of the representation determines whether sets of responses can be given for which normative models from probability theory do or do not hold.

THE CHARACTERISTICS OF WIND-WAVES GENERATED IN THE LABORATORY

Wind-wave characteristics were recorded in the laboratory for the primary purposes of (a) analysis of the probability distribution of wave height and wave period with wind speed, water depth, and fetch length as major parameters, and (b) comparison of the test results with existing theory and empirical formulae. An important aspect of this study was to test the validity of the Tucker and Draper method (Draper, 1966) for the presentation of ocean wave data as applicable to wave-data analysis for simulated wind waves. It was interesting to note that some corrections were necessary when the method proposed by Draper at the 10th Coastal Engineering Conference was used for analyzing waves generated in the laboratory. Approximately a positive 20% correction was necessary for this study in which the wave spectra distribution is of very narrow range, the wave width parametere = V1-(T /T ) varles from 0.25 to 0.50, where Tc and T2 represent crest wave period ana zero-crossing wave period, respectively. However, only a negative 5% correction was necessary when the method was used to analyze sea waves (e = 0 73 to 0 76) measured off the shoreline near Look Laboratory Therefore, it was concluded that the Tucker and Draper Method is quite feasible for engineering purposes in analyzing wind-waves having a spectral width parameter of 0.60 to 0.75 The experimental data were compared with those wave heights predicted by the Darbyshire formulas (Francis, 1959) developed for ocean waves. A significant correction factor was necessary for laboratory waves produced by low-speed wi nds. The "fetch graph" was prepared and compared with those developed theoretically by Hino (1966) and empirically by Ijima and Tang (1966) at the 10th Conference on Coastal Engineering, Tokyo, Japan Comparison was also made with the previous empirical formulae by Bretschneider (1951, 1957), Sverdrup and Munk (1947), and Wilson (1961,1962). The experimental results compared well with the Hino theory for both wave heights and wave periods, and fairly well with Bretschneider's fetch graph for wave heights The difference in the comparison of wave data with other investigators is illustrated in this paper. It is recommended that further study be made with emphasis on (a) theoretical and experimental studies of wind-wave characteristics on pre-existing waves, particularly moving storms, (b) wave-energy spectra involving stochastic characteristics and extreme values of wind waves

Probability Distribution of Wave Force

In many design problems the sea state is specified as part of the design criteria. For offshore structures it is important to know the maximum probable wave and the maximum probable wave force which might be experienced during the life expectancy of the structure, for example the 50 yr or 100 yr wave and period and the 50 yr or 100 yr wave Based on previous analysis of wave and wave force measurements, practically no correlation was found between the measured apparent wave height and apparent wave force. Several authors have proposed statistical distribution of drag and mass coefficients, with recommendations for use in design. The statistical distribution of the calculated drag (or mass) coefficients has no relationship to the statistical distribution of the measured wave drag forces (or inertial forces). Borgman (1964) has considered the statistical distribution of wave forces. Methods are presented for predicting the probability distributions of peak wave drag and inertial forces, and a method is proposed which might be used to predict the most probable maximum wave force once the sea state is specified. It is found that there is a good correlation between the probability distributions of wave heights and the probability distributions of peak drag forces. For example, if the most probable maximum wave is given from a statistical distribution of wave height, then it is possible to predict the most probable maximum drag (or inertial) force, and the most probable maximum force (combined drag and inertial force).

A comparison of step‐, pressure‐, and continuous‐wire‐gage wave recordings in the Golden Gate Channel

Step‐, pressure‐, and continuous‐wire‐typewave gages were installed on a steel pile located in 35 to 40 ft of water approximately 600 ft off the northeastern end of Baker's Beach, San Francisco. Simultaneous measurements with all gages were made on a nearly continuous basis during most of April, 1953. These data have been evaluated to obtain characteristic wave periods and heights, height probability distributions, autocorrelation functions, and power spectra. In addition, direct recordings of wave slopes were made possible by using a three‐wire continuous‐wire gage, and a brief description is given of certain of the characteristics of these data. While the frequency responses of all three instruments were nearly identical, surface waves derived from the subsurface pressure‐gage recordings were shown to underestimate true values by an average factor of about 25 pct. The rather complex oceanographic structure of the channel is emphasized by occasional well‐marked surges having periods of about three minutes with heights up to one foot and by significant changes occurring in the characteristic wave period.