Snap-Through Buckling of a Viscoelastic von Mises Truss in a Random Temperature Field

1969 ◽  
Vol 36 (2) ◽  
pp. 338-340 ◽  
Author(s):  
Franz Ziegler
Keyword(s):  
Temperature Field ◽  
Probability Distribution ◽  
Probability Density ◽  
Symmetric Function ◽  
Temperature Fluctuations ◽  
Temperature Sensitive ◽  
Von Mises ◽  
Random Temperature Field

The reduction of the expected lifetime of a temperature-sensitive viscoelastic von Mises truss caused by small random temperature fluctuations is calculated, assuming the probability density of the temperature process to be a known (symmetric) function. Results are derived for a normal and a rectangular probability distribution of the temperature fluctuations.

A note on inverse probability

1932 ◽  
Vol 28 (1) ◽  
pp. 55-61 ◽  
Author(s):  
J. B. S. Haldane
Keyword(s):  
Probability Distribution ◽  
Probability Density ◽  
A Priori ◽  
Bayes Theorem ◽  
Statistical Investigation ◽  
Reasonable Assumption ◽  
Inverse Probability ◽  
Von Mises

The problem of statistical investigation is the description of a population, or Kollektiv, of which a sample has been observed. At best we can only state the probability that certain parameters of this population lie within assigned limits, i.e. specify their probability density. It has been shown, e.g. by von Mises(1), that this is only possible if we know the probability distribution of the parameter before the sample is taken. Bayes' theorem is based on the assumption that all values of the parameter in the neighbourhood of that observed are equally probable a priori. It is the purpose of this paper to examine what more reasonable assumption may be made, and how it will affect the estimate based on the observed sample.

Exact Stationary Response Solution for Second Order Nonlinear Systems Under Parametric and External White Noise Excitations: Part II

1988 ◽  
Vol 55 (3) ◽  
pp. 702-705 ◽  
Author(s):  
Y. K. Lin ◽  
Guoqiang Cai
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Probability Distribution ◽  
White Noise ◽  
Probability Density ◽  
Detailed Balance ◽  
Stationary Probability ◽  
Probability Flow ◽  
Parametric And External Excitations ◽  
White Noises

A systematic procedure is developed to obtain the stationary probability density for the response of a nonlinear system under parametric and external excitations of Gaussian white noises. The procedure is devised by separating the circulatory portion of the probability flow from the noncirculatory flow, thus obtaining two sets of equations that must be satisfied by the probability potential. It is shown that these equations are identical to two of the conditions established previously under the assumption of detailed balance; therefore, one remaining condition for detailed balance is superfluous. Three examples are given for illustration, one of which is capable of exhibiting limit cycle and bifurcation behaviors, while another is selected to show that two different systems under two differents sets of excitations may result in the same probability distribution for their responses.

A novel prediction model of traffic accidents based on big data

2019 ◽  
Vol 10 (04) ◽  
pp. 1950022 ◽  
Author(s):  
Minglei Song ◽  
Rongrong Li ◽  
Binghua Wu
Keyword(s):  
Feature Extraction ◽  
Big Data ◽  
Probability Distribution ◽  
Prediction Model ◽  
Probability Density ◽  
Traffic Accidents ◽  
Joint Probability ◽  
Distributed Database ◽  
Joint Probability Distribution ◽  
Joint Probability Density

The occurrence of traffic accidents is regular in probability distribution. Using big data mining method to predict traffic accidents is conducive to taking measures to prevent or reduce traffic accidents in advance. In recent years, prediction methods of traffic accidents used by researchers have some problems, such as low calculation accuracy. Therefore, a prediction model of traffic accidents based on joint probability density feature extraction of big data is proposed in this paper. First, a function of big data joint probability distribution for traffic accidents is established. Second, establishing big data distributed database model of traffic accidents with the statistical analysis method in order to mine the association rules characteristic quantity reflecting the law of traffic accidents, and then extracting the joint probability density feature of big data for traffic accident probability distribution. According to the result of feature extraction, adaptive functional and directivity are predicted, and then the regularity prediction of traffic accidents is realized based on the result of association directional clustering, so as to optimize the design of the prediction model of traffic accidents based on big data. Simulation results show that in predicting traffic accidents, the model in this paper has advantages of relatively high accuracy, relatively good confidence and stable prediction result.

Age Reporting of Very Old Samples

Radiocarbon ◽  
1980 ◽  
Vol 22 (4) ◽  
pp. 1021-1027 ◽  
Author(s):  
Adam Walanus ◽  
Mieczysław F Pazdur
Keyword(s):  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Density Function ◽  
Statistical Interpretation ◽  
Very Old ◽  
Radiocarbon Age ◽  
Fiducial Probability ◽  
Limiting Value

Problems of the statistical interpretation of radiocarbon age measurements of old samples are discussed, based on the notion of fiducial probability distribution. A probability density function of age has been given. A detailed discussion of different facets of the probability distribution of age has led us to the confirmation of the use of 2σ as the best limiting value between the regions of finite and infinite dates. It has been proposed to make use of the principle of constant probability P = 0.68 in the regions of both finite and infinite ages instead of the criterion N + kσ.

Interpretation of the photon: wave–particle duality

2012 ◽  
Vol 90 (9) ◽  
pp. 855-863
Author(s):  
Gilbert R. Hoy ◽  
Jos Odeurs
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Coherence Length ◽  
Probability Distribution Function ◽  
Three Dimensional ◽  
Space Time ◽  
Maximum Probability ◽  
Excited System ◽  
Wave Particle Duality

A simple model is provided to obtain the space–time probability-distribution function of a photon emitted without recoil by an excited system (atom, nucleus, …) in one dimension. A three-dimensional formulation is not needed for our discussion. A quantum mechanical calculation, using the Heitler method, is employed to obtain the solution. The space–time probability-distribution function is not the photon wavefunction. In fact, the area under the space–time probability-distribution function is time dependent. It obtains its final value only as t → ∞. The frequency composition of the photon is found and its time dependence determined to be in accord with the time–energy uncertainty principle. In the wave picture, the coherence length of a photon is found to be equal to the distance from the maximum probability-density position in the photon back toward the source to a position where the probability density has decreased to e–1 of its maximum value. The concept of the coherence length is applied to understand the exponential lifetime curve in the wave picture. This latter measurement is usually explained by saying, in the particle picture, that the photon can appear immediately after formation of the excited state or at a variety of later times according to an exponential probability distribution.

Body temperature fluctuations in free-ranging eastern foxsnakes (Elaphe gloydi) during cold-water swimming

2006 ◽  
Vol 84 (1) ◽  
pp. 9-19 ◽  
Author(s):  
Carrie A MacKinnon ◽  
Anna Lawson ◽  
E D Stevens ◽  
Ronald J Brooks
Keyword(s):  
Body Temperature ◽  
Water Temperature ◽  
Swimming Speed ◽  
Cold Water ◽  
Temperature Fluctuations ◽  
Temperature Sensitive ◽  
Clear Trend ◽  
Thermal Biology ◽  
Rapid Temperature ◽  
Free Ranging

We examined the thermal biology of free-ranging terrestrial eastern foxsnakes (Elaphe gloydi Conant, 1940) that were voluntarily swimming in cold water during spring, in Georgian Bay, Ontario, Canada. Using temperature-sensitive radiotelemetry, we recorded body temperatures of foxsnakes during 12 cold-water swims, and subsequent warming on shore. During these swims, water temperatures were from 11 to 22 °C and distances of 85–1330 m were travelled. Snakes that were in cold water long enough equilibrated with water temperature and did not maintain a body temperature above ambient. The largest observed drop in body temperature was 22.6 °C (over 11 min) and the largest increase was 23 °C (over 66 min). Such large, rapid temperature fluctuations have not previously been reported in detail from snakes in the field. Twice as many telemetry observations as expected occurred between 1200 and 1400, suggesting that snakes chose to swim midday. Additionally, our results suggest that foxsnakes bask to raise their body temperature prior to swimming in cold water. We compared swimming speed and the coefficient of temperature change among foxsnakes and other snake species. Swimming speed was positively correlated with water temperature, similar to other findings. We found no clear trend between mass and the coefficients of cooling and warming; however, snakes cooled in water 2.8–8.6 times faster than they warmed in air.

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