MONTE CARLO TECHNIQUES

Revised September 2011 by G. Cowan （RHUL）. Monte Carlo techniques are often the only practical way to evaluate difficult integrals or to sample random variables governed by complicated probability density functions. Here we describe an assortment of methods for sampling some commonly occurring probability density functions.

Technique for Estimating the Cone Bearing Smoothing Parameters

Cone penetration testing (CPT) is an extensively utilized and cost effective tool for geotechnical site characterization. CPT consists of pushing at a constant rate an electronic cone into penetrable soils and recording the resistance to the cone tip (qc value). The measured qc values (after correction for the pore water pressure) are utilized to estimate soil type and associated soil properties based predominantly on empirical correlations. The most common cone tips have associated areas of 10 cm2 and 15 cm2. Investigators also utilized significantly larger cone tips (33 cm2 and 40 cm2) so that gravelly soils can be penetrated. Small cone tips (2 cm2 and 5 cm2) are utilized for shallow soil investigations. The cone tip resistance measured at a particular depth is affected by the values above and below the depth of interest which results in a smoothing or blurring of the true bearing values. Extensive work has been carried out in mathematically modelling the smoothing function which results in the blurred cone bearing measurements. This paper outlines a technique which facilitates estimating the dominant parameters of the cone smoothing function from processing real cone bearing data sets. This cone calibration technique is referred to as the so-called CPSPE algorithm. The mathematical details of the CPSPE algorithm are outlined in this paper along with the results from a challenging test bed simulation.

SHAPE OF POLYMER CHAINS ON A TETRAHEDRAL LATTICE

The shape of unperturbed polymer chains was studied using the Monte Carlo technique on a tetrahedral lattice. The asphericity A, the ratios <L-2(2)>/<L-1(2)> and <L-3(2)>/<L-1(2)> were calculated for different Values of polymer chain length n, conformational energy epsilon (epsilon greater than or equal to 0) and temperature T. The asphericity A decreases with the increase of chain length and tends to reach its limiting value rapidly with the decrease of gamma (gamma = epsilon/k(B)T). For large n, A is about 0.525 +/- 0.005, the ratios <L-2(2)>/<L-1(2)> and <L-3(2)>/<L-1(2)> are about 2.7 and 12.0, respectively, and are almost independent of gamma, but for short chains, they depend on gamma.

Noise analysis for sensitivity-based structural damage detection

As vibration-based structural damage detection methods are easily affected by environmental noise, a new statistie-based noise analysis method is proposed together with the Monte Carlo technique to investigate the influence of experimental noise of modal data on sensitivity-based damage detection methods. Different from the com- monly used random perturbation technique, the proposed technique is deduced directly by Moore-Pen＂ose generalized inverse of the sensitivity matrix, which does not only make the analysis process more efficient but also can analyze the influence of noise on both frequencies and mode shapes for three commonly used sensitivity-based damage detection methods in a similar way. A one-story portal frame is adopted to evaluate the efficiency of the proposed noise analysis technique.

Study of photometric phase curve:assuming a cellinoid ellipsoid shape for asteroid(106)Dione

We carried out new photometric observations of asteroid （106） Dione at three apparitions （2004, 2012 and 2015） to understand its basic physical properties. Based on a new brightness model, new photometric observational data and published data of （106） Dione were analyzed to characterize the morphology of Dione＇s photometric phase curve. In this brightness model, a cellinoid ellipsoid shape and three-parameter （H, G1, G2） magnitude phase function system were involved. Such a model can not only solve the phase function system parameters of （106） Dione by considering an asymmetric shape of an asteroid, but also can be applied to more asteroids, especially those without enough photometric data to solve the convex shape. Using a Markov Chain Monte Carlo （MCMC） method, Dione＇s absolute magnitude of H = 7.66＋0.03-0.03 mag, and phase function parameters G1 = 0.682＋0.077-0.077 and G2 = 0.081＋0.042-0.042 were obtained. Simultaneously, Dione＇s simplistic shape, orientation of pole and rotation period were also determined preliminarily.