Simplified estimation of anisotropic non-homogeneous extinction coefficients in porous solids considering spherical and cylindrical pore networks

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Manuel A. Ramirez-Cabrera ◽  
Patricio J. Valades-Pelayo
Keyword(s):  
Distribution Functions ◽  
Porous Solids ◽  
Diffuse Emission ◽  
Extinction Coefficients ◽  
Cylindrical Pore ◽  
Pore Networks ◽  
Probability Distribution Functions ◽  
Simplified Analysis ◽  
Mean Square Errors ◽  
Tracing Method

Abstract This manuscript presents a simplified analysis for estimating anisotropic, non-homogeneous extinction coefficients in porous solids as a function of the pore morphology and size distribution. The model contains two main simplifications: (1) the pore network consists of hollow interspersed spheres and cylinders, and (2) each surface exchanges radiation (through diffuse emission) only with itself and adjacent surfaces. The model yields photon flight length (PFL) probability distribution functions (PDFs), describing Beerian and non-Beerian anisotropic extinction processes. The method is three orders of magnitude faster than the Monte Carlo Ray Tracing Method (MCRT), yielding Root Mean Square Errors between 0 and 35% for the PFL–PDFs and 0–25% for the anisotropic extinction coefficients. Finally, this work presents a local geometric criterium determining whether the model applies to some given area of the porous solid, so it remains useful even when not applicable to the whole domain.

Extended two-dimensional belief function based on divergence measurement

2020 ◽  
pp. 1-8
Author(s):  
Jianping Fan ◽  
Jing Wang ◽  
Meiqin Wu
Keyword(s):  
Belief Function ◽  
Distribution Functions ◽  
Divergence Measure ◽  
Uncertain Information ◽  
Belief Functions ◽  
Two Dimensional ◽  
Probability Distribution Functions ◽  
Basic Probability ◽  
The Difference ◽  
Supporting Degree

The two-dimensional belief function (TDBF = (mA, mB)) uses a pair of ordered basic probability distribution functions to describe and process uncertain information. Among them, mB includes support degree, non-support degree and reliability unmeasured degree of mA. So it is more abundant and reasonable than the traditional discount coefficient and expresses the evaluation value of experts. However, only considering that the expert’s assessment is single and one-sided, we also need to consider the influence between the belief function itself. The difference in belief function can measure the difference between two belief functions, based on which the supporting degree, non-supporting degree and unmeasured degree of reliability of the evidence are calculated. Based on the divergence measure of belief function, this paper proposes an extended two-dimensional belief function, which can solve some evidence conflict problems and is more objective and better solve a class of problems that TDBF cannot handle. Finally, numerical examples illustrate its effectiveness and rationality.

scholarly journals Development and Evaluation of a Fluctuating Plume Model for Odor Impact Assessment

2021 ◽  
Vol 11 (8) ◽  
pp. 3310
Author(s):  
Marzio Invernizzi ◽  
Federica Capra ◽  
Roberto Sozzi ◽  
Laura Capelli ◽  
Selena Sironi
Keyword(s):  
Experimental Data ◽  
Distribution Functions ◽  
Plume Model ◽  
Probability Distribution Functions ◽  
Weibull Pdf ◽  
Fluctuating Plume ◽  
Concentration Statistics ◽  
Modified Weibull ◽  
Instantaneous Concentration ◽  
Mean Concentration

For environmental odor nuisance, it is extremely important to identify the instantaneous concentration statistics. In this work, a Fluctuating Plume Model for different statistical moments is proposed. It provides data in terms of mean concentrations, variance, and intensity of concentration. The 90th percentile peak-to-mean factor, R90, was tested here by comparing it with the experimental results (Uttenweiler field experiment), considering different Probability Distribution Functions (PDFs): Gamma and the Modified Weibull. Seventy-two percent of the simulated mean concentration values fell within a factor 2 compared to the experimental ones: the model was judged acceptable. Both the modelled results for standard deviation, σC, and concentration intensity, Ic, overestimate the experimental data. This evidence can be due to the non-ideality of the measurement system. The propagation of those errors to the estimation of R90 is complex, but the ranges covered are quite repeatable: the obtained values are 1–3 for the Gamma, 1.5–4 for Modified Weibull PDF, and experimental ones from 1.4 to 3.6.

Probability Distribution Functions for the Random Forced Burgers Equation

1997 ◽  
Vol 78 (10) ◽  
pp. 1904-1907 ◽  
Author(s):  
Weinan E ◽  
Konstantin Khanin ◽  
Alexandre Mazel ◽  
Yakov Sinai
Keyword(s):  
Probability Distribution ◽  
Burgers Equation ◽  
Distribution Functions ◽  
Probability Distribution Functions

Exploring probability distribution functions best-fitting the kinetic energy of coarse particles at above threshold flow conditions

2021 ◽  
Author(s):  
Hamed Farhadi ◽  
Manousos Valyrakis
Keyword(s):  
Probability Distribution ◽  
Kinetic Energy ◽  
Test Section ◽  
Particle Transport ◽  
River Flow ◽  
Distribution Functions ◽  
Transport Processes ◽  
Flow Conditions ◽  
Probability Distribution Functions ◽  
Transport Regime

<p>Applying an instrumented particle [1-3], the probability density functions of kinetic energy of a coarse particle (at different solid densities) mobilised over a range of above threshold flow conditions conditions corresponding to the intermittent transport regime, were explored. The experiments were conducted in the Water Engineering Lab at the University of Glasgow on a tilting recirculating flume with 800 (length) × 90 (width) cm dimension. Twelve different flow conditions corresponding to intermittent transport regime for the range of particle densities examined herein, have been implemented in this research. Ensuring fully developed flow conditions, the start of the test section was located at 3.2 meters upstream of the flume outlet. The bed surface of the flume is flat and made up of well-packed glass beads of 16.2 mm diameter, offering a uniform roughness over which the instrumented particle is transported. MEMS sensors are embedded within the instrumented particle with 3-axis gyroscope and 3-axis accelerometer. At the beginning of each experimental run, instrumented particle is placed at the upstream of the test section, fully exposed to the free stream flow. Its motion is recorded with top and side cameras to enable a deeper understanding of particle transport processes. Using results from sets of instrumented particle transport experiments with varying flow rates and particle densities, the probability distribution functions (PDFs) of the instrumented particles kinetic energy, were generated. The best-fitted PDFs were selected by applying the Kolmogorov-Smirnov test and the results were discussed considering the light of the recent literature of the particle velocity distributions.</p><p>[1] Valyrakis, M.; Alexakis, A. Development of a “smart-pebble” for tracking sediment transport. In Proceedings of the International Conference on Fluvial Hydraulics (River Flow 2016), St. Louis, MO, USA, 12–15 July 2016.</p><p>[2] Al-Obaidi, K., Xu, Y. & Valyrakis, M. 2020, The Design and Calibration of Instrumented Particles for Assessing Water Infrastructure Hazards, Journal of Sensors and Actuator Networks, vol. 9, no. 3, 36.</p><p>[3] Al-Obaidi, K. & Valyrakis, M. 2020, Asensory instrumented particle for environmental monitoring applications: development and calibration, IEEE sensors journal (accepted).</p>

Design for Project Change Management: Part 2 — Attribute Design

2004 ◽  
Author(s):  
D. Xue ◽  
S. Y. Cheing ◽  
P. Gu
Keyword(s):  
Optimal Design ◽  
Probability Distribution ◽  
Taguchi Method ◽  
Systematic Approach ◽  
Distribution Functions ◽  
Probability Distribution Functions ◽  
Construction Tasks ◽  
Design Attribute ◽  
Value Changes ◽  
Design Aspect

This research introduces a new systematic approach to identify the optimal design configuration and attributes to minimize the potential construction project changes. The second part of this paper focuses on the attribute design aspect. In this research, the potential changes of design attribute values are modeled by probability distribution functions. Attribute values of the design whose construction tasks are least sensitive to the changes of these attribute values are identified based upon Taguchi Method. In addition, estimation of the potential project change cost due to the potential design attribute value changes is also discussed. Case studies in pipeline engineering design and construction have been conducted to show the effectiveness of the introduced approach.

scholarly journals Using Percentiles to Communicate Snowfall Uncertainty

2014 ◽  
Vol 29 (5) ◽  
pp. 1259-1265 ◽  
Author(s):  
David R. Novak ◽  
Keith F. Brill ◽  
Wallace A. Hogsett
Keyword(s):  
Probability Distribution ◽  
False Alarm ◽  
Weather Prediction ◽  
Winter Precipitation ◽  
Risk Tolerance ◽  
Distribution Functions ◽  
Precipitation Forecast ◽  
Ensemble Forecasts ◽  
False Alarm Ratio ◽  
Probability Distribution Functions

Abstract An objective technique to determine forecast snowfall ranges consistent with the risk tolerance of users is demonstrated. The forecast snowfall ranges are based on percentiles from probability distribution functions that are assumed to be perfectly calibrated. A key feature of the technique is that the snowfall range varies dynamically, with the resultant ranges varying based on the spread of ensemble forecasts at a given forecast projection, for a particular case, for a particular location. Furthermore, this technique allows users to choose their risk tolerance, quantified in terms of the expected false alarm ratio for forecasts of snowfall range. The technique is applied to the 4–7 March 2013 snowstorm at two different locations (Chicago, Illinois, and Washington, D.C.) to illustrate its use in different locations with different forecast uncertainties. The snowfall range derived from the Weather Prediction Center Probabilistic Winter Precipitation Forecast suite is found to be statistically reliable for the day 1 forecast during the 2013/14 season, providing confidence in the practical applicability of the technique.

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