Search results for "Mathematical model"
showing 10 items of 346 documents
Generalised bisection method for optimum ultrasonic ray tracing and focusing in multi-layered structures
2021
Ultrasonic testing has been used for many decades, proving itself very efficient for detecting defects in many industrial sectors. The desire to apply ultrasonic testing to geometrically complex structures, and to anisotropic, inhomogeneous materials, together with the advent of more powerful electronics and software, is constantly pushing the applicability of ultrasonic waves to their limits. General ray tracing models, suitable for calculating the proper incident angle of single element probes and the proper time delay of phased array, are currently required. They can support the development of new imaging techniques, as Full Matrix Capture and Total Focusing Method, and the execution of …
Modelling of thermal field and point defect dynamics during silicon single crystal growth using CZ technique
2018
Abstract Silicon single crystal growth by the Czochralski (CZ) technique is studied numerically using non-stationary mathematical models which allow to predict the evolution of the CZ system in time, including Dash neck, cone and cylindrical growth stages. The focus is on the point defect dynamics, also considering the effect of the thermal stresses. During the cylindrical stage, the crystal pull rate is temporarily reduced as in experiments by Abe et al. The crystal radius and heater power change is explicitly considered in the calculations for crystal diameters of 50, 100 and 200 mm and the agreement with experiments is discussed.
Pressure‐induced widths and shifts for the ν3 band of methane
1994
International audience; Widths and shifts of methane lines perturbed by nitrogen are calculated using a complex-valued implementation of Robert-Bonamy (RB) theory. The static intermolecular potential is described as a sum of electrostatic forces and Lennard-Jones (6-12) atom-atom terms, using literature values for all physical parameters. Vibrational dependence of the isotropic potential is obtained from the polarizability of methane assuming a dispersion interaction. The repulsive part of the Lennard-Jones accounts for the greatest part of widths, while dispersion interactions are largely responsible for shifts. Although the average error between calculated and observed linewidths (up to J…
Mapping land surface emissivity from NDVI: Application to European, African, and South American areas
1996
Thermal infrared emissivity is an important parameter both for surface characterization and for atmospheric correction methods. Mapping the emissivity from satellite data is therefore a very important question to solve. The main problem is the coupling of the temperature and emissivity effects in the thermal radiances. Several methods have been developed to obtain surface emissivity from satellite data. In this way we propose a theoretical model that relates the emissivity to the NDVI (normalized difference vegetation index) of a given surface and explains the experimental behavior observed by van de Griend and Owe. We can use it to obtain the emissivity in any thermal channel, but in this …
Predicting plot soil loss by empirical and process-oriented approaches. A review
2018
Soil erosion directly affects the quality of the soil, its agricultural productivity and its biological diversity. Many mathematical models have been developed to estimate plot soil erosion at different temporal scales. At present, empirical soil loss equations and process-oriented models are considered as constituting a complementary suite of models to be chosen to meet the specific user need. In this paper, the Universal Soil Loss Equation and its revised versions are first reviewed. Selected methodologies developed to estimate the factors of the model with the aim to improve the soil loss estimate are described. Then the Water Erosion Prediction Project which represents a process-oriente…
Biotrickling filter modeling for styrene abatement. Part 1: Model development, calibration and validation on an industrial scale
2017
Abstract A three-phase dynamic mathematical model based on mass balances describing the main processes in biotrickling filtration: convection, mass transfer, diffusion, and biodegradation was calibrated and validated for the simulation of an industrial styrene-degrading biotrickling filter. The model considered the key features of the industrial operation of biotrickling filters: variable conditions of loading and intermittent irrigation. These features were included in the model switching from the mathematical description of periods with and without irrigation. Model equations were based on the mass balances describing the main processes in biotrickling filtration: convection, mass transfe…
Decision support systems (DSS) for wastewater treatment plants - A review of the state of the art.
2019
The use of decision support systems (DSS) allows integrating all the issues related with sustainable development in view of providing a useful support to solve multi-scenario problems. In this work an extensive review on the DSSs applied to wastewater treatment plants (WWTPs) is presented. The main aim of the work is to provide an updated compendium on DSSs in view of supporting researchers and engineers on the selection of the most suitable method to address their management/operation/design problems. Results showed that DSSs were mostly used as a comprehensive tool that is capable of integrating several data and a multi-criteria perspective in order to provide more reliable results. Only …
A plant-wide modelling comparison between membrane bioreactors and conventional activated sludge
2020
Abstract A comprehensive plant-wide mathematical modelling comparison between conventional activated sludge (CAS) and Membrane bioreactor (MBR) systems is presented. The main aim of this study is to highlight the key features of CAS and MBR in order to provide a guide for an effective plant operation. A scenario analysis was performed to investigate the influence on direct and indirect greenhouse gas (GHG) emissions and operating costs of (i) the composition of inflow wastewater (scenario 1), (ii) operating conditions (scenario 2) and (iii) oxygen transfer efficiency (scenario 3). Scenarios show higher indirect GHG emissions for MBR than CAS, which result is related to the higher energy con…
Dynamic Mathematical Modelling of the Removal of Hydrophilic VOCs by Biotrickling Filters
2015
A mathematical model for the simulation of the removal of hydrophilic compounds using biotrickling filtration was developed. The model takes into account that biotrickling filters operate by using an intermittent spraying pattern. During spraying periods, a mobile liquid phase was considered, while during non-spraying periods, a stagnant liquid phase was considered. The model was calibrated and validated with data from laboratory- and industrial-scale biotrickling filters. The laboratory experiments exhibited peaks of pollutants in the outlet of the biotrickling filter during spraying periods, while during non-spraying periods, near complete removal of the pollutant was achieved. The gaseou…
Non-unique population dynamics: basic patterns
2000
We review the basic patterns of complex non-uniqueness in simple discrete-time population dynamics models. We begin by studying a population dynamics model of a single species with a two-stage, two-habitat life cycle. We then explore in greater detail two ecological models describing host‐macroparasite and host‐parasitoid interspecific interactions. In general, several types of attractors, e.g. point equilibria vs. chaotic, periodic vs. quasiperiodic and quasiperiodic vs. chaotic attractors, may coexist in the same mapping. This non-uniqueness also indicates that the bifurcation diagrams, or the routes to chaos, depend on initial conditions and are therefore non-unique. The basins of attrac…