Duration-based model

The emission of NH3 from field application of manure and mineral fertiliser takes place at distinct times of the year and has a relatively short duration compared with point source emissions. Soil type [49] and the application method are crucial for the magnitude of the emission. Very high emissions are related to the broad spread application methods, whereas soil injection leads to very low emissions. For these emissions, the temporal variations can be described by process-based models on the... 

Risk assessment frequently involves estimating safe exposure concentrations for exposure durations that were not tested experimentally. Generally applicable biologically based models have to be applied. Before developing such a model, extensive data are needed to build its form as well as to estimate how well it conforms to the observed data to support confidence in results. 

The likelihood can be used to estimate not only the secular terns (birth cohort and period effects), but also the parameters of the biologically based model. In addition, if the data can be broken further by carcinogen(s) exposure (dose and duration) by age and period, one can also estimate in principle dose-response parameters. 

Sexton, L.T., Mukaibo, H., Katira, R, Hess, H., Sherrih, S.A., Home, L.R, Martin, C.R. An adsorption-based model for pulse duration in resistive-pulse protein sensing. J. Am. Chem. Soc. 132, 6755-6763, 2010. 

Riley, M. Tree-based modelling of segmental duration. n In Talking Machines Theories, Models and Designs, C. B. G Bailly and T. R. Sawallis, Eds. Elsevier Science Publishers, 1992, pp. 265-273. 

The paper is structured as follows in section 2 we examine the characteristics of event duration focussing on what determines this variable. We also describe how the performance of implemented controls can be modelled by a Bayesian Network. Section 3 contains the suggested model for event duration based on a performance measure for implemented controls. In section 4 we describe how the suggested model can contribute to reduced size and complexity of large scale BN models for operational risk and finally in section 5 we provide concluding remarks. 

Tappeiner, U., Tappeiner, G., Aschenwald, J., Tasser, E., Ostendorf, B. (2001). GIS-based modelling of spatial pattern of snow cover duration in an alpine area. Ecological Modelling, 138, 265-275. 

Researchers have used 3D quantitative structural activity relationship (QSAR) of deet and related analogs to construct pharmacophores to better understand the structural basis that leads to repellency by these amide compounds."- Their model was constructed primarily from the protection time data of Suryanarayana and others. Ma and others" showed that one could predict repellent duration based on compound structure and specifically that the amide group and attached substituents played a significant role in the experimentally determined repellent efficacy. Using the same data set, Katritzky and others applied Codessa Pro software to develop a QSAR model for the prediction of complete protection time (CPT) from descriptors related to the structural and electronic properties of deet analogs. This work is the foundation for current projects that involve the examination of repellency and toxicity data for subsets of compounds within the U.S. Department of Agriculture (USDA) archive. 

As a consequence of this observation, the essential dynamics of the molecular process could as well be modelled by probabilities describing mean durations of stay within different conformations of the system. This idea is not new, cf. [10]. Even the phrase essential dynamics has already been coined in [2] it has been chosen for the reformulation of molecular motion in terms of its almost invariant degrees of freedom. But unlike the former approaches, which aim in the same direction, we herein advocate a different line of method we suggest to directly attack the computation of the conformations and their stability time spans, which means some global approach clearly differing from any kind of statistical analysis based on long term trajectories. 

Absorption, distribution, biotransformation, and excretion of chemical compounds have been discussed as separate phenomena. In reality all these processes occur simultaneously, and are integrated processes, i.e., they all affect each other. In order to understand the movements of chemicals in the body, and for the delineation of the duration of action of a chemical m the organism, it is important to be able to quantify these toxicokinetic phases. For this purpose various models are used, of which the most widely utilized are the one-compartment, two-compartment, and various physiologically based pharmacokinetic models. These models resemble models used in ventilation engineering to characterize air exchange. 

Explosively Dispersed Vapor Cloud Explosions (Giesbrecht et al. 1981). The Giesbrecht et al. (1981) model is based on a series of small-scale experiments in which vessels of various sizes (0.226-10001) containing propylene were ruptured. (See Section 4.1.2, especially Figure 4.5.) Flame speed, maximum overpressure, and positive-phase duration observed in explosively dispersed clouds are represented as a function of fuel mass. 

This section covers radiation due to BLEVEs with accompanying fireballs. First, a brief description is given of experimental investigations of BLEVEs and their fireballs. Next, some fireball models, primarily for predicting fireball diameter and combustion duration, are presented. Most of these models evolved from experimental results. Finally, some radiation models, based on experiments and theory, are given. 

I Estimate the thermal impact. The thermal impact of a fireball on humans is a function of both the radiation received and the fireball duration. The impact can be estimated from Figure 9.1. In this case, the fireball duration is estimated to be about 10 seconds, while the estimated radiation is presented in Table 9.1. Based on these data the impact to unprotected humans can be estimated and is shown in Table 9.2. Note that while there is a difference of about 15% in the radiation levels estimated from the two models, the estimated impact on humans is essentially the same. 

The model is based on a fixed duration of tasks as shown in constraint (3.7). This constraints states that the time at which the output state from unit j exits, is the time at which the input state entered the unit at the previous time point plus the duration of the task. The binary variable ensures that the constraints holds whenever the unit is used at the precise time, i.e. p — 1. 

A mathematical formulation based on uneven discretization of the time horizon for the reduction of freshwater utilization and wastewater production in batch processes has been developed. The formulation, which is founded on the exploitation of water reuse and recycle opportunities within one or more processes with a common single contaminant, is applicable to both multipurpose and multiproduct batch facilities. The main advantages of the formulation are its ability to capture the essence of time with relative exactness, adaptability to various performance indices (objective functions) and its structure that renders it solvable within a reasonable CPU time. Capturing the essence of time sets this formulation apart from most published methods in the field of batch process integration. The latter are based on the assumption that scheduling of the entire process is known a priori, thereby specifying the start and/or end times for the operations of interest. This assumption is not necessary in the model presented in this chapter, since water reuse/recycle opportunities can be explored within a broader scheduling framework. In this instance, only duration rather start/end time is necessary. Moreover, the removal of this assumption allows problem analysis to be performed over an unlimited time horizon. The specification of start and end times invariably sets limitations on the time horizon over which water reuse/recycle opportunities can be explored. In the four scenarios explored in... 

The separation between substrates in batch-produced CBD CdS is also a likely important factor for reproducibility. Arias-Carbajal Readigos et al.29 studied thin-film yield in the CBD technique as a function of separation between substrates in batch production. Based on a mathematical model, scientists proposed and experimentally verified that, in the case of CdS thin films, the film thickness reaches an asymptotic maximum with an increase in substrate separation. This behavior is explained on the basis of a critical layer of solution that exists near the substrate, within which the relevant ionic species have a higher probability of interacting with the thin-film layer than of contributing to precipitate formation. The critical layer depends on the solution composition and the temperature of the bath, as well as on the duration of deposition. 

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