in Wiley Online Library (wileyonlinelibrary.com).Bacteria being disinfected in fluid media are discrete entities and mesoscopic in size; moreover, they are incessantly as well as irregularly in motion and in collision among themselves or with the surrounding solid surfaces. As such, it is highly likely that some of the attributes of the bacterial population, for example, their number concentration, will fluctuate randomly. This is especially the case at the tail-end of disinfection when the population of bacteria is sparse. It might be effectual, therefore, to explore the resultant random fluctuations via a stochastic paradigm. Proposed herein is a Markovian stochastic model for the rate of bacterial disinfection, whose intensity of transition takes into account the contact time of the bacteria with the disinfecting agent to eliminate any given percentage of the bacteria in terms of a nonlinear function of time. The model's master equation has been simulated by resorting to the Monte Carlo method to circumvent the undue complexities in solving it analytically or numerically via conventional numerical techniques. For illustration, the mean, the variance (standard deviation), and the coefficient of variation of the number concentration of bacteria during disinfection have been estimated through Monte Carlo simulation. The results of simulation compare favorably with the available experimental data as well as with those computed from the corresponding deterministic model.

The design of sustainable manufacturing processes and supply chains is rapidly becoming a critical issue. The reason is the necessity of providing for the needs of a growing human population which is increasingly prosperous across the globe. To this purpose, this review article explores the most important elements of sustainability science and couples them with the P‐graph framework, thereby rendering it possible to design feasible process and supply structures with great ease. Structure is an often‐overlooked aspect of process and supply chain design, in part because even relative simple processes or supply chains can have an enormous number of feasible structures. We further illustrate the application of these ideas with examples of energy generation processes and supply chains. © 2017 American Institute of Chemical Engineers Environ Prog, 37: 624–636, 2018

This contribution presents a sequel to our previously published nonlinear stochastic model for bacterial disinfection whose intensity function is explicitly proportional to the contact time of the bacteria with the disinfecting agent. In the current model, the intensity function is proportional to the square of the contact time to account for an accelerated rate of a disinfection process. The model gives rise to the process’ master equation whose solution renders it possible to obtain the analytical expressions of the process’ mean, variance (or standard deviation), and coefficient of variation. Moreover, the master equation has been simulated via the Monte Carlo method, thereby yielding the numerical estimates of these quantities. The estimates’ values are compared with those computed via the analytical expressions; they are in excellent accord. They are also compared with the available experimental data as well as with the results obtained from our earlier model.

In this work, we propose a method and its concomitant software for the identification and assessment of building-evacuation routes. First, the building floor map is represented via P-graphs, thereby facilitating the identification of the evacuation routes. Second, each route identified is transformed into a time-expanded, process-network synthesis (PNST) problem, which can be algorithmically solved by the P-graph methodology. In the proposed method, each location and passage in the building is defined by a set of attributes to be taken into account in the evacuation-route planning. Third, the evacuation routes are ranked in terms of the evacuation time computed as the minimum cost of the corresponding PNST problem. Furthermore, the evacuation routes can be ranked according to specific criteria (e.g., bottlenecks, route utilization, etc.).Resumen-Este trabajo propone un método y software para la identificación y análisis de los planes de rutas de evacuación en edificios. Inicialmente, el plano arquitectónico del edificio se representa mediante P-graphs para facilitar la identificación de las rutas de evacuación. Posteriormente, cada una de estas rutas se transforma en un problema de síntesis de redes de procesos de tiempo expandido (PNST); el cual se resuelve algorítmicamente con base en la metodología P-graph. En el método propuesto, cada ubicación y corredor en el edificio se describe por medio de un conjunto de atributos que debe considerarse en el plan de rutas de evacuación. Finalmente, las rutas de evacuación se organizan con base en el tiempo de evacuación que se calcula como el costo mínimo del correspondiente problema PNST. Además, las rutas de evacuación pueden organizarse según diferentes criterios (e.g., cuellos de botella, utilización de rutas, etc.).

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Thermal treatment under controlled conditions results in almost complete destruction, or disinfection, of cell or bacterial populations. Medical needs and public health concerns often demand that such disinfection be as complete as possible. The bacteria, particulate and mesoscopic in size, undergo complex motion and behavior, and thus, they die off at irregular rates during disinfection. Hence, in addition to the average death rates of bacteria, the fluctuations around these average rates must be known, especially in the final period, or tail end, of disinfection where the number concentration of bacteria becomes exceedingly low, thereby magnifying the fluctuations.It is natural and often desirable that various aspects of a process involving mesoscopic, particulate entities undergoing complex motion and behavior, such as the aforementioned bacterial disinfection, be explored on the basis of the statistical framework or a stochastic paradigm. Such aspects can range from the analysis and modeling of the particulate entities involved in the process to the optimization and control of the process itself. 1-6 Unambiguous discourses have been given as to the need of statistical or stochastic treatment of bacteriapopulation dynamics in disinfection. 7,8 This note is concerned with the stochastic analysis and modeling of thermal disinfection of bacteria as a pure-death process based on a nonlinear mechanistic rate law, that is, the logistic law. Hitherto, the linear (that is, first-order) rate law has been predominantly adopted for stochastically analyzing and modeling the thermal disinfection rate of bacteria. 9-13 Nevertheless, the growth-positive or negative-of biological populations, including microbial populations, has been increasingly formulated according to nonlinear mechanistic rate laws, 14-18 such as the logistic law. 19,20 In this regard, Soboleva and Pleasants 21 incorporated the logistic law into the modeling of the growth of a biological population. In their work, the mean and variance of the process were computed numerically from the Fokker-Plank equation under the assumption that the random variable characterizing the process-the size or number density of a discrete biological population-is continuous. The adoption of the logistic law has been proposed for modeling the death rate of microorganisms in thermal disinfection 22 ; apparently, no attempt has been made to incorporate this law into the stochastic formulation because of the computational complexity arising from its nonlinearity. Herein, this complexity is circumvented by resorting to the system-size expansion, a rational or logical approximation method, of the master equation of the process. 2,23,24 The numerical results are compared with the available experimental data obtained with S. aureus 25 as well as with those obtained with M. paratuberculosis. 26 Model FormulationThe system under consideration is the population of bacteria that are being thermally deactivated. The population decreases as a result of the death of bacteria, one at a time, ...

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Activated carbons (ACs) have been widely deployed in the purification of gases and liquids or the separation of their mixtures. The formation of ACs entails the modification of the original internal surfaces of carbonaceous substrates, for example, coal or biomass, which can be effected by a variety of chemical or physical methods, thereby augmenting the carbonaceous substrates' adsorbing capacities. The formation of ACs tends to proceed randomly or stochastically in view of the discrete and mesoscopic nature of the carbonaceous substrates, as well as the random encounters between the activation agent and carbon on the carbonaceous substrates' internal surfaces; in addition, the carbonaceous substrates' internal surfaces exhibit an intricate morphology or structure. Naturally, these traits of the formation of ACs render the process to vary incessantly with time. Thus, it is highly desirable that the analysis, modeling, and simulation of the formation of ACs from carbonaceous substrates be performed in light of a stochastic paradigm. Herein, a stochastic model for the formation of ACs is formulated as a pure-death process based on a nonlinear intensity of transition. The model gives rise to the process' nonlinear master equation whose solution is obtained by resorting to a rational approximation method, the system-size expansion. This solution renders it possible to compute the mean as well as higher moments about this mean, for example, variance or standard deviation, which reveal and quantify the process' inherent fluctuations. The results of modeling are validated by comparing them with the available experimental data.