Modeling and simulation of population balances for particulate processes

This work focuses on the modeling and numerical approximations of population balance equations (PBEs) for the simulation of different phenomena occurring in process engineering. The population balance equation (PBE) is considered to be a statement of continuity. It tracks the change in particle size distribution as particles are born, die, grow or leave a given control volume. In the population balance models the one independent variable represents the time, the other(s) are property coordinate(s), e.g., the particle volume (size) in the present case. They typically describe the temporal evolution of the number density functions and have been used to model various processes such as granulation, crystallization, polymerization, emulsion and cell dynamics. The semi-discrete high resolution schemes are proposed for solving PBEs modeling one and two-dimensional batch crystallization models. The schemes are discrete in property coordinates but continuous in time. The resulting ordinary differential equations can be solved by any standard ODE solver. To improve the numerical accuracy of the schemes a moving mesh technique is introduced in both one and two-dimensional cases ...

Dynamical modeling and analysis of large cellular regulatory networks.

The dynamical analysis of large biological regulatory networks requires the development of scalable methods for mathematical modeling. Following the approach initially introduced by Thomas, we formalize the interactions between the components of a network in terms of discrete variables, functions, and parameters. Model simulations result in directed graphs, called state transition graphs. We are particularly interested in reachability properties and asymptotic behaviors, which correspond to terminal strongly connected components (or "attractors") in the state transition graph. A well-known problem is the exponential increase of the size of state transition graphs with the number of network components, in particular when using the biologically realistic asynchronous updating assumption. To address this problem, we have developed several complementary methods enabling the analysis of the behavior of large and complex logical models: (i) the definition of transition priority classes to simplify the dynamics; (ii) a model reduction method preserving essential dynamical properties, (iii) a novel algorithm to compact state transition graphs and directly generate compressed representations, emphasizing relevant transient and asymptotic dynamical properties. The power of an approach combining these different methods is demonstrated by applying them to a recent multilevel logical model for the network controlling CD4+ T helper cell response to antigen presentation and to a dozen cytokines. This model accounts for the differentiation of canonical Th1 and Th2 lymphocytes, as well as of inflammatory Th17 and regulatory T cells, along with many hybrid subtypes. All these methods have been implemented into the software GINsim, which enables the definition, the analysis, and the simulation of logical regulatory graphs.

An introductory review on gravitational-deformation induced structures, fabrics and modeling

Recent studies have pointed out a similarity between tectonics and slope tectonic-induced structures. Numerous studies have demonstrated that structures and fabrics previously interpreted as of purely geodynamical origin are instead the result of large slope deformation, and this led in the past to erroneous interpretations. Nevertheless, their limit seems not clearly defined, but it is somehow transitional. Some studies point out continuity between failures developing at surface with upper crust movements. In this contribution, the main studies which examine the link between rock structures and slope movements are reviewed. The aspects regarding model and scale of observation are discussed together with the role of pre-existing weaknesses in the rock mass. As slope failures can develop through progressive failure, structures and their changes in time and space can be recognized. Furthermore, recognition of the origin of these structures can help in avoiding misinterpretations of regional geology. This also suggests the importance of integrating different slope movement classifications based on distribution and pattern of deformation and the application of structural geology techniques. A structural geology approach in the landslide community is a tool that can greatly support the hazard quantification and related risks, because most of the physical parameters, which are used for landslide modeling, are derived from geotechnical tests or the emerging geophysical approaches.

Binary classification of dyslipidemia from the waist-to-hip ratio and body mass index: a comparison of linear, logistic, and CART models.

BACKGROUND: We sought to improve upon previously published statistical modeling strategies for binary classification of dyslipidemia for general population screening purposes based on the waist-to-hip circumference ratio and body mass index anthropometric measurements. METHODS: Study subjects were participants in WHO-MONICA population-based surveys conducted in two Swiss regions. Outcome variables were based on the total serum cholesterol to high density lipoprotein cholesterol ratio. The other potential predictor variables were gender, age, current cigarette smoking, and hypertension. The models investigated were: (i) linear regression; (ii) logistic classification; (iii) regression trees; (iv) classification trees (iii and iv are collectively known as "CART"). Binary classification performance of the region-specific models was externally validated by classifying the subjects from the other region. RESULTS: Waist-to-hip circumference ratio and body mass index remained modest predictors of dyslipidemia. Correct classification rates for all models were 60-80%, with marked gender differences. Gender-specific models provided only small gains in classification. The external validations provided assurance about the stability of the models. CONCLUSIONS: There were no striking differences between either the algebraic (i, ii) vs. non-algebraic (iii, iv), or the regression (i, iii) vs. classification (ii, iv) modeling approaches. Anticipated advantages of the CART vs. simple additive linear and logistic models were less than expected in this particular application with a relatively small set of predictor variables. CART models may be more useful when considering main effects and interactions between larger sets of predictor variables.

Patients' and physicians' preferences for type 2 diabetes mellitus treatments in Spain and Portugal: a discrete choice experiment.

OBJECTIVE To assess Spanish and Portuguese patients' and physicians' preferences regarding type 2 diabetes mellitus (T2DM) treatments and the monthly willingness to pay (WTP) to gain benefits or avoid side effects. METHODS An observational, multicenter, exploratory study focused on routine clinical practice in Spain and Portugal. Physicians were recruited from multiple hospitals and outpatient clinics, while patients were recruited from eleven centers operating in the public health care system in different autonomous communities in Spain and Portugal. Preferences were measured via a discrete choice experiment by rating multiple T2DM medication attributes. Data were analyzed using the conditional logit model. RESULTS Three-hundred and thirty (n=330) patients (49.7% female; mean age 62.4 [SD: 10.3] years, mean T2DM duration 13.9 [8.2] years, mean body mass index 32.5 [6.8] kg/m(2), 41.8% received oral + injected medication, 40.3% received oral, and 17.6% injected treatments) and 221 physicians from Spain and Portugal (62% female; mean age 41.9 [SD: 10.5] years, 33.5% endocrinologists, 66.5% primary-care doctors) participated. Patients valued avoiding a gain in bodyweight of 3 kg/6 months (WTP: €68.14 [95% confidence interval: 54.55-85.08]) the most, followed by avoiding one hypoglycemic event/month (WTP: €54.80 [23.29-82.26]). Physicians valued avoiding one hypoglycemia/week (WTP: €287.18 [95% confidence interval: 160.31-1,387.21]) the most, followed by avoiding a 3 kg/6 months gain in bodyweight and decreasing cardiovascular risk (WTP: €166.87 [88.63-843.09] and €154.30 [98.13-434.19], respectively). Physicians and patients were willing to pay €125.92 (73.30-622.75) and €24.28 (18.41-30.31), respectively, to avoid a 1% increase in glycated hemoglobin, and €143.30 (73.39-543.62) and €42.74 (23.89-61.77) to avoid nausea. CONCLUSION Both patients and physicians in Spain and Portugal are willing to pay for the health benefits associated with improved diabetes treatment, the most important being to avoid hypoglycemia and gaining weight. Decreased cardiovascular risk and weight reduction became the third most valued attributes for physicians and patients, respectively.

Modeling of hybrid systems by piecewise decomposition

Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

Prediction of fat-free mass using bioelectrical impedance analysis in young adults from five populations of African origin.

Background/objectives:Bioelectrical impedance analysis (BIA) is used in population and clinical studies as a technique for estimating body composition. Because of significant under-representation in existing literature, we sought to develop and validate predictive equation(s) for BIA for studies in populations of African origin.Subjects/methods:Among five cohorts of the Modeling the Epidemiologic Transition Study, height, weight, waist circumference and body composition, using isotope dilution, were measured in 362 adults, ages 25-45 with mean body mass indexes ranging from 24 to 32. BIA measures of resistance and reactance were measured using tetrapolar placement of electrodes and the same model of analyzer across sites (BIA 101Q, RJL Systems). Multiple linear regression analysis was used to develop equations for predicting fat-free mass (FFM), as measured by isotope dilution; covariates included sex, age, waist, reactance and height(2)/resistance, along with dummy variables for each site. Developed equations were then tested in a validation sample; FFM predicted by previously published equations were tested in the total sample.Results:A site-combined equation and site-specific equations were developed. The mean differences between FFM (reference) and FFM predicted by the study-derived equations were between 0.4 and 0.6âeuro0/00kg (that is, 1% difference between the actual and predicted FFM), and the measured and predicted values were highly correlated. The site-combined equation performed slightly better than the site-specific equations and the previously published equations.Conclusions:Relatively small differences exist between BIA equations to estimate FFM, whether study-derived or published equations, although the site-combined equation performed slightly better than others. The study-derived equations provide an important tool for research in these understudied populations.

Continuum formalism for modeling growing networks with deletion of nodes

We present a continuum formalism for modeling growing random networks under addition and deletion of nodes based on a differential mass balance equation. As examples of its applicability, we obtain new results on the degree distribution for growing networks with a uniform attachment and deletion of nodes, and complete some recent results on growing networks with preferential attachment and uniform removal

New Trends in Public Facility Location Modeling

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.

Preliminary slope mass movement susceptibility mapping using DEM and LiDAR DEM

Hazard mapping in mountainous areas at the regional scale has greatly changed since the 1990s thanks to improved digital elevation models (DEM). It is now possible to model slope mass movement and floods with a high level of detail in order to improve geomorphologic mapping. We present examples of regional multi-hazard susceptibility mapping through two Swiss case studies, including landslides, rockfall, debris flows, snow avalanches and floods, in addition to several original methods and software tools. The aim of these recent developments is to take advantage of the availability of high resolution DEM (HRDEM) for better mass movement modeling. Our results indicate a good correspondence between inventories of hazardous zones based on historical events and model predictions. This paper demonstrates that by adapting tools and methods issued from modern technologies, it is possible to obtain reliable documents for land planning purposes over large areas.

Interaction of a discrete breather with a lattice junction

We study the scattering of a moving discrete breather (DB) on a junction in a Fermi-Pasta-Ulam chain consisting of two segments with different masses of the particles. We consider four distinct cases: (i) a light-heavy (abrupt) junction in which the DB impinges on the junction from the segment with lighter mass, (ii) a heavy-light junction, (iii) an up mass ramp in which the mass in the heavier segment increases continuously as one moves away from the junction point, and (iv) a down mass ramp. Depending on the mass difference and DB characteristics (frequency and velocity), the DB can either reflect from, or transmit through, or get trapped at the junction or on the ramp. For the heavy-light junction, the DB can even split at the junction into a reflected and a transmitted DB. The latter is found to subsequently split into two or more DBs. For the down mass ramp the DB gets accelerated in several stages, with accompanying radiation (phonons). These results are rationalized by calculating the Peierls-Nabarro barrier for the various cases. We also point out implications of our results in realistic situations such as electron-phonon coupled chains.

Confinement of discrete breathers in inhomogeneously profiled nonlinear chains

We investigate numerically the scattering of a moving discrete breather on a pair of junctions in a Fermi-Pasta-Ulam chain. These junctions delimit an extended region with different masses of the particles. We consider (i) a rectangular trap, (ii) a wedge shaped trap, and (iii) a smoothly varying convex or concave mass profile. All three cases lead to DB confinement, with the ease of trapping depending on the profile of the trap. We also study the collision and trapping of two DBs within the profile as a function of trap width, shape, and approach time at the two junctions. The latter controls whether one or both DBs are trapped.

Budgeting rockfall and modeling sedimentary delivery in torrent systems

This thesis is a compilation of projects to study sediment processes recharging debris flow channels. These works, conducted during my stay at the University of Lausanne, focus in the geological and morphological implications of torrent catchments to characterize debris supply, a fundamental element to predict debris flows. Other aspects of sediment dynamics are considered, e.g. the coupling headwaters - torrent, as well as the development of a modeling software that simulates sediment transfer in torrent systems. The sediment activity at Manival, an active torrent system of the northern French Alps, was investigated using terrestrial laser scanning and supplemented with geostructural investigations and a survey of sediment transferred in the main torrent. A full year of sediment flux could be observed, which coincided with two debris flows and several bedload transport events. This study revealed that both debris flows generated in the torrent and were preceded in time by recharge of material from the headwaters. Debris production occurred mostly during winter - early spring time and was caused by large slope failures. Sediment transfers were more puzzling, occurring almost exclusively in early spring subordinated to runoffconditions and in autumn during long rainfall. Intense rainstorms in summer did not affect debris storage that seems to rely on the stability of debris deposits. The morpho-geological implication in debris supply was evaluated using DEM and field surveys. A slope angle-based classification of topography could characterize the mode of debris production and transfer. A slope stability analysis derived from the structures in rock mass could assess susceptibility to failure. The modeled rockfall source areas included more than 97% of the recorded events and the sediment budgets appeared to be correlated to the density of potential slope failure. This work showed that the analysis of process-related terrain morphology and of susceptibility to slope failure document the sediment dynamics to quantitatively assess erosion zones leading to debris flow activity. The development of erosional landforms was evaluated by analyzing their geometry with the orientations of potential rock slope failure and with the direction of the maximum joint frequency. Structure in rock mass, but in particular wedge failure and the dominant discontinuities, appear as a first-order control of erosional mechanisms affecting bedrock- dominated catchment. They represent some weaknesses that are exploited primarily by mass wasting processes and erosion, promoting not only the initiation of rock couloirs and gullies, but also their propagation. Incorporating the geological control in geomorphic processes contributes to better understand the landscape evolution of active catchments. A sediment flux algorithm was implemented in a sediment cascade model that discretizes the torrent catchment in channel reaches and individual process-response systems. Each conceptual element includes in simple manner geomorphological and sediment flux information derived from GIS complemented with field mapping. This tool enables to simulate sediment transfers in channels considering evolving debris supply and conveyance, and helps reducing the uncertainty inherent to sediment budget prediction in torrent systems. Cette thèse est un recueil de projets d'études des processus de recharges sédimentaires des chenaux torrentiels. Ces travaux, réalisés lorsque j'étais employé à l'Université de Lausanne, se concentrent sur les implications géologiques et morphologiques des bassins dans l'apport de sédiments, élément fondamental dans la prédiction de laves torrentielles. D'autres aspects de dynamique sédimentaire ont été abordés, p. ex. le couplage torrent - bassin, ainsi qu'un modèle de simulation du transfert sédimentaire en milieu torrentiel. L'activité sédimentaire du Manival, un système torrentiel actif des Alpes françaises, a été étudiée par relevés au laser scanner terrestre et complétée par une étude géostructurale ainsi qu'un suivi du transfert en sédiments du torrent. Une année de flux sédimentaire a pu être observée, coïncidant avec deux laves torrentielles et plusieurs phénomènes de charriages. Cette étude a révélé que les laves s'étaient générées dans le torrent et étaient précédées par une recharge de débris depuis les versants. La production de débris s'est passée principalement en l'hiver - début du printemps, causée par de grandes ruptures de pentes. Le transfert était plus étrange, se produisant presque exclusivement au début du printemps subordonné aux conditions d'écoulement et en automne lors de longues pluies. Les orages d'été n'affectèrent guère les dépôts, qui semblent dépendre de leur stabilité. Les implications morpho-géologiques dans l'apport sédimentaire ont été évaluées à l'aide de MNT et études de terrain. Une classification de la topographie basée sur la pente a permis de charactériser le mode de production et transfert. Une analyse de stabilité de pente à partir des structures de roches a permis d'estimer la susceptibilité à la rupture. Les zones sources modélisées comprennent plus de 97% des chutes de blocs observées et les bilans sédimentaires sont corrélés à la densité de ruptures potentielles. Ce travail d'analyses des morphologies du terrain et de susceptibilité à la rupture documente la dynamique sédimentaire pour l'estimation quantitative des zones érosives induisant l'activité torrentielle. Le développement des formes d'érosion a été évalué par l'analyse de leur géométrie avec celle des ruptures potentielles et avec la direction de la fréquence maximale des joints. Les structures de roches, mais en particulier les dièdres et les discontinuités dominantes, semblent être très influents dans les mécanismes d'érosion affectant les bassins rocheux. Ils représentent des zones de faiblesse exploitées en priorité par les processus de démantèlement et d'érosion, encourageant l'initiation de ravines et couloirs, mais aussi leur propagation. L'incorporation du control géologique dans les processus de surface contribue à une meilleure compréhension de l'évolution topographique de bassins actifs. Un algorithme de flux sédimentaire a été implémenté dans un modèle en cascade, lequel divise le bassin en biefs et en systèmes individuels répondant aux processus. Chaque unité inclut de façon simple les informations géomorpologiques et celles du flux sédimentaire dérivées à partir de SIG et de cartographie de terrain. Cet outil permet la simulation des transferts de masse dans les chenaux, considérants la variabilité de l'apport et son transport, et aide à réduire l'incertitude liée à la prédiction de bilans sédimentaires torrentiels. Ce travail vise très humblement d'éclairer quelques aspects de la dynamique sédimentaire en milieu torrentiel.

On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management

The choice network revenue management (RM) model incorporates customer purchase behavioras customers purchasing products with certain probabilities that are a function of the offeredassortment of products, and is the appropriate model for airline and hotel network revenuemanagement, dynamic sales of bundles, and dynamic assortment optimization. The underlyingstochastic dynamic program is intractable and even its certainty-equivalence approximation, inthe form of a linear program called Choice Deterministic Linear Program (CDLP) is difficultto solve in most cases. The separation problem for CDLP is NP-complete for MNL with justtwo segments when their consideration sets overlap; the affine approximation of the dynamicprogram is NP-complete for even a single-segment MNL. This is in contrast to the independentclass(perfect-segmentation) case where even the piecewise-linear approximation has been shownto be tractable. In this paper we investigate the piecewise-linear approximation for network RMunder a general discrete-choice model of demand. We show that the gap between the CDLP andthe piecewise-linear bounds is within a factor of at most 2. We then show that the piecewiselinearapproximation is polynomially-time solvable for a fixed consideration set size, bringing itinto the realm of tractability for small consideration sets; small consideration sets are a reasonablemodeling tradeoff in many practical applications. Our solution relies on showing that forany discrete-choice model the separation problem for the linear program of the piecewise-linearapproximation can be solved exactly by a Lagrangian relaxation. We give modeling extensionsand show by numerical experiments the improvements from using piecewise-linear approximationfunctions.