Hybrid mathematical and informational modeling of beam-to-column connections

The analysis of steel and composite frames has traditionally been carried out by idealizing beam-to-column connections as either rigid or pinned. Although some advanced analysis methods have been proposed to account for semi-rigid connections, the performance of these methods strongly depends on the proper modeling of connection behavior. The primary challenge of modeling beam-to-column connections is their inelastic response and continuously varying stiffness, strength, and ductility. In this dissertation, two distinct approaches—mathematical models and informational models—are proposed to account for the complex hysteretic behavior of beam-to-column connections. The performance of the two approaches is examined and is then followed by a discussion of their merits and deficiencies. To capitalize on the merits of both mathematical and informational representations, a new approach, a hybrid modeling framework, is developed and demonstrated through modeling beam-to-column connections. Component-based modeling is a compromise spanning two extremes in the field of mathematical modeling: simplified global models and finite element models. In the component-based modeling of angle connections, the five critical components of excessive deformation are identified. Constitutive relationships of angles, column panel zones, and contact between angles and column flanges, are derived by using only material and geometric properties and theoretical mechanics considerations. Those of slip and bolt hole ovalization are simplified by empirically-suggested mathematical representation and expert opinions. A mathematical model is then assembled as a macro-element by combining rigid bars and springs that represent the constitutive relationship of components. Lastly, the moment-rotation curves of the mathematical models are compared with those of experimental tests. In the case of a top-and-seat angle connection with double web angles, a pinched hysteretic response is predicted quite well by complete mechanical models, which take advantage of only material and geometric properties. On the other hand, to exhibit the highly pinched behavior of a top-and-seat angle connection without web angles, a mathematical model requires components of slip and bolt hole ovalization, which are more amenable to informational modeling. An alternative method is informational modeling, which constitutes a fundamental shift from mathematical equations to data that contain the required information about underlying mechanics. The information is extracted from observed data and stored in neural networks. Two different training data sets, analytically-generated and experimental data, are tested to examine the performance of informational models. Both informational models show acceptable agreement with the moment-rotation curves of the experiments. Adding a degradation parameter improves the informational models when modeling highly pinched hysteretic behavior. However, informational models cannot represent the contribution of individual components and therefore do not provide an insight into the underlying mechanics of components. In this study, a new hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections. Mechanics-based components of deformation such as angles, flange-plates, and column panel zone, are idealized to a mathematical model by using a complete mechanical approach. Although the mathematical model represents envelope curves in terms of initial stiffness and yielding strength, it is not capable of capturing the pinching effects. Pinching is caused mainly by separation between angles and column flanges as well as slip between angles/flange-plates and beam flanges. These components of deformation are suitable for informational modeling. Finally, the moment-rotation curves of the hybrid models are validated with those of the experimental tests. The comparison shows that the hybrid models are capable of representing the highly pinched hysteretic behavior of beam-to-column connections. In addition, the developed hybrid model is successfully used to predict the behavior of a newly-designed connection.

Hybrid modeling of convective laminar flow in a permeable tube associated with the cross-flow process

The confined flows in tubes with permeable surfaces arc associated to tangential filtration processes (microfiltration or ultrafiltration). The complexity of the phenomena do not allow for the development of exact analytical solutions, however, approximate solutions are of great interest for the calculation of the transmembrane outflow and estimate of the concentration, polarization phenomenon. In the present work, the generalized integral transform technique (GITT) was employed in solving the laminar and permanent flow in permeable tubes of Newtonian and incompressible fluid. The mathematical formulation employed the parabolic differential equation of chemical species conservation (convective-diffusive equation). The velocity profiles for the entrance region flow, which are found in the connective terms of the equation, were assessed by solutions obtained from literature. The velocity at the permeable wall was considered uniform, with the concentration at the tube wall regarded as variable with an axial position. A computational methodology using global error control was applied to determine the concentration in the wall and concentration boundary layer thickness. The results obtained for the local transmembrane flux and the concentration boundary layer thickness were compared against others in literature. (C) 2007 Elsevier B.V. All rights reserved.

Heterogeneous modeling of an anaerobic sequencing batch biofilm reactor (ASBBR)

The objective of this study was to estimate the first-order intrinsic kinetic constant (k(1)) and the liquid-phase mass transfer coefficient (k(c)) in a bench-scale anaerobic sequencing batch biofilm reactor (ASBBR) fed with glucose. A dynamic heterogeneous mathematical model, considering two phases (liquid and solid), was developed through mass balances in the liquid and solid phases. The model was adjusted to experimental data obtained from the ASBBR applied for the treatment of glucose-based synthetic wastewater with approximately 500 mg L-1 of glucose, operating in 8 h batch cycles, at 30 degrees C and 300 rpm. The values of the parameters obtained were 0.8911 min(-1) for k(1) and 0.7644 cm min(-1) for kc. The model was validated utilizing the estimated parameters with data obtained from the ASBBR operating in 3 h batch cycles, with a good representation of the experimental behavior. The solid-phase mass transfer flux was found to be the limiting step of the overall glucose conversion rate.

Solution of a heterogeneous modeling of a horizontal-flow anaerobic immobilized biomass (HAIB) reactor by the sequencing method

A modeling study was completed to develop a methodology that combines the sequencing and finite difference methods for the simulation of a heterogeneous model of a tubular reactor applied in the treatment of wastewater. The system included a liquid phase (convection diffusion transport) and a solid phase (diffusion reaction) that was obtained by completing a mass balance in the reactor and in the particle, respectively. The model was solved using a pilot-scale horizontal-flow anaerobic immobilized biomass (HAIB) reactor to treat domestic sewage, with the concentration results compared with the experimental data. A comparison of the behavior of the liquid phase concentration profile and the experimental results indicated that both the numerical methods offer a good description of the behavior of the concentration along the reactor. The advantage of the sequencing method over the finite difference method is that it is easier to apply and requires less computational time to model the dynamic simulation of outlet response of HAIB.

Kinetics and Modeling of Fatty Alcohol Ethoxylation in an Industrial Spray Loop Reactor

The kinetics of the ethoxylation of fatty alcohols catalyzed by potassium hydroxide was studied to obtain the rate constants for modeling of the industrial process. Experimental data obtained in a lab-scale semibatch autoclave reactor were used to evaluate kinetic and equilibrium parameters. The kinetic model was employed to model the performance of an industrial-scale spray tower reactor for fatty alcohol ethoxylation. The reactor model considers that mass transfer and reaction occur independently in two distinct zones of the reactor. Good agreement between the model predictions and real data was found. These findings confirm the reliability of the kinetic and reactor model for simulating fatty alcohol ethoxylation processes under industrial conditions.

Structured modeling of recombinant protein production in batch and fed-batch culture of baculovirus-infected insect cells

The infection of insect cells with baculovirus was described in a mathematical model as a part of the structured dynamic model describing whole animal cell metabolism. The model presented here is capable of simulating cell population dynamics, the concentrations of extracellular and intracellular viral components, and the heterologous product titers. The model describes the whole processes of viral infection and the effect of the infection on the host cell metabolism. Dynamic simulation of the model in batch and fed-batch mode gave good agreement between model predictions and experimental data. Optimum conditions for insect cell culture and viral infection in batch and fed-batch culture were studied using the model.

A NEUROECONOMIC MODELING OF ATTENTION-DEFICIT/HYPERACTIVITY DISORDER (ADHD)

In this paper we present a new neuroeconomics model for decision-making applied to the Attention-Deficit/Hyperactivity Disorder (ADHD). The model is based on the hypothesis that decision-making is dependent on the evaluation of expected rewards and risks assessed simultaneously in two decision spaces: the personal (PDS) and the interpersonal emotional spaces (IDS). Motivation to act is triggered by necessities identified in PDS or IDS. The adequacy of an action in fulfilling a given necessity is assumed to be dependent on the expected reward and risk evaluated in the decision spaces. Conflict generated by expected reward and risk influences the easiness (cognitive effort) and the future perspective of the decision-making. Finally, the willingness (not) to act is proposed to be a function of the expected reward (or risk), adequacy, easiness and future perspective. The two most frequent clinical forms are ADHD hyperactive (AD/HDhyp) and ADHD inattentive (AD/HDdin). AD/HDhyp behavior is hypothesized to be a consequence of experiencing high rewarding expectancies for short periods of time, low risk evaluation, and short future perspective for decision-making. AD/HDin is hypothesized to be a consequence of experiencing high rewarding expectancies for long periods of time, low risk evaluation, and long future perspective for decision-making.

Modeling of a solid-state bipolar blumlein generator for N stages

This paper models an n-stage stacked Blumlein generator for bipolar pulses for various load conditions. Calculation of the voltage amplitudes in time domain at the load and between stages is described for an n-stage generator. For this, the reflection and transmission coefficients are mathematically modeled where impedance discontinuity occurs (i.e., at the junctions between two transmission lines). The mathematical model developed is assessed by comparing simulation results to experimental data from a two-stage Blumlein solid-state prototype.

Modeling and optimization of extracellular polysaccharides production by Enterobacter A47

Polysaccharides are gaining increasing attention as potential environmental friendly and sustainable building blocks in many fields of the (bio)chemical industry. The microbial production of polysaccharides is envisioned as a promising path, since higher biomass growth rates are possible and therefore higher productivities may be achieved compared to vegetable or animal polysaccharides sources. This Ph.D. thesis focuses on the modeling and optimization of a particular microbial polysaccharide, namely the production of extracellular polysaccharides (EPS) by the bacterial strain Enterobacter A47. Enterobacter A47 was found to be a metabolically versatile organism in terms of its adaptability to complex media, notably capable of achieving high growth rates in media containing glycerol byproduct from the biodiesel industry. However, the industrial implementation of this production process is still hampered due to a largely unoptimized process. Kinetic rates from the bioreactor operation are heavily dependent on operational parameters such as temperature, pH, stirring and aeration rate. The increase of culture broth viscosity is a common feature of this culture and has a major impact on the overall performance. This fact complicates the mathematical modeling of the process, limiting the possibility to understand, control and optimize productivity. In order to tackle this difficulty, data-driven mathematical methodologies such as Artificial Neural Networks can be employed to incorporate additional process data to complement the known mathematical description of the fermentation kinetics. In this Ph.D. thesis, we have adopted such an hybrid modeling framework that enabled the incorporation of temperature, pH and viscosity effects on the fermentation kinetics in order to improve the dynamical modeling and optimization of the process. A model-based optimization method was implemented that enabled to design bioreactor optimal control strategies in the sense of EPS productivity maximization. It is also critical to understand EPS synthesis at the level of the bacterial metabolism, since the production of EPS is a tightly regulated process. Methods of pathway analysis provide a means to unravel the fundamental pathways and their controls in bioprocesses. In the present Ph.D. thesis, a novel methodology called Principal Elementary Mode Analysis (PEMA) was developed and implemented that enabled to identify which cellular fluxes are activated under different conditions of temperature and pH. It is shown that differences in these two parameters affect the chemical composition of EPS, hence they are critical for the regulation of the product synthesis. In future studies, the knowledge provided by PEMA could foster the development of metabolically meaningful control strategies that target the EPS sugar content and oder product quality parameters.

Population Dynamics Modeling of Arapaima gigas

Pirarucu (Arapaima gigas) has been of the most important natural fishing resources of the Amazon region. Due to its economic importance, and the necessity to preserve the species hand, field research concerning the habits and behavior of the pirarucu has been increasing for the last 20 years. The aim of this paper is to present a mathematical model for the pirarucu population dynamics considering the species peculiarities, particularly the male parental care over the offspring. The solution of the dynamical systems indicates three possible equilibrium points for the population. The first corresponds to extinction; the third corresponds to a stable population close to the environmental carrying capacity. The second corresponds to an unstable equilibrium located between extinction and full use of the carrying capacity. It is shown that lack of males’ parental care closes the gap between the point corresponding to the unstable equilibrium and the point of stable non-trivial equilibrium. If guarding failure reaches a critical point the two points coincide and the population tends irreversibly to extinction. If some event tends to destabilize the population equilibrium, as for instance inadequate parental care, the model responds in such a way as to restore the trajectory towards the stable equilibrium point avoiding the route to extinction. The parameters introduced to solve the system of equations are partially derived from limited but reliable field data collected at the Mamirauá Sustainable Development Reserve (MSDR) in the Brazilian Amazonian Region.

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on E. coli have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with E. coli. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion.

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

Comment on recent modeling studies of astrocyte-neuron metabolic interactions.

Recent years have seen a surge in mathematical modeling of the various aspects of neuron-astrocyte interactions, and the field of brain energy metabolism is no exception in that regard. Despite the advent of biophysical models in the field, the long-lasting debate on the role of lactate in brain energy metabolism is still unresolved. Quite the contrary, it has been ported to the world of differential equations. Here, we summarize the present state of this discussion from the modeler's point of view and bring some crucial points to the attention of the non-mathematically proficient reader.

MODELING OF SOIL LOAD-BEARING CAPACITY AS A FUNCTION OF SOIL MECHANICAL RESISTANCE TO PENETRATION

Estimation of soil load-bearing capacity from mathematical models that relate preconsolidation pressure (σp) to mechanical resistance to penetration (PR) and gravimetric soil water content (U) is important for defining strategies to prevent compaction of agricultural soils. Our objective was therefore to model the σp and compression index (CI) according to the PR (with an impact penetrometer in the field and a static penetrometer inserted at a constant rate in the laboratory) and U in a Rhodic Eutrudox. The experiment consisted of six treatments: no-tillage system (NT); NT with chiseling; and NT with additional compaction by combine traffic (passing 4, 8, 10, and 20 times). Soil bulk density, total porosity, PR (in field and laboratory measurements), U, σp, and CI values were determined in the 5.5-10.5 cm and 13.5-18.5 cm layers. Preconsolidation pressure (σp) and CI were modeled according to PR in different U. The σp increased and the CI decreased linearly with increases in the PR values. The correlations between σp and PR and PR and CI are influenced by U. From these correlations, the soil load-bearing capacity and compaction susceptibility can be estimated by PR readings evaluated in different U.