Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

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.

Finite element computational modeling of externally bonded CFRP composites flexural behavior in RC beams

This paper focuses on the flexural behavior of RC beams externally strengthened with Carbon Fiber Reinforced Polymers (CFRP) fabric. A non-linear finite element (FE) analysis strategy is proposed to support the beam flexural behavior experimental analysis. A development system (QUEBRA2D/FEMOOP programs) has been used to accomplish the numerical simulation. Appropriate constitutive models for concrete, rebars, CFRP and bond-slip interfaces have been implemented and adjusted to represent the composite system behavior. Interface and truss finite elements have been implemented (discrete and embedded approaches) for the numerical representation of rebars, interfaces and composites.

Experimental data and modeling of the thermodynamic properties of bread dough at refrigeration and freezing temperatures

Thermodynamic properties of bread dough (fusion enthalpy, apparent specific heat, initial freezing point and unfreezable water) were measured at temperatures from -40 degrees C to 35 degrees C using differential scanning calorimetry. The initial freezing point was also calculated based on the water activity of dough. The apparent specific heat varied as a function of temperature: specific heat in the freezing region varied from (1.7-23.1) J g(-1) degrees C(-1), and was constant at temperatures above freezing (2.7 J g(-1) degrees C(-1)). Unfreezable water content varied from (0.174-0.182) g/g of total product. Values of heat capacity as a function of temperature were correlated using thermodynamic models. A modification for low-moisture foodstuffs (such as bread dough) was successfully applied to the experimental data. (C) 2010 Elsevier Ltd. All rights reserved.

Different Approaches for Modeling Grouped Survival Data: A Mango Tree Study

Interval-censored survival data, in which the event of interest is not observed exactly but is only known to occur within some time interval, occur very frequently. In some situations, event times might be censored into different, possibly overlapping intervals of variable widths; however, in other situations, information is available for all units at the same observed visit time. In the latter cases, interval-censored data are termed grouped survival data. Here we present alternative approaches for analyzing interval-censored data. We illustrate these techniques using a survival data set involving mango tree lifetimes. This study is an example of grouped survival data.

Spatio-temporal modeling of agricultural yield data with an application to pricing crop insurance contracts

This article presents a statistical model of agricultural yield data based on a set of hierarchical Bayesian models that allows joint modeling of temporal and spatial autocorrelation. This method captures a comprehensive range of the various uncertainties involved in predicting crop insurance premium rates as opposed to the more traditional ad hoc, two-stage methods that are typically based on independent estimation and prediction. A panel data set of county-average yield data was analyzed for 290 counties in the State of Parana (Brazil) for the period of 1990 through 2002. Posterior predictive criteria are used to evaluate different model specifications. This article provides substantial improvements in the statistical and actuarial methods often applied to the calculation of insurance premium rates. These improvements are especially relevant to situations where data are limited.

Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Water table waves in an unconfined aquifer: Experiments and modeling

[1] Comprehensive measurements are presented of the piezometric head in an unconfined aquifer during steady, simple harmonic oscillations driven by a hydrostatic clear water reservoir through a vertical interface. The results are analyzed and used to test existing hydrostatic and nonhydrostatic, small-amplitude theories along with capillary fringe effects. As expected, the amplitude of the water table wave decays exponentially. However, the decay rates and phase lags indicate the influence of both vertical flow and capillary effects. The capillary effects are reconciled with observations of water table oscillations in a sand column with the same sand. The effects of vertical flows and the corresponding nonhydrostatic pressure are reasonably well described by small-amplitude theory for water table waves in finite depth aquifers. That includes the oscillation amplitudes being greater at the bottom than at the top and the phase lead of the bottom compared with the top. The main problems with respect to interpreting the measurements through existing theory relate to the complicated boundary condition at the interface between the driving head reservoir and the aquifer. That is, the small-amplitude, finite depth expansion solution, which matches a hydrostatic boundary condition between the bottom and the mean driving head level, is unrealistic with respect to the pressure variation above this level. Hence it cannot describe the finer details of the multiple mode behavior close to the driving head boundary. The mean water table height initially increases with distance from the forcing boundary but then decreases again, and its asymptotic value is considerably smaller than that previously predicted for finite depth aquifers without capillary effects. Just as the mean water table over-height is smaller than predicted by capillarity-free shallow aquifer models, so is the amplitude of the second harmonic. In fact, there is no indication of extra second harmonics ( in addition to that contained in the driving head) being generated at the interface or in the interior.

Multi-scale modeling of the mechanical behavior of polymer-based materials

Polymers have become the reference material for high reliability and performance applications. In this work, a multi-scale approach is proposed to investigate the mechanical properties of polymeric based material under strain. To achieve a better understanding of phenomena occurring at the smaller scales, a coupling of a Finite Element Method (FEM) and Molecular Dynamics (MD) modeling in an iterative procedure was employed, enabling the prediction of the macroscopic constitutive response. As the mechanical response can be related to the local microstructure, which in turn depends on the nano-scale structure, the previous described multi-scale method computes the stress-strain relationship at every analysis point of the macro-structure by detailed modeling of the underlying micro- and meso-scale deformation phenomena. The proposed multi-scale approach can enable prediction of properties at the macroscale while taking into consideration phenomena that occur at the mesoscale, thus offering an increased potential accuracy compared to traditional methods.

Three-dimensional modeling of tongue during speech using MRI data

The tongue is the most important and dynamic articulator for speech formation, because of its anatomic aspects (particularly, the large volume of this muscular organ comparatively to the surrounding organs of the vocal tract) and also due to the wide range of movements and flexibility that are involved. In speech communication research, a variety of techniques have been used for measuring the three-dimensional vocal tract shapes. More recently, magnetic resonance imaging (MRI) becomes common; mainly, because this technique allows the collection of a set of static and dynamic images that can represent the entire vocal tract along any orientation. Over the years, different anatomical organs of the vocal tract have been modelled; namely, 2D and 3D tongue models, using parametric or statistical modelling procedures. Our aims are to present and describe some 3D reconstructed models from MRI data, for one subject uttering sustained articulations of some typical Portuguese sounds. Thus, we present a 3D database of the tongue obtained by stack combinations with the subject articulating Portuguese vowels. This 3D knowledge of the speech organs could be very important; especially, for clinical purposes (for example, for the assessment of articulatory impairments followed by tongue surgery in speech rehabilitation), and also for a better understanding of acoustic theory in speech formation.

Comments on ‘‘Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions

Applied Mathematical Modelling, Vol.33

Agile modeling data warehouse development

Most of the traditional software and database development approaches tend to be serial, not evolutionary and certainly not agile, especially on data-oriented aspects. Most of the more commonly used methodologies are strict, meaning they’re composed by several stages each with very specific associated tasks. A clear example is the Rational Unified Process (RUP), divided into Business Modeling, Requirements, Analysis & Design, Implementation, Testing and Deployment. But what happens when the needs of a well design and structured plan, meet the reality of a small starting company that aims to build an entire user experience solution. Here resource control and time productivity is vital, requirements are in constant change, and so is the product itself. In order to succeed in this environment a highly collaborative and evolutionary development approach is mandatory. The implications of constant changing requirements imply an iterative development process. Project focus is on Data Warehouse development and business modeling. This area is usually a tricky one. Business knowledge is part of the enterprise, how they work, their goals, what is relevant for analyses are internal business processes. Throughout this document it will be explained why Agile Modeling development was chosen. How an iterative and evolutionary methodology, allowed for reasonable planning and documentation while permitting development flexibility, from idea to product. More importantly how it was applied on the development of a Retail Focused Data Warehouse. A productized Data Warehouse built on the knowledge of not one but several client needs. One that aims not just to store usual business areas but create an innovative sets of business metrics by joining them with store environment analysis, converting Business Intelligence into Actionable Business Intelligence.

Building a person home behavior model based on data from smart house sensors 2015

Dissertação para a obtenção do grau de Mestre em Engenharia Electrotécnica Ramo de Energia