Development of mathematical models to elaborate strategies, select alternatives and development of plans for adaptation of communities to climate change in different geographical areas including costs to implement it.

There is evidence that the climate changes and that now, the change is influenced and accelerated by the CO2 augmentation in atmosphere due to combustion by humans. Such ?Climate change? is on the policy agenda at the global level, with the aim of understanding and reducing its causes and to mitigate its consequences. In most countries and international organisms UNO (e.g. Rio de Janeiro 1992), OECD, EC, etc . . . the efforts and debates have been directed to know the possible causes, to predict the future evolution of some variable conditioners, and trying to make studies to fight against the effects or to delay the negative evolution of such. The Protocol of Kyoto 1997 set international efforts about CO2 emissions, but it was partial and not followed e.g. by USA and China . . . , and in Durban 2011 the ineffectiveness of humanity on such global real challenges was set as evident. Among all that, the elaboration of a global model was not boarded that can help to choose the best alternative between the feasible ones, to elaborate the strategies and to evaluate the costs, and the authors propose to enter in that frame for study. As in all natural, technological and social changes, the best-prepared countries will have the best bear and the more rapid recover. In all the geographic areas the alternative will not be the same one, but the model must help us to make the appropriated decision. It is essential to know those areas that are more sensitive to the negative effects of climate change, the parameters to take into account for its evaluation, and comprehensive plans to deal with it. The objective of this paper is to elaborate a mathematical model support of decisions, which will allow to develop and to evaluate alternatives of adaptation to the climatic change of different communities in Europe and Latin-America, mainly in especially vulnerable areas to the climatic change, considering in them all the intervening factors. The models will consider criteria of physical type (meteorological, edaphic, water resources), of use of the ground (agriculturist, forest, mining, industrial, urban, tourist, cattle dealer), economic (income, costs, benefits, infrastructures), social (population), politician (implementation, legislation), educative (Educational programs, diffusion) and environmental, at the present moment and the future. The intention is to obtain tools for aiding to get a realistic position for these challenges, which are an important part of the future problems of humanity in next decades.

Development of mathematical models to elaborate strategies, to select alternatives and the development of plans for the adaptation of communities to climate change in different geographical areas including costs to implement it

Climate change is on the policy agenda at the global level, with the aim of understanding and reducing its causes and to mitigate its consequences. In most of the countries and international organisms UNO, OECD, EC, etc … the efforts and debates have been directed to know the possible causes, to predict the future evolution of some variable conditioners, and trying to make studies to fight against the effects or to delay the negative evolution of such. Nevertheless, the elaboration of a global model was not boarded that can help to choose the best alternative between the feasible ones, to elaborate the strategies and to evaluate the costs. As in all natural, technological and social changes, the best-prepared countries will have the best bear and the more rapid recover. In all the geographic areas the alternative will not be the same one, but the model should help us to make the appropriated decision. It is essential to know those areas that are more sensitive to the negative effects of climate change, the parameters to take into account for its evaluation, and comprehensive plans to deal with it. The objective of this paper is to elaborate a mathematical model support of decisions, that will allow to develop and to evaluate alternatives of adaptation to the climatic change of different communities in Europe and Latin-America, mainly, in vulnerable areas to the climatic change, considering in them all the intervening factors. The models will take into consideration criteria of physical type (meteorological, edaphic, water resources), of use of the ground (agriculturist, forest, mining, industrial, urban, tourist, cattle dealer), economic (income, costs, benefits, infrastructures), social (population), politician (implementation, legislation), educative (Educational programs, diffusion), sanitary and environmental, at the present moment and the future.

Competitive exclusion in a two-especies chemotasis model

We consider a mathematical model for the spatio-temporal evolution of two biological species in a competitive situation. Besides diffusing, both species move toward higher concentrations of a chemical substance which is produced by themselves. The resulting system consists of two parabolic equations with Lotka–Volterra-type kinetic terms and chemotactic cross-diffusion, along with an elliptic equation describing the behavior of the chemical. We study the question in how far the phenomenon of competitive exclusion occurs in such a context. We identify parameter regimes for which indeed one of the species dies out asymptotically, whereas the other reaches its carrying capacity in the large time limit.

Application of a SPH depth-integrated model to landslide run-out analysis

Hazard and risk assessment of landslides with potentially long run-out is becoming more and more important. Numerical tools exploiting different constitutive models, initial data and numerical solution techniques are important for making the expert’s assessment more objective, even though they cannot substitute for the expert’s understanding of the site-specific conditions and the involved processes. This paper presents a depth-integrated model accounting for pore water pressure dissipation and applications both to real events and problems for which analytical solutions exist. The main ingredients are: (i) The mathematical model, which includes pore pressure dissipation as an additional equation. This makes possible to model flowslide problems with a high mobility at the beginning, the landslide mass coming to rest once pore water pressures dissipate. (ii) The rheological models describing basal friction: Bingham, frictional, Voellmy and cohesive-frictional viscous models. (iii) We have implemented simple erosion laws, providing a comparison between the approaches of Egashira, Hungr and Blanc. (iv) We propose a Lagrangian SPH model to discretize the equations, including pore water pressure information associated to the moving SPH nodes

Analysing the complexity of the model-based decision making processes within the industrial management context

PURPOSE The decision-making process plays a key role in organizations. Every decision-making process produces a final choice that may or may not prompt action. Recurrently, decision makers find themselves in the dichotomous question of following a traditional sequence decision-making process where the output of a decision is used as the input of the next stage of the decision, or following a joint decision-making approach where several decisions are taken simultaneously. The implication of the decision-making process will impact different players of the organization. The choice of the decision- making approach becomes difficult to find, even with the current literature and practitioners’ knowledge. The pursuit of better ways for making decisions has been a common goal for academics and practitioners. Management scientists use different techniques and approaches to improve different types of decisions. The purpose of this decision is to use the available resources as well as possible (data and techniques) to achieve the objectives of the organization. The developing and applying of models and concepts may be helpful to solve managerial problems faced every day in different companies. As a result of this research different decision models are presented to contribute to the body of knowledge of management science. The first models are focused on the manufacturing industry and the second part of the models on the health care industry. Despite these models being case specific, they serve the purpose of exemplifying that different approaches to the problems and could provide interesting results. Unfortunately, there is no universal recipe that could be applied to all the problems. Furthermore, the same model could deliver good results with certain data and bad results for other data. A framework to analyse the data before selecting the model to be used is presented and tested in the models developed to exemplify the ideas. METHODOLOGY As the first step of the research a systematic literature review on the joint decision is presented, as are the different opinions and suggestions of different scholars. For the next stage of the thesis, the decision-making process of more than 50 companies was analysed in companies from different sectors in the production planning area at the Job Shop level. The data was obtained using surveys and face-to-face interviews. The following part of the research into the decision-making process was held in two application fields that are highly relevant for our society; manufacturing and health care. The first step was to study the interactions and develop a mathematical model for the replenishment of the car assembly where the problem of “Vehicle routing problem and Inventory” were combined. The next step was to add the scheduling or car production (car sequencing) decision and use some metaheuristics such as ant colony and genetic algorithms to measure if the behaviour is kept up with different case size problems. A similar approach is presented in a production of semiconductors and aviation parts, where a hoist has to change from one station to another to deal with the work, and a jobs schedule has to be done. However, for this problem simulation was used for experimentation. In parallel, the scheduling of operating rooms was studied. Surgeries were allocated to surgeons and the scheduling of operating rooms was analysed. The first part of the research was done in a Teaching hospital, and for the second part the interaction of uncertainty was added. Once the previous problem had been analysed a general framework to characterize the instance was built. In the final chapter a general conclusion is presented. FINDINGS AND PRACTICAL IMPLICATIONS The first part of the contributions is an update of the decision-making literature review. Also an analysis of the possible savings resulting from a change in the decision process is made. Then, the results of the survey, which present a lack of consistency between what the managers believe and the reality of the integration of their decisions. In the next stage of the thesis, a contribution to the body of knowledge of the operation research, with the joint solution of the replenishment, sequencing and inventory problem in the assembly line is made, together with a parallel work with the operating rooms scheduling where different solutions approaches are presented. In addition to the contribution of the solving methods, with the use of different techniques, the main contribution is the framework that is proposed to pre-evaluate the problem before thinking of the techniques to solve it. However, there is no straightforward answer as to whether it is better to have joint or sequential solutions. Following the proposed framework with the evaluation of factors such as the flexibility of the answer, the number of actors, and the tightness of the data, give us important hints as to the most suitable direction to take to tackle the problem. RESEARCH LIMITATIONS AND AVENUES FOR FUTURE RESEARCH In the first part of the work it was really complicated to calculate the possible savings of different projects, since in many papers these quantities are not reported or the impact is based on non-quantifiable benefits. The other issue is the confidentiality of many projects where the data cannot be presented. For the car assembly line problem more computational power would allow us to solve bigger instances. For the operation research problem there was a lack of historical data to perform a parallel analysis in the teaching hospital. In order to keep testing the decision framework it is necessary to keep applying more case studies in order to generalize the results and make them more evident and less ambiguous. The health care field offers great opportunities since despite the recent awareness of the need to improve the decision-making process there are many opportunities to improve. Another big difference with the automotive industry is that the last improvements are not spread among all the actors. Therefore, in the future this research will focus more on the collaboration between academia and the health care sector.

Mathematical modelling of neural processes within the oculomotor system

It is presented a mathematical model of the oculomotor plant, based on experimental data in cats. The system that generates, from the neuronal processes at the motoneuron, the control signals to the eye muscles that moves the eye. In contrast with previous models, that base the eye movement related motoneuron behavior on a first order linear differential equation, non-linear effects are described: A dependency on the eye angular position of the model parameters.

The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

A model of excitation and adaptation in bacterial chemotaxis

Bacterial chemotaxis is widely studied because of its accessibility and because it incorporates processes that are important in a number of sensory systems: signal transduction, excitation, adaptation, and a change in behavior, all in response to stimuli. Quantitative data on the change in behavior are available for this system, and the major biochemical steps in the signal transduction/processing pathway have been identified. We have incorporated recent biochemical data into a mathematical model that can reproduce many of the major features of the intracellular response, including the change in the level of chemotactic proteins to step and ramp stimuli such as those used in experimental protocols. The interaction of the chemotactic proteins with the motor is not modeled, but we can estimate the degree of cooperativity needed to produce the observed gain under the assumption that the chemotactic proteins interact directly with the motor proteins.

A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system’s behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken’s cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.

Mathematical modeling of drying process of unripe banana slices

Unripe banana flour (UBF) production employs bananas not submitted to maturation process, is an interesting alternative to minimize the fruit loss reduction related to inappropriate handling or fast ripening. The UBF is considered as a functional ingredient improving glycemic and plasma insulin levels in blood, have also shown efficacy on the control of satiety, insulin resistance. The aim of this work was to study the drying process of unripe banana slabs (Musa cavendishii, Nanicão) developing a transient drying model through mathematical modeling with simultaneous moisture and heat transfer. The raw material characterization was performed and afterwards the drying process was conducted at 40 ºC, 50 ºC e 60 ºC, the product temperature was recorded using thermocouples, the air velocity inside the chamber was 4 m·s-1. With the experimental data was possible to validate the diffusion model based on the Fick\'s second law and Fourier. For this purpose, the sorption isotherms were measured and fitted to the GAB model estimating the equilibrium moisture content (Xe), 1.76 [g H2O/100g d.b.] at 60 ºC and 10 % of relative humidity (RH), the thermophysical properties (k, Cp, ?) were also measured to be used in the model. Five cases were contemplated: i) Constant thermophysical properties; ii) Variable properties; iii) Mass (hm), heat transfer (h) coefficient and effective diffusivity (De) estimation 134 W·m-2·K-1, 4.91x10-5 m-2·s-1 and 3.278?10-10 m·s-2 at 60 ºC, respectively; iv) Variable De, it presented a third order polynomial behavior as function of moisture content; v) The shrinkage had an effect on the mathematical model, especially in the 3 first hours of process, the thickness experienced a contraction of about (30.34 ± 1.29) % out of the initial thickness, finding two decreasing drying rate periods (DDR I and DDR II), 3.28x10-10 m·s-2 and 1.77x10-10 m·s-2, respectively. COMSOL Multiphysics simulations were possible to perform through the heat and mass transfer coefficient estimated by the mathematical modeling.

Mathematical modelling of the lower urinary tract

The lower urinary tract is one of the most complex biological systems of the human body as it involved hydrodynamic properties of urine and muscle. Moreover, its complexity is increased to be managed by voluntary and involuntary neural systems. In this paper, a mathematical model of the lower urinary tract it is proposed as a preliminary study to better understand its functioning. Furthermore, another goal of that mathematical model proposal is to provide a basis for developing artificial control systems. Lower urinary tract is comprised of two interacting systems: the mechanical system and the neural regulator. The latter has the function of controlling the mechanical system to perform the voiding process. The results of the tests reproduce experimental data with high degree of accuracy. Also, these results indicate that simulations not only with healthy patients but also of patients with dysfunctions with neurological etiology present urodynamic curves very similar to those obtained in clinical studies.

MINLP Model for the Synthesis of Heat Exchanger Networks with Handling Pressure of Process Streams

This paper introduces a new mathematical model for the simultaneous synthesis of heat exchanger networks (HENs), wherein the handling pressure of process streams is used to enhance the heat integration. The proposed approach combines generalized disjunctive programming (GDP) and mixed-integer nonlinear programming (MINLP) formulation, in order to minimize the total annualized cost composed by operational and capital expenses. A multi-stage superstructure is developed for the HEN synthesis, assuming constant heat capacity flow rates and isothermal mixing, and allowing for streams splits. In this model, the pressure and temperature of streams must be treated as optimization variables, increasing further the complexity and difficulty to solve the problem. In addition, the model allows for coupling of compressors and turbines to save energy. A case study is performed to verify the accuracy of the proposed model. In this example, the optimal integration between the heat and work decreases the need for thermal utilities in the HEN design. As a result, the total annualized cost is also reduced due to the decrease in the operational expenses related to the heating and cooling of the streams.

A numerical model for predicting shoreline changes /

A mathematical model for long-term, three-dimensional shoreline evolution is developed. The combined effects of variations of sea level; wave refraction and diffraction; loss of sand by density currents during storms, by rip currents, and by wind; bluff erosion and berm accretion; effects of manmade structures such as long groin or navigational structures; and beach nourishment are all taken into account. A computer program is developed with various subroutines which permit modification as the state-of-the-art progresses. The program is applied to a test case at Holland Harbor, Michigan. (Author).

Functional-structural plant modelling using a combination of architectural analysis, L-systems and a canonical model of function

This paper presents a new method for producing a functional-structural plant model that simulates response to different growth conditions, yet does not require detailed knowledge of underlying physiology. The example used to present this method is the modelling of the mountain birch tree. This new functional-structural modelling approach is based on linking an L-system representation of the dynamic structure of the plant with a canonical mathematical model of plant function. Growth indicated by the canonical model is allocated to the structural model according to probabilistic growth rules, such as rules for the placement and length of new shoots, which were derived from an analysis of architectural data. The main advantage of the approach is that it is relatively simple compared to the prevalent process-based functional-structural plant models and does not require a detailed understanding of underlying physiological processes, yet it is able to capture important aspects of plant function and adaptability, unlike simple empirical models. This approach, combining canonical modelling, architectural analysis and L-systems, thus fills the important role of providing an intermediate level of abstraction between the two extremes of deeply mechanistic process-based modelling and purely empirical modelling. We also investigated the relative importance of various aspects of this integrated modelling approach by analysing the sensitivity of the standard birch model to a number of variations in its parameters, functions and algorithms. The results show that using light as the sole factor determining the structural location of new growth gives satisfactory results. Including the influence of additional regulating factors made little difference to global characteristics of the emergent architecture. Changing the form of the probability functions and using alternative methods for choosing the sites of new growth also had little effect. (c) 2004 Elsevier B.V. All rights reserved.

Analysis of cardiac ventricular wall motion based on a three-dimensional electromechanical biventricular model

This paper describes a biventricular model, which couples the electrical and mechanical properties of the heart, and computer simulations of ventricular wall motion and deformation by means of a biventricular model. In the constructed electromechanical model, the mechanical analysis was based on composite material theory and the finite-element method; the propagation of electrical excitation was simulated using an electrical heart model, and the resulting active forces were used to calculate ventricular wall motion. Regional deformation and Lagrangian strain tensors were calculated during the systole phase. Displacements, minimum principal strains and torsion angle were used to describe the motion of the two ventricles. The simulations showed that during the period of systole, (1) the right ventricular free wall moves towards the septum, and at the same time, the base and middle of the free wall move towards the apex, which reduces the volume of the right ventricle; the minimum principle strain (E3) is largest at the apex, then at the middle of the free wall and its direction is in the approximate direction of the epicardial muscle fibres; (2) the base and middle of the left ventricular free wall move towards the apex and the apex remains almost static; the torsion angle is largest at the apex; the minimum principle strain E3 is largest at the apex and its direction on the surface of the middle wall of the left ventricle is roughly in the fibre orientation. These results are in good accordance with results obtained from MR tagging images reported in the literature. This study suggests that such an electromechanical biventricular model has the potential to be used to assess the mechanical function of the two ventricles, and also could improve the accuracy ECG simulation when it is used in heart torso model-based body surface potential simulation studies.