Mathematical model for manoeuvrability of a riverine support patrol vessel with a pump-jet propulsion system

A study on the manoeuvrability of a riverine support patrol vessel is made to derive a mathematical model and simulate maneuvers with this ship. The vessel is mainly characterized by both its wide-beam and the unconventional propulsion system, that is, a pump-jet type azimuthal propulsion. By processing experimental data and the ship characteristics with diverse formulae to find the proper hydrodynamic coefficients and propulsion forces, a system of three differential equations is completed and tuned to carry out simulations of the turning test. The simulation is able to accept variable speed, jet angle and water depth as input parameters and its output consists of time series of the state variables and a plot of the simulated path and heading of the ship during the maneuver. Thanks to the data of full-scale trials previously performed with the studied vessel, a process of validation was made, which shows a good fit between simulated and full-scale experimental results, especially on the turning diameter

Hemodynamic performance of different stent strategies for coronary bifurcations. Evaluation with a mathematical model

Purpose: Best percutaneous treatment strategy for lesions in coronary bifurcations is an ongoing subject of debate. There is limited data that analyses the effect of the different bifurcation strategies on coronary flow. Our aim is to evaluate the influence of different bifurcation stenting strategies on hemodynamic parameters, both in the main vessel (MV) and side branch (SB).

A mathematical model of a criminal-prone society

Criminals are common to all societies. To fight against them the community takes different security measures as, for example, to bring about a police. Thus, crime causes a depletion of the common wealth not only by criminal acts but also because the cost of hiring a police force. In this paper, we present a mathematical model of a criminal-prone self-protected society that is divided into socio-economical classes. We study the effect of a non-null crime rate on a free-of-criminals society which is taken as a reference system. As a consequence, we define a criminal-prone society as one whose free-of-criminals steady state is unstable under small perturbations of a certain socio-economical context. Finally, we compare two alternative strategies to control crime: (i) enhancing police efficiency, either by enlarging its size or by updating its technology, against (ii) either reducing criminal appealing or promoting social classes at risk

Applicability of the GP Device to the Circle of Willis Arteries by Using a Mathematical Model

According to the World Health Organization, 15 million people suffer stroke worldwide each year, of these, 5 million die and 5 million are permanently disabled. Stroke is therefore a major cause of mortality world-wide. The majority of strokes are caused by a blood clot that occludes an artery in the brain, and although thrombolytic agents such as Alteplase are used to dissolve clots that arise in the arteries of the brain, there are limitations on the use of these thrombolytic agents. However over the past decade, other methods of treatment have been developed which include Thrombectomy Devices e.g. the 'GP' Thrombus Aspiration Device ('GP' TAD). Such devices may be used as an alternative to thrombolytics or in conjunction with them to extract blood clots in arteries such as the middle cerebral artery of the midbrain brain, and the posterior inferior cerebellar artery (PICA) of the posterior aspect of the brain. In this paper, we mathematically model the removal of blood clots using the 'GP' TAD from selected arteries of the brain where blood clots may arise taking into account factors such as the resistances, compliances and inertances effects. Such mathematical modelling may have potential uses in predicting the pressures necessary to extract blood clots of given lengths, and masses from arteries in the Circle of Willis - posterior circulation of the brain

On a mathematical model arising in MHD perturbed equilibrium for Stellarator devices. A numerical approach.

Abstract?We consider a mathematical model related to the stationary regime of a plasma of fusion nuclear, magnetically confined in a Stellarator device. Using the geometric properties of the fusion device, a suitable system of coordinates and averaging methods, the mathematical problem may be reduced to a two dimensional free boundary problem of nonlocal type, where the corresponding differential equation is of the Grad?Shafranov type. The current balance within each flux magnetic gives us the possibility to define the third covariant magnetic field component with respect to the averaged poloidal flux function. We present here some numerical experiences and we give some numerical approach for the averaged poloidal flux and for the third covariant magnetic field component.

Criteria for mathematical model selection for satellite vibro-acoustic analysis depending on frequency range

Satellites and space equipment are exposed to diffuse acoustic fields during the launch process. The use of adequate techniques to model the response to the acoustic loads is a fundamental task during the design and verification phases. Considering the modal density of each element is necessary to identify the correct methodology. In this report selection criteria are presented in order to choose the correct modelling technique depending on the frequency ranges. A model satellite’s response to acoustic loads is presented, determining the modal densities of each component in different frequency ranges. The paper proposes to select the mathematical method in each modal density range and the differences in the response estimation due to the different used techniques. In addition, the methodologies to analyse the intermediate range of the system are discussed. The results are compared with experimental testing data obtained in an experimental modal test.

Asymptotic stability of a mathematical model of cell population

We consider a simplified system of a growing colony of cells described as a free boundary problem. The system consists of two hyperbolic equations of first order coupled to an ODE to describe the behavior of the boundary. The system for cell populations includes non-local terms of integral type in the coefficients. By introducing a comparison with solutions of an ODE's system, we show that there exists a unique homogeneous steady state which is globally asymptotically stable for a range of parameters under the assumption of radially symmetric initial data.

On a mathematical model of tumor growth based on cancer stem cells

We consider a simple mathematical model of tumor growth based on cancer stem cells. The model consists of four hyperbolic equations of first order to describe the evolution of different subpopulations of cells: cancer stem cells, progenitor cells, differentiated cells and dead cells. A fifth equation is introduced to model the evolution of the moving boundary. The system includes non-local terms of integral type in the coefficients. Under some restrictions in the parameters we show that there exists a unique homogeneous steady state which is stable.

A simple mathematical model that describes the growth of the area and the number of total and viable cells in yeast colonies

We propose a model, based on the Gompertz equation, to describe the growth of yeasts colonies on agar medium. This model presents several advantages: (i) one equation describes the colony growth, which previously needed two separate ones (linear increase of radius and of the squared radius); (ii) a similar equation can be applied to total and viable cells, colony area or colony radius, because the number of total cells in mature colonies is proportional to their area; and (iii) its parameters estimate the cell yield, the cell concentration that triggers growth limitation and the effect of this limitation on the specific growth rate. To elaborate the model, area, total and viable cells of 600 colonies of Saccharomyces cerevisiae, Debaryomyces fabryi, Zygosaccharomyces rouxii and Rhodotorula glutinis have been measured. With low inocula, viable cells showed an initial short exponential phase when colonies were not visible. This phase was shortened with higher inocula. In visible or mature colonies, cell growth displayed Gompertz-type kinetics. It was concluded that the cells growth in colonies is similar to liquid cultures only during the first hours, the rest of the time they grow, with near-zero specific growth rates, at least for 3 weeks.

Experimental Model to estimate shading losses on PV arrays

This paper presents a simple mathematical model to estimateshadinglosses on PVarrays. The model is applied directly to power calculations, without the need to consider the whole current–voltage curve. This allows the model to be used with common yield estimation software. The model takes into account both the shaded fraction of the array area and the number of blocks (a group of solar cells protected by a bypass diode) affected by shade. The results of an experimental testing campaign on several shaded PVarrays to check the validity of model are also reported.

Experimental model to estimate shading losses on PV arrays

This paper presents a simple mathematical model to estimate shading losses on PV arrays. The model is applied directly to power calculations, without the need to consider the whole current–voltage curve. This allows the model to be used with common yield estimation software. The model takes into account both the shaded fraction of the array area and the number of blocks (a group of solar cells protected by a bypass diode) affected by shade. The results of an experimental testing campaign on several shaded PV arrays to check the validity of model are also reported.

A mathematical framework for finite strain elastoplastic consolidation. Part 1: Balance laws, variational formulation, and linearization

A mathematical formulation for finite strain elasto plastic consolidation of fully saturated soil media is presented. Strong and weak forms of the boundary-value problem are derived using both the material and spatial descriptions. The algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the Kirchhoff pore water pressure. Balance laws are written for the soil-water mixture following the motion of the soil matrix alone. It is shown that the motion of the fluid phase only affects the Jacobian of the solid phase motion, and therefore can be characterized completely by the motion of the soil matrix. Furthermore, it is shown from energy balance consideration that the effective, or intergranular, stress is the appropriate measure of stress for describing the constitutive response of the soil skeleton since it absorbs all the strain energy generated in the saturated soil-water mixture. Finally, it is shown that the mathematical model is amenable to consistent linearization, and that explicit expressions for the consistent tangent operators can be derived for use in numerical solutions such as those based on the finite element method.

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.