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This paper presents a mathematical model capable to reproduce a celebrated phenomenon in blood microcirculation known as Fåhræus effect, since its discovery by Robin Fåhræus (1929). This consists in a decaying of the relative hematocrit in small vessels as the vessel diameter decreases. The key point of the model is a formula, direct consequence of the basic principles of fluid dynamics, that links the relative hematocrit to the reservoir hematocrit and the vessel diameter, which confirms the observed behavior. To test the model we selected, among the few experiments carried on since then, those performed by Barbee and Cokelet (1971). The agreement is remarkable. An extended comparison is also carried out with a celebrated empirical formula proposed by Pries et al. (1992) to describe the same phenomenon.

We consider the flow of blood, treated as an incompressible Newtonian fluid, through vessels undergoing periodic oscillations. As remarked by many authors, in the absence of valves oscillations hinder the flow because of the lumen reduction. The underlying biological mechanism is the so-called vasomotion, observed long ago in small blood vessels. Here, we study the vasomotion in arterioles and provide its theoretical justification by analyzing the effect when the network of vessels downstream of the arterioles is considered. We thus explain both quantitatively and qualitatively, why the oscillations of the arteriole walls, a phenomenon that undoubtedly reduces blood flow at the level of the single arteriole, play a fundamental role in microcirculation. In "large" arterioles we analyze also the coupling between the vasomotion and the Fåhræus-Lindqvist effect (the tendency of the erythrocytes to accumulate towards the center). In particular, we prove that the presence of a cell depleted layer close to the vessel walls mitigates the disadvantage caused by the lumen reduction.

In this paper, the constrained thrust allocation problem is studied and solved for the class of over-actuated Remotely Operated Vehicles. In detail, we find the solution of the thrust allocation when the thrusters are affected by possible faults and, simultaneously, taking into account the thrusters’ saturation limits. The proposed thrust allocation algorithm is tested both numerically, with randomly generated input samples, and applied in simulation for the trajectory tracking of a Remotely Operated Vehicle, with real parameters and in combination with different control laws. The algorithm is compared with two commonly used approaches, that are the saturated pseudo-inverse method and the Matlab Quadratic Programming solver; both accuracy and computation time are considered in the analysis of the performances. The simulations show that the proposed algorithm performs better, in terms of computation time, w.r.t. the Matlab Quadratic Programming solver, while still retaining the optimality of the solution despite the saturation constraints; moreover, there is also an improvement in the tracking error regardless of the adopted control law.

An active failure and fault tolerant control scheme for an underwater remotely operated vehicle is proposed in this work. The proposed solution is based on a fault tolerant allocation, which takes into account an estimate of the faults on the vehicle’s thrusters for an accurate redistribution of the control effort. The diagnosis is based on a sliding mode observer, which generates three residuals and allows to evaluate the health condition of each actuator of the vehicle. The scheme can be adapted to any control law for the vehicle dynamics, and has been tested in simulation using a backstepping controller for the dynamics and with real world parameters, demonstrating the effectiveness of the proposed active fault tolerant control scheme.

Neurotoxic chemicals including several pesticides have been suggested to play a role in the etiology of amyotrophic lateral sclerosis (ALS). We investigated the relation between organochlorine pesticides and their metabolites (OCPs), polychlorinated biphenyls (PCBs) and polycyclic aromatic hydrocarbons (PAHs) in the etiology of sporadic ALS, determining for the first time their levels in cerebrospinal fluid as indicator of antecedent exposure. We recruited 38 ALS patients and 38 controls referred to an Italian clinical center for ALS care, who underwent a lumbar puncture for diagnostic purposes between 1994-2013, and had 1mL of cerebrospinal fluid available for the determination of OCPs, PCBs and PAHs. Many chemicals were undetectable in both case and control CSF samples, and we found little evidence of any increased disease risk according to higher levels of exposure. Among males >60 years, we found a slight but statistically very unstable increased ALS risk with higher levels of the congener PCB 28 and the OCP metabolite p,p'-DDE. Overall, these results do not suggest an involvement of the neurotoxic chemicals investigated in this study in disease etiology, although small numbers limited the precision of our results.

We study the flow of a viscous fluid through a slender tapered tube whose radius may reduce to zero. The vessel is closed at the end, so that the flow is made possible owing to the fact that a portion of the tube wall is permeable. The smallness of the tube aspect ratio is exploited using an upscaling technique leading to a degenerate differential equation for pressure. Solutions are found either in explicit form or as power series expansions. This class of flows may represent, though in a largely approximated way, the blood flow though a coronary artery.

The role of cancer stem cells (CSC) in tumour growth has received increasing attention in the recent literature. Here we stem from an integro-differential system describing the evolution of a population of CSC and of ordinary (non-stem) tumour cells formulated and studied in a previous paper, and we investigate an approximation in which the system reduces to a pair of nonlinear coupled parabolic equation. We prove that the new system is well posed and we examine some general properties. Numerical simulations show more on the qualitative behaviour of the solutions, concerning in particular the so-called tumour paradox, according to which an increase of the mortality rate of ordinary (non-stem) tumour cells results asymptotically in a faster growth.

Purpose. The paper analyses the impact of active management styles on portfolios’ risk-return profiles, in a country specific — the BRIC market area — and in the integrated context. Our aim is to see how and if the local and global results differ and if we can outline a BRIC specific consistent behaviour. Methodology. First, we identify formally the notion of active management as an investment policy focusing on specific assets/styles; therefore we measure this concentration a) in terms of the portfolio distance from a diversified index and b) with respect to the (opposite notion of) portfolio style breadth . Given these assumptions, to test empirically how the active policies affect the fund performances we propose to use the R-square as a diversification reverse proxy . The rationale behind is that the more the fund’s tracking error the more the fund wealth is focused on a given industry or sector, and therefore on few assets, deviating from a passive portfolio strategy replicating the benchmark. Thereafter we propose to reimplement Grinold’s qualitative notion of breadth. To approximate the breadth of the fund strategies, we consider the number of factors in a predictive model to which the funds are exposed. In particular, with a factor model we investigate whether being exposed to multiple factors simultaneously is important for improving performance. Finally we assess the impact of the local risk factors, by ranking local/global portfolios through the Spearman correlation of both symmetric (Sharpe ratio) and asymmetric (Sortino-Satchel ratio, Farinelli-Tibiletti ratio) risk measures. Results. The main finding of the paper is that, contrary to similar works, not related to BRIC markets, we do not find a sound relationship between concentration and performance. This is true whether we measure the concentration in terms of higher tracking error levels or we consider portfolio concentration in terms of breadth of strategies. Based on these findings, investors called for picking for best-performing funds should take into account that the Fundamental Law of Active Management is not always true in BRIC context. As for the impact of local risk factors the rank correlation analysis between the local risk benchmark and global risk index, shows that there are some specific local factor effects coupled to the change of ratios’ benchmark. We also find that Farinelli-Tibiletti ratio, among our RAP measures, is the one exhibiting more consistent behaviour for the cross-country ranking analysis. The theoretical contribution. Some original, while grounded in the literature, approaches are introduced with respect to the study of active investment policies. Results are presented contrasting the BRIC regions with the global context, which might add new evidence to the literature of domestic CAPM and helps identifying BRIC pricing behaviours. Practical implications Traders and portfolio managers committed to active investment strategies can find new evidences concerning the implications and formal effects of these policies, particularly with respect to BRIC or BRIC focused funds. Keywords: BRIC Markets, Active Investment, Performance, Alpha, Risk. Paper type : Research paper.

In Fasano et al. (2012) a new reduced mathematical model for blood coagulation was proposed, incorporating biochemical and mechanical actions of blood flow and including platelets activity. The model was characterized by a considerable simplification of the differential system associated to the biochemical network and it incorporated the role of blood slip at the vessel wall as an extra source of activated platelets. The purpose of this work is to check the validity of the reduced mathematical model, using as a benchmark the model presented in Anand et al. (2008) , and to investigate the importance of the blood slip velocity in the blood coagulation process.

This paper presents a preliminary set of results on the design of a virtual thruster-based failure tolerant control scheme for underwater vehicles. The proposed control scheme is based on the use of a suitable thruster allocation algorithm, which consists on a modified version of the Moore-Penrose pseudo inverse. When a thruster experencies a failure, the “virtual” thruster concept is introduced, as an ideal faultless thruster that operates in places of the real failed one. Thus, the resulting thrust force, which should be allocated to the failed actuator (i.e., virtual thrust), is instead reallocated to the still functional thrusters. A bank of controllers is built so that each controller is designed to control the considered underwater vehicle under a specific actuator failure scenario.

Baseline wander is a low-frequency additive noise affecting almost all bioelectrical signals, in particular the ECG. In this paper, we propose a novel approach to baseline wander estimation and removal for bioelectrical signals, based on the notion of quadratic variation reduction. The quadratic variation is meant as a measure of variability for vectors or sampled functions, and is a consistent measure in this regard. Baseline wander is estimated solving a constrained convex optimization problem where quadratic variation enters as a constraint. The solution depends on a single parameter whose value is not critical, as proven by a sensitivity analysis. Numerical results confirm the effectiveness of the approach, which outperforms state-of-the-art algorithms. The algorithm compares favorably also in terms of computational complexity, which is linear in the size of the vector to detrend. This makes it suitable for real-time applications as well as for applications on devices with reduced computing power, such as handheld devices.

In this paper we consider the problem of state estimation for linear discrete-time non-Gaussian systems with random observation matrices. This is the model for systems with observation losses due to propagation through unreliable communication channels. Losses may result from intermittent failures that cause packet dropouts, as in the case of networks, or fading phenomena in propagation channel, as in the case of wireless networks. These are common problems in wireless sensor network, or networked control systems. In this paper, we do not make any assumption about the distribution of the observation matrix, thus encompassing a great variety of possible scenarios. We derive the quadratic estimate of the state by means of a recursive algorithm. The solution is obtained by applying the Kalman filter to a suitably augmented system, which is fully observable. The augmented system is constructed as the aggregate of the actual system and the observable part of a system having as state the second Kronecker power of the original state, namely the quadratic system. To extract the observable part of the quadratic system we exploit the knowledge of the rank of the corresponding observability matrix. This approach guarantees the internal stability of the estimation filter.

We study the laminar flow of binary liquid mixture, whose components are a Newtonian fluid (solvent) and a solute, in a hollow fiber. The fiber walls are porous, but the pores size is small enough preventing the solute molecules to be transported across the membrane. This produces an osmotic pressure that offers resistance (in many cases non negligible) to the fluid cross flow. We model the phenomenon by means of a two scale procedure, introducing a small parameter e ≪ 1 (the ratio between the radius and the length of the fiber) and expanding all relevant quantities in powers of e . Thus, considering just the e 0 order approximation, we obtain a set of two equations governing both the solute concentration and the pressure along the fibers. Performing some numerical simulations we point out the critical importance of the osmosis in order to make the device working properly.

This paper presents the results of a study aimed at estimating the efficiency of the ultrafiltration process for the treatment of secondary effluents to be reused in wet textile industries. This approach was experienced at pilot scale at Baciacavallo wastewater treatment plant in Prato (Italy). During the experimental trials the membrane filtration process was optimized in terms of running time, backwash, chemicals addition, cleaning procedures and running cost. A transmembrane pressure of 270 mbar and a hydraulic permeability of 200 l/(h bar m 2 ) were ensured. According to the experimental results the treatment guaranteed the compliance with the target values for wastewater reuse in wet textile industries. Mathematical tools were used to simulate the efficiency of the hydraulic properties, showing different behaviors of the filters by varying the process parameters (such as filtration time and flux), so that the selection of the best configuration can be approached easier and faster. The process was optimized both in terms of volume of treated water and energy costs, providing an accurate procedure to improve the filter performance: an example of application is reported, where the volume of treated water can be increased by 43% reducing the 45.5% of the energy cost.

We formulate a mathematical model for a geothermal basin with an idealized geometry characterized by: (1) radial symmetry around an extracting well (or a cluster of wells), (2) a relatively thin horizontal fractured layer lying underneath a low permeability, low porosity rock layer, saturated with water. Vaporization is allowed only at the boundary of the extracting well (or well cluster). The model is based on the assumption that the flow from the reservoir to the well is fed by a gravity driven flow through the overstanding rocks. Despite the various simplifying assumptions, the resulting mathematical problem is considerably difficult also because we consider the effect of thermal expansion and thermal variation of viscosity. Though there is no evidence that the assumed configuration of the basin approaches the structure of a known geothermal field, the results obtained match with surprising accuracy the data of a specific field in the Mt. Amiata area (data kindly provided by ENEL Green Power through Tuscany Region).

The aim of this paper is to propose a very simple way of computing the quantities relevant to the lifetime of a granular active carbon (GAC) filter. Our analysis is based on a sorption law, which, being linear separately in the adsorbed and non-adsorbed pollutant concentrations, allows the explicit computation of solutions in the form of a travelling wave. It is then easy to realize that, if the wave speed is much smaller than the advection velocity in the filter (as it happens in usual cases), then the travelling wave is an excellent approximation of the real profile of the pollutant concentration. The model is calibrated using laboratory experiments on a reduced scale. A linear stability analysis of the travelling waves is performed. Phenomena of diffusion–dispersion are neglected, however their effects are considered in the last sections, showing when they are really negligible and how they may influence the wave shape. The case of more pollutant species competing for the same adsorption sites on the GAC is also considered.

We illustrate a mathematical model for the evolution of multicellular tumour spheroids in a host tissue, including the effect of the excess H + ions and the nutrient dynamics. Both the avascular and the vascular case are considered. The model is a nontrivial generalization of the simple scheme proposed in [K. Smallbone, D.J. Gavaghan, R.A. Gatenby, P.K. Maini, The role of acidity in solid tumour growth and invasion, J. Theoret. Biol. 235 (2005) 476–484]. Many different situations may occur, depending on the values of the physical parameters involved. Existence of solutions and qualitative properties are investigated.

This work is concerned with a reaction-diffusion system that has been proposed as a model to describe acid-mediated cancer invasion. More precisely, we consider the properties of travelling waves that can be supported by such a system, and show that a rich variety of wave propagation dynamics, both fast and slow, is compatible with the model. In particular, asymptotic formulae for admissible wave profiles and bounds on their wave speeds are provided.

The aim of this paper is to give a contribution within the mathematical modelling of the deformation and breakup of a droplet in a continuous immiscible liquid phase in impulsively started shear flow. Starting from the results of Cristini et al. [V. Cristini, S. Guido, A. Alfani, J. Blawzdziewicz, M. Loewenberg, Drop breakup and fragment distribution in shear flow, J. Rheol. 47 (5) (2003) 1283–1298] we extrapolate a general scheme for the whole breakage process, on the basis of which we formulate a procedure for the computation of the size distribution function at the end of the process.

We present a non-trivial generalization of the one-dimensional model proposed in [A. Fasano, A. Mancini, A mathematical model for a class of frying processes, Comput. Math. Appl. (2007) (doi:10.1016/j.camwa.2006.02.046) (in press)] with several purposes. The first goal is to consider a multidimensional case (so that, for instance, the model can be applicable to French fries). We want also to provide a more realistic description of the mechanism of transport of liquid water within the sample, considering the effect of capillarity.

In this paper we show how to obtain wax diffusivity and solubility values in crude oils from deposition measurements in the cold finger device with stirring. Providing a rather accurate knowledge of such quantities is of great importance in predicting the wax deposition rate in pipelines. We present a mathematical model in which the physical quantities are assumed to be space-independent in the bulk region of the device, because of agitation, so that mass transport occur in relatively thin boundary layers. As a consequence the deposition phenomenon is accelerated with respect to the static device (see [S. Correra, A. Fasano, L. Fusi, M. Primicerio, F. Rosso. Wax diffusivity under given thermal gradient: a mathematical model, to appear on ZAMM]), shortening the duration of experiments. Comparison with some available laboratory measurements shows a satisfactory agreement and the values obtained are in the range of those usually adopted by practitioners.

The model for the evolution of a liquid–liquid dispersion including the so-called volume scattering effect introduced by the authors in [A. Fasano, F. Rosso, A new model for the dynamics of dispersions in a batch reactor, in: H.J. Bungartz, R.H.W. Hoppe, C. Zenger (Eds.), Proceedings of the Symposium Organized by the Sonderforschungsbereich 438 on the Occasion of Karl-Heinz Hoffman’s 60th Birthday, in: Lectures in Applied Mathematics, Springer Verlag, Berlin, 2000, pp. 123–141] and incorporating multiple breakage –see [A. Fasano, F. Rosso, Dynamics of droplets in an agitated dispersion with multiple breakage. I. Formulation of the model and physical consistency, Math. Methods Appl. Sci. 28 (6) (2005) 631–659; A. Fasano, F. Rosso, Dynamics of droplets in an agitated dispersion with multiple breakage. II. Uniqueness and global existence, Math. Methods Appl. Sci. 28 (9) (2005) 1061–1088]–is considered from a viewpoint closer to applications. The choice of kernels is discussed on the basis of the technical literature (not just using very abstract kernels like in most mathematical papers) and simulations are performed utilizing data from different sources.

this paper, we investigate the formation of tumour cords (cylindrical arrangements of tumour cells around blood vessels) within a tumour tissue. The shrinkage and the expansion of the cord following a stepwise decrease or, respectively, increase of oxygen tension in the blood vessel are also described. The model represents the tumour cell population as a continuum and includes two novel aspects with respect to our previous works: cell death does not occur instantaneously, but is preceded by a reversible prenecrotic state; the recruitment of cells from quiescence into proliferation may require a recovery period. Model predictions are compared with experimental data reported by Hirst et al. [1].

This paper deals with the modelling of the rain water infiltration through the soil above the aquifer in case of runoff of the excess water. The main feature of the model lies on the correct definition of the boundary condition on the ground surface. The latter allows to estimate, after saturation, the real amount of the water that penetrates the soil and the one which runs off. The quantity playing a key role is the so-called rain pressure, defined as the pressure exerted by the rain on the soil. Although its importance is basically theoretical and it can be neglected for practical purposes, it helps understanding the real evolution of the physical problem, providing a theoretical justification of the empirical procedures.

A mathematical model is developed that describes the proliferative behaviour at the stationary state of the cell population within a tumour cord, i.e.~in a cylindrical arrangement of tumour cells growing around a blood vessel and surrounded by necrosis. The model, that represents the tumour cord as a continuum, accounts for the migration of cells from the inner to the outer zone of the cord and describes the cell cycle by a sequence of maturity compartments plus a possible quiescent compartment. Cell-to-cell variability of cycle phase transit times and changes in the cell kinetic parameters within the cord, related to changes of the microenvironment, can be represented in the model. The theoretical predictions are compared against literature data of the time course of the labelling index (LI) and of the fraction of labelled mitoses (FLM) in an experimental tumour after pulse labelling with 3H-thymidine. It is shown that the presence of cell migration within the cord can lead to a marked underestimation of the actual changes along cord radius of the kinetics of cell cycle progression.

We analyse the relationship between large cap returns and sentiment indexes, using a Capital Asset Pricing Model (CAPM) framework. We try to provide a better explanation of asset prices and their deviations from standard theories by means of sentiment indicators, assuming the latter being measures of the very inclination to speculate. Therefore, when sentiment is high, investor demand for speculative investment is high; conversely when it is low, investor demand for speculative investments is low. Unlike other studies, based on proxies, we use the European Sentiment Indicator and its constituents, based on direct surveys, to assess business and consumer confidence.

Waxy crude oils are, at low temperatures, highly non-Newtonian fluids. The crystallization of wax seems to be the cause of their non-Newtonian behavior. Moreover, the flow properties show time-dependence indicating an evolution of the structure with continued shear (termed ''thixotropy''). In this paper, on the basis of the experimental data, we have developed a physical model which tries to describe the low temperature behavior of waxy crudes in laboratory experimental loops. The correspondent mathematical problem has been investigated performing a quasisteady approximation which we have shown to be physically consistent.

The influence of thermophysical property variations on the resulting temperature fields is investigated with reference to quasilinear heat-conduction problems. Both theoretical and experimental evidence is produced to show that errors in the calculation of temperature distributions, brought about by an inaccurate estimate of thermal properties, are small if approximate heat capacities, even exhibiting large local differences with respect to the actual ones in a small range of temperatures, retain enthalpy variations and if the integral across the whole working temperature interval of the absolute value of the difference between approximate and actual thermal conductivities is small. Then the practical relevance of these results is pointed out with reference to freezing and thawing processes of biological materials whose thermal coefficients vary sharply over the phase change zone, where only mean values of thermophysical properties can be easily measured.

A three-time level implicit scheme, which is unconditionally stable and convergent, is employed for the numerical solution of phase-change problems, on the basis of an analytical approach consisting in the approximation of the latent heat effect by a large heat capacity over a small temperature range. Since the temperature dependent coefficients in the resulting parabolic equations are evaluated at the intermediate time level, the complication of solving a set of nonlinear algebraic equations at each time step is avoided. The numerical results thus obtained are satisfactorily compared with the available analytical solutions.