We propose a model of a density-dependent compressible-incompressible fluid, which is intended as a simplified version of models based on mixture theory as, for instance, those arising in the study of biofilms, tumor growth and vasculogenesis. Though our model is, in some sense, close to the density-dependent incompressible Euler equations, it presents some differences that require a different approach from an analytical point of view. In this paper, we establish a result of local existence and uniqueness of solutions in Sobolev spaces to our model, using the Leray projector. Besides, we show the convergence of both a continuous version of the Chorin-Temam projection method, viewed as a singular perturbation approximation, and the artificial compressibility method.

[object Object]Metals, extensively used in technology applications as well as in art metal works, have a chemical affinity for oxygen, water, sulphur and are particularly susceptible to electrochemical processes due to the environment. For this reason the monitoring of the effect of environmental conditions (temperature, humidity, pollutant concentration) on their mechanical and physical properties are considered a primary necessity for metal conservation and preservation. The complexity of the degradation phenomena requires to develop predictive tools, able to simulate involved chemical processes. In the present work a mathematical model, based on partial differential equation, is proposed. The model describes the evolution of corrosion processes, which occur on copper-tin alloy specimens exposed to sulphur dioxide atmosphere (SO 2 ).

Che differenza c'è tra un papiro e una pergamena? Che cos'è un palinsesto? In quale modo nell'antichità si conservavano i testi scritti? Sono domande importanti per la trasmissione della scienza e del sapere, sullo sfondo dello straordinario Archimede 2.0 di Giuseppe Palumbo. La storia appassionante e vera fino all'ultimo dettaglio di come le scoperte del genio di Siracusa sono arrivate sino a noi.

Cosa ha cambiato maggiormente la nostra vita negli ultimi 60 anni? Sicuramente il computer. Un'idea antica di uomini geniali come Pascal e Leibniz, tra gli altri. ...E di un signore forse meno conosciuto, Charles Babbage, che nella Londra vittoriana, in compagnia della brillante discepola Ada Lovelace, aveva progettato una "macchina analitica" che forse già assomigliava ai computer di oggi.

Laure Saint-Raymond is a French mathematician working in partial differential equations, fluid mechanics and statistical mechanics. She is a professor at École Normale Supérieure de Lyon. In 2008, she was awarded the EMS Prize and, in 2013, when she was 38 years old, she became the youngest member of the French Academy of Sciences.

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Infrared thermography is widely used in non-destructive testing and in the non-destructive evaluation of subsurface defects in several materials. The detection and reconstruction (location and shape) of a defect inside a material from thermal data requires the solution of an inverse heat conduction problem. Here the problem is tackled by the thin-plate approximation of the investigated domain. A number of physical quantities must be known for the reconstruction procedure to be successful: some relating to the material (thermal conductivity, heat capacity, density), usually known, and others relating to the heating process. This paper proposes procedures for accurately measuring the latter, whose importance is often not given due consideration. Those procedures allow us to accurately measure the heat flux distribution produced by the sources on the heated surface, and the heat exchange coefficient at the remaining surfaces, and are easily applicable in 'on field' situations.

Interleukin-6 (IL-6) has been recently shown to play a central role in glucose homeostasis, since it stimulates the production and secretion of Glucagon-like Peptide-1 (GLP-1) from intestinal L-cells and pancreas, leading to an enhanced insulin response. In resting conditions, IL-6 is mainly produced by the adipose tissue whereas, during exercise, skeletal muscle contractions stimulate a marked IL-6 secretion as well. Available mathematical models describing the effects of exercise on glucose homeostasis, however, do not account for this IL-6 contribution. This study aimed at developing and validating a system model of exercise's effects on plasma IL-6 dynamics in healthy humans, combining the contributions of both adipose tissue and skeletal muscle. A two-compartment description was adopted to model plasma IL-6 changes in response to oxygen uptake's variation during an exercise bout. The free parameters of the model were estimated by means of a cross-validation procedure performed on four different datasets. A low coefficient of variation (< 10%) was found for each parameter and the physiologically meaningful parameters were all consistent with literature data. Moreover, plasma IL-6 dynamics during exercise and post-exercise were consistent with literature data from exercise protocols differing in intensity, duration and modality. The model successfully emulated the physiological effects of exercise on plasma IL-6 levels and provided a reliable description of the role of skeletal muscle and adipose tissue on the dynamics of plasma IL-6. The system model here proposed is suitable to simulate IL-6 response to different exercise modalities. Its future integration with existing models of GLP-1-induced insulin secretion might provide a more reliable description of exercise's effects on glucose homeostasis and hence support the definition of more tailored interventions for the treatment of type 2 diabetes.

Results: Tests were performed to select the appropriate doses of vaccine and infectious bacteria to set up the model. Simulation outputs were compared with the specific antibody production and the expression of BcR and TcR gene transcripts in spleen. The model has shown a good ability to be used in sea bass and could be implemented for different routes of vaccine administration even with more than two pathogens. The model confirms the suitability of in silico methods to optimize vaccine doses and the immune response to them. This model could be applied to other species to optimize the design of new vaccination treatments of fish in aquaculture. Motivation: A computational model equipped with the main immunological features of the sea bass (Dicentrarchus labrax L.) immune system was used to predict more effective vaccination in fish. The performance of the model was evaluated by using the results of two in vivo vaccinations trials against L. anguillarum and P. damselae.

Fever plays a role in activating innate immunity while its relevance in activating adaptive immunity is less clear. Even brief exposure to elevated temperatures significantly impacts on the immunostimulatory capacity of dendritic cells (DCs), but the consequences on immune response remain unclear. To address this issue, we analyzed the gene expression profiles of normal human monocyte-derived DCs from nine healthy adults subjected either to fever-like thermal conditions (39 degrees C) or to normal temperature (37 degrees C) for 180 minutes. Exposure of DCs to 39 degrees C caused upregulation of 43 genes and downregulation of 24 genes. Functionally, the up/downregulated genes are involved in post-translational modification, protein folding, cell death and survival, and cellular movement. Notably, when compared to monocytes, DCs differentially upregulated transcription of the secreted protein IGFBP-6, not previously known to be specifically linked to hyperthermia. Exposure of DCs to 39 degrees C induced apoptosis/necrosis and resulted in accumulation of IGFBP-6 in the conditioned medium at 48 h. IGFBP-6 may have a functional role in the hyperthermic response as it induced chemotaxis of monocytes and T lymphocytes, but not of B lymphocytes. Thus, temperature regulates complex biological DC functions that most likely contribute to their ability to induce an efficient adaptive immune response.

Cyber insurance is a rapidly developing area which draws more and more attention of practitioners and researchers. Insurance, an alternative way to deal with residual risks, was only recently applied to the cyber world. The immature cyber insurance market faces a number of unique challenges on the way of its development.In this paper we summarise the basic knowledge about cyber insurance available so far from both market and scientific perspectives. We provide a common background explaining basic terms and formalisation of the area. We discuss the issues which make this type of insurance unique and show how different technologies are affected by these issues. We compare the available scientific approaches to analysis of cyber insurance market and summarise their findings with a common view. Finally, we propose directions for further advances in the research on cyber insurance.

We consider the mathematical modeling of the coupled mechanical-transport problem found in arterial physiopathology. The chapter provides an extensive description of the physiology and the microstructure of the arterial wall and explains how these are coupled to the molecular transport problem. The details of the most recent developments of the mechanistic descriptions of the multi-scale multi-physics are presented.

In this paper we investigate the extent to which variable porosity drug-eluting coatings can provide better control over drug release than coatings where the porosity is constant throughout. In particular, we aim to establish the potential benefits of replacing a single-layer with a two-layer coating of identical total thickness and initial drug mass. In our study, what distinguishes the layers (other than their individual thickness and initial drug loading) is the underlying microstructure, and in particular the effective porosity and the tortuosity of the material. We consider the effect on the drug release profile of varying the initial distribution of drug, the relative thickness of the layers and the relative resistance to diffusion offered by each layer's composition. Our results indicate that the contrast in properties of the two layers can be used as a means of better controlling the release, and that the quantity of drug delivered in the early stages can be modulated by varying the distribution of drug across the layers. We conclude that microstructural and loading differences between multi-layer variable porosity coatings can be used to tune the properties of the coating materials to obtain the desired drug release profile for a given application.

The topic of controlled drug release has received much attention in recent years, for example in the design of tablets and in local drug delivery devices such as stents, transdermal patches, therapeutic contact lenses and orthopaedic implants. In recent years, we have developed a series of models for such devices to describe drug release from a polymeric platform, drug transport in surrounding biological tissues and fully coupled models of them. These works have culminated in the development of the first mathematical model to demonstrate agreement with in-vivo drug release and tissue uptake data, for the case of a drug-eluting stent . If, on the one hand, these fully coupled models are indeed necessary to understand the spatio-temporal drug concentration in the surrounding environment, on the other hand it is clear that device manufacturers cannot intervene on the underlying biology. What they can control, however, are the properties of the polymeric platform to ensure the desired drug release profile is achieved. Indeed, the release profile is known to be a key predictor of device performance. Therefore, in the present work we take a step back from the fully coupled computational models and focus instead solely on the properties of the drug-containing coating. We consider two particular aspects of the drug coating design. Firstly, the delivery of two therapeutic agents, what we refer to as dual drug delivery. Depending on the particular application in question, it may be desirable for the drugs to be released at similar rates, or perhaps one of the drugs released rapidly with the other being eluted over a longer period of time. In the case of drug-eluting stents, for example, devices which release an anti-proliferative and a `pro-healing' drug have been proposed, whilst a combination of two of the early drug-eluting stent drugs - paclitaxel and sirolimus - has also been suggested. Secondly, motivated by today's advances in micro and nanotechnology, we propose variable porosity multi-layer coatings as an additional means of controlling the dual drug delivery.

In this paper we describe a theoretical mathematical model of dual drug delivery from a durable polymer coated medical device. We demonstrate how the release rate of each drug may in principle be controlled by altering the initial loading configuration of the two drugs. By varying the underlying microstructure of polymer coating, further control may be obtained, providing the opportunity to tailor the release profile of each drug for the given application.

We estimate the error of Gauss-Jacobi quadrature rule applied to a function f, which is supposed locally absolutely continuous in some Besov type spaces, or of bounded variation on [-1,1]. In the first case the error bound concerns the weighted main part phi-modulus of smoothness of f introduced by Z. Ditzian and V. Totik, while in the second case we deal with a Stieltjes integral with respect to f. The stated estimates generalize several error bounds from literature and, in both the cases, they assure the same convergence rate of the error of best polynomial approximation in weighted L-1 space. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.

In this paper we describe a combined in-vitro experimental and mathematical modelling approach to predict in-vivo drug-eluting stent kinetics. We coated stents with a mixture of sirolimus and a novel acrylic-based polymer in two different ratios. Our results indicate differential release kinetics between low and high drug dose formulations. Furthermore, mathematical model simulations of target receptor saturation suggest potential differences in efficacy.

Well-balanced schemes, nowadays well-known for 1D hyperbolic equations with source terms and systems of balance laws, are extended to strictly parabolic equations, first in 1D, then in 2D on Cartesian computational grids. The construction heavily relies on a particular type of piecewise-smooth interpolation of discrete data known as -splines. In 1D, several types of widely-used discretizations are recovered as particular cases, like the El-Mistikawy-Werle scheme or Scharfetter- Gummel's. Moreover, a distinctive feature of our 2D scheme is that dimensional-splitting never occurs within its derivation, so that all the multi-dimensional interactions are kept at the discrete level. This leads to improved accuracy, as illustrated on several types of drift-diffusion equations.

The numerical solution of reaction-diffusion systems modelling predator-prey dynamics using implicit-symplectic (IMSP) schemes is relatively new. When applied to problems with chaotic dynamics they perform well, both in terms of computational effort and accuracy. However, until the current paper, a rigorous numerical analysis was lacking. We analyse the semi-discrete in time approximations of a first-order IMSP scheme applied to spatially extended predator-prey systems. We rigorously establish semi-discrete a priori bounds that guarantee positive and stable solutions, and prove an optimal a priori error estimate. This analysis is an improvement on previous theoretical results using standard implicit-explicit (IMEX) schemes. The theoretical results are illustrated via numerical experiments in one and two space dimensions using fully-discrete finite element approximations.

Protected Areas are subject to long-term modifications associated with climate and environmental change, enhancing the risk of ecosystem collapse, tipping points and unexpected responses to droughts, fires, floods and other individual events. One of the goals of the EU H2020 Project ECOPOTENTIAL and of the GEO ECO Initiative of the Group on Earth Observations (GEO) is to quantify ongoing and expected changes in the drivers and the characteristics of Protected Areas in Europe and beyond, using gridded climatic datasets, in situ meteo-climatic and biological data and Remote Sensing observations. Several statistical approaches are used to this goal, with the aim of determining the patterns and properties of the changes currently affecting Protected Areas. Use of suitably downscaled climate scenarios allows for estimating how such changes are projected into the next decades. Here we report the results on the changes in meteo-climatic drivers and in some remotely-sensed variables for the set of Protected Areas participating in the ECOPOTENTIAL project, focusing on a few specific examples encompassing mountain, arid/semi-arid and coastal ecosystems.