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The present work aims at analyzing issues related to the data manifold dimensionality. The interest of the study is twofold: (i) first, when too many measurable variables are considered, manifold learning is expected to extract useless variables; (ii) second, and more important, the same technique, manifold learning, could be utilized for identifying the necessity of employing latent extra variables able to recover single-valued outputs. Both aspects are discussed in the modeling of materials and structural systems by using unsupervised manifold learning strategies. The first, third, and fourth authors are supported by their respective ESI Group research chairs; their support is gratefully acknowledged. The first author is supported by CREATE-ID ESI-ENSAM research chair. The third author is supported by the ESI Group Chair at the University of Zaragoza. The fourth author is supported by CREATE-ID ESI-ENSAM research chair.

International audience; In the recent years, automotive car industry is evolving towards a new generation of autonomous vehicles, where decision making is not fully perform by the driver but it partially relies on the technology of the car itself. Indeed, a CPU inside the car will process all information coming from the sensors, distinguishing different scenarios appearing in the real life and ultimately allowing decision making. Since the CPU will be confronted with plenty of information, tools like machine learning or big-data analysis will be a useful ally to separate data from information. These existing machine learning techniques, such as kernel Principal Component Analysis (k-PCA), Locally Linear Embedding (LLE) among many other techniques, are useful to unveil the latent parameters defining a given scenario. Indeed, these algorithms have been already used to perform real-time classification of signals appearing throughout the road. Selecting the modeling of the electromagnetic response of the radar plays an important role to achieve real time constraints. Even though Helmholtz equation represents accurately the physics, the computational cost of such simulation is not affordable for real-time applications due to high radar operating frequencies, resulting into a very fine finite element mesh. On the other hand, far field approaches are not so accurate when the objects are very close due to plane wave assumption. In the first part of this work, the Geometrical Optics method is investigated in this work as a possible route to fulfill both real-time and accuracy constraints. The main hypothesis under such model is that waves are treated as straight lines constrained to optical reflection laws. Therefore, there is no need to mesh the interior of the domain. However, the accuracy of such approach is compromised when the size of the objects inside the domain are comparable to the wave lengths or in the vicinity of angular points. The second part is mainly focused on of the application of manifold learning and big data analysis into a data set of precomputed scenarios. Indeed, the identification of an unknown scenario from electromagnetic signals is purchased. Nevertheless, current research lines are devoted to give an answer to questions such as how many receptors do we need to identify unequivocally the scenario, where to locate the receptors, or which parts of the scenario have a negligible impact in the electromagnetic response.

Upscaling behaviors of heterogeneous microstructures to define macroscopic effective media is of major interest in many areas of computational mechanics, in particular those related to materials and processes engineering. In this paper, we explore the possibility of defining a macroscopic behavior manifold from microscopic calculations, and then use it directly for efficiently performing manifold-based simulations at the macroscopic scale. We consider in this work upscaling of non-Newtonian flows in porous media, and more particularly the ones involving short-fibre suspensions.

The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy, $$\ldots $$ ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.

International audience; The present paper analyzes different integration schemes of solid dynamics in the frequency domain involving the so-called Proper Generalized Decomposition-PGD. The last framework assumes for the solution a parametric dependency with respect to frequency. This procedure allowed introducing other parametric dependences related to loading, geometry, and material properties. However, in these cases, affine decompositions are required for an efficient computation of separated representations. A possibility for circumventing such difficulty consists in combining modal and harmonic analysis for defining an hybrid integration scheme. Moreover, such a procedure, as proved in the present work, can be easily generalized to address nonlinear parametric dynamics, as well as to solve problems with non-symmetric stiffness matrices, always operating in the domain of low frequencies.

International audience; Compressed sensing is a signal compression technique with very remarkable properties. Among them, maybe the most salient one is its ability of overcoming the Shannon–Nyquist sampling theorem. In other words, it is able to reconstruct a signal at less than 2Q samplings per second, where Q stands for the highest frequency content of the signal. This property has, however, important applications in the field of computational mechanics, as we analyze in this paper. We consider a wide variety of applications, such as model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction. Examples are provided for all of them that show the potentialities of compressed sensing in terms of CPU savings in the field of computational mechanics.

International audience; Many electrical and structural components are constituted of a stacking of multiple thin layers with different electromagnetic, mechanical and thermal properties. When 3D descriptions become compulsory the approximation of the fields along the thickness direction could involve thousands of nodes. To circumvent the numerical difficulties that such a rich description imply, we recently propose an in-plane–out-of-plane separated representation with the aim of computing fully 3D solutions as a sequence of 2D problems defined in the plane and others (1D) in the thickness. The main contribution of the present work is the proposal of an efficient in-plane–out-of-plane separated representation of the double-curl formulation of Maxwell equations able to address thin-layer laminates while ensuring the continuity and discontinuity of the tangential and normal electric field components respectively at the plies interface

Standard simulation in classical mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy, ...), whereas the second one consists of models that scientists have extracted from collected, natural or synthetic data. Even if one can be confident on the first type of equations, the second one contains modeling errors. Moreover, this second type of equations remains too particular and often fails in describing new experimental results. The vast majority of existing models lack of generality, and therefore must be constantly adapted or enriched to describe new experimental findings. In this work we propose a new method, able to directly link data to computers in order to perform numerical simulations. These simulations will employ axiomatic, universal laws while minimizing the need of explicit, often phenomenological, models. This technique is based on the use of manifold learning methodologies, that allow to extract the relevant information from large experimental datasets.

The purpose of this paper is to combine a classical 1D twin-screw extrusion model with machine learning techniques to obtain accurate predictions of a complex system despite few data. Systems involving reactive polyethylene oligomer dispersed in situ in a polypropylene matrix by reactive twin-screw extrusion are studied for this purpose. The twin-screw extrusion simulation software LUDOVIC is used and machine learning techniques dealing with low data limit are used as a correction of the simulation. This research was funded by the French ANR through the DataBEST project.

International audience; This paper analyzes the ability of different machine learning techniques, able to operate in the low-data limit, for constructing the model linking material and process parameters with the properties and performances of parts obtained by reactive polymer extrusion. The use of data-driven approaches is justified by the absence of reliable modeling and simulation approaches able to predict induced properties in those complex processes. The experimental part of this work is based on the in situ synthesis of a thermoset (TS) phase during the mixing step with a thermoplastic polypropylene (PP) phase in a twin-screw extruder. Three reactive epoxy/amine systems have been considered and anhydride maleic grafted polypropylene (PP-g-MA) has been used as compatibilizer. The final objective is to define the appropriate processing conditions in terms of improving the mechanical properties of these new PP materials by reactive extrusion.

[EN]: There is a strong relationship between bird wing morphology and flight style. Wing shapes are related to manoeuvrability, flight speed, energetic costs during flight and take-off speed. Wing shape differences among species have been frequently studied but differences can also be found within species, between sexes and age groups. Many studies have assessed differences in wing shape between juveniles and adults in different passerine species but little is known about such differences in other bird orders. Performing a Size Constrained Components Analysis (SCCA) and a graphical approximation, we analysed the wing shape of juveniles and adults of eight species, including four passerines and four non-passerines of three different orders. According to a graphical approximation, we observed that wing shape differences between age groups differ among species. In the non-passerine species considered, juveniles have more pointed and concave wings than adults. In contrast, in the four passerine species, juveniles have more rounded wings than adults. However, the results for the C2 axis of SCCA (index of pointedness) do not completely agree with the graphical approximation. Our results showed that the C2 axis does not represent the same vector of wing shape variation in all species. The contribution of changes in C2 to variation in wing pointedness seemed to depend on the position of the wing tip, which is a good index of pointedness only when the wing tip is in the two most distal primary feathers. Surprisingly, the adults of some species do not have longer wings than the corresponding juveniles, because the feathers that define the wing tip do not grow longer during the first complete moult. We discuss the role of the first complete moult in changing the shape of juvenile wings into adult wings, and the implications of our results for the analysis of bird wing shape. [ES]: Existe una fuerte relación entre la morfología alar y el estilo de vuelo de un ave. La forma del ala está relacionada con la maniobrabilidad, la velocidad de vuelo, los costes energéticos durante el vuelo o la velocidad de despegue. Las diferencias en la forma del ala entre especies han sido estudiadas con frecuencia, pero también existen diferencias dentro de una especie, entre sexos y grupos de edad. Muchos estudios han evaluado las diferencias en la forma alar entre juveniles y adultos en diferentes especies de paseriformes, pero se sabe poco acerca de las diferencias en la forma alar entre grupos de edad en otros órdenes de aves. Realizando un análisis SCCA (‘Size Constrained Components Analysis’) y una aproximación gráfica, analizamos la forma alar de juveniles y adultos de ocho especies, cuatro paseriformes y cuatro no paseriformes de tres órdenes diferentes. De acuerdo con la aproximación gráfica, observamos que las diferencias en la forma alar entre grupos de edad difieren entre especies. En las especies de no paseriformes estudiadas, los juveniles tienen alas más puntiagudas y cóncavas que los adultos. En contraste, en las cuatro especies de paseriformes, los juveniles tienen alas más redondeadas que los adultos. Sin embargo, los resultados del eje C2 del SCCA no concuerdan completamente con la aproximación gráfica. nuestros resultados mostraron que el eje C2 no representa el mismo vector de variación de la forma del ala en todas las especies. La contribución de los cambios en C2 a la variación del apuntamiento del ala parece depender de la posición de la punta del ala, siendo un buen índice de apuntamiento solo cuando la punta del ala está en las dos plumas primarias más distales. Sorprendentemente, los adultos de algunas especies no tienen alas más largas que los respectivos juveniles, debido a que la pluma que define la punta del ala no tiene un incremento de tamaño durante la primera muda completa. Describimos cómo la primera muda completa es clave en el cambio de la morfología alar entre el ala de los juveniles y el ala de los adultos, y discutimos las implicaciones de nuestros resultados en relación con el análisis de la forma de las alas de las aves. Xabier Cabodevilla was supported by a PhD Grant, financed by the Basque Country Government (Grant no. PRE_2018_2_0273).

The use of constitutive equations calibrated from data collected from adequate testing has been implemented successfully into standard solvers for successfully addressing a variety of problems encountered in SBES (simulation based engineering sciences). However, the complexity remains constantly increasing due to the more and more fine models being considered as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in classical mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy...), whereas the second one consists of models that scientists have extracted from collected, natural or synthetic data. Data-driven simulation consists of directly linking data to computers in order to perform numerical simulations. These simulations will use universal laws while minimizing the need of explicit, often phenomenological, models. This work revisits our former work on data-driven computational linear and nonlinear elasticity and the rationale is extended for addressing computational inelasticity (viscoelastoplasticity).

International audience; The present paper extends in-plane-out-of-plane separated representations successfully used for addressing fully 3D model solutions defined in plate-like domain, to dynamics. Common time integration are performed using explicit or implicit strategies. Even if the implementation of implicit integration schemes into a 3D in-plane-out-of-plane separated representation does not imply major difficulties, the use of explicit integration preferable in many applications becomes a tricky issue. In fact the mesh employed for discretizing the out-of-plane dimension (thickness) determines the maximum time-step ensuring stability. In this paper we introduce a new efficient hybrid explicit/implicit in-plane-out-of-plane separated representation for dynamic problems defined in plate-like domains that allows computing 3D solutions with the stability constraint exclusively determined by the coarser in-plane discretization.

International audience; Sparse model identification by means of data is especially cumbersome if the sought dynamics live in a high dimensional space. This usually involves the need for large amount of data, unfeasible in such a high dimensional settings. This well-known phenomenon, coined as the curse of dimensionality, is here overcome by means of the use of separate representations. We present a technique based on the same principles of the Proper Generalized Decomposition that enables the identification of complex laws in the low-data limit. We provide examples on the performance of the technique in up to ten dimensions.

This is a post-peer-review, pre-copyedit version of an article published in International journal of material forming. The final authenticated version is available online at: http://dx.doi.org/10.1007/s12289-018-1417-4 The numerical modelling of forming processes involving the flow of foams requires taking into account the different problem scales. Thus, in industrial applications a macroscopic approach is suitable, whereas the macroscopic flow parameters depend on the cellular structure: cell size, shape, orientation, etc. Moreover, the shape and orientation of the cells are induced by the flow. A fully microscopic description remains useful to understand the foam behaviour and the topological changes induced by the cell elongation or distortion, however, from an industrial point of view, microscopic simulations remain challenging to address practical applications involving flows in complex 3D geometries. In this paper, we propose a viscoelastic flow model where the foam microstructure is represented from suitable microstructure descriptors whose evolution is governed by the macroscopic flow kinematics.

International audience; In recent times a growing interest has arose on the development of data-driven techniques to avoid the employ of phenomenological constitutive models. While it is true that, in general, data do not fit perfectly to existing models, and present deviations from the most popular ones, we believe that this does not justify (or, at least, not always) to abandon completely all the acquired knowledge on the constitutive characterization of materials. Instead, what we propose here is, by means of machine learning techniques, to develop correction to those popular models so as to minimize the errors in constitutive modeling.

Thermoplastic composites are widely considered in structural parts. In this paper attention is paid to squeeze flow of continuous fiber laminates. In the case of unidirectional prepregs, the ply constitutive equation is modeled as a transversally isotropic fluid, that must satisfy both the fiber inextensibility as well as the fluid incompressibility. When laminate is squeezed the flow kinematics exhibits a complex dependency along the laminate thickness requiring a detailed velocity description through the thickness. In a former work the solution making use of an in-plane-out-of-plane separated representation within the PGD – Poper Generalized Decomposition – framework was successfully accomplished when both kinematic constraints (inextensibility and in-compressibility) were introduced using a penalty formulation for circumventing the LBB constraints. However, such a formulation makes difficult the calculation on fiber tractions and compression forces, the last required in rheological characterizations. In this paper the former penalty formulation is substituted by a mixed formulation that makes use of two Lagrange multipliers, while addressing the LBB stability conditions within the separated representation framework, questions never until now addressed.

Microwave (MW) technology relies on volumetric heating. Thermal energy is transferred to the material that can absorb it at specific frequencies. In this paper, a coupled thermic and electromagnetic model is proposed in order to simulate the emerging process of microwave heating for composite materials. Solving the problem in a laminated composite material requires a high degree of discretization in the thickness direction which is made possible by introducing the in-plane-out-of-plane decomposition approach using the Proper Generalized Decomposition (PGD).

Standard simulation in classical mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy, ...), whereas the second one consists of models that scientists have extracted from collected, natural or synthetic data. In this work we propose a new method, able to directly link data to computers in order to perform numerical simulations. These simulations will employ universal laws while minimizing the need of explicit, often phenomenological, models. They are based on manifold learning methodologies.

Thermoplastic composites are widely considered in structural parts. In this paper attention is paid to sheet forming of continuous fiber laminates. In the case of unidirectional prepregs, the ply constitutive equation is modeled as a transversally isotropic fluid, that must satisfy both the fiber inextensibility as well as the fluid incompressibility. When the stacking sequence involves plies with different orientations the kinematics of each ply during the laminate deformation varies significantly through the composite thickness. In our former works we considered two different approaches when simulating the squeeze flow induced by the laminate compression, the first based on a penalty formulation and the second one based on the use of Lagrange multipliers. In the present work we propose an alternative approach that consists in modeling each ply involved in the laminate as a transversally isotropic fluid – TIF - that becomes 2D as soon as incompressibility constraint and plane stress assumption are taken into account. Thus, composites laminates can be analyzed as a stacking of 2D TIF models that could eventually interact by using adequate friction laws at the inter-ply interfaces.

The study of the electrostatic interactions in the ultrafiltration of single model proteins is an important topic for the biotechnology industry interested in the fractionation of protein mixtures. In this paper, the dynamics of the ultrafiltration of β-lactoglobulin and lysozyme through a 300 kDa tubular ceramic membrane was investigated. The time evolution of permeate flux and protein transmission were determined at a temperature of 30 °C, a cross-flow velocity of 3.5 m/s and a transmembrane pressure of 100 kPa. The influence of pH was monitored in the 3–9 interval for β-lactoglobulin and in the 5–12 interval for lysozyme. The effect of ionic strength was studied by increasing the addition of NaCl up to 15 mM. The curves of permeate flux were discussed according to the resistances in series model. Since β-lactoglobulin and lysozyme have acid and alkaline isoelectric points, respectively, the results showed different responses with respect to the electrostatic environment.

The availability of pediatric formulations of hepatitis A virus (HAV) vaccines would facilitate the introduction of universal mass vaccination against HAV. The objective of this study was to compare a pediatric dose (0.25 mL) of Epaxal, a virosomal, aluminum-free HAV vaccine, to 0.5 mL standard dose, and to alum-adsorbed HAV vaccine.Subjects aged 1-16 years, stratified for age, were randomized (2:2:1) into group A (0.25 mL Epaxal), group B (0.5 mL Epaxal), or group C (Havrix Junior). Vaccines were administered at months 0, 6. Seroprotection rates (or=10 mIU/mL anti-HAV antibodies) were assessed for noninferiority, defined as lower limit of 1-sided 97.5% CI-10%. Incidence of local solicited adverse events and unsolicited adverse events were recorded.Mean age of 308 enrolled subjects was 8.9 years (range, 1.0-17.0 years). All 3 vaccines were highly immunogenic. Noninferiority of group A versus group B and group C with regard to seroprotection was demonstrated after both vaccine doses for the entire study group and for all age subgroups (11-23 months, 2-4, 5-7, 8-10, 11-13, 14-16 years). One month after first vaccination, geometric mean antibody concentrations were 69.0, 83.5, and 50.5 mIU/mL for the 3 groups, respectively (A versus B, P = 0.0208; A versus C, P = 0.0015). Local injection site pain occurred more frequently in group C than in groups A and B. No subjects withdrew from study or reported any vaccine-related serious adverse event.In children aged 1-16 years, 0.25 mL dose of Epaxal is as immunogenic as standard 0.5 mL dose and Havrix Junior. The aluminum-free vaccine compares favorably to comparator vaccine regarding local reactogenicity.

In this paper, the influence of pH in the 4–8 interval and NaCl concentration up to 25 mM on the cross-flow microfiltration of BSA was investigated. A tubular ceramic membrane with a pore size of 0.14 μm was employed and its point of zero charge was calculated. The evolution of permeate flow and BSA transmission with time was determined at 45 °C, a cross-flow velocity of 3.5 m/s and a transmembrane pressure of 100 kPa. The curves of permeate flow were explained according to the resistances in series model. Maximum protein transmission was obtained at the isoelectric point of BSA (4.9), with significant transmission also at the point of zero charge of the membrane and null transmission at pH 4 and 8. The highest permeate flow was observed at pH 7 and the lowest at 4.9. Finally, the addition of salt resulted to some extent in an improvement of both protein transmission and permeate flow.

Travellers increasingly require hepatitis A virus (HAV) vaccine for overseas travel to highly endemic areas. While the inactivated HAV vaccines currently in use are all highly immunogenic, studies have shown the aluminium-free, virosome-adjuvanted vaccine Epaxal to possess a superior local tolerability profile. The objective of this study was to analyse the pattern of local reactions caused by the aluminium-free Epaxal compared with an aluminium-adjuvanted HAV vaccine.Subjects recruited from travel health centres were randomised in a 4:1 ratio to receive a single dose of either Epaxal or Havrix vaccine. Vaccinees noted adverse reactions on a 7-day diary card that was returned by mail to the centre.529 adults (or =16 years) were vaccinated, and 413 (78.1%) subjects returned diary cards, 338 (76.5%) in the Epaxal group and 75 (86.2%) in the Havrix group. Subjects reported fewer local adverse reactions for Epaxal (23.4% vs. 57.3%; p0.0001). Injection site pain categorised as Grade 2 (painful on movement) or Grade 3 (spontaneously painful) (4.7% vs. 22.7%, p=0.0001) was less frequent in the Epaxal group and resolved more quickly (or =3 days of pain, 8.6% vs. 22.7%, p=0.0001).The lower reactogenicity of the virosome-adjuvanted vaccine is an important feature for travellers.

soni, parasite des colonies d'abeilles. Le developpement de la resistance des populations de Varroa jacobsoni et le spectre de la contamination des produits du rucher ont fortement stimule la mise au point de nouvelles strategies de traitement qui diminuent la possibilite d'un developpement rapide de la resistance et l'accumulation de residus. Cet article passe en revue l'utilisation des huiles essentielles (h.e.) et de leurs composants dans la lutte contre V. jacobsoni. « Huiles essentielles » est un terme generique qui designe les composants liquides et hautement volatiles des plantes, marques par une odeur forte et caracteristique. Les terpenes (principalement les monoterpenes) representent la majeure partie (environ 90 %) de ces composants. L'eucalyptol, le camphre, le-menthol et le thymol sont des monoterpenes typiques. Chaque espece de plante tend a avoir une composition en h.e. unique. Pourtant, certaines especes ont des varietes denommees chemotypes, dont la composition en h.e. varie. On a utilise les methodes de criblage au laboratoire pour tester sur V. jacobsoni et sur les abeilles la toxicite, la repulsivite, l'attractivite, ainsi que les effets sur la reproduction, des h.e. et de leurs composants. Au total, c'est plus de 150 h.e. et composants d'h.e. qui ont ete testes (tableaux I-III), mais peu d'entre eux se sont montres efficaces lors de leur utilisation sur ruches en conditions de terrain. Une variation enorme des conditions du milieu local et des colonies, ainsi que la difficulte d'obtenir des h.e. standardisees, rendent difficile la prevision du resultat des nombreux traitements. Les residus dans le miel peuvent conduire a des effets negatifs sur le gout. L'analyse quantitative des residus est exigee pour l'enregistrement du produit. La nature complexe de beaucoup d'h.e. et le fait que de nombreux composants des h.e. sont presents a l'etat naturel dans le miel font que l'analyse des residus est difficile. Neanmoins ces difficultes disparaissent lorsqu'on utilise individuellement les composants des h.e. La plupart sont volatils et disponibles sur le marche a prix raisonnables. Parmi tous les composants testes des h.e., c'est le thymol qui a eu le meilleur resultat en apiculture pratique, Dans les essais en champ le thymol pur (tableau IV) et les melanges a base de thymol (tableau V) ont montre une activite varroacide elevee. Le thymol est bien tolere par les abeilles. Si les traitements sont effectues en dehors de la periode de miellee, les residus de thymol dans le miel n'augmentent pas lorsqu'on multiplie les traitements et restent sous le seuil de detection gustative, qui se situe entre 1,1 et 1,6 mg.kg -1 . Selon les etudes on a trouve iles residus compris entre 0,02 et 0,48 mg.kg -1 . Mais les traitements au thymol pendant la miellee peuvent conduire a des residus plus eleves qui modifient le gout du miel. Le thymol, de meme que d'autres monoterpenes tels que le menthol et le camphre, ont le statut GRAS (generally recognized as safe, generalement reconnu comme sans danger), de la FAO aux concentrations allant jusqu'a 50 mg.kg -1 . Les residus de ces substances dans le miel ne posent donc pas de probleme toxicologique. Apres un traitement au thymol les residus dans la cire sont 1 000 fois plus eleves que dans le miel, mais ils diminuent rapidement par evaporation des que le traitement est arrete.

A wide collection of proteins in relatively low concentrations but with an important biological activity is present in bovine whey. Among them, lactoferrin shows strong bacterial and antiviral properties, preventing the growth of pathogenic organisms in the gut, stimulating the immune system and enhancing iron absorption [1]. Lactoferrin recovery from whey is therefore of great interest since it can be used in the development of improved infant formula, functional foods and nutraceuticals. To this end, methods have been devised employing, for instance, surfactant-stabilized microbubbles [2] or ion exchage chromatography [3]. In the field of membrane technology, high performance tangential flow [4] filtration has been suggested as a feasible technique to allow the separation of lactoferrin at industrial scale [5]. In this work, the effect of pH in the selectivity of lactoferrin ultrafiltration through a ceramic membrane with respect to the major whey proteins has been studied. The results obtained are useful to design an optimal strategy to exploit the electrostatic protein–membrane interactions that takes place in this process. 2. Experimental

The final publication is available at Springer via http://dx.doi.org/10.1007/s12289-016-1309-4 Thermoplastic composites are widely considered in structural parts. In this paper attention is paid to squeeze flow of continuous fiber laminates. In the case of unidirectional prepregs, the ply constitutive equation is modeled as a transversally isotropic fluid, that must satisfy both the fiber inextensibility as well as the fluid incompressibility. When laminate is squeezed the flow kinematics exhibits a complex dependency along the laminate thickness requiring a detailed velocity description through the thickness. In a former work the solution making use of an in-plane-out-of-plane separated representation within the PGD – Poper Generalized Decomposition – framework was successfully accomplished when both kinematic constraints (inextensibility and incompressibility) were introduced using a penalty formulation for circumventing the LBB constraints. However, such a formulation makes difficult the calculation on fiber tractions and compression forces, the last required in rheological characterizations. In this paper the former penalty formulation is substituted by a mixed formulation that makes use of two Lagrange multipliers, while addressing the LBB stability conditions within the separated representation framework, questions never until now addressed.

This is the peer reviewed version of the following article: Ibáñez, R. [et al.]. Multiscale proper generalized decomposition based on the partition of unity. "International journal for numerical methods in engineering", 9 November 2019, vol. 120, núm. 6, p. 727-747, which has been published in final form at DOI: 10.1002/nme.6154. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Solutions of partial differential equations could exhibit a multiscale behavior. Standard discretization techniques are constraints to mesh up to the finest scale to predict accurately the response of the system. The proposed methodology is based on the standard proper generalized decomposition rationale; thus, the PDE is transformed into a nonlinear system that iterates between microscale and macroscale states, where the time coordinate could be viewed as a 2D time, representing the microtime and macrotime scales. The macroscale effects are taken into account because of an FEM-based macrodiscretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the domain. The proposed methodology can be seen as an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors.