Higher-Order Concurrency: Expressiveness and Decidability Results

Higher-order process calculi are formalisms for concurrency in which processes can be passed around in communications. Higher-order (or process-passing) concurrency is often presented as an alternative paradigm to the first order (or name-passing) concurrency of the pi-calculus for the description of mobile systems. These calculi are inspired by, and formally close to, the lambda-calculus, whose basic computational step ---beta-reduction--- involves term instantiation. The theory of higher-order process calculi is more complex than that of first-order process calculi. This shows up in, for instance, the definition of behavioral equivalences. A long-standing approach to overcome this burden is to define encodings of higher-order processes into a first-order setting, so as to transfer the theory of the first-order paradigm to the higher-order one. While satisfactory in the case of calculi with basic (higher-order) primitives, this indirect approach falls short in the case of higher-order process calculi featuring constructs for phenomena such as, e.g., localities and dynamic system reconfiguration, which are frequent in modern distributed systems. Indeed, for higher-order process calculi involving little more than traditional process communication, encodings into some first-order language are difficult to handle or do not exist. We then observe that foundational studies for higher-order process calculi must be carried out directly on them and exploit their peculiarities. This dissertation contributes to such foundational studies for higher-order process calculi. We concentrate on two closely interwoven issues in process calculi: expressiveness and decidability. Surprisingly, these issues have been little explored in the higher-order setting. Our research is centered around a core calculus for higher-order concurrency in which only the operators strictly necessary to obtain higher-order communication are retained. We develop the basic theory of this core calculus and rely on it to study the expressive power of issues universally accepted as basic in process calculi, namely synchrony, forwarding, and polyadic communication.

Designing and Programming Organizational Infrastructures for Agents situated in Artifact-based Environments

Actual trends in software development are pushing the need to face a multiplicity of diverse activities and interaction styles characterizing complex and distributed application domains, in such a way that the resulting dynamics exhibits some grade of order, i.e. in terms of evolution of the system and desired equilibrium. Autonomous agents and Multiagent Systems are argued in literature as one of the most immediate approaches for describing such a kind of challenges. Actually, agent research seems to converge towards the definition of renewed abstraction tools aimed at better capturing the new demands of open systems. Besides agents, which are assumed as autonomous entities purposing a series of design objectives, Multiagent Systems account new notions as first-class entities, aimed, above all, at modeling institutional/organizational entities, placed for normative regulation, interaction and teamwork management, as well as environmental entities, placed as resources to further support and regulate agent work. The starting point of this thesis is recognizing that both organizations and environments can be rooted in a unifying perspective. Whereas recent research in agent systems seems to account a set of diverse approaches to specifically face with at least one aspect within the above mentioned, this work aims at proposing a unifying approach where both agents and their organizations can be straightforwardly situated in properly designed working environments. In this line, this work pursues reconciliation of environments with sociality, social interaction with environment based interaction, environmental resources with organizational functionalities with the aim to smoothly integrate the various aspects of complex and situated organizations in a coherent programming approach. Rooted in Agents and Artifacts (A&A) meta-model, which has been recently introduced both in the context of agent oriented software engineering and programming, the thesis promotes the notion of Embodied Organizations, characterized by computational infrastructures attaining a seamless integration between agents, organizations and environmental entities.

Architectures and design patterns for functional design of logic control and diagnostics in industrial automation

Recently in most of the industrial automation process an ever increasing degree of automation has been observed. This increasing is motivated by the higher requirement of systems with great performance in terms of quality of products/services generated, productivity, efficiency and low costs in the design, realization and maintenance. This trend in the growth of complex automation systems is rapidly spreading over automated manufacturing systems (AMS), where the integration of the mechanical and electronic technology, typical of the Mechatronics, is merging with other technologies such as Informatics and the communication networks. An AMS is a very complex system that can be thought constituted by a set of flexible working stations, one or more transportation systems. To understand how this machine are important in our society let considerate that every day most of us use bottles of water or soda, buy product in box like food or cigarets and so on. Another important consideration from its complexity derive from the fact that the the consortium of machine producers has estimated around 350 types of manufacturing machine. A large number of manufacturing machine industry are presented in Italy and notably packaging machine industry,in particular a great concentration of this kind of industry is located in Bologna area; for this reason the Bologna area is called “packaging valley”. Usually, the various parts of the AMS interact among them in a concurrent and asynchronous way, and coordinate the parts of the machine to obtain a desiderated overall behaviour is an hard task. Often, this is the case in large scale systems, organized in a modular and distributed manner. Even if the success of a modern AMS from a functional and behavioural point of view is still to attribute to the design choices operated in the definition of the mechanical structure and electrical electronic architecture, the system that governs the control of the plant is becoming crucial, because of the large number of duties associated to it. Apart from the activity inherent to the automation of themachine cycles, the supervisory system is called to perform other main functions such as: emulating the behaviour of traditional mechanical members thus allowing a drastic constructive simplification of the machine and a crucial functional flexibility; dynamically adapting the control strategies according to the different productive needs and to the different operational scenarios; obtaining a high quality of the final product through the verification of the correctness of the processing; addressing the operator devoted to themachine to promptly and carefully take the actions devoted to establish or restore the optimal operating conditions; managing in real time information on diagnostics, as a support of the maintenance operations of the machine. The kind of facilities that designers can directly find on themarket, in terms of software component libraries provides in fact an adequate support as regard the implementation of either top-level or bottom-level functionalities, typically pertaining to the domains of user-friendly HMIs, closed-loop regulation and motion control, fieldbus-based interconnection of remote smart devices. What is still lacking is a reference framework comprising a comprehensive set of highly reusable logic control components that, focussing on the cross-cutting functionalities characterizing the automation domain, may help the designers in the process of modelling and structuring their applications according to the specific needs. Historically, the design and verification process for complex automated industrial systems is performed in empirical way, without a clear distinction between functional and technological-implementation concepts and without a systematic method to organically deal with the complete system. Traditionally, in the field of analog and digital control design and verification through formal and simulation tools have been adopted since a long time ago, at least for multivariable and/or nonlinear controllers for complex time-driven dynamics as in the fields of vehicles, aircrafts, robots, electric drives and complex power electronics equipments. Moving to the field of logic control, typical for industrial manufacturing automation, the design and verification process is approached in a completely different way, usually very “unstructured”. No clear distinction between functions and implementations, between functional architectures and technological architectures and platforms is considered. Probably this difference is due to the different “dynamical framework”of logic control with respect to analog/digital control. As a matter of facts, in logic control discrete-events dynamics replace time-driven dynamics; hence most of the formal and mathematical tools of analog/digital control cannot be directly migrated to logic control to enlighten the distinction between functions and implementations. In addition, in the common view of application technicians, logic control design is strictly connected to the adopted implementation technology (relays in the past, software nowadays), leading again to a deep confusion among functional view and technological view. In Industrial automation software engineering, concepts as modularity, encapsulation, composability and reusability are strongly emphasized and profitably realized in the so-calledobject-oriented methodologies. Industrial automation is receiving lately this approach, as testified by some IEC standards IEC 611313, IEC 61499 which have been considered in commercial products only recently. On the other hand, in the scientific and technical literature many contributions have been already proposed to establish a suitable modelling framework for industrial automation. During last years it was possible to note a considerable growth in the exploitation of innovative concepts and technologies from ICT world in industrial automation systems. For what concerns the logic control design, Model Based Design (MBD) is being imported in industrial automation from software engineering field. Another key-point in industrial automated systems is the growth of requirements in terms of availability, reliability and safety for technological systems. In other words, the control system should not only deal with the nominal behaviour, but should also deal with other important duties, such as diagnosis and faults isolations, recovery and safety management. Indeed, together with high performance, in complex systems fault occurrences increase. This is a consequence of the fact that, as it typically occurs in reliable mechatronic systems, in complex systems such as AMS, together with reliable mechanical elements, an increasing number of electronic devices are also present, that are more vulnerable by their own nature. The diagnosis problem and the faults isolation in a generic dynamical system consists in the design of an elaboration unit that, appropriately processing the inputs and outputs of the dynamical system, is also capable of detecting incipient faults on the plant devices, reconfiguring the control system so as to guarantee satisfactory performance. The designer should be able to formally verify the product, certifying that, in its final implementation, it will perform itsrequired function guarantying the desired level of reliability and safety; the next step is that of preventing faults and eventually reconfiguring the control system so that faults are tolerated. On this topic an important improvement to formal verification of logic control, fault diagnosis and fault tolerant control results derive from Discrete Event Systems theory. The aimof this work is to define a design pattern and a control architecture to help the designer of control logic in industrial automated systems. The work starts with a brief discussion on main characteristics and description of industrial automated systems on Chapter 1. In Chapter 2 a survey on the state of the software engineering paradigm applied to industrial automation is discussed. Chapter 3 presentes a architecture for industrial automated systems based on the new concept of Generalized Actuator showing its benefits, while in Chapter 4 this architecture is refined using a novel entity, the Generalized Device in order to have a better reusability and modularity of the control logic. In Chapter 5 a new approach will be present based on Discrete Event Systems for the problemof software formal verification and an active fault tolerant control architecture using online diagnostic. Finally conclusive remarks and some ideas on new directions to explore are given. In Appendix A are briefly reported some concepts and results about Discrete Event Systems which should help the reader in understanding some crucial points in chapter 5; while in Appendix B an overview on the experimental testbed of the Laboratory of Automation of University of Bologna, is reported to validated the approach presented in chapter 3, chapter 4 and chapter 5. In Appendix C some components model used in chapter 5 for formal verification are reported.

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

Hybrid portable systems for bio-nanosensors

The promising development in the routine nanofabrication and the increasing knowledge of the working principles of new classes of highly sensitive, label-free and possibly cost-effective bio-nanosensors for the detection of molecules in liquid environment, has rapidly increased the possibility to develop portable sensor devices that could have a great impact on many application fields, such as health-care, environment and food production, thanks to the intrinsic ability of these biosensors to detect, monitor and study events at the nanoscale. Moreover, there is a growing demand for low-cost, compact readout structures able to perform accurate preliminary tests on biosensors and/or to perform routine tests with respect to experimental conditions avoiding skilled personnel and bulky laboratory instruments. This thesis focuses on analysing, designing and testing novel implementation of bio-nanosensors in layered hybrid systems where microfluidic devices and microelectronic systems are fused in compact printed circuit board (PCB) technology. In particular the manuscript presents hybrid systems in two validating cases using nanopore and nanowire technology, demonstrating new features not covered by state of the art technologies and based on the use of two custom integrated circuits (ICs). As far as the nanopores interface system is concerned, an automatic setup has been developed for the concurrent formation of bilayer lipid membranes combined with a custom parallel readout electronic system creating a complete portable platform for nanopores or ion channels studies. On the other hand, referring to the nanowire readout hybrid interface, two systems enabling to perform parallel, real-time, complex impedance measurements based on lock-in technique, as well as impedance spectroscopy measurements have been developed. This feature enable to experimentally investigate the possibility to enrich informations on the bio-nanosensors concurrently acquiring impedance magnitude and phase thus investigating capacitive contributions of bioanalytical interactions on biosensor surface.

Development and characterization of micromachined devices for separation techniques

Nowadays microfluidic is becoming an important technology in many chemical and biological processes and analysis applications. The potential to replace large-scale conventional laboratory instrumentation with miniaturized and self-contained systems, (called lab-on-a-chip (LOC) or point-of-care-testing (POCT)), offers a variety of advantages such as low reagent consumption, faster analysis speeds, and the capability of operating in a massively parallel scale in order to achieve high-throughput. Micro-electro-mechanical-systems (MEMS) technologies enable both the fabrication of miniaturized system and the possibility of developing compact and portable systems. The work described in this dissertation is towards the development of micromachined separation devices for both high-speed gas chromatography (HSGC) and gravitational field-flow fractionation (GrFFF) using MEMS technologies. Concerning the HSGC, a complete platform of three MEMS-based GC core components (injector, separation column and detector) is designed, fabricated and characterized. The microinjector consists of a set of pneumatically driven microvalves, based on a polymeric actuating membrane. Experimental results demonstrate that the microinjector is able to guarantee low dead volumes, fast actuation time, a wide operating temperature range and high chemical inertness. The microcolumn consists of an all-silicon microcolumn having a nearly circular cross-section channel. The extensive characterization has produced separation performances very close to the theoretical ideal expectations. A thermal conductivity detector (TCD) is chosen as most proper detector to be miniaturized since the volume reduction of the detector chamber results in increased mass and reduced dead volumes. The microTDC shows a good sensitivity and a very wide dynamic range. Finally a feasibility study for miniaturizing a channel suited for GrFFF is performed. The proposed GrFFF microchannel is at early stage of development, but represents a first step for the realization of a highly portable and potentially low-cost POCT device for biomedical applications.

Coordination and Control of Autonomous Mobile Robots Swarms by using Particle Swarm Optimization Algorithm and Consensus Theory

This thesis presents some different techniques designed to drive a swarm of robots in an a-priori unknown environment in order to move the group from a starting area to a final one avoiding obstacles. The presented techniques are based on two different theories used alone or in combination: Swarm Intelligence (SI) and Graph Theory. Both theories are based on the study of interactions between different entities (also called agents or units) in Multi- Agent Systems (MAS). The first one belongs to the Artificial Intelligence context and the second one to the Distributed Systems context. These theories, each one from its own point of view, exploit the emergent behaviour that comes from the interactive work of the entities, in order to achieve a common goal. The features of flexibility and adaptability of the swarm have been exploited with the aim to overcome and to minimize difficulties and problems that can affect one or more units of the group, having minimal impact to the whole group and to the common main target. Another aim of this work is to show the importance of the information shared between the units of the group, such as the communication topology, because it helps to maintain the environmental information, detected by each single agent, updated among the swarm. Swarm Intelligence has been applied to the presented technique, through the Particle Swarm Optimization algorithm (PSO), taking advantage of its features as a navigation system. The Graph Theory has been applied by exploiting Consensus and the application of the agreement protocol with the aim to maintain the units in a desired and controlled formation. This approach has been followed in order to conserve the power of PSO and to control part of its random behaviour with a distributed control algorithm like Consensus.

Many-Core Architectures: Hardware-Software Optimization and Modeling Techniques

During the last few decades an unprecedented technological growth has been at the center of the embedded systems design paramount, with Moore’s Law being the leading factor of this trend. Today in fact an ever increasing number of cores can be integrated on the same die, marking the transition from state-of-the-art multi-core chips to the new many-core design paradigm. Despite the extraordinarily high computing power, the complexity of many-core chips opens the door to several challenges. As a result of the increased silicon density of modern Systems-on-a-Chip (SoC), the design space exploration needed to find the best design has exploded and hardware designers are in fact facing the problem of a huge design space. Virtual Platforms have always been used to enable hardware-software co-design, but today they are facing with the huge complexity of both hardware and software systems. In this thesis two different research works on Virtual Platforms are presented: the first one is intended for the hardware developer, to easily allow complex cycle accurate simulations of many-core SoCs. The second work exploits the parallel computing power of off-the-shelf General Purpose Graphics Processing Units (GPGPUs), with the goal of an increased simulation speed. The term Virtualization can be used in the context of many-core systems not only to refer to the aforementioned hardware emulation tools (Virtual Platforms), but also for two other main purposes: 1) to help the programmer to achieve the maximum possible performance of an application, by hiding the complexity of the underlying hardware. 2) to efficiently exploit the high parallel hardware of many-core chips in environments with multiple active Virtual Machines. This thesis is focused on virtualization techniques with the goal to mitigate, and overtake when possible, some of the challenges introduced by the many-core design paradigm.

Systems medicine and integrated care to combat chronic noncommunicable diseases

We propose an innovative, integrated, cost-effective health system to combat major non-communicable diseases (NCDs), including cardiovascular, chronic respiratory, metabolic, rheumatologic and neurologic disorders and cancers, which together are the predominant health problem of the 21st century. This proposed holistic strategy involves comprehensive patient-centered integrated care and multi-scale, multi-modal and multi-level systems approaches to tackle NCDs as a common group of diseases. Rather than studying each disease individually, it will take into account their intertwined gene-environment, socio-economic interactions and co-morbidities that lead to individual-specific complex phenotypes. It will implement a road map for predictive, preventive, personalized and participatory (P4) medicine based on a robust and extensive knowledge management infrastructure that contains individual patient information. It will be supported by strategic partnerships involving all stakeholders, including general practitioners associated with patient-centered care. This systems medicine strategy, which will take a holistic approach to disease, is designed to allow the results to be used globally, taking into account the needs and specificities of local economies and health systems.

Farming Systems and Resilience Building in a Changing Climate On-Farm Comparisons of Organic and Conventional Cocoa Cultivation in Alto Beni, Bolivia

Resilience research has been applied to socioeconomic as well as for agroecological studies in the last 20 years. It provides a conceptual and methodological approach for a better understanding of interrelations between the performance of ecological and social systems. In the research area Alto Beni, Bolivia, the production of cocoa (Theobroma cacao L.), is one of the main sources of income. Farmers in the region have formed producers’ associations to enhance organic cocoa cultivation and obtain fair prices since the 1980s. In cooperation with the long-term system comparisons by the Research Institute of Organic Agriculture (FiBL) in Alto Beni, aspects of the field trial are applied for the use in on-farm research: a comparison of soil fertility, biomass and crop diversity is combined with qualitative interviews and participatory observation methods. Fieldwork is carried out together with Bolivian students through the Swiss KFPE-programme Echanges Universitaires. For the system comparisons, four different land-use types were classified according to their ecological complexity during a preliminary study in 2009: successional agroforestry systems, simple agroforestry systems (both organically managed and certified), traditional systems and conventional monocultures. The study focuses on interrelations between different ways of cocoa cultivation, livelihoods and the related socio-cultural rationales behind them. In particular this second aspect is innovative as it allows to broaden the biophysical perspective to a more comprehensive evaluation with socio-ecological aspects thereby increasing the relevance of the agronomic field studies for development policy and practice. Moreover, such a socio-ecological baseline allows to assess the potential of organic agriculture regarding resilience-building face to socio-environmental stress factors. Among others, the results of the pre-study illustrate local farmers’ perceptions of climate change and the consequences for the different crop-systems: all interviewees mentioned rising temperatures and/or an extended dry season as negative impacts more with regard to their own working conditions than to their crops. This was the case in particular for conventional monocultures and in plots where slash-and-burn cultivation was practised whereas for organic agroforestry systems the advantage of working in the shade was stressed indicating that their relevance rises in the context of climate change.

New Trends in Networking, Computing, E-learning, Systems Sciences, and Engineering

This book provides the latest in a series of books growing out of the International Joint Conferences on Computer, Information and Systems Sciences and Engineering. It includes chapters in the most advanced areas of Computing, Informatics, Systems Sciences and Engineering. It has accessible to a wide range of readership, including professors, researchers, practitioners and students. This book includes a set of rigorously reviewed world-class manuscripts addressing and detailing state-of-the-art research projects in the areas of Computer Science, Informatics, and Systems Sciences, and Engineering. It includes selected papers form the conference proceedings of the Ninth International Joint Conferences on Computer, Information, and Systems Sciences, and Engineering (CISSE 2013). Coverage includes topics in: Industrial Electronics, Technology & Automation, Telecommunications and Networking, Systems, Computing Sciences and Software Engineering, Engineering Education, Instructional Technology, Assessment, and E-learning.

Semantic Methods for Intelligent Distributed Design Environments

Continuous advancements in technology have led to increasingly comprehensive and distributed product development processes while in pursuit of improved products at reduced costs. Information associated with these products is ever changing, and structured frameworks have become integral to managing such fluid information. Ontologies and the Semantic Web have emerged as key alternatives for capturing product knowledge in both a human-readable and computable manner. The primary and conclusive focus of this research is to characterize relationships formed within methodically developed distributed design knowledge frameworks to ultimately provide a pervasive real-time awareness in distributed design processes. Utilizing formal logics in the form of the Semantic Web’s OWL and SWRL, causal relationships are expressed to guide and facilitate knowledge acquisition as well as identify contradictions between knowledge in a knowledge base. To improve the efficiency during both the development and operational phases of these “intelligent” frameworks, a semantic relatedness algorithm is designed specifically to identify and rank underlying relationships within product development processes. After reviewing several semantic relatedness measures, three techniques, including a novel meronomic technique, are combined to create AIERO, the Algorithm for Identifying Engineering Relationships in Ontologies. In determining its applicability and accuracy, AIERO was applied to three separate, independently developed ontologies. The results indicate AIERO is capable of consistently returning relatedness values one would intuitively expect. To assess the effectiveness of AIERO in exposing underlying causal relationships across product development platforms, a case study involving the development of an industry-inspired printed circuit board (PCB) is presented. After instantiating the PCB knowledge base and developing an initial set of rules, FIDOE, the Framework for Intelligent Distributed Ontologies in Engineering, was employed to identify additional causal relationships through extensional relatedness measurements. In a conclusive PCB redesign, the resulting “intelligent” framework demonstrates its ability to pass values between instances, identify inconsistencies amongst instantiated knowledge, and identify conflicting values within product development frameworks. The results highlight how the introduced semantic methods can enhance the current knowledge acquisition, knowledge management, and knowledge validation capabilities of traditional knowledge bases.

REE and Hf distribution among mineral phases in the CV-CK clan : a way to explain present-day Hf isotopic variations in chondrites

Chondrites are among the most primitive objects in the Solar System and constitute the main building blocks of telluric planets. Among the radiochronometers currently used for dating geological events, Sm–Nd and Lu–Hf are both composed of refractory, lithophile element. They are thought to behave similarly as the parent elements (Sm and Lu) are generally less incompatible than the daughter elements (Nd and Hf) during geological processes. As such, their respective average isotopic compositions for the solar system should be well defined by the average of chondrites, called Chondritic Uniform Reservoir (CHUR). However, while the Sm–Nd isotopic system shows an actual spread of less than 4% in the average chondritic record, the Lu–Hf system shows a larger variation range of 28% [Bouvier A., Vervoort J. D. and Patchett P. J. (2008) The Lu–Hf and Sm–Nd isotopic composition of CHUR: Constraints from unequilibrated chondrites and implications for the bulk composition of terrestrial planets. Earth Planet. Sci. Lett.273, 48–57]. To better understand the contrast between Sm–Nd and Lu–Hf systems, the REE and Hf distribution among mineral phases during metamorphism of Karoonda (CK) and Vigarano-type (CV) carbonaceous chondrites has been examined. Mineral modes were determined from elemental mapping on a set of five CK chondrites (from types 3–6) and one CV3 chondrite. Trace-element patterns are obtained for the first time in all the chondrite-forming minerals of a given class (CK chondrites) as well as one CV3 sample. This study reveals that REE are distributed among both phosphates and silicates. Only 30–50% of Sm and Nd are stored in phosphates (at least in chondrites types 3–5); as such, they are not mobilized during early stages of metamorphism. The remaining fraction of Sm and Nd is distributed among the same mineral phases; these elements are therefore not decoupled during metamorphism. Of the whole-rock total of Lu, the fraction held in phosphate decreases significantly as the degree of metamorphism increases (30% for types 3 and 4, less than 5% in type 6). In contrast to Lu, Hf is mainly hosted by silicates with little contribution from phosphates throughout the CK metamorphic sequence. A significant part of Sm and Nd are stored in phosphates in types 3–5, and these elements behave similarly during CK chondrite metamorphism. That explains the robustness of the Sm/Nd ratios in chondrites through metamorphism, and the slight discrepancies observed in the present-day isotopic Nd values in chondrites. On the contrary, Lu and Hf are borne by several different minerals and consequently they are redistributed during metamorphism–induced recrystallization. The Lu/Hf ratios are therefore significantly disturbed during chondrites metamorphism, leading to the high discrepancies observed in present-day Hf isotopic values in chondrites.