Variability of the radius growth at 25 years old Pinus uncinata Miller ex Mirbel in the North-East Spanish Pyrenees

It has been studied the variability of stem radial growth in four radius orientations at the age of 25 years old trees. The species was Pinus uncinata. The sampling sites, located in the North East Spanish Pyrenees belong to different plant communities. An ANOVA analysis was performed in order to find out which factors, the radio orientation, plant community of the site and tree itself are significative or have some kind of influence on the tree radial growth.

Interferon-gamma is a critical modulator of CB(2) cannabinoid receptor signaling during neuropathic pain

Nerve injuries often lead to neuropathic pain syndrome. The mechanisms contributing to this syndrome involve local inflammatory responses, activation of glia cells, and changes in the plasticity of neuronal nociceptive pathways. Cannabinoid CB(2) receptors contribute to the local containment of neuropathic pain by modulating glial activation in response to nerve injury. Thus, neuropathic pain spreads in mice lacking CB(2) receptors beyond the site of nerve injury. To further investigate the mechanisms leading to the enhanced manifestation of neuropathic pain, we have established expression profiles of spinal cord tissues from wild-type and CB(2)-deficient mice after nerve injury. An enhanced interferon-gamma (IFN-gamma) response was revealed in the absence of CB(2) signaling. Immunofluorescence stainings demonstrated an IFN-gamma production by astrocytes and neurons ispilateral to the nerve injury in wild-type animals. In contrast, CB(2)-deficient mice showed neuronal and astrocytic IFN-gamma immunoreactivity also in the contralateral region, thus matching the pattern of nociceptive hypersensitivity in these animals. Experiments in BV-2 microglia cells revealed that transcriptional changes induced by IFN-gamma in two key elements for neuropathic pain development, iNOS (inducible nitric oxide synthase) and CCR2, are modulated by CB(2) receptor signaling. The most direct support for a functional involvement of IFN-gamma as a mediator of CB(2) signaling was obtained with a double knock-out mouse strain deficient in CB(2) receptors and IFN-gamma. These animals no longer show the enhanced manifestations of neuropathic pain observed in CB(2) knock-outs. These data clearly demonstrate that the CB(2) receptor-mediated control of neuropathic pain is IFN-gamma dependent.

Small but thick enough-the Arabidopsis hypocotyl as a model to study secondary growth.

The continuous production of vascular tissues through secondary growth results in radial thickening of plant organs and is pivotal for various aspects of plant growth and physiology, such as water transport capacity or resistance to mechanical stress. It is driven by the vascular cambium, which produces inward secondary xylem and outward secondary phloem. In the herbaceous plant Arabidopsis thaliana (Arabidopsis), secondary growth occurs in stems, in roots and in the hypocotyl. In the latter, radial growth is most prominent and not obscured by parallel ongoing elongation growth. Moreover, its progression is reminiscent of the secondary growth mode of tree trunks. Thus, the Arabidopsis hypocotyl is a very good model to study basic molecular mechanisms of secondary growth. Genetic approaches have succeeded in the identification of various factors, including peptides, receptors, transcription factors and hormones, which appear to participate in a complex network that controls radial growth. Many of these players are conserved between herbaceous and woody plants. In this review, we will focus on what is known about molecular mechanisms and regulators of vascular secondary growth in the Arabidopsis hypocotyl.

Metabolic activation pattern of distinct hippocampal subregions during spatial learning and memory retrieval.

Activation dynamics of hippocampal subregions during spatial learning and their interplay with neocortical regions is an important dimension in the understanding of hippocampal function. Using the (14C)-2-deoxyglucose autoradiographic method, we have characterized the metabolic changes occurring in hippocampal subregions in mice while learning an eight-arm radial maze task. Autoradiogram densitometry revealed a heterogeneous and evolving pattern of enhanced metabolic activity throughout the hippocampus during the training period and on recall. In the early stages of training, activity was enhanced in the CA1 area from the intermediate portion to the posterior end as well as in the CA3 area within the intermediate portion of the hippocampus. At later stages, CA1 and CA3 activations spread over the entire longitudinal axis, while dentate gyrus (DG) activation occurred from the anterior to the intermediate zone. Activation of the retrosplenial cortex but not the amygdala was also observed during the learning process. On recall, only DG activation was observed in the same anterior part of the hippocampus. These results suggest the existence of a functional segmentation of the hippocampus, each subregion being dynamically but also differentially recruited along the acquisition, consolidation, and retrieval process in parallel with some neocortical sites.

Forecasting the Earth"s radiation belts and modeling solar energetic particle events: Recent results from SPACECAST

High-energy charged particles in the van Allen radiation belts and in solar energetic particle events can damage satellites on orbit leading to malfunctions and loss of satellite service. Here we describe some recent results from the SPACECAST project on modelling and forecasting the radiation belts, and modelling solar energetic particle events. We describe the SPACECAST forecasting system that uses physical models that include wave-particle interactions to forecast the electron radiation belts up to 3 h ahead. We show that the forecasts were able to reproduce the >2 MeV electron flux at GOES 13 during the moderate storm of 7-8 October 2012, and the period following a fast solar wind stream on 25-26 October 2012 to within a factor of 5 or so. At lower energies of 10- a few 100 keV we show that the electron flux at geostationary orbit depends sensitively on the high-energy tail of the source distribution near 10 RE on the nightside of the Earth, and that the source is best represented by a kappa distribution. We present a new model of whistler mode chorus determined from multiple satellite measurements which shows that the effects of wave-particle interactions beyond geostationary orbit are likely to be very significant. We also present radial diffusion coefficients calculated from satellite data at geostationary orbit which vary with Kp by over four orders of magnitude. We describe a new automated method to determine the position at the shock that is magnetically connected to the Earth for modelling solar energetic particle events and which takes into account entropy, and predict the form of the mean free path in the foreshock, and particle injection efficiency at the shock from analytical theory which can be tested in simulations.

Pro-inflammatory cytokines induce the transcription factors C/EBPbeta and C/EBPdelta in astrocytes.

The transcription factors CCAAT/enhancer binding protein (C/EBP)-beta and -delta are key regulators for the expression of the acute phase genes in the liver, such as complement component C3 and antichymotrypsin. In the brain, these acute phase proteins are produced in response to pro-inflammatory cytokines by the reactive astrocytes, in particular those surrounding the amyloid plaques of Alzheimer's disease brains. Here we show that lipopolysaccharides (LPS), IL-1beta, and TNFalpha induce the expression of the c/ebpbeta and -delta genes in mouse primary astrocytes. This induction precedes the expression of the acute phase genes coding for the complement component C3 and the mouse homologue of antichymotrypsin. The induction of these two acute phase genes by LPS is blocked by cycloheximide, whereas this protein synthesis inhibitor does not affect the expression of the c/ebp genes. Altogether, our data support a role as immediate-early genes for c/ebpbeta and -delta, whose expression is induced by pro-inflammatory cytokines in mouse cortical astrocytes. In the liver, these transcription factors are known to play an important role in inflammation and energy metabolism regulation. Therefore, C/EBPbeta and -delta could be pivotal transcription factors involved in brain inflammation, in addition to their previously demonstrated role in brain glycogen metabolism regulation (Cardinaux and Magistretti. J Neurosci 16:919-929, 1996).

Multi-scale systems analysis of plant development : beyond cellular signaling and tissue morphodynamics

Les plantes sont essentielles pour les sociétés humaines. Notre alimentation quotidienne, les matériaux de constructions et les sources énergétiques dérivent de la biomasse végétale. En revanche, la compréhension des multiples aspects développementaux des plantes est encore peu exploitée et représente un sujet de recherche majeur pour la science. L'émergence des technologies à haut débit pour le séquençage de génome à grande échelle ou l'imagerie de haute résolution permet à présent de produire des quantités énormes d'information. L'analyse informatique est une façon d'intégrer ces données et de réduire la complexité apparente vers une échelle d'abstraction appropriée, dont la finalité est de fournir des perspectives de recherches ciblées. Ceci représente la raison première de cette thèse. En d'autres termes, nous appliquons des méthodes descriptives et prédictives combinées à des simulations numériques afin d'apporter des solutions originales à des problèmes relatifs à la morphogénèse à l'échelle de la cellule et de l'organe. Nous nous sommes fixés parmi les objectifs principaux de cette thèse d'élucider de quelle manière l'interaction croisée des phytohormones auxine et brassinosteroïdes (BRs) détermine la croissance de la cellule dans la racine du méristème apical d'Arabidopsis thaliana, l'organisme modèle de référence pour les études moléculaires en plantes. Pour reconstruire le réseau de signalement cellulaire, nous avons extrait de la littérature les informations pertinentes concernant les relations entre les protéines impliquées dans la transduction des signaux hormonaux. Le réseau a ensuite été modélisé en utilisant un formalisme logique et qualitatif pour pallier l'absence de données quantitatives. Tout d'abord, Les résultats ont permis de confirmer que l'auxine et les BRs agissent en synergie pour contrôler la croissance de la cellule, puis, d'expliquer des observations phénotypiques paradoxales et au final, de mettre à jour une interaction clef entre deux protéines dans la maintenance du méristème de la racine. Une étude ultérieure chez la plante modèle Brachypodium dystachion (Brachypo- dium) a révélé l'ajustement du réseau d'interaction croisée entre auxine et éthylène par rapport à Arabidopsis. Chez ce dernier, interférer avec la biosynthèse de l'auxine mène à la formation d'une racine courte. Néanmoins, nous avons isolé chez Brachypodium un mutant hypomorphique dans la biosynthèse de l'auxine qui affiche une racine plus longue. Nous avons alors conduit une analyse morphométrique qui a confirmé que des cellules plus anisotropique (plus fines et longues) sont à l'origine de ce phénotype racinaire. Des analyses plus approfondies ont démontré que la différence phénotypique entre Brachypodium et Arabidopsis s'explique par une inversion de la fonction régulatrice dans la relation entre le réseau de signalisation par l'éthylène et la biosynthèse de l'auxine. L'analyse morphométrique utilisée dans l'étude précédente exploite le pipeline de traitement d'image de notre méthode d'histologie quantitative. Pendant la croissance secondaire, la symétrie bilatérale de l'hypocotyle est remplacée par une symétrie radiale et une organisation concentrique des tissus constitutifs. Ces tissus sont initialement composés d'une douzaine de cellules mais peuvent aisément atteindre des dizaines de milliers dans les derniers stades du développement. Cette échelle dépasse largement le seuil d'investigation par les moyens dits 'traditionnels' comme l'imagerie directe de tissus en profondeur. L'étude de ce système pendant cette phase de développement ne peut se faire qu'en réalisant des coupes fines de l'organe, ce qui empêche une compréhension des phénomènes cellulaires dynamiques sous-jacents. Nous y avons remédié en proposant une stratégie originale nommée, histologie quantitative. De fait, nous avons extrait l'information contenue dans des images de très haute résolution de sections transverses d'hypocotyles en utilisant un pipeline d'analyse et de segmentation d'image à grande échelle. Nous l'avons ensuite combiné avec un algorithme de reconnaissance automatique des cellules. Cet outil nous a permis de réaliser une description quantitative de la progression de la croissance secondaire révélant des schémas développementales non-apparents avec une inspection visuelle classique. La formation de pôle de phloèmes en structure répétée et espacée entre eux d'une longueur constante illustre les bénéfices de notre approche. Par ailleurs, l'exploitation approfondie de ces résultats a montré un changement de croissance anisotropique des cellules du cambium et du phloème qui semble en phase avec l'expansion du xylème. Combinant des outils génétiques et de la modélisation biomécanique, nous avons démontré que seule la croissance plus rapide des tissus internes peut produire une réorientation de l'axe de croissance anisotropique des tissus périphériques. Cette prédiction a été confirmée par le calcul du ratio des taux de croissance du xylème et du phloème au cours de développement secondaire ; des ratios élevés sont effectivement observés et concomitant à l'établissement progressif et tangentiel du cambium. Ces résultats suggèrent un mécanisme d'auto-organisation établi par un gradient de division méristématique qui génèrent une distribution de contraintes mécaniques. Ceci réoriente la croissance anisotropique des tissus périphériques pour supporter la croissance secondaire. - Plants are essential for human society, because our daily food, construction materials and sustainable energy are derived from plant biomass. Yet, despite this importance, the multiple developmental aspects of plants are still poorly understood and represent a major challenge for science. With the emergence of high throughput devices for genome sequencing and high-resolution imaging, data has never been so easy to collect, generating huge amounts of information. Computational analysis is one way to integrate those data and to decrease the apparent complexity towards an appropriate scale of abstraction with the aim to eventually provide new answers and direct further research perspectives. This is the motivation behind this thesis work, i.e. the application of descriptive and predictive analytics combined with computational modeling to answer problems that revolve around morphogenesis at the subcellular and organ scale. One of the goals of this thesis is to elucidate how the auxin-brassinosteroid phytohormone interaction determines the cell growth in the root apical meristem of Arabidopsis thaliana (Arabidopsis), the plant model of reference for molecular studies. The pertinent information about signaling protein relationships was obtained through the literature to reconstruct the entire hormonal crosstalk. Due to a lack of quantitative information, we employed a qualitative modeling formalism. This work permitted to confirm the synergistic effect of the hormonal crosstalk on cell elongation, to explain some of our paradoxical mutant phenotypes and to predict a novel interaction between the BREVIS RADIX (BRX) protein and the transcription factor MONOPTEROS (MP),which turned out to be critical for the maintenance of the root meristem. On the same subcellular scale, another study in the monocot model Brachypodium dystachion (Brachypodium) revealed an alternative wiring of auxin-ethylene crosstalk as compared to Arabidopsis. In the latter, increasing interference with auxin biosynthesis results in progressively shorter roots. By contrast, a hypomorphic Brachypodium mutant isolated in this study in an enzyme of the auxin biosynthesis pathway displayed a dramatically longer seminal root. Our morphometric analysis confirmed that more anisotropic cells (thinner and longer) are principally responsible for the mutant root phenotype. Further characterization pointed towards an inverted regulatory logic in the relation between ethylene signaling and auxin biosynthesis in Brachypodium as compared to Arabidopsis, which explains the phenotypic discrepancy. Finally, the morphometric analysis of hypocotyl secondary growth that we applied in this study was performed with the image-processing pipeline of our quantitative histology method. During its secondary growth, the hypocotyl reorganizes its primary bilateral symmetry to a radial symmetry of highly specialized tissues comprising several thousand cells, starting with a few dozens. However, such a scale only permits observations in thin cross-sections, severely hampering a comprehensive analysis of the morphodynamics involved. Our quantitative histology strategy overcomes this limitation. We acquired hypocotyl cross-sections from tiled high-resolution images and extracted their information content using custom high-throughput image processing and segmentation. Coupled with an automated cell type recognition algorithm, it allows precise quantitative characterization of vascular development and reveals developmental patterns that were not evident from visual inspection, for example the steady interspace distance of the phloem poles. Further analyses indicated a change in growth anisotropy of cambial and phloem cells, which appeared in phase with the expansion of xylem. Combining genetic tools and computational modeling, we showed that the reorientation of growth anisotropy axis of peripheral tissue layers only occurs when the growth rate of central tissue is higher than the peripheral one. This was confirmed by the calculation of the ratio of the growth rate xylem to phloem throughout secondary growth. High ratios are indeed observed and concomitant with the homogenization of cambium anisotropy. These results suggest a self-organization mechanism, promoted by a gradient of division in the cambium that generates a pattern of mechanical constraints. This, in turn, reorients the growth anisotropy of peripheral tissues to sustain the secondary growth.

Expression of the glucagon-like peptide-1 receptor gene in rat brain.

Evidence that glucagon-like peptide-1 (GLP-1) (7-36) amide functions as a novel neuropeptide prompted us to study the gene expression of its receptor in rat brain. Northern blot analysis showed transcripts of similar size in RINm5F cells, hypothalamus, and brain-stem. First-strand cDNA was prepared by using RNA from hypothalamus, brainstem, and R1Nm5F cells and subsequently amplified by PCR. Southern blot analysis of the PCR products showed a major 1.4-kb band in all these preparations. PCR products amplified from hypothalamus were cloned, and the nucleotide sequence of one strand was identical to that described in rat pancreatic islets. In situ hybridization studies showed specific labeling in both neurons and glia of the thalamus, hypothalamus, hippocampus, primary olfactory cortex, choroid plexus, and pituitary gland. In the hypothalamus, ventromedial nuclei cells were highly labeled. These findings indicate that GLP-1 receptors are actually synthesized in rat brain. In addition, the colocalization of GLP-1 receptors, glucokinase, and GLUT-2 in the same areas supports the idea that these cells play an important role in glucose sensing in the brain.

Free-breathing T2 mapping at 3T for the monitoring of cardiac allograft rejection: initial results

rejection can lead to loss of function. Histological reading of endomyocardial biopsy remains the "gold standard" for guiding immunosuppression, despite its methodological limitations (sampling error and interobserver variability). The measurement of the T2 relaxation time has been suggested for detection of allograft rejection, on the pathophysiological basis that the T2 relaxation time prolongs with local edema resulting from acute allograft rejection. Using breath-held cardiac magnetic resonance T2 mapping at 1.5 T, Usman et al. (CircCardiovascImaging2012) detected moderate allograft rejection (grade 2R, ISHLT 2004). With modern immunosuppression grade 2R rejection has become a rare event, but the need remains for a technique that permits the discrimination of absent (grade 0R) and mild rejection (grade 1R). We therefore investigated whether an increase of magnetic field strength to 3T and the use of real-time navigator-gated respiration compensation allow for an increase in the sensitivity of T2 relaxation time detection that is necessary to achieve this discrimination. Methods: Eighteen patients received EMB (Tan et al., ArchPatholLabMed2007) and cardiac T2 mapping on the same day. Reading of T2 maps was blinded to the histological results. For final analysis, 3 cases with known 2R rejection at the time of T2 mapping were added, yielding 21 T2 mapping sessions. A respiration-navigator-gated radial gradient-recalled-echo pulse sequence (resolution 1.17 mm2, matrix 2562, trigger time 3 heartbeats, T2 preparation duration TET2 Prep = 60/30/0 ms) was applied to obtain 3 short-axis T2 maps (van Heeswijk et al., JACCCardiovascImaging2012), which were segmented according to AHA guidelines (Cerqueira et al, Circulation2001). The highest segmental T2 values were grouped according to histological rejection grade and differences were analyzed by Student's t-test, except for the non-blinded cases with 2R rejection. The degree of discrimination was determined using the Spearman's ranked correlation test. Results: The high-quality T2 maps allowed for visual differentiation of the rejection degrees (Figure 1), and the correlation of T2 mapping with the histological grade of acute cellular rejection was significant (Spearman's r = 0.56, p = 0.007). The 0R (n = 15) and 1R (n = 3) degrees demonstrated significantly different T2 values (46.9 ± 5.0 and 54.3 ± 3.0 ms, p = 0.02, Figure 2). Cases with 2R rejection showed clear T2 elevation (T2 = 60.3 ± 16.2 ms). Conclusions: This pilot study demonstrates that non-invasive free-breathing cardiac T2 mapping at 3T discriminates between no and mild cardiac allograft rejection. Confirmation of these encouraging results in a larger cohort should consider a study able to show equivalency or superiority of T2 mapping.

Glial hyaluronate-binding protein expression in aggregating brain cell cultures.

We analyzed the expression of glial hyaluronate-binding protein (GHAP), an integral component of the extracellular matrix, in aggregating brain cell cultures of fetal rat telencephalon using immunofluorescence. GHAP immunoreactivity appeared after 1 week in culture, simultaneous with the first deposits of myelin basic protein, and showed a development-dependent increase. Comparison of glia-enriched and neuron-enriched cultures showed that only glial cells express GHAP. Three peptide growth factors, epidermal growth factor, fibroblast growth factor and platelet-derived growth factor, which are known to stimulate the differentiation of glial cells, modulated the deposit of GHAP immunoreactivity. The 3-dimensional structure of aggregate cultures promoted GHAP deposition, suggesting that cell-cell interactions are required for extracellular matrix formation. Furthermore GHAP production seemed to depend on the developmental stage of the glial cells.

Direct mapping of 19F in 19FDG-6P in brain tissue at subcellular resolution using soft X-ray fluorescence

Low energy x-ray fluorescence (LEXRF) detection was optimized for imaging cerebral glucose metabolism by mapping the fluorine LEXRF signal of 19 F in 19 FDG, trapped as intracellular 19 F-deoxyglucose-6-phosphate ( 19 FDG-6P) at 1μm spatial resolution from 3μm thick brain slices. 19 FDG metabolism was evaluated in brain structures closely resembling the general cerebral cytoarchitecture following formalin fixation of brain slices and their inclusion in an epon matrix. 2-dimensional distribution maps of 19 FDG-6P were placed in a cytoarchitectural and morphological context by simultaneous LEXRF mapping of N and O, and scanning transmission x-ray (STXM) imaging. A disproportionately high uptake and metabolism of glucose was found in neuropil relative to intracellular domains of the cell body of hypothalamic neurons, showing directly that neurons, like glial cells, also metabolize glucose. As 19 F-deoxyglucose-6P is structurally identical to 18 F-deoxyglucose-6P, LEXRF of subcellular 19 F provides a link to in vivo 18 FDG PET, forming a novel basis for understanding the physiological mechanisms underlying the 18 FDG PET image, and the contribution of neurons and glia to the PET signal.

MORFOLOGIA FLORAL DA GOIABEIRA SERRANA (Feijoa sellowiana) E SUAS IMPLICAÇÕES NA POLINIZAÇÃO

Esse estudo teve por objetivo caracterizar variações na arquitetura floral da Feijoa sellowiana e determinar sua influência sobre a polinização. Foram avaliados o comprimento do pistilo, a distância entre estigma e estames, o diâmetro de abertura e a distribuição dos estames na flor, com base em 7 flores de 15 acessos do Banco de Germoplasma da espécie. Distinguiram-se 3 classes de distâncias médias entre estigma e estames: 0,2 (C1), 0,7 (C2) e 1,2 cm (C3), e duas classes de distribuição de estames na flor (radial e aleatória). Sorteou-se uma planta por classe de distância entre estigma e estames, a qual teve 50 flores marcadas para cada um dos seguintes tratamentos: T1-polinização aberta; T2-tela contra pássaros e T3-tela contra pássaros e insetos. A frutificação foi de 47% em T1 para C2 e de 22% para C3, diferença que pode ser devida ao genótipo e/ou alternância de produção. No T2, a frutificação foi 31% em C2, 15,4% em C1 e 3% em C3. A superioridade de T1 sobre T2 pode ser devida à polinização por pássaros. Essa superioridade foi mais expressiva em C3 do que em C2, o que sugere que C3 é mais dependente de pássaros. A frutificação em T2 pode ainda evidenciar a polinização por insetos e foi menor para C3, o que pode estar sendo causado pelo maior afastamento do estigma. A frutificação em T3 para C1 (7%) e C2 (15%) sugere que o vento ou a autopolinização também possam efetuar a polinização.

Efectos del muérdago (Viscum album L.) sobre el crecimiento secundario del pino silvestre (Pinus sylvestris L.) en la Sierra de Gúdar (Teruel): Interacciones con el clima

El visc és la planta hemiparàsita més estesa en els boscos de coníferes. No obstant, a penes hi ha estudis que avaluen els seus efectes sobre el creixement i el vigor dels arbres. Els peus amb major presència de visc mostren una major grandària i en el passat presentaven un creixement major que els que actualment no n'alberguen. L'increment d'àrea basimètrica es redueix a mesura que augmenta l'abundància de visc, mostrant un declivi major en l'àpex on les mates de visc estan agregades. El creixement radial dels arbres amb visc es va reduir molt després de fortes sequeres.

Torque vibration model of axial-flux surface-mounted permanent magnet synchronous machine

In order that the radius and thus ununiform structure of the teeth and otherelectrical and magnetic parts of the machine may be taken into consideration the calculation of an axial flux permanent magnet machine is, conventionally, doneby means of 3D FEM-methods. This calculation procedure, however, requires a lotof time and computer recourses. This study proves that also analytical methods can be applied to perform the calculation successfully. The procedure of the analytical calculation can be summarized into following steps: first the magnet is divided into slices, which makes the calculation for each section individually, and then the parts are submitted to calculation of the final results. It is obvious that using this method can save a lot of designing and calculating time. Thecalculation program is designed to model the magnetic and electrical circuits of surface mounted axial flux permanent magnet synchronous machines in such a way, that it takes into account possible magnetic saturation of the iron parts. Theresult of the calculation is the torque of the motor including the vibrations. The motor geometry and the materials and either the torque or pole angle are defined and the motor can be fed with an arbitrary shape and amplitude of three-phase currents. There are no limits for the size and number of the pole pairs nor for many other factors. The calculation steps and the number of different sections of the magnet are selectable, but the calculation time is strongly depending on this. The results are compared to the measurements of real prototypes. The permanent magnet creates part of the flux in the magnetic circuit. The form and amplitude of the flux density in the air-gap depends on the geometry and material of the magnetic circuit, on the length of the air-gap and remanence flux density of the magnet. Slotting is taken into account by using the Carter factor in the slot opening area. The calculation is simple and fast if the shape of the magnetis a square and has no skew in relation to the stator slots. With a more complicated magnet shape the calculation has to be done in several sections. It is clear that according to the increasing number of sections also the result will become more accurate. In a radial flux motor all sections of the magnets create force with a same radius. In the case of an axial flux motor, each radial section creates force with a different radius and the torque is the sum of these. The magnetic circuit of the motor, consisting of the stator iron, rotor iron, air-gap, magnet and the slot, is modelled with a reluctance net, which considers the saturation of the iron. This means, that several iterations, in which the permeability is updated, has to be done in order to get final results. The motor torque is calculated using the instantaneous linkage flux and stator currents. Flux linkage is called the part of the flux that is created by the permanent magnets and the stator currents passing through the coils in stator teeth. The angle between this flux and the phase currents define the torque created by the magnetic circuit. Due to the winding structure of the stator and in order to limit the leakage flux the slot openings of the stator are normally not made of ferromagnetic material even though, in some cases, semimagnetic slot wedges are used. In the slot opening faces the flux enters the iron almost normally (tangentially with respect to the rotor flux) creating tangential forces in the rotor. This phenomenon iscalled cogging. The flux in the slot opening area on the different sides of theopening and in the different slot openings is not equal and so these forces do not compensate each other. In the calculation it is assumed that the flux entering the left side of the opening is the component left from the geometrical centre of the slot. This torque component together with the torque component calculated using the Lorenz force make the total torque of the motor. It is easy to assume that when all the magnet edges, where the derivative component of the magnet flux density is at its highest, enter the slot openings at the same time, this will have as a result a considerable cogging torque. To reduce the cogging torquethe magnet edges can be shaped so that they are not parallel to the stator slots, which is the common way to solve the problem. In doing so, the edge may be spread along the whole slot pitch and thus also the high derivative component willbe spread to occur equally along the rotation. Besides forming the magnets theymay also be placed somewhat asymmetric on the rotor surface. The asymmetric distribution can be made in many different ways. All the magnets may have a different deflection of the symmetrical centre point or they can be for example shiftedin pairs. There are some factors that limit the deflection. The first is that the magnets cannot overlap. The magnet shape and the relative width compared to the pole define the deflection in this case. The other factor is that a shifting of the poles limits the maximum torque of the motor. If the edges of adjacent magnets are very close to each other the leakage flux from one pole to the other increases reducing thus the air-gap magnetization. The asymmetric model needs some assumptions and simplifications in order to limit the size of the model and calculation time. The reluctance net is made for symmetric distribution. If the magnets are distributed asymmetrically the flux in the different pole pairs will not be exactly the same. Therefore, the assumption that the flux flows from the edges of the model to the next pole pairs, in the calculation model from one edgeto the other, is not correct. If it were wished for that this fact should be considered in multi-pole pair machines, this would mean that all the poles, in other words the whole machine, should be modelled in reluctance net. The error resulting from this wrong assumption is, nevertheless, irrelevant.

Experimental and Numerical Analysis of Different Volutes in a Centrifugal Compressor

In a centrifugal compressor the flow around the diffuser is collected and led to the pipe system by a spiral-shaped volute. In this study a single-stage centrifugal compressor with three different volutes is investigated. The compressorwas first equipped with the original volute, the cross-section of which was a combination of a rectangle and semi-circle. Next a new volute with a fully circular cross-section was designed and manufactured. Finally, the circular volute wasmodified by rounding the tongue and smoothing the tongue area. The overall performance of the compressor as well as the static pressure distribution after the impeller and on the volute surface were measured. The flow entering the volute was measured using a three-hole Cobra-probe, and flow visualisations were carriedout in the exit cone of the volute. In addition, the radial force acting on theimpeller was measured using magnetic bearings. The complete compressor with thecircular volute (inlet pipe, full impeller, diffuser, volute and outlet pipe) was also modelled using computational fluid dynamics (CFD). A fully 3-D viscous flow was solved using a Navier-Stokes solver, Finflo, developed at Helsinki University of Technology. Chien's k-e model was used to take account of the turbulence. The differences observed in the performance of the different volutes were quite small. The biggest differences were at low speeds and high volume flows,i.e. when the flow entered the volute most radially. In this operating regime the efficiency of the compressor with the modified circular volute was about two percentage points higher than with the other volutes. Also, according to the Cobra-probe measurements and flow visualisations, the modified circular volute performed better than the other volutes in this operating area. The circumferential static pressure distribution in the volute showed increases at low flow, constant distribution at the design flow and decrease at high flow. The non-uniform static pressure distribution of the volute was transmitted backwards across the vaneless diffuser and observed at the impeller exit. At low volume flow a strong two-wave pattern developed into the static pressure distribution at the impeller exit due to the response of the impeller to the non-uniformity of pressure. The radial force of the impeller was the greatest at the choke limit, the smallest atthe design flow, and moderate at low flow. At low flow the force increase was quite mild, whereas the increase at high flow was rapid. Thus, the non-uniformityof pressure and the force related to it are strong especially at high flow. Theforce caused by the modified circular volute was weaker at choke and more symmetric as a function of the volume flow than the force caused by the other volutes.