A geometric approach to alternating kk-linear forms

Given an $n$-dimensional vector space $V$ over a field $\mathbb K$, let $2\leq k < n$. There is a natural correspondence between the alternating $k$-linear forms $\varphi$ of $V$ and the linear functionals $f$ of $\bigwedge^kV$. Let $\varepsilon_k:{\mathcal G}_k(V)\rightarrow {\mathrm{PG}}(\bigwedge^kV)$ be the Plucker embedding of the $k$-Grassmannian ${\mathcal G}_k(V)$ of $V$. Then $\varepsilon_k^{-1}(\ker(f)\cap\varepsilon_k(\mathcal{G}_k(V)))$ is a hyperplane of the point-line geometry ${\mathcal G}_k(V)$. All hyperplanes of ${\mathcal G}_k(V)$ can be obtained in this way. For a hyperplane $H$ of ${\mathcal G}_k(V)$, let $R^\uparrow(H)$ be the subspace of ${\mathcal G}_{k-1}(V)$ formed by the $(k-1)$-subspaces $A\subset V$ such that $H$ contains all $k$-subspaces that contain $A$. In other words, if $\varphi$ is the (unique modulo a scalar) alternating $k$-linear form defining $H$, then the elements of $R^\uparrow(H)$ are the $(k-1)$-subspaces $A = \langle a_1,\ldots, a_{k-1}\rangle$ of $V$ such that $\varphi(a_1,\ldots, a_{k-1},x) = 0$ for all $x\in V$. When $n-k$ is even it might be that $R^\uparrow(H) = \emptyset$. When $n-k$ is odd, then $R^\uparrow(H) \neq \emptyset$, since every $(k-2)$-subspace of $V$ is contained in at least one member of $R^\uparrow(H)$. If every $(k-2)$-subspace of $V$ is contained in precisely one member of $R^\uparrow(H)$ we say that $R^\uparrow(H)$ is spread-like. In this paper we obtain some results on $R^\uparrow(H)$ which answer some open questions from the literature and suggest the conjecture that, if $n-k$ is even and at least $4$, then $R^\uparrow(H) \neq \emptyset$ but for one exception with ${\mathbb K}\leq{\mathbb R}$ and $(n,k) = (7,3)$, while if $n-k$ is odd and at least $5$ then $R^\uparrow(H)$ is never spread-like.Comment: 29 Page

Grassmann embeddings of polar Grassmannians

In this paper we compute the dimension of the Grassmann embeddings of the polar Grassmannians associated to a possibly degenerate Hermitian, alternating or quadratic form with possibly non-maximal Witt index. Moreover, in the characteristic $2$ case, when the form is quadratic and non-degenerate with bilinearization of minimal Witt index, we define a generalization of the so-called Weyl embedding (see [I. Cardinali and A. Pasini, Grassmann and Weyl embeddings of orthogonal Grassmannians. J. Algebr. Combin. 38 (2013), 863-888]) and prove that the Grassmann embedding is a quotient of this generalized "Weyl-like" embedding. We also estimate the dimension of the latter.Comment: 25 pages/revised version after revie

Line Polar Grassmann Codes of Orthogonal Type

Polar Grassmann codes of orthogonal type have been introduced in I. Cardinali and L. Giuzzi, \emph{Codes and caps from orthogonal Grassmannians}, {Finite Fields Appl.} {\bf 24} (2013), 148-169. They are subcodes of the Grassmann code arising from the projective system defined by the Pl\"ucker embedding of a polar Grassmannian of orthogonal type. In the present paper we fully determine the minimum distance of line polar Grassmann Codes of orthogonal type for $q$ odd

On transparent embeddings of point-line geometries

We introduce the class of transparent embeddings for a point-line geometry $\Gamma = ({\mathcal P},{\mathcal L})$ as the class of full projective embeddings $\varepsilon$ of $\Gamma$ such that the preimage of any projective line fully contained in $\varepsilon({\mathcal P})$ is a line of $\Gamma$. We will then investigate the transparency of Pl\"ucker embeddings of projective and polar grassmannians and spin embeddings of half-spin geometries and dual polar spaces of orthogonal type. As an application of our results on transparency, we will derive several Chow-like theorems for polar grassmannians and half-spin geometries.Comment: 28 Pages/revised version after revie

Optimisation des jonctions de dispositifs (FDSOI, TriGate) fabriqués à faible température pour l’intégration 3D séquentielle

3D sequential integration is a promising candidate for the scaling sustainability for technological nodes beyond 14 nm. The main challenge is the development of a low temperature process for the top transistor level that enables to avoid the degradation of the bottom transistor level. The most critical process step for the top transistor level fabrication is the dopant activation that is usually performed at temperature higher than 1000 °C. In the frame of this Ph.D. work, different solutions for the dopant activation optimization at low temperature (below 600 °C) are proposed and integrated in FDSOI and TriGate devices. The technique chosen for the dopant activation at low temperature is the solid phase epitaxial regrowth. First, doping conditions have been optimized in terms of activation level and process time for low temperatures (down to 450 °C) anneals. The obtained conditions have been implemented in FDSOI and TriGate devices leading to degraded electrical results compared to the high temperature process of reference (above 1000 °C). By means of TCAD simulation and electrical measurements comparison, the critical region of the transistor in terms of activation appears to be below the offset spacer. The extension first integration scheme is then shown to be the best candidate to obtain high performance low temperature devices. Indeed, by performing the doping implantation before the raised source and drain epitaxial growth, the absence of diffusion at low temperature can be compensated. This conclusion can be extrapolated for TriGate and FinFET on insulator devices. Extension first integration scheme has been demonstrated for the first time on N and PFETs in 14 nm FDSOI technology showing promising results in terms of performance. This demonstration evidences that the two challenges of this integration i.e. the partial amorphization of very thin films and the epitaxy regrowth on implanted access are feasible. Finally, heated implantation has been investigated as a solution to dope thin access regions without full amorphization, which is particularly critical for FDSOI and FinFET devices. The as-implanted activation levels are shown to be too low to obtain high performance devices and the heated implantation appears a promising candidate for low temperature devices if used in combination with an alternative activation mechanism.L’intégration 3D séquentielle représente une alternative potentielle à la réduction des dimensions afin de gagner encore en densité d’une génération à la suivante. Le principal défi concerne la fabrication du transistor de l’étage supérieur avec un faible budget thermique; ceci afin d’éviter la dégradation du niveau inférieur. L’étape de fabrication la plus critique pour la réalisation du niveau supérieur est l’activation des dopants. Celle-ci est généralement effectuée par recuit à une température supérieure à 1000 °C. Dans ce contexte, cette thèse propose des solutions pour activer les dopants à des températures inférieures à 600 °C par la technique dite de recristallisation en phase solide. Les conditions de dopage ont été optimisées pour améliorer le niveau d’activation et le temps de recuit tout en réduisant la température d’activation jusqu’à 450°C. Les avancées obtenues ont été implémentées sur des dispositifs avancés FDSOI et TriGate générant des dispositifs avec des performances inférieures aux références fabriquées à hautes températures (supérieures à 1000 °C). En utilisant des simulations TCAD et en les comparant aux mesures électriques, nous avons montré que la région la plus critique en termes d’activation se trouve sous les espaceurs de la grille. Nous montrons alors qu’une intégration dite « extension first » est le meilleur compromis pour obtenir de bonnes performances sur des dispositifs fabriqués à faible température. En effet, l’implantation des dopants avant l’épitaxie qui vise à surélever les sources et drains compense l’absence de diffusion à basse température. Ces résultats ont par la suite été étendus pour des dispositifs TriGate et FinFETs sur isolants. Pour la première fois, l’intégration « extension first » a été démontrée pour des N et PFETs d’une technologie 14 nm FDSOI avec des résultats prometteurs en termes de performances. Les résultats obtenus montrent notamment qu’il est possible d’amorphiser partiellement un film très mince avant d’effectuer une recroissance épitaxiale sur une couche dopée. Finalement, une implantation ionique à relativement haute température (jusqu’à 500 °C) a été étudiée afin de doper les accès sans amorphiser totalement le film mince, ce qui est critique dans le cas des dispositifs FDSOI et FinFET. Nous montrons que les niveaux d’activation après implantation sont trop faibles pour obtenir des bonnes performances et que l’implantation ionique « chaude » est prometteuse à condition d’être utilisée avec un autre mécanisme d’activation comme le recuit laser

MAGNETIC INDUCTION BRAZING

openL'obiettivo dell'elaborato è lo studio del comportamento dei materiali metallici quando sottoposti ad un campo magnetico variabil

Experimental Performance of a Tapered Axial Inducer: Comparison with Analytical Predictions

The present paper illustrates the results of an experimental campaign conducted in the CPRTF (Cavitating Pump Rotordynamic Test Facility) at Alta S.p.A. for the characterization of the pumping and suction performance of a three-bladed, tapered-hub, variable-pitch inducer, indicated as DAPAMITO3. The test inducer has been sized and designed by means of the reduced order model recently developed at Alta S.p.A. for the definition of the geometry and the prediction of the non-cavitating performance of typical high-head space rocket inducers. The pumping performance of the inducer proved to be in good accordance with the model predictions. The effects of the blade tip clearance have been investigated and the corresponding performance degradation has been correctly predicted by means of a semi-empirical extension of the model. Finally, the effects of the working fluid temperature on both the non-cavitating and cavitating performance of the inducer have been analysed. At higher ..

Characterizations of symplectic polar spaces

A polar space S is said to be symplectic if it admits an embedding e in a projective geometry PG(V) such that the e-image e(S) of S is defined by an alternating form of V. In this paper we characterize symplectic polar spaces in terms of their incidence properties, with no mention of peculiar properties of their embeddings. This is relevant especially when S admits different (non isomorphic) embeddings, as it is the case (precisely) when S is defined over a field of characteristic 2.Comment: 20 pages/extensively revise

Cavitation and Flow Instabilities in a 3- Bladed Axial Inducer Designed by Means of a Reduced Order Analytical Model

The present paper illustrates the main results of an experimental campaign conducted using the CPRTF (Cavitating Pump Rotordynamic Test Facility) at Alta S.p.A. The tests were carried out on the DAPAMITO inducer, a three-bladed axial pump designed and manufactured by Alta S.p.A. using a simplified analytical model for the prediction of geometry and noncavitating performance of typical space rocket inducers. The transparent inlet section of the facility was instrumented with several piezoelectric pressure transducers located at three axial stations: inducer inlet, outlet and the middle of the axial chord of the blades. At each axial station at least two transducers were mounted with given angular spacing in order to cross-correlate their signals for amplitude, phase and coherence analysis. However, probably because of the high value of the blade tip clearance, very few flow instabilities have been detected on the inducer, including: steady asymmetric cavitation caused by the different extension of the cavitating regions on the blades; cavitation surge at a frequency equal to 0.16 times the inducer rotational frequency; a higher-order axial phenomenon at 7.2 times the rotational frequency

Line polar Grassmann codes of orthogonal type

Polar Grassmann codes of orthogonal type have been introduced in I. Cardinali and L. Giuzzi, \emph{Codes and caps from orthogonal Grassmannians}, {Finite Fields Appl.} {\bf 24} (2013), 148-169. They are subcodes of the Grassmann code arising from the projective system defined by the Pl\"ucker embedding of a polar Grassmannian of orthogonal type. In the present paper we fully determine the minimum distance of line polar Grassmann Codes of orthogonal type for q odd