On the existence of right adjoints for surjective mappings between fuzzy structures0

En este trabajo los autores continúan su estudio de la caracterización de la existencia de adjunciones (conexiones de Galois isótonas) cuyo codominio no está dotado de estructura en principio. En este artículo se considera el caso difuso en el que se tiene un orden difuso R definido en un conjunto A y una aplicación sobreyectiva f:A-> B compatible respecto de dos relaciones de similaridad definidas en el dominio A y en el condominio B, respectivamente. Concretamente, el problema es encontrar un orden difuso S en B y una aplicación g:B-> A compatible también con las correspondientes similaridades definidas en A y en B, de tal forma que el par (f,g) constituya un adjunción.

Nature of the spin-glass phase in dense packings of Ising dipoles with random anisotropy axes

By Monte Carlo simulations, we study the character of the spinglass (SG) phase in dense disordered packings of magnetic nanoparticles (NPs). We focus on NPs which have large uniaxial anisotropies and can be well represented as Ising dipoles. Dipoles are placed on SC lattices and point along randomly oriented axes. From the behaviour of a SG correlation length we determine the transition temperature Tc between the paramagnetic and a SG phase. For temperatures well below Tc we find distributions of the SG overlap parameter q that are strongly sample-dependent and exhibit several spikes. We find that the average width of spikes, and the fraction of samples with spikes higher than a certain threshold does not vary appreciably with the system sizes studied. We compare these results with the ones found previously for 3D site-diluted systems of parallel Ising dipoles and with the behaviour of the Sherrington-Kirkpatrick model.

NONLINEAR EFFECTS IN MAGNETIC GARNET FILMS AND NONRECIPROCAL OPTICAL BLOCH OSCILLATIONS IN WAVEGUIDE ARRAYS

This dissertation presents detailed experimental and theoretical investigations of nonlinear and nonreciprocal effects in magnetic garnet films. The dissertation thus comprises two major sections. The first section concentrates on the study of a new class of nonlinear magneto-optic thin film materials possessing strong higher order magnetic susceptibility for nonlinear optical applications. The focus was on enlarging the nonlinear performance of ferrite garnet films by strain generation and compositional gradients in the sputter-deposition growth of these films. Under this project several bismuth-substituted yttrium iron garnet (Bi,Y) 3 (Fe,Ga)5 O12(acronym as Bi:YIG) films have been sputter-deposited over gadolinium gallium garnet (Gd 3 Ga5 O12 ) substrates and characterized for their nonlinear optical response. One of the important findings of this work is that lattice mismatch strain drives the second harmonic (SH) signal in the Bi:YIG films, in agreement with theoretical predictions; whereas micro-strain was found not to correlate significantly with SH signal at the micro-strain levels present in these films. This study also elaborates on the role of the film's constitutive elements and their concentration gradients in nonlinear response of the films. Ultrahigh sensitivity delivered by second harmonic generation provides a new exciting tool for studying magnetized surfaces and buried interfaces, making this work important from both a fundamental and application point of view. The second part of the dissertation addresses an important technological need; namely the development of an on-chip optical isolator for use in photonic integrated circuits. It is based on two related novel effects, nonreciprocal and unidirectional optical Bloch oscillations (BOs), recently proposed and developed by Professor Miguel Levy and myself. This dissertation work has established a comprehensive theoretical background for the implementation of these effects in magneto-optic waveguide arrays. The model systems we developed consist of photonic lattices in the form of one-dimensional waveguide arrays where an optical force is introduced into the array through geometrical design turning the beam sideways. Laterally displaced photons are periodically returned to a central guide by photonic crystal action. The effect leads to a novel oscillatory optical phenomenon that can be magnetically controlled and rendered unidirectional. An on-chip optical isolator was designed based on the unidirectionality of the magneto-opticBloch oscillatory motion. The proposed device delivers an isolation ratio as high as 36 dB that remains above 30 dB in a 0.7 nm wavelength bandwidth, at the telecommunication wavelength 1.55 μm. Slight modifications in isolator design allow one to achieve an even more impressive isolation ratio ~ 55 dB, but at the expense of smaller bandwidth. Moreover, the device allows multifunctionality, such as optical switching with a simultaneous isolation function, well suited for photonic integrated circuits.

Hybrid Monte Carlo algorithm for the double exchange model

The Hybrid Monte Carlo algorithm is adapted to the simulation of a system of classical degrees of freedom coupled to non self-interacting lattices fermions. The diagonalization of the Hamiltonian matrix is avoided by introducing a path-integral formulation of the problem, in d + 1 Euclidean space–time. A perfect action formulation allows to work on the continuum Euclidean time, without need for a Trotter–Suzuki extrapolation. To demonstrate the feasibility of the method we study the Double Exchange Model in three dimensions. The complexity of the algorithm grows only as the system volume, allowing to simulate in lattices as large as 163 on a personal computer. We conclude that the second order paramagnetic–ferromagnetic phase transition of Double Exchange Materials close to half-filling belongs to the Universality Class of the three-dimensional classical Heisenberg model.

Développement d’un dispositif d’extrusion tridimensionnelle de sucre vitrifié pour la production de réseaux fluidiques complexes par moulage rapide

L’objectif du vaste projet de recherche dans lequel s’inscrit ce mémoire est de guérir le diabète de type 1 en fabriquant un pancréas bioartificiel vascularisé contenant des cellules bêta (i.e. les cellules sécrétant l’insuline). Ce dispositif permettrait de rendre aux personnes atteintes par le diabète de type 1 la capacité de sécréter par elles-mêmes de l’insuline et de réguler leur glycémie. La vascularisation est actuellement un enjeu de taille dans le domaine du génie tissulaire. La plupart des tissus incorporant des cellules générées par le génie tissulaire sont actuellement fortement limités en épaisseur faute d’être vascularisés adéquatement. Pour les tissus dont l’épaisseur dépasse 400 μm, la vascularisation est nécessaire à la survie de la plupart des cellules qui autrement souffriraient d’hypoxie, les empêchant ainsi d’accomplir leurs fonctions [1]. Ce mémoire présente le développement et la mise en service d’un dispositif d’extrusion tridimensionnelle de sucre vitrifié pour la vascularisation d’un pancréas bioartificiel. Ce dispositif a été développé au laboratoire de recherche sur les procédés d’impression 3D ainsi qu’au bureau de design du département de génie mécanique de l’Université Laval. Grâce à cette technique d’impression 3D novatrice et à la caractérisation du procédé, il est maintenant possible de produire rapidement et avec précision des structures temporaires en sucre vitrifié pour la fabrication de réseaux vasculaires tridimensionnels complexes. Les structures temporaires peuvent, après leur production, être utilisées pour réaliser le moulage rapide de constructions vascularisées avec des matériaux tels que du polydiméthylsiloxane (PDMS) ou des hydrogels chargés de cellules biologiques. De par la nature du matériel utilisé, les moules temporaires peuvent être facilement et rapidement dissous dans une solution aqueuse et laisser place à un réseau de canaux creux sans créer de rejets toxiques, ce qui représente un avantage majeur dans un contexte de bio-ingénierie.