321 research outputs found
Un enfoque geométrico a los sistemas de Lie : formalismo de las deformaciones de álgebras de Poisson–Hopf
Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leÃda el 22-01-2021The notion of quantum algebras is merged with that of Lie systems in order to establish a new formalism called Poisson–Hopf algebra deformations of Lie systems. The procedure can be naturally applied to Lie systems endowed with a symplectic structure, the so-called Lie–Hamilton systems.This is quite a general approach, as it can be applied to any quantum deformation and any underlying manifold. One of its main features is that, under quantum deformations, Lie systems are extended to generalized systems described by involutive distributions. As a consequence, a quantum deformed Lie system no longer has an underlying Vessiot–Guldberg Lie algebra or a quantum algebra one, but keeps a Poisson–Hopf algebra structure that enables us to obtain, in an explicit way, the t-independent constants of the motion from quantum deformed Casimir invariants, which are potentially useful in a further construction of the generalized notion of superposition rules. We illustrate this approach by considering the non-standard quantum deformation of sl(2) applied to well-known Lie systems, such as the oscillator problem or Milne–Pinney equation, as well as several types of Riccati equations. In this way, we obtain their new generalized (deformed) counterparts that cover, in particular, a new oscillator system with a time-dependent frequency and a position-dependent mass...La noción de álgebras cuánticas se fusiona con la de sistemas de Lie para establecer un nuevo formalismo, las deformaciones del álgebra de Poisson–Hopf de los sistemas de Lie. El procedimiento puede aplicarse a sistemas de Lie dotados de una estructura simpléctica, los denominados sistemas de Lie–Hamilton. Este es un enfoque bastante general, ya que se puede aplicar a cualquier deformación cuántica y a cualquier variedad subyacente. Una de sus principales caracterÃsticas es que, bajo deformaciones cuánticas, los sistemas de Lie se extienden a distribuciones involutivas generalizadas. Como consecuencia, un sistema de Lie deformado cuánticamente ya no tiene un álgebra de Vessiot–Guldberg Lie subyacente o un álgebra cuántica, sino que mantiene una estructura de álgebra de Poisson–Hopf que permite obtener, de manera explÃcita, las constantes del movimientot-independientes a partir de los invariantes de Casimir deformados, que son potencialmente útiles en una construcción adicional de la noción generalizada de reglas de superposición. Ilustramos este enfoque considerando la deformación cuántica no estándar de sl(2) aplicada a sistemas de Lie conocidos, como el problema del oscilador o la ecuación de Milne–Pinney, asà como varios tipos de ecuaciones de Riccati. De esta manera, se obtienen sus análogos generalizados (deformados) quedan lugar, en particular, a un nuevo sistema de tipo oscilatorio con una frecuencia dependiente del tiempo y una masa dependiente de la posición...Fac. de Ciencias MatemáticasTRUEunpu
Freeze casting of hydroxyapatite scaffolds for bone tissue engineering
International audienceAlthough extensive efforts have been put into the development of porous scaffolds for bone regeneration, with encouraging results, all porous materials have a common limitation: the inherent lack of strength associated with porosity. Hence, the development of porous hydroxyapatite scaffolds has been hindered to non-load bearing applications. We report here how freeze-casting can be applied to synthesize porous hydroxyapatite scaffolds exhibiting unusually high compressive strength, e.g. up to 145 MPa for 47% porosity and 65 MPa for 56% porosity. The materials are characterized by well-defined pore connectivity along with directional and completely open porosity. Various parameters affecting the porosity and compressive strength have been investigated, including initial slurry concentration, freezing rate, and sintering conditions. The implications and potential application as bone substitute are discussed. These results might open the way for hydroxyapatite-based materials designed for load-bearing applications. The biological response of these materials is yet to be tested
Ice-templated porous alumina structures
International audienceThe formation of regular patterns is a common feature of many solidification processes involving cast materials. We describe here how regular patterns can be obtained in porous alumina by controlling the freezing of ceramic slurries followed by subsequent ice sublimation and sintering, leading to multilayered porous alumina structures with homogeneous and well-defined architecture. We discuss the relationships between the experimental results, the physics of ice and the interaction between inert particles and the solidification front during directional freezing. The anisotropic interface kinetics of ice leads to numerous specific morphologies features in the structure. The structures obtained here could have numerous applications including ceramic filters, biomaterials, and could be the basis for dense multilayered composites after infiltration with a selected second phase
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