Time-multiscale methods for the simulation of slow transport problems in atomistic systems

En esta tesis presentamos una teoría adaptada a la simulación de fenómenos lentos de transporte en sistemas atomísticos. En primer lugar, desarrollamos el marco teórico para modelizar colectividades estadísticas de equilibrio. A continuación, lo adaptamos para construir modelos de colectividades estadísticas fuera de equilibrio. Esta teoría reposa sobre los principios de la mecánica estadística, en particular el principio de máxima entropía de Jaynes, utilizado tanto para sistemas en equilibrio como fuera de equilibrio, y la teoría de las aproximaciones del campo medio. Expresamos matemáticamente el problema como un principio variacional en el que maximizamos una entropía libre, en lugar de una energía libre. La formulación propuesta permite definir equivalentes atomísticos de variables macroscópicas como la temperatura y la fracción molar. De esta forma podemos considerar campos macroscópicos no uniformes. Completamos el marco teórico con reglas de cuadratura de Monte Carlo, gracias a las cuales obtenemos modelos computables. A continuación, desarrollamos el conjunto completo de ecuaciones que gobiernan procesos de transporte. Deducimos la desigualdad de disipación entrópica a partir de fuerzas y flujos termodinámicos discretos. Esta desigualdad nos permite identificar la estructura que deben cumplir los potenciales cinéticos discretos. Dichos potenciales acoplan las tasas de variación en el tiempo de las variables microscópicas con las fuerzas correspondientes. Estos potenciales cinéticos deben ser completados con una relación fenomenológica, del tipo definido por la teoría de Onsanger. Por último, aportamos validaciones numéricas. Con ellas ilustramos la capacidad de la teoría presentada para simular propiedades de equilibrio y segregación superficial en aleaciones metálicas. Primero, simulamos propiedades termodinámicas de equilibrio en el sistema atomístico. A continuación evaluamos la habilidad del modelo para reproducir procesos de transporte en sistemas complejos que duran tiempos largos con respecto a los tiempos característicos a escala atómica. ABSTRACT In this work, we formulate a theory to address simulations of slow time transport effects in atomic systems. We first develop this theoretical framework in the context of equilibrium of atomic ensembles, based on statistical mechanics. We then adapt it to model ensembles away from equilibrium. The theory stands on Jaynes' maximum entropy principle, valid for the treatment of both, systems in equilibrium and away from equilibrium and on meanfield approximation theory. It is expressed in the entropy formulation as a variational principle. We interpret atomistic equivalents of macroscopic variables such as the temperature and the molar fractions, wich are not required to be uniform, but can vary from particle to particle. We complement this theory with Monte Carlo summation rules for further approximation. In addition, we provide a framework for studying transport processes with the full set of equations driving the evolution of the system. We first derive a dissipation inequality for the entropic production involving discrete thermodynamic forces and fluxes. This discrete dissipation inequality identifies the adequate structure for discrete kinetic potentials which couple the microscopic field rates to the corresponding driving forces. Those kinetic potentials must finally be expressed as a phenomenological rule of the Onsanger Type. We present several validation cases, illustrating equilibrium properties and surface segregation of metallic alloys. We first assess the ability of a simple meanfield model to reproduce thermodynamic equilibrium properties in systems with atomic resolution. Then, we evaluate the ability of the model to reproduce a long-term transport process in complex systems.

On a mathematical model arising in MHD perturbed equilibrium for Stellarator devices. A numerical approach.

Abstract?We consider a mathematical model related to the stationary regime of a plasma of fusion nuclear, magnetically confined in a Stellarator device. Using the geometric properties of the fusion device, a suitable system of coordinates and averaging methods, the mathematical problem may be reduced to a two dimensional free boundary problem of nonlocal type, where the corresponding differential equation is of the Grad?Shafranov type. The current balance within each flux magnetic gives us the possibility to define the third covariant magnetic field component with respect to the averaged poloidal flux function. We present here some numerical experiences and we give some numerical approach for the averaged poloidal flux and for the third covariant magnetic field component.

Novel poly(3-hydroxybutyrate) nanocomposites containing WS2 inorganic nanotubes with improved thermal, mechanical and tribological properties

Poly(3-hydroxybutyrate) (PHB) nanocomposites containing environmentally-friendly tungsten disulphide inorganic nanotubes (INTeWS2) have been successfully prepared by a simple solution blending method. The dynamic and isothermal crystallization studies by differential scanning calorimetry (DSC) demonstrated that the INTeWS2 exhibits much more prominent nucleation activity on the crystallization of PHB than specific nucleating agents or other nanoscale fillers. Both crystallization rate and crystallinity significantly increase in the nanocomposites compared to neat PHB. These changes occur without modifying the crystalline structure of PHB in the nanocomposites, as shown by wide-angle X-ray diffraction (WAXS) and infrared/Raman spectroscopy. Other parameters such as the Avrami exponent, the equilibrium melting temperature, global rate constant and the fold surface free energy of PHB chains in the nanocomposites were obtained from the calorimetric data in order to determine the influence of the INTeWS2 filler. The addition of INTeWS2 remarkably influences the energetics and kinetics of nucleation and growth of PHB, reducing the fold surface free energy by up to 20%. Furthermore, these nanocomposites also show an improvement in both tribological and mechanical (hardness and modulus) properties with respect to pure PHB evidenced by friction and nanoindentation tests, which is of important potential interest for industrial and medical applications.