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In this Thesis, we study some of the classical properties of an extension of the Skyrme model defined by adding a sixth order derivative term to the Lagrangian. In chapter 1, we review the physical as well as the mathematical motivation behind the study of the Skyrme model and in chapter 2, we give a brief summary of various extended Skyrme models that have been proposed over the last few years. We then define a new sixth order Skyrme model by introducing a dimensionless parameter λ that denotes the mixing between the two higher order terms, the Skyrme term and the sixth order term. In chapter 3 we compute numerically the multi-skyrmion solutions of this extended model and show that they have the same symmetries with the usual skyrmion solutions. In addition, we analyse the dependence of the energy and radius of these classical solutions with respect to the coupling constant λ. We compare our results with experimental data and determine whether this modified model can provide us with better theoretical predictions than the original one. In chapter 4, we use the rational map ansatz, introduced by Houghton, Manton and Sutcliffe, to approximate minimum energy multi-skyrmion solutions with B ≤ 9 of the SU(2) model and with B ≤ 6 of the SU(3) model. We compare our results with the ones obtained numerically and show that the rational map ansatz works just as well for the generalised model as for the pure Skyrme model, at least for B ≤ 5. In chapter 5, we use a generalisation of the rational map ansatz, introduced by loannidou, Piette and Zakrzewski, to construct analytically some topologically non-trivial solutions of the extended model in SU(3). These solutions are spherically symmetric and some of them can be interpreted as bound states of skyrmions. Finally, we use the same ansatz to construct low energy configurations of the SU(N) sixth order Skyrme model.

Le modèle physique masses interactions est puissant pour la simulation de comportements dynamiques très divers et pour la production de mouvements expressifs, riches et d'une grande complexité. En revanche, une difficulté inhérente à ce type de formalisme pour la production d'images animées réside dans le fait que les masses ponctuelles n'ont pas de spatialité ; il est donc difficile de produire des séquences d'images animées par le rendu direct des masses ponctuelles décrivant le mouvement. D'une manière générale, il est donc nécessaire de développer des méthodes qui étendent la spatialité de ces masses ponctuelles pour compléter la chaîne de production d'images animées par modèle physique particulaire. Une méthode, proposée par le laboratoire ICA, répond à ce type de problématique en permettant d'étendre la spatialité des masses ponctuelles en considérant l'interaction physique entre ces masses et un milieu. Il s'agit d'une métaphore du procédé physique de la gravure. Celle ci a permis de produire des images animées convaincantes de divers phénomènes visuels. Nous présentons dans ce document un élargissement de cette méthode notamment au cas 3D, ainsi qu'à de nouveaux comportements. De plus, l'algorithme de cette méthode a été parallélisé, ce qui nous a permis d'obtenir des simulations calculées en temps réel en utilisant la puissance actuelle des cartes graphiques. Afin de maitriser au mieux les possibilités de la méthode, nous avons développé un logiciel comprenant une interface graphique manipulable et interactive permettant de modéliser avec aisance différents comportements. Cette méthode a été intégrée dans des installations interactives artistiques multi-sensorielles fournissant un comportement dynamique riche et configurable, tout en permettant une interaction en temps réel avec le spectateur. / Mass – Interaction physical modeling is a powerful formalism for the simulation of various dynamic behaviors and for the production of expressive, rich and complex motions. However, there is an inherent matter of this type of formalism for animation production, which resides on the fact that masses have no spatiality. Thus, it is difficult to produce animation sequences directly from rendering mass point describing the movement. It is then necessary to develop methods that extend the masses spatiality in order to complete the animation process. ICA Laboratory addressed the problem with a method based on the physical simulation of interaction between these masses and a dynamic milieu, according to the metaphor of engraving. We present in this document an extension of this method notably towards 3D and other effects. Besides, the parallel implementation on Graphic Cards (GPU) allowed obtaining real time simulation. An interactive graphical interface was also developed to facilitate the creation of different models. We used this process in multi-sensory interactive art installations for its rich and dynamic ability to create shape from motion and interact in real time with spectators.

In this thesis the properties of proteins and membranes are studied by molecular dynamics simulations. The subject is decomposed into parts addressing free energy calculations in proteins, mechanical inclusion models for lipid bilayers, phase transitions and structural correlations in lipid bilayers and atomistic lipid bilayer models. The work is based on results from large scale computer simulations, quantum mechanical and continuum models. Efficient statistical sampling and the coarseness of the models needed to describe the ordered and disordered states are of central concern. Classical free energy calculations of zinc binding, in metalloproteins, require a quantum mechanical correction in order to obtain realistic binding energies. Classical electrostatic polarisation will influence the binding energy in a large region surrounding the ion and produce reasonable equilibrium structures in the bound state, when compared to experimental evidence. The free energy for inserting a protein into a membrane is calculated with continuum theory. The free energy is assumed quadratic in the mismatch and depend on two elastic constants of the membrane. Under these circumstances, the free energy can then be written as a line tension multiplied by the circumference of the membrane inclusion. The inclusion model and coarse grained particle simulations of the membranes show that the thickness profile around the protein will be an exponentially damped oscillation. Coarse-grained particle simulations of model membranes containing mixtures of phospholipid and cholesterol molecules at different conditions were performed. The gel-to-liquid crystalline phase transition is successively weakened with increasing amounts of cholesterol without disappearing even at a concentration of cholesterol as high as 60%. A united atom parameterization of diacyl lipids was constructed. The aim was to construct a new force field that retains and improves the good agreement for the fluid phase and at the same time produces a gel phase at low temperatures, with properties coherent with experimental findings. The global bilayer tilt obtains an azimuthal value of 31◦ and is aligned between lattice vectors in the bilayer plane. It is also shown that the model yield a correct heat of melting as well as heat capacities in the fluid and gel phase of DPPC. / <p>QC 20140919</p>

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-10T17:54:50Z No. of bitstreams: 1 JAMILSON RAMOS CAMPOS - DISSERTAÇÃO PPGMAT 2006..pdf: 6748825 bytes, checksum: 592fc0c2a05c38766aae5d672c3c4708 (MD5) / Made available in DSpace on 2018-07-10T17:54:50Z (GMT). No. of bitstreams: 1 JAMILSON RAMOS CAMPOS - DISSERTAÇÃO PPGMAT 2006..pdf: 6748825 bytes, checksum: 592fc0c2a05c38766aae5d672c3c4708 (MD5) Previous issue date: 2006-12 / Este trabalho apresenta um estudo de dois modelos computacionais deformáveis aplicados à simulação de tecidos, ambos modelos de mecânica de partículas fisicamente embasados, contemplando algoritmos, um para cada modelo, para o tratamento de colisões. Estudamos um modelos de malha retangular (clássico e pouco robusto) e um baseado em malha triangular (moderno e robusto) através da implementação, simulações e uma análise qualitativa simples entre os resultados visuais obtidos com ambos. Nenhum destes modelos apresenta relações entre deformações tangenciais e normais e portanto, não geram rugas e/ou dobras espontaneamente. Para torná-los mais realísticos, em nossa implementação, propomos o uso de uma força de acoplamento entre as deformações tangenciais normais. / This work presents a study of two deformable computational models applied to the simulation of cloths, both physically based models of particle mechanics, contemplating one per model, collision treatment algorithms. We study a rectangular grid model (classic and not very robust one) and a triangular mesh based model (modern and robust one) throught implementation, simulations and a simple qualitative analysis between visual results reached with them. Neither of these models presents a relationship with tangent and normal deformations therefore don't build folds and/or wrinkles spontaneously. to turn then more realistic, in our implementation, we propose to make use of a coupling force between tangent and normal deformations.