This thesis studies two Markov processes describing the evolution of a system of many interacting random components. These processes undergo an absorbing-state phase transition, i.e., as one variates the parameter values, the process exhibits a transition from a convergence regime to one of the absorbing-states to an active regime. In Chapter 2 we study Activated Random Walk, which is an interacting particle system where the particles can be of two types and their number is conserved. Firstly, we provide a new lower bound for the critical density on Z as a function of the jump distribution and of the sleeping rate and we prove that the critical density is not a constant function of the jump distribution. Secondly, we prove that on Zd in the case of biased jump distribution the critical density is strictly less than one, provided that the sleeping rate is small enough. This answers a question that has been asked by Dickman, Rolla, Sidoravicius [9, 28] in the case of biased jump distribution. Our results have been presented in [33]. In Chapter 3 we study a class of probabilistic cellular automata which are related by a natural coupling to a special type of oriented percolation model. Firstly, we consider the process on a finite torus of size n, which is ergodic for any parameter value. By employing dynamic-renormalization techniques, we prove that the average absorption time grows exponentially (resp. logarithmically) with n when the model on Z is in the active (resp. absorbing) regime. This answers a question that has been asked by Toom [37]. Secondly, we study how the neighbourhood of the model affects the critical probability for the process on Z. We provide a lower bound for the critical probability as a function of the neighbourhood and we show that our estimates are sharp by comparing them with our numerical estimates. Our results have been presented in [34, 35].

Background. Real-time applications like video games use particle systems for special effects to add visual aesthetics and realism. However, when complex behaviour that requires interaction between particles and geometry is desired, problems arise. The developer has to choose between having consistent and precise collisions or higher performance. This thesis goes over two particle collision implementations that try to solve these problems. Objectives. The objective of this thesis is to create an application that has support for two collision methods and compare them on performance and accuracy to decide which one is more suitable for real-time applications. Methods. To answer the research questions proposed the implementation methodology was used, as a result of that, a 3D-application was created using the graphics API OpenGL to render. Two simple GPGPU implementations were made for each method, to have a more fair comparison. To be able to measure performance the application logs frame-time every frame. A fixed time-step was added in the main loop to allow the users to stop the application at a certain time to be able to capture images of the scene that will then be used for pixel comparison to measure accuracy. Results. Screen space particle collision is almost three times faster than the octree-based method. Both methods had different behavior in both the real-time simulation and at specific time-steps resulting in loss of accuracy from the screen space particle collision. Conclusions. The tests allowed the authors to show that the screen space particle collision is faster and scales better than the octree-based method. However, it did lack precision as shown by the comparison by the images taken from the test. For particle simulations that require consistent and accurate collision checks the octree-based method is better due to the fact that screen space particle collision can result in false collisions checks and has problems with hidden geometry.

This work is studying real-time generation of smoke simulation based on a particle system. In order to enhance the realism of the effect, we used texture mapping (Perlin noise) and transparency disturbance to shade the 3D smoke. Furthermore, it uses simple physical function to simulate smoke movement. Classical smoke simulation is using a great amount of particles which makes computing more complex. Compared with traditional methods, the method we propose can generate realistic visual effect of smoke in real-time and reduce the time consumed.

Context. Particle systems are an important part for enhancing the player experience in games, simulating fire, smoke and water. The higher and higher demands from modern games to provide visual stunning experiences puts a strain on performance that the CPU is not able to handle. That is why ideas about moving data from the CPU over to the GPU have begun being promoted. Objectives. In this paper we test how the performance is affected when moving a particle system from the CPU to reside completely on the GPU. Methods. This is measured by using time stamps to determine the execution time for different steps needed to inject, update and render the particles in the particle system. Results. The results of these tests showed that the particle system on the GPU performed significantly better than the one on the CPU in all areas except one which was the injection step. Conclusions. This paper concludes that it is better to keep a particle system on the GPU at all times if possible when the particle system is not needed to interact with the rest of the game world.

<p> This thesis examines the rotation-vibration spectra of systems of two and three particles (spin zero). The results in the two-particle case agree with many of the gross features of the spectra of deformed axially symmetric even-even nuclei. In the three-particle case, the set of basis functions used i n the expansions of the wavefunctions was too small to give accurate eigenvalues and eigenvectors, but nevertheless the spectrum clearly corresponds to that of an asymmetric even-even nucleus. </p> / Thesis / Master of Science (MSc)

Background. Particle systems render groups of points in space that are used to add various effects to a scene. When rendering particles, there are various advantages and disadvantages for rendering an effect in either object-space or image-space. The former uses calculations in a 3D environment, while the latter adds particles to a 2D image. There is a lack of existing research to understand the trade-off in performance and in effort when applying these two techniques. Objectives. This thesis aims to compare the performance difference between particle systems in object-space versus image-space. The intent is to do this using a C++ DirectX11 implementation. Methods. The primary methodology of this thesis was an implementation complemented by a performance evaluation. Two particle systems were made to render the same particle effect. The systems were run at five different particle amounts and the FPS was recorded for 30 seconds while the simulations ran. Results. The data presented displays the average FPS recorded, with different line graphs for the various particle amounts. The results show an overall better performance of the O-system. Conclusions. While the O-system performed better, the various techniques and optimizations available to particle systems that render in image-space would allow avastly different result. This thesis would be well complemented with further research. It would also be furthered by comparing performance while additional geometry interacts with the particles.

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Nosso trabalho considera o processo de exclusão simples do vizinho mais próximo evoluindo com taxas de salto aleatórias . Demonstramos o limite hidrodinâmico deste processo. Este resultado è obtido através do limite hidrodinâmico do processo de exclusão onde as taxas de salto iniciais são substituidas pelas taxas cx,N que tem a mesma distribuição para cada N maior ou igal a 1. Fazemos algumas suposições no meio c_N e consideramos que as partículas estão inicialmente distribuidas de acordo à medida produto de Bernoulli associada a um perfil inicial. / Consider a Poisson process with rate equal to 1 in IR. Consider the nearest neighbor simple exclusion process with random jump rates § where §x =\\lambda, \\lambda > 0 if there is a Poisson mark between (x, x + 1) and §x = 1 otherwise. We prove the hydrodynamic limit of this process. This result follows from the hydrodynamic limit in the case that the jump rates {§x : x inteiro} are replaced by an array {cx,N : x inteiro} having the same distribution for each N >=1.

Nosso trabalho considera o processo de exclusão simples do vizinho mais próximo evoluindo com taxas de salto aleatórias . Demonstramos o limite hidrodinâmico deste processo. Este resultado è obtido através do limite hidrodinâmico do processo de exclusão onde as taxas de salto iniciais são substituidas pelas taxas cx,N que tem a mesma distribuição para cada N maior ou igal a 1. Fazemos algumas suposições no meio c_N e consideramos que as partículas estão inicialmente distribuidas de acordo à medida produto de Bernoulli associada a um perfil inicial. / Consider a Poisson process with rate equal to 1 in IR. Consider the nearest neighbor simple exclusion process with random jump rates § where §x =\\lambda, \\lambda > 0 if there is a Poisson mark between (x, x + 1) and §x = 1 otherwise. We prove the hydrodynamic limit of this process. This result follows from the hydrodynamic limit in the case that the jump rates {§x : x inteiro} are replaced by an array {cx,N : x inteiro} having the same distribution for each N >=1.

<p>Create the realistic motion of a character is a very complicated work.</p><p>This thesis aims to create interactive animation for characters in three dimensions using position based approach. Our character is pictured from ragdoll, which is a structure of system particles where all particles are linked by equidistance constraints.</p><p>The goal of this thesis is observed the fall in the space of our ragdoll after creating all constraints, as structure, contact and environment constraints.</p><p>The structure constraint represents all joint constraints which have one, two or three Degree of Freedom (DOF).</p><p>The contact constraints are represented by collisions between our ragdoll and other objects in the space.</p><p>Finally, the environment constraints are represented by means of the wall constraint.</p><p>The achieved results allow to have a realist fall of our ragdoll in the space.</p>