In this work, I propose a hybrid particle simulator for charged particles. The simulator consists of a physics-informed neural network, which can handle arbitrary external electric fields with continuous coordinates by solving the Poisson equation, and a graph-based algorithm that computes the interacting forces between the particles. The simulator is then applied to a set of particles inside a square domain under the influence of some external electric field. As the system evolves in time, particles will gradually leave the domain causing the particle density of the domain to change. This work aims to find a model which describes the particle density evolution of the system.

No description available.

Accurate theoretical predictions of optical rotation are of substantial utility to the chemical community enabling the determination of absolute configuration without the need for poten- tially lengthy total synthesis. The requirements for robust calculation of gas-phase optical rotation are well understood, but too expensive for routine use. In an effort to reduce this cost we have examined the performance of the LPol and ORP basis sets, created for use in density functional theory calculations of optical rotation, finding that at the coupled cluster level of theory they perform the same or better than comparably sized general basis sets that are often used. We have also examined the performance of a perturbational approach to inclusion of explicit solvent molecules in an effort to extend the calculation of response properties from the gas phase to the condensed phase. This N-body approach performs admirably for interaction energies and even dipole moments but breaks down for optical rotation, exhibiting large basis set superposition errors and requiring higher-order terms in the expansion to provide reasonable accuracy. In addition, we have begun the process of implementing a gauge invariant version of coupled cluster response properties to address the fundamentally unphysical lack of gauge invariance in coupled cluster optical rotations. Correcting this problem, which arises from the non- variational nature of the coupled cluster wavefunction, involves reformulating the response amplitude and function expressions and solving for all necessary amplitudes simultaneously. / Ph. D.

Il est bien établit théoriquement et observationnellement que les amas de galaxies ne sont pas des objets sphèriques, et qu'ils sont beaucoup mieux décrits par la géométrie triaxiale. Malgré cela, les travaux sur la forme tri-dimensionnelle des amas de galaxies sont encore trés rares. L'objet de cette thèse est de contribuer à cette problématique naissante. L'originalité de ce travail est d'aborder ce sujet théoriquement et observationnellement. J'ai mesuré la forme d'amas de galaxies simulés, proposant des prédictions sur la forme des haloes de matière noire. J'ai ensuite développé un algorithme qui se propose de combiner des données en lentilles gravitationnelles et en rayons X afin de contraindre un modèle de haloe triaxial. L'algorithme est testé sur des données simulées. Finalement, je présente l'analyse en rayons X de Abell 1703, qui, combinée avec l'analyse en lentilles gravitationnelles, permettra de déterminer la forme de Abell 1703. / It is well established both theoretically and observationally that galaxy clusters are not spherical objects and that they are much better approximated as triaxial objects. This thesis focusses on the three dimencional shape of galaxy clusters. The originality of my approach is to tackle the problem both theoretically and observationally. First, I have measured the shape of dark matter haloes in the Millenium XXL and Sbarbine simulations, providing predictions for dark matter halo shape over 5 order in magnitude in mass. Then, I have developed an algorithm aimed at fitting simultaneously lensing and X-ray data in order to constrain a triaxial mass distribution. The algorithm is tested and characterized on mock data sets. It is found to be able to recover the input parameters. Finally, I present the X-ray analysis of galaxy cluster Abell 1703, which will be combined with the existing lensing analysis in order to investigate its shape.

No description available.

In this thesis we investigate the existence and stability of periodic solutions of Hamiltonian systems with a discrete symmetry. The global existence of periodic motions can be proven using the classical techniques of the calculus of variations; our particular interest is in how the stability type of the solutions thus obtained can be determined analytically using solely the variational problem and the symmetries of the system -- we make no use of numerical or perturbation techniques. Instead, we use a method introduced in [41] in the context of a special case of the three-body problem. Using techniques from symplectic geometry, and specifically the Maslov index for curves of Lagrangian subspaces along the minimizing trajectories, we verify conditions which preclude the existence of eigenvalues of the monodromy matrix on the unit circle. We study the applicability of this method in two specific cases. Firstly, we consider another special case from celestial mechanics: the hip-hop solutions of the 2N-body problem. This is a family of Z_2-symmetric, periodic orbits which arise as collision-free minimizers of the Lagrangian action on a space of symmetric loops [14, 53]. Following a symplectic reduction, it is shown that the hip-hop solutions are brake orbits which are generically hyperbolic on the reduced energy-momentum surface. Secondly we consider a class of natural Hamiltonian systems of two degrees of freedom with a homogeneous potential function. The associated action functional is unbounded above and below on the function space of symmetric curves, but saddle points can be located by minimization subject to a certain natural constraint of a type first considered by Nehari [37, 38]. Using the direct method of the calculus of variations, we prove the existence of symmetric solutions of both prescribed period and prescribed energy. In the latter case, we employ a variational principle of van Groesen [55] based upon a modification of the Jacobi functional, which has not been widely used in the literature. We then demonstrate that the (constrained) minimizers are again hyperbolic brake orbits; this is the first time the method has been applied to solutions which are not globally minimizing. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-09-25 10:47:53.257

Changes of semimajor axes of giant planets, which took place 4 billion years ago and evolved the Solar System towards its present state, affected various populations of minor Solar-System bodies. One of these populations was a group of dynamically stable asteroids in the 2:1 mean-motion resonance with Jupiter which reside in two islands of the phase space, denoted A and B, and exhibit lifetimes comparable to the age of the Solar System. The origin of stable asteroids has not been explained so far. Our main goal is to create a viable hypothesis of their origin. We update the resonant population and its physical properties on the basis of up-to-date observational data. Using an N-body model with seven giant planets and the Yarkovsky effect included, we demonstrate that the depletion of island A is faster compared to island B. We then investigate: (i) survivability of primordial resonant asteroids and (ii) capture of the population during planetary migration, using a recently described scenario with an escaping fifth giant planet and a jumping-Jupiter instability. We employ simulations with prescribed migration, smooth late migration and we statistically evaluate the results using dynamical maps. We also model collisions during the last 4 billion years. We conclude that the long-lived group was created by a...

<div><div>N-body problems, such as simulating the motion of stars in a galaxy and evaluating the spatial statistics through n-point correlation function, are popularly solved. The naive approaches to n-body problems are typically O(n^2) algorithms. Tree codes take advantages of the fact that a group of bodies can be skipped or approximated as a union if their distance is far away from one body’s sight. It reduces the complexity from O(n^2) to O(n*lgn). However, tree codes rely on pointer chasing and have massive branch instructions. These are highly irregular and thus prevent tree codes from being easily parallelized. </div><div><br></div><div>GPU offers the promise of massive, power-efficient parallelism. However, exploiting this parallelism requires the code to be carefully structured to deal with the limitations of the SIMT execution model. This dissertation focusses on optimizations for n-body problems on the heterogeneous system. A general inspector-executor based framework is proposed to automatically schedule GPU threads to achieve high performance. Essentially, the framework lets the GPU execute partial of the tree codes and profile threads behaviors, then it assigns the CPU to re-organize these threads to minimize the divergence before executing the remaining portion of the traversals on the GPU. We apply this framework to six tree traversal algorithms, achieving significant speedups over optimized GPU code that does not perform application-specific scheduling. Further, we show that in many cases, our hybrid approach is able to deliver better performance even than GPU code that uses hand tuned, application-specific scheduling. </div><div> </div><div>For large scale input, ChaNGa is the best-of-breed n-body platform. It uses an asymp-totically-efficient tree traversal strategy known as a dual-tree walk to quickly provide an accurate simulation result. On GPUs, ChaNGa uses a hybrid strategy where the CPU performs the tree walk to determine which bodies interact while the GPU performs the force computation. In this dissertation, we show that a highly optimized single-tree walk approach is able to achieve better GPU performance by significantly accelerating the tree walk and reducing CPU/GPU communication. Our experiments show that this new design can achieve a 8.25x speedup over baseline ChaNGa using one node, one process per node configuration. We also point out that ChaNGa's implementation doesn't satisfy the inclusion condition so that GPU-centric remote tree walk doesn't perform well.</div></div>

Agglomeration of nanoparticles occurs in a number of colloidal systems related, for example, to material processing and drug delivery. The present work is motivated by the need to improve fundamental understanding of the agglomeration and structure formation processes that occur in catalyst inks used for the fabrication of polymer electrolyte fuel cells (PEMFCs). Particle dynamics simulations are performed to investigate agglomeration under various conditions. The interaction between particles is defined using realistic physical potentials, rather than commonly used potential models, and a novel analysis of the agglomeration and structure formation process is performed using network science concepts. The simulated systems correspond to catalyst inks consisting primarily of carbon nanoparticles in solution. The effect of various conditions such as different force magnitude, shape of the force function, concentration etc. are investigated in terms of network science parameters such as average degree and shortest path. An "agglomeration timescale" and a "restructuring timescale" introduced to interpret the evolution of the agglomeration process suggest that the structure, which has a strong impact on the performance of the eventual catalyst layer, can be controlled by tuning the rate at which particles are added based on the restructuring timescale. / Graduate

In the context of future human space exploration missions in the solar system (with an horizon of 2025) and according to the roadmap proposed by ISECG (International Space Exploration Coordination Group) [1], a new step could be to maintain as an outpost, at one of the libration points of the Earth-Moon system, a space station. This would ease access to far destinations as Moon, Mars and asteroids and would allow testing some innovative technologies, before employing them for far distant human missions. One of the main challenges will be to maintain permanently, and ensure on board crew health thanks to an autonomous space medical center docked to the proposed space station, as a Space haven. Then the main problem to solve is to manage the station servitude, during deployment (modules integration) and operational phase. Challenges lie, on a global point of view, in the design of the operational scenarios and, on a local point of view, in trajectories selection, so as to minimize velocity increments (energy consumption) and transportation duration (crew safety). Which recommendations could be found out as far as trajectories optimization is concerned, that would fulfill energy consumption, transportation duration and safety criterion? What would technological hurdles be to rise for the building of such Space haven? What would be performances to aim at for critical sub-systems? Expected results of this study could point out research and development perspectives for human spaceflight missions and above all, in transportation field for long lasting missions. Thus, the thesis project, presented here, aims starting from global system life-cycle decomposition, to identify by phase operational scenario and optimize resupply vehicle mission. The main steps of this project consist of: - Bibliographical survey, that covers all involved disciplines like mission analysis (Astrodynamics, Orbital mechanics, Orbitography, N-Body Problem, Rendezvous…), Applied Mathematics, Optimization, Systems Engineering…. - Entire system life-cycle analysis, so as to establish the entire set of scenarios for deployment and operations (nominal cases, degraded cases, contingencies…) and for all trajectories legs (Low Earth Orbit, Transfer, Rendezvous, re-entry…) - Trade-off analysis for Space Station architecture - Modeling of the mission legs trajectories - Trajectories optimization Three main scenarios have been selected from the results of the preliminary design of the Space Station, named THOR: the Space Station deployment, the resupply cargo missions and the crew transportation. The deep analysis of those three main steps pointed out the criticality of the rendezvous strategies in the vicinity of Lagrangian points. A special effort has been set on those approach maneuvers. The optimization of those rendezvous trajectories led to consolidate performances (in term of energy and duration) of the global transfer from the Earth to the Lagrangian point neighborhood and return. Finally, recommendations have been deduced that support the Lagrangian points importance for next steps of Human Spaceflight exploration of the Solar system.