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The water stored in and flowing through the subsurface is fundamental for sustaining human activities and needs, feeding water and its constituents to surface water bodies and supporting the functioning of their ecosystems. Quantifying the changes that affect the subsurface water is crucial for our understanding of its dynamics and changes driven by climate change and other changes in the landscape, such as in land-use and water-use. It is inherently difficult to directly measure soil moisture and groundwater levels over large spatial scales and long times. Models are therefore needed to capture the soil moisture and groundwater level dynamics over such large spatiotemporal scales. This thesis develops a modeling framework that allows for long-term catchment-scale screening of soil moisture and groundwater level changes. The novelty in this development resides in an explicit link drawn between catchment-scale hydroclimatic and soil hydraulics conditions, using observed runoff data as an approximation of soil water flux and accounting for the effects of snow storage-melting dynamics on that flux. Both past and future relative changes can be assessed by use of this modeling framework, with future change projections based on common climate model outputs. By direct model-observation comparison, the thesis shows that the developed modeling framework can reproduce the temporal variability of large-scale changes in soil water storage, as obtained from the GRACE satellite product, for most of 25 large study catchments around the world. Also compared with locally measured soil water content and groundwater level in 10 U.S. catchments, the modeling approach can reasonably well reproduce relative seasonal fluctuations around long-term average values. The developed modeling framework is further used to project soil moisture changes due to expected future climate change for 81 catchments around the world. The future soil moisture changes depend on the considered radiative forcing scenario (RCP) but are overall large for the occurrence frequency of dry and wet events and the inter-annual variability of seasonal soil moisture. These changes tend to be higher for the dry events and the dry season, respectively, than for the corresponding wet quantities, indicating increased drought risk for some parts of the world.

With the widespread use of deformation simulations in medical applications, the realism of the force feedback has become an important issue. In order to reach real-time performance with sufficient realism the approach of adaptivity, solution of different parts of the system with different resolutions and refresh rates, has been commonly deployed. The change in accuracy resulting from the use of adaptivity, however, has been been paid scant attention in the deformation simulation field. Presentation of error metrics is rare, while more focus is given to the real-time stability. We propose an abstract pipeline to perform error analysis for different types of deformation techniques which can consider different simulation parameters. A case study is also performed using the pipeline, and the various uses of the error estimation are discussed.

It is well known that biological structures such as human brains, although may contain the same global structures, differ in shape, orientation, and fine structures across individuals and at different times. Such variabilities during registration are usually represented by nonrigid transformations. This research seeks to address this issue by developing physically based models in which transformations are constructed to obey certain physical laws. <br /><br /> In this thesis, a novel registration technique is presented based on the physical behavior of particles. Regarding the image as a particle system without mutual interaction, we simulate the registration process by a set of free particles moving toward the target positions under applied forces. The resulting partial differential equations are a nonlinear hyperbolic system whose solution describes the spatial transformation between the images to be registered. They can be numerically solved using finite difference methods. <br /><br /> This technique extends existing physically based models by completely excluding mutual interaction and highly localizing image deformations. We demonstrate its performance on a variety of images including two-dimensional and three-dimensional, synthetic and clinical data. Deformable images are achieved with sharper edges and clearer texture at less computational cost.

It is well known that biological structures such as human brains, although may contain the same global structures, differ in shape, orientation, and fine structures across individuals and at different times. Such variabilities during registration are usually represented by nonrigid transformations. This research seeks to address this issue by developing physically based models in which transformations are constructed to obey certain physical laws. <br /><br /> In this thesis, a novel registration technique is presented based on the physical behavior of particles. Regarding the image as a particle system without mutual interaction, we simulate the registration process by a set of free particles moving toward the target positions under applied forces. The resulting partial differential equations are a nonlinear hyperbolic system whose solution describes the spatial transformation between the images to be registered. They can be numerically solved using finite difference methods. <br /><br /> This technique extends existing physically based models by completely excluding mutual interaction and highly localizing image deformations. We demonstrate its performance on a variety of images including two-dimensional and three-dimensional, synthetic and clinical data. Deformable images are achieved with sharper edges and clearer texture at less computational cost.

I propose a particle-based technique for simulating incompressible uid that includes adaptive re nement of particle sampling. Each particle represents a mass of uid in its local region. Particles are split into several particles for ner sampling in regions of complex ow. In regions of smooth ow, neghboring particles can be merged. Depth below the surface and Reynolds number are exploited as our criteria for determining whether splitting or merging should take place. For the uid dynamics calculations, I use the hybrid FLIP method, which is computationally simple and e cient. Since the uid is incompressible, each particle has a volume proportional to its mass. A kernel function, whose e ective range is based on this volume, is used for transferring and updating the particle's physical properties such as mass and velocity. In addition, the particle sampling technique is extended to a fully adaptive approach, supporting adaptive splitting and merging of uid particles and adaptive spatial sampling for the reconstruction of the velocity and pressure elds. Particle splitting allows a detailed sampling of uid momentum in regions of complex ow. Particle merging, in regions of smooth ow, reduces memory and computational overhead. An octree structure is used to compute inter-particle interactions and to compute the pressure eld. The octree supporting eld-based calculations is adapted to provide a ne spatial reconstruction where particles are small and a coarse reconstruction where particles are large. This scheme places computational resources where they are most needed, to handle both ow and surface complexity. Thus, incompressibility can be enforced even in very small, but highly turbulent areas. Simultaneously, the level of detail is very high in these areas, allowing the direct support of tiny splashes and small-scale surface tension e ects. This produces a nely detailed and realistic representation of surface motion.

Outlined is a new approach to the problem of surfacing particle-based fluid simulations. The key idea is to construct a surface that is as smooth as possible while remaining faithful to the particle locations. We describe a mesh-based algorithm that expresses the surface in terms of a constrained optimization problem. Our algorithm incorporates a secondary contribution in Marching Tiles, a generalization of the Marching Cubes isosurfacing algorithm. Marching Tiles provides guarantees on the minimum vertex valence, making the surface mesh more amenable to numerical operators such as the Bilaplacian.

Outlined is a new approach to the problem of surfacing particle-based fluid simulations. The key idea is to construct a surface that is as smooth as possible while remaining faithful to the particle locations. We describe a mesh-based algorithm that expresses the surface in terms of a constrained optimization problem. Our algorithm incorporates a secondary contribution in Marching Tiles, a generalization of the Marching Cubes isosurfacing algorithm. Marching Tiles provides guarantees on the minimum vertex valence, making the surface mesh more amenable to numerical operators such as the Bilaplacian.

Lifelike animation of manipulation must account for the dynamicinteraction between animated characters, objects, and their environment. Failing to do so would ignore the often significant effects objectshave on the motion of the character. For example, lifting a heavy objectwould appear identical to lifting a light one. Physical simulationhandles such interaction correctly, with a principled approach thatadapts easily to different circumstances, changing environments, andunexpected disturbances. Our work shows how to control lifelike animatedcharacters so that they accomplish manipulation tasks within aninteractive physical simulation. Our new multi-task control algorithmsimplifies descriptions of manipulation by supporting prioritized goalsin both the joint space of the character and the task-space of theobject. The end result is a versatile algorithm that incorporatesrealistic force limits and recorded motion postures to portray lifelikemanipulation automatically.

Outlined is a new approach to the problem of surfacing particle-based fluid simulations. The key idea is to construct a surface that is as smooth as possible while remaining faithful to the particle locations. We describe a mesh-based algorithm that expresses the surface in terms of a constrained optimization problem. Our algorithm incorporates a secondary contribution in Marching Tiles, a generalization of the Marching Cubes isosurfacing algorithm. Marching Tiles provides guarantees on the minimum vertex valence, making the surface mesh more amenable to numerical operators such as the Bilaplacian. / Science, Faculty of / Computer Science, Department of / Graduate