This research seeks to expand the role of variational and adjoint processing methods into segments of the sonar, radar, and nondestructive testing communities where they have not yet been widely introduced. First, synthetic aperture reconstruction is expressed in terms of the adjoint operator. Many, if not all, practical imaging modalities can be traced back to this general result, as the adjoint is the foundation for backprojection-type algorithms. Next, active surfaces are developed in the context of the Helmholtz equation for the cases of opaque scatterers (i.e., with no interior field) embedded in free space, and penetrable scatterers embedded in a volume which may be bounded. The latter are demonstrated numerically using closed-form solutions based on spherical harmonics. The former case was chosen as the basis for a laboratory experiment using Lamb waves in an aluminum plate. Lamb wave propagation in plates is accurately described by the Helmholtz equation, where the field quantity is the displacement potential. However, the boundary conditions associated with the displacement potential formulation of Lamb waves are incompatible with the shape gradient derived for the Helmholtz equation, except for very long or very short wavelengths. Lastly, optical flow is used to solve a new and unique problem in the field of synthetic aperture sonar. Areas of acoustic focusing and dilution attributable to refraction can sometimes resemble the natural bathymetry of the ocean floor. The difference is often visually indistinguishable, so it is desirable to have a means of detecting these transient refractive effects without having to repeat the survey. Optical flow proved to be effective for this purpose, and it is shown that the parameters used to control the algorithm can be linked to known properties of the data collection and scattering physics.

One of prospective procedures of absorbing thermal energy and releasing it during the required time is the application of phase change materials known as PCMs in building envelopes. High thermal energy storage (TES) materials has been a technology that effects the energy efficiency of a building by contributing in using onsite resources and reducing cooling or heating loads. Currently, many TES systems are emerging and contributing in building assemblies, however using an appropriate type of TES in a specific building and climate requires an in-depth knowledge of their properties. This research aims to provide a thorough review of a broad range of thermal energy storage technologies including their potential application in buildings. Subsequently, a comparative study and simulation between a basecase and an optimized model by PCM is thoroughly considered to understand the effect of high thermal storage building's shell on energy efficiency and indoor thermal comfort. Specifically this study proposes that the incorporation of PCM into glazing system as a high thermal capacity system will improve windows thermal performance and thermal capacity to varying climatic conditions. The generated results by eQUEST energy modeling software demonstrates approximately 25% reduction in cooling loads during the summer and 10% reduction in heating loads during the winter for optimized office building by PCM in hot arid climate of Arizona. Besides, using PCM in glazing system will reduce heat gain through the windows by conduction phenomenon. The hourly results indicates the effect of PCM as a thermal energy storage system in building envelopes for building's energy efficiency and thermal regulation. However, several problems need to be tackled before LHTES can reliably and practically be applied. We conclude with some suggestions for future work.

Pattern formation on self deforming materials is playing an increasingly vital role in the study of many biological processes. An example is the cell cortex, a network of interlinked actin filaments connected to the inside of the cell membrane. The stiffness of these filaments makes the cortex rigid and gives the cortex a strong influence in the shape of the cell. Additionally, molecular turnover and motor proteins allow shape changes necessary for the cell to divide and to adapt to its environment. Due to the incredible number of proteins that make up the cell cortex, simulation of the molecular dynamics for the entire cortex is impossible. However, when considering a larger scale, these dynamics can be approximated, making it possible to model the cortex as an active viscoelastic surface. To implement this, we use the surface equivalent of a Maxwell material, additionally distinguishing between shear and dilational stress. The motor proteins are modelled by an advection diffusion equation on the surface combined with a concentration dependent surface tension. Surrounding the surface is a fluid modelled by the Navier-Stokes equations. We study the formation of patterns both analytically and numerically. In the analytical study the 2-dimensional curved surface is reduced to a flat 2-dimensional surface with periodic boundary conditions and no surrounding fluid. We then show, that despite the minimal complexity of this model, spatiotemporal patterns can develop on a viscoelastic surface if the relaxation times are different. For the numerical study the Arbitrary Lagrangian Eulerian method (ALE) is applied. The equations for the surface and bulk are solved separately, but this partial method is numerically unstable for dominantly viscous surfaces. With that in mind, we also implemented a monolithic model for viscous surfaces, solving the bulk and surface equations simultaneously. As a special case the influence of a chiral flow field on a sphere is studied. These chiral flows have been observed in biological experiments and are hypothesised to originate from the small scale torques caused by the helix structure of the actin filaments. We found that a high shear elastic modulus in combination with a chiral force field can induce neck formation. Additionally, for a concentration dependent chiral force field combined with active surface tension and a high dilational elastic modulus, the chiral forces can stabilise a contractile ring. These results provide mechanistic evidence that chiral flows can play a role during cell division.