2 resultados para Adiabatic Compression

em DRUM (Digital Repository at the University of Maryland)


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A battery powered air-conditioning device was developed to provide an improved thermal comfort level for individuals in inadequately cooled environments. This device is a battery powered air-conditioning system with the phase change material (PCM) for heat storage. The condenser heat is stored in the PCM during the cooling operation and is discharged while the battery is charged by using the vapor compression cycle as a thermosiphon loop. The main focus of the current research was on the development of the cooling system. The cooling capacity of the vapor compression cycle measured was 165.6 W with system COP at 2.85. It was able to provide 2 hours cooling without discharging heat to the ambient. The PCM was recharged in nearly 8 hours under thermosiphon mode.

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In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.