3 resultados para Variational methods for second-order elliptic equations

em Digital Commons - Michigan Tech


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Multi-input multi-output (MIMO) technology is an emerging solution for high data rate wireless communications. We develop soft-decision based equalization techniques for frequency selective MIMO channels in the quest for low-complexity equalizers with BER performance competitive to that of ML sequence detection. We first propose soft decision equalization (SDE), and demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered, and linear in the signal constellation size. Building upon the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems. Motivated by the need for low-complexity receiver processing, we further present an alternative low-complexity soft-decision equalization approach for frequency selective MIMO communication systems. With the help of iterative processing, two detection and estimation schemes based on second-order statistics are harmoniously put together to yield a two-part receiver structure: local multiuser detection (MUD) using soft-decision Probabilistic Data Association (PDA) detection, and dynamic noise-interference tracking using Kalman filtering. The proposed Kalman-PDA detector performs local MUD within a sub-block of the received data instead of over the entire data set, to reduce the computational load. At the same time, all the inter-ference affecting the local sub-block, including both multiple access and inter-symbol interference, is properly modeled as the state vector of a linear system, and dynamically tracked by Kalman filtering. Two types of Kalman filters are designed, both of which are able to track an finite impulse response (FIR) MIMO channel of any memory length. The overall algorithms enjoy low complexity that is only polynomial in the number of information-bearing bits to be detected, regardless of the data block size. Furthermore, we introduce two optional performance-enhancing techniques: cross- layer automatic repeat request (ARQ) for uncoded systems and code-aided method for coded systems. We take Kalman-PDA as an example, and show via simulations that both techniques can render error performance that is better than Kalman-PDA alone and competitive to sphere decoding. At last, we consider the case that channel state information (CSI) is not perfectly known to the receiver, and present an iterative channel estimation algorithm. Simulations show that the performance of SDE with channel estimation approaches that of SDE with perfect CSI.

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ab-initio Hartree Fock (HF), density functional theory (DFT) and hybrid potentials were employed to compute the optimized lattice parameters and elastic properties of perovskite 3-d transition metal oxides. The optimized lattice parameters and elastic properties are interdependent in these materials. An interaction is observed between the electronic charge, spin and lattice degrees of freedom in 3-d transition metal oxides. The coupling between the electronic charge, spin and lattice structures originates due to localization of d-atomic orbitals. The coupling between the electronic charge, spin and crystalline lattice also contributes in the ferroelectric and ferromagnetic properties in perovskites. The cubic and tetragonal crystalline structures of perovskite transition metal oxides of ABO3 are studied. The electronic structure and the physics of 3-d perovskite materials is complex and less well considered. Moreover, the novelty of the electronic structure and properties of these perovskites transition metal oxides exceeds the challenge offered by their complex crystalline structures. To achieve the objective of understanding the structure and property relationship of these materials the first-principle computational method is employed. CRYSTAL09 code is employed for computing crystalline structure, elastic, ferromagnetic and other electronic properties. Second-order elastic constants (SOEC) and bulk moduli (B) are computed in an automated process by employing ELASTCON (elastic constants) and EOS (equation of state) programs in CRYSTAL09 code. ELASTCON, EOS and other computational algorithms are utilized to determine the elastic properties of tetragonal BaTiO3, rutile TiO2, cubic and tetragonal BaFeO3 and the ferromagentic properties of 3-d transition metal oxides. Multiple methods are employed to crosscheck the consistency of our computational results. Computational results have motivated us to explore the ferromagnetic properties of 3-d transition metal oxides. Billyscript and CRYSTAL09 code are employed to compute the optimized geometry of the cubic and tetragonal crystalline structure of transition metal oxides of Sc to Cu. Cubic crystalline structure is initially chosen to determine the effect of lattice strains on ferromagnetism due to the spin angular momentum of an electron. The 3-d transition metals and their oxides are challenging as the basis functions and potentials are not fully developed to address the complex physics of the transition metals. Moreover, perovskite crystalline structures are extremely challenging with respect to the quality of computations as the latter requires the well established methods. Ferroelectric and ferromagnetic properties of bulk, surfaces and interfaces are explored by employing CRYSTAL09 code. In our computations done on cubic TMOs of Sc-Fe it is observed that there is a coupling between the crystalline structure and FM/AFM spin polarization. Strained crystalline structures of 3-d transition metal oxides are subjected to changes in the electromagnetic and electronic properties. The electronic structure and properties of bulk, composites, surfaces of 3-d transition metal oxides are computed successfully.

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Hardboard processing wastewater was evaluated as a feedstock in a bio refinery co-located with the hardboard facility for the production of fuel grade ethanol. A thorough characterization was conducted on the wastewater and the composition changes of which during the process in the bio refinery were tracked. It was determined that the wastewater had a low solid content (1.4%), and hemicellulose was the main component in the solid, accounting for up to 70%. Acid pretreatment alone can hydrolyze the majority of the hemicellulose as well as oligomers, and over 50% of the monomer sugars generated were xylose. The percentage of lignin remained in the liquid increased after acid pretreatment. The characterization results showed that hardboard processing wastewater is a feasible feedstock for the production of ethanol. The optimum conditions to hydrolyze hemicellulose into fermentable sugars were evaluated with a two-stage experiment, which includes acid pretreatment and enzymatic hydrolysis. The experimental data were fitted into second order regression models and Response Surface Methodology (RSM) was employed. The results of the experiment showed that for this type of feedstock enzymatic hydrolysis is not that necessary. In order to reach a comparatively high total sugar concentration (over 45g/l) and low furfural concentration (less than 0.5g/l), the optimum conditions were reached when acid concentration was between 1.41 to 1.81%, and reaction time was 48 to 76 minutes. The two products produced from the bio refinery were compared with traditional products, petroleum gasoline and traditional potassium acetate, in the perspective of sustainability, with greenhouse gas (GHG) emission as an indicator. Three allocation methods, system expansion, mass allocation and market value allocation methods were employed in this assessment. It was determined that the life cycle GHG emissions of ethanol were -27.1, 20.8 and 16 g CO2 eq/MJ, respectively, in the three allocation methods, whereas that of petroleum gasoline is 90 g CO2 eq/MJ. The life cycle GHG emissions of potassium acetate in mass allocation and market value allocation method were 555.7 and 716.0 g CO2 eq/kg, whereas that of traditional potassium acetate is 1020 g CO2/kg.