977 resultados para Exact solution


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Most real-life data analysis problems are difficult to solve using exact methods, due to the size of the datasets and the nature of the underlying mechanisms of the system under investigation. As datasets grow even larger, finding the balance between the quality of the approximation and the computing time of the heuristic becomes non-trivial. One solution is to consider parallel methods, and to use the increased computational power to perform a deeper exploration of the solution space in a similar time. It is, however, difficult to estimate a priori whether parallelisation will provide the expected improvement. In this paper we consider a well-known method, genetic algorithms, and evaluate on two distinct problem types the behaviour of the classic and parallel implementations.

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This thesis is concerned with two-dimensional free surface flows past semi-infinite surface-piercing bodies in a fluid of finite-depth. Throughout the study, it is assumed that the fluid in question is incompressible, and that the effects of viscosity and surface tension are negligible. The problems considered are physically important, since they can be used to model the flow of water near the bow or stern of a wide, blunt ship. Alternatively, the solutions can be interpreted as describing the flow into, or out of, a horizontal slot. In the past, all research conducted on this topic has been dedicated to the situation where the flow is irrotational. The results from such studies are extended here, by allowing the fluid to have constant vorticity throughout the flow domain. In addition, new results for irrotational flow are also presented. When studying the flow of a fluid past a surface-piercing body, it is important to stipulate in advance the nature of the free surface as it intersects the body. Three different possibilities are considered in this thesis. In the first of these possibilities, it is assumed that the free surface rises up and meets the body at a stagnation point. For this configuration, the nonlinear problem is solved numerically with the use of a boundary integral method in the physical plane. Here the semi-infinite body is assumed to be rectangular in shape, with a rounded corner. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterised by a train of waves upstream. In the limit that the height of the body above the horizontal bottom vanishes, the flow approaches that due to a submerged line sink in a $90^\circ$ corner. This limiting problem is also examined as a special case. The second configuration considered in this thesis involves the free surface attaching smoothly to the front face of the rectangular shaped body. For this configuration, nonlinear solutions are computed using a similar numerical scheme to that used in the stagnant attachment case. It is found that these solution exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a corner is also considered. Finally, the flow of a fluid emerging from beneath a semi-infinite flat plate is examined. Here the free surface is assumed to detach from the trailing edge of the plate horizontally. A linear problem is formulated under the assumption that the elevation of the plate is close to the undisturbed free surface level. This problem is solved exactly using the Wiener-Hopf technique, and subcritical solutions are found which are characterised by a train of sinusoidal waves in the far field. The nonlinear problem is also considered. Exact relations between certain parameters for supercritical flow are derived using conservation of mass and momentum arguments, and these are confirmed numerically. Nonlinear subcritical solutions are computed, and the results are compared to those predicted by the linear theory.

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Synthesis of high quality boron carbide (B4C) powders is achieved by carbothermal reduction of boron oxide (B2O3) from a condensed boric acid (H3BO3)/polyvinyl acetate (PVAc) product. Precursor solutions are prepared via free radical polymerisation of vinyl acetate (VA) monomer in methanol in the presence of dissolved H3BO3. A condensed product is then formed by flash evaporation under vacuum. As excess VA monomer is removed at the evaporation step, the polymerisation time is used to manage availability of carbon for reaction. This control of carbon facilitates dispersion of H3BO3 in solution due to the presence of residual VA monomer. B4C powders with very low residual carbon are formed at temperatures as low as 1,250 °C with a 4 hour residence time.

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I am an academic who has spent a career using a strengths-based approach in researching ways to promote and maintain mental health in people who have experienced trauma. When I read the title of the book, the notion of “post traumatic success” immediately brought many questions to my mind. What is success anyway? How do we measure success following trauma? Who decides if a person has been successful? However, as I started to read, the intention of the book became clear and my bias regarding the title lessened...

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Management of sodic soils under irrigation often requires application of chemical ameliorants to improve permeability combined with leaching of excess salts. Modeling irrigation, soil treatments, and leaching in these sodic soils requires a model that can adequately represent the physical and chemical changes in the soil associated with the amelioration process. While there are a number of models that simulate reactive solute transport, UNSATCHEM and HYDRUS-1D are currently the only models that also include an ability to simulate the impacts of soil chemistry on hydraulic conductivity. Previous researchers have successfully applied these models to simulate amelioration experiments on a sodic loam soil. To further gauge their applicability, we extended the previous work by comparing HYDRUS simulations of sodic soil amelioration with the results from recently published laboratory experiments on a more reactive, repacked sodic clay soil. The general trends observed in the laboratory experiments were able to be simulated using HYDRUS. Differences between measured and simulated results were attributed to the limited flexibility of the function that represents chemistry-dependent hydraulic conductivity in HYDRUS. While improvements in the function could be made, the present work indicates that HYDRUS-UNSATCHEM captures the key changes in soil hydraulic properties that occur during sodic clay soil amelioration and thus extends the findings of previous researchers studying sodic loams.

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We have prepared p-n junction organic photovoltaic cells using an all solution processing method with poly(3-hexylthiophene) (P3HT) as the donor and phenyl-C 61-butyric acid methyl ester (PCBM) as the acceptor. Interdigitated donor/acceptor interface morphology was observed in the device processed with the lowest boiling point solvent for PCBM used in this study. The influences of different solvents on donor/acceptor morphology and respective device performance were investigated simultaneously. The best device obtained had characteristically rough interface morphology with a peak to valley value ∼15 nm. The device displayed a power conversion efficiency of 1.78%, an open circuit voltage (V oc) 0.44 V, a short circuit current density (J sc) 9.4 mA/cm 2 and a fill factor 43%.

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It is well known that the neutralisation of Bayer liquor with seawater causes the precipitation of stable alkaline products and a reduction in pH and dissolved metal concentrations in the effluent. However, there is limited information available on solution chemistry effects on the stability and reaction kinetics of these precipitates. This investigation shows the influence of reactive species (magnesium and calcium) in seawater on precipitate stabilities and volumetric efficiencies during the neutralisation of bauxite refinery residues. Correlations between synthetic seawater solutions and real samples of seawater (filtered seawater, nanofiltered seawater and reverse osmosis brine) have been made. These investigations have been used to confirm that alternative seawater sources can be used to increase the productivity potential of the neutralisation process with minimal implications on the composition and stability of precipitates formed. The volume efficiency of the neutralisation process using synthetic analogues has been shown to be almost directly proportional with the concentration of magnesium. This was further confirmed in the nanofiltered seawater and reverse osmosis brine that showed increases in the efficiency of neutralisation by factors of 3 and 2 compared to seawater, which corresponds with relatively the same increase in the concentration of magnesium in these alternative seawater sources. An assessment of the chemical stability of the precipitates, volumetric efficiency, and discharge water quality have been determined using numerous techniques that include pH, conductivity, inductively coupled plasma optical emission spectroscopy, infrared spectroscopy, thermogravimetric analysis coupled to mass spectrometry and X-ray diffraction. Correlations between synthetic solution compositions and alternative seawater sources have been used to determine if alternative seawater sources are potential substitutes for seawater based on improvements in productivity, implementation costs, savings to operations and environmental benefits.

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An understanding of the influence of soil chemistry on soil hydraulic properties is of critical importance for the management of sodic soils under irrigation. The hydraulic conductivity of sodic soils has been shown to be affected by properties of the applied solution including pH (Suarez et al. 1984), sodicity and salt concentration (McNeal and Coleman 1966). The changes in soil hydraulic conductivity are the result of changes in the spacing between clay layers in response to changes in soil solution chemistry. While the importance o f soil chemistry in controlling hydraulic conductivity is known, the exact impacts of sodic soil amelioration on hydraulic conductivity and deep drainage at a given location are difficult to predict. This is because the relationships between soil chemical factors and hydraulic conductivity are soil specific and because local site specific factors also need to be considered to determine the actual impacts on deep drainage rates.

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In the mining optimisation literature, most researchers focused on two strategic-level and tactical-level open-pit mine optimisation problems, which are respectively termed ultimate pit limit (UPIT) or constrained pit limit (CPIT). However, many researchers indicate that the substantial numbers of variables and constraints in real-world instances (e.g., with 50-1000 thousand blocks) make the CPIT’s mixed integer programming (MIP) model intractable for use. Thus, it becomes a considerable challenge to solve the large scale CPIT instances without relying on exact MIP optimiser as well as the complicated MIP relaxation/decomposition methods. To take this challenge, two new graph-based algorithms based on network flow graph and conjunctive graph theory are developed by taking advantage of problem properties. The performance of our proposed algorithms is validated by testing recent large scale benchmark UPIT and CPIT instances’ datasets of MineLib in 2013. In comparison to best known results from MineLib, it is shown that the proposed algorithms outperform other CPIT solution approaches existing in the literature. The proposed graph-based algorithms leads to a more competent mine scheduling optimisation expert system because the third-party MIP optimiser is no longer indispensable and random neighbourhood search is not necessary.

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We have designed, synthesized and utilized a new non-fullerene electron acceptor, 9,9′-(9,9-dioctyl-9H-fluorene-2,7-diyl)bis(2,7-dioctyl-4-(octylamino)benzo[lmn][3,8]phenanthroline-1,3,6,8(2H,7H)-tetraone) (B2), for use in solution-processable bulk-heterojunction devices. B2 is based on a central fluorene moiety, which was capped at both ends with an electron-accepting naphthalenediimide functionality. B2 exhibited excellent solubility (>30 mg mL−1 in chloroform), high thermal and photochemical stability, and appropriate energy levels for use with the classical polymer donor regioregular poly(3-hexylthiophene). A power conversion efficiency of 1.16 % was achieved for primitive bulk-heterojunction devices with a high fill factor of approximately 54 %.

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A solution-processable, non-fullerene electron acceptor, 2,2′-(((5,5-dioctyl-5 H-dibenzo[b,d]silole-3,7-diyl)bis(thiophene-5,2-diyl))bis(methanylylidene))bis(1 H-indene-1,3(2 H)-dione) (called N5) comprised of dibenzosilole and 1,3-indanedione building blocks was designed, synthesized, and fully characterized. N5 is highly soluble in various organic solvents, has high thermal stability, and has energy levels matching those of archetypal donor poly(3-hexylthiophene). Solution-processable, bulk-heterojunction solar cells afforded promising power conversion efficiency of 2.76 % when N5 was used as a non-fullerene electron acceptor along with the conventional donor polymer poly(3-hexylthiophene). As per our knowledge, the material reported herein is the first example in the literature where synchronous use of such building blocks is demonstrated in the design an efficient, non-fullerene acceptor.

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The work reported hen was motivated by a desire to verify the existence of structure - specifically MP-rich clusters induced by sodium bromide (NaBr) in the ternary liquid mixture 3-methylpyridine (Mf) + water(W) + NaBr. We present small-angle X-ray scattering (SAXS) measurements in this mixture. These measurements were obtained at room temperature (similar to 298 K) in the one-phase region (below the relevant lower consolute points, T(L)s) at different values of X (i.e., X = 0.02 - 0.17), where X is the weight fraction of NaBr in the mixture. Cluster-size distribution, estimated on the assumption that the clusters are spherical, shows systematic behaviour in that the peak of the distribution shifts rewards larger values of cluster radius as X increases. The largest spatial extent of the clusters (similar to 4.5 nm) is seen at X = 0.17. Data analysis assuming arbitrary shapes and sizes of clusters gives a limiting value of cluster size (- 4.5 nm) that is not very sensitive to X. It is suggested that the cluster size determined may not be the same as the usual critical-point fluctuations far removed from the critical point (T-L). The influence of the additional length scale due to clustering is discussed from the standpoint of crossover from Ising to mean-field critical behaviour, when moving away from the T-L.

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A rare example of a two-dimensional Heisenberg model with an exact dimerized ground state is presented. This model, which can be regarded as a variation on the kagome' lattice, has several features of interest: it has a highly (but not macroscopically) degenerate ground state; it is closely related to spin chains studied by earlier authors; in particular, it exhibits domain-wall-like "kink" excitations normally associated only with one-dimensional systems. In some limits it decouples into noninteracting chains; unusually, this happens in the limit of strong, rather than weak, interchain coupling. [S0163-1829(99)50338-X].

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A new theory of shock dynamics has been developed in the form of a finite number of compatibility conditions along shock rays. It has been used to study the growth or decay of shock strength for accelerating or decelerating piston starting with a nonzero piston velocity. The results show good agreement with those obtained by Harten's high resolution TVD scheme.