Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation

We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm - for staged patterns - also uses a recurrence formula. We show that if the items are not so small compared to the dimensions of the bin, then these algorithms require polynomial time. Using these algorithms we solved all instances of the RK problem found at the OR-LIBRARY, including one for which no optimal solution was known. We also consider the Two-dimensional Cutting Stock problem. We present a column generation based algorithm for this problem that uses the first algorithm above mentioned to generate the columns. We propose two strategies to tackle the residual instances. We also investigate a variant of this problem where the bins have different sizes. At last, we study the Two-dimensional Strip Packing problem. We also present a column generation based algorithm for this problem that uses the second algorithm above mentioned where staged patterns are imposed. In this case we solve instances for two-, three- and four-staged patterns. We report on some computational experiments with the various algorithms we propose in this paper. The results indicate that these algorithms seem to be suitable for solving real-world instances. We give a detailed description (a pseudo-code) of all the algorithms presented here, so that the reader may easily implement these algorithms. (c) 2007 Elsevier B.V. All rights reserved.

Minimizing the object dimensions in circle and sphere packing problems

Given a fixed set of identical or different-sized circular items, the problem we deal with consists on finding the smallest object within which the items can be packed. Circular, triangular, squared, rectangular and also strip objects are considered. Moreover, 2D and 3D problems are treated. Twice-differentiable models for all these problems are presented. A strategy to reduce the complexity of evaluating the models is employed and, as a consequence, instances with a large number of items can be considered. Numerical experiments show the flexibility and reliability of the new unified approach. (C) 2007 Elsevier Ltd. All rights reserved.

Gas-filled, flat plate solar collectors

This work treats the thermal and mechanical performances of gas-filled, flat plate solar collectors in order to achieve a better performance than that of air filled collectors. The gases examined are argon, krypton and xenon which all have lower thermal conductivity than air. The absorber is formed as a tray connected to the glass. The pressure of the gas inside is near to the ambient and since the gas volume will vary as the temperature changes, there are potential risks for fatigue in the material. One heat transfer model and one mechanical model were built. The mechanical model gave stresses and information on the movements. The factors of safety were calculated from the stresses, and the movements were used as input for the heat transfer model where the thermal performance was calculated. It is shown that gas-filled, flat plate solar collectors can be designed to achieve good thermal performance at a competitive cost. The best yield is achieved with a xenon gas filling together with a normal thick absorber, where normal thick means a 0.25 mm copper absorber. However, a great deal of energy is needed to produce the xenon gas, and if this aspect is taken into account, the krypton filling is better. Good thermal performance can also be achieved using less material; a collector with a 0.1 mm thick copper absorber and the third best gas, which is argon, still gives a better operating performance than a common, commercially produced, air filled collector with a 0.25 mm absorber. When manufacturing gas-filled flat plate solar collectors, one way of decreasing the total material costs significantly, is by changing absorber material from copper to aluminium. Best yield per monetary outlay is given by a thin (0.3 mm) alu-minium absorber with an argon filling. A high factor of safety is achieved with thin absorbers, large absorber areas, rectangular constructions with long tubes and short distances between glass and absorber. The latter will also give a thin layer of gas which gives good thermal performance. The only doubtii ful construction is an argon filled collector with a normal thick (> 0.50 mm) aluminium absorber. In general, an assessment of the stresses for the proposed construction together with appropriate tests are recommended before manufacturing, since it is hard to predict the factor of safety; if one part is reinforced, some other parts can experience more stress and the factor of safety actually drops.

Thomas-Fermi ground state of dipolar fermions in a circular storage ring

Recent developments in the field of ultracold gases has led to the production of degenerate samples of polar molecules. These have large static electric-dipole moments, which in turn causes the molecules to interact strongly. We investigate the interaction of polar particles in waveguide geometries subject to an applied polarizing field. For circular waveguides, tilting the direction of the polarizing field creates a periodic inhomogeneity of the interparticle interaction. We explore the consequences of geometry and interaction for stability of the ground state within the Thomas-Fermi model. Certain combinations of tilt angles and interaction strengths are found to preclude the existence of a stable Thomas-Fermi ground state. The system is shown to exhibit different behavior for quasi-one-dimensional and three-dimensional trapping geometries.

Dimensionamento de pilares esbeltos de concreto armado

O objetivo deste trabalho é o dimensionamento de pilares esbeltos de concreto armado, sob cargas de curta e longa duração, baseado numa análise realística das deformações do mesmo. Apresenta-se três algoritmos numéricos para a obtencão das relações momento fletor-esforço normal-curvatura de uma seção arbitrária de concreto armado, sob flexo-compressão normal. Inclue-se as deformações específicas de fluência e retração do concreto na análise, através de uma alteração nas referidas relações. Apresenta-se alguns critérios de normas, relativos ao dimensionamento de pilares esbeltos de concreto armado e uma comparação dos mesmos, entre si e com o algoritmo numérico desenvolvido. Considerações da NB-1/78 relativas ao projeto de pilares são analisadas, verificando o nivel da precisão obtida. Um procedimento simplificado para a inclusão da fluência do concreto no dimensionamento, proposto pelo CEB, é testado e uma solução para pilares de concreto armado com engastamento elástico simétrico é apresentada, para verificar o nível: do erro cometido ao se estender o conceito de comprimento de flambagem a pilares de concreto armado. Uma série de exemplos experimentais são apresentados, onde a solução numérica para o dimensionamento tem sua precisão verificada. Diversas tabelas foram desenvolvidas para o dimensionamento de pilares esbeltos com secão transversal retangular e armadura simétrica. Todo o estudo é restrito ao caso de flexo-compressão normal.

A climatologia aplicada ao ambiente construído : uma contribuição à caracterização climática de Porto Alegre/RS

Com caráter informativo, inicia-se apresentando a relação entre a climatologia e o ambiente construído, em seus campos especificos de aplicação (urbanismo, projeto de edificações, execução de obras, e manutenção e uso das construções), considerando-se os aspectos históricos, econômico-ecológicos e os ligados à súde e ao conforto do usuário, abrangidos por tal relação. A importância da disponibilidade de informações climatológicas é então comentada, bem como diversas metodalagias de análise e representação de dados climáticos. Com caráter aplicativo, apresenta-se uma contribuigão à caracterização climática da cidade de Porto Alegre, RS. São analisadas os valores médios horários-mensais doa principais parâmetros climáticos disponíveis (temperatura, umidade, velocidade e direção do vento, e nebulosidade), propondo-se uma representação gráfica sintética alternativa para os mesmos. A análise é complementada pala execução de dois procedimentos técnicos: avaliação do conforto térmico, com identificação do período critico de verão, e projeto de dispositivo de sombreamento de aberturas retangulares. Embora esteja em foco o caso específico de Porto Alegre, tais metodologias encontram-se descritas de modo a serem aplicadas a qualquer outra localidade, procurando-se ampliar a utilidade prática do presente estudo.

Sistemas de produção de carvão vegetal existentes no Brasil: uma análise de viabilidade econômica

O carvão vegetal tem um papel de destaque entre as biomassas consumidas no Brasil. Seu uso em larga escala na indústria siderúrgica para a produção de ferro gusa fez do país um dos maiores produtores e consumidores mundiais de carvão vegetal. A matéria-prima abundante, bem como a falta de preocupação com fatores ambientais e sociais, permitiu no passado que se atentasse apenas ao fator econômico; e a tecnologia de produção deste combustível/insumo se desenvolveu muito pouco ao longo de quase toda a sua história no Brasil até os anos mais recentes. Nas duas últimas décadas, quando se intensificou a preocupação social e ambiental e esses fatores ganharam relevância na análise da viabilidade de projetos tanto a serem implantados, quanto já existentes, a produção de carvão vegetal passou a ser identificada como extremamente rudimentar e impactante ao meio ambiente e sociedade onde se localiza. Neste trabalho buscou-se analisar a viabilidade econômica de quatro sistemas de produção de carvão existentes no Brasil. O sistema mais rudimentar, comumente chamado de “rabo quente”, um sistema ainda de alvenaria, com um pouco mais desenvolvimento tecnológico conhecido como forno retangular, e dois sistemas que utilizam fornos metálicos para buscar menor tempo do processo de carbonização (devido ao mais rápido resfriamento do sistema) e que têm, ambos, uma preocupação ambiental maior e buscam emitir menos poluentes e oferecer uma condição de trabalho mais adequada, refletindo também positivamente sob o aspecto sócio-ambiental. Percebe-se que em termos de implantação, obviamente, os sistemas que envolvem um pouco mais de tecnologia são bem mais dispendiosos em investimento inicial, porém, há resultados animadores do ponto de vista de retorno do investimento e possibilidades de agregação de valor que tendem a atrair o investimento especialmente dos grandes grupos siderúrgicos consumidores, que têm se preocupado cada vez mais em investir tanto na produção de matéria-prima, com grandes áreas de reflorestamento, quanto na produção sustentável do carvão vegetal.

Valorização dos gases da carbonização da madeira via rota de combustão

A produção de carvão vegetal a partir de florestas plantadas mudou de forma determinante a logística desta atividade dotando-a de escala e fixando a estrutura de produção composta por fornos e periféricos. A lógica de se ter os fornos construídos ao lado das frentes de exploração florestal, e se deslocando junto com ela à medida em que a colheita é realizada foi abandonada. A partir de então, tem-se buscado uma forma de aproveitar a disponibilidade energética contida nos gases da carbonização, que segue sem uso, tendo quando muito um aproveitamento incipiente e marginal. Esta dissertação apresenta uma proposta de lay out para a Unidade de Produção de Carvão (UPC) de fornos retangulares tradicionais em alvenaria projetados e posicionados de forma a possibilitar seu acoplamento a um sistema de coleta e queima dos gases da carbonização. Após exaustiva pesquisa bibliográfica e visitas técnicas para conhecimento de diferentes tecnologias de carbonização, elaborou-se o projeto, com objetivo de eliminar as limitações identificadas nas tecnologias tradicionais em uso atualmente pelas empresas com produção em escala industrial, reduzindo as perdas e dificuldades operacionais para aproveitamento dos gases. É caracterizado pela saída dos gases somente por uma chaminé instalada no fundo do forno, possui entradas de ar do processo em minicâmaras, que atuam evitando excesso de ar, queima excessiva de madeira e consequente geração excessiva de CO2 e metano – dois gases causadores de efeito estufa. Preconiza-se a queima dos gases da carbonização para uso posterior em geração de energia elétrica e/ou secagem da madeira antes da carbonização. Os resultados dos indicadores técnicos (ciclos dos fornos e produtividade, etc.) e de produção obtidos até o momento na planta em operação vêm confirmando a operacionalidade do conjunto de fornos na nova disposição concebida. Não houve perda de produtividade dos fornos causada pela nova disposição, e as modificações no projeto do forno não impactaram negativamente em seu desempenho operacional. A capacidade produtiva da Unidade vem se confirmando até o momento. Tivemos frustradas nossas expectativas de já apresentar nesta dissertação os resultados operacionais dos fornos juntamente com os do sistema de queima dos gases dado que houve considerável atraso na construção do mesmo impedindo-nos de tê-los antes da data limite de entrega da dissertação. Apresentamos os conceitos que nos levaram à tomada de decisão para o novo lay out e propomos a continuidade dos estudos comprobatórios da viabilidade econômica operacional do sistema, tão logo ele entre em operação.

Estruturas cerâmicas a base de zircônia e alumina utilizadas na confecção de infra - estruturas para coroas e pontes fixas

The continuous advances in ceramic systems for crowns and bridges infrastructure getting researchers and manufacturers looking for a material that has good mechanical properties and aesthetic. The purpose of this study was to verify in which composition and sintering temperature the ceramic system for infrastructure composed of alumina and zirconia would have the best mechanical properties. With this objective we made in UFRN laboratories 45 test bodies in the form of rectangular bars with the following dimensions: 30mm x 8mm x 3mm, where we separated by the sintering temperature: 1200°C, 1300ºC and 1400ºC, and by comp osition: 33% Zirconia + 67% Alumina; 50% Zirconia + 50% Alumina and 25% Zirconia + 75% Alumina, these test bodies were not infiltrated with glass. Also, were made nine test bodies by a technical from a laboratory with a commercial ceramic system: in the Ceram Zircônia (Vita - Zahnfabrik) with the following dimensions: 20mm x 10mm x 0.5mm, these test bodies following all recommendations of the manufacturer and were infiltrated with glass. Were realized optical and electronic microscopy analyses, hardness testing, resistance to bending in three points, porosity and bulk density. After analysis of the results we verified that with the increasing of sintering temperature, increased the value of resistance to bending, but with the same temperature there was no significant difference between the different compositions, samples made with the commercial ceramic that were infiltrated, presented a resistance to bending six times greater than the samples sintered to 1400°C and which have not been infiltra ted. There was no significant difference between the values of apparent porosity for the samples made in UFRN laboratories, but the samples of commercial ceramic obtained 0% in porosity apparent value. In tests of Rockwell Hardness there is an increase in the value of Hardness, with the increase of sintering temperature for the samples not infiltrated. Samples infiltrated showed similar values as the samples sintered in 1400°C. There was no significant difference between the values of apparent density among samples manufactured in UFRN laboratories and samples made with a commercial ceramic

Estudo da sinterização de cavacos de aço ferritico

This research studies the sintering of ferritic steel chips from the machining process. Were sintered metal powder obtained from machining process chips for face milling of a ferritic steel. The chip was produced by machining and characterized by SEM and EDS, and underwent a process of high energy mill powder characterized also by SEM and EDS. Were constructed three types of matrixes for uniaxial compression (relation l / d greater than 2.5). The differences in the design of the matrixes were essentially in the direction of load application, which for cylindrical case axial direction, while for the rectangular arrays, the longer side. Two samples were compressed with different geometries, a cylindrical and rectangular with the same compaction pressure of 700 MPa. The samples were sintered in a vacuum resistive furnace, heating rate 20 °C / min., isotherm 1300 °C for 60 minutes, and cooling rate of 25 °C / min to room temperature. The starting material of the rectangular sample was further annealed up to temperature of 800 ° C for 30 min. Sintered samples were characterized by scanning electron microscopy, optical microscopy and EDS. The sample compressed in the cylindrical matrix did not show a regular density reflecting in the sintered microstructure revealed by the irregular geometry of the pores, characterizing that the sintering was not complete, reaching only the second phase. As for the specimen compacted in the rectangular array, the analysis performed by scanning electron microscopy, optical microscopy and EDS indicate a good densification, and homogeneous microstructure in their full extent. Additionally, the EDS analyzes indicate no significant changes in chemical composition in the process steps. Therefore, it is concluded that recycling of chips, from the processed ferritic steel is feasible by the powder metallurgy. It makes possible rationalize raw material and energy by manufacture of known properties components from chips generated by the machining process, being benefits to the environment

Efeito da adição de feldspato e/ou resíduo de caulin em formulações à base de argila ilítica

The red pottery industry in Piauí state is well developed and stands out at the national context for the technical quality of its products. The floor and wall tile industry, however, is little developed since the state has only one company that produces red clay-based ceramic tiles. This thesis aims at using the predominantly illitic basic mass of the above mentioned industry, with the addition of feldspar and/or kaolin residue in order to obtain products of higher technical quality. Kaolin residue consists basically of kaolinite, muscovite mica and quartz; the feldspar used was potassic. In this experiment, basic mass (MB) was used for experimental control and fifteen formulations codified as follows: F2, F4, F8, F16, F32, FR2, FR4, FR8, FR16, FR32, R2, R4, R8, R16 and R32. All raw materials were dry-milled, classified, formulated and then humidified to 10% water. Thereafter, test samples were produced by unixial pressing process in a rectangular steel matrix (60.0 x 20.0 x 5.0) mm3 at (25 MPa). They were fired at four temperatures: 1080°C, 1120°C, 1160°C, with a heating rate of 10°C/min during up to 10 min in an electric oven, and the last one in an industrial oven with a peak of 1140°C, aim ing to confirm the results found in laboratory and, finally, technological tests were performed: MEA, RL, AA, PA, TRF and PF. The results revealed that the residue under study can be considered a raw material with large potential in the industry of red clay-based ceramic tiles, since the results found both in laboratory and in the industry have shown that the test samples produced from the formulations with up to 4% feldspar and those produced with up to 8% feldspar and residue permitted a reduction in the water absorption rate and an increase in the mechanical resistance while those samples produced with up to 4% residue had an increase in the mechanical resistance when compared to those produced from the basic mass and that the formulation with 2% feldspar and residue presented the best technological properties, lowering the sintering temperature down to 1120°C

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Estudo de pré-formulação para dose fixa combinada dos tuberculostáticos rifampicina, isoniazida, pirazinamida e etambutol (4 em 1)

According to the global framework regarding new cases of tuberculosis, Brazil appears at the 18th place. Thus, the Ministry of Health has defined this disease as a priority in the governmental policies. As a consequence, studies concerning treatment and prevention have increased. Fixed-dose combination formulations (FDC) are recognized as beneficial and are recommended by WHO, but they present instability and loss on rifampicin bioavailability. The main purpose of this work was to carry out a pre-formulation study with the schedule 1 tuberculosis treatment drugs: rifampicin, isoniazid, pyrazinamide and ethambutol and pharmaceutical excipients (lactose, cellulose, magnesium stearate and talc), in order to develop an FDC product (150 mg of rifampicin + 75 mg of isoniazid + 400 mg of pyrazinamide + 250 mg of ethambutol). The studies consisted of the determination of particle size and distribution (Ferret s diameter) and shape through optical microscopy, as well as rheological and technological properties (bulk and tapped densities, Hausner Factor, Carr s Index, repose angle and flux rate) and interactions among drugs and drug excipient through thermal analysis (DSC, DTA, TG and your derivate). The results showed that, except isoniazid, the other drugs presented poor rheological properties, determined by the physical characteristics of the particles: small size and rod like particles shape for rifampicin; rectangular shape for pyrazinamide and ethambutol, beyond its low density. The 4 drug mixture also not presented flowability, particularly that one containing drug quantity indicated for the formulation of FDC products. In this mixture, isoniazid, that has the best flowability, was added in a lower concentration. The addition of microcrystalline cellulose, magnesium stearate and talc to the drug mixtures improved flowability properties. In DSC analysis probable interactions among drugs were found, supporting the hypothesis of ethambutol and pyrazinamide catalysis of the rifampicin-isoniazid reaction resulting in 3- formylrifamycin isonicotinyl hydrazone (HYD) as a degradation product. In the mixtures containing lactose Supertab® DSC curves evidenced incompatibility among drugs and excipient. In the DSC curves of mixtures containing cellulose MC101®, magnesium stearate and talc, no alterations were observed comparing to the drug profiles. The TG/DTG of the binary and ternary mixtures curves showed different thermogravimetrics profiles relating that observed to the drug isolated, with the thermal decomposition early supporting the evidences of incompatibilities showed in the DSC and DTA curves

Effect of density on population development in the Amazon River prawn Macrobrachium amazonicum

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Perdas de grãos e distribuição de palha na colheita mecanizada de soja

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)