Browsing by Subject "elasticity"

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  • Dudarev, Sergei L.; Mason, Daniel R.; Tarleton, Edmund; Ma, Pui-Wai; Sand, Andrea E. (2018)
    Predicting strains, stresses and swelling in nuclear power plant components exposed to irradiation directly from the observed or computed defect and dislocation microstructure is a fundamental problem of fusion power plant design that has so far eluded a practical solution. We develop a model, free from parameters not accessible to direct evaluation or observation, that is able to provide estimates for irradiation-induced stresses and strains on a macroscopic scale, using information about the distribution of radiation defects produced by high-energy neutrons in the microstructure of materials. The model exploits the fact that elasticity equations involve no characteristic spatial scale, and hence admit a mathematical treatment that is an extension to that developed for the evaluation of elastic fields of defects on the nanoscale. In the analysis given below we use, as input, the radiation defect structure data derived from ab initio density functional calculations and large-scale molecular dynamics simulations of high-energy collision cascades. We show that strains, stresses and swelling can be evaluated using either integral equations, where the source function is given by the density of relaxation volumes of defects, or they can be computed from heterogeneous partial differential equations for the components of the stress tensor, where the density of body forces is proportional to the gradient of the density of relaxation volumes of defects. We perform a case study where strains and stresses are evaluated analytically and exactly, and develop a general finite element method implementation of the method, applicable to a broad range of predictive simulations of strains and stresses induced by irradiation in materials and components of any geometry in fission or fusion nuclear power plants.
  • Virri, Maria (Helsingin yliopisto, 2021)
    Bonus-malus systems are used globally to determine insurance premiums of motor liability policy-holders by observing past accident behavior. In these systems, policy-holders move between classes that represent different premiums. The number of accidents is used as an indicator of driving skills or risk. The aim of bonus-malus systems is to assign premiums that correspond to risks by increasing premiums of policy-holders that have reported accidents and awarding discounts to those who have not. Many types of bonus-malus systems are used and there is no consensus about what the optimal system looks like. Different tools can be utilized to measure the optimality, which is defined differently according to each tool. The purpose of this thesis is to examine one of these tools, elasticity. Elasticity aims to evaluate how well a given bonus-malus system achieves its goal of assigning premiums fairly according to the policy-holders’ risks by measuring the response of the premiums to changes in the number of accidents. Bonus-malus systems can be mathematically modeled using stochastic processes called Markov chains, and accident behavior can be modeled using Poisson distributions. These two concepts of probability theory and their properties are introduced and applied to bonus-malus systems in the beginning of this thesis. Two types of elasticities are then discussed. Asymptotic elasticity is defined using Markov chain properties, while transient elasticity is based on a concept called the discounted expectation of payments. It is shown how elasticity can be interpreted as a measure of optimality. We will observe that it is typically impossible to have an optimal bonus-malus system for all policy-holders when optimality is measured using elasticity. Some policy-holders will inevitably subsidize other policy-holders by paying premiums that are unfairly large. More specifically, it will be shown that, for bonus-malus systems with certain elasticity values, lower-risk policy-holders will subsidize the higher-risk ones. Lastly, a method is devised to calculate the elasticity of a given bonus-malus system using programming language R. This method is then used to find the elasticities of five Finnish bonus-malus systems in order to evaluate and compare them.
  • Siljander, Eero (2004)
    This thesis deals with labour demand, the elasticises of labour demand and adjustment through the theory of labour economics, an econometric model and its application to panel data set of finnish firms. First a continues and discrete time model of labour demand are specified with strictly convex or quadratic adjustment costs. In the econometric part of the study a model for labour demand with firm and time specific elasticises and adjustment are specified. The adjustment parameter is also explicitly modeled. From the econometric model for labour demand the wage-, output-, capital- and trend elasticity are calculated for each observation in time. Then these elasticities are averaged according to the factor of interest which in this thesis are 1. time, 2. industry and 3. size of firm. The same applies for the adjustment parameter. Especially the wage elasticity is of special interest as it describes the effects of the tax wedge of labour on labour demand. In the econometric part of the thesis the elasticises and adjustment of labour demand are estimated from an unbalanced panel data set of the 500 largest enterprises in Finland as measured by turnover. The data covers the years from 1986 to 2003 and has a total of 8185 observations. As an econometric research method a fixed effects nonlinear seemingly unrelated regressions (SUR) algorithm is used to estimate labour demand. The results indicate that the wage and output elasticity of labour demand have increased during the observed period from 1986 to 2003. The wage elasticity has increased from -0.6 to -0.75 and the output elasticity from 0.8 to 0.9 in the long run during the data period. The same pattern is observed for these elasticises in the short run as well. Technical change has decreased labour demand by approximately two percent p.a. in the short and long run. These results confirm that finnish labour markets have become more flexible due to increased competition and integration of product markets which in turn are due to the single market policies of the EU and the effects of globalization on labour markets. The only surprise in the results is that the adjustment parameter has decreased slightly during the end of the observation period which points to mounting adjustment costs of labour demand and rigidities in the adjustment of labour markets. The results also show that the elasticises and adjustment of labour demand vary strongly with the industry of the firm. This points to the heterogeneity across firms and industries which validates the research strategy and methodology used here and should not be overlooked in empirical research in general. On the other hand firm size is not found to be a significant factor in determining the elasticises or adjustment. Therefore the explicit modeling of firm and time specific adjustment should be taken into account in future research on labour demand and its elasticises.
  • Viskari, Ansa (Helsingfors universitet, 2012)
    The purpose of this study was to investigate how the mixing time of the magnesium stearate affects on the compressibility of partially pregelatinized maize starch. Pregelatinized maize starch is used in pharmaceuticals as a filler, binder and as disintegrant. Because pregelatinized maize starch has lubricant characteristics itself, it is known to be sensitive for the amount and the mixing time of magnesium stearate. The aim is that magnesium stearate is not totally homogenously mixed on the powder surfaces so that even, clean powder surfaces exist. Homogeneous mixing means that particles are coated with magnesium stearate, which as a hydrophobic ingredient prevents bond formation between plastically and elastically behaving particles. Too much magnesium stearate and/or too long mixing time may cause weakening of tablet tensile strength, laminating and capping. The weakening of the tensile strength of the tablet increases friability, which causes problems during packaging process and the transportation. Too much magnesium stearate may also lengthen the disintegration time and slow down the dissolution. The aim of this study was to compare four different brands of pregelatinized maize starch. The purpose was to find differences affecting the compressibility behavior. Also the effect of the mixing time of magnesium stearate for compression behavior of masses were studied. The brands investigated were C*PharmGel DC 93000, Lycatab® C, Starch 1500® and SuperStarch 200®. First mentioned was a reference product which is not manufactured any more. There was only one batch of the reference product but three batches from other products to be able to investigate also batch to batch variation. The characteristics studied from pregelatinized starch samples were bulk density, apparent density and true density, flowability, moisture sorption, moisture content, pH value, swelling volume and particle size. Also NIR, FTIR and Raman spectroscopy and X-ray powder diffraction method were used. Weight, tensile strength, dimensions, friability, disintegration time and moisture sorption were studied for tablets. The compressibility of the mass and elastic behavior of tablets was studied. Pictures of the tablets were also taken by scanning electron microscope. When the mixing time of magnesium stearate was increased from 2 minutes to 5 minutes, the compression pressure needed for pressing tablets for 80 N strength increased 200-700 N depending on the brand of pregelatinized maize starch. Based on the results the best alternative to replace C*PharmGel DC 93000 was chosen to be SuperStarch 200®. Scanning electron microscope pictures showed that C*PharmGel DC 93000 deviates from other qualities studied by being roundish and regular in shape. SuperStarch 200® and Starch 1500® reminded remarkably each other. Lycatab® C was the biggest in particle size and very irregular in shape. The differences found in tabletting followed the expectations based on the SEM-pictures. SuperStarch 200® showed to best compressibility in lowest strain strength and after C*PharmGel DC 93000 it was least sensitive for mixing time of the magnesium stearate. It also has least elastic recovery. The differences between SuperStarch 200® and Starch 1500® in compression properties were moderate but clear. Lycatab® C had clearly the weakest compression properties.
  • Chan, Tommy; Hölttä, Teemu; Berninger, Frank; Mäkinen, Harri; Nöjd, Pekka; Mencuccini, Maurizio; Nikinmaa, Eero (2016)
    The quantification of cambial growth over short time periods has been hampered by problems to discern between growth and the swelling and shrinking of a tree stem. This paper presents a model, which separates cambial growth and reversible water-potential induced diurnal changes from simultaneously measured whole stem and xylem radial variations, from field-measured Scots pine trees in Finland. The modelled growth, which includes osmotic concentration changes, was compared with (direct) dendrometer measurements and microcore samples. In addition, the relationship of modelled growth and dendrometer measurements to environmental factors was analysed. The results showed that the water-potential induced changes of tree radius were successfully separated from stem growth. Daily growth predicted by the model exhibited a high correlation with the modelled daily changes of osmotic concentration in phloem, and a temperature dependency in early summer. Late-summer growth saw higher dependency on water availability and temperature. Evaluation of the model against dendrometer measurements showed that the latter masked a true environmental signal in stem growth due to water-potential induced changes. The model provides better understanding of radial growth physiology and offers potential to examine growth dynamics and changes due to osmotic concentration, and how the environment affects growth.
  • Palomäki, Emmi (Helsingfors universitet, 2012)
    3D-imaging is based on combining two or more pictures to form one three-dimensional picture. Most of the methods used provide only surface pictures, but tomography acquires also information about the inside-structure of investigated material. Young's modulus is a method, which has been used for long time to determine toughness hard materials, such as steal. In traditional method a beam-shaped piece is bent. When the size of piece, used force and amount of bending are known, Young's modulus of piece can be calculated. Although the method has traditionally been used to research very hard materials, it has been applied without changes with pharmaceutical materials. It is, however, open to the question whether or not the method is appropriate for those materials. There are also methods to determine Young's modulus based on compressing a tablet or using ultrasound. Determining tablet's toughness with ultimate strength test is complicated because it breaks tablet. For that reason it would be good to find compensatory methods to measure strength of tablet. The aim of the study was to validate Flash Sizer 3D appliance, which is used in 3D-imiging. Another goal was to investigate possible correlations between 3D-imiging, Young's modulus and traditional ultimate strength method. Lastly, the feasibility of Young's modulus as a substitute for traditional ultimate strength measurement in self life studies was investigated. Flash Sizer 3D was validated by measuring particle size distribution of pellets, which were made of microcrystalline cellulose (Cellets). Sizes of the investigated pellets were 100 µm, 200 µm and 500 µm. Also binary mixture of 100 µm and 200 µm was investigated. From microcrystalline cellulose was made tablets and 3D-pictures were taken. Ultimate strength test was made for half of the tablets. Young's modulus was measured from half of the tablets in tableting day, day after that and nine days after tableting. Results show that Flash Sizer 3D is suitable for investigating bigger Cellet. With smaller particles distinguishing of tablets wasn't probably good enough. Still it seems to be quite good method to determine surface roughness of tablet. Young's modulus seems to be very promising as compensating method for traditional ultimate strength measurement. In future in self life studies tablets hardness might be able to investigate by measuring Young's modulus and not measuring ultimate strength. If correlation between Young's modulus and solubility meets the case, Young's modulus might also replace also solubility measurements in self life studies.