Finite size effects in superconducting nanocomposites

The present Master’s thesis presents theoretical description of the extraodinary behavior of the confined Indium nanoparticles. Superconducting properties of nanoparticles and nanocomposites are extensively reviewed. Special attention has been paid to phase fluctuation, shell and disordered effects. The experimental data has been obtained and provided by Dmitry Shamshur from Ioffe Physical Technical Institute. The investigated material represents a highly ordered system of silicate spheres filled with indium metal, where the In nanoparticles are interconnected between each other. Bulk indium is a superconductor with crititcal superconducting temperature Tc0 = 3:41 K. But indium nanoparticles exhibit different behavior, the critical temperature rise by approximately 20% up to 4.15 K. As well as transition of the indium particles to type-II superconductivity with high critical magnetic fields. Such diversity is explained by finite size effects which originate from nanosize of the samples.

Effects of cage size and obstructed view from cage on use of resting platforms by farmed silver foxes

Selostus: Häkin koon ja häkissä olevien näköesteiden vaikutus tarhattujen hopeakettujen makuuhyllyn käyttöön

Effects of group size and early handling on some behavioural and physiological welfare parameters in farmed blue foxes

Selostus: Ryhmäkoon ja varhaisen käsittelyn vaikutus tarhattujen sinikettujen hyvinvointiin

Effects of group size and space allocation on physiological, behavioural and production-related welfare parameters in farmed silver fox cubs

Selostus: Ryhmäkoon ja käytössä olevan tilan vaikutus tarhattujen hopeakettupentujen hyvinvointiin

The effects of productivity on profitability: a case study at firm level using an activity-based costing approach

Productivity and profitability are important concepts and measures describing the performance and success of a firm. We know that increase in productivity decreases the costs per unit produced and leads to better profitability. This common knowledge is not, however, enough in the modern business environment. Productivity improvement is one means among others for increasing the profitability of actions. There are many means to increase productivity. The use of these means presupposes operative decisions and these decisions presuppose informationabout the effects of these means. Productivity improvement actions are in general made at floor level with machines, cells, activities and human beings. Profitability is most meaningful at the level of the whole firm. It has been very difficult or even impossible to analyze closely enough the economical aspects of thechanges at floor level with the traditional costing systems. New ideas in accounting have only recently brought in elements which make it possible to considerthese phenomena where they actually happen. The aim of this study is to supportthe selection of objects to productivity improvement, and to develop a method to analyze the effects of the productivity change in an activity on the profitability of a firm. A framework for systemizing the economical management of productivity improvement is developed in this study. This framework is a systematical way with two stages to analyze the effects of productivity improvement actions inan activity on the profitability of a firm. At the first stage of the framework, a simple selection method which is based on the worth, possibility and the necessity of the improvement actions in each activity is presented. This method is called Urgency Analysis. In the second stage it is analyzed how much a certain change of productivity in an activity affects the profitability of a firm. A theoretical calculation model with which it is possible to analyze the effects of a productivity improvement in monetary values is presented. On the basis of this theoretical model a tool is made for the analysis at the firm level. The usefulness of this framework was empirically tested with the data of the profit center of one medium size Finnish firm which operates in metal industry. It is expressedthat the framework provides valuable information about the economical effects of productivity improvement for supporting the management in their decision making.

The effects of some variables on CO2 laser-MAG hybrid welding

The CO2-laser-MAG hybrid welding process has been shown to be a productive choice for the welding industry, being used in e.g. the shipbuilding, pipe and beam manufacturing, and automotive industries. It provides an opportunity to increase the productivity of welding of joints containing air gaps compared with autogenous laser beam welding, with associated reductions in distortion and marked increases in welding speeds and penetration in comparison with both arc and autogenous laser welding. The literature study indicated that the phenomena of laser hybrid welding are mostly being studied using bead-on-plate welding or zero air gap configurations. This study shows it very clearly that the CO2 laser-MAG hybrid welding process is completely different, when there is a groove with an air gap. As in case of industrial use it is excepted that welding is performed for non-zero grooves, this study is of great importance for industrial applications. The results of this study indicate that by using a 6 kW CO2 laser-MAG hybrid welding process, the welding speed may also be increased if an air gap is present in the joint. Experimental trials indicated that the welding speed may be increased by 30-82% when compared with bead-on-plate welding, or welding of a joint with no air gap i.e. a joint prepared as optimum for autogenous laser welding. This study demonstrates very clearly, that the separation of the different processes, as well as the relative configurations of the processes (arc leading or trailing) affect welding performance significantly. These matters influence the droplet size and therefore the metal transfer mode, which in turn determined the resulting weld quality and the ability to bridge air gaps. Welding in bead-onplate mode, or of an I butt joint containing no air gap joint is facilitated by using a leading torch. This is due to the preheating effect of the arc, which increases the absorptivity of the work piece to the laser beam, enabling greater penetration and the use of higher welding speeds. With an air gap present, air gap bridging is more effectively achieved by using a trailing torch because of the lower arc power needed, the wider arc, and the movement of droplets predominantly towards the joint edges. The experiments showed, that the mode of metal transfer has a marked effect on gap bridgeability. Transfer of a single droplet per arc pulse may not be desirable if an air gap is present, because most of the droplets are directed towards the middle of the joint where no base material is present. In such cases, undercut is observed. Pulsed globular and rotational metal transfer modes enable molten metal to also be transferred to the joint edges, and are therefore superior metal transfer modes when bridging air gaps. It was also found very obvious, that process separation is an important factor in gap bridgeability. If process separation is too large, the resulting weld often exhibits sagging, or no weld may be formed at all as a result of the reduced interaction between the component processes. In contrast, if the processes are too close to one another, the processing region contains excess molten metal that may create difficulties for the keyhole to remain open. When the distance is optimised - i.e. a separation of 0-4 mm in this study, depending on the welding speed and beam-arc configuration - the processes act together, creating beneficial synergistic effects. The optimum process separation when using a trailing torch was found to be shorter (0-2 mm) than when a leading torch is used (2-4 mm); a result of the facilitation of weld pool motion when the latter configuration is adopted. This study demonstrates, that the MAG process used has a strong effect on the CO2-laser-MAG hybrid welding process. The laser beam welding component is relatively stable and easy to manage, with only two principal processing parameters (power and welding speed) needing to be adjusted. In contrast, the MAG process has a large number of processing parameters to optimise, all of which play an important role in the interaction between the laser beam and the arc. The parameters used for traditional MAG welding are often not optimal in achieving the most appropriate mode of metal transfer, and weld quality in laser hybrid welding, and must be optimised if the full range of benefits provided by hybrid welding are to be realised.

Size Effect and Notch Size Effect in Metal Fatigue

It is a well known phenomenon that the constant amplitude fatigue limit of a large component is lower than the fatigue limit of a small specimen made of the same material. In notched components the opposite occurs: the fatigue limit defined as the maximum stress at the notch is higher than that achieved with smooth specimens. These two effects have been taken into account in most design handbooks with the help of experimental formulas or design curves. The basic idea of this study is that the size effect can mainly be explained by the statistical size effect. A component subjected to an alternating load can be assumed to form a sample of initiated cracks at the end of the crack initiation phase. The size of the sample depends on the size of the specimen in question. The main objective of this study is to develop a statistical model for the estimation of this kind of size effect. It was shown that the size of a sample of initiated cracks shall be based on the stressed surface area of the specimen. In case of varying stress distribution, an effective stress area must be calculated. It is based on the decreasing probability of equally sized initiated cracks at lower stress level. If the distribution function of the parent population of cracks is known, the distribution of the maximum crack size in a sample can be defined. This makes it possible to calculate an estimate of the largest expected crack in any sample size. The estimate of the fatigue limit can now be calculated with the help of the linear elastic fracture mechanics. In notched components another source of size effect has to be taken into account. If we think about two specimens which have similar shape, but the size is different, it can be seen that the stress gradient in the smaller specimen is steeper. If there is an initiated crack in both of them, the stress intensity factor at the crack in the larger specimen is higher. The second goal of this thesis is to create a calculation method for this factor which is called the geometric size effect. The proposed method for the calculation of the geometric size effect is also based on the use of the linear elastic fracture mechanics. It is possible to calculate an accurate value of the stress intensity factor in a non linear stress field using weight functions. The calculated stress intensity factor values at the initiated crack can be compared to the corresponding stress intensity factor due to constant stress. The notch size effect is calculated as the ratio of these stress intensity factors. The presented methods were tested against experimental results taken from three German doctoral works. Two candidates for the parent population of initiated cracks were found: the Weibull distribution and the log normal distribution. Both of them can be used successfully for the prediction of the statistical size effect for smooth specimens. In case of notched components the geometric size effect due to the stress gradient shall be combined with the statistical size effect. The proposed method gives good results as long as the notch in question is blunt enough. For very sharp notches, stress concentration factor about 5 or higher, the method does not give sufficient results. It was shown that the plastic portion of the strain becomes quite high at the root of this kind of notches. The use of the linear elastic fracture mechanics becomes therefore questionable.

Climate driven changes in temperature, pH and food quality : effects on copepod reproduction

Increased emissions of greenhouse gases into the atmosphere are causing an anthropogenic climate change. The resulting global warming challenges the ability of organisms to adapt to the new temperature conditions. However, warming is not the only major threat. In marine environments, dissolution of carbon dioxide from the atmosphere causes a decrease in surface water pH, the so called ocean acidification. The temperature and acidification effects can interact, and create even larger problems for the marine flora and fauna than either of the effects would cause alone. I have used Baltic calanoid copepods (crustacean zooplankton) as my research object and studied their growth and stress responses using climate predictions projected for the next century. I have studied both direct temperature and pH effects on copepods, and indirect effects via their food: the changing phytoplankton spring bloom composition and toxic cyanobacterium. The main aims of my thesis were: 1) to find out how warming and acidification combined with a toxic cyanobacterium affect copepod reproductive success (egg production, egg viability, egg hatching success, offspring development) and oxidative balance (antioxidant capacity, oxidative damage), and 2) to reveal the possible food quality effects of spring phytoplankton bloom composition dominated by diatoms or dinoflagellates on reproducing copepods (egg production, egg hatching, RNA:DNA ratio). The two copepod genera used, Acartia sp. and Eurytemora affinis are the dominating mesozooplankton taxa (0.2 – 2 mm) in my study area the Gulf of Finland. The 20°C temperature seems to be within the tolerance limits of Acartia spp., because copepods can adapt to the temperature phenotypically by adjusting their body size. Copepods are also able to tolerate a pH decrease of 0.4 from present values, but the combination of warm water and decreased pH causes problems for them. In my studies, the copepod oxidative balance was negatively influenced by the interaction of these two environmental factors, and egg and nauplii production were lower at 20°C and lower pH, than at 20°C and ambient pH. However, presence of toxic cyanobacterium Nodularia spumigena improved the copepod oxidative balance and helped to resist the environmental stress, in question. In addition, adaptive maternal effects seem to be an important adaptation mechanism in a changing environment, but it depends on the condition of the female copepod and her diet how much she can invest in her offspring. I did not find systematic food quality difference between diatoms and dinoflagellates. There are both good and bad diatom and dinoflagellate species. Instead, the dominating species in the phytoplankton bloom composition has a central role in determining the food quality, although copepods aim at obtaining as a balanced diet as possible by foraging on several species. If the dominating species is of poor quality it can cause stress when ingested, or lead to non-optimal foraging if rejected. My thesis demonstrates that climate change induced water temperature and pH changes can cause problems to Baltic Sea copepod communities. However, their resilience depends substantially on their diet, and therefore the response of phytoplankton to the environmental changes. As copepods are an important link in pelagic food webs, their future success can have far reaching consequences, for example on fish stocks.

Effects of mineral sorting on concentrator design and economics

Ore sorting after crushing is an effective way to enhance the feed quality of a concentrator. Sorting by hand is the oldest way of concentrating minerals but it has become outdated because of low capacities. Older methods of sorting have also been difficult to use in large scale productions due to low capacities of sorters. Data transfer and processing and the speed of rejection mechanisms have been the bottlenecks for effective use of sorters. A fictive chalcopyrite ore body was created for this thesis. The properties of the ore were typical of chalcopyrite ores and economical limit was set for design. Concentrator capacity was determined by the size of ore body and the planned mine life. Two concentrator scenarios were compared, one with the sorting facility and the other without sorting. Comparison was made for quality and amount of feed, size of equipment and economics. Concentrator with sorting had lower investment and operational cost but also lower incomes due to the ore loss in sorting. Net cash flow, net present value and internal rate of interest were calculated for comparison of the two scenarios.

The effects of maternal hyperglycemia on human umbilical vascular gene expression and neonatal rat lung development

Background: Maternal diabetes affects many fetal organ systems, including the vasculature and the lungs. The offspring of diabetic mothers have respiratory adaptation problems after birth. The mechanisms are multifactorial and the effects are prolonged during the postnatal period. An increasing incidence of diabetic pregnancies accentuates the importance of identifying the pathological mechanisms, which cause the metabolic and genetic changes that occur in offspring, born to diabetic mothers. Aims and methods: The aim of this thesis was to determine changes both in human umbilical cord exposed to maternal type 1 diabetes and in neonatal rat lungs after streptozotocin-induced maternal hyperglycemia, during pregnancy. Rat lungs were used as a model for the potential disease mechanisms. Gene expression alterations were determined in human umbilical cords at birth and in rat pup lungs at two week of age. During the first two postnatal weeks, rat lung development was studied morphologically and histologically. Further, the effect of postnatal hyperoxia on hyperglycemia-primed rat lungs was investigated at one week of age to mimic the clinical situation of supplemental oxygen treatment. Results: In the umbilical cord, maternal diabetes had a major negative effect on the expression of genes involved in blood vessel development. The genes regulating vascular tone were also affected. In neonatal rat lungs, intrauterine hyperglycemia had a prolonged effect on gene expression during late alveolarization. The most affected pathway was the upregulation of extracellular matrix proteins. Newborn rat lungs exposed to intrauterine hyperglycemia had thinner saccular walls without changes in airspace size, a smaller relative lung weight and lung total tissue area, and increased cellular apoptosis and proliferation compared to control lungs, possibly reflecting an aberrant maturational adaptation. At one and two weeks of age, cell proliferation and secondary crest formation were accelerated in hyperglycemia-exposed lungs. Postnatal hyperoxic exposure, alone caused arrested alveolarization with thin-walled and enlarged alveoli. In contrast, the dual exposure of intrauterine hyperglycemia and postnatal hyperoxia resulted in the phenotype of thick septa together with arrested alveolarization and decreased number of small pulmonary arteries. Conclusions: Maternal diabetic environment seems to alter the umbilical cord gene expression profile of the regulation of vascular development and function. Fetal hyperglycemia may additionally affect the genetic regulation of the postnatal lung development and may actually induce prolonged structural alterations in neonatal lungs together with a modifying effect on the deleterious pulmonary exposure of postnatal hyperoxia. This, combined with the novel human umbilical cord gene data could serve as stepping stones for future therapies to curb developmental aberrations.

Membrane properties of structurally modified ceramides : effects on lipid lateral distribution and sphingomyelin-interactions in artificial bilayer membranes

Ceramides comprise a class of sphingolipids that exist only in small amounts in cellular membranes, but which have been associated with important roles in cellular signaling processes. The influences that ceramides have on the physical properties of bilayer membranes reach from altered thermodynamical behavior to significant impacts on the molecular order and lateral distribution of membrane lipids. Along with the idea that the membrane physical state could influence the physiological state of a cell, the membrane properties of ceramides have gained increasing interest. Therefore, membrane phenomena related to ceramides have become a subject of intense study both in cellular as well as in artificial membranes. Artificial bilayers, the so called model membranes, are substantially simpler in terms of contents and spatio-temporal variation than actual cellular membranes, and can be used to give detailed information about the properties of individual lipid species in different environments. This thesis focuses on investigating how the different parts of the ceramide molecule, i.e., the N-linked acyl chain, the long-chain sphingoid base and the membrane-water interface region, govern the interactions and lateral distribution of these lipids in bilayer membranes. With the emphasis on ceramide/sphingomyelin(SM)-interactions, the relevance of the size of the SMhead group for the interaction was also studied. Ceramides with methylbranched N-linked acyl chains, varying length sphingoid bases, or methylated 2N (amide-nitrogen) and 3O (C3-hydroxyl) at the interface region, as well as SMs with decreased head group size, were synthesized and their bilayer properties studied by calorimetric and fluorescence spectroscopic techniques. In brief, the results showed that the packing of the ceramide acyl chains was more sensitive to methyl-branching in the mid part than in the distal end of the N-linked chain, and that disrupting the interfacial structure at the amide-nitrogen, as opposed to the C3-hydroxyl, had greater effect on the interlipid interactions of ceramides. Interestingly, it appeared that the bilayer properties of ceramides could be more sensitive to small alterations in the length of the long-chain base than what was previously reported for the N-linked acyl chain. Furthermore, the data indicated that the SM-head group does not strongly influence the interactions between SMs and ceramides. The results in this thesis illustrate the pivotal role of some essential parts of the ceramide molecules in determining their bilayer properties. The thesis provides increased understanding of the molecular aspects of ceramides that possibly affect their functions in biological membranes, and could relate to distinct effects on cell physiology.

Bumblebees in a Changing Climate: Evaluating the Effects of Temperature on Queen Performance

Bumblebees are a very essential group of pollinating insects, but their populations have declined drastically during the past decades. We need to understand why their numbers are decreasing and what can be done to reverse this trend. Climate change-related phenomena, such as changes in the overwintering temperatures and spring conditions, are among the most prominent threats to bumblebees. Queens have a special role in the lifecycle of bumblebees because they overwinter and start new colonies the next year. Their successful performance: survival, overwintering ability, longevity, immune competence, and nest establishing capability in spring, is highly important for bumblebee populations. However, the effects of climate change on bumblebee queen performance remain unknown. The main objective of this thesis was to assess how temperature affects the performance of bumblebee queens during and after overwintering. The effects of warm temperature predicted by climate change scenarios on queen survival and stress-tolerance were studied by a four-month artificial diapause of bumblebee queens at two temperatures (9°C and 1.8°C). Bumblebee colonies were also reared in a laboratory and factors affecting colony characteristics were examined. In addition, queen performance during spring was studied in a starvation experiment using two temperatures (15°C as normal; 24°C as warmer than average) and queens collected from nature right after their emergence. My research revealed how temperature affects queen performance, and queen size was found to be an important factor determining the direction of some of these effects. We found a 0.4g weight threshold for bumblebee queens to be able to survive overwintering. In addition, during mild winters, larger queens have a higher chance than smaller ones to survive through winter and also to cope with immunological stresses after overwintering. During cold conditions, which are normal in the current climatic situation, this advantage disappears. In the spring starvation experiment, the starved queens survived approximately eight days longer in 15°C than in 24°C, which means that starvation risk rises significantly with increasing spring temperature, in a situation where food is scarce due to for example frost damage or asynchrony between bumblebees and their important food plants. These results could mean that in the future climate, larger queens are better able to survive the winter, initiate their nests and start rearing their offspring. This may be problematic, because I also detected two alternative strategies of colony development that differ between large and small queens; larger queens start to lay eggs earlier at nest initiation, their colonies mature later, they produce more workers, and they have a more strongly male biased sex allocation compared with smaller queens. If larger queens have a greater change of producing offspring after a mild winter, this could lead to a significant decline in the total production of new queens at a population level. Thus, it seems that queen size could act as one mechanism regulating the population level outcomes in different temperatures. The new information presented in my thesis reinforces that basic research, monitoring, and local species conservation of bumblebees both in Finland and globally must be increased to ensure that this highly important pollinator group survives in the face of climate change.

Effects of algal turbidity on foraging and antipredator behaviour of the three-spined stickleback (Gasterosteus aculeatus)

The aim of this thesis was to examine how aquatic organisms, such as fish, behave in an altered environmental condition. Many species of fish use vision as their primary tool to gain information about their surrounding environment. The visual conditions of aquatic habitats are often altered as a result of anthropogenic disturbance, such as eutrophication that initiates algal turbidity. In general, turbidity reduces the visibility and can be hypothesized to have an influence on the behaviour of fish. I used the three-spined stickleback (Gasterosteus aculeatus) as a model species and conducted four studies in the laboratory to test how algal turbidity affects its behaviour. In this thesis, two major behavioural aspects are discussed. The first is antipredator behaviour. In study I, the combined effects of turbidity and shoot density on habitat choice (shelter vs open) behaviour was tested on a group of sticklebacks (20 fish) in the presence and absence of piscivorous perch (Perca fluviatilis). In study II, I examined the behavioural responses of feeding sticklebacks when they were exposed to the sudden appearance of an avian predator (the silhouette of a common tern, Sterna hirundo). The study was done in turbid and clear water using three different groups sizes (1, 3 and 6 fish). The second aspect is foraging behaviour. Study III & IV focused on the effects of algal turbidity on the foraging performance of sticklebacks. In study III, I conducted two separate experiments to examine the effects of turbidity on prey consumption and prey choice of sticklebacks. In this experiment turbidity levels and the proportion of large and small prey (Daphnia spp.) were manipulated. In study IV, I studied whether a group of six sticklebacks can distribute themselves according to food input at two feeding stations in a way that provided each fish with the same amount of food in clear and turbid water. I also observed whether the fish can follow changes in resource distribution between the foraging patches. My results indicate an overall influence of algal turbidity on the antipredator and foraging behaviour of sticklebacks. In the presence of a potential predator, the use of the sheltered habitat was more pronounced at higher turbidity. Besides this, sticklebacks reduced their activity levels with predator presence at higher turbidity and shoot density levels, suggesting a possible antipredator adaptation to avoid a predator. When exposed to a sudden appearance of an avian predator, sticklebacks showed a weaker antipredator response in turbid water, which suggests that turbidity degrades the risk assessment capabilities of sticklebacks. I found an effect of group size but not turbidity in the proportion of sticklebacks that fled to the shelter area, which indicates that sticklebacks are able to communicate among group members at the experimental turbidity levels. I found an overall negative effect of turbidity on food intake. Both turbidity and changes in the proportion of prey sizes played a significant role in a stickleback’s prey selection. At lower turbidity levels (clear <1 and 5 NTU) sticklebacks showed preferences for large prey, whereas in more turbid conditions and when the proportion of large to small prey increased sticklebacks became increasingly random in their prey selection. Finally, my results showed that groups of sticklebacks disperse themselves between feeding stations according to the reward ratios following the predictions of the ideal free distribution theory. However, they took a significantly longer time to reach the equilibrium distribution in turbid water than in clear water. In addition, they showed a slower response to changes in resource distribution in a turbid environment. These findings suggest that turbidity interferes with the information transfer among group foragers. It is important to understand that aquatic animals are often exposed to a degraded environment. The findings of this thesis suggest that algal turbidity negatively affects their behavioural performance. The results also shed light on the underlying behavioural strategies of sticklebacks in turbid conditions that might help them adapt to an altered environmental situation and increase their survival. In conclusion, I hold that although algal turbidity has detrimental effects on the antipredator and foraging behaviour of sticklebacks, their behavioural adjustment might help them adapt to a changing environment.

Coolability of porous core debris beds : Effects of bed geometry and multi-dimensional flooding

This thesis addresses the coolability of porous debris beds in the context of severe accident management of nuclear power reactors. In a hypothetical severe accident at a Nordic-type boiling water reactor, the lower drywell of the containment is flooded, for the purpose of cooling the core melt discharged from the reactor pressure vessel in a water pool. The melt is fragmented and solidified in the pool, ultimately forming a porous debris bed that generates decay heat. The properties of the bed determine the limiting value for the heat flux that can be removed from the debris to the surrounding water without the risk of re-melting. The coolability of porous debris beds has been investigated experimentally by measuring the dryout power in electrically heated test beds that have different geometries. The geometries represent the debris bed shapes that may form in an accident scenario. The focus is especially on heap-like, realistic geometries which facilitate the multi-dimensional infiltration (flooding) of coolant into the bed. Spherical and irregular particles have been used to simulate the debris. The experiments have been modeled using 2D and 3D simulation codes applicable to fluid flow and heat transfer in porous media. Based on the experimental and simulation results, an interpretation of the dryout behavior in complex debris bed geometries is presented, and the validity of the codes and models for dryout predictions is evaluated. According to the experimental and simulation results, the coolability of the debris bed depends on both the flooding mode and the height of the bed. In the experiments, it was found that multi-dimensional flooding increases the dryout heat flux and coolability in a heap-shaped debris bed by 47–58% compared to the dryout heat flux of a classical, top-flooded bed of the same height. However, heap-like beds are higher than flat, top-flooded beds, which results in the formation of larger steam flux at the top of the bed. This counteracts the effect of the multi-dimensional flooding. Based on the measured dryout heat fluxes, the maximum height of a heap-like bed can only be about 1.5 times the height of a top-flooded, cylindrical bed in order to preserve the direct benefit from the multi-dimensional flooding. In addition, studies were conducted to evaluate the hydrodynamically representative effective particle diameter, which is applied in simulation models to describe debris beds that consist of irregular particles with considerable size variation. The results suggest that the effective diameter is small, closest to the mean diameter based on the number or length of particles.