Search

A set of postulates, called the remanent curvature hypothesis, is proposed to de scribe the behavior of cloth in creasing. The differential equations describing the behavior of a loop of fabric in loading and unloading are established and integrated for a range of values of a parameter which measures the susceptibility of a fabric to retain a crease or wrinkle. The loading and unloading curves so obtained are compared with experimental results. Up to loads of 4 kg, the geometric similarity predicted by the theory is maintained, although the shape of the experimental unloading curves differs from the theoretical curves at low loads.

A group of Cutthroat flumes was rated under both free flow and submerged flow conditions. Generalized discharge rating curves can be developed due to the simplicity of the structure and the geometric similarity between flume sizes. Twelve flumes were used in this study, including three flume lengths of 1.5 ft (0.45 m), 3 ft (0.90 m), and 4.5 ft (1.35 m), with four different throat widths for each length. In addition, the flume sizes were selected so as to permit correlation with the initial Cutthroat flume studies, wherein a flume length of 9 ft. (2.7 m), and throat widths varying from 1 ft (0.3 m) to 6 ft (1.8 m), were studied.

This paper reports on the theoretical conversions between Rockwell, Brinell and Vickers hardnesses. Theoretical hardness conversions based on the principle of geometric similarity and Meyer's law agree well with experimental conversions now used in general. Furthermore, the authors show that variation of conversion relationship for various metals can be explainable with Meyer's index almost clearly.

To understand the effect of workhardening in large plastic flow and how it relates to nonhardening theory, an experimental program of wedge flattening has been performed. Wedges of 20°, 30°, 45° and 60° semi-angle were prepared from copper with five levels of prestrain and from two aluminum alloys. Testing was undertaken with care to insure meaningful quantitative data and to permit geometric similarity to occur. Systematic and large effects occurred in the behavior of the specimens as a result of workhardening. For instance, it was found that the width of the deformed top could be less than the truncated wedge value, constraint factors could be twice those predicted by nonhardening analysis, and the anvil pressure could decrease with increasing angle whereas nonhardening theory predicts an increase. An existing nonhardening slip-line solution which contains strain discontinuities produced by velocity discontinuities was verified by extrapolating the experimentally obtained results to zero workhardening. This suggests that workhardening solutions may reveal strain discontinuities at the limiting case of zero workhardening and that perturbation techniques based on nonhardening solutions may be useful in solving workhardening problems.

The coefficient b of the power function y = bxa has long been misinterpreted as a measure of size-independent differences between regressions. Just the opposite is true; b is a scale factor that expresses differences in size between comparable animals of the same shape on two or more regressions of constant α. When α is invariant for two regressions, a similarity criterion s can be extracted from the two b-values (s = [b1/b2]1/(1-α)); s measures the relative difference in size at which animals on the two curves have the same shape. If this calculated difference equals the observed difference in size, then the transposition (shift of regression line without change of slope) occurred in order to maintain geometric similarity in a new size range. I present examples of geometric similarity via transposition for body shape in gulls, brain weight in felids and primates, tooth shape in canids, skull form in bovids, the evolution of Gryphaea, the growth of horses, and differences between local races of lobsters a...

Stress-concentration factors are analytically determined for relatively deep U-shaped edge notches of constant radii in a semi-infinite sheet with uniaxial tension applied parallel to the sheet edge. Because a strong geometric similarity exists between a U-notch and a semi-elliptical notch of the same tip radius, a comparison of such analytical data is effected. Stress-concentration factors for U-notches in a semi-infinite sheet are also compared with other comparable analytical and experimental data available in the literature.Finite-width correction factors are applied to the results of the semi-infinite-sheet analysis to provide practical design data. These data are compared with experimental results provided by a number of investigators.

1. The vortex formation is determined by criteria which are part of Eq. (11) with allowance for the Weber criterion. 2. In respect of FrH, ReH and WeH there are self-modelling areas characterized by conditions of Eq. (12). 3. At the areas of self-modelling in respect of FrH, ReH and WeH, and for a case of a geometric similarity between a model and the prototype, the vortex formation is modelled in accordance with Froude number for a rotary motion. 4. For each R* there exists a minimum value of a discharge coefficient which is attained with Γsp → ∞. Practically, there exists a certain Γcr value above which the decrease of μ is insignificant.

Realizar estudios hidráulicos en plantas de tratamiento a escala real, resulta complejo y costoso. Una alternativa para crearlo, es mediante la construcción de un modelo físico calibrado que representa las condiciones semejantes al prototipo. El objetivo de este estudio fue la modelación física de un RAFA para simular su patrón de flujo. La metodología consistió en el diseño, cálculo de las relaciones de longitud relativa y construcción, empleando una escala de reducción de 1:8 entre el prototipo y el modelo físico (MF). El reactor fue alimentado con agua residual municipal del colector C de la ciudad de Maracaibo, Venezuela. Se utilizó Li+ (LiCl) como trazador usando como prototipo el reactor anaerobio de flujo ascendente (RAFA) ubicado en Ginebra, Colombia. El MF se logró con una relación de longitud relativa (Lr) de 0,1239 para la similitud física al igual que la similitud cinemática para la velocidad y aceleración; usando el número de Peclet se logró una similitud dinámica con Lr = 0,1290 obteniendo una superposición de la distribución de los tiempos de residencia (DTR) a un tiempo de retención hidráulico teórico (t o) de 5 h con un coeficiente de determinación ajustado (R²a) de 0,928. Las eficiencias hidráulicas (β) obtenidas variaron desde 0,798 a 0,988 en el MF y 0,902 a 0,943 en el prototipo, superando a la obtenida en lagunas de estabilización (0,17 a 67%). Hydraulic studies Wastewater Treatment Plants Works on field are complex and expensive. An alternative to have done these studies is by building a up a calibrated physical model to simulate the conditions of similarity to the prototype. The aim of this study was a physical modeling to simulate flow at UASB pattern and to observe whether or not agreement are found prototype with it. The methodology involved in the design, calculation of relative length relations and construction, using a reduced scale of 1:8 between the prototype and physical model (PM). The reactor was fed with municipal wastewater flooding from collector C of the city of Maracaibo, Venezuela. Tracer study with Li+ (LiCl) was used either prototype reactor (UASB) located in Ginebra, Colombia. Geometric similarities were achieved with a ratio of relative length (Lr) of 0.1239 and similarity kinematics for a speed and acceleration, dynamic was found by using the Peclet number. Match distribution of residence time (DTR) to a theoretical hydraulic retention time (t0) for 5 h was found with a coefficient of determination adjusted (R²a) to 0.928. Hydraulic efficiencies (β) obtained were ranged from 0.798 to 0.988 in the MF and from 0.902 to 0.943 in the prototype, exceeding that obtained instabilization ponds (0.17 to 67%).

The research of moss greening material (Sphagnum sp.) as a rooftop panel is prior to commercial industry. Scale up of production must be prepared for maintaining quality of product through. Production system of moss greening panel consists of aquaculture and panel assembly process. This paper highlighted scale up of panel assembly using dimensional analysis. It is a method based on the principle of geometric similarity which were used in scale up of aquaculture process. Subsequently, it is used as a basic assumption to design an analog models in panel assembly process. The research aims are: 1) To design an analog models in scale up of panel assembly process based on scale up of aquaculture process; 2) To identify the critical variables in the scale up of panel assembly process. Research results concluded that an analog model can be designed for panel assembly. Critical variables was identified and calculated in scale up of panel assembly process by increasing length of panel were air flow rate (v), mass of dry moss (m), width of panel (l), and thickness of panel (t).

Los sistemas de tratamiento de aguas municipales tales como lagunas de estabilización maduración, LEM y reactores anaerobios de flujo ascendente, RAFA presentan diferencia entre el tiempo de retención nominal, TRN y el tiempo de retención hidráulico, TRH, debido a problemas en el interior del reactor tales como: cortos circuitos, flujo reverso y viento. Realizar estudios hidráulicos en plantas de tratamiento reales resulta complejo y costoso. Una alternativa para analizar el TRH es mediante la construcción de un modelo físico calibrado que simule las condiciones de similitud y semejanza entre el modelo y el prototipo. El objetivo de este estudio fue determinar el TRH y patrón de flujo utilizando dos casos de estudios con modelos físico: LEM y RAFA. La metodología consistió en el diseño, calculo de las relaciones de longitud y construcción, empleando una reducción a escala de 1:18 (LEM) y 1:90 (RAFA) entre el prototipo y el modelo. Se utilizo un trazador Rodamina WT con agua potable y LiCl con agua sintética en los modelos para la obtención del TRH y se comparó con el obtenido en los prototipos en Lidsey, Inglaterra (LEM) y Ginebra, Colombia (RAFA). Los resultados indicaron superposición de la distribución de los tiempos, TRH de 0,77 d (prototipo) y 0,89 d (modelo) para LEM, y de 4,8 h (prototipo) y 6,17 h (modelo) para el RAFA para un nivel de confiabilidad promedio fue mayor de 96%. En ambos casos se encontró patrón de flujo disperso Wastewater Treatment Plant Works has been facing hydraulic problem refers to back-mixing, short-circuiting and wind effect, thus reducing of the Mean Hydraulic Retention Time, MHRT. Tracer studies for full-scale WSPs and UASB is complex and expensive. For that, a calibrated physical model, PM is better alternative to determine MHRT even though similarities between prototype and physical model are achieved. The aim of this study is to determine the MHRT through out two physical models by using Rhodamine WT dye and LiCl then it was compared with one obtained previously from the prototype. The methodology was the construction and calibration of the models scale reduced 1:18 and 1:90 from prototype (maturation pond, Lidsey UK) and (UASB, Colombia), respectively. Hydraulic pathways using tracer’s techniques in still and artificial solution water was analysed. The results found an agreement of the layout match in terms of MHRT (0.77d against to 0.89d) for WSPs and (4,8h against to 6,17) for an UASB between P.M and prototypes over 96% of confidence level. Dispersed-mixed flow was achieved

The physical vacuum affects not only the natural processes in deep space but also identifies the key features of the structure of ordinary matter. This sphere of work intersects the fields of chemistry and biology. The condition of the objective existence of elementary particles and the objectivity of quantum measurements require the presence of real physical analogues of clocks and lines that participate directly and literally in particle interactions. The analogue of the clock results from the existence of elementary particles in the form of the alternation of two states with different properties that can be modelled in terms of probabilistic behaviour, the uncertainty principle, and similar concepts. The analogue line appears due to the quasi-crystalline structure of the physical vacuum, thereby generating a real observed mass ratio and other features of the microworld. The emergence of life and sense is regulated by deterministic processes. Biological evolution is a process directed toward a slow and gradual adaptation to the physical vacuum as the real component of the environment. Because of such evolution, the geometric structure of living organisms transforms into a fractal increased in absolute terms by chemical simulation. Therefore, the analogue model defines the key structures of the vacuum. The geometric similarity of the structures allows cells to live in accordance with the laws of the quantum world without requiring the solving of equations.

1. Approximate geometric similarity has been experimentally established for the minimum amount of stemming resulting in the formation of an underground cavity upon explosion of a cylindrical charge. 2. With increase in the amount of stemming (up to a certain limit) the radius of the cavity increases linearly. Experiments have established that, other things being equal, the volume of the underground cylindrical cavity is greater than the volume of the cavity obtained without stemming (at H=0) by a factor of 2.2.

Heart weight scaling among members of the primate tribe Papionini is analyzed in relation to the proposal that evolutionary size change may sometimes come about in such a way that geometric similarity is maintained across species. The results indicate that in terms of relative heart weight, the six species examined can be divided into two groups of geometric variants. Although these groupings do not conform to any hypothesized phylogenetic relationships, there is some evidence to support the associations based on shared patterns of ontogenetic development. An account is proposed for the differences between the two groups in terms of derived versus primitive patterns of relative heart weight growth.

Extant terrestrial mammals span an enormous size range, from tiny pygmy shrews weighing in at less than 5 g to massive African elephants tipping the scales at over 2500 kg (Eisenberg, 1981). Despite such marked differences in adult body mass, Alexander et al. (1979) report that the lengths and diameters of limb bones in a shrew-to-elephant size series scale surprisingly close to geometric similarity; i.e., linear dimensions are almost proportional to (mass)173. Although adult members of the order Primates cannot match the overall range of body sizes in mammals, the size distribution of living primate species is still quite impressive, ranging from dwarf galagos and mouse lemurs (—60–70 g) at one end of the spectrum to male gorillas (>200 kg in some individuals) at the other. Given the unexpected results of the Alexander et al. (1979) study, it is reasonable to wonder if the linear dimensions of the long bones of adult primates also conform to the expectations of geometric similarity. A few minutes of casual observation at the zoo or natural history museum would probably suffice to allow one to reject this null hypothesis for primate limb proportions. Galagos and tarsiers simply do not resemble gibbons or gorillas very much with regard to their respective bodily proportions. Locomotor differences between these extremes seem equally obvious and appear to be correlated with differences in limb proportions.

Dimensional analysis of animal with regard to those structures and functions which affects the rate of energy metabolism can be conducted on the basis of either geometric or eleastic similarity. Predictions of the trelationships between various structures and functions and body mass are dependent of the type of similarity assumed. Comparison of the relationships between numerous physiological variables and body mass resported in the literature and those predicted from geometric and elastic similarity indicates that the preponderance of predications from elastic similarity are in better agreement with the observed values than are the prediction from geometric similarity. It appears that the components of the cardiovascular system are scaled in accordance with elastic similarity. For this reason, cardiac output is proportional to body mass raised to the 3 4 power. The biochemical basis for the relationship between cardiac output and the rate of energy metabolism is discussed.

Surface area/volume arguments have been extensively used in biology. They are valid provided, first, that one of the properties being considered scales as the surface area of an organism and the other as the volume of an organism and, secondly, given that this is the case, that the surface area/volume ratio represents an important evolutionary constraint pertinent to the problem under consideration. This chapter looks at some instances where surface area/volume arguments may have been misappropriated or misapplied. It also considers when they may be valid. Why cannot large animals rely solely on diffusion for gaseous exchange? The universal answer given in school (Mackean, 1973; Revised Nuffield Biology, 1975; Soper & Tyrell Smith, 1979; Rowlinson & Jenkins, 1982; Jones & Jones, 1984; Green, Stout & Taylor, 1984; Roberts, 1986a, b; Hill & Holman, 1986) and university (Marshall & Hughes, 1965; Barrington, 1967; Alexander, 1971, 1979; Barnes, 1974; Bligh, Cloudsley-Thompson & MacDonald, 1976; Schmidt-Nielsen, 1983, 1984) text-books to the question ‘Why do large species of animals have lungs, gills or other structures specialized for gaseous exchange while smaller species manage by diffusion’ is that the larger an organism, the smaller its surface area to volume ratio. This answer makes two implicit assumptions. First, that the oxygen requirements of an animal are proportional to its volume or weight. Secondly, that diffusion can only provide oxygen at a rate proportional to an animal's surface area. The former of these assumptions is incorrect (Reiss, 1987b). The oxygen requirements of animals scale on body weight with exponents of less than one.

Experiments with an anthropomorphic dummy for blast research demonstrated that pressures recorded in the lung model of the dummy could be correlated to primary air blast effects on the lungs of experimental animals. The results presented here were obtained with a dummy of the type mentioned above, but with the lung model modified to improve geometric similarity to man. Blast experiments were performed in a shock tube, and impact experiments in a special impact machine. Experiments with nonpenetrating missiles were performed with small-caliber firearms and the dummy protected by body armor. Severity indices derived from the blast experiments were related to established criteria for primary lung injury in man. Impacts delivered in the impact machine and by nonpenetrating missiles are compared. Relationships between severity of impact based on experiments with animals and primary lung injury in man are discussed.

The geometric similarity has been detected between the curves τ(∑) and the slip band source spectrum in single crystals of Bi and LiF. This similarity means that the strain hardening curve for the studied crystals can be considered as a reflection of the integral slip band source spectrum nh(τ).

An organism’s size affects virtually all aspects of its physiology and ecology. There are presently no theoretical models which can explain the broad patterns of shape and functional changes observed; empirical descriptions of these patterns have suffered from a lack of rigor in choice and analysis of data.

The allometric relations of diameter and length of humerus, ulna, femur, and tibia of 108 specimens, from 63 different breeds of dogs and 12 specimens of wolves, were calculated by means of model II of regression or major axis method. Only for the tibia were the values of wolves included in the cluster formed for dog breeds. Consequently, separate lines of regression were calculated for the other bones. Results agree in general with the exponents predicted by the theory of geometric similarity; however, the slope obtained for femur (0.865) differed significantly from this. Morphology of the long bones of the legs does not differentiate dogs and wolves; this probably reflects secondary convergence among wolves with relatively modern breeds of dogs.

Todays CAD applications become less and less manageable if no database system is used. One of the most important queries in these applications is the retrieval of parts with geometric similarity. The information obtained from such similar parts will drastically reduce the overhead for production planning and construction.

A relation between tensile curves and critical punch force in the deep drawing of cylindrical products is developed. Both the work hardening effect and the geometry of the drawing punch are taken into account. A reasonable correspondence between the analytical results and the experimental data can be established. Finally, the practical significance of the mathematical model is shown by giving a criterion for the minimum corner radius of the punch. Moreover, the usefulness of the model is confirmed on the basis of some observations on deep drawability and geometric similarity in formability tests.

A limited experimental program has been conducted to determine the heat transfer and pressure loss characteristics of Griscom-Russel special small K-Fin tubes arranged in twelve different surface arrangements. The data are presented in graphical form using the Colburm factor, j, and the Fanning friction factor, f, versus the Reynolds Number, Re. Certain comparisons have been made among the surfaces tested to establish behaviorpatterns when there was only one geometrical variable. in addition a comparison is made where the finned tube is changed but approximate geometric similarity is maintained. (auth)

I have often imagined that La Gioconda’s enigmatic smile is directed towards the scholars who write turgid books to explain her beauty. In length alone, literature about Shakespeare must exceed the Bard’s works by an order of magnitude usually reserved for interstellar distances. Yet if every profession must have its Drosophila, shall we begrudge a Jurassic oyster yet one more article?

It is shown that Junge's (1978) geometric similarity model corresponds to Tversky's set-theoretical model of similarity.

DURING an investigation of the icing characteristics of solid surfaces, Schaefer1 observed that certain protein films induced supercooled water drops to freeze at temperatures near zero. The possible importance of proteins as a source of natural ice nuclei cannot be over-emphasized because proteins are able to concentrate irreversibly at water surfaces and thereafter find their way into the atmosphere in particles large enough to act as ice nuclei. The ocean surface, in particular, would be an immense source of air-borne protein2. Furthermore, protein films are of great fundamental interest because they possess the unique property that their state of compression, and therefore their geometric similarity to an ice lattice, can be varied continuously, thus providing a means of testing the relationship between ‘fit’ and nucleation temperature. It is therefore surprising that while several authors3–5 have accepted proteins as ice nucleators, no confirmation or extension of Schaefer's work has been reported.

Kokshaysky, N. V. (A. N. Severtzov Institute of Animal Evolutionary Morphology and Ecology, Academy of Sciences USSR, Leninsky Prospekt 33, Moscotv W-71, USSR) 1974. Functional Aspects of some details of Bird Wing Configuration. Syst. Zool. 22: 442-450. -In four species of herons with uniform ecological requirements of flight, size-induced differences in values of circumferential wing velocities (and, as a result, increasing angles of incidence in distal sections of the wing with increasing body size) are discovered. To neutralize this departure from dynamic similarity among the four species, regular sizelinked departure from geometric similarity develops; this departure manifests itself most obviously in the appearance of wing-tip slots, growing in number with increase in bird size. These slots are an adaptation for utilizing large angles of incidence and for redistributing generated values of thrust and lift. From the viewpoint of the concept of evolutionary transformation of functions, these relationships may be referred to the principle of the evolutionary stabilization of functions.

The unique measure of “size” that is statistically independent of “shape” for random vectors of measurements following a multivariate lognormal distribution is derived. This size measure is a weighted geometric mean (possibly including negative weights) and generalizes work of Mosimann (1970) on size and shape variables. It is also closely related to White and Gould's (1965) measure of size differences for constant shape. Estimation of the size measure and an example of its application are discussed.