Geometric Proportions Research Articles

Leonardo industrial designer

Leonardo Industrial DesignerWas Leonardo the first industrial designer? Leonardo tries to identify some matrices governing the extreme variety of things inside the whole. Such matrices are supposed to be archetypical entities which can be reproduced countless times in different ways, following geometric rules and standard proportions. We can therefore talk about a grammar of shapes that can be applied to several proportional rapports, symmetries and conceptual analogies which can generate concrete images of a stunning beauty. Leonardo was particularly keen on intertwining figures − dynamic matrices with a really high decorative potential. Leonardo makes use of twined and twisted shapes to describe very different phenomena. Matrix shapes consequently feature two different functions: they are used to investigate and better understand nature, and work as a precious tool for artistic and technical design. The decorations Leonardo creates by using them are therefore neither simple visual ornament, nor accessories to other works of art; on the contrary, they are fundamental and functional elements of a whole. Ornaments thus comply with the criteria of order, beauty and invention, which correspond to the definition of Industrial Designer formulated in the 20th century.

Hepatitis A vaccine immunogenicity 25 years after vaccination in Alaska.

The hepatitis A vaccine is recommended for all children greater than or equal to 1 year of age, however, the duration of vaccine protection is unknown and protection through adulthood is crucial to prevent symptomatic hepatitis later in life. We report on 25 years of follow-up of a cohort of Alaska Native individuals who were vaccinated in early childhood. We assessed the duration of vaccine protection by calculating the geometric mean concentration and proportion of participants with protective levels of IgG antibody to hepatitis A virus (anti-HAV) (≥20 mIU/mL) every 2 to 3 years. We estimated the amount of time until the anti-HAV dropped below protective levels using survival analyses. At 25 years, 43 of the original 144 participants were available, mean anti-HAV levels were 91.5 mIU/mL, and 35 (81.4%) had protective levels of anti-HAV. Using data from all persons and all time points, a survival analysis estimated 78.7% of participants had protective levels of anti-HAV at 25 years. The high level of protective antibodies in this cohort indicate that supplemental doses of hepatitis A vaccine are not needed 25 years after completion of the vaccine series.

Effects of Temperature Differences in Optimization of Spiral Plate Heat Exchangers

In this research, three aspects of modeling, analyzing, and optimizing spiral plate heat exchangers (SPHEs) are studied. The main objective of this work is to pave the way for comparing manufacturers’ designed SPHEs with theoretical designed SPHEs without involving designers in using computational methods. To begin, with assumption of constant overall heat transfer coefficient and specific heat capacities, a mathematical modeling of SPHE based on energy balance equations is developed to model the SPHE as a network of series-connected equivalent internal heat exchangers to determine the temperature distribution in spiral turns. This modeling can facilitate the usage of temperature-enthalpy diagram in SPHEs’ analysis and design. Furthermore, a new algorithm for thermal design optimization of SPHEs has been proposed. The proposed algorithm is based on maximizing pressure drops at channels, considering geometric proportion of SPHE and minimizing the total cost simultaneously. To show the proposed method applicability in analyzing thermal and hydraulic design parameters, a single-phase counter-current SPHE is assessed and optimized for different design cases with temperature approach variations. Results of comparing manufacturers’/standard designed SPHEs and research/theoretical designed SPHEs by defining appropriate geometric proportion ranges confirmed that temperature approach variations can improve SPHE performance to a higher extent, such as finding temperature approach ranges for optimized SPHEs with higher compactness to reduce the manufacturing cost. This fact is revealed by introducing compactness-temperature approach diagram which depicts the geometric optimization of SPHEs and the effects of temperature differences in SPHE’s optimization.

A comparative study of morphological characteristics of medium-density fiberboard dust by sieve and image analyses

Sanding dust is the main source of dust emission during the manufacturing process of medium-density fiberboard (MDF), and particle size and shape characteristics are the fundamental properties influencing its environmental influence and handling behaviors. However, there are few deep and comprehensive researches on the morphology of MDF sanding dust. In this study, the morphological characteristics of MDF sanding dust were explored by sieve and image analyses. It was found that more than 95% of MDF sanding dust was inhalable particles smaller than 100 μm, which poses a considerable potential risk to human health and safety, especially with the presence of other chemical constituents. The particle size span of MDF dust was relatively wide though the particle surface texture was quite uniform. The particle geometric proportion represented by aspect ratio decreased markedly with the reduction of particle size. The larger particles presented typical anisotropic structure, while the smaller ones showed homogeneous appearance, indicating quite complex handling behaviors. In addition, image analysis was found to provide a better insight into the morphological characteristics of MDF sanding dust compared to sieve analysis, and could be a promising dust morphology evaluation technology.

Determination of the scale factor in the physical modeling of reinforced concrete structures exposed to emergency loads

The article proposes a solution to the problem of more accurately taking into account the influence of scale factors on the qualitative and quantitative indicators of the stress-strain state obtained by testing both individual structures and structural systems made of reinforced concrete. Methodical approaches to modeling tests for static and dynamic loads are considered, with the aim of taking into account the scale effects that occur during the manufacture of prototypes of models of individual structures and structural systems made of reinforced concrete. Comparative analysis estimated effect of different geometric proportions for free opera statically determinate beams and for a fragment of a monolithic reinforced concrete frame multistory buildings, experimental studies which were performed by the authors earlier. Analytical patterns were established to assess the impact of large-scale factors on the particular static and dynamic deformation of structures and structural systems of reinforced concrete. The results can be taken into account when conducting experimental studies of model reinforced concrete structures for dynamic emergency loads

A geometric ratio to predict the flexion gap in total knee arthroplasty.

Measured resection is a common technique for obtaining symmetric flexion and extension gaps in posterior-stabilized (PS) total knee arthroplasty (TKA). A known limitation of measured resection, however, is its reliance on osseous landmarks to guide bone resection and component alignment while ignoring the geometry of the surrounding soft tissues such as the medial collateral ligament (MCL), a possible reason for knee instability. To address this clinical concern, we introduce a new geometric proportion, the MCL ratio, which incorporates features of condylar geometry and MCL anterior fibers. The goal of this study was to determine whether the MCL ratio can predict the flexion gaps and to determine whether a range of MCL ratio corresponds to balanced gaps. Six computational knee models each implanted with PS TKA were utilized. Medial and lateral gaps were measured in response to varus and valgus loads at extension and flexion. The MCL ratio was related to the measured gaps for each knee. We found that the MCL ratio was associated with the flexion gaps and had a stronger association with the medial gap (β = -7.2 ± 3.05, P < .001) than with the lateral gap (β = 3.9 ± 7.26, P = .04). In addition, an MCL ratio ranging between 1.1 and 1.25 corresponded to balanced flexion gaps in the six knee models. Future studies will focus on defining MCL ratio targets after accounting for variations in ligament properties in TKA patients. Our results suggest that the MCL ratio could help guide femoral bone resections in measured resection TKA, but further clinical validation is required.

Dynamics of Plane Waves in a Semi-Bounded Electro-Magneto-Elastic Medium

The problem of harmonic oscillations in electro-electromagnetic composites is studied. Oscillations can be initiated by the extended load vector, including the horizontal and vertical components of mechanical displacements, and electrical induction distributed on top of the surface. Boundary conditions assume full mechanical coupling for all layers of the structure. Electrical conditions on the surface top can be both electrically open, and electrically shorted. Magnetic conditions are similar to electric ones and describe the continuity of fields in between two mediums, or indicate the isolation of the magnetic field between them. The Green's function of electro–magneto–elastic medium is constructed. Phase velocities are obtained for various geometric proportions and materials.

10-Valent pneumococcal non-typeable H. influenzae protein D conjugate vaccine (PHiD-CV10) versus 13-valent pneumococcal conjugate vaccine (PCV13) as a booster dose to broaden and strengthen protection from otitis media (PREVIX_BOOST) in Australian Aboriginal children: study protocol for a randomised controlled trial

IntroductionStreptococcus pneumoniae and non-typeable Haemophilus influenzae (NTHi) are major otitis media pathogens that densely co-colonise the nasopharynx and infect the middle ear of Australian Aboriginal infants from very early in...

The polarization effect in electro-magneto-elastic semi-bounded heterostructures

In this paper, we consider the effect of the polarization effect of electro-elastic and magneto-elastic parts of an electro-magneto-elastic heterostructure on its dynamic characteristics. As the studied heterostructure, a packet of layers lying on half-space was selected. It is assumed that the layers are mechanically rigidly adhered to each other. The electrical and magnetic conditions at the layer boundary can be either completely open or completely shorted. Given the variable boundary conditions, the Green’s function of the heterostructure was constructed and the phase velocities were obtained. The electromechanical coupling coefficient in the heterostructure is obtained for various geometric proportions of its constituent layers.

Algorithms for Functioning of the Magneto-Metric System to Provide Search and Rescue Operations Using Unmanned Flying Vehicles

Purpose of research. Reducing the time and increasing the efficiency of search and rescue of crews of land vehicles, air, surface and underwater craft. Combining physical, informational, and geometric parameters allows reliable detection of single ferromagnetic bodies by analyzing additional information in working algorithms.Methods. The paper contains a practically significant variant of building a search engine that is implemented on two or more unmanned flying vehicles moving in the search area in a coordinated formation at the basic distance. The solution system is based on using magnetic field components as magnetometric information without using primary gradient information. This feature allows us to get compact and functionally complete algorithms. Calculations using such algorithms ensure the stability of an unmanned flying vehicle in various combinations of vector, roll and pitch.Results. Algorithms for the functioning of the magnetometric system for searching ferromagnetic bodies based on the magnetostatic equations have been constructed in the article,. The intelligent system is based on the scheme of a measuring and computing circuit with staggered vector three-axis blocks of magnetometers in space. The system is able to solve the whole range of problems of search, detection, direction finding, localization, positioning and identification of metal objects that have their own magnetic field.Conclusion. The main result of the study is that the working algorithms for detecting ferromagnetic bodies take into account the characteristics of the air environment, the instrumental error of measurement units of physical quantities and the geometric proportions of measuring equipment location on board the unmanned and manned search and rescue helicopters. The obtained research results have been used in the development of a hardware and software complex with helicopter-type unmanned flying vehicles designed to support search and rescue operations in the Arctic.

First steps to establishing an equestrian morphology: can Vitruvian ratios help?

Within equestrianism there is increasing focus on rider position and posture, not only in terms of aesthetics and the overall harmonious picture it may portray of the horse-rider combination, but more importantly on the rider’s physical ability to deliver clear, well-timed signals to the horse during training and competitive performance. Anthropometry has been successfully used in a wide range of non-equestrian sports to identify morphologies that are more likely to be successful than others in completing the tasks required by the particular sport or discipline. As physical data have become more readily accessible questions have arisen regarding the rider’s physical ability to achieve and maintain ‘ideal’ and symmetrical riding positions allowing them to transfer their weight and manage their limbs and consequently deliver distinguishable signals to the horse. Clearly identified ideal morphologies exist for a wide range of sports, but there is nothing for equestrianism. Da Vinci’s Vitruvian ‘man’ possesses ideal geometric proportions that depict perfect symmetry and proportion. Within equestrian it is common belief that riders (and horses) should be symmetrical. This study explored how the dimensions of a population of 51 female riders (24.8±8.29 years) aligned with Vitruvian ideals. Ten relative body proportions, selected as potentially the most relevant to horse riding, were obtained for each subject and ratios with total height derived. Only arm span, shoulder width and upper chest to the top of the head in relation to total height aligned with Vitruvian ratios (all P&gt;0.05). Two primary principal components were identified – total height and arm span that could be of potential use for development of an equestrian morphology. Although horse riders’ physical dimensions failed to align well with Vitruvian measures, total height and arm length may have the potential to explain differences in riders’ ability to physically interact with horses and consequently impact their welfare.

Investigation of stable boundary conditions for the Jet-electrolytic Plasma Polishing (Jet-ePP)

Jet-electrolytic Plasma Polishing (Jet-ePP) is a modified form of Bath-ePP to selectively polish and clean local areas with lower-power. When Jet-ePP is used, it must be taken into account how the changed boundary conditions and the additional electrolyte jet parameters influence the basic process. It can be assumed that the plasma polishing changes into electrolytic polishing due to changed boundary conditions, which is not desirable. The non-existent closed boundary conditions must be compensated by setup adjustments. Changes in the phenomenological model of the removal are necessary.The paper shows how the additional and changed process parameters such as fluid flow, distance between anode and cathode influence the individual process phases. Current-time curves are used to investigate the changes in ignition and polishing phases, which are influencing the machining results. Due to these combined data it is possible to find stable process windows. For special changes of the phenomenological model, the physical changes have to be described.To compare the electric parameters such as the voltage drop over the electrolyte of both processes: Jet-ePP and Bath-ePP, equivalent circuit diagrams are used. These describe which changed conditions also lead to the formation of a plasma layer and produce the same effect as in Bath-ePP. In combination with the geometric proportions and the function of the workpiece, the most suitable scientific and industrial application areas are pointed out, making use of the localized jet in comparison with the well-established Bath-ePP process.

Trees as a Shading System for Streets on the East–West Axis: Computer Simulations for the Selected Geometrical Proportions of Building Developments in Humid Continental Climate

The study is aimed at investigating the possibilities for solar protection provided to the street canyon located on the E–W axis and with the following profiles: shallow (height/width (H/W) = 0.2, 0.6, and 1) and deep (H/W = 2) by two rows of trees located at a distance of 3 m away from southern and northern façades. The research was based on numerical simulation analyses conducted in the Rhinoceros® program, with the application of the Ladybug Tools environmental plugin for a street set in the city of Płock (52° 32′50″N 19°42′00″E) for the day characterized with the highest total intensity of insolation within the year, 7 June, between 8:00 a.m. and 5:00 p.m. The research yielded no differences in terms of shading the surface of the southern façade of streets with low, medium, and high building developments. However, slight differences (40 m²) were noted for the model with highrise building developments (h = 60 m) characterized with a deep section (H/W = 2). The simulation also revealed that the H/W ratio parameter only slightly (0.88%–1.93%) affected the share trees have in shading the street floor, except in the case of very shallow profiles (H/W = 0.2).

In Vitro Study of Particle Transport in Successively Bifurcating Vessels.

To reach a predictive understanding of how particles travel through bifurcating vessels is of paramount importance in many biomedical settings, including embolization, thromboembolism, and drug delivery. Here we utilize an in vitro model in which solid particles are injected through a rigid vessel that symmetrically bifurcates in successive branching generations. The geometric proportion and fluid dynamics parameters are relevant to the liver embolization. The volumetric flow field is reconstructed via phase-contrast magnetic resonance imaging, from which the particle trajectories are calculated for a range of size and density using the particle equation of motion. The method is validated by directly tracking the injected particles via optical imaging. The results indicate that, opposite to the common assumption, the particles distribution is fundamentally different from the volumetric flow partition. In fact, the amount of delivered particles vary substantially between adjacent branches even when the flow is uniformly distributed. This is not due to the inertia of the particles, nor to gravity. The particle distribution is rather rooted in their different pathways, which in turn are linked to their release origin along the main vessel cross-section. Therefore, the tree geometry and the associated flow streamlines are the prime determinant of the particle fate, while local changes of volumetric flow rate to selected branches do not generally produce proportional changes of particle delivery.

MOSAICING FIDELITY GEOMETRICAL ASSESSMENT BASED ON SURF POINT CLASSIFICATION

Abstract. The recent development of automated UAV imaging applications for geomatics is leading to an unprecedented rapid growth in mosaic and DEM images. Newer, more advanced algorithms are being extensively studied to fulfill constantly increasing requirements. Sequences of georeferenced images that cannot be shot at once are merged with ideally no geometrical distortion to allow for 3D reconstruction and orthophotography generation. If newer robust mosaicing algorithms are being developed to withstand UAV tighter real-time constraints, very little attention has been given to objectively assess their capacity to coherently combine different image geometries. Changes in FOV and illumination, oblique scenes and dynamic sequences featuring movement and object occlusion are not yet fully handled by state-of-the-art algorithms. Despite the large panel of existing applications featuring different quality constraints, our work focuses on the geomatics context, where the main requirement is the respect of geometrical proportions among images. Geometrically coherent mosaics and 3D reconstructions can only result from fully static, high-altitude orthogonal views. GCPs or well known geographical landmarks are employed with RTK-GPS for scene georeferencing. The overall fidelity is computed as the global variance of the distances between SGPs. However, very few ways seem to exist to measure the content coherence of large geographical scenes, interiors or unreferenced scenes. Distances are mostly expressed in a local coordinate system and GCPs are often unavailable. The main contribution of this paper consists in the definition of a formal metric for measuring local coordinate geometrical fidelity of mosaics issued of UAV image sequences, in real operating conditions. A Mosaicing Fidelity Assessment (MSF) index is therefore computed for every couple of consecutive images of a sequence. The metric generates an index based on the distances of SURF feature points extracted in the images and compares them to estimate geometrical changes transferred to the mosaic. The solution can detect perspective inaccuracies caused by residual registration errors. It can fulfill the requirements of most of imaging and geomatics applications and can be executed as nearly real-time due to its low computational complexity.

Stable Length in Inelastic Design Considering Ductility Requirement

The region close to plastic hinge is vulnerable to lateral instability due to the formation of the mechanism. A stable length between lateral restraint at the plastic hinge and adjacent lateral restraint plays a significant role in preventing lateral instability and until after the required hinge rotation has taken place. This phenomenon is studied for beams under uniform moment loading by carrying out an extensive parametric study on a mixed set of I-shaped hybrid and homogeneous plate girders using nonlinear finite element analysis. Geometric dimensions and steel grade of plate girder elements are varied to account for their effect on member slenderness. Effect of overall slenderness is included by varying lateral bracing configuration. Attention is given to the interaction between local and lateral buckling and their influence on inelastic rotation. Regression analysis of the database is carried out to arrive at a prediction equation for stable length to achieve the required rotation capacity. The equation is validated by applying it to thirty-nine selected experiments conducted by others and comparing results with the results of available prediction equations. Statistical analysis of the validation study shows that the proposed equation provides more refined results as compared to available equations. It is observed that use of the new prediction equation when used along with rotation capacity prediction equation suggested by authors in the previous study proves to be a rational solution as available stable length equations that are based only on geometric proportions of sections. At the end of the paper, a flowchart and demonstration examples for use of these equations are presented.

Serendipity? The Inspiration of the Medieval Masons in Cathedral Floor-plan Design

Cathedrals as very large religious buildings spread worldwide, but in medieval times were peculiar to Europe. It seems that the design of cathedrals often had various symbolic implications. Usually, cathedral floor plans are considered as the first step in the whole construction process, and are related to other parts of the cathedral’s construction. Previous literature suggested that complicated geometrical and numerical proportions were found in the measurements. The masons, including the master masons, were not likely to have had a sophisticated understanding of mathematical and geometrical systems. This paper suggests some simple geometric methods which may used in the design of the whole cathedral floor plan, based on the square and its derivative constructions, including golden-section rectangles, √2 and other root rectangles and sacred cut squares. It is argued that simple methods were adopted by the masons in the planning and design process associated with cathedrals in medieval times. Keywords: Cathedral, Proportion, Floor plans, Medieval masons

The Two Supreme Principles of Plato’s Cosmos—the One and the Indefinite Dyad—the Division of a Straight Line into Extreme and Mean Ratio, and Pingala’s Mātrāmeru

The objective of this paper is to propose a mathematical interpretation of the continuous geometric proportion (Timaeus, 32a) with which Plato accomplishes the goal to unify, harmonically and symmetrically, the Two Opposite Elements of Timaeus Cosmos—Fire and Earth—through the Mean Ratio. As we know, from the algebraic point of view, it is possible to compose a continuous geometric proportion just starting from two different quantities a (Fire) and b (Earth); their sum would be the third term, so that we would obtain the continuous geometric proportion par excellence, which carries out the agreement of opposites most perfectly: (a + b)/a = a/b. This equal proportion, applied to linear geometry, corresponds to what Euclid called the Division into Extreme and Mean Ratio (DEMR) or The Golden Proportion. In fact, according to my mathematical interpretation, in the Timaeus 32b and in the Epinomis 991 a–b, Plato uses Pingala’s Mātrāmeru or The First Analogy of the Double to mould the body of the Cosmos as a whole, to the point of identifying the two supreme principles of the Cosmos—the One (1) and the Indefinite Dyad (Φ and1/Φ)—with the DEMR. In effect, Fire and Earth are joined not by a single Mean Ratio but by two (namely, Air and Water). Moreover, using the Platonic approach to analyse the geometric properties of the shape of the Cosmos as a whole, I think that Timaeus constructed the 12 pentagonal faces of Dodecahedron by means of elementary Golden Triangles (a/b = Φ) and the Mātrāmeru sequence. And, this would prove that my mathematical interpretation of the platonic texts is at least plausible.

Geometric Proportions in Measured Plans of the Pantheon of Rome

The Pantheon in Rome has been depicted in countless paintings and measured drawings. This paper considers how the building and its subsequent representations express meaning through elementary geometric symbols, patterns, and proportions. The author observes notable discrepancies between a sampling of measured plans from Sebastiano Serlio’s woodcut engravings in the Renaissance to current laser campaigns. She analyzes the different drawings for underlying geometric patterns. A pattern of rotated squares, in root-two proportion, appears consistently in the horizontal plan of each measured set and complements Mark Wilson Jones’s proposed scheme of a conjoined sphere and cube. This comparative method of analysis offers students and scholars of descriptive geometry a useful tool for interpretation.

Soft and Stiff Simplex Tensegrity Lattices as Extreme Smart Metamaterials.

The present paper is dedicated to an evaluation of novel cellular metamaterials based on a tensegrity pattern. The materials are constructed from supercells, each of which consists of a number of simplex modules with different geometrical proportions. Mechanical properties of the metamaterial can be controlled by adjusting the level of self-equilibrated forces or by changing the properties of structural members. A continuum model based on the equivalence of strain energy of the 3D theory of elasticity with a discrete formulation is used to identify the qualitative properties of the considered metamaterials. The model allows the inclusion of nonlinearities related to the equations of equilibrium in actual configuration of the structure with self-equilibrated set of normal forces typical for tensegrities. The lattices are recognised as extreme metamaterials according to the eigensolution of the equivalent elasticity matrices of the continuum model. The six representative deformation modes are defined and discussed: stiff, soft and medium extensional modes and high (double) as well as low shear modes. The lattices are identified as unimode or nearly bimode according to the classification of extreme materials.