Geometric Similarity Research Articles

Similarity Law between Centrifuge Scale Test and Prototype Underwater Explosion

Shock wave and bubble pulsation caused by underwater explosion destroy the hydraulic structure. However, the realization of the underwater explosion prototype test is restricted by many factors, such as the site environment. Furthermore, the repeatability of the test scheme is not strong. The centrifuge scale test provides a new way of studying the damage degree of the structure under the action of underwater explosion. The similarity relationship refers to the bridge between the scaled model and the prototype, which cannot achieve complete similarity in practice. The centrifuge-scaled model test is performed by increasing the acceleration of a certain multiple. Meanwhile, the model reduces the corresponding ratio in the geometric layout to achieve the geometric similarity with the prototype test. Therefore, the applicability of the centrifuge scaling method in the study of the dynamic response of the structure in underwater explosion needs to be explored further. In this work, the underwater explosion scaling test numerical model for 1 g RDX (equivalent to 1.62 g TNT) charge under different centrifugal acceleration conditions is established, and the calculation results of underwater pressure and dynamic response of the steel plate are compared with the centrifuge test results. A prototype model is established to study the similarity relationship between the centrifuge scale test and the prototype model when the steel plate structure is in the stage of small deformation and linear elasticity. The application of the similarity ratio in the scale test of underwater explosion the centrifuge is discussed. The application of the centrifuge in the study of the failure response of the hydraulic structure in underwater explosion is expanded by establishing the model and comparing with the experimental results.

Flight system morphology and minimum flight temperature in North American cicadas (Insecta: Hemiptera: Cicadidae).

Thermal responses in cicadas have been studied for many years. The minimum flight temperature (MFT) does not show the same relationship to habitat and behavior as other thermal responses. We measured live mass, wing length, wingspan, wing area and wing loading in an attempt to correlate these morphological parameters to the MFT. We analyzed both intraspecific (in Magicicada cassinii (Fisher, 1852)) and interspecific relationships of the wing morphology and the ability of the cicadas to fly in a large number of North American cicada taxa (n=119). A total of 109 species and 10 subspecies from 17 genera, six tribes, and three subfamilies including all major North American habitats were studied. Analyses show that wing morphology (wing length, wingspan, wing area and wing loading) scales to body size as predicted by geometric similarity (all P<0.0001) for all species and wing area and wing loading (both P<0.0001) in M. cassinii. Mass (P=0.0105), wing length (P=0.0006), wingspan (P=0.0006), wing area (P=0.0055), and wing loading (P=0.0455) all demonstrate a significant correlation to MFT between species, as would be predicted by aerodynamic theory, but not within species. However, the low correlation coefficients suggest the flight system has minimal influence on the MFT of cicadas. Specific physiological adaptations appear to be responsible for the between species variability in MFT rather than being the result of modifications to the flight system morphology.

Constrained mutual convex cone method for image set based recognition

In this paper, we propose convex cone-based frameworks for image-set classification. Image-set classification aims to classify a set of images, usually obtained from video frames or multi-view cameras, into a target object. To accurately and stably classify a set, it is essential to accurately represent structural information of the set. There are various image features, such as histogram-based features and convolutional neural network features. We should note that most of them have non-negativity and thus can be effectively represented by a convex cone. This leads us to introduce the convex cone representation to image-set classification. To establish a convex cone-based framework, we mathematically define multiple angles between two convex cones, and then use the angles to define the geometric similarity between them. Moreover, to enhance the framework, we introduce two discriminant spaces. We first propose a discriminant space that maximizes gaps between cones and minimizes the within-class variance. We then extend it to a weighted discriminant space by introducing weights on the gaps to deal with complicated data distribution. In addition, to reduce the computational cost of the proposed methods, we develop a novel strategy for fast implementation. The effectiveness of the proposed methods is demonstrated experimentally by using five databases.

Unsupervised learning for cuboid shape abstraction via joint segmentation from point clouds

Representing complex 3D objects as simple geometric primitives, known as shape abstraction, is important for geometric modeling, structural analysis, and shape synthesis. In this paper, we propose an unsupervised shape abstraction method to map a point cloud into a compact cuboid representation. We jointly predict cuboid allocation as part segmentation and cuboid shapes and enforce the consistency between the segmentation and shape abstraction for self-learning. For the cuboid abstraction task, we transform the input point cloud into a set of parametric cuboids using a variational auto-encoder network. The segmentation network allocates each point into a cuboid considering the point-cuboid affinity. Without manual annotations of parts in point clouds, we design four novel losses to jointly supervise the two branches in terms of geometric similarity and cuboid compactness. We evaluate our method on multiple shape collections and demonstrate its superiority over existing shape abstraction methods. Moreover, based on our network architecture and learned representations, our approach supports various applications including structured shape generation, shape interpolation, and structural shape clustering.

3D Printing Experimental Validation of the Finite Element Analysis of the Maxillofacial Model.

Contacts used in finite element (FE) models were considered as the best simulation for interactions in the temporomandibular joint (TMJ). However, the precision of simulations should be validated through experiments. Three-dimensional (3D) printing models with the high geometric and loading similarities of the individuals were used in the validation. This study aimed to validate the FE models of the TMJ using 3D printing models. Five asymptomatic subjects were recruited in this study. 3D models of mandible, disc, and maxilla were reconstructed according to cone-beam CT (CBCT) image data. PLA was chosen for 3D printing models from bottom to top. Five pressure forces corresponding to the central occlusion were applied to the 3D printing models. Ten strain rosettes were distributed on the mandible to record the horizontal and vertical strains. Contact was used in the FE models with the same geometries, material properties, loadings, and boundary conditions as 3D printing models to simulate the interaction of the disc-condyle, disc-temporal bone, and upper-lower dentition. The differences of the simulated and experimental results for each sample were less than 5% (maximum 4.92%) under all five loadings. In conclusion, it was accurate to use contact to simulate the interactions in TMJs and upper-lower dentition.

Competing Sorption of Se(IV) and Se(VI) on Schwertmannite

Schwertmannite (SHM) is a naturally occurring mineral that has been shown to effectively scavenge oxyanions from contaminated water. In this study, Fourier-transform infrared spectroscopy and X-ray absorption spectroscopy techniques in combination with wet-chemical techniques were used to study the competitive sorption of Se(IV) and Se(VI) at pH 3. The experiments were conducted with three types of schwertmannite obtained from oxidative synthesis, biogenic synthesis and high-pressure compaction at different initial Se concentrations and mixing ratios for 48 h and 56 days, respectively. A threshold value for the uptake mechanisms was identified, which reflects the amount of easily exchangeable sulphate (~0.5 mmol/g). At adsorbate concentrations below this threshold, an inner-sphere corner-sharing bidentate binuclear complex forms upon exchange with sulphate. At higher concentrations, both oxyanions become bound to SHM through co-occurrence of mainly inner-sphere and partly outer-sphere corner-sharing bidentate binuclear complexes with Fe(III) containing surface sites. Single species experiments clearly indicate a higher affinity of SHM for Se(IV). However, in mixed species experiments, competitive sorption occurs with equal or even preferential uptake of Se(VI) at concentrations much lower than the threshold value, presumably due to geometrical similarity between selenate and sulphate, and increasing preference for Se(IV) at high Se concentrations.

An overview of planar flow casting of thin metallic glasses and its relation to slot coating of liquid films

Planar flow casting (PFC) is a method that can be used to make thin, long, and wide metallic alloy foils by extruding molten liquid through a nozzle slot and immediately quenching on a moving roller. The quenching rates are high enough that amorphous metallic glasses may be formed that have many desirable properties for a wide variety of applications. This paper reviews how PFC processes were developed, examines the typical operability range of PFC, and reviews the defects that commonly form. The geometrical similarities between PFC and slot coating process are apparent, and this paper highlights differences between the operability ranges of both processes.

Reconciling similarity across models of continuous selections.

Recently developed models of decision-making have provided accounts of the cognitive processes underlying choice on tasks where responses can fall along a continuum, such as identifying the color or orientation of a stimulus. Even though nearly all of these models seek to extend diffusion decision processes to a continuum of response options, they vary in terms of complexity, tractability, and their ability to predict patterns of data such as multimodal distributions of responses. We suggest that these differences are almost entirely due to differences in how these models account for the similarity among response options. In this theoretical note, we reconcile these differences by characterizing the existing models under a common framework, where the assumptions about psychological representations of similarity, and their implications for behavioral data (e.g., multimodal responses), are made explicit. Furthermore, we implement a simulation-based approach to computing model likelihoods that allows for greater freedom in constructing and implementing continuous response models. The resulting geometric similarity representation (GSR) can supplement approaches like the circular/spherical diffusion models by allowing them to generate multimodal distributions of responses from a single drift, or simplify models like the spatially continuous diffusion model (SCDM) by condensing their representations of similarity and allowing them to generate simulations more efficiently. To illustrate its utility, we apply this approach to multimodal distributions responses, two-dimensional responses (such as locations on a computer screen), and continuous response options with nontrivial, nonlinear similarity relations between response options. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Analysis of granulation systems using idealistic modeling-principle of similarity for scaling up sustainable production lines

Pharmaceutical industry produces safe, effective, affordable, and quality medicines used to guarantee a healthy life and promote the well-being of the entire population in a sustainable way. Currently, the solid dosage form is the preferred formulation for human use. However, the large scale production of these medicines it requires well-tested formulation and appropriate equipment because any substantial variation in the development of the pharmaceutical product can alter the final quality of the product, causing the entire manufactured batch to be discarded. For this reason, this research aimed to analyze and understand the behavior of the variables involved in the wet granulation process while scaling from a laboratory system and a production line unit to transfer the results obtained to a large-scale production unit of solid dosage forms to meet the health needs of the world population. This study was carried out under a mixed approach applying quantitative and qualitative technologies to explain and predict the behavior of the involved variables while scaling from a laboratory system to a production line unit. It was found that there are some regularities and causal relationships between geometric, kinematic, and dynamic similarities.

Physical modeling of a skip pneumatic winder

Introduction. The analytical phase of research on mine skip pneumatic winders has been passed, so the theoretical provisions have to be tested by the methods of physical modeling which is aimed at confirming the mathematical model adequacy and assessing the effectiveness of different types of sealing devices. Research methods. Physical modeling phases have been formulated, including modeling by geometric and aerodynamic similarity criteria, constructing aerodynamic characteristics of the installation, carrying out experiments with non-contacting and combined seals, and calculating the values of the installation volumetric efficiency based on the experimental data obtained. Research results. The lifting time of the skip model with different masses of material and seal types has been determined. The installation working points in the “flow rate–pressure” coordinate system have been identified, and the values of the volumetric efficiency have been calculated for each working point. Analysis of the results. A satisfactory convergence of calculated and experimental parameters of the physical model has been established. The model's volumetric efficiency has reached a technically acceptable level. The expected value of the experimental model’s volumetric efficiency has been calculated according to the similarity constants. Conclusions. The model's study revealed the convergence of the experimentally obtained volumetric efficiency of the model with its calculated values and proved the applicability of the mathematical model to experimental sample parameters calculation. The volumetric efficiency of the installation with both non-contacting and combined seals is quite high allowing to recommend the studied sealing devices for mine pneumatic winders.

Geometrical Similarity Error Function-Innovative Adaptive Algorithm methodology in path generation synthesis of the four-bar mechanism using metaheuristic algorithms

This paper presents a novel methodology for path generation synthesis of the four-bar mechanism. A new objective function for the path generation synthesis problem, namely, the Geometrical Similarity Error Function (GSEF), is introduced. Indeed, GSEF assesses the similarity between generated and desired paths, and its number of design variables is less than those in the other synthesis methods. Then, using an Innovative Adaptive Algorithm (IAA), some operators are utilized for matching two similar paths. GSEF-IAA methodology has some significant advantages over the reported synthesis methods. The method is fast, takes much less CPU time, and saves a large amount of computer memory. Four path generation problems are solved using GSEF-IAA, and the results are compared with those of previous methods using some well-known optimization algorithms to demonstrate the efficiency of GSEF-IAA methodology.

The reflection of a blast wave by a very intense explosion.

We demonstrate that the geometric similarity of Taylor’s blast wave persists beyond reflection from an ideal surface. Upon impacting the surface, the spherical symmetry of the blast wave is lost but its cylindrical symmetry endures. As the flow acquires dependence on a second spatial dimension, an analytic solution of the Euler equations becomes elusive. However, the preservation of axisymmetry, geometric similarity and planar symmetry in the presence of a mirror-like surface causes all flow solutions to collapse when scaled by the height of burst (HOB) and the shock arrival time at the surface. The scaled blast volume for any yield, HOB and ambient air density follows a single universal trajectory for all scaled time, both before and after reflection.

Spatial Distributions of At‐Many‐Stations Hydraulic Geometry for Mountain Rivers Originated From the Qinghai‐Tibet Plateau

AbstractAt‐many‐stations hydraulic geometry (AMHG) has provided a novel way to understand river network development, simulate water flow, and retrieve river discharge in data‐scared regions. Based on in‐situ measurements of six major rivers originating from the Qinghai‐Tibet Plateau (QTP), this study verifies the existence of AMHG relations along the rivers and explores AMHG relations for cross sections that are not located in the same river reach. The mainstreams and tributaries of the studied rivers in the southern and the eastern portions of the QTP have satisfactory AMHG relation strengths with R2 &gt; 0.9 for over 60% of the relations. For cross sections located in the same stream order or within a certain range of contributing area (CA), approximately 60% (9/15) and 53% (8/15) of the AMHG relations have an R2 &gt; 0.6. AMHG strength increases with increasing stream order and CA; this finding reflects the increasing coherence and maturity of the river networks associated with the geomorphic shaping power of increased discharge. Width‐AMHG intercepts are larger than those of depth‐AMHG and velocity‐AMHG for all stream orders and CAs. Most of the congruent hydraulics generated from cross sections located in middle‐scale rivers (orders 7–8) are within the observed range. Congruent hydraulics generally increase with an increase in in‐situ measured hydraulics when the stream order or the CA increases. The AMHG relations existing among cross sections that are not located in the same reach, which is named as cross channel AMHG, indicate linear variability of cross‐sectional geometric and hydraulic similarities in the same stream order or within a certain CA range. The results break the watershed divide boundary control on AMHG and have the potential to provide background knowledge for discharge estimation in mountain rivers located in the QTP.

Использование теории подобия при проектировании турбин газотурбинных двигателей

At present, in the promising development of gas turbine engines compared to at least the fourth generation products, there have been significant changes in the approaches to the design of engine. First of all, it is an increase in maximum values of temperature, gas pressure and circumferential flow speeds, an increase in power of the turbine stage, as well as improvement of the turbine manufacturing technology. All these factors lead to the fact that when designing the flow parts of the gas turbine, it is necessary at the fixed design flow rate of the working medium in the engine, i.e. at the fixed diameters, lengths of the nozzle and rotor blades forming the outline of the inter-blade channels, to increase the blade chords with the corresponding reduction of the number of blades in the row. The increase in turbine stage power associated with the increase in temperature, pressure (density), and circumferential velocity increases the bending stresses leading to the need to increase chords at a fixed blade length. Significant reduction of number of blades in stages, simplifies technology of blades manufacturing. A substantial increase in the maximum gas temperature, in the perspective of more than 2000 K, also leads to the need to increase the blade chords, due to the need to place cooling cavities in the blades. As a result, contradictions arise with the use of similarity theory in the design of stages of turbines of different purpose, as some of the main requirements of similarity are violated — geometric similarity of blade channels of the flow part and then the use of the generally accepted number Re by the chord of blades loses meaning. Therefore, it is necessary to carry out detailed investigations of all flow parameters in four stages of turbines with detection of influence of change of rotor blade chords at equal length of blades. And justify the effect of change of rotor blade chords on physical processes in flow parts of turbines in engines of various purpose.

The impact of image and performance enhancing drugs on bi-ventricular structure and function in strength-trained athletes and the association to fat-free mass

Abstract Funding Acknowledgements Type of funding sources: Private grant(s) and/or Sponsorship. Main funding source(s): Canadian Institute of Health Research Michael Smith Foreign Study Supplement Background Image and performance enhancing drugs (IPED) cause cardiac enlargement and dysfunction. Previous work has not assessed impact of user status (current [CU] vs. past [PU]) or allometric scaling cardiac dimensions for individual differences in fat-free mass (FFM). Purpose To investigate CU and PU of IPED and allometric scaling on LV and RV remodeling in strength-trained athletes. Methods Thirty-four (29 ± 6 years; 82% male) strength-trained athletes were recruited. Fourteen were CU, 9 PU and 11 non-users (NU) of IPEDs. Participants underwent bioelectric impedance body composition analysis, IPED and training questionnaire and 2D echocardiography with strain imaging. All structural data was allometrically scaled to FFM according to the laws of geometric similarity. Results CU and PU had significantly higher FFM compared to NU (82.4 ± 10.1 kg vs. 72.0 ± 6.3 kg vs. 58.2 ± 14.0 kg). Absolute values of all RV and LV size were larger between CU and NU. LV mean wall thickness (MWT) was larger in CU compared to PU but there were no differences between PU and NU. Allometric scaling eliminated all differences with exception of LV mass and LVMWT. LVEF was significantly lower in CU and PU compared to NU (55 ± 3 vs. 57 ± 4 vs. 61 ± 4) whilst LV GLS was lower in CU compared to PU and NU and LV GCS was lower in CU compared to NU but not PU. There was no significant difference between groups for RV functional indices. Conclusion Strength-trained athletes currently using IPEDs have bi-ventricular enlargement as well as reduced LV function. Allometric scaling highlights that increased size is partially associated with a larger FFM, with exception of LVMWT which is independently increased through IPED use. PUs demonstrate reverse structural remodeling whilst functional differences partially remain. CU PU NU RVD1 (mm) 45 ± 5* 43 ± 6 37 ± 6 Scaled RVD1 (mm/kg^0.33) 10.5 ± 0.9 10.4 ± 1.5 9.7 ± 1.0 LVd (mm) 58 ± 7* 55 ± 4 50 ± 4 Scaled LVd (mm/kg^0.33) 13.4 ± 1.2 13.3 ± 0.7 13.1 ± 0.6 MWT (mm) 10 ± 1*” 8 ± 1 8 ± 1 Scaled MWT (mm/kg^0.33) 2.3 ± 0.2*” 2.0 ± 0.1 2.0 ± 0.2 LVEDV (ml) 169 ± 42* 135 ± 28 116 ± 28 Scaled LVEDV (ml/kg) 2.0 ± 0.4 1.9 ± 0.3 2.0 ± 0.2 LV Mass (g) 255 ± 85*” 179 ± 30 137 ± 40 LV mass index (g/kg) 3.1 ± 0.8* 2.5 ± 0.3 2.4 ± 0.4 * CU and NU “ CU and PU ^ PU and NU Abstract Figure. Myocardial strain imaging

Time Series Clustering with Topological and Geometric Mixed Distance

Time series clustering is an essential ingredient of unsupervised learning techniques. It provides an understanding of the intrinsic properties of data upon exploiting similarity measures. Traditional similarity-based methods usually consider local geometric properties of raw time series or the global topological properties of time series in the phase space. In order to overcome their limitations, we put forward a time series clustering framework, referred to as time series clustering with Topological-Geometric Mixed Distance (TGMD), which jointly considers local geometric features and global topological characteristics of time series data. More specifically, persistent homology is employed to extract topological features of time series and to compute topological similarities among persistence diagrams. The geometric properties of raw time series are captured by using shape-based similarity measures such as Euclidean distance and dynamic time warping. The effectiveness of the proposed TGMD method is assessed by extensive experiments on synthetic noisy biological and real time series data. The results reveal that the proposed mixed distance-based similarity measure can lead to promising results and that it performs better than standard time series analysis techniques that consider only topological or geometrical similarity.

Ionospheric spatial decorrelation assessment for GBAS daytime operations in Brazil

<h3>Abstract</h3> Extensive ionospheric studies were conducted to support the initial phase of system design approval for the existing SLS-4000 GBAS installed at Antonio Carlos Jobim International Airport (formerly Galeão International Airport) (GIG) in Rio de Janeiro, Brazil. This paper focuses on determining the broadcast value of the standard deviation of vertical ionospheric gradients (or 𝜎_vig) that is required to bound ionospheric spatial gradients in Brazil under nominal conditions during daytime hours. The time-step method is useful for gaining sufficient samples at distances less than the physical separation distance of ground stations and was utilized to estimate ionospheric spatial gradients. A new method called “geometric similarity” was developed to estimate ionospheric temporal gradients and evaluate the temporal effect added to the bounding 𝜎_vig values. As a result, a 𝜎_vig of 13 mm/km, including a temporal gradient contribution of approximately 2 mm/km, is conservative enough to bound ionospheric spatial decorrelation for daytime GBAS operations in Brazil.

Measurements methodologies for basic oxygen furnace cold modeling

Abstract In the initial stage, as well as today, physical models are frequently applied for basic oxygen furnace (BOF) process development. BOF cold model simulations have as fundament the geometric, kinematic, and dynamic similarity. The dimensionless numbers warranty the similarity. Based on the similarity criteria, it is possible to transpose the laboratory results for the industry. Develop the right methodology to get precise measurements of proposed experiments is a critical step in cold modeling. Due to different characteristics available regarding cold modeling, the work summarized in this paper offer a literature review centered in measurements methodologies for BOF cold modeling and describes the methodologies developed at Processes Simulation Laboratory (LaSiP) to measure and define mixing time, mass transfer, jet penetration, decarburization area, slopping and projection rate on cold models.

Robotic integration enables autonomous operation of laboratory scale stirred tank bioreactors with model‐driven process analysis

Given its geometric similarity to large-scale production plants and the excellent possibilities for precise process control and monitoring, the classic stirred tank bioreactor (STR) still represents the gold standard for bioprocess development at a laboratory scale. However, compared to microbioreactor technologies, bioreactors often suffer from a low degree of process automation and deriving key performance indicators (KPIs) such as specific rates or yields often requires manual sampling and sample processing. A widely used parallelized STR setup was automated by connecting it to a liquid handling system and controlling it with a custom-made process control system. This allowed for the setup of a flexible modular platform enabling autonomous operation of the bioreactors without any operator present. Multiple unit operations like automated inoculation, sampling, sample processing and analysis, and decision making, for example for automated induction of protein production were implemented to achieve such functionality. The data gained during application studies was used for fitting of bioprocess models to derive relevant KPIs being in good agreement with literature. By combining the capabilities of STRs with the flexibility of liquid handling systems, this platform technology can be applied to a multitude of different bioprocess development pipelines at laboratory scale.

Effects of geometric similarity ratio on the disturbance amplitude of shock-wave front in viscosity measurement

Geometric similarity ratio is one of the important factors that affects the disturbance amplitude of shock-wave front in viscosity measurement. In this paper, the Euler difference scheme of two-dimensional (2D) equations of viscous fluid mechanics is used to simulate the disturbance amplitude damping curves under different geometric similarity ratios, and the corresponding numerical solutions are shown. The samples of aluminum shocked to 80 GPa are taken as an example. The simulation results show that the initial conditions, material viscosity, wavelength, and sample geometric similarity ratio affect the evolution of the shock front sine wave disturbance. For flyer-impact flow field, the phase shift increases from 0 to a certain value with the viscosity coefficient for sample with wavelength [Formula: see text] mm and geometric similarity ratio [Formula: see text], 0.1. So, the geometric similarity method can be used to measure the viscosity of material. But it is found that the phase shift is sensitive to the geometric similarity ratio, which should be considered in Zaidel’s equation. So, some flyer-impact experiments will be carried out to determine the simulation results, and find the quantity relation of phase shift and viscosity of material in the future investigation.