scholarly journals Graphical Representation of Separatrices of Attraction Basins in Two and Three-Dimensional Dynamical Systems

2017 ◽  
Vol 14 (01) ◽  
pp. 1750008 ◽  
Author(s):  
Roberto Cavoretto ◽  
Alessandra De Rossi ◽  
Emma Perracchione ◽  
Ezio Venturino
Keyword(s):  
Dynamical Systems ◽  
Approximation Scheme ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Partition Of Unity ◽  
Basins Of Attraction ◽  
Reconstruction Scheme ◽  
Stable Equilibria ◽  
Attraction Basins ◽  
Three Dimensional Models

In this paper we consider the problem of reconstructing separatrices in dynamical systems. In particular, here we aim at partitioning the domain approximating the boundaries of the basins of attraction of different stable equilibria. We start from the 2D case sketched in Cavoretto et al. [2011] and the approximation scheme presented in [Cavoretto et al. (2011); Cavoretto et al. (2015)], and then we extend the reconstruction scheme of separatrices in the cases of three-dimensional models with two and three stable equilibria. For this purpose we construct computational algorithms and procedures for the detection and the refinement of points located on the separatrix manifolds that partition the phase space. The use of the so-called Radial Basis Function (RBF) Partition of Unity (PU) method is used to reconstruct the separatrices.

scholarly journals Three-dimensional interpolation of soil data: fertility and pedomorphological features in southern Brazil

2014 ◽  
Vol 38 (4) ◽  
pp. 1091-1100
Author(s):  
Tales de Campos Piedade ◽  
Vander de Freitas Melo ◽  
Luiz Cláudio de Paula Souza ◽  
Jeferson Dieckow
Keyword(s):  
Soil Texture ◽  
Graphical Representation ◽  
Plant Root ◽  
Three Dimensional ◽  
Three Dimension ◽  
Southern Brazil ◽  
Soil Matrix ◽  
Continuous Space ◽  
Continuous Surface ◽  
Three Dimensional Models

The graphical representation of spatial soil properties in a digital environment is complex because it requires a conversion of data collected in a discrete form onto a continuous surface. The objective of this study was to apply three-dimension techniques of interpolation and visualization on soil texture and fertility properties and establish relationships with pedogenetic factors and processes in a slope area. The GRASS Geographic Information System was used to generate three-dimensional models and ParaView software to visualize soil volumes. Samples of the A, AB, BA, and B horizons were collected in a regular 122-point grid in an area of 13 ha, in Pinhais, PR, in southern Brazil. Geoprocessing and graphic computing techniques were effective in identifying and delimiting soil volumes of distinct ranges of fertility properties confined within the soil matrix. Both three-dimensional interpolation and the visualization tool facilitated interpretation in a continuous space (volumes) of the cause-effect relationships between soil texture and fertility properties and pedological factors and processes, such as higher clay contents following the drainage lines of the area. The flattest part with more weathered soils (Oxisols) had the highest pH values and lower Al3+ concentrations. These techniques of data interpolation and visualization have great potential for use in diverse areas of soil science, such as identification of soil volumes occurring side-by-side but that exhibit different physical, chemical, and mineralogical conditions for plant root growth, and monitoring of plumes of organic and inorganic pollutants in soils and sediments, among other applications. The methodological details for interpolation and a three-dimensional view of soil data are presented here.

scholarly journals Perpetual Points: New Tool for Localization of Coexisting Attractors in Dynamical Systems

2017 ◽  
Vol 27 (04) ◽  
pp. 1750063 ◽  
Author(s):  
Dawid Dudkowski ◽  
Awadhesh Prasad ◽  
Tomasz Kapitaniak
Keyword(s):  
Dynamical Systems ◽  
Critical Points ◽  
Basins Of Attraction ◽  
Physical Significance ◽  
Stationary Points ◽  
Coexisting Attractors ◽  
Potential Applicability ◽  
Stable Equilibria ◽  
Perpetual Points ◽  
Damped Oscillator

Perpetual points (PPs) are special critical points for which the magnitude of acceleration describing the dynamics drops to zero, while the motion is still possible (stationary points are excluded), e.g. considering the motion of the particle in the potential field, at perpetual point, it has zero acceleration and nonzero velocity. We show that using PPs we can trace all the stable fixed points in the system, and that the structure of trajectories leading from former points to stable equilibria may be similar to orbits obtained from unstable stationary points. Moreover, we argue that the concept of perpetual points may be useful in tracing unexpected attractors (hidden or rare attractors with small basins of attraction). We show potential applicability of this approach by analyzing several representative systems of physical significance, including the damped oscillator, pendula, and the Henon map. We suggest that perpetual points may be a useful tool for localizing coexisting attractors in dynamical systems.

scholarly journals Pynamical: Model and visualize discrete nonlinear dynamical systems, chaos, and fractals

2018 ◽  
Author(s):  
Geoff Boeing
Keyword(s):  
Dynamical Systems ◽  
Phase Diagrams ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Models ◽  
Logistic Map ◽  
Three Dimensional ◽  
Basins Of Attraction ◽  
Nonlinear Dynamical ◽  
One Dimensional ◽  
One Dimensional Maps

Pynamical is an educational Python package for introducing the modeling, simulation, and visualization of discrete nonlinear dynamical systems and chaos, focusing on one-dimensional maps (such as the logistic map and the cubic map). Pynamical facilitates defining discrete one-dimensional nonlinear models as Python functions with just-in-time compilation for fast simulation. It comes packaged with the logistic map, the Singer map, and the cubic map predefined. The models may be run with a range of parameter values over a set of time steps, and the resulting numerical output is returned as a pandas DataFrame. Pynamical can then visualize this output in various ways, including with bifurcation diagrams, two-dimensional phase diagrams, three-dimensional phase diagrams, and cobweb plots. These visualizations enable simple qualitative assessments of system behavior including phase transitions, bifurcation points, attractors and limit cycles, basins of attraction, and fractals.

Plastic replicas as three-dimensional models of pulps

1975 ◽  
Vol 39 (8) ◽  
pp. 544-546
Author(s):  
HL Wakkerman ◽  
GS The ◽  
AJ Spanauf
Keyword(s):  
Three Dimensional ◽  
Dimensional Models ◽  
Three Dimensional Models

Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire4

2009 ◽  
Vol 37 (2) ◽  
pp. 62-102 ◽  
Author(s):  
C. Lecomte ◽  
W. R. Graham ◽  
D. J. O’Boy
Keyword(s):  
Internal Pressure ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Prediction Method ◽  
Analytical Models ◽  
Beam Model ◽  
Impedance Boundary ◽  
Bending Waves ◽  
Tire Rotation ◽  
Three Dimensional Models

Abstract An integrated model is under development which will be able to predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. Here, the tire belt model used as part of this prediction method is first briefly presented and discussed, and it is then compared to other models available in the literature. This component will be linked to the tread blocks through normal and tangential forces and to the sidewalls through impedance boundary conditions. The tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and prestresses included. The associated equations of motion are derived by a variational approach and are investigated for both unforced and forced motions. The model supports extensional and bending waves, which are believed to be the important features to correctly predict the hub forces in the midfrequency (50–500 Hz) range of interest. The predicted waves and forced responses of a benchmark structure are compared to the predictions of several alternative analytical models: two three dimensional models that can support multiple isotropic layers, one of these models include curvature and the other one is flat; a one-dimensional beam model which does not consider axial variations; and several shell models. Finally, the effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed.

In Silico Identification and Molecular Characterization of Extracellular Cathepsin L Proteases from Giardia duodenalis

2020 ◽  
Vol 17 (4) ◽  
pp. 342-351
Author(s):  
Sergio A. Durán-Pérez ◽  
José G. Rendón-Maldonado ◽  
Lucio de Jesús Hernandez-Diaz ◽  
Annete I. Apodaca-Medina ◽  
Maribel Jiménez-Edeza ◽  
...  
Keyword(s):  
In Silico ◽  
Cathepsin L ◽  
Three Dimensional ◽  
Giardia Duodenalis ◽  
Evolutionary Genetics ◽  
Extracellular Proteins ◽  
In Silico Identification ◽  
Dimensional Models ◽  
Three Dimensional Models

Background: The protozoan Giardia duodenalis, which causes giardiasis, is an intestinal parasite that commonly affects humans, mainly pre-school children. Although there are asymptomatic cases, the main clinical features are chronic and acute diarrhea, nausea, abdominal pain, and malabsorption syndrome. Little is currently known about the virulence of the parasite, but some cases of chronic gastrointestinal alterations post-infection have been reported even when the infection was asymptomatic, suggesting that the cathepsin L proteases of the parasite may be involved in the damage at the level of the gastrointestinal mucosa. Objective: The aim of this study was the in silico identification and characterization of extracellular cathepsin L proteases in the proteome of G. duodenalis. Methods: The NP_001903 sequence of cathepsin L protease from Homo sapienswas searched against the Giardia duodenalisproteome. The subcellular localization of Giardia duodenaliscathepsin L proteases was performed in the DeepLoc-1.0 server. The construction of a phylogenetic tree of the extracellular proteins was carried out using the Molecular Evolutionary Genetics Analysis software (MEGA X). The Robetta server was used for the construction of the three-dimensional models. The search for possible inhibitors of the extracellular cathepsin L proteases of Giardia duodenaliswas performed by entering the three-dimensional structures in the FINDSITEcomb drug discovery tool. Results: Based on the amino acid sequence of cathepsin L from Homo sapiens, 8 protein sequences were identified that have in their modular structure the Pept_C1A domain characteristic of cathepsins and two of these proteins (XP_001704423 and XP_001704424) are located extracellularly. Threedimensional models were designed for both extracellular proteins and several inhibitory ligands with a score greater than 0.9 were identified. In vitrostudies are required to corroborate if these two extracellular proteins play a role in the virulence of Giardia duodenalisand to discover ligands that may be useful as therapeutic targets that interfere in the mechanism of pathogenesis generated by the parasite. Conclusion: In silicoanalysis identified two proteins in the Giardia duodenalisprotein repertoire whose characteristics allowed them to be classified as cathepsin L proteases, which may be secreted into the extracellular medium to act as virulence factors. Three-dimensional models of both proteins allowed the identification of inhibitory ligands with a high score. The results suggest that administration of those compounds might be used to block the endopeptidase activity of the extracellular cathepsin L proteases, interfering with the mechanisms of pathogenesis of the protozoan parasite Giardia duodenalis.

Handheld Laser Scanner Research

2019 ◽  
Vol 952 (10) ◽  
pp. 47-54
Author(s):  
A.V. Komissarov ◽  
A.V. Remizov ◽  
M.M. Shlyakhova ◽  
K.K. Yambaev
Keyword(s):  
Point Cloud ◽  
Three Dimensional ◽  
Laser Scanner ◽  
Test Site ◽  
Optical Systems ◽  
Advantages And Disadvantages ◽  
Site Survey ◽  
Laser Scanners ◽  
Three Dimensional Models ◽  
The Stability

The authors consider hand-held laser scanners, as a new photogrammetric tool for obtaining three-dimensional models of objects. The principle of their work and the newest optical systems based on various sensors measuring the depth of space are described in detail. The method of simultaneous navigation and mapping (SLAM) used for combining single scans into point cloud is outlined. The formulated tasks and methods for performing studies of the DotProduct (USA) hand-held laser scanner DPI?8X based on a test site survey are presented. The accuracy requirements for determining the coordinates of polygon points are given. The essence of the performed experimental research of the DPI?8X scanner is described, including scanning of a test object at various scanner distances, shooting a test polygon from various scanner positions and building point cloud, repeatedly shooting the same area of the polygon to check the stability of the scanner. The data on the assessment of accuracy and analysis of research results are given. Fields of applying hand-held laser scanners, their advantages and disadvantages are identified.

scholarly journals Comparative Analysis of Digital Models of Objects of Cultural Heritage Obtained by the “3D SLS” and “SfM” Methods

2021 ◽  
Vol 11 (12) ◽  
pp. 5321
Author(s):  
Marcin Barszcz ◽  
Jerzy Montusiewicz ◽  
Magdalena Paśnikowska-Łukaszuk ◽  
Anna Sałamacha
Keyword(s):  
Cultural Heritage ◽  
Low Cost ◽  
Three Dimensional ◽  
3D Models ◽  
Silk Road ◽  
Digital Models ◽  
Global Pandemic ◽  
University Of Technology ◽  
Three Dimensional Models ◽  
3D Digitisation

In the era of the global pandemic caused by the COVID-19 virus, 3D digitisation of selected museum artefacts is becoming more and more frequent practice, but the vast majority is performed by specialised teams. The paper presents the results of comparative studies of 3D digital models of the same museum artefacts from the Silk Road area generated by two completely different technologies: Structure from Motion (SfM)—a method belonging to the so-called low-cost technologies—and by Structured-light 3D Scanning (3D SLS). Moreover, procedural differences in data acquisition and their processing to generate three-dimensional models are presented. Models built using a point cloud were created from data collected in the Afrasiyab museum in Samarkand (Uzbekistan) during “The 1st Scientific Expedition of the Lublin University of Technology to Central Asia” in 2017. Photos for creating 3D models in SfM technology were taken during a virtual expedition carried out under the “3D Digital Silk Road” program in 2021. The obtained results show that the quality of the 3D models generated with SfM differs from the models from the technology (3D SLS), but they may be placed in the galleries of the vitrual museum. The obtained models from SfM do not have information about their size, which means that they are not fully suitable for archiving purposes of cultural heritage, unlike the models from SLS.

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