Cartesian System Research Articles

Fundamentals of Soft Logic

In this paper, we develop a new theory termed Soft Logic. This theory addresses the need to combine real processes and cognitive ones in the same framework. At the same time, we develop a new concept of modeling and dealing with uncertainty: the uncertainty of time and space. We develop a language that can talk in two reference frames, and also suggest a way to combine them. This constitutes a fundamental new mathematics. In this paper, we present the theory from its foundation. In Soft Logic, we refer to situations of uncertainty occurring in the present. Ambiguity is created from the possible point of view of the observer of the phenomenon. Sometimes reality contains contradictory or opposite situations at the same time, which can be interpreted in different ways by the observer. Such is the case of the Necker cube or the Fechner color effect, in which a texture of black and white colors moving in a certain pattern creates a rainbow of colors. Another example is the Mobius strip, which from a local point of view seems to have two sides, but from a global point of view has only one. The mathematical solution for expressing uncertainty in Soft Logic is the blow-up of the number zero by distinguishing between multiples of this number. In this manner, we create a zero-axis and define a new type of number called Soft Numbers, which have the following form: [Formula: see text] The zero-axis expresses the inner world of the observer and is the component of a subjective interpretation and a certain type of uncertainty that occurs in the present. Soft Numbers are similar to complex numbers, but the specific mathematical definitions are different and therefore Soft Numbers are a different world. This paper presents five axioms of Soft Logic, which form a new system of coordinates that differs from the Cartesian system and Gauss’s complex plane. We define the algebra of Soft Numbers, show the connection to differential and integral calculus, expand analytical functions to soft functions, and describe continuous curves in the soft coordinate system. In conclusion, we suggest several avenues for theoretical and practical research.

2-D Semi-Analytical Magnetic Field Calculation for Flat Permanent-Magnet Linear Machines Using Exact Subdomain Technique

This article proposes an extended linear analytical solution based on the exact subdomain (SD) technique applied to any flat linear electromagnetic device for no-load and armature reaction current conditions. A slotted linear synchronous machine with surface-mounted permanent magnet (PM) having Halbach magnetization is proposed in this article. The magnetic field derived from the formal solution of Maxwell's equations is calculated by solving Laplace's and Poisson's equations on a 2-D Cartesian system. The magnetic field distribution is determined in all regions by considering the finite magnetic permeability of soft-magnetic materials in iron parts. It was performed for two different values of iron core relative permeability (viz., 2 and 1000). Finite-element analysis (FEA) demonstrates excellent results of the developed technique.

Non-hydrostatic model for internal wave generations and propagations using immersed boundary method

A non-hydrostatic model is developed to predict internal wave generations and propagations. The model employs a semi-implicit, fractional step algorithm to solve the governing equations based on the Cartesian grid system. Immersed boundary method is incorporated to deal with the complex geometry of uneven bottoms. The combination of the z-level vertical coordinate and the immersed boundary method enables the model to treat uneven bottoms and meanwhile to avoid numerical errors in the calculation of the baroclinic pressure force. To consider the effect of stratification, a variant of the Smagorinsky sub-grid scale model is employed to calculate the eddy viscosity and diffusivity. The capability of the model in resolving internal wave generation by tidal forcing over an idealized Gaussian-shaped topography is firstly validated by comparing the developed model with a terrain-following non-hydrostatic model. Then, two laboratory-scale test cases involving internal solitary wave propagations over variable topographies are considered. It can be found that the model captures the main characteristics of waveform evolution including internal hydraulic jump, wave breaking and waveform inversion. Thus, the proposed model provide an alternative to simulate internal wave generations and propagations.

High-order conservative and oscillation-suppressing transport on irregular hexagonal grids

A third-order numerical scheme was developed for 2D irregular hexagonal meshes for the advection problems in this study. The scheme is based on a multi-moment constrained finite-volume method (MCV) in Cartesian coordinates and entails the introduction of a general integration method over a hexagonal cell. Unlike in the conventional finite-volume method, various discrete moments, that is, point value and volume-integrated average, are adopted as computational constraints to achieve high-order computation. The high-order spatial reconstruction can therefore be built in a local space, which considerably reduces the stencil length. The numerical scheme is tested using various idealized experiments. Compared with the existing schemes, this scheme is demonstrated to be flexible for application in irregular hexagonal meshes without increasing cost or compromising on accuracy. The general integration formulation based on a third-order polynomial helps to expand the application to arbitrary hexagons that does not require the use of centroids as computational points or Voronoi tessellation. It is also convenient to define the orthogonal wind components in the Cartesian system to directly drive the atmospheric transport.

Experimental and statistical analysis of robotic 3D printing process parameters for continuous fiber reinforced composites

3D printing technology has gradually taken its place in many sectors. However, expected performance cannot be obtained from the structural parts with this method due to the raw material properties and constraints of Cartesian motion systems. This technology cannot replace structural parts produced by traditional manufacturing methods. In order to avoid these constraints, it is preferred to use continuous fiber reinforced polymer composites in many areas such as automotive and aerospace industries due to their low weight and high specific strength properties. These automated composite manufacturing methods currently have limited production of geometric shapes due to the need for additional molds and production as flat surfaces. To overcome all these constraints, fiberglass reinforced ultraviolet ray-curing polymer matrix composite material are selected for robotic 3 D printing process and various parameters are examined. Fiber-polymer combination and layer structure formation was examined. Scanning Electron Microscopy (SEM) images of sections of 3 D printed test samples were taken and fiber resin curing was examined. The nozzle diameter, printing speed, fiber density and Ultra Violet (UV) light intensity parameters, which will provide effective 3 D printing process, are optimized with the Taguchi method. Tensile strength, flexural strength and izod impact values are considered as result parameters for optimization. It was found that it would be appropriate for 3D printing with a 1.0 mm nozzle diameter, 600 tex fiber density, 4 UV light, 600 mm/min printing speed. With these 3D printing process parameters, approximately 125 MPa tensile strength and 450 MPa flexural strength can be obtained. With this study, support and contribution was provided to researchers, composite producers, tool manufacturer and literature who want to use and develop this 3D printing process.

On the boundary conditions of magnetic field in OpenFOAM and a magnetic field solver for multi-region applications

This work begins with the discretization of the governing equations of magnetic field for different type of magnetic media over a two-dimensional rectangular domain using a Cartesian grid system. The basic rules that the coefficients of the discretization equation should obey, to ensure physical realism and overall balance, are discussed. In order to satisfy the rule, “consistency at control-volume faces”, the formulation of the permeability at the interface between two adjacent control volumes is derived. It reveals that the interface permeability is equal to the anti-linear interpolation of that on the cell centroids under the assumption of flux consistency at control-volume faces. For the purpose of effectively calculating magnetic fields using the FVM based OpenFOAM toolbox, the representations of boundary conditions on the interfaces between different type of media are for the first time derived. A C++ class named magPhiMixedFvPatchField describing the newly derived boundary conditions is defined based on OpenFOAM libraries. The new open-source solver labeled as magneticMultiRegionFoam, for the simulation of static magnetic field with multi-regions, based on FVM in the OpenFOAM framework is for the first time developed and validated. Comparison of the results of the predicted magnetic field for a cylindrical magnet in air with those obtained from Comsol software and the analytical method verifies the fidelity of the solver implementation. For the case of calculating the magnetic levitation forces exerted on a magnet immersed in ferrofluid, the results obtained from magneticMultiRegionFoam show better consistency with the experimental ones than Comsol software. Program summaryProgram Title: magneticMultiRegionFoamCPC Library link to program files:https://doi.org/10.17632/858w9rpf58.1Licensing provisions: GNU General Public License v3Programming language: C++External routines/libraries: OpenFOAM (http://www.openfoam.org)Nature of problem: Solving the magnetic field with multi-regionsSolution method: Finite Volume Method (FVM) with a self-defined class describing the boundary conditions between different type of magnetic media.Additional comments including restrictions and unusual features: The current version of the solver can only be applied at static magnetic field.

Geometric phase and in-phase superpositions: A fresh perspective on interference in phase space

We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. The motivating idea is Pancharatnam's concept of two Hilbert space vectors being ’’in phase”. This leads to special sums and integrals of vectors which are locally in-phase superpositions. Geometric phase considerations naturally lead to the emergence of phase space areas. Applied to the overcomplete family of coherent states, we are led to preferred in-phase integral representations for various states of physical significance, such as the position, momentum and Fock states as well as the squeezed vacuum state. Interestingly, the Husimi-Kano Q function is maximized along the line of such superpositions. We also get a fresh perspective on the Bohr-Sommerfeld quantization condition. Finally, we use our exact integral representations to obtain asymptotic expansions for state overlaps and matrix elements, leading to phase space area considerations similar to the ones noted earlier in the seminal works of Schleich, Wheeler and collaborators, but now from a geometric phase perspective.

An accurate edge‐based FEM for electromagnetic analysis with its applications to multiscale structures

AbstractThis paper introduces an accurate edge‐based smoothed finite element method (ES‐FEM) for electromagnetic analysis for both two‐dimensional cylindrical and three‐dimensional Cartesian systems, which shows much better performance in terms of accuracy and numerical stability for mesh distortion compared with the traditional FEM. Unlike the traditional FEM, the computational domain in ES‐FEM is divided into non‐overlapping smoothing domains associated with each edge of elements, triangles in two‐dimensional domain and tetrahedrons in three‐dimensional domain. Then, the gradient smoothing technique is used to smooth the gradient components in the stiff matrix of the FEM. Several numerical experiments are carried out to validate its accuracy and numerical stability. Results show that the ES‐FEM can obtain much more accurate results compared with the traditional FEM and is almost independent of mesh distortion.

ДЕКАРТОВА СИСТЕМА КООРДИНАТ ЯК ІНСТРУМЕНТ ПОЗИЦІОНУВАННЯ ОБ’ЄДНАНИХ ТЕРИТОРІАЛЬНИХ ГРОМАД УКРАЇНИ

Problem statement. The need for positioning of amalgamated territorial communities (ATC) is due to their large number and lack of identification. Effective ATC positioning requires the development of appropriate tools to take advantage of the territory. The purpose of the article is to highlight the results of using the Cartesian system of coordination of the rear positioning of ATC in the context of their sustainable development, examples of ATC Luhansk region. The research object is ATC of Luhansk region. The methods used in the reaserch are: system, comparative and graphical analysis (the Cartesian coordinate system in space). The reaserch hypothesis was the preparation that the Cartesian coordinate system can be used as a tool for assessing the positions of ATCs in the context of their sustainable development. Presentation of the main material: on the basis of sustainable development estimates of ATC of Luhansk region their positions in the Cartesian coordinate system are determined with the help of geogebra software; to determine the best positions in the ATC of Luhansk region, it is proposed to use the vector of balanced positioning; it is established that the Lozno-Oleksandrivska ATC has the best balanced positioning.The originality and practical significance of the reaserch polarize the propositions of vicoristic Cartesian coordinate systems for the simplest tools for controlling the positions of ATC . Conclusions and prospects fot the further reaserches. For the assessment of ATC positions, it was used a middle ball of the development by three warehouse (economy, social, environmental). The result of the positioning of ATC of the Luhansk region was filled with a rosary behind an additional Cartesian coordinate system and software geogebra protection. The positions of ATC of the Luhansk region are displayed in the areas XOZ, XYZ, XOY. For setting the best positions at the ATC of the Luhansk region, the reference station is assigned to the vector of the balanced position, which dials up, for the most unbalanced positions from the Lozno-Oleksandrivska position. Subsequent reaserches may be directed to the value of visits for the purpose of the balanced development of ATC.

On the structure of the orthotropic 3D permeability tensor of an anisotropic porous body in heat and mass transfer problems

The structure of a 3D permeability tensor with orthotropic properties is proposed to describe various heat and mass transfer processes in anisotropic porous media. This structure of the permeability tensor has advantages over the monoclinic and triclinic because of the minimum number of elements to be determined, which greatly simplifies the formulation, conduct and processing of the corresponding experiments. In addition, the confirmation of the operability of such a structure opens up new opportunities for the artificial creation of porous materials with specified properties and the required anisotropy architecture on 3D printers. Using the Jacobians of rotations in the Cartesian reference system, the matrix of rotations is found as a result of successive multiplication of Jacobians by different angles around the axes of the base coordinate system. The final form of the tensor is identified as the product of the orthotropic tensor on the left and right by the turn matrix and the transposed turn matrix, respectively. This representation allowed us to calculate the inverse permeability tensor and synthesize a mathematical 3D model of Darcy-Brinkman type of unidirectional flow in a porous channel of rectangular cross-section on the example of hydrodynamic filtration of a Newtonian fluid. It is shown that such linearization does not level the property of anisotropy in a porous medium, while maintaining three-dimensionality.

Numerical Simulation of Green Water on Deck with a Hybrid Eulerian-Lagrangian Method

Green water on the ship deck in rough sea conditions may induce extreme impulsive wave impacts on superstructures and result in severe structural damage. It is of great importance to consider green water loads in ship structure design. However, there are many challenges in predicting green water loads due to the strongly nonlinear wave–ship interactions and the multiphase, multi-scale nature of the wave impact phenomena. In this article, a three-dimensional hybrid Eulerian–Lagrangian approach is proposed for simulating green water loads on the ship deck. It is extended from an efficient and accurate two-dimensional method developed for fluid–structure interaction problems. In this method, the flow field is solved on a fixed regular Cartesian grid system in an Eulerian framework, whereas the solid body motion is tracked with a set of markers immersed in the fluid and solved in a Lagrangian framework. Two benchmark cases, green water on a fixed simplified Floating Production Storage and Offloading (FPSO) model and green water on ship, are simulated. Comparison between experimental data and numerical results shows that our method is a viable choice for predicting green water loads. Introduction In rough sea conditions, ships may undergo large-amplitude motions and suffer green water impacts due to the strongly nonlinear wave–body interaction. Large waves run up to the ship deck and impact on superstructures with huge volume of water impulsively. It can induce extreme impulsive wave impact loads on superstructures and result in severe structural damage. Thus, it is important to predict wave impact loads for ship structure design. However, there are still great challenges in predicting green water impact loads accurately because it is a flow phenomenon of high complexity and randomness due to its multiphase, highly turbulent nature with wave breaking, air entrainment, etc (Temarel et al. 2016).

Analitical definition of the law of change in the traction resistance of the plowshare and justification of its model

An analytical definition of the law of change in the traction resistance of the plowshare is proposed, and its mathematical model is justified. To confirm these theoretical studies, experiments were conducted in the soil channel of the North-Caucasus Research Institute of Horticulture and Viticulture. According to a specially developed program, solutions in numerical form were carried out on a PC. To solve this problem, we used the Fourier, Sturm-Liouville equations, transformed from the polar system to the Cartesian system. The results obtained for the first eight harmonics were processed by the spline-approximation program, and then a regression analysis was performed. The pair correlation coefficient was calculated. Based on the obtained values, a graph of the dependence of the soil layer’s movement in the transverse plane on the forward movement was constructed.

Subproduct Systems and Cartesian Systems: New Results on Factorial Languages and their Relations with Other Areas

We point out that a sequence of natural numbers is the dimension sequence of a subproduct system if and only if it is the cardinality sequence of a word system (or factorial language). Determining such sequences is, therefore, reduced to a purely combinatorial problem in the combinatorics of words. A corresponding (and equivalent) result for graded algebras has been known in abstract algebra, but this connection with pure combinatorics has not yet been noticed by the product systems community. We also introduce Cartesian systems, which can be seen either as a set theoretic version of subproduct systems or an abstract version of word systems. Applying this, we provide several new results on the cardinality sequences of word systems and the dimension sequences of subproduct systems.

Development of an integrated 3R end-effector with a cartesian manipulator for pruning apple trees

Robotic pruning is a potential solution to address the issues of labor shortages and high associated costs, but it has challenges due to the unstructured working environment. For successful robotic pruning, target branches have to be reached with fewer spatial requirements for the end-effector cutter and the manipulator. A three-rotational (3R) degrees of freedom (DoF) end-effector was designed considering maneuvering, spatial, mechanical, and horticultural requirements. Simulations were conducted with the end-effector to investigate the reachable workspace, the cutter frame orientation, and the manipulability index. The simulation results suggested that the proposed design has a spherical reachable workspace with a void due to the presence of a physical constraint of the linear arm. The manipulability index was determined to be independent of the rotation of the first and last joint of the end-effector. The prototype of the proposed end-effector was integrated with a cartesian manipulator. An Arduino-based control system was developed along utilizing a Matlab graphical user interface (GUI). A series of field tests were conducted on ‘Fuji’/Bud. 9 apple trees with trellis-trained architecture. The field tests validated the simulation results, and the end-effector successfully cut branches up to ~25 mm diameter at wide range of orientations. This study provides the foundation for future investigations of branch accessibility for pruning with an integrated 3R end-effector and a cartesian manipulator system following a collision free trajectory.

MODERN RATIONALISM AND EPISTEMOLOGICAL IDEAS OF RENE DESCARTES

The article discusses the main aspects of the paradigm of scientific thinking, which was created by Rene Descartes in the middle of the 17th century. The author focuses on the problem of metaphysical validity of the human mind, as well as the subject-object relations in the epistemological ideas of the French thinker. These questions are explored through the consideration of the “I”-God-nature triad, which is central to Descartes' philosophical concept. The idea of a created mind was for the philosopher the fundamental basis for obtaining reliable knowledge about the world and discoveries in the scientific field. Descartes defined the mind as an instrument of knowledge and paid great attention to the problem of controlling one's own thinking using the method he invented. The thought process becomes an object of observation and reflection on the part of the “I”. The article examines the relationship between freedom and necessity in Cartesian philosophy. One of the most important tasks set by Descartes is to free thinking from prejudice and build a new philosophy. The basic principle of the Cartesian philosophical system was total doubt. The act of doubt reveals the ability of thinking to manifest freedom. Free will is considered by Descartes as one of the registers of human thinking, through which the control of the thought process is carried out.

ФРОНТАЛЬНАЯ ГЕОМЕТРИЧЕСКАЯ МОДЕЛЬ ОПРЕДЕЛЕНИЯ ПАРАМЕТРОВ НЕДОСТУПНОЙ ТОЧКИ ОБЪЕКТА

The present work analyses the geometric model of the determination of the inaccessible point of the object. The common issues and essential steps of their resolution are identified. A geometrical model of measurements is defined. This model connects measuring devices and object of research in certain system of co-ordinates with planes of projections using collimating rays and their projections. The problem essence is that a complicated procedure is needed for binding of model of measurements to the Cartesian system of coordinates. This contradicts to a requirement of simplification of a measurement technique, reduction of operations of processing of the obtained results, and decreasing the cost of the experiments. The purpose of the present research is to prove a rational way of a binding of geometrical model of measurements to the Cartesian system of coordinates. The objectives of the paper are: 1. To analyze the possible ways of binding of a two-dimensional geometrical model to the Cartesian system of coordinates using the criterion of minimization of the number of experimental measurements. 2. To define a rational variant of the geometrical model of experimental measurements including an analysis of its merits and drawbacks. Two hypotheses are formulated. Hypothesis 1 is that it is possible to define parameters of an inaccessible point of object using the parameters of four points accessible to measurement. Hypothesis 2 is that. the binding of geometrical model of measurements to the Cartesian system of coordinates defines the procedure of measurements, structure of a technique of processing measured results and, finally, the cost of geodetic works. A rational variant to the geometric model of experimental measurements and processing result is suggested. In the best variant (7) measurements of parameters of projections F1 and A1 of points F and A, coordinate measurement y for projection B1 of point B and coordinate measurement x for projection D1 of point D are excluded. Thus the coordinate x a directing vector directional ray BD has negative value. Keywords: a building, a roof, the analysis, directional ray, collimating ray, measurement of coordinates of a point, geometrical model, a way of a binding of model to system of coordinates.

Alfabetizar letrando: possibilidades para uma cartografia porosa

Este artigo objetiva contribuir para o debate sobre o sentido do significante cartografia escolar que, ora fixa-se na defesa do processo de alfabetização, ora no de letramento, como se fossem processos incomunicáveis e totalizantes. Assumindo os fundamentos da Teoria do Discurso, nossa proposição aqui é a da articulação em detrimento da dicotomização desses conceitos, defendendo o sentido de alfabetizar letrando. Trata-se de uma proposta que parte da compreensão de que o processo de letramento vai além, e não contra o entendimento de alfabetização. Na bibliografia dominante, a alfabetização cartográfica é compreendida como um processo específico e imprescindível, que exige um trabalho metodológico e didático-pedagógico para se ensinar a lógica do sistema cartesiano do mapa, ao passo que o letramento estaria atrelado ao domínio e uso social das linguagens cartográficas. Defendemos aqui uma ação pedagógica sob a perspectiva do alfabetizar letrando, que desloca a ênfase habitual da localização espacial como centro do processo, criando condições para uma cartografia porosa que permita aos alunos se apropriarem da linguagem cartográfica também como práticas socioespaciais de significação.
 Palavras-chave: Cartografia escolar, alfabetizar letrando, linguagem cartográfica, práticas socioespaciais de significação.

Numerical simulation and prediction model development of multiple flexible filaments in viscous shear flow using immersed boundary method and artificial neural network techniques

Many chemical and biological systems have applications involving fluid–structure interaction (FSI) of flexible filaments in viscous fluid. The dynamics of single- and multiple-filament interaction are of interest to engineers and biologists working in the area of DNA fragmentation, protein synthesis, polymer segmentation, folding–unfolding analysis of natural and synthetic fibers, etc. To perform numerical simulation of the above-mentioned FSI applications is challenging. In this direction, methods like the immersed boundary method (IBM) have been quite successful. We simulate the dynamics of multiple flexible filaments subjected to planar shear flow at low Reynolds number using the finite volume method-based IBM. The governing continuity and Navier–Stokes equations are solved by the SIMPLE algorithm on a staggered Cartesian grid system. The validation of the developed model is done using previous works. The length of the filament, its bending rigidity and fluid shear rate are taken as parametric variables and numerical simulations are carried out. Viscous flow forcing and fractional contraction terms are incorporated so as to effectively categorize filament motion into various deformation regimes. The effects of tumbling motion on the filament migration and recuperative aspects are studied. The mutual interaction of two filaments placed side by side is thus observed. Finally, an artificial neural network model is developed from the IBM simulation results to predict tumbling counts for different filament parameters.

Numerical Simulation of Flow in a Wavy Wall Microchannel Using Immersed Boundary Method

Background: Fluid flow in microchannels is restricted to low Reynolds number regimes and hence inducing chaotic mixing in such devices is a major challenge. Over the years, the Immersed Boundary Method (IBM) has proved its ability in handling complex fluid-structure interaction problems. Objectives: Inspired by recent patents in microchannel mixing devices, we study passive mixing effects by performing two-dimensional numerical simulations of wavy wall in channel flow using IBM. Methods: The continuity and Navier-Stokes equations governing the flow are solved by fractional step based finite volume method on a staggered Cartesian grid system. Fluid variables are described by Eulerian coordinates and solid boundary by Lagrangian coordinates. A four-point Dirac delta function is used to couple both the coordinate variables. A momentum forcing term is added to the governing equation in order to impose the no-slip boundary condition between the wavy wall and fluid interface. Results: Parametric study is carried out to analyze the fluid flow characteristics by varying amplitude and wavelength of wavy wall configurations for different Reynolds number. Conclusion: Configurations of wavy wall microchannels having a higher amplitude and lower wavelengths show optimum results for mixing applications.

Workspace analysis of Cartesian robot system for kiwifruit harvesting

Purpose This paper aims to investigate if a Cartesian robot system for kiwifruit harvesting works more effectively and efficiently than an articulated robot system. The robot is a key component in agricultural automation. For instance, multiple robot arm system has been developed for kiwifruit harvesting recently because of the significant labor shortage issue. The industrial robots for factory automation usually have articulated configuration which is suitable for the tasks in the manufacturing and production environment. However, this articulated configuration may not fit for agricultural application due to the large outdoor environment. Design/methodology/approach The kiwifruit harvesting tasks are completed step by step so that the robot workspace covers the canopy completely. A two-arm, Cartesian kiwifruit harvesting robot system and several field experiments are developed for the investigation. The harvest cycle time of the Cartesian robot system is compared to that of an articulated robot system. The difference is analyzed based on the workspace geometries of these two robot configurations. Findings It is found that the kiwifruit harvesting productivity is increased by using a multiple robot system with Cartesian configuration owing to its regular workspace geometry. Originality/value An articulated robot is a common configuration for manufacturing because of its simple structure and the relatively static factory environment. Most of the agricultural robotics research studies use single articulated robot for their implementation. This paper pinpoints how the workspace of a multiple robot system affects the harvest cycle time for kiwifruit harvesting in a pergola style kiwifruit orchard.