Cartesian Method Research Articles

An octree-based solution-adaptive Cartesian grid generator and Euler solver for the simulation of three-dimensional inviscid compressible flows

Cartesian grid generation methods are especially designed algorithms to generate automatic grids for complex geometries and to simulate flows around such geometries regardless of the body shape. Cartesian grids are generated by constructing an octree-based data structure for the purpose of connecting the Cartesian cells to each other. Entire algorithm is implemented in object-oriented FORTRAN programming language. Some special Cartesian algorithms, namely, Ray-Casting method and cut-cell adaptation are used around three-dimensional closed bodies. The flow field around the solid body is obtained by employing Euler equations which are discretised by using finite volume method. Validation of the numerical results is accomplished by comparison with the experimentally obtained data from the flow around ONERA M6 wing. Employing the solution adaptation techniques, pressure coefficients and contours of the flow around the wing have verified and captured two shock waves (weak leading edge shock and midchord shock) by the developed grid-generator-with-eULER-solver-for-3D-applications (GeULER3D) code.

WORKSPACE CONTROL OF TWO LINK PLANAR ROBOT USING MICRO-BOX 2000

This paper presents the workspace/task space control of a two degree of freedom (DOF) two link planar robot manipulator with DC geared motor actuation. Due to the nature of the DC geared motor, PD controller system is designed for each joint of the actuator to minimize the error, improve performance and obtain desired response. This paper includes the modelling of the planar structure and the simulation of workspace control by two methods, inverse kinematics and Direct Cartesian. Then a disturbance compensation called Workspace Observer (WOB) is introduced to improve the Direct Cartesian method. Comparison between the three methods was done. The Direct Cartesian with DOB shows a better trajectory response compared to inverse kinematics.

An Improved Method of Capturing the Surface Boundary of a Ti-6Al-4V Fusion Weld Bead for Finite Element Modeling

Weld simulation methods have often employed mathematical functions to describe the size and shape of the molten pool of material transiently present in a weld. However, while these functions can sometimes accurately capture the fusion boundary for certain welding parameters in certain materials, they do not necessarily offer a robust methodology for the more intricate weld pool shapes that can be produced in materials with a very low thermal conductivity, such as the titanium alloy Ti-6Al-4V. Cross-sections of steady-state welds can be observed which contain a dramatic narrowing of the pool width at roughly half way in to the depth of the plate of material, and a significant widening again at the base. These effects on the weld pool are likely to do with beam focusing height. However, the resultant intricacy of the pool means that standard formulaic methods to capture the shape may prove relatively unsuccessful. Given how critical the accuracy of pool shape is in determining the mechanical response to the heating, an alternative method is presented. By entering weld pool width measurements for a series of depths in a Cartesian co-ordinate system using FE weld simulation software Sysweld, a more representative weld pool size and shape can be predicted, compared to the standard double ellipsoid method. Results have demonstrated that significant variations in the mid-depth thermal profile are observed between the two, even though the same values for top and bottom pool-widths are entered. Finally, once the benefits of the Cartesian co-ordinate method are demonstrated, the robustness of this approach to predict a variety of weld pool shapes has been demonstrated upon a series of nine weld simulations, where the two key process parameters (welding laser power and travel speed) are explored over a design space ranging from 1.5 to 3 kW and 50 to 200 mm/s. Results suggest that for the faster travel speeds, the more detailed Cartesian co-ordinate method is better, whereas for slower welds, the traditional double ellipsoid function captures the fusion boundary as successfully as the Cartesian method, and in faster computation times.

„Radikali“ abejonė Descartes’o filosofijoje

Descartes’o kūriniai paprastai laikomi takoskyra tarp scholastinės ir Naujųjų laikų filosofijos. Vyrauja nuostata, kad šiuose kūriniuose pristatytas ir praktikuojamas radikalios abejonės metodas atveria naujus minties horizontus – leidžia pasiekti neabejotiną tikrumą, laikantis „pirmojo asmens perspektyvos“ ir nesiremiant iš principo nepatikrinamomis prielaidomis apie suvokiančio subjekto santykį su suvokimo objektais. Straipsnyje mėginama parodyti, kad toks požiūris į kartezinę filosofiją yra gana paviršutiniškas. Įdėmesniam žvilgsniui atsiskleidžia tiek „eksplicistinės“, tiek „implicistinės“ Descartes’o presupozicijos, kurios, praktikuojant radikaliąją abejonę, lieka jo nekvestionuotos ir, maža to, ilgainiui įtvirtinamos kaip fundamentalūs pasaulėžiūriniai principai ar racionalios mąstysenos normos.

A atuação do Poder Judiciário no Estado Constitucional em face do fenômeno da judicialização das políticas públicas no Brasil

The article was prepared with the aim of explaining about the new role assigned to the judiciary in the effectiveness of fundamental social rights. Based on the identified phenomenon of judicialization of social relations perquire-about judicial activism. The commitment of the Constitutional State in the implementation of public policies, we seek to contextualize the legitimation of social achievements. Upon review of the history of the origin of the formation of the Brazilian colonial society from the analysis of the participation of indigenous and black in national economic construction investigating the origin of government debt to be rescued through social policies with a significant portion the present society. The inductive method was used to drive the technical category, the operational concept and literature; the treatment phase of the data was chosen Cartesian method and, given the results of the analysis, we used the inductive method in reporting the research. Finally, there was a necessary evolution for the contemporary state saving of the rule of law and democracy as incorporating substantive value to give effect to fundamental social rights. As a means of giving concrete social promises, the judiciary assumes the mission of imposing fixes the performance of the government through the phenomenon of judicialization of social relations.

A second-order Cartesian method for the simulation of electropermeabilization cell models

In this paper, we present a new finite differences method to simulate electropermeabilization models, like the model of Neu and Krassowska or the recent model of Kavian et al. These models are based on the evolution of the electric potential in a cell embedded in a conducting medium. The main feature lies in the transmission of the voltage potential across the cell membrane: the jump of the potential is proportional to the normal flux thanks to the well-known Kirchoff law. An adapted scheme is thus necessary to accurately simulate the voltage potential in the whole cell, notably at the membrane separating the cell from the outer medium. We present a second-order finite differences scheme in the spirit of the method introduced by Cisternino and Weynans for elliptic problems with immersed interfaces. This is a Cartesian grid method based on the accurate discretization of the fluxes at the interface, through the use of additional interface unknowns. The main novelty of our present work lies in the fact that the jump of the potential is proportional to the flux, and therefore is not explicitly known. The original use of interface unknowns makes it possible to discretize the transmission conditions with enough accuracy to obtain a second-order spatial convergence. We prove the second-order spatial convergence in the stationary linear one-dimensional case, and the first-order temporal convergence for the dynamical non-linear model in one dimension. We then perform numerical experiments in two dimensions that corroborate these results.

Conformal Cartesian Grids for Symmetric Bodies: A Novel Boundary Fitted Grid Method

A novel Cartesian grid discretization method is developed to simulate two and three dimensional problems, governed by partial differential equations. In the present approach, the grid points lie exactly onto the surface of an immersed object or of the domain’s boundaries, allowing for accurate imposition of the surface boundary conditions. This is well demonstrated for symmetric objects, but it can be also extended for non-symmetric shapes. The method intrinsically possesses higher accuracy than the conventional body fitted or Immersed Boundary Methods, since the implemented grid is universally orthogonal and the boundary conditions are imposed precisely onto the surface, without any interpolation or tuning of the governing equations. Conformal Cartesian Grids bridge the topology of Cartesian grid methods with the treatment of the surface boundary conditions, which is adopted in conventional bodyfitted grid approaches. Emphasis is given in a two dimensional fluid dynamics problem to demonstrate this approach. A finite difference code has been developed, which encompasses the present methodology. Space discretization is performed via the second order accurate central difference scheme and time discretization by the fourth order accurate Runge-Kutta method. The flow past a cylinder at low Reynolds number is resolved to validate the accuracy and performance of the method. Two different flow regimes are thoroughly investigated at Re numbers varying from 10 up to 100 based on the cylinder’s diameter. Computed results agree well with the available measurements and numerical computations in literature. Three dimensional results are also briefly presented mainly for revealing the applicability of the method.

Kinematics Modelling and Simulation of Aero-Engine Fuel Piston Pump

Kinematics parameters calculation is the basis of piston pump design and performance analysis. Taking an axial piston pump with incline piston and spherical swash plate as the research object, Aimed at the deficiency of current formula for calculating piston pump kinematics parameters which included displacement, velocity and acceleration. In this paper, according to piston pump part motion geometry relationship, a correction kinematics algorithm is deduced by using the the spherical coordinate and cartesian coordinate transformation method, the analyse method and deduction procedure ensure the new calculating formula are precise in theory. Applying the calculating formula to an aero engine fuel axial piston pump, results show that. The displacement, velocity, acceleration according to the kinematics principle of piston pump, it can be used in the kind of piston pump kinematics parameters calculation and current calculating method evaluation.

Intertextuality and sense production in the learning of algebraic methods

In studies carried out in the 1980s the algebraic symbols and expressions are revealed through prealgebraic readers as non-independent texts, as texts that relate to other texts that in some cases belong to the reader’s native language or to the arithmetic sign system. Such outcomes suggest that the act of reading algebraic texts submerges the reader into a network of intertextual relations derived from that reader’s prior mathematics and linguistic experiences. In this article we propose an analytical perspective of algebraic activity that is based on intertextuality and that makes it possible to advance our knowledge concerning the production of sense in said activity. In particular, we resort to the notion of intertextuality as a means of theoretically describing and explaining sense production processes in the learning of two algebraic methods: the Cartesian Method (for the algebraic solution of word problems) and the Substitution Method (for the solution of systems of two linear equations with two unknowns). We support our arguments via a series of episodes of empirical study interviews with secondary school students, in order to demonstrate the pertinence and relevance of carrying out their analysis from the perspective proposed.

An Accurate Cartesian Method for Incompressible Flows with Moving Boundaries

AbstractAn accurate cartesian method is devised to simulate incompressible viscous flows past an arbitrary moving body. The Navier-Stokes equations are spatially discretized onto a fixed Cartesian mesh. The body is taken into account via the ghost-cell method and the so-called penalty method, resulting in second-order accuracy in velocity. The accuracy and the efficiency of the solver are tested through two-dimensional reference simulations. To show the versatility of this scheme we simulate a three-dimensional self propelled jellyfish prototype.

Applied Research in Cartesian Impedance Control for 6-UPS Space Docking Mechanism

In order to ensure the security buffer of the 6-UPS space docking mechanism, real-time control based on contact force is needed. In this paper, a highly effective Cartesian impedance control method based on the feedback signal from 6 force sensors is presented, and a brief introduction to the mechanical structure of the 6-UPS docking mechanism and the control structure of the docking system is given. According to the data analysis of ground experiment, this control method can tremendously improve the buffer effect in the docking stage with the parameters optimized in Simulink.

Study on complicated solid modeling and Cartesian grid generation method

A Cartesian grid generation method is developed in this study. Two kinds of solid modeling methods, CSG and STL models, are used for complicated solid modeling. The staircase boundary approximation is implemented to handle irregular geometries and the computational domain is discretized using a regular Cartesian grid. Using the edge-based integral slice algorithm, the models are sliced with a set of parallel planes to generate 2D slices information. The scan line filling technique is used to achieve grid generation after slicing. Two grid generation examples with a CSG model and a STL model are given to test the capability of the grid generation method. For grid displaying, a method is proposed to remove the hidden surfaces fasten based on the topology of orthogonal hexahedral grids. The parallelization of grid displaying is achieved by employing multi-threaded parallel technique. Parallel test results show that the parallel algorithm has the absolute advantage on speed compared to the serial algorithm.

Putting Faith to the Test: Anne de Gonzague and the Incombustible Relic

This article explores the cognitive struggle against “doubt” that impeded the conversion of the female aristocrat Anne de Gonzague, princesse Palatine, in seventeenth-century France. Anne's conversion came only after a life-long intellectual battle that climaxed when she held a fragment of the True Cross in the fire to test whether it could withstand the flames. The intellectual premise for her experiment with the holy relic can be found in her own écrit or conversion narrative. Analysis of this narrative demonstrates that Anne's application of philosophical skepticism and the Cartesian method—to which she was exposed in the Scientific Academy of her physician, Pierre Michon Bourdelot—to her own irreligion actually brought about her conversion to orthodoxy. Anne's “test” of faith therefore compels us to rethink the relationship between the New Philosophy and faith in the seventeenth century.

Noncontrast enhanced four‐dimensional dynamic MRA with golden angle radial acquisition and k‐space weighted image contrast (KWIC) reconstruction

To explore the feasibility of 2D and 3D golden-angle radial acquisition strategies in conjunction with k-space weighted image contrast (KWIC) temporal filtering to achieve noncontrast enhanced dynamic MRA (dMRA) with high spatial resolution, low streaking artifacts and high temporal fidelity. Simulations and in vivo examinations in eight normal volunteers and an arteriovenous malformation patient were carried out. Both 2D and 3D golden angle radial sequences, preceded by spin tagging, were used for dMRA of the brain. The radial dMRA data were temporally filtered using the KWIC strategy and compared with matched standard Cartesian techniques. The 2D and 3D dynamic MRA image series acquired with the proposed radial techniques demonstrated excellent image quality without discernible temporal blurring compared with standard Cartesian based approaches. The image quality of radial dMRA was equivalent to or higher than that of Cartesian dMRA by visual inspection. A reduction factor of up to 10 and 3 in scan time was achieved for 2D and 3D radial dMRA compared with the Cartesian-based counterparts. The proposed 2D and 3D radial dMRA techniques demonstrated image quality comparable or even superior to those obtained with standard Cartesian methods, but within a fraction of the scan time.

Technical note: algebraic iterative image reconstruction using a cylindrical image grid for tetrahedron beam computed tomography.

To accelerate iterative algebraic reconstruction algorithms using a cylindrical image grid. Tetrahedron beam computed tomography (TBCT) is designed to overcome the scatter and detector problems of cone beam computed tomography (CBCT). Iterative algebraic reconstruction algorithms have been shown to mitigate approximate reconstruction artifacts that appear at large cone angles, but clinical implementation is limited by their high computational cost. In this study, a cylindrical voxelization method on a cylindrical grid is developed in order to take advantage of the symmetries of the cylindrical geometry. The cylindrical geometry is a natural fit for the circular scanning trajectory employed in volumetric CT methods such as CBCT and TBCT. This method was implemented in combination with the simultaneous algebraic reconstruction technique (SART). Both two- and three-dimensional numerical phantoms as well as a patient CT image were utilized to generate the projection sets used for reconstruction. The reconstructed images were compared to the original phantoms using a set of three figures of merit (FOM). The cylindrical voxelization on a cylindrical reconstruction grid was successfully implemented in combination with the SART reconstruction algorithm. The FOM results showed that the cylindrical reconstructions were able to maintain the accuracy of the Cartesian reconstructions. In three dimensions, the cylindrical method provided better accuracy than the Cartesian methods. At the same time, the cylindrical method was able to provide a speedup factor of approximately 40 while also reducing the system matrix storage size by 2 orders of magnitude. TBCT image reconstruction using a cylindrical image grid was able to provide a significant improvement in the reconstruction time and a more compact system matrix for storage on the hard drive and in memory while maintaining the image quality provided by the Cartesian voxelization on a Cartesian grid.

TH‐C‐103‐04: Computed Tomography Image Reconstruction with a Cylindrical Voxelization Method

Purpose: To accelerate the image reconstruction process for iterative algebraic reconstruction techniques using a cylindrical voxelization method. Methods: Iterative image reconstruction has many advantages, such as noise reduction and mitigation of approximate cone reconstruction artifacts, over analytical image reconstruction. But its high computational cost prohibits its use in many clinical applications, such as image guided radiotherapy (IGRT). The system matrix used in iterative reconstruction is often too large to store on the hard drive or in RAM. The cylindrical geometry is a natural fit for the circular scanning trajectory employed in volumetric CT methods such as cone beam computed tomography (CBCT) and tetrahedron beam computed tomography (TBCT). In this study, the iterative simultaneous algebraic reconstruction technique (SART) algorithm using a cylindrical voxelization method is developed for TBCT. The new algorithm takes advantage of the symmetries of the axial scanning geometry used in TBCT and greatly reduces the size of the system matrix. An additional step is needed for interpolating the cylindrical data onto a Cartesian grid. The reconstruction algorithms were tested with numerical phantoms as well as patient CT data. Results: The system matrix with the cylindrical voxelization method is compact and can be easily stored in the computer RAM. SART reconstruction using the cylindrical voxelization method was implemented for the TBCT. The FOM results for the cylindrical voxelization method were slightly better than for the Cartesian voxelization. The cylindrical method was able to provide a speedup of 40 times over the traditional Cartesian method and to provide a reduction of two orders of magnitude in the storage requirement for the system matrix. Conclusion: Image reconstruction using a cylindrical voxelization method was able to provide a significant improvement in the reconstruction speed while maintaining the image quality provided by the conventional reconstruction method using a Cartesian image grid. This work is partially supported by NIH SBIR contract #HHSN261201100045C.

Domain-specific knowledge representation and inference engine for an intelligent tutoring system

One of the most challenging steps in learning algebra is the translation of word problems into symbolic notation. This paper describes an Intelligent Tutoring System (ITS) that focuses on this stage of the problem solving process. On the one hand, a domain specific inference engine and a knowledge representation mechanism are proposed. These are based on a description language based on hypergraphs, and the idea of using conceptual schemes to represent the student’s knowledge. As a result, the system is able to simultaneously: (a) represent all potential algebraic solutions to a given word problem; (b) keep track of the student’s actions; (c) univocally determine the current state of the resolution process; (d) build a student model; and (e) provide adaptive automatic remediation. On the other hand, the Graphical User Interface (GUI) has been designed to force the student to follow the sequence of steps described in the Cartesian method. The ITS has been evaluated in an educational environment. The results show significant gains for the experimental group and hence support the use of the ITS in practice.

Rousseau's Descartes: The Rejection of Theoretical Philosophy as First Philosophy

Rousseau's Savoyard Vicar makes creative use of Descartes's meditative method by applying it to practical life. This ‘misuse’ of the Cartesian method highlights the limits of the thinking thing as a ground for morality. Taking practical philosophy as first philosophy, the Vicar finds bedrock certainty of the self as an agent in the world and of moral truths while distancing himself from Cartesian positions on the distinction, union and interaction of mind and body. Rousseau's Moral Letters harmonize with the Vicar's view. Descartes would reject the Vicar's appropriation, as real-life problems cannot wait on meditation to answer them.

頸動脈プラーク性状評価におけるk-space充填法 (Radial Scan)撮像条件の検討

The purpose of this study was to optimize scan parameters for evaluation of carotid plaque characteristics by k-space trajectory (radial scan method), using a custom-made carotid plaque phantom. The phantom was composed of simulated sternocleidomastoid muscle and four types of carotid plaque. The effect of chemical shift artifact was compared using T1 weighted images (T1WI) of the phantom obtained with and without fat suppression, and using two types of k-space trajectory (the radial scan method and the Cartesian method). The ratio of signal intensity of simulated sternocleidomastoid muscle to the signal intensity of hematoma, blood (including heparin), lard, and mayonnaise was compared among various repetition times (TR) using T1WI and T2 weighted imaging (T2WI). In terms of chemical shift artifacts, image quality was improved using fat suppression for both the radial scan and Cartesian methods. In terms of signal ratio, the highest values were obtained for the radial scan method with TR of 500 ms for T1WI, and TR of 3000 ms for T2WI. For evaluation of carotid plaque characteristics using the radial scan method, chemical shift artifacts were reduced with fat suppression. Signal ratio was improved by optimizing the TR settings for T1WI and T2WI. These results suggest the potential for using magnetic resonance imaging for detailed evaluation of carotid plaque.

Forms of Knowledge/Knowledge of Forms: The Epistemology of Goethe’s West-östlicher Divan and Cavellian Skepticism

UnbegrenztDas du nicht enden kannst, das macht dich gros,Und das du nie beginnst, das ist dein Loos.Dein Lied ist drehend wie das Sterngewolbe,Anfang und Ende immer fort dasselbe,Und was die Mitte bringt ist offenbarDas, was zu Ende bleibt und anfangs war.Du bist der Freuden achte Dichterquelle,Und ungezahlt entfliest dir Well' auf Welle.Zum Kussen stets bereiter Mund,Ein Brustgesang der lieblich flieset,Zum Trinken stets gereizter Schlund,Ein gutes Herz das sich ergieset.Und mag die ganze Welt versinken,Hafis, mit dir, mit dir alleinWill ich wetteifern! Lust und PeinSey uns den Zwillingen gemein!Wie du zu lieben und zu trinkenDas soll mein Stolz, mein Leben seyn.Nun tone Lied mit eignem Feuer!Denn du bist alter, du bist neuer.1The poem Unbegrenzt in the Buch Hafis of Goethe's West-ostlicher Divan offers several problems for interpretation. Perhaps most obviously it is marked by the presence of, if not direct contradiction, then at least strong paradox. The poem's opening two lines address an unclear and attribute to that addressee the polar problems of being unable to come to an end (Das Du nicht enden kannst) and never beginning (das Du nie beginnst). And its final lines state in playful contradiction: Nun tone Lied mit eignem Feuer! / Denn du bist alter, du bist neuer. Second, as indicated by its situation in the Buch Hafis and its explicit naming of the earlier poet,Unbegrenzt calls into question both Goethe's and the poetic speaker's relations to their poetic predecessor(s). And finally, the ambiguity of the address in the first lines raises questions about self-address, selfreflection, and self-thematization: there are moments when the poem's address is unambiguous (most obviously in the last two lines), but it is not always clear when refers to Hafis, the poetic voice, or the poem. Moreover, the poem's self-reference asks for an inquiry into the relation between the title and the poem (what exactly is, or is described as, unbegrenzt?) and between the different parts of the poem-that is to say, it asks for an inquiry into the poem's form.In this paper, I will give a reading of Unbegrenzt that focuses on each of these three questions: Why is the poem so paradoxical? What is the relation to the poetic predecessor? And who is (are) the addressee(s)? I will begin by demonstrating how these topics appear and unfold throughout the poem. I will then investigate the interrelation of the three topics both as overarching themes in Goethe's poetic oeuvre and as central components of his scientific and literary epistemology. In order to support the connection between the Divan project and Goethe's investigations of the potential of human (including scientific and poetic) knowledge, I will draw on both his morphological writings and the discussions of the formation of knowledge in the Farbenlehre. It is something of a commonplace to cast Goethe as offering an alternative to the Cartesian method of gaining and validating knowledge; in the final section of this paper, I will elucidate the breadth and depth of this alternative and its implications for modern conceptions of human subjectivity by appealing to the anthropological conception of skepticism worked out by the American philosopher Stanley Cavell. Cavell offers an account of the struggles for knowledge and world orientation faced by human subjects that shows why and how poetry has a particular role to play in those struggles by virtue of its deployment of deliberately fluid form that registers conflicting tendencies both of poetic production and human subjects. I will use Cavell to address this role with reference to the questions of predecessor relationships and originality, paradox, and self-reference that I will identify in Goethe.1. Reading: Limited and LimitlessGoethe manages to enclose a remarkable number of oppositions in twenty lines; these oppositions, which would normally preclude one another, instead emerge as simultaneous characteristics of both poet and poetry. …