• Title/Summary/Keyword: Non-Cartesian

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ON WEAKLY S-PRIME SUBMODULES

  • Hani A., Khashan;Ece Yetkin, Celikel
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.6
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    • pp.1387-1408
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    • 2022
  • Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :R M)∩S = ∅ to be weakly S-prime if there exists s ∈ S such that whenever a ∈ R and m ∈ M with 0 ≠ am ∈ N, then either sa ∈ (N :R M) or sm ∈ N. Many properties, examples and characterizations of weakly S-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly S-prime.

Determination of Identifiable Parameters and Selection of Optimum Postures for Calibrating Hexa Slide Manipulators

  • Park, Jong-Hyuck;Kim, Sung-Gaun;Rauf, Abdul;Ryu, Je-Ha
    • 제어로봇시스템학회:학술대회논문집
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    • 2003.10a
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    • pp.2737-2742
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    • 2003
  • Kinematic calibration enhances absolute accuracy by compensating for the fabrication tolerances and installation errors. Effectiveness of calibration procedures depends greatly on the measurements performed. While the Cartesian postures are measured completely, all of the geometric parameters can be identified to their true values. With partial pose measurements, however, few geometric parameters may not be identifiable and effectiveness of the calibration results may vary significantly within the workspace. QR decomposition of the identification Jacobian matrix can reveal the non-identifiable parameters. Selecting postures for measurement is also an important issue for efficient calibration procedure. Typically, the condition number of the identification Jacobian is minimized to find optimum postures. This paper investigates identifiable parameters and optimum postures for four different calibration procedures - measuring postures completely with inverse kinematic residuals, measuring postures completely with forward kinematics residuals, measuring only the three position components, and restraining the mobility of the end-effector using a constraint link. The study is performed for a six degree-of-freedom fully parallel HexaSlide type paralle manipulator, HSM. Results verify that all parameters are identifiable with complete posture measurements. For the case of position measurements, one and for the case of constraint link, three parameters were found non-identifiable. Optimal postures showed the same trend of orienting themselves on the boundaries of the search space.

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A Study of Applicability of a RNG $k-\varepsilon$ Model (RNG $k-\varepsilon$ 모델의 적용성에 대한 연구)

  • Yang, Hei-Cheon;Ryou, Hong-Sun;Lim, Jong-Han
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.21 no.9
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    • pp.1149-1164
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    • 1997
  • In this study, the applicability of the RNG k-.epsilon. model to the analysis of the complex flows is studied. The governing equations based on a non-orthogonal coordinate formulation with Cartesian velocity components are used and discretized by the finite volume method with non-staggered variable arrangements. The predicted results using the RNG k-.epsilon. model of three complex flows, i.e., the flow over a backward-facing step and a blunt flat plate, the flow around a 2D model car are compared to these from the standard k-.epsilon. model and experimental data. That of the unsteady axisymmetric turbulent flow within a cylinder of reciprocating model engine including port/valve assembly and the spray characteristics within a chamber of direct injection model engine are compared to these from the standard k-.epsilon. model and experimental data. The results of reattachment length, separated eddy size, average surface pressure distribution using the RNG k-.epsilon. model show more reasonable trends comparing with the experimental data than those using the modified k-.epsilon. model. Although the predicted rms velocity using the modified k-.epsilon. model is lower considerably than the experimental data in incylinder flow with poppet valve, predicted axial and radial velocity distributions at the valve exit and in-cylinder region show good agreements with the experimental data. The spray tip penetration predicted using the RNG k-.epsilon. model is more close to the experimental data than that using the modified k-.epsilon. model. The application of the RNG k-.epsilon. model seems to have some potential for the simulations of the unsteady turbulent flow within a port/valve-cylinder assembly and the spray characteristics over the modified k-.epsilon. model.

A Study on the Development of Geometry as the Natural Laws and the Concepts of Space - Focus on the Whitehead's theories of natural laws - (자연법칙으로서 기하학과 공간 개념의 전개에 관한 연구 - 화이트헤드의 자연법칙 학설을 중심으로 -)

  • Hwang, Tae-Joo
    • Korean Institute of Interior Design Journal
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    • v.19 no.2
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    • pp.90-98
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    • 2010
  • The concepts of laws like regularity or persistence or recurrence those are discovered in nature, became the essential elements in speculative philosophy, study and scientific technology. Western civilization was spread out by these natural laws. As this background, this study is aimed to research the theories of natural laws and the development of geometry as the descriptive tools and the development aspects of the concepts of space. According to Whitehead's four theories on the natural laws, the result of this study that aimed like that as follows. First, the theories on the immanence and imposition of the natural laws were the predominant ideas from ancient Greek to before the scientific revolution, the theory on the simple description like the positivism made the Newton-Cartesian mechanism and an absolutist world view. The theory on the conventional interpretation made the organicism and relativism world view according to non-Euclidean geometry. Second, the geometrical composition of ancient Greek architecture was an aesthetics that represented the immanence of natural laws. Third, in the basic symbol of medieval times, the numeral symbol was the frame of thought and was an important principal of architecture. Fourth, during the Renaissance, architecture was regarded as mathematics that made the order of universe to visible things and the geometry was regarded as an important architectural principal. Fifth, according to the non-Euclidean geometry, it was possible to present the natural phenomena and the universe. Sixth, topology made to lapse the division of traditional floor, wall and ceiling in contemporary architecture and made to build the continuous space. Seventy, the new nature was explained by fractal concepts not by Euclidean shapes, fractal presented that the essence of nature had not mechanical and linear characteristic but organic and non-linear characteristic.

Object Position Estimation and Optimal Moving Planning of Mobile Manipulator based on Active Camera (능동카메라기반 이동매니퓰레이터의 물체위치추정 및 최적동작계획)

  • Jin, Tae-Seok;Lee, Jang-Myung
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.42 no.5 s.305
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    • pp.1-12
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    • 2005
  • A Mobile manipulator - a serial connection of a mobile robot and a task robot - is a very useful system to achieve various tasks in dangerous environment. because it has the higher performance than a fixed base manipulator in regard to the size of it's operational workspace. Unfortunately the use of a mobile robot introduces non-holonomic constraints, and the combination of a mobile robot and a manipulator generally introduces kinematic redundancy. In this paper, first a method for estimating the position of object at the cartesian coordinate system acquired by using the geometrical relationship between the image captured by 2-DOF active camera mounted on mobile robot and real object is proposed. Second, we propose a method to determine a optimal path between current the position of mobile manipulator whose mobile robot is non-holonomic and the position of object estimated by image information through the global displacement of the system in a symbolic way, using homogenous matrices. Then, we compute the corresponding joint parameters to make the desired displacement coincide with the computed symbolic displacement and object is captured through the control of a manipulator. The effectiveness of proposed method is demonstrated by the simulation and real experiment using the mobile manipulator.

A Numerical Simulation of Unsteady Axisymmetric Turbulent Flow in a Reciprocating Engine Including Port/Valve Assembly (축대칭 왕복엔진의 비정상 난류유동에 대한 수치해석)

  • 조진행;유홍선;최영기
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.1
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    • pp.139-149
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    • 1994
  • A numerical simulation of unsteady axisymmetric turbulent flow was performed for a reciprocating engine including port/valve assembly. The governing equations based on a nonorthogonal coordinate formulation with Cartesian velocity components were used and discretised by the finite volume method with non-staggered variable arrangements. The modified $\kappa-\xi$. turbulence model which included the effect of compressibility was used. The results of twodimensional transient calculation for the axisymmetric configuration were compared with the experimental data. Although slightly low rms velocity was predicted compared to the experimental data, predicted velocity distributions at the valve exit and in-cylinder region showed good agreements with the experimental data. The flow at the valve exit was separated at the same valve lift position with the experimental data. Two vortices incylinder region were generated during the initial intake process. The clockwise main vortex became strong and moved upward to the top wall. The counter-clockwise second vortex became weak and stick to the upper left corner of the cylinder. After middle intake process, new vortex adjacent to upper cylinder wall appeared by the piston motion and therefore, the in-cylinder flow was formed into three vortices. The cylinder pressure just before bottom dead center of piston was higher than inlet pressure and then the reverse flow occured at the valve exit. The in-cylinder flow characteristics were strongly dependent on piston motion, but insensitive to valve motion.

Assessment of Tip Shape Effect on Rotor Aerodynamic Performance in Hover

  • Hwang, Je Young;Kwon, Oh Joon
    • International Journal of Aeronautical and Space Sciences
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    • v.16 no.2
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    • pp.295-310
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    • 2015
  • In the present study, an unstructured mixed mesh flow solver was used to conduct a numerical prediction of the aerodynamic performance of the S-76 rotor in hover. For the present mixed mesh methodology, the near-body flow domain was modeled by using body-fitted prismatic/tetrahedral cells while Cartesian mesh cells were filled in the off-body region. A high-order accurate weighted essentially non-oscillatory (WENO) scheme was employed to better resolve the flow characteristics in the off-body flow region. An overset mesh technique was adopted to transfer the flow variables between the two different mesh regions, and computations were carried out for three different blade configurations including swept-taper, rectangular, and swept-taper-anhedral tip shapes. The results of the simulation were compared against experimental data, and the computations were also made to investigate the effect of the blade tip Mach number. The detailed flow characteristics were also examined, including the tip-vortex trajectory, vortex core size, and first-passing tip vortex position that depended on the tip shape.

Direct forcing/fictitious domain-Level set method for two-phase flow-structure interaction (이상 유동에서의 유체-구조 연성해석을 위한 Direct Forcing/Ficititious Domain-Level Set Method)

  • Jeon, Chung-Ho;Yoon, Hyun-Sik;Jung, Jae-Hwan
    • Journal of Ocean Engineering and Technology
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    • v.25 no.4
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    • pp.36-41
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    • 2011
  • In the present paper, a direct forcing/fictitious domain (DF/FD) level set method is proposed to simulate the FSI (fluid-solid interaction) in two-phase flow. The main idea is to combine the direct-forcing/fictitious domain (DF/FD) method with the level set method in the Cartesian coordinates. The DF/FD method is a non-Lagrange-multiplier version of a distributed Lagrange multiplier/fictitious domain (DLM/FD) method. This method does not sacrifice the accuracy and robustness by employing a discrete ${\delta}$ (Dirac delta) function to transfer quantities between the Eulerian nodes and Lagrangian points explicitly as the immersed boundary method. The advantages of this approach are the simple concept, easy implementation, and utilization of the original governing equation without modification. Simulations of various water-entry problems have been conducted to validate the capability and accuracy of the present method in solving the FSI in two-phase flow. Consequently, the present results are found to be in good agreement with those of previous studies.

SMALL AMPLITUDE WAVE IN SHALLOW WATER OVER LINEAR AND QUADRATIC SLOPING BEDS

  • Bhatta, Dambaru D.;Debnath, Lokenath
    • Journal of applied mathematics & informatics
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    • v.13 no.1_2
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    • pp.53-65
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    • 2003
  • Here we present a study of small-amplitude, shallow water waves on sloping beds. The beds considered in this analysis are linear and quadratic in nature. First we start with stating the relevant governing equations and boundary conditions for the theory of water waves. Once the complete prescription of the water-wave problem is available based on some assumptions (like inviscid, irrotational flow), we normalize it by introducing a suitable set of non-dimensional variables and then we scale the variables with respect to the amplitude parameter. This helps us to characterize the various types of approximation. In the process, a summary of equations that represent different approximations of the water-wave problem is stated. All the relevant equations are presented in rectangular Cartesian coordinates. Then we derive the equations and boundary conditions for small-amplitude and shallow water waves. Two specific types of bed are considered for our calculations. One is a bed with constant slope and the other bed has a quadratic form of surface. These are solved by using separation of variables method.

Analysis of Flows in the Combustor with Recirculating Flow Regime (재순환영역을 가지는 연소기내의 연소유동해석)

  • 신동신;허남건
    • Journal of the Korean Society of Propulsion Engineers
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    • v.1 no.2
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    • pp.22-31
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    • 1997
  • We developed a general purpose program for the analysis of flows in the combustor with recirculating flow regime and simulated the flows. The program uses non-staggered grids based on finite volume method and the primitive variables are cartesian velocities. The combustion model is irreversible one step reaction with infinite chemistry The Favre averaged governing equations are considered and the clipped gaussian distribution is considered as a probability density function of the conserved scalar. We calculated turbulent diffusion flame with recirculating flow regime. Simulation shows two recirculating regions like experimental results. Velocity, turbulent kinetic energy, temperature and concentration distribution in simulation agree well with experimental data.

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