• 제목/요약/키워드: Differential Geometry

검색결과 189건 처리시간 0.023초

Numerical and experimental simulation of the wind field in the EXPO '98 area

  • Ferreira, A.D.;Sousa, A.C.M.;Viegas, D.X.
    • Wind and Structures
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    • 제1권4호
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    • pp.337-349
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    • 1998
  • A numerical and experimental study was performed for the wind flow field in one area, comprising a group of several pavilions separated by passageways, of the EXPO '98 - a World Exposition (Lisbon, Portugal). The focus of this study is the characterization of the flow field to assess pedestrian comfort. The predictions were obtained employing the Reynolds averaged Navier-Stokes equations with the turbulence effects dealt with the ${\kappa}-{\varepsilon}$ RNG model. The discretization of the differential equations was accomplished with the control volume formulation in a Cartesian coordinate system, and an advanced segregated procedure was used to achieve the link between continuity and momentum equations. The evaluation of the overall numerical model was performed by comparing its predictions against experimental data for a square cylinder placed in a channel. The predicted values, for the practical geometry studied, are in a good agreement with the experimental data, showing the performance and the reliability of the ${\kappa}-{\varepsilon}$ RNG model and suggesting that the numerical simulation is a reliable methodology to provide the required information.

Effects of plasmaspheric density structure on the characteristics of geomagnetic ULF pulsations

  • 최지원;이동훈;김관혁;이은상
    • 천문학회보
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    • 제37권2호
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    • pp.116.2-116.2
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    • 2012
  • The structure of plasmasphere plays an important role in determining properties of geomagnetic ULF pulsations such as Pi 2 pulsations and field line resonances (FLRs) in the Earth's magnetosphere. We have performed a 3-D MHD wave simulation to investigate the generation and propagation of ULF waves in dipole geometry. Various 3-D density structures are assumed, which include a relatively sharp density gradient and gradually less slopes at the plasmapause. The former condition can refer to the plasmasphere from local midnight to dawn, whereas the latter represents the region near noon to dusk where it bulges out. We show how Pi 2 pulsations and FLRs differentially appear at both multi-point satellite locations and ground stations for different local times. Our results suggest that 1) the local radial density structure significantly affects the peak frequencies for Pi 2 oscillations, while the polarization changes remain similar in the radial direction, and 2) the radial location of strong FLRs varies for different density profiles. It is also suggested how multi satellite measurements and ground-based observations can confirm this differential feature in space.

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DEM generation from an IKONOS stereo pair using EpiMatch and Graph-Cut algorithms

  • Kim, Tae-Jung;Im, Yong-Jo;Kim, Ho-Won;Kweon, In-So
    • 대한원격탐사학회:학술대회논문집
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    • 대한원격탐사학회 2002년도 Proceedings of International Symposium on Remote Sensing
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    • pp.524-529
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    • 2002
  • In this paper, we report the development of two DEM (digital elevation model) generation algorithms over urban areas from an IKONOS stereo pair. One ("EpiMatch") is originally developed for SPOT images and modified for IKONOS images. It uses epipolar geometry for accurate DEM generation. The other is based on graph-cut algorithm in 3D voxel space. This algorithm is believed to work better on height discontinuities than EpiMatch. An IKONOS image pair over Taejon city area was used for tests. Using ground control points obtained from differential GPS, camera model was set up and stereo matching applied. As a result, two DEMs over urban areas were produced. Within a DEM from EpiMatch small houses appear as small "cloudy" patches and large apartment and industrial buildings are visually identifiable. Within the DEM from graph-cut we could achieve better height information on building boundaries. The results show that both algorithms can generate DEMs from IKONOS images although more research is required on handling height discontinuities (for "EpiMatch") and on faster computation (for "Graph-cut").

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Equilibrium Geometries of the Neutral and Ionic Clusters of $Ag_7$, $Ag_8$, and $Ag_9$ Studied by Intermediate Neglect of Differential Overlap Method

  • 유창현;선호성
    • Bulletin of the Korean Chemical Society
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    • 제21권10호
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    • pp.953-954
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    • 2000
  • The equilibrium geometrical structures of silver atom clusters at their electronic ground states have been theo-retically determined by using the nonrelativistic semiempirical INDO/1 method. The clusters investigated are Agn, Agn+, and Agn- (n = 7 , 8, 9). In order to find the most stable structure, i.e., the global minimum in energy hypersurface, geometry optimization and energy calculation processes have been repeatedly performed for all the possible graphical models by changing the bond parameters (resonance integral values). The heptamers are pentagonal bipyramidal-Ag7(D5h), Ag7+ (D5h), Ag7- (D5h); the octamers are pentagonal bipyramidal with one atom capped-Ag8(D2d), Ag8+ (Cs), Ag8- (D2d); the nonamers are pentagonal bipyramidal with two atoms capped -Ag9(C2v), Ag9+ (C2v), Ag9- (C2v). Our structures are in good agreement with those by ab initio calculations ex-cept for the anionic Ag9- cluster. And it is noted that the INDO/1 method can accurately predict the Ag cluster geometries when a proper set of bond parameters is used.

Flapwise and non-local bending vibration of the rotating beams

  • Mohammadnejad, Mehrdad;Saffari, Hamed
    • Structural Engineering and Mechanics
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    • 제72권2호
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    • pp.229-244
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    • 2019
  • Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

An analytical solution to the mapping relationship between bridge structures vertical deformation and rail deformation of high-speed railway

  • Feng, Yulin;Jiang, Lizhong;Zhou, Wangbao;Lai, Zhipeng;Chai, Xilin
    • Steel and Composite Structures
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    • 제33권2호
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    • pp.209-224
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    • 2019
  • This paper describes a study of the mapping relationship between the vertical deformation of bridge structures and rail deformation of high-speed railway, taking the interlayer interactions of the bridge subgrade CRTS II ballastless slab track system (HSRBST) into account. The differential equations and natural boundary conditions of the mapping relationship between the vertical deformation of bridge structures and rail deformation were deduced according to the principle of stationary potential energy. Then an analytical model for such relationship was proposed. Both the analytical method proposed in this paper and the finite element numerical method were used to calculate the rail deformations under three typical deformations of bridge structures and the evolution of rail geometry under these circumstances was analyzed. It was shown that numerical and analytical calculation results are well agreed with each other, demonstrating the effectiveness of the analytical model proposed in this paper. The mapping coefficient between bridge structure deformation and rail deformation showed a nonlinear increase with increasing amplitude of the bridge structure deformation. The rail deformation showed an obvious "following feature"; with the increase of bridge span and fastener stiffness, the curve of rail deformation became gentler, the track irregularity wavelength became longer, and the performance of the rail at following the bridge structure deformation was stronger.

Analytical and multicoupled methods for optimal steady-state thermoelectric solutions

  • Moreno-Navarro, Pablo;Perez-Aparicio, Jose L.;Gomez-Hernandez, J.J.
    • Coupled systems mechanics
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    • 제11권2호
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    • pp.151-166
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    • 2022
  • Peltier cells have low efficiency, but they are becoming attractive alternatives for affordable and environmentally clean cooling. In this line, the current article develops closed-form and semianalytical solutions to improve the temperature distribution of Bi2Te3 thermoelements. From the distribution, the main objective of the current work-the optimal electric intensity to maximize cooling-is inferred. The general one-dimensional differential coupled equation is integrated for linear and quadratic geometry of thermoelements, under temperature constant properties. For a general shape, a piece-wise solution based on heat flux continuity among virtual layers gives accurate analytical solutions. For variable properties, another piece-wise solution is developed but solved iteratively. Taking advantage of the formulae, the optimal intensity is directly derived with a minimal computational cost; its value will be of utility for more advanced designs. Finally, a parametric study including straight, two linear, barrel, hourglass and vase geometries is presented, drawing conclusions on how the shape of the thermoelement affects the coupled phenomena. A specially developed coupled and non-linear finite element research code is run taking into account all the materials of the cell and using symmetries and repetitions. These accurate results are used to validate the analytical ones.

A semi-analytical procedure for cross section effect on the buckling and dynamic stability of composite imperfect truncated conical microbeam

  • Zhang, Peng;Gao, Yanan;Moradi, Zohre;Ali, Yasar Ameer;Khadimallah, Mohamed Amine
    • Steel and Composite Structures
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    • 제44권3호
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    • pp.371-388
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    • 2022
  • The present study tackles the problem of forced vibration of imperfect axially functionally graded shell structure with truncated conical geometry. The linear and nonlinear large-deflection of the structure are considered in the mathematical formulation using von-Kármán models. Modified coupled stress method and principle of minimum virtual work are employed in the modeling to obtain the final governing equations. In addition, formulations of classical elasticity theory are also presented. Different functions, including the linear, convex, and exponential cross-section shapes, are considered in the grading material modeling along the thickness direction. The grading properties of the material are a direct result of the porosity change in the thickness direction. Vibration responses of the structure are calculated using the semi-analytical method of a couple of homotopy perturbation methods (HPM) and the generalized differential quadrature method (GDQM). Contradicting effects of small-scale, porosity, and volume fraction parameters on the nonlinear amplitude, frequency ratio, dynamic deflection, resonance frequency, and natural frequency are observed for shell structure under various boundary conditions.

Physics-informed neural network for 1D Saint-Venant Equations

  • Giang V. Nguyen;Xuan-Hien Le;Sungho Jung;Giha Lee
    • 한국수자원학회:학술대회논문집
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    • 한국수자원학회 2023년도 학술발표회
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    • pp.171-171
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    • 2023
  • This study investigates the capability of Physics-Informed Neural Networks (PINNs) for solving the solution of partial differential equations. Particularly, the 1D Saint-Venant Equations (SVEs) were considered, which describe the movement of water in a domain with shallow depth compared to its horizontal extent, and are widely adopted in hydrodynamics, river, and coastal engineering. The core contribution of this work is to combine the robustness of neural networks with the physical constraints of the SVEs. The PINNs method utilized a neural network to approximate the solutions of SVEs, while also enforcing the underlying physical principles of the equations. This allows for a more effective and reliable solution, especially in areas with complex geometry and varying bathymetry. To validate the robustness of the PINNs method, numerical experiments were conducted on several benchmark problems. The results show that the PINNs could be achieved high accuracy when compared with the solution from the numerical solution. Overall, this study demonstrates the potential of using PINNs and highlights the benefits of integrating neural network and physics information for improved efficiency and accuracy in solving SVEs.

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이산미분기하 기반의 동적 비누막 모델 (Dynamic Soap Film Model based on Discrete Differential Geometry)

  • 박민기;김현수;최한균;이승주;고광희;이관행
    • 한국정보처리학회:학술대회논문집
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    • 한국정보처리학회 2010년도 춘계학술발표대회
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    • pp.523-526
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    • 2010
  • 주어진 경계선에 대해 비누막이 생성하는 표면 모델링 및 시간에 따른 변형 시뮬레이션은 컴퓨터 그래픽스 응용 프로그램의 한 분야이다. 이 문제에 대한 이전의 연구들은 주로 기하적인 방법들을 이용하였기 때문에 물리적으로 정확한 변형을 다루지 못하였다. 본 연구에서는 정확한 기하를 바탕으로 물리기반 변형을 다루기 위해 이산미분기하학으로부터 비누막의 동적인 모델을 제안한다. 우선, 비누 성분의 물리적인 특성들을 고려한 에너지 모델을 정의하고, 이를 이산 영역에서 나타내기 위해 이산미분기하 및 이산화 기법들을 이용한다. 제안하는 모델은 평형 상태에서의 비누막 형상뿐만 아니라 외력에 대한 표면의 변형까지 정확하게 나타내며, 실시간 시뮬레이션이 가능하여 게임, 애니메이션 목적으로 활용될 수 있다.