• 대한수학회논문집
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• 제37권2호
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• pp.631-634
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• 2022

In this short paper, we investigate the existence of non-trivial almost Ricci solitones on static manifolds. As a result we show any compact nontrivial static manifold is isometric to a Euclidean sphere.

• 대한수학회보
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• 제59권5호
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• pp.1167-1176
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• 2022

In this paper, we study Einstein-type manifolds generalizing static spaces and V-static spaces. We prove that if an Einstein-type manifold has non-positive complete divergence of its Weyl tensor and non-negative complete divergence of Bach tensor, then M has harmonic Weyl curvature. Also similar results on an Einstein-type manifold with complete divergence of Riemann tensor are proved.

• 대한수학회지
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• 제61권2호
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• pp.255-277
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• 2024

In this paper, we introduce the notion of stress-energy tensor Q of the traceless Ricci tensor for Riemannian manifolds (Mⁿ, g), and investigate harmonicity of Riemannian curvature tensor and Weyl curvature tensor when (M, g) satisfies some geometric structure such as critical point equation or vacuum static equation for smooth functions.

• 대한수학회지
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• 제57권6호
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• pp.1435-1449
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• 2020

In this article we make a local classification of n-dimensional Riemannian manifolds (M, g) with harmonic curvature and less than four Ricci eigenvalues which admit a smooth non constant solution f to the following equation $$(1)\hspace{20}{\nabla}df=f(r-{\frac{R}{n-1}}g)+x{\cdot} r+y(R)g,$$ where ∇ is the Levi-Civita connection of g, r is the Ricci tensor of g, x is a constant and y(R) a function of the scalar curvature R. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, either (i) or (ii) below holds; (i) (V, g, f + x) is a static space and isometric to a domain in the Riemannian product of an Einstein manifold N and a static space (W, gW, f + x), where gW is a warped product metric of an interval and an Einstein manifold. (ii) (V, g) is isometric to a domain in the warped product of an interval and an Einstein manifold. For the proof we use eigenvalue analysis based on the Codazzi tensor properties of the Ricci tensor.

• 대한수학회지
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• 제55권2호
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• pp.253-292
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• 2018

In this paper, we introduce a general Ricci flow system, which is closely linked with the Ricci flow and the renormalization group flow, etc. We prove the short-time existence, the entropy functionals, the higher derivatives estimates and the compactness theorem for this general Ricci flow system on closed Riemannian manifolds. These basic results are useful tools to understand the singularities of this system.

• Kyungpook Mathematical Journal
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• 제58권3호
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• pp.559-571
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• 2018

In this paper, we give some results on the stability of f-harmonic maps with potential from or into spheres and any Riemannian manifold. We study the constant boundary-value problems of such maps defined on a specific Cartan-Hadamard manifolds, and obtain a Liouville-type theorem. It can also be applied to the static Landau-Lifshitz equations. We also prove a Liouville theorem for f-harmonic maps with finite f-energy or slowly divergent f-energy.

• International Journal of Advanced Culture Technology
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• 제3권1호
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• pp.1-12
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• 2015

The current scenario of the transportation sector reflects the urgent need to address issues such as depletion of traditional fuel reserves and ever growing pollution levels. Researchers around the world are focussing on alternatives as well as optimisation of currently employed devices to reduce the pollution levels generated by the commonly used fuels. One such optimisation involves the study of air flow within the intake manifolds of SI engines. It is a well-known fact that alterations in the air manifolds of engines have a significant impact on the engine performance parameters, fuel consumption and emission levels. Previous works have demonstrated the impacts of runner lengths, diameter, plenum volume, taper angle of distribution manifolds and other factors on in-cylinder fluid motion and engine performance. However, a static setup provides an optimal configuration only at a specific engine speed. This paper aims to investigate the variations in the same parameters on a four stroke, naturally aspirated single cylinder SI engine through varying the cross section design over the intake runner with the aid of Computational Fluid Dynamics. The system consists of segments that form the intake runner with projections on the inside that allow various permutations of the intake runner segments. The various configurations provide the optimised fluid flow characteristics within the intake manifold at specific engine speed intervals. The variations such as turbulence, air fuel mixing are analysed using the three dimensional CFD software FLUENT. The results can be used further for developing an automated or manually adjustable intake manifold.

• 한국자동차공학회논문집
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• 제21권1호
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• pp.43-50
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• 2013

The stringent emission regulation and future shortage of fossil fuel motivate the research of alternative powertrain. In this study, a system of proton exchange membrane fuel cell has been modeled to analyze the performance of the fuel cell system for automotive application. The model is composed of the fuel cell stack, air compressor, humidifier, and intercooler, and hydrogen supply which are implemented by using the Matlab/Simulink(R). Fuel cell stack model is empirical model but the water transport model is included so that the system performance can be predicted over various humidity conditions. On the other hand, the model of air compressor is composed of motor, static air compressor, and some manifolds so that the motor dynamics and manifold dynamics can be investigated. Since the model is concentrated on the strategic operation of compressor to reduce the power consumption, other balance of components (BOP) are modeled to be static components. Since the air compressor model is empirical model which is based on curve fitting of experiments, the stack model is validated with the commercial software and the experiments. The dynamics of air compressor is investigated over unit change of system load. The results shows that the power consumption of air compressor is about 12% to 25% of stack gross power and dynamic response should be reduced to optimize the system operation.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2005년도 제24회 춘계학술대회논문집
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• pp.269-273
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• 2005

실용형이라 할 수 있는 30 tonf급의 연소기가 설계/제작되어 연소 시험을 마쳤다. 첫 연소 시험은 연소기의 기능 점검을 위해 저유량 공급을 통한 저압 조건에서 이루어졌다. 설계 연소 조건은 저압 단계를 거쳐 도달하였으며, 모든 압력 및 추력 형성이 정상적으로 이루어졌다. 연소실 및 매니폴드에서 측정된 동압 또한 특별한 주파수 대역을 보이지 않으면서 안정적인 연소 특성을 보였으며 동압 섭동 세기가 허용 수준이내에서 발생하였다. 수회의 연소 시험 결과, 연소기의 물리적 손상은 발생하지 않았으며, 만족할 만한 기능적 특성을 나타내었다.