• Communications of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.631-634
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.5
• /
• pp.1167-1176
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.255-277
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.57 no.6
• /
• pp.1435-1449
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.253-292
• /
• 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
• /
• v.58 no.3
• /
• pp.559-571
• /
• 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
• /
• v.3 no.1
• /
• pp.1-12
• /
• 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.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.21 no.1
• /
• pp.43-50
• /
• 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.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• v.y2005m4
• /
• pp.269-273
• /
• 2005

A practical, 30-tonf-class fullscale thrust chamber has been combustion tested using real propellants for the first time in the domestic technology scene. The very first combustion test was conducted at a low mass flow rate condition for the preliminary assessment of any problems associated with its function and performance while reducing risks from a high chamber pressure never achieved before. A test for the design condition achieved through a low-pressure stage shows stable characteristics of all the static pressures and thrust. Dynamic pressures measured in the manifolds and the chamber did not reveal any distinct wave coupled to a specific frequency and their intensities reside in the allowable range. Moreover, it is encouraging to find no physical failures with a thrust chamber hardware.