• Title, Summary, Keyword: steep potential well

Search Result 9, Processing Time 0.047 seconds

EXISTENCE AND CONCENTRATION RESULTS FOR KIRCHHOFF-TYPE SCHRÖ DINGER SYSTEMS WITH STEEP POTENTIAL WELL

  • Lu, Dengfeng
    • Bulletin of the Korean Mathematical Society
    • /
    • v.52 no.2
    • /
    • pp.661-677
    • /
    • 2015
  • In this paper, we consider the following Kirchhoff-type Schr$\ddot{o}$dinger system $$\{-\(a_1+b_1{\int}_{\mathbb{R^3}}{\mid}{\nabla}u{\mid}^2dx\){\Delta}u+{\gamma}V(x)u=\frac{2{\alpha}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha-2}u{\mid}v{\mid}^{\beta}\;in\;\mathbb{R}^3,\\-\(a_2+b_2{\int}_{\mathbb{R^3}}{\mid}{\nabla}v{\mid}^2dx\){\Delta}v+{\gamma}W(x)v=\frac{2{\beta}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha}{\mid}v{\mid}^{\beta-2}v\;in\;\mathbb{R}^3,\\u,v{\in}H^1(\mathbb{R}^3),$$ where $a_i$ and $b_i$ are positive constants for i = 1, 2, ${\gamma}$ > 0 is a parameter, V (x) and W(x) are nonnegative continuous potential functions. By applying the Nehari manifold method and the concentration-compactness principle, we obtain the existence and concentration of ground state solutions when the parameter ${\gamma}$ is sufficiently large.

Comparison of Intelligent Charging Algorithms for Electric Vehicles to Reduce Peak Load and Demand Variability in a Distribution Grid

  • Mets, Kevin;D'hulst, Reinhilde;Develder, Chris
    • Journal of Communications and Networks
    • /
    • v.14 no.6
    • /
    • pp.672-681
    • /
    • 2012
  • A potential breakthrough of the electrification of the vehicle fleet will incur a steep rise in the load on the electrical power grid. To avoid huge grid investments, coordinated charging of those vehicles is a must. In this paper, we assess algorithms to schedule charging of plug-in (hybrid) electric vehicles as to minimize the additional peak load they might cause. We first introduce two approaches, one based on a classical optimization approach using quadratic programming, and a second one, market based coordination, which is a multi-agent system that uses bidding on a virtual market to reach an equilibrium price that matches demand and supply. We benchmark these two methods against each other, as well as to a baseline scenario of uncontrolled charging. Our simulation results covering a residential area with 63 households show that controlled charging reduces peak load, load variability, and deviations from the nominal grid voltage.

An Ecological Study on the Flora of Bijin Island (비진도 식물상에 관한 생태학적 연구)

  • Kim, Chang Ho;Kwang Seung Lee;Kyu Ha Park
    • The Korean Journal of Ecology
    • /
    • v.5 no.4
    • /
    • pp.164-175
    • /
    • 1982
  • This paper contains the results obtained by the ecological investigation in Bijin island. The investigation was conducted during 3 dyas from Aug. 3 to Aug. 5, 1981. The results are followings. The tracheophyta of this island was recoreded as 64 families, 128 genera, 142 species, 21 varieties and 2 forma. Twenty eight species of ever-green broad-leaved trees comprising Gardenia jasminoides for. grandiflora, Castanopsis cuspidata var. thunbergii, Camellia japonica, etc. wad distributed in the southern area of the island. And there was the wind-break forest mainly consisting of aged Machilus thunbergii, Celtis sinensis and Zelkova serrata in the northern area. The northern area dominated by the second forest of Pinus thunbergii, where the whole residents lead their lives, shows the high population density and pure farming rate, so the natural degree is low. The other hand, there was the well-preserved forest of broad-leaved trees containing Zelkoba serrata. Acer palmatum and Quercus serrata, etc. in southern area having a steep peak, Seonyudai, and no resident. So, the potential vegetation of this island is assumed as the forest of ever-green broad-leaved trees which belongs to the forest of subtropics.

  • PDF

Entertainment Agencies' Role in the Development of the Drama Production Industry (연예기획사가 드라마제작산업 발전에 미친 영향)

  • Rho, Dong-Ryul
    • The Journal of the Korea Contents Association
    • /
    • v.16 no.6
    • /
    • pp.82-93
    • /
    • 2016
  • The latest development of the Korean drama production industry has been accompanied by the steep rise in the number of players and the contraction of the advertizing market, which have combined to intensify the competition severely. Then, China happened. Entertainment agencies' logical strategic choice to maximize production revenue potential was to secure A-list actors who can sell, pushing up their prices, that process has continued to even compromise the health of the production industry as well as the agencies' financial integrity. The drama production industry, including entertainment agencies, should shift the strategic focus from simple production revenue generation to profit maximization through diversifying revenue sources like securing IP rights.

Mach Reflection of Sinusoidally- Modulated Nonlinear Stokes Waves by a Thin Wedge (쐐기에 의한 비선형파의 마하반사)

  • Hang-S. Choi;Won-S. Chee
    • Journal of the Society of Naval Architects of Korea
    • /
    • v.28 no.1
    • /
    • pp.53-59
    • /
    • 1991
  • By employing multiple-scale expansion techniques, the diffraction of sinusoidally-modulated nonlinear Stokes waves by a stationary thin wedge has been studied within the framework of potential theory. It is found that the evolution of diffracted waves can be described by the Zakharov equation to the leading order and it can be replaced by the cubic $Schr\ddot{o}dinger$ equation with an additional linear term for stable modulations. Computations are made for the cubic $Schr\ddot{o}dinger$ equation with different values of nonlinear and dispersion parameters. Numerical results well reflect the experimental findings in the amplitude and width of generated stem waves. It is numerically confirmed that the nonlinearity dominates the wave field, while the dispersion hardly affects the wave evolution, and stem waves are likely to be formed for steep incident waves in the case of stable sinusoidal modulations.

  • PDF

Two Layer Modelling with Applications to Exchange Flow and Internal Tide (이층류 모델링의 교환류와 내부조석파 연구에의 적용)

  • Kang, Sok-Kuh;Abbott, Michael-B.;Heung, Jae-Lie;Yum, Ki-Dai
    • Journal of Korean Society of Coastal and Ocean Engineers
    • /
    • v.9 no.1
    • /
    • pp.9-23
    • /
    • 1997
  • A numerical study of a two-layer, stratified flow is investigated, using the implicit finite difference method in one dimension. The results of computational method have been tested and, in case of lock exchange flow, compared with the results of experimental data. The results of model experiments with various interfacial, bottom friction coefficients along with various time weighting factor of numerical scheme and dissipative interface are shown and discussed. Two-layer model experiment has been also carried out to investigate the generation and propagation characteristics of internal tidal wave over the steep bottom topography under stratified condition. The internal wave seems to well radiate through the downstream boundary under the experiments adopting radiation conditions both at two layers and only at upper layer, confirming the applicability of radiational boundary condition in stratified flows. It is also shown that the internal wave through the downstream boundary propagates more actively with increasing thickness of lower layer in the downstream. This implies that the potential tidal energy in the interface will depend upon the thickness of lower layer for the constant thickness of upper layer.

  • PDF

APPLICATION OF HF COASTAL OCEAN RADAR TO TSUNAMI OBSERVATIONS

  • Heron, Mal;Prytz, Arnstein;Heron, Scott;Helzel, Thomas;Schlick, Thomas;Greenslade, Diana;Schulz, Eric
    • Proceedings of the KSRS Conference
    • /
    • v.1
    • /
    • pp.34-37
    • /
    • 2006
  • When tsunami waves propagate across open ocean they are steered by Coriolis force and refraction due to gentle gradients in the bathymetry on scales longer than the wavelength. When the wave encounters steep gradients at the edges of continental shelves and at the coast, the wave becomes non-linear and conservation of momentum produces squirts of surface current at the head of submerged canyons and in coastal bays. HF coastal ocean radar is well-conditioned to observe the current bursts at the edge of the continental shelf and give a warning of 40 minutes to 2 hours when the shelf is 50-200km wide. The period of tsunami waves is invariant over changes in bathymetry and is in the range 2-30 minutes. Wavelengths for tsunamis (in 500-3000 m depth) are in the range 8.5 to over 200 km and on a shelf where the depth is about 50 m (as in the Great Barrier Reef) the wavelengths are in the range 2.5 - 30 km. It is shown that the phased array HF ocean surface radar being deployed in the Great Barrier Reef (GBR) and operating in a routine way for mapping surface currents, can resolve surface current squirts from tsunamis in the wave period range 20-30 minutes and in the wavelength range greater than about 6 km. There is a trade-off between resolution of surface current speed and time resolution. If the radar is actively managed with automatic intervention during a tsunami alert period (triggered from the global seismic network) then it is estimated that the time resolution of the GBR radar may be reduced to about 2 minutes, which corresponds to a capability to detect tsunamis at the shelf edge in the period range 5-30 minutes. It is estimated that the lower limit of squirt velocity detection at the shelf edge would correspond to a tsunami with water elevation of less than 5 cm in the open ocean. This means that the GBR HF radar is well-conditioned for use as a monitor of small and medium scale tsunamis, and has the potential to contribute to the understanding of tsunami genesis research.

  • PDF

Estimating of the Greenhouse Gas Mitigation and Function of Water Resources Conservation through Conservation of Surface Soils Erosion and Policy Suggestion (표토유실 보전을 통한 온실가스배출 저감과 수자원 보전 기능의 산출 및 정책제안)

  • Oh, Seung-Min;Kim, Hyuck Soo;Lee, Sang-Pil;Lee, Jong Geon;Jeong, Seok Soon;Lim, Kyung Jae;Kim, Sung-Chul;Park, Youn Shik;Lee, Giha;Hwang, Sang-Il;Yang, Jae-E
    • Journal of Soil and Groundwater Environment
    • /
    • v.22 no.6
    • /
    • pp.74-84
    • /
    • 2017
  • Soil erosion is often extreme in Korea due to high rainfall intensities and steep slopes, and climate change has also increased the risk of erosion. Despite its significane, erosion-induced soil organic carbon (SOC) emission and water resource loss are not well understood, along with the lack of an integrated surface soil erosion protection policy. Therefore, to design adequate protection policies, land users, scientists, engineers and decision makers need proper information about surface soil and watershed properties related to greenhouse gas emission potential and water conservation capability, respectively. Assuming the total soil erosion of $346Tg\;yr^{-1}$, soil organic matter (SOM) content of 2% (58% of SOM is SOC), and mineralization rate of 20% of the displaced carbon, erosion-induced carbon emission could reach $800Gg\;C\;yr^{-1}$. Also the available water capacity of the soil was estimated to be 15.8 billion tons, which was 14 times higher than the yearly water supply demand in Seoul, Korea. Therefore, in order to prevent of soil erosion, this study proposes a three-stage plan for surface soil erosion prevention: 1) classification of soil erosion risk and scoring of surface soil quality, 2) selection of priority areas for conservation and best management practices (BMP), and 3) application of BMP and post management.

Interaction between Raindrops Splash and Sheet Flow in Interrill Erosion of Steep Hillslopes (급경사면의 세류간 침식에서 빗물튀김과 면상흐름의 상호작용)

  • Nam, Myeong Jun;Park, Sang Deog;Lee, Seung Kyu;Shin, Seung Sook
    • Journal of Korea Water Resources Association
    • /
    • v.48 no.7
    • /
    • pp.595-604
    • /
    • 2015
  • Interrill erosion by the rainfall is divided into a detachment of soil particles by raindrop splash when raindrops having kinetic energy strike on the surface soil and a sediment transport by sheet flow of surface runoff. Rainfall kinetic energy is widely used as an indicator expressing the potential ability to separate the soil particles from soil mass. In this study, the soil erosion experiments of rainfall simulation were operated to evaluate the effects of rainfall kinetic energy on interrill erosion as using the strip cover to control raindrop impact. The kinetic energy from rainfall simulator was 0.58 times to that of natural rainfall. Surface runoff and subsurface runoff increased and decreased respectively with increase of rainfall intensity. Surface runoff discharge from plots of non-cover was 1.82 times more than that from plots with cover. The rainfall kinetic energy influenced on the starting time of surface and subsurface runoff. Soil erosion quantity greatly varied according to existence of the surface cover that can intercept rainfall energy. Sediment yields by the interaction between raindrop splash and sheet flow increased 3.6~5.9 times and the increase rates of those decreased with rainfall intensity. As a results from analysis of relationship between stream power and sediment yields, rainfall kinetic energy increased the transport capacity according to increase of surface runoff as well as the detachment of soil particles by raindrop splash.