• Title/Summary/Keyword: upper solutions

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Upper and Lower Bound Solutions for Pile-Soil-Tunnel Interaction (한계해석법에 의한 파일-지반-터널 상호작용 해석)

  • Lee Yong-Joo;Shin Jong-Ho
    • 한국터널공학회:학술대회논문집
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    • 2005.04a
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    • pp.77-86
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    • 2005
  • In urban areas, new tunnel construction work is often taking place adjacent to existing piled foundations. In this case, careful assessment for the pile-soil-tunnel interaction is required. However, research on this topic has not been much reported, and currently only limited information is available. In this study, the complex pile-soil-tunnel interaction is investigated using the upper and lower bound methods based on kinematically possible failure mechanism and statically admissible stress field respectively. It is believed that the limit theorem is useful in understanding the complicated interaction behaviour mechanism and applicable to the pile-soil-tunnel interaction problem. The results are compared with numerical analysis. The material deformation patterns and strain data from the FE output are shown to compare well with the equivalent physical model tests. Admissible stress fields and the failure mechanisms are presented and used to develop upper and lower bound solutions to assess minimum support pressures within the tunnel.

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UNIQUENESS OF POSITIVE STEADY STATES FOR WEAK COMPETITION MODELS WITH SELF-CROSS DIFFUSIONS

  • Ko, Won-Lyul;Ahn, In-Kyung
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.2
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    • pp.371-385
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    • 2004
  • In this paper, we investigate the uniqueness of positive solutions to weak competition models with self-cross diffusion rates under homogeneous Dirichlet boundary conditions. The methods employed are upper-lower solution technique and the variational characterization of eigenvalues.

EXISTENCE AND UNIQUENESS OF A SOLUTION FOR FIRST ORDER NONLINEAR LIOUVILLE-CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS

  • Nanware, J.A.;Gadsing, Madhuri N.
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.5
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    • pp.1011-1020
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    • 2021
  • In this paper, first order nonlinear Liouville-Caputo fractional differential equations is studied. The existence and uniqueness of a solution are investigated by using Krasnoselskii and Banach fixed point theorems and the method of lower and upper solutions. Finally, an example is given to illustrate our results.

NUMERICAL ANALYSIS OF THERMAL STRATIFICATION IN THE UPPER PLENUM OF THE MONJU FAST REACTOR

  • Choi, Seok-Ki;Lee, Tae-Ho;Kim, Yeong-Il;Hahn, Dohee
    • Nuclear Engineering and Technology
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    • v.45 no.2
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    • pp.191-202
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    • 2013
  • A numerical analysis of thermal stratification in the upper plenum of the MONJU fast breeder reactor was performed. Calculations were performed for a 1/6 simplified model of the MONJU reactor using the commercial code, CFX-13. To better resolve the geometrically complex upper core structure of the MONJU reactor, the porous media approach was adopted for the simulation. First, a steady state solution was obtained and the transient solutions were then obtained for the turbine trip test conducted in December 1995. The time dependent inlet conditions for the mass flow rate and temperature were provided by JAEA. Good agreement with the experimental data was observed for steady state solution. The numerical solution of the transient analysis shows the formation of thermal stratification within the upper plenum of the reactor vessel during the turbine trip test. The temporal variations of temperature were predicted accurately by the present method in the initial rapid coastdown period (~300 seconds). However, transient numerical solutions show a faster thermal mixing than that observed in the experiment after the initial coastdown period. A nearly homogenization of the temperature field in the upper plenum is predicted after about 900 seconds, which is a much shorter-term thermal stratification than the experimental data indicates. This discrepancy may be due to the shortcoming of the turbulence models available in the CFX-13 code for a natural convection flow with thermal stratification.

HIGHER ORDER NONLOCAL NONLINEAR BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

  • Khan, Rahmat Ali
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.2
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    • pp.329-338
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    • 2014
  • In this paper, we study the method of upper and lower solutions and develop the generalized quasilinearization technique for the existence and approximation of solutions to some three-point nonlocal boundary value problems associated with higher order fractional differential equations of the type $$^c{\mathcal{D}}^q_{0+}u(t)+f(t,u(t))=0,\;t{\in}(0,1)$$ $$u^{\prime}(0)={\gamma}u^{\prime}({\eta}),\;u^{\prime\prime}(0)=0,\;u^{\prime\prime\prime}(0)=0,{\ldots},u^{(n-1)}(0)=0,\;u(1)={\delta}u({\eta})$$, where, n-1 < q < n, $n({\geq}3){\in}\mathbb{N}$, 0 < ${\eta},{\gamma},{\delta}$ < 1 and $^c\mathcal{D}^q_{0+}$ is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.

MIXED BOUNDARY VALUE PROBLEMS FOR SECOND ORDER DIFFERENTIAL EQUATIONS WITH DIFFERENT DEVIATED ARGUMENTS

  • Zhang, Lihong;Wang, Guotao;Song, Guangxing
    • Journal of applied mathematics & informatics
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    • v.29 no.1_2
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    • pp.191-200
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    • 2011
  • This paper deals with second order differential equations with different deviated arguments ${\alpha}$(t) and ${\beta}$(t, ${\mu}$(t)). We investigate the existence of solutions of such problems with nonlinear mixed boundary conditions. To obtain corresponding results we apply the monotone iterative technique and the lower-upper solutions method. Two examples demonstrate the application of our results.

Analysis of Attenuation Poles using Closed-form Solutions for Bandpass Filters

  • Shin, Yoon-mi;Lee, Bom-Son
    • Journal of electromagnetic engineering and science
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    • v.1 no.2
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    • pp.156-160
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    • 2001
  • Very convenient equivalent circuits fur the design of bandpass filters with an attenuation pole in the lower or upper stopband are provided together with necessary closed-form solutions. The proposed approach gives us much flexibility and simplifies the design of inserting attenuation poles.

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Pseudostatic analysis of bearing capacity of embedded strip footings in rock masses using the upper bound method

  • Saeed Shamloo;Meysam Imani
    • Geomechanics and Engineering
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    • v.34 no.4
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    • pp.381-396
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    • 2023
  • The present paper evaluates seismic bearing capacity of rock masses subjected to loads of strip footings using the upper bound method. A general formula was proposed to evaluate the seismic bearing capacity considering both the horizontal and vertical accelerations of the earthquake and the effects of footing embedment depth simultaneously. Modified Hoek-Brown failure criterion was employed for the rock mass. Some comparisons were made with the available solutions and the finite element numerical models to show the accuracy of the developed upper bound formulations. The obtained results show significant improvement compared to the other available solutions. By increasing the horizontal earthquake acceleration from 0.1 to 0.3, the bearing capacity was reduced by up to 39%, while the effect of the vertical earthquake acceleration depends on its direction. An upward acceleration in the range of zero to 0.2 results in an increase in the bearing capacity by up to 24%, while the downward earthquake acceleration has an adverse effect. Also, by increasing the embedment depth of the footing from zero to 5 times the footing width, the value of seismic bearing capacity was raised about 86%. The obtained results were presented as design tables for use in practical applications.

WAVEFRONT SOLUTIONS IN THE DIFFUSIVE NICHOLSON'S BLOWFLIES EQUATION WITH NONLOCAL DELAY

  • Zhang, Cun-Hua
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.49-58
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    • 2010
  • In the present article we consider the diffusive Nicholson's blowflies equation with nonlocal delay incorporated into an integral convolution over all the past time and the whole infinite spatial domain $\mathbb{R}$. When the kernel function takes a special function, we construct a pair of lower and upper solutions of the corresponding travelling wave equation and obtain the existence of travelling fronts according to the existence result of travelling wave front solutions for reaction diffusion systems with nonlocal delays developed by Wang, Li and Ruan (J. Differential Equations, 222(2006), 185-232).