• Journal of Mechanical Science and Technology
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• 제15권9호
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• pp.1339-1345
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• 2001

Laminar film condensation of a saturated pure vapor in forced flow over a flat plate is analyzed as boundary layer solutions. Similarity solutions for some real fluids are presented as a function of modified Jakob number (C$\_$pι/ ΔΤ/Prh$\_$fg/) with property ratio (No Abstract.see full/text) and Pγ as parameters and compared with approximate solutions which were obtained from energy and momentum equations without convection and inertia terms in liquid flow. Approximate solutions agree well with the similarity solutions when the values of modified Jakob number are less then 0.1 near 1 atmospheric pressure.

• Korean Journal of Mathematics
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• 제23권2호
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• pp.269-282
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• 2015

In this paper, we investigate bounds for solutions of perturbed functional differential systems using the notion of $t_{\infty}$-similarity.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권3호
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• pp.215-227
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• 2015

In this paper, we investigate bounds for solutions of nonlinear functional differential systems using the notion of t_∞-similarity.

• Geomechanics and Engineering
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• 제13권4호
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• pp.585-600
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• 2017

This study deals with simple solutions for a spherical or circular opening excavated in elastic-brittle plastic rock mass compatible with a linear Mohr-Coulomb (M-C) or a nonlinear Hoek-Brown (H-B) yield criterion. Based on total strain approach, the closed-form solutions of stresses and displacement are derived simultaneously for circular and spherical openings using original H-B and M-C yield criteria. Two simple numerical procedures are proposed for the solution of generalized H-B and M-C yield criteria. Based on incremental approach, the similarity solution is derived for circular and spherical openings using generalized H-B and M-C yield criteria. The classical Runge-Kutta method is used to integrate the first-order ordinary differential equations. Using three data sets for M-C and H-B models, the results of the radial displacements, the spreading of the plastic radius with decreasing pressure, and the radial and circumferential stresses in the plastic region are compared. Excellent agreement among the solutions is obtained for all cases of spherical and circular openings. The importance of the use of proper initial values in the similarity solution is discussed.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.631-642
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• 2013

In this paper we reconsider the problem of steady mixed convection boundary-layer flow over a vertical flat plate studied in [6],[7] and [13]. Under favorable assumptions, we prove existence of multiple similarity solutions, we study also their asymptotic behavior. Numerical solutions are carried out using a shooting integration scheme.

• 천문학회지
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• 제36권3호
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• pp.89-95
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• 2003

Observations of dark matter dominated dwarf and low surface brightness disk galaxies favor density profiles with a flat-density core, while cold dark matter (CDM) N-body simulations form halos with central cusps, instead. This apparent discrepancy has motivated a re-examination of the microscopic nature of the dark matter in order to explain the observed halo profiles, including the suggestion that CDM has a non-gravitational self-interaction. We study the formation and evolution of self-interacting dark matter (SIDM) halos. We find analytical, fully cosmological similarity solutions for their dynamics, which take proper account of the collisional interaction of SIDM particles, based on a fluid approximation derived from the Boltzmann equation. The SIDM particles scatter each other elastically, which results in an effective thermal conductivity that heats the halo core and flattens its density profile. These similarity solutions are relevant to galactic and cluster halo formation in the CDM model. We assume that the local density maximum which serves as the progenitor of the halo has an initial mass profile ${\delta}M / M {\propto} M^{-{\epsilon}$, as in the familiar secondary infall model. If $\epsilon$ = 1/6, SIDM halos will evolve self-similarly, with a cold, supersonic infall which is terminated by a strong accretion shock. Different solutions arise for different values of the dimensionless collisionality parameter, $Q {\equiv}{\sigma}p_br_s$, where $\sigma$ is the SIDM particle scattering cross section per unit mass, $p_b$ is the cosmic mean density, and $r_s$ is the shock radius. For all these solutions, a flat-density, isothermal core is present which grows in size as a fixed fraction of $r_s$. We find two different regimes for these solutions: 1) for $Q < Q_{th}({\simeq} 7.35{\times} 10^{-4}$), the core density decreases and core size increases as Q increases; 2) for $Q > Q_{th}$, the core density increases and core size decreases as Q increases. Our similarity solutions are in good agreement with previous results of N-body simulation of SIDM halos, which correspond to the low-Q regime, for which SIDM halo profiles match the observed galactic rotation curves if $Q {\~} [8.4 {\times}10^{-4} - 4.9 {\times} 10^{-2}]Q_{th}$, or ${\sigma}{\~} [0.56 - 5.6] cm^2g{-1}$. These similarity solutions also show that, as $Q {\to}{\infty}$, the central density acquires a singular profile, in agreement with some earlier simulation results which approximated the effects of SIDM collisionality by considering an ordinary fluid without conductivity, i.e. the limit of mean free path ${\lambda}_{mfp}{\to} 0$. The intermediate regime where $Q {\~} [18.6 - 231]Q_{th}$ or ${\sigma}{\~} [1.2{\times}10^4 - 2.7{\times}10^4] cm^2g{-1}$, for which we find flat-density cores comparable to those of the low-Q solutions preferred to make SIDM halos match halo observations, has not previously been identified. Further study of this regime is warranted.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권2호
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• pp.145-158
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• 2015

In this paper, we investigate h-stability and boundedness for solutions of the functional perturbed differential systems using the notion of t_∞-similarity.

• Journal of applied mathematics & informatics
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• 제33권3_4호
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• pp.447-457
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• 2015

In this paper, we investigate bounds for solutions of the nonlinear perturbed functional differential systems using the notion of t_∞-similarity.

• 충청수학회지
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• 제28권2호
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• pp.217-228
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• 2015

In this paper, we investigate bounds for solutions of the perturbed nonlinear functional differential systems with a $t_{\infty}$-similarity condition using the notion of h-stability.

• 한국해양공학회지
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• 제25권2호
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• pp.62-66
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• 2011

In this paper, a liquid-filled long membrane container resting on a horizontal foundation is considered. All of the quantities are normalized to obtain similarity solutions. A system of nonlinear ordinary differential equations with undetermined boundary conditions is solved analytically. The integration of the curvature gives the solutions, which are expressed in terms of the elliptic integrals. A method for finding the shape and characteristic values is proposed for a given cross-sectional volume. The validity of these solutions is confirmed, and some results are shown for characteristic values and shapes.