Elastic constants. Ill

Johnson, F.A.

doi:10.1098/rspa.1977.0170

Cited by 3 publications

(3 citation statements)

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“…In the model shown in Figure 2, the velocity distribution in the oil film is given as follows: (7) where C, and C, are constants. Two kinds of boundary condition at the maximum shear stress surface, x = 0 and z = 0, are adopted, i.e., a non-slip condition and a slip condition.…”

Section: Discussionmentioning

confidence: 99%

Possibility of slip in hydrodynamic oil films under sliding contact conditions

Ono

Yamamoto

2002

Lubrication Science

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In hydrodynamic lubrication theory, the oil film thickness build‐up increases with increasing sliding speed or oil viscosity, and the viscous resistance or shear stress also increases, both without limit. The entraining force forming the oil film is given by the moving surfaces, or by the adhesive force of the oil molecules on the rubbing surfaces and the interaction force between them. Therefore, the maximum friction force and maximum oil film thickness will be limited by the operating conditions, such as oil properties, rubbing materials, sliding speed, and load. In this study, friction tests were conducted using a plate‐on‐cylinder sliding contact apparatus. It was found that a critical shear stress existed, above which the friction force and oil thickness decreased from theoretical values. Slip in an oil film seems to occur when the theoretical shear stress exceeds the critical value of the oil, according to test conditions. The occurrence of slip in an oil film is responsible for the reduction in the oil film and friction force from theoretical values, leading to the lower‐viscosity components of the oil selectively passing through the conjunction zone.

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Section: Discussionmentioning

confidence: 99%

Possibility of slip in hydrodynamic oil films under sliding contact conditions

Ono

Yamamoto

2002

Lubrication Science

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“…β is a real constant, β 2 is the quintic nonlinear coefficient, and the last term represents the Raman effect, which is responsible for the self-frequency shift. The KE equation was proposed by Kundu when he studied the gauge connections among some generalized Landau-Lifshitz and higher-order NLS systems; it adequately describes the propagation process of ultrashort optical pulses in nonlinear optics [31] and examines the stability of the Stokes wave in weakly nonlinear dispersive matter waves [32]. A series of important results related to equation (2) have been obtained, such as the gauge connections between equation 2and other soliton equations [30], the Lax pair and the Hamiltonian structure [33], and soliton solutions through the Darboux transformation [34][35][36], based on an extended Ablowitz-Kaup-Newell-Segur (AKNS) spectral problem, Zhaqilao constructed a generalized Darboux transformation (DT) for equation (2), and the explicit first-order rogue wave solution and the modulus form of the second-order rogue wave solution were given.…”

Section: Introductionmentioning

confidence: 99%

Higher-order rogue wave solutions of the Kundu–Eckhaus equation

et al. 2014

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In this paper, we investigate higher-order rogue wave solutions of the Kundu-Eckhaus equation, which contains quintic nonlinearity and the Raman effect in nonlinear optics. By means of a gauge transformation, the Kundu-Eckhaus equation is converted to an extended nonlinear Schrödinger equation. We derive the Lax pair, the generalized Darboux transformation, and the Nth-order rogue wave solution for the extended nonlinear Schrödinger equation. Then, by using the gauge transformation between the two equations, a concise unified formula of the Nth-order rogue wave solution with several free parameters for the Kundu-Eckhaus equation is obtained. In particular, based on symbolic computation, explicit rogue wave solutions to the Kundu-Eckhaus equation from the first to the third order are presented. Some figures illustrate dynamic structures of the rogue waves from the first to the fourth order. Moreover, through numerical calculations and plots, we show that the quintic and Raman-effect nonlinear terms affect the spatial distributions of the humps in higher-order rogue waves, although the amplitudes and the time of appearance of the humps are unchanged.

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“…The required équation may be expressed as It may be noted the set of equations (12) show an equivalence with those derived on the basis of homogeneous deformation theory [23]. The relations (12) used for evaluating the model parameters are consistent with the condition of zero initial stress playing a key role in the methods of long wave [24] and homogeneous deformation [25] for the components of the elastic constant tensor. A similar consistency is contained in equation (13).…”

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confidence: 98%

Modified krebs model and its application to fcc cobalt

Rathore

1978

J. Phys. France

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Dispersion frequencies for face centred cobalt have been computed along the principal symmetry directions on the basis of a lattice dynamical model which takes into account central and angular interaction coupling with the first neighbours only. The electron-ion interaction has been described along the lines suggested by Krebs. Ionic pressure has been introduced to maintain the crystal equilibrium. The simple model gives a satisfactory explanation of phonon dispersion curves and a reasonably good agreement with measured data has been obtained

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Elastic constants. Ill

Cited by 3 publications

References 0 publications

Possibility of slip in hydrodynamic oil films under sliding contact conditions

Possibility of slip in hydrodynamic oil films under sliding contact conditions

Higher-order rogue wave solutions of the Kundu–Eckhaus equation

Modified krebs model and its application to fcc cobalt

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