• The Pure and Applied Mathematics
• /
• v.22 no.3
• /
• pp.215-227
• /
• 2015

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

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.2
• /
• pp.383-389
• /
• 2010

In this paper, we investigate h-stability of the nonlinear differential systems using the notion of $t_{\infty}$-similarity.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.24 no.5
• /
• pp.219-232
• /
• 2020

The slip-weakening model developed by Ohnaka and Yamashita is extended over the breakdown zone by equating the scaling relationships for the breakdown zone and the whole rupture area. For the extension, the study uses the relationship between rupture velocity and radiation efficiency, which was derived in the theory of linear elastic fracture mechanics, and the definition of f_max given in the specific barrier model proposed by Papageorgiou and Aki. The results clearly show that the extended scaling relationship is governed by the ratio of rupture velocity to S wave velocity, and the velocity ratio can be determined by the ratio of characteristic frequencies of a Fourier amplitude spectrum, which are corner frequency, f_c, and source-controlled cut-off frequency, f_max, or vice versa. The derived relationship is tested by using the characteristic frequencies extracted from previous studies of more than 130 shallow crustal events (focal depth less than 25 km, M_W 3.0~7.5) that occurred in Japan. Under the assumption of a dynamic similarity, the rupture velocity estimated from f_max/f_c and the modified integral timescale give quite similar scale-dependence of the rupture area to that given by Kanamori and Anderson. Also, the results for large earthquakes show good agreement to the values from a kinematic inversion in previous studies. The test results also indicate the unavailability of the spectral self-similarity proposed by Aki because of the scale-dependent rupture velocity and the rupture velocity-dependent f_max/f_c; however, the results do support the local similarity asserted by Ohnaka. It is also remarkable that the relationship between the rupture velocity and f_max/f_c is quite similar to Kolmogorov's hypothesis on a similarity in the theory of isotropic turbulence.

• Nuclear Engineering and Technology
• /
• v.54 no.8
• /
• pp.2898-2914
• /
• 2022

When evaluating energy balance and temperature in reduced-scale fire experiments, which are conducted as an alternative to full-scale fire experiments, it is important to consider the similarity in the scale among these experiments. In this paper, a method considering the similarity of energy balance is proposed for setting the conditions for reduced-scale experiments of mechanically ventilated compartment fires. A small-scale fire experiment consisting of various cases with different compartment geometries (aspect ratios between 0.2 and 4.7) and heights of vents and fire sources was conducted under mechanical ventilation, and the energy balance in the quasi-steady state was evaluated. The results indicate the following: (1) although the compartment geometry varies the energy balance in a mechanically ventilated compartment, the variation in the energy balance can be evaluated irrespective of the compartment size and geometry by considering scaling factor F (∝h_effA_wR_T, where h_eff is the effective heat transfer coefficient, A_w is the total wall area, and R_T is the ratio of the spatial mean gas temperature to the exhaust temperature); (2) the value of R_T, which is a part of F, reflects the effects of the compartment geometry and corresponds to the distributions of the gas temperature and wall heat loss.

• Journal of applied mathematics & informatics
• /
• v.33 no.3_4
• /
• pp.447-457
• /
• 2015

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

• Korean Journal of Mathematics
• /
• v.23 no.2
• /
• pp.269-282
• /
• 2015

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

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.4
• /
• pp.695-702
• /
• 2011

In this paper, we investigate h-stability of the non-linear perturbed differential systems using the the notion of $t_{\infty}$-similarity.

• Geomechanics and Engineering
• /
• v.25 no.4
• /
• pp.303-315
• /
• 2021

A rigorous and generic similarity solution is developed for assessment of the undrained expansion responses of a cylindrical cavity expansion in K₀-consolidated anisotropic soils. A K₀-consolidated anisotropic modified Cam-clay (K₀-AMCC) model that can represent the initial stress anisotropy and the effects of stress-induced anisotropy is used to model the soil behaviors during cavity expansion. All the seven basic unknowns, the three stress components, the pore water pressure, the particle velocity, the specific volume and the hardening parameter, are reduced to the functions of a dimensionless radial coordinate and are taken as coupled variables to formulate the problem. The governing equations are formulated by making use of the equilibrium equation, the constitutive equation, the consistency condition, the continuity condition and the undrained condition, which are then solved as an initial value problem. The proposed rigorous similarity solution is compared with some well-documented rigorous solutions to validate the solution and to highlight the special expansion responses in anisotropic soils. The results reveal that the present solution can yield more predictions for cavity expansion problems in soils with initial anisotropic stresses.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.811-819
• /
• 2013

In this paper we investigate h-stability for linear impulsive equations using the notion of $t_{\infty}$-similarity and an impulsive integral inequality.

• The Pure and Applied Mathematics
• /
• v.19 no.2
• /
• pp.171-177
• /
• 2012

The main purpose of this paper is to investigate $h$-stability of the nonlinear perturbed differential systems using the notion of $t_{\infty}$-similarity. As results, we generalize some previous $h$-stability results on this topic.