• Geomechanics and Engineering
• /
• v.34 no.1
• /
• pp.51-67
• /
• 2023

In this research, the degradation rate of physical properties of the Angouran pit bedrock (calc-schist) is first investigated under the specific numbers of freeze-thaw (F-T) cycles. Then, the durability of calc-schist specimens against the F-T cycle number (N) is examined considering the mechanical parameters, and using the decay function and half-time techniques. For this purpose, point load strength (I_S(50)), second durability index (I_d2), Brazilian tensile strength (BTS), and compressive (V_P) and shear (V_S) wave velocities of calc-schist specimens are measured after 0, 7, 15, 40, and 75 N. For comparing the degradation rate of mechanical properties of available rock types on the Angouran mine walls, these tests are also carried out on the limestone and amphibolite schist specimens beside the calc-schist. According to test results, the exponential regression models are developed between the mechanical parameters of rock specimen's and N variable. Also, the long-term durability of each rock type versus N is studied using the decay function and half-time techniques. Results indicated that the degradation rate differs for the above rock types in which amphibolite schist and calc-schist specimens have the highest and least resistance against the N, respectively. The obtained results from this study can play a key role in the optimal design of the mine's final walls.

• Nuclear Engineering and Technology
• /
• v.54 no.1
• /
• pp.275-282
• /
• 2022

The aim of this work is to develop the fractional Bateman equations, which can model memory effects in successive isotopes transformations. Such memory effects have been previously reported in the alpha decay, which exhibits a non-Markovian behavior. Since there are radioactive decay series with consecutive alpha decays, it is convenient to include the mentioned memory effects, developing the fractional Bateman Equations, which can reproduce the standard ones when the fractional order is equal to one. The proposed fractional model preserves the mathematical shape and the symmetry of the standard equations, being the only difference the presence of the Mittag-Leffler function, instead of the exponential one. This last is a very important result, because allows the implementation of the proposed fractional model in burnup and activation codes in a straightforward way. Numerical experiments show that the proposed equations predict high decay rates for small time values, in comparison with the standard equations, which have high decay rates for large times. This work represents a novelty approach to the theory of successive transformations, and opens the possibility to study properties of the Bateman equation from a fractional approach.

• Communications of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.379-385
• /
• 2014

For a bandlimited function with polynomial growth on the real line, we derive a nonuniform sampling expansion using a special bandlimited function which has polynomial decay on the real line. The series converges uniformly on any compact subsets of the real line.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.22 no.1
• /
• pp.1-8
• /
• 1985

The buckling characteristics of cylindrical shells with a circular hole, under axially compressed loads, have been analyzed and the results have been compared with existed experimental results. Deflection function with decay factor is assumed, and stress distribution around a circular hole in tensioned infinite plate is used for formulating buckling energy function. Applying Rayleigh Ritz procedure to this energy function, characteristic equation of eigenvalue problem is determined. Buckling load is defined by the minimum value of eigenvalues calculated according to several decay factors, and as the radius ratios of a circular hole (a/R) and shell thickness ratios (R/t) are varied, the reducing characteristics of buckling load are studied. As a result, buckling loads are reduced by about 50% according to some radius ratios ($a/R{\geq}0.15$) of circular hole and are not nearly affected by shell thickness ratio(R/t).

• Journal of Astronomy and Space Sciences
• /
• v.6 no.2
• /
• pp.101-108
• /
• 1989

The algorithm was developed for the estimation of orbital decay of the Soviet Satellite COMOS 1402 which divides into three body-COSMOS 14020-A, B and C-and fell down early in 1983. The perturbation effects due to the nonspherical geopotential and air drag were considered and the standard atmospheric model were built for obtaining the atmospheric density as a function of the height. The orbital elements of NASA GSFC during orbital decay used in estimation of orbital decay. We compared the estimation values with the published ones of the American State Department. In the case of COSMOS 1402-C, the estimated values accorded with the published ones but, in the case of COSMOS 1402-A, the decay time and the approximated position differed respectively one minute and two degrees in both latitude and longitude from the published ones.

• Progress in Superconductivity
• /
• v.14 no.1
• /
• pp.1-10
• /
• 2012

We fabricated a closed coils by using resistive-joint method and the joint resistance of the coils were estimated by field decay technique in liquid nitrogen. We used the Runge-kutta method for the numerical analysis to calculate the decay properties. The closed coil was wound by $(Bi,Pb)_2Sr_2Ca_2Cu_3O_x$/Ag tape. Both ends the tape were overlapped and soldered to each other. The current was induced in a closed coils by external magnetic flux density. Its decay characteristic was observed by means of measuring the magnetic flux density generated by induced current at the center of the closed coil with hall sensor. The joint resistance was calculated as the ratio of the inductance of the loop to the time constants. The joint resistances were evaluated as a function of critical current of loop, contact length, sweep time, and external magnetic flux density in a contact length of 7 cm. It was observed that joint resistance was dependent on contact length of a closed coil, but independent of critical current, sweep time, and external magnetic flux density. The joint resistance was measured to be higher for a standard four-probe method, compared with that for the field decay technique. This implies that noise of measurement in a standard four-probe method is larger than that of field decay technique. It was estimated that joint resistance was $8.0{\times}10^{-9}{\Omega}$ to $11.4{\times}10^{-9}{\Omega}$ for coils of contact length for 7 cm. It was found that 40Pb/60Sn solder are unsuitable for persistent mode.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.281-294
• /
• 2020

The initial-boundary value problem for a class of semilinear Klein-Gordon equation with logarithmic nonlinearity in bounded domain is studied. The existence of global solution for this problem is proved by using potential well method, and obtain the exponential decay of global solution through introducing an appropriate Lyapunov function. Meanwhile, the blow-up of solution in the unstable set is also obtained.

• Journal of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.325-342
• /
• 2012

It is well-known that the m-th order cardinal B-spline wave-let, $\psi_m$, decays exponentially. Our aim in this paper is to determine the exact rate of this decay and thereby to describe the asymptotic behaviour of $\psi_m$.

• Journal of the Korean Solar Energy Society
• /
• v.25 no.4
• /
• pp.133-139
• /
• 2005

In this paper, the ventilation performance of suspended particulates in indoor side was investigated by step-down method. Experiments were performed in function of mechanical ventilation types and locations of supply and extract air. The type 2 ventilation system shows the highest removal characteristics rather than other 2 types. It means that the displacement ventilation has also good decay rates of concentration compared to mixing ventilation.

• East Asian mathematical journal
• /
• v.32 no.1
• /
• pp.117-128
• /
• 2016

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source $$u^{{\prime}{\prime}}-M(x,t,{\parallel}{\bigtriangledown}u(t){\parallel}^2){\bigtriangleup}u+{\int}_0^th(t-{\tau})div[a(x){\bigtriangledown}u({\tau})]d{\tau}+{\mid}u{\mid}^{\gamma}u=0$$. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.