• Nuclear Engineering and Technology
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• v.25 no.4
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• pp.539-547
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• 1993

A stochastic approach using continuous time Markov process is presented to model the one-dimensional nuclide transport in fractured rock media as a further extension for previous works［1-3］. Nuclide transport of decay chain of arbitrary length in the single planar fractured rock media in the vicinity of the radioactive waste repository is modeled using a continuous time Markov process. While most of analytical solutions for nuclide transport of decay chain deal with the limited length of decay chain, do not consider the case of having rock matrix diffusion, and have very complicated solution form, the present model offers rather a simplified solution in the form of expectance and its variance resulted from a stochastic modeling. As another deterministic way, even numerical models of decay chain transport, in most cases, show very complicated procedure to get the solution and large discrepancy for the exact solution as opposed to the stochastic model developed in this study. To demonstrate the use of the present model and to verify the model by comparing with the deterministic model, a specific illustration was made for the transport of a chain of three member in single fractured rock medium with constant groundwater flow rate in the fracture, which ignores the rock matrix diffusion and shows good capability to model the fractured media around the repository.

• Journal of Korean Society of Transportation
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• v.20 no.5
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• pp.67-79
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• 2002

In this paper, observed trajectories of a vehicle platoon are viewed as one realization of a finite sequence of random trajectories. In this point of view, we develop novel and mathematically rigorous concept of traffic flow variables such as local traffic density, instantaneous traffic flow, and velocity field and investigate their nature on a general probability space of a sequence of random trajectories which represent vehicle trajectories. We present a simple model of random trajectories as an illustrative example and, derive the values of traffic flow variables based on the new definitions in this model. In particular, we construct the model for the sequence of random vehicle trajectories with a system of stochastic differential equations. Each equation of the system nay represent microscopic random maneuvering behavior of each vehicle with properly designed drift coefficient functions and diffusion coefficient functions. The system of stochastic differential equations nay generate a well-defined probability space of a sequence of random vehicle trajectories. We derive the partial differential equation for the expected cumulative plot with appropriate initial conditions. By solving the equation with numerical methods, we obtain the values of expected cumulative plot, local traffic density, and instantaneous traffic flow. In addition, we derive the partial differential equation for the expected travel time to a certain location with appropriate initial and/or boundary conditions, which is solvable numerically. We apply this model to a case of single vehicle trajectory.

• Structural Engineering and Mechanics
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• v.56 no.2
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• pp.257-273
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• 2015

Numerical value of correlation between effective parameters in the strength of a structure is as important as its stochastic properties in determining the safety of the structure. In this article investigation is made about the variation of coefficient of correlation between effective parameters in corrosion initiation time of reinforcement and the time of concrete cover cracking in reinforced concrete (RC) structures. Presence of many parameters and also error in measurement of these parameters results in uncertainty in determination of corrosion initiation and the time to crack initiation. In this paper, assuming diffusion process as chloride ingress mechanism in RC structures and considering random properties of effective parameters in this model, correlation between input parameters and predicted time to corrosion is calculated using the Monte Carlo (MC) random sampling. Results show the linear correlation between corrosion initiation time and effective input parameters increases with increasing uncertainty in the input parameters. Diffusion coefficient, concrete cover, surface chloride concentration and threshold chloride concentration have the highest correlation coefficient respectively. Also the uncertainty in the concrete cover has the greatest impact on the coefficient of correlation of corrosion initiation time and the time of crack initiation due to the corrosion phenomenon.

• Nuclear Engineering and Technology
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• v.51 no.6
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• pp.1616-1625
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• 2019

Measuring occurrence times of random events, aimed to determine the statistical properties of the governing stochastic process, is a basic topic in science and engineering, and has been the subject of numerous mathematical modeling approaches. Often, true statistical properties deviate from measured properties due to the so called dead time phenomenon, where for a certain time period following detection, the detection system is not operational. Understanding the dead time effect is especially important in radiation measurements, often characterized by high count rates and a non-reducible detector dead time (originating in the physics of particle detection). The effect of dead time can be interpreted as a suitable rarefied sequence of the original time sequence. This paper provides a limit theorem for a high rate (diffusion-scale) counter with extendable (Type II) dead time, where the underlying counting process is a renewal process with finite second moment for the inter-event distribution. The results are very general, in the sense that they refer to a general inter arrival time and a random dead time with general distribution. Following the theoretical results, we will demonstrate the applicability of the results in three applications: serially connected components, multiplicity counting and measurements of aerosol spatial distribution.

• Journal of Korea Port Economic Association
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• v.34 no.1
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• pp.99-110
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• 2018

This study empirically examines simple methodology to quantify the risk resulted from the uncertainty of bunker price and foreign exchange rate, which cause main resources of the cost in shipping industry during the periods between $1^{st}$ of January 2010 and $31^{st}$ of January 2018. To shed light on the risk measurement in cash flows we tested GBM(Geometric Brownian Motion) frameworks such as the model with conditional heteroskedasticity and jump diffusion process. The main contribution based on empirical results are summarized as following three: first, the risk analysis, which is dependent on a single variable such as freight yield, is extended to analyze the effects of multiple factors such as bunker price and exchange rate return volatility. Second, at the individual firm level, the need for risk management in bunker price and exchange rate is presented as cash flow. Finally, based on the scale of the risk presented by the analysis results, the shipping companies are required that there is a need to consider what is appropriate as a means of risk management.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.34 no.7
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• pp.679-688
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• 2010

The major objective of the present study is to extend the applications of inverse analysis to more realistic engineering fields with a complex combustion process rather than the traditional simple heat-transfer problems. In order to do this, the unknown initial mass fractions of $CH_4/O_2$ are estimated from the temperature measurement data by inverse analysis in the practical diffusion-controlled turbulent combustion problem. In order to ensure efficient inverse analysis, the repulsive particle swarm optimization (RPSO) method, which belongs to the class of stochastic evolutionary global optimization methods, is implemented as an inverse solver. Based on this study, it is expected that useful information can be obtained when inverse analysis is used in the diagnosis, design, or optimization of real combustion systems involving unknown parameters.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2165-2170
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• 2007

At nanoscales, the Boltzmann transport equation (BTE) can best describe the behavior of phonons which are energy carriers in crystalline materials. Through this study, the phonon transport in some micro/nanoscale problems was simulated with the Monte Carlo method which is a kind of the stochastic approach to the BTE. In the Monte Carlo method, the superparticles of which the number is the weighted value to the actual number of phonons are allowed to drift and be scattered by other ones based on the scattering probability. Accounting for the phonon dispersion relation and polarizations, we have confirmed the one-dimensional transient phonon transport in ballistic and diffusion limits, respectively. The thermal conductivity for GaAs was also calculated from the kinetic theory by using the proposed model. Besides, we simulated the electrostatic discharge event in the NMOS transistor as a two-dimensional problem by applying the Monte Carlo method.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.3
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• pp.350-357
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• 1997

The transient incompressible flow behind the axisymmetric bluff body is numerically simulated using the random vortex method(RVM). Based on the vorticity formulation of the unsteady Navier-Stokes equations, the Lagrangian approach with a stochastic simulation of diffusion using random walk technique is employed to account for the transport processes of the vortex elements. The numerical solutions for 2-dimensional recirculating flow behind a backward-facing step in the laminar range of Reynolds number are compared with experimental data. The present simulation focuses on the transitional flow regime where the recirculation zone behind the bluff body becomes highly unsteady and large-scale vortex eddies are shed from the bluff body wake due to intrinsic shear layer instabilities. The unsteady vertical flow structures and the mixing characteristics behind the bluff body are discussed in detail.

• Journal of the Korean Physical Society
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• v.73 no.9
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• pp.1219-1224
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• 2018

We investigate the evolutionary dynamics and the phase transitions of the island model which consists of subdivided populations of individuals confined to two islands. In the island model, the population is subdivided so that migration acts to determine the evolutionary dynamics along with selection and genetic drift. The individuals are assumed to be haploid and to be one of two species, X or Y. They reproduce according to their fitness values, die at random, and migrate between the islands. The evolutionary dynamics of an individual based model is formulated in terms of a master equation and is approximated by using the diffusion method as the multidimensional Fokker-Planck equation (FPE) and the coupled non-linear stochastic differential equations (SDEs) with multiplicative noise. We analyze the infinite population limit to find the phase transitions from the monomorphic state of one type to the polymorphic state to the monomorphic state of the other type as we vary the ratio of the fitness values in two islands and complete the phase diagram of our island model.

• Journal of the Korean Data and Information Science Society
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• v.22 no.1
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• pp.9-18
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• 2011

After the launch of PCS in 1997, the mobile telephone industry has achieved a remarkable growth in market share and sales, and substituted for long-distance wire communication market. This study investigates the interrelationships between the two markets in transition and attempts to perform the statistical tests if the diffusion of mobile telephone was the direct factor for the reduction in sales of long-distance communication industry. The evidence of the direct substitution effect between the two markets is not likely to be found. Unlike the general expectations, the test result seems to prove the sustained initial complementary relation for awhile.