• 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.

• Journal of Korea Multimedia Society
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• v.13 no.8
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• pp.1128-1141
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• 2010

This paper proposes a method of moving object detection in crowded scene using clustered trajectory. Unlike previous appearance based approaches, the proposed method employes motion information only to isolate moving objects. In the proposed method, feature points are extracted from input frames first and then feature tracking is followed to create feature trajectories. Based on an assumption that feature points originated from the same objects shows similar motion as the object moves, the proposed method detects moving objects by clustering trajectories of similar motions. For this purpose an energy function based on spatial proximity, motion coherence, and temporal continuity is defined to measure the similarity between two trajectories and the clustering is achieved by minimizing the energy function in CRFs (conditional random fields). Compared to previous methods, which are unable to separate falsely merged trajectories during the clustering process, the proposed method is able to rearrange the falsely merged trajectories during iteration because the clustering is solved my energy minimization in CRFs. Experiment results with three different crowded scenes show about 94% detection rate with 7% false alarm rate.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.29A no.11
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• pp.40-48
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• 1992

The wave-kinetic numerical method is used in simulating the irradiance scintillations of optical wave through a two-dimensional random medium containing weak Gaussian fluctuations of the refractive index. The results are compared to existing analytical or numerical results. The wave-kinetic method is a phase-space ray-tracing method for certain key ray trajectories, and the irradiance is calculated by reconstructing the entire beam from these trajectories. The strength of the wave-kinetic method lies in the fact that it can be applied to any type of random media.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.737-746
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• 1999

We consider a class of discrete parameter processes on a locally compact Banach space S arising from successive compositions of strictly stationary random maps with state space C(S,S), where C(S,S) is the collection of continuous functions on S into itself. Sufficient conditions for stationary solutions are found. Existence of pth moments and convergence of empirical distributions for trajectories are proved.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.9
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• pp.1163-1171
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• 1999

Superdiffusive transport motions of passive scalars are numerically considered for various advection velocity fields. Calculated exponents ${\alpha}$ in the superdiffusion-defining relation ${\sigma}^2(t){\sim}t^{\alpha}$ for model flow fields agree to the theoretically predicted values. Simulation results show that the superdiffusion takes place as the tracers' motion become less random, compared to their motion at the pure molecular diffusion. Whether the flow field is random or not, degrees of superdiffusion are directly related to the velocity autocorrelation functions along the tracers Lagrangian trajectories that characterize degrees of randomness of the tracers' motion.

• Structural Engineering and Mechanics
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• v.63 no.5
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• pp.659-667
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• 2017

Rail support failure is inevitably subjected to track geometric deformations. Due to the randomness and evolvements of track irregularities, it is naturally a hard work to grasp the trajectories of dynamic responses of railway systems. This work studies the influence of rail fastener failure on dynamic behaviours of wheel/rail interactions and the railway tracks by jointly considering the effects of track random irregularities. The failure of rail fastener is simulated by setting the stiffness and damping of rail fasteners to be zeroes in the compiled vehicle-track coupled model. While track random irregularities will be transformed from the PSD functions using a developed probabilistic method. The novelty of this work lays on providing a method to completely reveal the possible responses of railway systems under jointly excitation of track random irregularities and rail support failure. The numerical results show that rail fastener failure has a great influence on both the wheel/rail interactions and the track vibrations if the number of rail fastener failure is over three. Besides, the full views of time-dependent amplitudes and probabilities of dynamic indices can be clearly presented against different failing status.

• 한국해양학회지
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• v.29 no.4
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• pp.392-401
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• 1994

We examined the temporal characteristics of the oceanic eddy diffusion at 5 coastal regions of Korea by measuring the separation distances of multiple drifters released simultaneously at the same by the GPS and Decca transponder system. The observed variance of separation distance, for the time scales from minutes to hours, is proportional to t/SUP m/ with scaling exponent m between 1.2 and 2.0. The observed Lagrangian trajectories of drifters show fractal characteristics instead of random walk or Brown motion. As an effort toward a development of a realistic model of the oceanic eddy diffusion, we simulated the Lagrangian trajectories of drifters by fractional Brown motion (FBM) model. The observed variances of drifter separations can be generated by the FBM process provided the Hurst exponent is the same as the observed one. We further showed that the observed power law in the variance of drifter separations cannot be simulated with an ordinary Brown motion or random walk process.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.5
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• pp.1330-1337
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• 1994

This study is to predict the lateral dispersion of the particles with time in a vertical pipe. Particle is released downward and located in the center of a pipe through which stationary, homogeneous turbulent air is flowing. We assume that gas turbulence velocities have a Gaussian probability density distribution and the presence of particle is not to alter turbulent structures. Particle trajectory is computed by numerically integrating the particle Lagrangian equation of motion, with a random sampling to determine the fluctuating air velocity experienced by each particle, which considered inertia effect and crossing-trajectories effect. The result shows characterestics of particle dispersion according to flow field condition and droplet size by using the parameters and scales, which expressed characterestics of flow field and particle. Predictions agree reasonably with experimental data.

• Mass Spectrometry Letters
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• v.6 no.4
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• pp.91-98
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• 2015

The Brownian motion or Wiener process, as the physical model of the stochastic procedure, is observed as an indexed collection random variables. Stochastic procedure are quite influential on the confinement potential fluctuation in the quadrupole ion trap (QIT). Such effect is investigated for a high fractional mass resolution Δm/m spectrometry. A stochastic procedure like the Wiener or Brownian processes are potentially used in quadrupole ion traps (QIT). Issue examined are the stability diagrams for noise coefficient, η=0.07;0.14;0.28 as well as ion trajectories in real time for noise coefficient, η=0.14. The simulated results have been obtained with a high precision for the resolution of trapped ions. Furthermore, in the lower mass range, the impulse voltage including the stochastic potential can be considered quite suitable for the quadrupole ion trap with a higher mass resolution.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.2
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• pp.206-214
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• 2003

In this paper, we propose a method to avoid obstacles that have unstable limit cycles in a chaos trajectory surface. We assume all obstacles in the chaos trajectory surface have a Van der Pol equation with an unstable limit cycle. When a chaos robot meets an obstacle in an Arnold equation or Chua's equation trajectory, the obstacle reflects the robot. We also show computer simulation results of Arnold equation and Chua's equation and random walk chaos trajectories with one or more Van der Pol obstacles and compare the coverage rates of each trajectory. We show that the Chua's equation is slightly more efficient in coverage rates when two robots are used, and the optimal number of robots in either the Arnold equation or the Chua's equation is also examined.