• The Bulletin of The Korean Astronomical Society
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• v.36 no.2
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• pp.111.2-111.2
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• 2011

While many astrophysical disks are vertically stratified and obey a polytropic equation of state, most studies on gravitational instability (GI) of flattened systems consider isothermal, razor-thin disks by taking vertical averages of disk properties. We investigate local GI of rotating pressure-confined polytropic disks with resolved vertical stratification by performing linear stability analysis. We find that the GI of vertically-stratified disks is in general a combination of conventional razor-thin Jeans modes and incompressible modes. The incompressible modes that dominate in the limit of the maximal disk compression require surface distortion and are an unstable version of terrestrial water waves. Disks with a steeper equation of state are found to be more Jeans unstable because they tend to have a smaller vertical scale height as well as a steeper temperature gradient corresponding to lower pressure support. GI depends more sensitively on the vertical temperature than density distribution. The density-weighted, harmonic mean, rather than the simple mean, of the adiabatic sound speed well describes the dispersion relation of horizontal modes, and thus is appropriate in the expression for Toomre Q stability parameter of razor-thin disks. We generalize Q into vertically-stratified disks, and discuss astrophysical application of our work.

• The Journal of Korea Robotics Society
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• v.13 no.2
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• pp.103-112
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• 2018

In this paper, a high performance underwater vehicle which can be manufactured at low cost is designed and fabricated, and its performance is verified through experiments. To improve efficiency, the Myring equation is used to design the appearance and the duct structure including the thruster is planned to increase the propulsion efficiency while reducing the drag force. Through various methods, it is secured stable waterproof performance, and also is devised to have high speed movement and turning performance. The developed underwater vehicle is equipped with a high output BLDC motor to achieve a linear speed of up to 2 m/s and can change direction rapidly with stability through four rudders. The rudders are driven by coupling a timing belt and a pulley by extending the axis of a servo motor, and are equipped at the end of the body to turn heading. In addition, for stable posture control, the roll keeps its internal center of gravity low and maintains its stability due to restoring force. By controlling the four rudders, pitch and yaw are handled by the PID controller and show stable performance. To investigate the horizontal turning performance, it is confirmed that the yaw rate controller is designed and stable yaw rate control is performed.

• Journal of the Korean Physical Society
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• v.73 no.11
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• pp.1774-1786
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• 2018

Phenotypic variation among clones (individuals with identical genes, i.e. isogenic individuals) has been recognized both theoretically and experimentally. We investigate the effects of phenotypic variation on evolutionary dynamics of a population. In a population, the individuals are assumed to be haploid with two genotypes : one genotype shows phenotypic variation and the other does not. We use an individual-based Moran model in which the individuals reproduce according to their fitness values and die at random. The evolutionary dynamics of an individual-based model is formulated in terms of a master equation and is approximated as the Fokker-Planck equation (FPE) and the coupled non-linear stochastic differential equations (SDEs) with multiplicative noise. We first analyze the deterministic part of the SDEs to obtain the fixed points and determine the stability of each fixed point. We find that there is a discrete phase transition in the population distribution when the probability of reproducing the fitter individual is equal to the critical value determined by the stability of the fixed points. Next, we take demographic stochasticity into account and analyze the FPE by eliminating the fast variable to reduce the coupled two-variable FPE to the single-variable FPE. We derive a quasi-stationary distribution of the reduced FPE and predict the fixation probabilities and the mean fixation times to absorbing states. We also carry out numerical simulations in the form of the Gillespie algorithm and find that the results of simulations are consistent with the analytic predictions.

• Interaction and multiscale mechanics
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• v.3 no.3
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• pp.235-255
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• 2010

This paper investigates the heat equation for domains subjected to an internal source with a sharp spatial gradient. The solution is first approximated using linear finite elements, and sufficiently small time-step sizes to yield stable simulations. The main area of interest is then in the ability to approximate the solution using Generalized Finite Elements, and again explore the time-step limitations required for stable simulations. Both high order elements, as well as elements with special enrichments are used to generate solutions. When compared to linear finite elements, the high order elements deliver better accuracy at a given level of mesh refinement, but do not offer an increase in critical time-step size. When special enrichment functions are used, the solution can be approximated accurately on very coarse meshes, while yielding solutions which are both accurate and computationally efficient. The major conclusion of interest is that the significantly larger element size yields larger allowable time-step sizes while still maintaining stability of the time-stepping algorithm.

• Journal of the Korea Institute of Military Science and Technology
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• v.12 no.4
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• pp.540-547
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• 2009

In the near future, military robots are likely to be substituted for military personnel in the field of battle. The power system of a legged robot is considerably more complex than the one used for a land vehicle because of the coordination and stability issues due to the large number of degree of freedom. In this paper, a servovalve-piston combination system for a straight-line motion of robot leg is modeled as three degree of freedom based on double inputs and single output transfer function. The output is the displacement of piston from neutral. The inputs are valve displacement from neutral and arbitrary load force in this system. LQR(Linear Quadratic Regulator) technique is applied in order to achieve robust stability and fast responses of the system. The Kalman filter loop, rejection of disturbance and noise, riccati equation, filter gain matrix, and frequency domain equality are analyzed and designed.

• Steel and Composite Structures
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• v.16 no.1
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• pp.45-58
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• 2014

EC3 provides several methodologies for the stability verification of members and frames. However, when dealing with the verification of non-uniform members in general, with tapered cross-section, irregular distribution of restraints, non-linear axis, castellated, etc., several difficulties are noted. Because there are yet no guidelines to overcome any of these issues, safety verification is conservative. In recent research from the authors of this paper, an Ayrton-Perry based procedure was proposed for the flexural buckling verification of web-tapered columns. However, in order to apply this procedure, Linear Buckling Analysis (LBA) of the tapered column must be performed for determination of the critical load. Because tapered members should lead to efficient structural solutions, it is therefore of major importance to provide simple and accurate formula for determination of the critical axial force of tapered columns. In this paper, firstly, the fourth order differential equation for non-uniform columns is derived. For the particular case of simply supported web-tapered columns subject to in-plane buckling, the Rayleigh-Ritz method is applied. Finally, and followed by a numerical parametric study, a formula for determination of the critical axial force of simply supported linearly web-tapered columns buckling in plane is proposed leading to differences up to 8% relatively to the LBA model.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.1
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• pp.6-11
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• 2014

Repetitive control is a specialized control scheme to track and/or attenuate a periodic reference trajectory and/or disturbance. Most researches about repetitive control have been performed in the frequency domain. Recently, several approaches to deal with repetitive control systems in the state space are developed by representing a q filter as a state-space equation. This paper presents a design method of a repetitive control system in the state space to satisfy $H_{\infty}$ performance. The overall system is composed of a plant, a repetitive controller, and a state-feedback controller, which can be converted to a standard form used in $H_{\infty}$ control. A LMI (Linear Matrix Inequality)-based stability condition is derived for fixed state-feedback gains. Under a given q filter, another LMI condition is derived to improve $H_{\infty}$ performance and is employed to find state-feedback gains by solving an optimization problem. Finally, to verify the feasibility of the proposed method, a numerical example is demonstrated.

• Journal of IKEEE
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• v.23 no.4
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• pp.1265-1272
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• 2019

We analyze the robustness of the existing predictor feedback controller for discrete-time linear systems with constant input delays against the structured model uncertainty. By modeling the constant input delay with a first-order PdE (Partial difference Equation), we replace the input delay with the PdE states. By applying a backstepping transformation, we build a target system that enables to construct an explicit Lyapunov function. Constructing the explicit Lyapunov function that covers the entire state variables, we prove the existence of an allowable maximum size of the structured model uncertainty to maintain stability and establish the robustness of the predictor feedback controller. The numerical example demonstrates that the stability of closed-loop system is maintained in the presence of the structured model uncertainty, and verifies the robustness of the predictor feedback controller.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10a
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• pp.729-733
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• 1987

Stability of Co Semigroups perturbed via the steady state Riccati equation (SSRE) is studied. We consider an infinite dimensional system : .chi. over dot = A.chi. + Bu, in, (A), domain of A, where A is the infinitesimal generator of a Co semigroup [T(t), t.geq.0] in H. If the original Co semigroup [T(t), t.geq.0] has a lower bound : vertical bar T(t).chi. vertical bar .geq. k vertical bar .chi. vertical bar, for all .chi. in H. t.geq. 0 and k>0, then the perturbed Co semigroup via the SSRE, where the feedback operator B is compact, cannot be exponentially stable. Physical interpretation of this result is as follows : in real applications, a finite number of actuators are available, therefore the operator B is compact. When the original system is inherently unstable, that is, has an infinite number of unstable modes, the perturbed system via the SSRE cannot be stable with a uniform decay rate.

• Structural Engineering and Mechanics
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• v.5 no.4
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• pp.369-383
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• 1997

The classical theory of thin-walled members is unable to reflect the shear lag phenomenon since it is based on the assumption of no shearing strains in the middle surface of the walls. In this paper, an energy equation for the lateral buckling of thin-walled members has been derived which includes the effects of torsion, warping and, especially, the shearing strains which reflect the shear lag phenomenon. A numerical analysis for the lateral buckling of thin-walled members with openings by using Galerkin's method of weighted residuals has been presented. The proposed numerical values and the predictions by experiment for the lateral buckling loads are to agree closely in the paper. The results from these comparisons show that the proposed method here is capable of predicting the lateral buckling of thin-walled members with openings. The fast convergence of the results indicates the numerical stability of the method. By the study, a very complex practical eigenvalue problem is transformed into a very simple one of solving only a linear equation with one variable.