• Journal of The Korean Astronomical Society
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• v.35 no.4
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• pp.159-174
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• 2002

Cosmological hydrodynamic simulations of large scale structure in the universe have shown that accretion shocks and merger shocks form due to flow motions associated with the gravitational collapse of nonlinear structures. Estimated speed and curvature radius of these shocks could be as large as a few 1000 km/s and several Mpc, respectively. According to the diffusive shock acceleration theory, populations of cosmic-ray particles can be injected and accelerated to very high energy by astrophysical shocks in tenuous plasmas. In order to explore the cosmic ray acceleration at the cosmic shocks, we have performed nonlinear numerical simulations of cosmic ray (CR) modified shocks with the newly developed CRASH (Cosmic Ray Amr SHock) numerical code. We adopted the Bohm diffusion model for CRs, based on the hypothesis that strong Alfven waves are self-generated by streaming CRs. The shock formation simulation includes a plasma-physics-based 'injection' model that transfers a small proportion of the thermal proton flux through the shock into low energy CRs for acceleration there. We found that, for strong accretion shocks, CRs can absorb most of shock kinetic energy and the accretion shock speed is reduced up to $20\%$, compared to pure gas dynamic shocks. For merger shocks with small Mach numbers, however, the energy transfer to CRs is only about $10-20\%$ with an associated CR particle fraction of $10^{-3}$. Nonlinear feedback due to the CR pressure is insignificant in the latter shocks. Although detailed results depend on models for the particle diffusion and injection, these calculations show that cosmic shocks in large scale structure could provide acceleration sites of extragalactic cosmic rays of the highest energy.

• Journal of the Korea Concrete Institute
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• v.14 no.6
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• pp.883-891
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• 2002

The chloride penetration in concrete structures is influenced by many factors such as types of cement and admixture proportion. Therefore, the effects of these factors on chloride diffusion must be correctly considered. The conventional diffusion analysis also neglected the existence of reinforcing bar in concrete structures. The purpose of the present paper is therefore to investigate the effect of reinforcing bar on the chloride diffusion in concrete structures. For this purpose, a comprehensive finite element analyses have been conducted to obtain chloride penetration profile. The results indicate that the chlorides are accumulated in front of a reinforcing bar and that the accumulation is much larger for the case of large diameter bars. The higher accumulation of chloride at bar location causes much faster corrosion of reinforcing steel. It can be concluded from the present study that the effects of reinforcing bars must be considered in chloride diffusion analysis for more realistic prediction of durable life of concrete structures.

• Structural Engineering and Mechanics
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• v.75 no.1
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• pp.59-69
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• 2020

The purpose of this study is to develop practical tools for the mechanical design of cylindrical porous media subjected to a broad gap in a hygrothermal environment. The planar axisymmetrical and transient hygrothermoelastic field in a porous hollow cylinder that is exposed to a broad gap of temperature and dissolved moisture content and is free from mechanical constraint on all surfaces is investigated considering the nonlinear coupling between heat and binary moisture and the diffusive properties of both phases of moisture. The system of hygrothermal governing equations is derived for the cylindrical case and solved to illustrate the distributions of hygrothermal-field quantities and the effect of diffusive properties on the distributions. The distribution of the resulting stress is theoretically analyzed based on the fundamental equations for hygrothermoelasticity. The safety hazard because of the analysis disregarding the nonlinear coupling underestimating the stress is illustrated. By comparing the cylinder with an infinitesimal curvature with the straight strip, the significance to consider the existence of curvature, even if it is infinitesimally small, is demonstrated qualitatively and quantitatively. Moreover, by investigating the bending moment, the necessities to consider an actual finite curvature and to perform the transient analysis are illustrated.

• Steel and Composite Structures
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• v.26 no.1
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• pp.17-29
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• 2018

The thermal effects on the buckling, postbuckling and nonlinear vibration behaviors of composite laminated trapezoidal plates are studied. Aiming at the complex plate structure and to simulate the temperature distribution of the plate, a finite element method (FEM) is applied in this paper. In the temperature model, based on the thermal diffusion equation, the Galerkin's method is employed to establish the temperature equation of the composite laminated trapezoidal plate. The geometrical nonlinearity of the plate is considered by using the von Karman large deformation theory, and combining the thermal model and aeroelastic model, Hamilton's principle is employed to establish the thermoelastic equation of motion of the composite laminated trapezoidal plate. The thermal buckling and postbuckling of the composite laminated rectangular plate are analyzed to verify the validity and correctness of the present methodology by comparing with the results reported in the literature. Moreover, the effects of the temperature with the ply-angle on the thermal buckling and postbuckling of the composite laminated trapezoidal plates are studied, the thermal effects on the nonlinear vibration behaviors of the composite laminated trapezoidal plates are discussed, and the frequency-response curves are also presented for the different temperatures and ply angles.

• Computers and Concrete
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• v.8 no.2
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• pp.125-142
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• 2011

In the present paper, a numerical simulation method based on mesoscopic composite structure of concrete, the truss network model, is developed to evaluate the diffusivity of concrete in order to account for the microstructure of concrete, the binding effect of chloride ions and the chloride concentration dependence. In the model, concrete is described as a three-phase composite, consisting of mortar, coarse aggregates and the interfacial transition zones (ITZs) between them. The advantage of the current model is that it can easily represent the movement of mass (e.g. water or chloride ions) through ITZs or the potential cracks within concrete. An analytical method to estimate the chloride diffusivity of mortar and ITZ, which are both treated as homogenious materials in the model, is introduced in terms of water-to-cement ratio (w/c) and sand volume fraction. Using the newly developed approaches, the effect of cracking of concrete on chloride diffusion is reflected by means of the similar process as that in the test. The results of calculation give close match with experimental observations. Furthermore, with consideration of the binding capacity of chloride ions to cement paste and the concentration dependence for diffusivity, the one-dimensional nonlinear diffusion equation is established, as well as its finite difference form in terms of the truss network model. A series of numerical analysises performed on the model find that the chloride diffusion is substantially influenced by the binding capacity and concentration dependence, which is same as that revealed in some experimental investigations. This indicates the necessity to take into account the binding capacity and chloride concentration dependence in the durability analysis and service life prediction of concrete structures.

• Journal of The Korean Astronomical Society
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• v.37 no.5
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• pp.405-412
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• 2004

Cosmological shocks form as an inevitable consequence of gravitational collapse during the large scale structure formation and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration (DSA). We have calculated the evolution of CR modified shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of DSA in 1D quasi-parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc $\ge$ 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that $10^{-4} - 10^{-3}$ of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The CR acceleration efficiency increases with shock Mach number, but it asymptotes to ${\~}50\%$ in high Mach number shocks, regardless of the injection rate and upstream CR pressure. On the other hand, in moderate strength shocks ($M_s {\le} 5$), the pre-existing CRs increase the overall CR energy. We conclude that the CR acceleration at cosmological shocks is efficient enough to lead to significant nonlinear modifications to the shock structures.

• Journal of Korean Institute of Industrial Engineers
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• v.37 no.1
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• pp.74-82
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• 2011

The Bass model is a cornerstone in diffusion theory which is used for forecasting demand of durables or new services. Three well-known estimation methods for parameters of the Bass model are Ordinary Least Square (OLS), Maximum Likelihood Estimator (MLE), Nonlinear Least Square (NLS). In this paper, a hybrid method incorporating OLS and NLS is presented and it's performance is analyzed and compared with OLS and NLS by using simulation data and empirical data. The results show that NLS has the best performance in terms of accuracy and our hybrid method has the best performance in terms of stability. Specifically, hybrid method has better performance with less data. This result means much in practical aspect because the avaliable data is little when a diffusion model is used for forecasting demand of a new product.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2003.08a
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• pp.208-215
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• 2003

Convective-diffusion equations appear in various disciplines such as hydrology, chemical engineering and oceanography dealing with the transport problem of scalar quantities. Since it is nonlinear, numerical methods are generally used to obtain its solution. Very limited number of analytical solutions are available usually in cases when the convective velocity is constant or has a simple functional form (for some collection of the solutions, see Noye, 1987). There is however a continuing need to develop analytical solutions because of its practical importance. Analytical solutions of the convection-diffusion equation are valuable not only for the better understanding on the transport process but the verification of numerical schemes. (omitted)

• Journal of Power Electronics
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• v.16 no.1
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• pp.238-248
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• 2016

The state-of-charge (SOC) and state-of-health (SOH) estimation of batteries play important roles in managing batteries for automotive applications. However, an accurate state estimation of a battery is difficult to achieve because of certain factors, such as measurement noise, highly nonlinear characteristics, strong hysteresis phenomenon, and diffusion effect of batteries. In certain vehicular applications, such as idle stop-start systems (ISSs), significant errors in SOC/SOH estimation may lead to a failure in restarting a combustion engine after the shut-off period of the engine when the vehicle is at rest, such as at a traffic light. In this paper, a dual extended Kalman filter algorithm with a dynamic equivalent circuit model of a lead-acid battery is proposed to deal with this problem. The proposed algorithm adopts a battery model by taking into account the hysteresis phenomenon, diffusion effect, and parameter variations for accurate state estimations of the battery. The validity of the proposed algorithm is verified through experiments by using an absorbed glass mat valve-regulated lead-acid battery and a battery sensor cable for commercial ISS vehicles.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.3
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• pp.189-200
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• 2010

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.