• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.33-50
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• 2023

Foreign exchange options are derivative financial instruments that can exchange one currency for another at a prescribed exchange rate on a specified date. In this study, we examine the analytic formulas for vulnerable foreign exchange options based on multi-scale stochastic volatility driven by two diffusion processes: a fast mean-reverting process and a slow mean-reverting process. In particular, we take advantage of the asymptotic analysis and the technique of the Mellin transform on the partial differential equation (PDE) with respect to the option price, to derive approximated prices that are combined with a leading order price and two correction term prices. To verify the price accuracy of the approximated solutions, we utilize the Monte Carlo method. Furthermore, in the numerical experiments, we investigate the behaviors of the vulnerable foreign exchange options prices in terms of model parameters and the sensitivities of the stochastic volatility factors to the option price.

• Coupled systems mechanics
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• v.5 no.4
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• pp.355-369
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• 2016

Changes in chemical structure have profound effects on the physical properties of epoxy-based materials, and eventually affect the durability of the entire system. Microscopic structural voids generally existing in the epoxy cross-linked networks have a detrimental influence on the epoxy mechanical properties, but the relation remains elusive, which is hindered by the complex structure of epoxy-based materials. In this paper, we investigate the effect of structural voids on the epoxy-based materials by using our developed mesoscale model equipped with the concept of multiscale modeling, and SU-8 photoresist is used as a representative of epoxy-based materials. Developed from the results of full atomistic simulations, the mesoscopic model is validated against experimental measurements, which is suitable to describe the elastic deformation of epoxy-based materials over several orders of magnitude in time- and length scales. After that, a certain quantity of the structure voids is incorporated in the mesoscale model. It is found that the existence of structural voids reduces the tensile stiffness of the mesoscale epoxy network, when compared with the case without any voids in the model. In addition, it is noticed that a certain number of the structural voids have an insignificant effect on the epoxy elastic properties, and the mesoscale model containing structural voids is close to those found in real systems.

• Proceedings of the Korea Air Pollution Research Association Conference
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• 2009.10a
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• pp.177-178
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• 2009

• Journal of the Korean Society of Safety
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• v.32 no.4
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• pp.1-6
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• 2017

Functionally Graded Materials (FGM) as advanced heterogeneous composite materials have a higher performance than a conventional composite or bimaterial composite under some severe environments. As a heterogeneous material, FGM is commonly used in spacecraft, defense, nuclear and automotive industries due to its excellent properties. The purposes of this study are to evaluate the stress distribution and crack behaviors by the multiscale simulation. FGM contains two or more than two materials that the composition is structured continuously. Two types of FGM model are suggested, which are created by arbitrary prediction of the volume fraction and the exponential function. Aluminum as the metal matrix constituent and silicon carbide as the ceramic particle constituent are structured gradually by two types and the three point bending test also estimated. Moreover, two kinds of crack location were introduced in order to get the influences of material property distribution on the stress intensity factor. From the results we found that the stress intensity factors are increased in the case from softer to stiffer material, while vice versa.

• Interaction and multiscale mechanics
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• v.2 no.1
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• pp.69-89
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• 2009

Reinforced and prestressed concrete (RC and PC) thin walls are crucial to the safety and serviceability of structures subjected to shear. The shear strengths of elements in walls depend strongly on the softening of concrete struts in the principal compression direction due to the principal tension in the perpendicular direction. The past three decades have seen a rapid development of knowledge in shear of reinforced concrete structures. Various rational models have been proposed that are based on the smeared-crack concept and can satisfy Navier's three principles of mechanics of materials (i.e., stress equilibrium, strain compatibility and constitutive laws). The Cyclic Softened Membrane Model (CSMM) is one such rational model developed at the University of Houston, which is being efficiently used to predict the behavior of RC/PC structures critical in shear. CSMM for RC has already been implemented into finite element framework of OpenSees (Fenves 2005) to come up with a finite element program called Simulation of Reinforced Concrete Structures (SRCS) (Zhong 2005, Mo et al. 2008). CSMM for PC is being currently implemented into SRCS to make the program applicable to reinforced as well as prestressed concrete. The generalized program is called Simulation of Concrete Structures (SCS). In this paper, the CSMM for RC/PC in material scale is first introduced. Basically, the constitutive relationships of the materials, including uniaxial constitutive relationship of concrete, uniaxial constitutive relationships of reinforcements embedded in concrete and constitutive relationship of concrete in shear, are determined by testing RC/PC full-scale panels in a Universal Panel Tester available at the University of Houston. The formulation in element scale is then derived, including equilibrium and compatibility equations, relationship between biaxial strains and uniaxial strains, material stiffness matrix and RC plane stress element. Finally the formulated results with RC/PC plane stress elements are implemented in structure scale into a finite element program based on the framework of OpenSees to predict the structural behavior of RC/PC thin-walled structures subjected to earthquake-type loading. The accuracy of the multiscale modeling technique is validated by comparing the simulated responses of RC shear walls subjected to reversed cyclic loading and shake table excitations with test data. The response of a post tensioned precast column under reversed cyclic loads has also been simulated to check the accuracy of SCS which is currently under development. This multiscale modeling technique greatly improves the simulation capability of RC thin-walled structures available to researchers and engineers.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.1
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• pp.29-38
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• 1994

Linear composite theory as well as a finite element program is developed for axisymmetric elastomeric bearings. This study is limited to axisymmetrically loaded horizontal layered systems with linear, elastic, small' deformation conditions. A multiscale method is used in the development of the composite theory which enables us to model inhomogeneous layered composites as equivalent homogeneous, orthotropic material. Only continuity of the prime variables is required for the finite element analysis, allowing the use of simple $C_o$ elements whereas rather complicated theories presented in the past need more requirements. Four node isoparametric elements are used in the study. The developed theory of this paper is limited to linear conditions, however, the analysis can be extended to nonlinear behavior of flexible material in elastomeric bearing by using multiscale method presented here. Two numerical examples are examined and compared to the results of discrete and previously obtained composite analysis to verify the theory.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.6
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• pp.577-582
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• 2016

In this study, a multiscale method for solving a thermoelasticity problem for interphase in the polymeric nanocomposites is developed. Molecular dynamics simulation and finite element analysis were numerically combined to describe the geometrical boundaries and the local mechanical response of the interfacial region where the polymer networks were highly interacted with the nanoparticle surface. Also, the micrmechanical thermoelasticity equations were applied to the obtained equivalent continuum unit to compute the growth of interphase thickness according to the size of nanoparticles, as well as the thermal phase transition behavior at a wide range of temperatures. Accordingly, the equivalent continuum model obtained from the multiscale analysis provides a meaningful description of the thermoelastic behavior of interphase as well as its nanoparticle size effect on thermoelasticity at both below and above the glass transition temperature.

• Interaction and multiscale mechanics
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• v.4 no.2
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• pp.165-171
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• 2011

In this study, we proposed a three-dimensional dynamic model under the diffuse interface description for the single crawling cell. From the developed model, we described the clear evolution processes for crawling neutrophil and assessed the reliable quantitative chemotactic property, which confirmed the high possibility of adequate predictions. To establish the system considering of multiple mechanisms such as, diffusion, chemotaxis, and interaction with surface, a diffuse interface model is employed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.6
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• pp.571-575
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• 2016

Photo responsive polymer(PRP) is well known for its photo deformation under UV light, and goes back to its original shape in visible light due to the photoisomerization of the azobenzene inside the PRP. In this paper, dynamic study of the vibration in PRP is discussed. In order to predict photo-deformation of the PRP a multiscale modeling is introduced which covers quantum level photo excitation, microscopic morphology, and macroscopic deformation of the PRP. A simple 1D beam model is introduced to model dynamic bending behavior of the PRP. Through fast Fourious transformation analysis, we identify that vibration frequency of the PRP can be controlled by light polarization angle.

• Interaction and multiscale mechanics
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• v.1 no.1
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• pp.83-101
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• 2008

A derivation is given of two-scale models that are able to describe deformation and flow in a fluid-saturated and progressively fracturing porous medium. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for a fluid-saturated porous medium, which are assumed to hold on the macroscopic scale. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The finite element equations are derived for this two-scale approach and integrated over time. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton-Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach.