• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.517-526
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• 2001

In this paper, we study the continuous wavelet transform on the Heisenberg group H$^n$, and describe the related continuous multiscale analysis. By using the wavelet packet transform we obtain a reconstruction formula on L$^2$(H$^n$).

• Coupled systems mechanics
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• v.7 no.1
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• pp.1-4
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• 2018

This special issue contains selected papers first presented in a short format at the $3^{rd}$ International Conference ECCOMAS MSF 2017-Multiscale Computations for Solids and Fluids, organized in Slovenian capital Ljubljana, September 20-22, 2017.

• Coupled systems mechanics
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• v.9 no.1
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• pp.1-4
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• 2020

This special issue contains selected papers first presented in a short format at the 4th International Conference ECCOMAS MSF 2019 - Multiscale Computations for Solids and Fluids, organized in Bosnian capital Sarajevo, September 18-20, 2019.

• Coupled systems mechanics
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• v.10 no.6
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• pp.469-473
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• 2021

This special issue contains selected papers first presented in a short format at the 5th International Conference ECCOMAS MSF 2019-Multiscale Computations for Solids and Fluids, organized in Dalmatian capital Split, Croatia, June 30-July 2, 2021.

• Computers and Concrete
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• v.15 no.6
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• pp.865-878
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• 2015

In order to construct a multiscale model for the compressive strength of plain concrete columns with circular cross section subjected to central longitudinal compressive load, a column failure mechanism is proposed based on the theory of internal instability. Based on an energy analysis, the multiscale model is developed to describe the failure process and predict the column's compressive strength. Comparisons of the predicted results with experimental data show that the proposed multiscale model can accurately represent both the compressive strength of the concrete columns with circular cross section, and the effect of column size on its strength.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.404-409
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• 2004

The electrical contact resistance is here estimated using the multiscale microcontact distribution of elastic contact between rough surfaces, simulated from the Archard's model, and the electrical contact conduction theory suggested by Greenwood. These analysis confirms that the electrical contact resistance is converged to a values, larger than would be obtained if the contact spots were widely separated and hence independent. In multiscale process, the base potential is close to the value of the potential difference between the contact surface and the extremity of body, suggesting a possibility to obtain the multiscale electrical contact resistance relations.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.3
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• pp.251-258
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• 2004

Since the multiscale wavelet-based numerical methods allow effective adaptive analysis, they have become new analysis tools. However, the main applications of these methods have been mainly on elliptic problems, they are rarely used for eigenvalue analysis. The objective of this paper is to develop a new multiscale wavelet-based adaptive Galerkin method for eigenvalue analysis. To this end, we employ the hat interpolation wavelets as the basis functions of the finite-dimensional trial function space and formulate a multiresolution analysis approach using the multiscale wavelet-Galerkin method. It is then shown that this multiresolution formulation makes iterative eigensolvers very efficient. The intrinsic difference-checking nature of wavelets is shown to play a critical role in the adaptive analysis. The effectiveness of the present approach will be examined in terms of the total numbers of required nodes and CPU times.

• Nuclear Engineering and Technology
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• v.36 no.3
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• pp.229-236
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• 2004

Radiation hardening is a multiscale phenomenon involving various processes over a wide range of time and length. We present a multiscale model for estimating the amount of radiation hardening in pressure vessel steel in the environment of a light water reactor. The model comprises two main parts: molecular dynamics (MD) simulation and a point defect cluster (PDC) model. The MD simulation was used to investigate the primary damage caused by displacement cascades. The PDC model mathematically formulates interactions between point defects and their clusters, which explains the evolution of microstructures. We then used a dislocation barrier model to calculate the hardening due to the PDCs. The key input for this multiscale model is a neutron spectrum at the inner surface of reactor pressure vessel steel of the Younggwang Nuclear Power Plant No.5. A combined calculation from the MD simulation and the PDC model provides a convenient tool for estimating the amount of radiation hardening.

• Nuclear Engineering and Technology
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• v.50 no.5
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• pp.698-708
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• 2018

This article introduces a methodology of designing a wavelet operator suitable for multiscale modeling. The operator matrix transforms states of a multivariable system onto projection space. In addition, it imposes a specific structure on the system matrix in a multiscale environment. To be specific, the article deals with a diagonalizing transform that is useful for decoupled control of a system. It establishes that there exists a definite relationship between the model in the measurement space and that in the projection space. Methodology for deriving the multirate perfect reconstruction filter bank, associated with the wavelet operator, is presented. The efficacy of the proposed technique is demonstrated by modeling the point kinetics nuclear reactor. The outcome of the multiscale modeling approach is compared with that in the single-scale approach to bring out the advantage of the proposed method.

• Computers and Concrete
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• v.33 no.3
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• pp.325-340
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• 2024

The growing demands for sustainable and high-performance construction materials necessitate a deep understanding of their physicochemical properties by that of these heterogeneities. This paper presents a comprehensive review of the state-of-the-art hierarchical multiscale modeling approach aimed at predicting the intricate physicochemical characteristics of construction materials. Emphasizing the heterogeneity inherent in these materials, the review briefly introduces single-scale analyses, including the ab initio method, molecular dynamics, and micromechanics, through a scale-bridging technique. Herein, the limitations of these models are also overviewed by that of effectively scale-bridging methods of length or time scales. The hierarchical multiscale model demonstrates these physicochemical properties considering chemical reactions, material defects from nano to macro scale, microscopic properties, and their influence on macroscopic events. Thereby, hierarchical multiscale modeling can facilitate the efficient design and development of next-generation construction.