Ductile fracture simulation using phase field approach under higher order regime

Nitin Khandelwal,Ramachandra A. Murthy 국제구조공학회 2024 Structural Engineering and Mechanics, An Int'l Jou Vol.89 No.2

The loading capacity of engineering structures/components reduces after the initiation and propagation of crack eventually leads to the final failure. Hence, it becomes essential to deal with the crack and its effects at the design and simulation stages itself, by detecting the prone area of the fracture. The phase-field (PF) method has been accepted widely in simulating fracture problems in complex geometries. However, most of the PF methods are formulated with second order continuity theoryinvolving C0 continuity. In the present study, PF method based on fourth-order (i.e., higher order) theory, maintaining C1 continuity has been proposed for ductile fracture simulation. The formulation includes fourth-order derivative terms of phase field variable, varying between 0 and 1. Applications of fourth-order PF theory to ductile fracture simulation resulted in novelty in this area. The proposed formulation is numerically solved using a two-dimensional finite element (FE) framework in 3- layered manner system. The solutions thus obtained from the proposed fourth order theory for different benchmark problems portray the improvement in the accuracy of the numerical results and are well matched with experimental results available in the literature. These results are also compared with second-order PF theory and a comparison study demonstrated the robustness of the proposed model in capturing ductile behaviour close to experimental observations.

헌법의 경제질서와 헌법 제32조 및 제33조에서의 근로자 개념의 재검토

한광수 한국노동법학회 2023 노동법학 Vol.- No.87

Unlike traditional wage workers, the new types of workers produced by the digital economy are excluded from the scope of protection of the Labor Relations Act and the social security system. I wrote this article out of an awareness of how to protect workers in the digital economy who are not protected by labor laws because they are not classified as existing labor relations. This is not a problem unique to Korea, but a common problem faced by other countries around the world. However, other countries protect these workers through court rulings while maintaining the existing labor law system. These countries classify workers in the digital economy into the realm of economic law and protect them through special laws by adding some labor law protection elements. Whether this method is desirable or is not should not be hastily judged. However, it is not desirable to exclude these workers from the scope of protection of the labor law because they have the status of workers who provide labor and make a living. This article aims to clarify the principles of the economic order pursued by the Constitution, and to study the constitutional significance of the concept of workers stipulated in the labor rights of Articles 32 and 33 of the Constitution in terms of these economic orders. Through our research, I learned several implications. First, the economic order stipulated in Article 119 of the Constitution is a social market economic order, and it functions as an independent economic order. Second, the meaning of ‘social’ in the social economic order can be subject to certain restrictions(limitation of basic rights, principle of prohibition of excess, etc.), and these restrictions must be balanced with the liberal value order and the socialist value order. Third, the significance of the social market economy order's function to improve the free (capital) market economy and the social rights value-oriented order principle are meaningful in understanding the concept of workers in Articles 32 and 33 of the Constitution. Fourth, the workers of Article 32 of the Constitution(Paragraph 1, Paragraph 3) and the workers of Article 33 are functionally related to each other. And when we judge subordination as an indicator of the concept of workers, we must consider the conceptual indicators of ‘employment(promotion)’ and ‘(decent)wages’ together. The constitutional implications of the concept of worker in Articles 32 and 33 of the Constitution are not limited to the traditional labor relationship. Fifth, the types of work in the digital economy of the 4th industrial revolution are diversifying, and these types of work are significantly increasing. Now, we must prepare a legal system that protects these labors without excluding them from the protection of the labor law. We must reconstruct the concept of workers suitable for the diversified types of work in the digital economy of the future society according to the value system of the Constitution.

Path-integral Monte Carlo Study of Asymmetric Quantum Quadrupolar Rotors with Fourth-order Propagators

박성진,신현덕,권용경 한국물리학회 2012 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.61 No.4

The recently-proposed fourth-order propagator based on the multi-product expansion has been applied to path-integral Monte Carlo calculations for asymmetric quantum quadruploar rotors fixed at face-centered cubic lattice sites. The rotors are observed to undergo an orientational orderdisorder phase transition at a low temperature when the electric quadrupole-quadrupole interaction is strong enough. At intermediate interaction strength, a further decrease of temperature after the first transition to the ordered phase results in a reentrant transition back to the disordered phase. The theoretical phase diagram of these asymmetric rotors determined by using fourth-order path-integral Monte Carlo calculations is found to be in good quantitative agreement with the experimental one for solid hydrogen deuteride. This leads us to conclude that the fourth-order propagator can be effectively implemented for an accurate path-integral Monte Carlo calculation of a quantum many-body system with rotational degrees of freedom.

4차 산업 시대 한국불교의 출가문제와 미래적 대안

염중섭(자현) 한국선학회 2018 한국선학 Vol.0 No.50

3차 산업에서 4차 산업으로 넘어가는 과도기임에도 불구하고, 한국불교는 탈종교화 등에 따른 출가자 수 급감이라는 극심한 위기상황에 직면해 있다. 이는 4차 산업 시대의 본격적인 전개가 출가문제와 관련해 더 큰 문제로 존재할 수 있음을 의미한다. 본고는 4차 산업 시대에 한국불교, 그중에서도 조계종의 타당성을 출가문제와 결부 지어 검토해본 것이다. 이를 위해 먼저 4차 산업 시대의 특징을 정리하고, 조계종의 시대적 타당성을 살펴본다. 이와 같은 결과로 확인되는 것은 4차 산업 시대에 인간소외와 행복추구가 보다 극명해질 것이며, 수행과 인간 행복을 기반으로 하는 조계종의 필연성이 증대된다는 것이다. 특히 남종선(南宗禪)을 계승한 조계종의 수행론은 현실과 유리된 명상이 아닌 현실을 긍정하는 수행의 완성을 주장한다. 이는 현실의 변화가 조계종과 충돌하지 않는다는 의미다. 즉 조계종은 4차 산업 시대의 빠른 변화를 수용하면서 변모될 수 있는 가능성을 내포하고 있는 것이다. 끝으로 4차 산업 시대의 출가와 관련된 해법으로, 본고에서는 세계적인 추세인 명상에 대한 요청과 이와 연관된 마음의 출가 부분을 제시했다. 육체적인 출가에 사회와의 단절이라는 인식이 존재한다면, 명상과 행복추구와 관련된 마음의 출가는 현대인이 선호하는 측면에 다름 아니다. 그러므로 마음의 출가를 통해 조계종의 외연을 확대하고, 이를 통한 육체적인 출가구조를 재정립할 필요가 있다. 이는 조계종이 4차 산업 시대에 주류의 위상을 확보하는 핵심이 될 수 있다는 점에서 주목된다. In this transition era moving from the 3rd industry to the 4th industry, Korean Buddhism is facing a severe crisis of sudden drop in the number of those who leave their houses to be priests due to de-religiousization. The full-scale development of the 4th industry era will result in a rational and massive change due to the super-intelligence and the super-connection. This means that there may be a bigger problem in relation to the house-leaving. This paper examines the validity of Korean Buddhism, especially the Jogye Order, in the 4th industrial era, in conjunction with the issue of being a Buddhist priest. For this purpose, the characteristics of the 4th industrial age are first summarized and the feasibility of the Jogye Order in this period is examined. As a result, it is confirmed that human alienation and pursuit of happiness will become more clear in the fourth industrial age, and the Jogye Order will be more necessary, for it is based on the discipline and human happiness. Especially, the discipline theory of Jogye Order that inherited the Namjongseon(南宗禪) insists on the fulfillment of the discipline that admits the reality rather than the meditation separated from the reality. This means that the change of reality does not conflict with the Jogye Order. In other words, the Jogye Order can accommodate the rapid change of the 4th industrial age and can transform itself according to the change. Finally, as a solution to the fourth industrialization era, this paper proposes the request for meditation that has become a global trend and the house-leaving of mind in relation to it. If there is a perception that the physical house-leaving is the disconnection from society, the mental house-leaving related to the meditation and the pursuit of happiness is no different to what modern people prefer. Therefore, it is necessary to expand the outline of the Jogye Order through the mental house-leaving, and to reestablish the structure of physical house-leaving through it. It is noteworthy that Jogye Order can be the key to secure the mainstream status in the 4th industrial era in this way.

A fourth-order spatial accurate and practically stable compact scheme for the Cahn-Hilliard equation

Lee, C.,Jeong, D.,Shin, J.,Li, Y.,Kim, J. North-Holland 2014 PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIO Vol.409 No.-

We present a fourth-order spatial accurate and practically stable compact difference scheme for the Cahn-Hilliard equation. The compact scheme is derived by combining a compact nine-point formula and linearly stabilized splitting scheme. The resulting system of discrete equations is solved by a multigrid method. Numerical experiments are conducted to verify the practical stability and fourth-order accuracy of the proposed scheme. We also demonstrate that the compact scheme is more robust and efficient than the non-compact fourth-order scheme by applying to parallel computing and adaptive mesh refinement.

4차 하천에서의 GIUH의 유도 및 초기확률의 보정에 관한 연구

함대헌,주진걸,전환돈,김중훈 한국수자원학회 2008 한국수자원학회논문집 Vol.41 No.2

본 연구는 3차 하천에 대하여 유도되었던 지형형태학적순간단위도(GIUH)를 4차 하천유역까지 확장하여 다양한 유역에 적용할 수 있도록 하였다. 차 하천에 대한 GIUH를 비교하였으며 유역의 지형매개변수가 동일할 경우 하천차수를 높게 가정할수록 단위도의 첨두유출량은 작아지고 첨두발생시간은 늦어지는 경향을 확인할 수 있었다. GIUH의 적용을 위해서는 면적비와 분기비 등 지형매개변수를 사용하여 초기확률을 산정하는데, 이때 지형매개변수가 가지는 오차 때문에 This study is to derive the fourth-order Geomorphologic Instantaneous Unit Hydrograph (GIUH), driven for only third-order basin, for the application of GIUH to various types of basin. The second, third, and fourth order GIUHs were compared for various top

Blind channel equalization using fourth-order cumulants and a neural network

Soowhan Han 한국지능시스템학회 2005 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.5 No.1

This paper addresses a new blind channel equalization method using fourth-order cumulants of channel inputs and a three-layer neural network equalizer. The proposed algorithm is robust with respect to the existence of heavy Gaussian noise in a channel and does not require the minimum-phase characteristic of the channel. The transmitted signals at the receiver are over-sampled to ensure the channel described by a full-column rank matrix. It changes a single-input/single-output (SISO) finite-impulse response (FIR) channel to a single-input/multi-output (SIMO) channel. Based on the properties of the fourth-order cumulants of the over-sampled channel inputs, the iterative algorithm is derived to estimate the deconvolution matrix which makes the overall transfer matrix transparent, i.e., it can be reduced to the identity matrix by simple recordering and scaling. By using this estimated deconvolution matrix, which is the inverse of the over-sampled unknown channel, a three-layer neural network equalizer is implemented at the receiver. In simulation studies, the stochastic version of the proposed algorithm is tested with three-ray multi-path channels for on-line operation, and its performance is compared with a method based on conventional second-order statistics. Relatively good results, withe fast convergence speed, are achieved, even when the transmitted symbols are significantly corrupted with Gaussian noise.

An efficient and stable compact fourth-order finite difference scheme for the phase field crystal equation

Li, Yibao,Kim, Junseok North-Holland Pub. Co 2017 Computer methods in applied mechanics and engineer Vol.319 No.-

<P><B>Abstract</B></P> <P>In this paper, we present a high-order accurate compact scheme for the phase field crystal model in two- and three-dimensional spaces. The proposed scheme is derived by combining a fourth-order compact finite difference formula in space and a backward differentiation for the time derivative term, which is second-order accurate in time. Furthermore, a nonlinearly stabilized splitting scheme is used and thus a larger time step can be allowed. Since the equations at the implicit time level are nonlinear, we introduce a Newton-type iterative method and employ a fast and efficient nonlinear multigrid solver to solve the resulting discrete system. In particular, we implement the compact scheme in the adaptive mesh refinement framework. An adaptive time step method for the phase field crystal model is also proposed. Various numerical experiments are presented and confirm the accuracy, stability, and efficiency of our proposed method.</P> <P><B>Highlights</B></P> <P> <UL> <LI> We propose an efficient and stable compact fourth-order method for the phase field crystal equation. </LI> <LI> The proposed numerical method with second order accuracy of time exhibits excellent stability. </LI> <LI> We implement the compact scheme in the adaptive mesh refinement framework. </LI> <LI> An adaptive time step method for the phase field crystal model is also presented. </LI> </UL> </P>

EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTIONS TO A FOURTH-ORDER DEGENERATE PARABOLIC EQUATION

Bo Liang,Meishan Wang,Ying Wang 대한수학회 2015 대한수학회보 Vol.52 No.4

The paper is devoted to studying a fourth-order degenerate parabolic equation, which arises in fluid, phase transformation and biology. Based on the existence and uniqueness of one semi-discrete problem, two types of approximate solutions are introduced. By establishing some necessary uniform estimates for those approximate solutions, the existence and uniqueness of the corresponding parabolic problem are obtained. Moreover, the long time asymptotic behavior is established by the entropy functional method.

EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTIONS TO A FOURTH-ORDER DEGENERATE PARABOLIC EQUATION

LIANG, BO,WANG, MEISHAN,WANG, YING Korean Mathematical Society 2015 대한수학회보 Vol.52 No.4

The paper is devoted to studying a fourth-order degenerate parabolic equation, which arises in fluid, phase transformation and biology. Based on the existence and uniqueness of one semi-discrete problem, two types of approximate solutions are introduced. By establishing some necessary uniform estimates for those approximate solutions, the existence and uniqueness of the corresponding parabolic problem are obtained. Moreover, the long time asymptotic behavior is established by the entropy functional method.