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Multiscale and Multiphysics Mechanics
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Volume 1, Issue 3 - Jul 2016
Volume 1, Issue 2 - Apr 2016
Volume 1, Issue 1 - Jan 2016
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A split kinetic energy solution scheme applied to various delta potentials in quantum mechanical systems
Chen, Yu-Hsin ; Chao, Sheng D. ;
Multiscale and Multiphysics Mechanics, volume 1, issue 3, 2016, Pages 189~200
DOI : 10.12989/mmm.2016.1.3.189
In this work, we extend the split previously developed kinetic energy (dubbed as KEP) method Mineo and Chao (2012) by modifying the mass parameter to include the negative mass. We first show how to separate the total system into the subsystems with 3 attractive delta potentials by using the KEP method. For repulsive delta potentials, we introduce "negative" mass terms. Two cases are demonstrated using the "negative" mass terms for repulsive delta potential problems in quantum mechanics. Our work shows that the KEP solution scheme can be used to obtain not only the exact energies but also the exact wavefuctions very precisely.
Heat jet approach for finite temperature atomic simulations of two-dimensional square lattice
Liu, Baiyili ; Tang, Shaoqiang ;
Multiscale and Multiphysics Mechanics, volume 1, issue 3, 2016, Pages 201~224
DOI : 10.12989/mmm.2016.1.3.201
We propose a heat jet approach for a two-dimensional square lattice with nearest neighbouring harmonic interaction. First, we design a two-way matching boundary condition that linearly relates the displacement and velocity at atoms near the boundary, and a suitable input in terms of given incoming wave modes. Then a phonon representation for finite temperature lattice motion is adopted. The proposed approach is simple and compact. Numerical tests validate the effectiveness of the boundary condition in reflection suppression for outgoing waves. It maintains target temperature for the lattice, with expected kinetic energy distribution and heat flux. Moreover, its linear nature facilitates reliable finite temperature atomic simulations with a correct description for non-thermal motions.
Design of silicon-on-nothing structure based on multi-physics analysis
Song, Jihwan ; Zhang, Linan ; Kim, Dongchoul ;
Multiscale and Multiphysics Mechanics, volume 1, issue 3, 2016, Pages 225~231
DOI : 10.12989/mmm.2016.1.3.225
The formation of silicon-on-nothing (SON) structure during an annealing process from the silicon substrate including the trench structures has been considered as an effective technique to construct the structure that has an empty space under the closed flat surface. Previous studies have demonstrated the mechanism of the formation of SON structure, which is based on the surface diffusion driven by the minimization of their surface energy. Also, it has been fragmentarily shown that the morphology of SON structure can be affected by the initial design of trench (e.g., size, number) and the annealing conditions (e.g., temperature, pressure). Based on the previous studies, here, we report a comprehensive study for the design of the cavity-embedded structure (i.e., SON structure). To do this, a dynamic model has been developed with the phase field approach. The simulation results represent that the morphology of SON structures could be detailedly designed, for example the position and thickness of cavity, the thickness of top and bottom layer, according to the design parameters. This study will give us an advantage in the effective design of SON structures.
Antiferroelectric and antiferrodistortive phase transitions in Ruddlesden-Popper Pb
Xu, Tao ; Shimada, Takahiro ; Wang, Jie ; Kitamura, Takayuki ;
Multiscale and Multiphysics Mechanics, volume 1, issue 3, 2016, Pages 233~244
DOI : 10.12989/mmm.2016.1.3.233
This work employed density functional theory to investigate the structural and ferroelectric properties of the Ruddlesden-Popper (RP) phase of lead titanate,
, as well as its phase transitions with epitaxial strain. A wealth of novel structural instabilities, which are absent in the host
material, were identified in the RP phase through phonon soft-mode analysis. Our calculations showed that the ground state of
is antiferroelectric, distinct from the dominant ferroelectric phase in the corresponding host material. In addition, applied epitaxial strain was found to play a key role in the interactions among the instabilities. The induction of a sequence of antiferroelectric and antiferrodistortive (AFD) phase transitions by epitaxial strain was demonstrated, in which the ferroic instability and AFD distortion were cooperative rather than competitive, as is the case in the host
. The RP phase in conjunction with strain engineering thus represents a new approach to creating ferroic orders and modifying the interplay among structural instabilities in the same constituent materials, enabling us to tailor the functionality of perovskite oxides for novel device applications.
Mechanics of lipid membranes subjected to boundary excitations and an elliptic substrate interactions
Kim, Chun IL ;
Multiscale and Multiphysics Mechanics, volume 1, issue 3, 2016, Pages 245~259
DOI : 10.12989/mmm.2016.1.3.245
We present relatively simple derivations of the Helfrich energy potential that has been widely adopted in the analysis of lipid membranes without detailed explanations. Through the energy variation methods (within the limit of Helfrich energy potential), we obtained series of analytical solutions in the case when the lipid membranes are excited through their edges. These affordable solutions can be readily applied in the related membrane experiments. In particular, it is shown that, in case of an elliptic cross section of a rigid substrate differing slightly from a circle and subjected to the incremental deformations, exact analytical expressions describing deformed configurations of lipid membranes can be obtained without the extensive use of Mathieu`s function.
Estimation of longitudinal velocity noise for rail wheelset adhesion and error level
Soomro, Zulfiqar Ali ;
Multiscale and Multiphysics Mechanics, volume 1, issue 3, 2016, Pages 261~270
DOI : 10.12989/mmm.2016.1.3.261
The longitudinal velocity (forward speed) having significant importance in proper running of railway wheelset on track, depends greatly upon the adhesion ratio and creep analysis by implementation of suitable dynamic system on contamination. The wet track condition causes slip and slide of vehicle on railway tracking, whereas high speed may also increase slip and skidding to severe wear and deterioration of mechanical parts. The basic aim of this research is to design appropriate model aimed estimator that can be used to control railway vehicle forward velocity to avoid slip. For the filtration of disturbance procured during running of vehicle, the kalman filter is applied to estimate the actual signal on preferered samples of creep co-efficient for observing the applied attitude of noise. Thus error level is detected on higher and lower co-efficient of creep to analyze adhesion to avoid slip and sliding. The skidding is usually occurred due to higher forward speed owing to procured disturbance. This paper guides to minimize the noise and error based upon creep coefficient.
Identification of crystal variants in shape-memory alloys using molecular dynamics simulations
Wu, Jo-Fan ; Yang, Chia-Wei ; Tsou, Nien-Ti ; Chen, Chuin-Shan ;
Multiscale and Multiphysics Mechanics, volume 1, issue 3, 2016, Pages 271~284
DOI : 10.12989/mmm.2016.1.3.271
Shape-memory alloys (SMA) have interesting behaviors and important mechanical properties due to the solid-solid phase transformation. These phenomena are dominated by the evolution of microstructures. In recent years, the microstructures in SMAs have been studied extensively and modeled using molecular dynamics (MD) simulations. However, it remains difficult to identify the crystal variants in the simulation results, which consist of large numbers of atoms. In the present work, a method is developed to identify the austenite phase and the monoclinic martensite crystal variants in MD results. The transformation matrix of each lattice is calculated to determine the corresponding crystal variant. Evolution of the volume fraction of the crystal variants and the microstructure in Ni-Ti SMAs under thermal and mechanical boundary conditions are examined. The method is validated by comparing MD-simulated interface normals with theoretical solutions. In addition, the results show that, in certain cases, the interatomic potential used in the current study leads to inconsistent monoclinic lattices compared with crystallographic theory. Thus, a specific modification is applied and the applicability of the potential is discussed.