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There are three criteria when we model with phase-field equations. The first one is the evolution of phase separation. The second one is energy dissipation law. The last one is whether we have the law of conservation of mass or not. If we minimize the Ginzburg–Landau free-energy functional, the kinetics of phase separation inherently follows. However, the other properties such as energy dissipation and mass conservation are more difficult to model. Hitherto, there have been a few proposals to conserve mass using the Allen–Cahn (AC) equation, but we do not have the energy dissipation law in these models when considered in light of local effects of mass-correction. For the reasons, certain researchers still prefer to use the Cahn–Hilliard equation, e.g. biharmonic equation instead of using the Allen–Cahn equation when we consider a mass conserving case. This paper is concerned with numerical solutions of the AC equation in the mass-conserving space, where the solution is corrected at each iteration for mass conservation. We introduce two different methods for solving the conservative AC equation with periodic boundary conditions. In this work, we have the AC equation in common, but use two different mass correction operators. Note that both of mass correction operators satisfy the discrete energy dissipation property. First, we project the solution of the AC equation to the mass conserving space, and then recover the linear convex splitting scheme for the conventional mass-conserving equation. The linear convex splitting scheme is well-known but the convergence of numerical solutions is elaborately studied in terms of gradient-projection. Next, we propose the other energy-minimizing method on the mass-conserving space. It translates the solution of the AC equation to the mass conserving space via an energy-dissipation operator. The dissipation of discrete energy functional for the proposed method is also established. As far as the author knows, no report has been presented for the numerical scheme having discrete energy dissipation property of the mass-conserving AC equation without using the nonlocal and constant multiplier. To verify the common properties of mass-projection and proposed methods numerically, we simulate the evolutions for phase separation, dissipation of energy, and mass conservation. We moreover consider the short and long time stages of evolutions to see the difference between two methods. These several tests are provided for its applications of the proposed method for modeling natural phenomena.

We extend the classical Allen–Cahn (AC) equation to the fractional Allen–Cahn equation (FAC) with triple-well potential. By replacing the spatial Laplacian and double-well potential with fractional Laplacian and triple-well potential, we observe different dynamics. This study leads us to understand different properties of the FAC equation. We seek the existence, boundedness, and unique solvability of numerical solutions for the FAC equation with triple-well potential. In addition, the inclusion principle for the Allen–Cahn equation is considered. These different properties make us enhance the applicability of the phase-field method to the mathematical modeling in materials science. In computation, the spectral decomposition for the fractional operator allows us to develop a numerical method for the fractional Laplacian problem. For the periodic and discrete Laplacian matrix and vector multiplication, circulant submatices are formed in more than two-dimensional case. Even if the fast Fourier transform (FFT) can be utilized in this modeling, we construct the inverse of the doubly-block-circulant matrix for the solution of the fractional Allen–Cahn equation. In doing so, it helps to straightforwardly understand the numerical treatment, and exploit the properties of the discrete Fourier transforms.

We present the image segmentation model using the modified Allen–Cahn equation with a fractional Laplacian. The motion of the interface for the classical Allen–Cahn equation is known as the mean curvature flows, whereas its dynamics is changed to the macroscopic limit of Lévy process by replacing the Laplacian operator with the fractional one. To numerical implementation, we prove the unconditionally unique solvability and energy stability of the numerical scheme for the proposed model. The effect of a fractional Laplacian operator in our own and in the Allen–Cahn equation is checked by numerical simulations. Finally, we give some image segmentation results with different fractional order, including the standard Laplacian operator.

We investigated the association of multiple single nucleotide polymorphisms (SNPs) with athlete status and power/speed performance in elite male youth soccer players (ESP) and control participants (CON) at different stages of maturity. ESP (n = 535; aged 8-23 years) and CON (n = 151; aged 9-26 years) were genotyped for 10 SNPs and grouped according to years from predicted peak-height-velocity (PHV), i.e. pre- or post-PHV, to determine maturity status. Participants performed bilateral vertical countermovement jumps, bilateral horizontal-forward countermovement jumps, 20m sprints and modified 505-agility tests. Compared to CON, pre-PHV ESP demonstrated a higher ACTN3 (rs1815739) XX ('endurance') genotype frequency distribution, while post-PHV ESP revealed a higher frequency distribution of the PPARA (rs4253778) C-allele, AGT (rs699) GG genotype and NOS3 (rs2070744) T-allele ('power' genotypes/alleles). BDNF (rs6265) CC, COL5A1 (rs12722) CC and NOS3 TT homozygotes sprinted quicker than A-allele carriers, CT heterozygotes and CC homozygotes, respectively. COL2A1 (rs2070739) CC and AMPD1 (rs17602729) GG homozygotes sprinted faster than their respective minor allele carrier counterparts in CON and pre-PHV ESP, respectively. BDNF CC homozygotes jumped further than T-allele carriers, while ESP COL5A1 CC homozygotes jumped higher than TT homozygotes. To conclude, we have shown for the first time that pre- and post-PHV ESP have distinct genetic profiles, with pre-PHV ESP more suited for endurance, and post-PHV ESP for power and speed (the latter phenotypes being crucial attributes for post-PHV ESP). We have also demonstrated that power, acceleration and sprint performance were associated with five SNPs, both individually and in combination, possibly by influencing muscle size and neuromuscular activation.

In this paper, we propose an unconditionally stable numerical scheme for the Allen–Cahn (AC) equation with high-order (higher than fourth) polynomial free energy. The AC equation was proposed by Allen and Cahn to model the anti-phase domain coarsening in a binary mixture. The AC equation has been extensively used as a building block equation for modeling many scientific problems such as image processing, dendritic growth, motion by mean curvature, and multi-phase fluid flows. The AC equation can be derived from a gradient flow of a total energy functional which consists of a double-well form potential and a gradient term. Practically, a quartic polynomial has been used for the double-well potential. High-order (greater than fourth) polynomial free energy potentials can be also used in the total energy functional and can better represent interfacial dynamics of the AC equation. However, the AC equation with the high-order polynomial is getting stiffer as the polynomial order increases. Typically, this type of double-well potential is solved using a convex splitting with a stabilizing parameter and effectively modifies the original governing equation. In the proposed method, we use a second-order operator splitting method and an interpolation method. First, we solve the nonlinear double-well potential term using interpolation from the pre-computed values. Second, we solve the diffusion equation using the Crank–Nicolson method and multigrid method. The overall scheme is unconditionally stable and we theoretically prove the unconditional stability. Computational experiments are performed to demonstrate the robustness and accuracy of the proposed method; and investigate the effect of the order of the double-well potential on the dynamics of the AC equation. Finally, we highlight the different dynamics for the AC equation with polynomial free energy of various orders. The computational results suggest that the proposed method will be useful for modeling various interfacial phenomena.

The goal of this paper is to present a brief review and a critical comparison of the performance of several numerical schemes for solving the Allen–Cahn equation representing a model for antiphase domain coarsening in a binary mixture. Explicit, fully implicit, Crank–Nicolson, and unconditionally gradient stable schemes are considered. In this paper, we show the solvability conditions of the numerical schemes and the decreasing property of total energy using eigenvalues of the Hessian matrix of the energy functional. We also present the pointwise boundedness of the numerical solution for the Allen–Cahn equation. To compare the accuracy and numerical efficiency of these methods, numerical experiments such as traveling wave and motion by mean curvature are performed. Numerical results show that Crank–Nicolson and nonlinearly stabilized splitting schemes are almost close to the analytic solution. However, if a large time step is used in the numerical test, we have only two results with linearly and nonlinearly stabilized splitting schemes in spite of having large gaps between analytic solution and numerical results. The other numerical schemes except for linearly and nonlinearly stabilized splitting schemes have unstable results when large time step is used.

In this paper, a comparison study of conservative Allen–Cahn and Cahn–Hilliard equations is presented. We consider two mass-conservative Allen–Cahn equations and two Cahn–Hilliard equations with constant and variable mobilities. The equations are discretized using finite difference schemes, and discrete systems of the equations are solved using a nonlinear multigrid method. The generation and motion of interface are investigated for the conservative equations. We then present numerical experiments which highlight different dynamics of the four equations.

There are several theoretically well-posed models for the Allen–Cahn equation under mass conservation. The conservative property is a gift from the additional nonlocal term playing a role of a Lagrange multiplier. However, the same term destroys the boundedness property that the original Allen–Cahn equation presents: The solution is bounded by 1 with an initial datum bounded by 1. In this paper, we propose a novel mass-conserving Allen–Cahn equation and prove the existence and uniqueness of a classical solution in the context of the theory of analytic semigroups as well as the boundedness property of the solution. From the numerical point of view, we investigate a linear unconditionally energy stable splitting scheme of the proposed model for the boundedness of numerical solutions. Various numerical experiments are presented to demonstrate the validity of the proposed method and to make distinctions from a few closely related methods.

In this paper, a precise relative positioning with TD(time differenced) carrier phase measurements from a low-cost GNSS(Global Navigation Satellite System) receiver is proposed and analysed. The proposed method is using carrier phase measurement from a single GNSS receiver that reference receiver is not required and stand alone positioning is possible. TD operation removes the troublesome integer ambiguity resolution problem, and if the time interval is short, other error, such as, ionospheric, tropospheric delay and ephemeris error are effectively eliminated. The error analysis of the proposed method shows that a precise and positioning with carrier phase is possible. The implemented system is evaluated using a real car experiments. The results show that the horizontal positioning error was less than 3m during 10 minutes experiments, which is 4 times more precise than the results of normal code based absolute positioning.

In this study, a Global Navigation Satellite System (GNSS) / Inertial Navigation System (INS) / odometer / barometer integrated navigation system that uses a commercial navigation device including Micro Electro Mechanical Systems (MEMS) accelerometer and gyroscope in addition to GNSS, odometer information obtained from a vehicle, and a separate MEMS barometer sensor was implemented, and the performance was verified. In the case of GNSS and GNSS/INS integrated navigation system that are generally used in a navigation device, the performance would deteriorate in areas where GNSS signals are not available. Therefore, an integrated navigation system that calculates a better navigation solution in areas where GNSS signals are not available compared to general GNSS/INS by correcting the velocity error of GNSS/INS using an odometer and by correcting the cumulative altitude error of GNSS/INS using a barometer was suggested. To verify the performance of the navigation system, a commercial navigation device (Softman, Hyundai Mnsoft, http://www.hyundai-mnsoft.com) and a barometer sensor (ST Company) were installed at a vehicle, and an actual driving test was performed. To examine the performance of the algorithm, the navigation solutions of general GNSS/INS and the GNSS/INS/odometer/barometer integrated navigation system were compared in an area where GNSS signals are not available. As a result, a navigation solution that has a smaller position error than that of GNSS/INS could be obtained in the area where GNSS signals are not available.

In this paper, we investigate motion by mean curvature using the Allen–Cahn (AC) equation in two and three space dimensions. We use an unconditionally stable hybrid numerical scheme to solve the equation. Numerical experiments demonstrate that we can use the AC equation for applications to motion by mean curvature. We also study the curve-shortening flow with a prescribed contact angle condition.

We briefly review and investigate the performance of various boundary conditions such as Dirichlet, Neumann, linear, and partial differential equation boundary conditions for the numerical solutions of the Black-Scholes partial differential equation. We use a finite difference method to numerically solve the equation. To show the efficiency of the given boundary condition, several numerical examples are presented. In numerical test, we investigate the effect of the domain sizes and compare the effect of various boundary conditions with pointwise error and root mean square error. Numerical results show that linear boundary condition is accurate and efficient among the other boundary conditions.

Brassinosteroids (BRs) play an essential role in plant growth, development, and responses to diverse abiotic stresses. However, previous studies mainly analyzed how exogenous BRs influenced plant physiological reactions to drought stress, therefore, genetic evidences for the endogenous BRs-mediated regulation of plant responses still remain elusive. In this study, a key BRs biosynthetic gene, SoCYP85A1 was cloned from Spinacia oleracea, which has a complete open reading frame of 1,392 bp encoding a 464 amino acid peptide and shares high sequence similarities with CYP85A1 from other plants. The expression of SoCYP85A1 which was higher in leaf compared with root and stem, was induced by treatments of PEG6000, abscisic acid (ABA), low temperature and high salt. Increases in both SoCYP85A1 transcripts and endogenous BRs in transgenic tobacco which resulted in longer primary root and more lateral roots enhanced drought tolerance compared with wild types. The transgenic tobacco accumulated much lower levels of reactive oxygen species and malondialdehyde (MDA) than wild types did, accompanied by significantly higher content of proline and notably enhanced activities of antioxidant enzymes. Besides, transcriptional expressions of six stress-responsive genes were regulated to higher levels in transgenic lines under drought stress. Taken together, our results demonstrated that SoCYP85A1 involves in response to drought stress by promoting root development, scavenging ROS, and regulating expressions of stress-responsive genes.

E-mail: ykim@kku.ac.krReceived July 1, 2014, Accepted July 31, 2014Key Words : Small CTD phosphatases, SCP1, SMAD2, Dephosphorylation, SMAD phosphataseProtein phosphatase is important for cellular events, and afamily of protein phosphatases, the so-called C-terminaldomain (CTD) of RNA polymerase II (RNAPII) phos-phatases, has recently attracted attention. The CTD is thelargest subunit of RNAPII and consists of a tandem repeatedheptapeptide (Y

In this paper, we present a novel fast and accurate numerical method for the surface embedding narrow volume reconstruction from unorganized points in R^3. Though the level set method prevails in the image processing, it requires a redistancing procedure to maintain a desired shape of the level set function. On the other hand, our method is based on the Allen-Cahn equation, which has been applied in image segmentation due to its motion by mean curvature property. We modify the original Allen-Cahn equation by multiplying a control function to restrict the evolution within a narrow band around the given surface data set. To improve the numerical stability of our proposed model, we split the governing equation into linear and nonlinear terms and use an operator splitting technique. The linear equation is solved by the multigrid method which is a fast solver and the nonlinear equation is solved analytically. The unconditional stability of the proposed scheme is also proved. Various numerical results are presented to demonstrate the robustness and accuracy of the proposed method.

To investigate the effects of hydrogen on crack propagation in the extremely low growth rate range, fully reversed bending fatigue tests were performed on low carbon steel (JIS S10C) in hydrogen and in nitrogen gas environments at a low pressure. A crack showed almost the same non-propagation behavior in nitrogen as that in air. However, a crack in hydrogen continued to propagate even near \(10^{7}\) cycles in the same testing strain range as that in nitrogen. In hydrogen gas, a crack grew intermittently by coalescing with a new micro-crack generated by slip behavior. This implies that hydrogen could inhibit the action of any factor affecting non-propagation.

The goal of this study is to find an experimental condition which enables us to perform enzymatic studies on the cellular behavior of PTEN (phosphatase and tensine homolog) through identification of molecular species of phosphatidylinositol 3,4,5- trisphosphates and their quantitative analysis in a mammalian cell line using mass spectrometry. We initially exployed a two-step extraction process using HCl for extraction of phosphatidylinositol 3,4,5-trisphosphates from two mammalian cell lines and further analyzed the extracted phosphatidylinositol 3,4,5-trisphosphates using tandem mass spectrometry for the identification of them. We finally quantified the concentration of phosphatidylinositol 3,4,5-trisphosphates using internal standard calibration. From these observation, we found that HEK 293-T cells is a good model to examine the enzymatic behavior of PTEN in a cell, and the minimum amount of phosphatidylinositol 3,4,5-trisphosphates is more than 50 pmol for quantification in a mass spectrometer. These results suggest that the well-optimized experimental conditions are required for the investigation of the cellular PTEN in terms of the catalytic mechanism and further for the detailed identification of cellular substrates.

We present a volume-preserving scheme for two-phase immiscible incompressible flows using an immersed boundary method (IBM) in a three-dimensional space. The two-phase IBM employs a mixture of Eulerian and Lagrangian variables, where the fluid interface is represented by discrete Lagrangian markers exerting surface tension forces to the Eulerian fluid domain and the markers are advected by the fluid velocity. The interactions between the Lagrangian markers and the fluid variables are linked by the discretized Dirac delta function. The present study extends the previous two-dimensional research (Li et al., Volume preserving immersed boundary methods for two-phase fluid flows, Int. J. Numer. Meth. Fluids 69 (2012) 842–858) to the three-dimensional space. The key idea of the proposed method is relocating surface points along the normal directions to conserve the total volume. We perform a number of numerical experiments to show the efficiency and accuracy of the proposed method.

We present a parallel finite difference scheme and its implementation for solving the Cahn–Hilliard equation, which describes the phase separation process. Our numerical algorithm employs an unconditionally gradient stable splitting discretization method. The resulting discrete equations are solved using a parallel multigrid method. This parallel scheme facilitates the solution of large-scale problems. We provide numerical results related to the speed-up, efficiency, and scalability to demonstrate the high performance of our proposed method. We also propose a linearly stabilized splitting scheme for the Cahn–Hilliard equation with logarithmic free energy.

Owing to energy conservation and environmental concerns, hydrogen has been suggested as a next-generation energy source. However, hydrogen known to seep into a metal, degrade its strength, and accelerate fatigue crack growth rates. We have investigated the effects of hydrogen gas on the small fatigue crack growth characteristics of low carbon steel JIS S10C by conducting bending fatigue tests on a specimen with a small blind hole and placed in a low-pressure hydrogen environment. The fatigue crack growth rate in hydrogen was higher than that in nitrogen. The fracture surface of the specimen in hydrogen showed intergranular facets in the low- growth-rate range and a quasi-cleavage fracture surface with brittle striations in the high-growth-rate range. The specimen only showed a ductile fracture surface for nitrogen. The small-fatigue-crack growth rate for nitrogen is given by $${dl/dN\propto \Delta \varepsilon_{p}^{n}l}$$ , where l, N, and $${\Delta \varepsilon_{p}}$$ represent the crack length, number of repetitions, and plastic strain range, respectively. This equation was also satisfied for hydrogen, but only over a short strain range from $${\Delta \varepsilon_t = 0.25}$$ to 0.37 % in which the fracture surface exhibited intergranular facets and a ductile morphology, but no quasi-cleavage fracture. The exponent n of the equation was 1.22 in nitrogen and 0.66 in hydrogen environment. The small-fatigue-crack growth law can be used for safe material designs in hydrogen environments.

In this paper we introduce 6-fold symmetry crystal growth using new phase-field models based on the modified Allen-Cahn equation. The proposed method is a hybrid method which uses both analytic and numerical solutions. We then show this method can be extended to k-fold case. The Wulff construction procedure is provided to understand and predict the shape of crystals. We also present a detailed mathematical proof of the validity of the Wulff construction. For computational results, we verify the accuracy and efficiency of the method for snow crystal growth.

Tissue engineering scaffolds provide temporary mechanical support for tissue regeneration. To regenerate tissues more efficiently, an ideal structure of scaffolds should have appropriate porosity and pore structure. In this paper, we generate the Schwarz primitive (P) surface with various volume fractions using a phase-field model. The phase-field model enables us to design various surface-to-volume ratio structures with high porosity and mechanical properties. Comparing the Schwarz P surface's von Mises stress with that of triply periodic cylinders and cubes, we draw conclusions about the mechanical properties of the Schwarz P surface.

The first purpose of this study was to examine the influence of delegation and perceived organizational support(POS) on organizational identification and contextual performance. And the second purpose was to examine the moderating effect of growth need strength(GNS) on the relationship between delegation and organizational identification, and the moderating effect of dispositional cynicism on the relationship between POS and organizational identification. Data were gathered from 202 employees who were working in various organizations in Korea. To reduce the effect from common method bias, the contextual performance was rated by both self and others(twenty-two peers or supervisors). As results, the delegation and perceived organizational support had positive relationships with organizational identification. and organizational identification had mediating effect on the relationship between predictors(delegation and POS) and self-rating contextual performance. But there was no mediating effect of organizational identification on the relationship between predictors(delegation and POS) and other-rating contextual performance. The growth need strength had moderating effect on th relationship delegation and organizational identification because the relationship was more positive when GNS was high. Also dispositional cynicism had moderating effect on the relationship perceived organizational support and organizational identification because the relationship was more positive when dispositional cynicism was low. Finally, implication of results and future research tasks were discussed with limitations

To better understand the effects of local topography and climate on soil respiration, we conducted field measurements and soil incubation experiments to investigate various factors influencing spatial and temporal variations in soil respiration for six mixedhardwood forest slopes in the midst of the Korean Peninsula. Soil respiration and soil water content (SWC) were significantly greater (P 50.09 and 0.003, respectively) on north-facing slopes compared to south-facing slopes, while soil temperature was not significantly different between slopes (P40.5). At all sites, soil temperature was the primary factor driving temporal variations in soil respiration (r 2 50.84‐0.96) followed by SWC, which accounted for 30% of soil respiration spatial and temporal variability. Results from both field measurements and incubation experiments indicate that variations in soil respiration due to aspect can be explained by a convex-shaped function relating SWC to normalized soil respiration rates. Annual soil respiration estimates (1070‐1246gCm � 2 yr � 1 ) were not closely related to mean annual air temperatures among sites from different climate regimes. When soils from each site were incubated at similar temperatures in a laboratory, respiration rates for mineral soils from wetter and cooler sites were significantly higher than those for the drier and warmer sites (n 54, Po0.01). Our results indicate that the application of standard temperature-based Q10 models to estimate soil respiration rates for larger geographic areas covering different aspects or climatic regimes are not adequate unless other factors, such as SWC and total soil nitrogen, are considered in addition to soil temperature.

In order to investigate the effects of hydrogen on the fatigue crack growth behavior of low carbon steel JIS S10C, bending fatigue tests were carried out using a specimen with a small blind artificial hole in a low pressure pure hydrogen gas atmosphere. The results show that the fatigue crack growth rate in hydrogen gas is higher than that in nitrogen gas, moreover, the degree of acceleration is greater in the high strain range. In fractography, intergranular facets mixed with ductile fracture and quasi-cleavage fracture with brittle striations appear in a hydrogen gas environment, while only ductile fracture mainly appears in nitrogen gas. In the low growth rate range, many intergranular facets are seen on the ductile fracture surface, and in the higher growth rate range, quasi-cleavage facets increase as the growth rate increases. The growth rate of a small crack in nitrogen gas can be expressed by dl/dN ∝ Δep n l in the wide range of applied total strain range Δet . The same type equation is also satisfied in hydrogen gas, but in the narrow range roughly from Δet = 0.25% to Δet = 0.37%. The fracture surface in this range shows only intergranular facets and a ductile morphology, but no quasi-cleavage fracture. Although the crack growth mechanism in hydrogen is different from that in nitrogen, observation of the mechanism of intergranular facet formation shows a similarity to the mechanism in nitrogen in which the slip-off mechanism of crack growth is valid. The formation of intergranular facets is also closely related to the slip behavior influenced by hydrogen. This means that there exists a high possibility for the application of the small crack growth law inhydrogen to not only S10C, but also to other carbon steels in which the intergranular facet appears.Copyright © 2009 by ASME

In recent years, increasing attention has been paid to the effect of a hydrogen environment on the fatigue limit of hydrogen-power systems and infrastructure. In carbon steel, strain aging is one of the important factors influencing non-propagating crack behavior, which is related to the fatigue limit. In the present study, to investigate the effects of hydrogen on the strain aging of low-carbon steel (0.13 % carbon steel), Vickers hardness tests were carried out on the carbon steel. A couple of 0.13 % carbon steel specimens with a large-scale plastic zone were aging heat-treated; one was a hydrogen-charged specimen, whereas the other was an uncharged specimen. The Vickers hardness of the hydrogen-charged specimen was found to be lower than that of the uncharged specimen. This observation implies that hydrogen inhibits strain-aging hardening of low-carbon steel. The observation also suggests that hydrogen could affect the non-propagating crack behavior through the inhibition of strain aging.