scholarly journals An Explicit Hybrid Method for the Nonlocal Allen–Cahn Equation

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1218
Author(s):  
Chaeyoung Lee ◽  
Sungha Yoon ◽  
Jintae Park ◽  
Junseok Kim
Keyword(s):  
Hybrid Method ◽  
Mean Curvature Flow ◽  
Growth Simulation ◽  
Cahn Equation ◽  
Numerical Tests ◽  
Hybrid Numerical Method ◽  
A Cell ◽  
Discrete Domains ◽  
Area Preserving ◽  
Good Agreement

We extend the explicit hybrid numerical method for solving the Allen–Cahn (AC) equation to the scheme for the nonlocal AC equation with isotropically symmetric interfacial energy. The proposed method combines the previous explicit hybrid method with a space-time dependent Lagrange multiplier which enforces conservation of mass. We perform numerical tests for the area-preserving mean curvature flow, which is the basic property of the nonlocal AC equation. The numerical results show good agreement with the theoretical solutions. Furthermore, to demonstrate the usefulness of the proposed method, we perform a cell growth simulation in a complex domain. Because the proposed numerical scheme is explicit, it is remarkably simple to implement the numerical solution algorithm on complex discrete domains.

The dynamics of drops and attached interfaces for the constrained Allen–Cahn equation

2001 ◽  
Vol 12 (1) ◽  
pp. 1-24 ◽  
Author(s):  
D. STAFFORD ◽  
M. J. WARD ◽  
B. WETTON
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Asymptotic Result ◽  
Interface Motion ◽  
Front Tracking Method ◽  
Cahn Equation ◽  
Area Preserving ◽  
Dimensional Domain

The motion of interfaces for a mass-conserving Allen–Cahn equation that are attached to the boundary of a two-dimensional domain is studied. In the limit of thin interfaces, the interface motion for this problem is known to be governed by an area-preserving mean curvature flow. A numerical front-tracking method, that allows for a numerical solution of this type of curvature flow, is used to compute the motion of interfaces that are attached orthogonally to the boundary. Results obtained from these computations are favourably compared with a previously-derived asymptotic result for the motion of attached interfaces that enclose a small area. The area-preserving mean curvature flow predicts that a semi-circular interface is stationary when it is attached to a flat segment of the boundary. For this case, the interface motion is shown to be metastable and an explicit characterization of the metastability is given.

Numerical evaluation of hydrodynamic characteristics of planing hulls by using a hybrid method

2021 ◽  
pp. 147509022199024
Author(s):  
Emre Kahramanoglu ◽  
Silvia Pennino ◽  
Huseyin Yilmaz
Keyword(s):  
Experimental Data ◽  
Hybrid Method ◽  
Design Stage ◽  
Hydrodynamic Characteristics ◽  
Calm Water ◽  
Preliminary Design Stage ◽  
Reduction Function ◽  
Hull Forms ◽  
Good Agreement

The hydrodynamic characteristics of the planing hulls in particular at the planing regime are completely different from the conventional hull forms and the determination of these characteristics is more complicated. In the present study, calm water hydrodynamic characteristics of planing hulls are investigated using a hybrid method. The hybrid method combines the dynamic trim and sinkage from the Zarnick approach with the Savitsky method in order to calculate the total resistance of the planing hull. Since the obtained dynamic trim and sinkage values by using the original Zarnick approach are not in good agreement with experimental data, an improvement is applied to the hybrid method using a reduction function proposed by Garme. The numerical results obtained by the hybrid and improved hybrid method are compared with each other and available experimental data. The results indicate that the improved hybrid method gives better results compared to the hybrid method, especially for the dynamic trim and resistance. Although the results have some discrepancies with experimental data in terms of resistance, trim and sinkage, the improved hybrid method becomes appealing particularly for the preliminary design stage of the planing hulls.

scholarly journals Comparative Results of QuantiFERON-TB Gold In-Tube and QuantiFERON-TB Gold Plus Assays for Detection of Tuberculosis Infection in Clinical Samples

2020 ◽  
Vol 58 (4) ◽  
Author(s):  
Dongju Won ◽  
Jung Yong Park ◽  
Hyon-Suk Kim ◽  
Younhee Park
Keyword(s):  
T Cells ◽  
Latent Tuberculosis ◽  
Clinical Samples ◽  
Negative Results ◽  
Kappa Value ◽  
A Cell ◽  
Ifn Γ ◽  
Comparative Results ◽  
Clinical Departments ◽  
Good Agreement

ABSTRACT The QuantiFERON-TB Gold plus (QFT-Plus) assay, an interferon gamma (IFN-γ) release assay (IGRA), was recently introduced as the next version of the QuantiFERON-TB Gold In-Tube (QFT-GIT) assay for diagnosing latent tuberculosis (TB). Whereas the QFT-GIT assay uses only one TB tube that induces a cell-mediated immune (CMI) response of CD4+ T cells, the QFT-Plus has an additional TB antigen 2 tube (TB2) for the CMI response of CD8+ T and CD4+ T cells, in addition to a TB antigen 1 (TB1) tube for the CMI response of CD4+ T cells only. We compared the results of the QFT-Plus and QFT-GIT assays as routine clinical tests for diagnosing TB. Samples from 220 patients referred for routine IGRA in various clinical departments were used. Correlations between IFN-γ levels in the QFT-GIT and QFT-Plus assays were strong and showed good agreement (kappa value = 0.69). Seven cases with positive QFT-GIT assay results and negative QFT-Plus assay results showed IFN-γ values near the cutoff value. However, 10 cases with active TB, recent TB, or immune problems showed discordance with the positive results only in the TB2 tube in QFT-Plus, unlike the negative results in TB1 and TB tubes. In these cases, IFN-γ levels in the TB2 tube were significantly higher than those in other tubes. This is the first study to compare these assays as routine IGRAs in the clinical setting. The QFT-Plus assay showed good agreement with the QFT-GIT assay and is presumably advantageous for patients with active TB, recent TB, and specific immune conditions involving CD8+ T-cell responses.

Matrix degradation regulates osteoblast protrusion dynamics and individual migration

2019 ◽  
Vol 11 (11) ◽  
pp. 404-413
Author(s):  
Nieves Movilla ◽  
Clara Valero ◽  
Carlos Borau ◽  
Jose Manuel García-Aznar
Keyword(s):  
Chemical Properties ◽  
Matrix Metalloproteinase Inhibitor ◽  
Surrounding Environment ◽  
Cell Velocity ◽  
The Matrix ◽  
3D Matrix ◽  
A Cell ◽  
Degradation Activity ◽  
Good Agreement ◽  
And Chemical Properties

Abstract Protrusions are one of the structures that cells use to sense their surrounding environment in a probing and exploratory manner as well as to communicate with other cells. In particular, osteoblasts embedded within a 3D matrix tend to originate a large number of protrusions compared to other type of cells. In this work, we study the role that mechanochemical properties of the extracellular matrix (ECM) play on the dynamics of these protrusions, namely, the regulation of the size and number of emanating structures. In addition, we also determine how the dynamics of the protrusions may lead the 3D movement of the osteoblasts. Significant differences were found in protrusion size and cell velocity, when degradation activity due to metalloproteases was blocked by means of an artificial broad-spectrum matrix metalloproteinase inhibitor, whereas stiffening of the matrix by introducing transglutaminase crosslinking, only induced slight changes in both protrusion size and cell velocity, suggesting that the ability of cells to create a path through the matrix is more critical than the matrix mechanical properties themselves. To confirm this, we developed a cell migration computational model in 3D including both the mechanical and chemical properties of the ECM as well as the protrusion mechanics, obtaining good agreement with experimental results.

scholarly journals Allen–Cahn approximation of mean curvature flow in Riemannian manifolds, II: Brakke's flows

2015 ◽  
Vol 17 (05) ◽  
pp. 1450041
Author(s):  
Adriano Pisante ◽  
Fabio Punzo
Keyword(s):  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Initial Conditions ◽  
Curvature Flow ◽  
Monotonicity Formula ◽  
Uniform Estimates ◽  
Cahn Equation ◽  
Motion By Mean Curvature ◽  
Density Of Solutions

We prove convergence of solutions to the parabolic Allen–Cahn equation to Brakke's motion by mean curvature in Riemannian manifolds with Ricci curvature bounded from below. Our results hold for a general class of initial conditions and extend previous results from [T. Ilmanen, Convergence of the Allen–Cahn equation to the Brakke's motion by mean curvature, J. Differential Geom. 31 (1993) 417–461] even in Euclidean space. We show that a sequence of measures, associated to energy density of solutions of the parabolic Allen–Cahn equation, converges in the limit to a family of rectifiable Radon measures, which evolves by mean curvature flow in the sense of Brakke. A key role is played by nonpositivity of the limiting energy discrepancy and a local almost monotonicity formula (a weak counterpart of Huisken's monotonicity formula) proved in [Allen–Cahn approximation of mean curvature flow in Riemannian manifolds, I, uniform estimates, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci.; arXiv:1308.0569], to get various density bounds for the limiting measures.

scholarly journals Density-Dependent Selection in Vesicular Stomatitis Virus

2004 ◽  
Vol 78 (11) ◽  
pp. 5799-5804 ◽  
Author(s):  
Isabel S. Novella ◽  
Daniel D. Reissig ◽  
Claus O. Wilke
Keyword(s):  
Vesicular Stomatitis Virus ◽  
Resistant Mutant ◽  
Relative Fitness ◽  
Wild Type ◽  
Common Pool ◽  
Model Predictions ◽  
A Cell ◽  
Vesicular Stomatitis ◽  
Average Fitness ◽  
Good Agreement

ABSTRACT We used vesicular stomatitis virus to test the effect of complementation on the relative fitness of a deleterious mutant, monoclonal antibody-resistant mutant (MARM) N, in competition with its wild-type ancestor. We carried out competitions of MARM N and wild-type populations at different multiplicities of infection (MOIs) and initial ratios of the wild type to the mutant and found that the fitness of MARM N relative to that of the wild type is very sensitive to changes in the MOI (i.e., the degree of complementation) but depends little, if at all, on the initial frequencies of MARM N and the wild type. Further, we developed a mathematical model under the assumption that during coinfection both viruses contribute to a common pool of protein products in the infected cell and that they both exploit this common pool equally. Under such conditions, the fitness of all virions that coinfect a cell is the average fitness in the absence of coinfection of that group of virions. In the absence of coinfection, complementation cannot take place and the relative fitness of each competitor is only determined by the selective value of its own products. We found good agreement between our experimental results and the model predictions, which suggests that the wild type and MARM N freely share all of their gene products under coinfection.

Study of event mixing for Bose–Einstein correlations in reactions with ππ X final states around 1 GeV

2017 ◽  
Vol 32 (23) ◽  
pp. 1750118
Author(s):  
Q. H. He
Keyword(s):  
Correlation Function ◽  
Momentum Distribution ◽  
Final States ◽  
Relative Momentum ◽  
Final State ◽  
Numerical Tests ◽  
Pion Energy ◽  
Simulation Results ◽  
Bose Einstein ◽  
Good Agreement

We present a new event mixing cut condition, named energy sum (ES) cut, aiming to investigate two-pion Bose–Einstein correlations (BEC) in reaction with only two identical pions among three final state particles. Unlike the previous proposed pion energy cut, which rejects original events with either pion’s energy beyond a given level, this cut does not eliminate any original events and hence improves the statistics of both original events and mixed events. It selects mixed events in terms of a weight proportional to the two-pion energy sum distribution of original events. Numerical tests using the [Formula: see text] events are carried out to verify the validity of the energy sum cut. Simulation results show this cut is able to reproduce the relative momentum distribution of the original events in the absence of BEC effects. Its ability to observe BEC effects and to extract correct BEC parameters is verified using event sample in the presence of BEC effects. It is found that the BEC effects can be obviously observed as an enhancement in the correlation function and the BEC parameters extracted by this event mixing cut are in good agreement with input values.

Mean curvature flow by the Allen–Cahn equation

2015 ◽  
Vol 26 (4) ◽  
pp. 535-559 ◽  
Author(s):  
D. S. LEE ◽  
J. S. KIM
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Curve Shortening Flow ◽  
Cahn Equation ◽  
Angle Condition ◽  
Motion By Mean Curvature ◽  
Curve Shortening ◽  
Three Space ◽  
Stable Hybrid

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.

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