scholarly journals Symmetric Boundary Condition for Laplacian on Net of Regular Hexagons

2017 ◽  
Vol 9 (3) ◽  
pp. 46
Author(s):  
Daniel Lee
Keyword(s):  
Boundary Condition ◽  
Matrix Theory ◽  
Three Dimensional ◽  
Cardiac Tissues ◽  
Energy Product ◽  
Symmetric Boundary Condition ◽  
Almost All ◽  
Wave Phenomena ◽  
Dimensional Cell ◽  
Theory Series

Hexagonal grid methods are found useful in many research works, including numerical modeling in spherical coordinates, in atmospheric and ocean models, and simulation of electrical wave phenomena in cardiac tissues. Almost all of these used standard Laplacian and mostly on one configuration of regular hexagons. In this work, discrete symmetric boundary condition and energy product for anisotropic Laplacian are investigated firstly on general net of regular hexagons, and then generalized to its most extent in two- or three-dimensional cell-center finite difference applications up to the usage of symmetric stencil in central differences. For analysis of Laplacian related applications, this provides with an approach in addition to the M-matrix theory, series method, functional interpolations and Fourier vectors.

A Concise Finite Element Model for the Analysis of Simple Wire Strand with a Broken Helical Wire

2012 ◽  
Vol 446-449 ◽  
pp. 745-750 ◽  
Author(s):  
Wen Guang Jiang ◽  
Li Juan Yan
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Finite Element Model ◽  
Cross Section ◽  
Axial Load ◽  
Three Dimensional ◽  
Element Model ◽  
Analysis Model ◽  
Symmetric Boundary Condition ◽  
Wire Strand

A concise finite element model for the analysis of simple wire strand with a broken helical wire under axial load is presented in this paper. Due to the implementation of accurate helically symmetric boundary condition, the analysis model can be established based only on a small slice of the wire strand cross-section consisting of all of the remaining intact wires excluding the broken helical wire. Full three-dimensional solid elements were used for structural discretization. The finite element results showed that the sharing of loads among the remaining helical wires is highly non-uniform. The two helical wires adjacent to the broken helical wire bear higher loads. The helical wire opposite to the broken wire bears least load.

Boundary Condition Design to Heat a Moving Object at Uniform Transient Temperature Using Inverse Formulation

2004 ◽  
Vol 126 (3) ◽  
pp. 619-626 ◽  
Author(s):  
Hakan Ertu¨rk ◽  
Ofodike A. Ezekoye ◽  
John R. Howell
Keyword(s):  
Boundary Condition ◽  
Temperature Distribution ◽  
Design Problem ◽  
Manufacturing Industry ◽  
Three Dimensional ◽  
Chemical Deposition ◽  
Iterative Solution ◽  
Conveyor Belt ◽  
Temperature History ◽  
Transient Temperature

The boundary condition design of a three-dimensional furnace that heats an object moving along a conveyor belt of an assembly line is considered. A furnace of this type can be used by the manufacturing industry for applications such as industrial baking, curing of paint, annealing or manufacturing through chemical deposition. The object that is to be heated moves along the furnace as it is heated following a specified temperature history. The spatial temperature distribution on the object is kept isothermal through the whole process. The temperature distribution of the heaters of the furnace should be changed as the object moves so that the specified temperature history can be satisfied. The design problem is transient where a series of inverse problems are solved. The process furnace considered is in the shape of a rectangular tunnel where the heaters are located on the top and the design object moves along the bottom. The inverse design approach is used for the solution, which is advantageous over a traditional trial-and-error solution where an iterative solution is required for every position as the object moves. The inverse formulation of the design problem is ill-posed and involves a set of Fredholm equations of the first kind. The use of advanced solvers that are able to regularize the resulting system is essential. These include the conjugate gradient method, the truncated singular value decomposition or Tikhonov regularization, rather than an ordinary solver, like Gauss-Seidel or Gauss elimination.

scholarly journals Can keratin scaffolds be used for creating three-dimensional cell cultures?

Open Medicine ◽  
2020 ◽  
Vol 15 (1) ◽  
pp. 249-253
Author(s):  
Marta Bochynska-Czyz ◽  
Patrycja Redkiewicz ◽  
Hanna Kozlowska ◽  
Joanna Matalinska ◽  
Marek Konop ◽  
...  
Keyword(s):  
Cell Cultures ◽  
Chemical Activation ◽  
Three Dimensional ◽  
Enzymatic Digestion ◽  
Pepsin Digestion ◽  
Cell Culturing ◽  
3D Cell Cultures ◽  
Associated Proteins ◽  
Positive Effect ◽  
Dimensional Cell

AbstractThree-dimensional (3D) cell cultures were created with the use of fur keratin associated proteins (F-KAPs) as scaffolds. The procedure of preparation F-KAP involves combinations of chemical activation and enzymatic digestion. The best result in porosity and heterogeneity of F-KAP surface was received during pepsin digestion. The F-KAP had a stable structure, no changes were observed after heat treatment, shaking and washing. The 0.15-0.5 mm fraction had positive effect for formation of 3D scaffolds and cell culturing. Living rat mesenchymal cells on the F-KAP with no abnormal morphology were observed by SEM during 32 days of cell culturing.

scholarly journals 3D Reconstruction of Cultural Heritage Sites as an Educational Approach. The Sanctuary of Delphi

2021 ◽  
Vol 11 (8) ◽  
pp. 3635
Author(s):  
Ioannis Liritzis ◽  
Pantelis Volonakis ◽  
Spyros Vosinakis
Keyword(s):  
University Students ◽  
3D Reconstruction ◽  
Cultural Heritage ◽  
New Technology ◽  
Three Dimensional ◽  
Computer Gaming ◽  
Educational Approach ◽  
Heritage Sites ◽  
3D Environment ◽  
Almost All

In the field of cultural heritage, three-dimensional (3D) reconstruction of monuments is a usual activity for many professionals. The aim in this paper focuses on the new technology educational application combining science, history, and archaeology. Being involved in almost all stages of implementation steps and assessing the level of participation, university students use tools of computer gaming platform and participate in ways of planning the virtual environment which improves their education through e-Learning. The virtual 3D environment is made with different imaging methods (helium-filled balloon, Structure for motion, 3D repository models) and a developmental plan has been designed for use in many future applications. Digital tools were used with 3D reconstructed buildings from the museum archive to Unity 3D for the design. The pilot study of Information Technology work has been employed to introduce cultural heritage and archaeology to university syllabuses. It included students with a questionnaire which has been evaluated accordingly. As a result, the university students were inspired to immerse themselves into the virtual lab, aiming to increasing the level of interaction. The results show a satisfactory learning outcome by an easy to use and real 3D environment, a step forward to fill in needs of contemporary online sustainable learning demands.

scholarly journals Factors to consider when interrogating 3D culture models with plate readers or automated microscopes

2021 ◽  
Author(s):  
Terry Riss ◽  
O. Joseph Trask
Keyword(s):  
Cell Culture ◽  
Three Dimensional ◽  
3D Culture ◽  
Fluorescent Imaging ◽  
Culture Models ◽  
Assay Methods ◽  
Diffusion Rates ◽  
Cell Culture Models ◽  
Dimensional Cell ◽  
Cells Cultured

AbstractAlong with the increased use of more physiologically relevant three-dimensional cell culture models comes the responsibility of researchers to validate new assay methods that measure events in structures that are physically larger and more complex compared to monolayers of cells. It should not be assumed that assays designed using monolayers of cells will work for cells cultured as larger three-dimensional masses. The size and barriers for penetration of molecules through the layers of cells result in a different microenvironment for the cells in the outer layer compared to the center of three-dimensional structures. Diffusion rates for nutrients and oxygen may limit metabolic activity which is often measured as a marker for cell viability. For assays that lyse cells, the penetration of reagents to achieve uniform cell lysis must be considered. For live cell fluorescent imaging assays, the diffusion of fluorescent probes and penetration of photons of light for probe excitation and fluorescent emission must be considered. This review will provide an overview of factors to consider when implementing assays to interrogate three dimensional cell culture models.

scholarly journals Bootstrapping boundary-localized interactions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Connor Behan ◽  
Lorenzo Di Pietro ◽  
Edoardo Lauria ◽  
Balt C. van Rees
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Parameter Space ◽  
Three Dimensional ◽  
Conformal Boundary ◽  
Dimensional Boundary ◽  
Dirichlet And Neumann Conditions ◽  
Boundary Fields ◽  
Boundary Dynamics

Abstract We study conformal boundary conditions for the theory of a single real scalar to investigate whether the known Dirichlet and Neumann conditions are the only possibilities. For this free bulk theory there are strong restrictions on the possible boundary dynamics. In particular, we find that the bulk-to-boundary operator expansion of the bulk field involves at most a ‘shadow pair’ of boundary fields, irrespective of the conformal boundary condition. We numerically analyze the four-point crossing equations for this shadow pair in the case of a three-dimensional boundary (so a four-dimensional scalar field) and find that large ranges of parameter space are excluded. However a ‘kink’ in the numerical bounds obeys all our consistency checks and might be an indication of a new conformal boundary condition.

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