scholarly journals A Simple Benchmark Problem for the Numerical Methods of the Cahn–Hilliard Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yibao Li ◽  
Chaeyoung Lee ◽  
Jian Wang ◽  
Sungha Yoon ◽  
Jintae Park ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Convergence Rates ◽  
Temporal Integration ◽  
Three Dimensional ◽  
Problem Solution ◽  
Benchmark Problem ◽  
Runge Kutta Method ◽  
Cahn Hilliard Equation ◽  
The One ◽  
Nicolson Scheme

We present a very simple benchmark problem for the numerical methods of the Cahn–Hilliard (CH) equation. For the benchmark problem, we consider a cosine function as the initial condition. The periodic sinusoidal profile satisfies both the homogeneous and periodic boundary conditions. The strength of the proposed problem is that it is simpler than the previous works. For the benchmark numerical solution of the CH equation, we use a fourth-order Runge–Kutta method (RK4) for the temporal integration and a centered finite difference scheme for the spatial differential operator. Using the proposed benchmark problem solution, we perform the convergence tests for an unconditionally gradient stable scheme via linear convex splitting proposed by Eyre and the Crank–Nicolson scheme. We obtain the expected convergence rates in time for the numerical schemes for the one-, two-, and three-dimensional CH equations.

The Generation Of Lump Solitons By A Bottom Topography In A Surface-Tension Dominated Flow

2005 ◽  
Vol 60 (5) ◽  
pp. 328-334 ◽  
Author(s):  
Zhiming Lu ◽  
Yulu Liu
Keyword(s):  
Surface Tension ◽  
Bottom Topography ◽  
Three Dimensional ◽  
Kutta Method ◽  
Third Order ◽  
The Third ◽  
Runge Kutta Method ◽  
The One ◽  
Nicolson Scheme ◽  
The Waves

The generation of lump solitons by a three-dimensional bottom topography is numerically investigated by use of a forced Kadomtsev-Petviashvili-I (KP-I) equation. The numerical method is based on the third order Runge-Kutta method and the Crank-Nicolson scheme. The main result is the pairwise periodic generation of two pairs of lump-type solitons downstream of the obstacle. The pair with the smaller amplitude is generated with a longer period and moves in a larger angle with respect to the positive x-axis than the one with the larger amplitude. Furthermore, the effects of the detuning parameter on the generation and evolution of lumps are studied. Finally the waves propagating upstream of the obstacle are also briefly investigated.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Sea Urchins and Circuses: The Modernist Natural Histories of Jean Painlevé and Alexander Calder

2018 ◽  
Vol 13 (2) ◽  
pp. 187-211
Author(s):  
Patricia E. Chu
Keyword(s):  
New Media ◽  
Sea Urchins ◽  
Life Sciences ◽  
Three Dimensional ◽  
Machine Age ◽  
Avant Garde ◽  
History Of ◽  
And Performance ◽  
The One ◽  
Natural Historian

The Paris avant-garde milieu from which both Cirque Calder/Calder's Circus and Painlevé’s early films emerged was a cultural intersection of art and the twentieth-century life sciences. In turning to the style of current scientific journals, the Paris surrealists can be understood as engaging the (life) sciences not simply as a provider of normative categories of materiality to be dismissed, but as a companion in apprehending the “reality” of a world beneath the surface just as real as the one visible to the naked eye. I will focus in this essay on two modernist practices in new media in the context of the history of the life sciences: Jean Painlevé’s (1902–1989) science films and Alexander Calder's (1898–1976) work in three-dimensional moving art and performance—the Circus. In analyzing Painlevé’s work, I discuss it as exemplary of a moment when life sciences and avant-garde technical methods and philosophies created each other rather than being classified as separate categories of epistemological work. In moving from Painlevé’s films to Alexander Calder's Circus, Painlevé’s cinematography remains at the forefront; I use his film of one of Calder's performances of the Circus, a collaboration the men had taken two decades to complete. Painlevé’s depiction allows us to see the elements of Calder's work that mark it as akin to Painlevé’s own interest in a modern experimental organicism as central to the so-called machine-age. Calder's work can be understood as similarly developing an avant-garde practice along the line between the bestiary of the natural historian and the bestiary of the modern life scientist.

scholarly journals Acoustic Cell Patterning in Hydrogel for Three-Dimensional Cell Network Formation

Micromachines ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 3
Author(s):  
Kyo-in Koo ◽  
Andreas Lenshof ◽  
Le Thi Huong ◽  
Thomas Laurell
Keyword(s):  
Network Formation ◽  
Umbilical Vein ◽  
Three Dimensional ◽  
Extrusion Process ◽  
Fibroblast Cells ◽  
Glass Capillary ◽  
Cell Network ◽  
Significant Difference ◽  
The One ◽  
Umbilical Vein Endothelial Cells

In the field of engineered organ and drug development, three-dimensional network-structured tissue has been a long-sought goal. This paper presents a direct hydrogel extrusion process exposed to an ultrasound standing wave that aligns fibroblast cells to form a network structure. The frequency-shifted (2 MHz to 4 MHz) ultrasound actuation of a 400-micrometer square-shaped glass capillary that was continuously perfused by fibroblast cells suspended in sodium alginate generated a hydrogel string, with the fibroblasts aligned in single or quadruple streams. In the transition from the one-cell stream to the four-cell streams, the aligned fibroblast cells were continuously interconnected in the form of a branch and a junction. The ultrasound-exposed fibroblast cells displayed over 95% viability up to day 10 in culture medium without any significant difference from the unexposed fibroblast cells. This acoustofluidic method will be further applied to create a vascularized network by replacing fibroblast cells with human umbilical vein endothelial cells.

scholarly journals Heritage Artefacts in the COVID-19 Era: The Aura and Authenticity of 3D Models

2021 ◽  
Vol 7 (1) ◽  
pp. 519-539
Author(s):  
Thiago Minete Cardozo ◽  
Costas Papadopoulos
Keyword(s):  
User Experience ◽  
Three Dimensional ◽  
3D Models ◽  
Essential Elements ◽  
The Other ◽  
Social Distancing ◽  
The Public ◽  
Affective Experiences ◽  
The One ◽  
Digital Engagement

Abstract Museums have been increasingly investing in their digital presence. This became more pressing during the COVID-19 pandemic since heritage institutions had, on the one hand, to temporarily close their doors to visitors while, on the other, find ways to communicate their collections to the public. Virtual tours, revamped websites, and 3D models of cultural artefacts were only a few of the means that museums devised to create alternative ways of digital engagement and counteract the physical and social distancing measures. Although 3D models and collections provide novel ways to interact, visualise, and comprehend the materiality and sensoriality of physical objects, their mediation in digital forms misses essential elements that contribute to (virtual) visitor/user experience. This article explores three-dimensional digitisations of museum artefacts, particularly problematising their aura and authenticity in comparison to their physical counterparts. Building on several studies that have problematised these two concepts, this article establishes an exploratory framework aimed at evaluating the experience of aura and authenticity in 3D digitisations. This exploration allowed us to conclude that even though some aspects of aura and authenticity are intrinsically related to the physicality and materiality of the original, 3D models can still manifest aura and authenticity, as long as a series of parameters, including multimodal contextualisation, interactivity, and affective experiences are facilitated.

Optimization of the Navy’s three-dimensional mine impact burial prediction simulation model, Impact35, using high-order numerical methods

2021 ◽  
pp. 154851292110286
Author(s):  
Athanasios Donas ◽  
Ioannis Famelis ◽  
Peter C Chu ◽  
George Galanis
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Prediction Model ◽  
Simulation Model ◽  
Three Dimensional ◽  
Simulation System ◽  
High Order ◽  
Alternative Methodology ◽  
Runge Kutta ◽  
Fifth Order

The aim of this paper is to present an application of high-order numerical analysis methods to a simulation system that models the movement of a cylindrical-shaped object (mine, projectile, etc.) in a marine environment and in general in fluids with important applications in Naval operations. More specifically, an alternative methodology is proposed for the dynamics of the Navy’s three-dimensional mine impact burial prediction model, Impact35/vortex, based on the Dormand–Prince Runge–Kutta fifth-order and the singly diagonally implicit Runge–Kutta fifth-order methods. The main aim is to improve the time efficiency of the system, while keeping the deviation levels of the final results, derived from the standard and the proposed methodology, low.

scholarly journals Analysis of the robustness of a steel frame structure with composite floors subject to multiple fire scenarios

2021 ◽  
pp. 136943322199249
Author(s):  
Riza Suwondo ◽  
Lee Cunningham ◽  
Martin Gillie ◽  
Colin Bailey
Keyword(s):  
Progressive Collapse ◽  
Three Dimensional ◽  
Steel Structure ◽  
Frame Structure ◽  
Worst Case ◽  
Collapse Resistance ◽  
Fire Scenarios ◽  
Element Approach ◽  
The One ◽  
Steel Frame Structure

This study presents robustness analyses of a three-dimensional multi-storey composite steel structure under the action of multiple fire scenarios. The main objective of the work is to improve current understanding of the collapse resistance of this type of building under different fire situations. A finite element approach was adopted with the model being firstly validated against previous studies available in the literature. The modelling approach was then used to investigate the collapse resistance of the structure for the various fire scenarios examined. Different sizes of fire compartment are considered in this study, starting from one bay, three bays and lastly the whole ground floor as the fire compartment. The investigation allows a fundamental understanding of load redistribution paths and member interactions when local failure occurs. It is concluded that the robustness of the focussed building in a fire is considerably affected by the size of fire compartments as well as fire location. The subject building can resist progressive collapse when the fire occurs only in the one-bay compartment. On the other hand, total collapse occurs when fire is located in the edge three-bay case. This shows that more than one fire scenario needs to be taken into consideration to ensure that a structure of this type can survive from collapse in the worst-case situation.

scholarly journals 3D Unsteady Diffusion and Reaction-Diffusion with Singularities by GFEM with 27-Node Hexahedrons

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Estaner Claro Romão
Keyword(s):  
Finite Element ◽  
Variable Temperature ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Third Order ◽  
Order Of Accuracy ◽  
Finite Element Approximations ◽  
Temperature Solution ◽  
The One ◽  
Primary Variable

The Galerkin Finite Element Method (GFEM) with 8- and 27-node hexahedrons elements is used for solving diffusion and transient three-dimensional reaction-diffusion with singularities. Besides analyzing the results from the primary variable (temperature), the finite element approximations were used to find the derivative of the temperature in all three directions. This technique does not provide an order of accuracy compatible with the one found in the temperature solution; thereto, a calculation from the third order finite differences is proposed here, which provide the best results, as demonstrated by the first two applications proposed in this paper. Lastly, the presentation and the discussion of a real application with two cases of boundary conditions with singularities are proposed.

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