Generalized length scales for three-dimensional dendritic growth

In the paper, a model basing on solute conservative in every unit is developed for solving the solute diffusion equation during solidification. The model includes time-dependent calculations for temperature distribution, solute redistribution in the liquid and solid phases. Three-dimensional computations are performed for Al-Cu dendritic growth into an adiabatic and highly supersaturated liquid phase. A numerical algorithm was developed to explicitly track the sharp solid/liquid (S/L) interface on a fixed Cartesian grid. Three-dimensional mesoscopic calculations were performed to simulate the evolution of equiaxed dendritic morphologies.

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Roles of cell and microvillus deformation and receptor-ligand binding kinetics in cell rolling

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.91536.2007 ◽

2008 ◽

Vol 295 (4) ◽

pp. H1439-H1450 ◽

Cited By ~ 37

Author(s):

Parag Pawar ◽

Sameer Jadhav ◽

Charles D. Eggleton ◽

Konstantinos Konstantopoulos

Keyword(s):

Ligand Binding ◽

Three Dimensional ◽

Theoretical Models ◽

Binding Kinetics ◽

Cell Deformation ◽

Receptor Ligand ◽

Length Scales ◽

Bond Behavior ◽

Cell Rolling ◽

Threshold Phenomenon

Polymorphonuclear leukocyte (PMN) recruitment to sites of inflammation is initiated by selectin-mediated PMN tethering and rolling on activated endothelium under flow. Cell rolling is modulated by bulk cell deformation (mesoscale), microvillus deformability (microscale), and receptor-ligand binding kinetics (nanoscale). Selectin-ligand bonds exhibit a catch-slip bond behavior, and their dissociation is governed not only by the force but also by the force history. Whereas previous theoretical models have studied the significance of these three “length scales” in isolation, how their interplay affects cell rolling has yet to be resolved. We therefore developed a three-dimensional computational model that integrates the aforementioned length scales to delineate their relative contributions to PMN rolling. Our simulations predict that the catch-slip bond behavior and to a lesser extent bulk cell deformation are responsible for the shear threshold phenomenon. Cells bearing deformable rather than rigid microvilli roll slower only at high P-selectin site densities and elevated levels of shear (≥400 s−1). The more compliant cells (membrance stiffness = 1.2 dyn/cm) rolled slower than cells with a membrane stiffness of 3.0 dyn/cm at shear rates >50 s−1. In summary, our model demonstrates that cell rolling over a ligand-coated surface is a highly coordinated process characterized by a complex interplay between forces acting on three distinct length scales.

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Phase-Field Simulation of Three-Dimensional Dendritic Growth

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.97-101.3769 ◽

2010 ◽

Vol 97-101 ◽

pp. 3769-3772 ◽

Cited By ~ 1

Author(s):

Chang Sheng Zhu ◽

Jun Wei Wang

Keyword(s):

Computational Methods ◽

Phase Field ◽

Interfacial Energy ◽

Dendritic Growth ◽

Field Model ◽

Three Dimensional ◽

Phase Field Model ◽

Computational Time ◽

Field Simulation ◽

Undercooled Melt

Based on a thin interface limit 3D phase-field model by coupled the anisotropy of interfacial energy and self-designed AADCR to improve on the computational methods for solving phase-field, 3D dendritic growth in pure undercooled melt is implemented successfully. The simulation authentically recreated the 3D dendritic morphological fromation, and receives the dendritic growth rule being consistent with crystallization mechanism. An example indicates that AADCR can decreased 70% computational time compared with not using algorithms for a 3D domain of size 300×300×300 grids, at the same time, the accelerated algorithms’ computed precision is higher and the redundancy is small, therefore, the accelerated method is really an effective method.

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Three-dimensional numerical simulation of soft-tissue wound healing using constrained-mixture anisotropic hyperelasticity and gradient-enhanced damage mechanics

Journal of The Royal Society Interface ◽

10.1098/rsif.2019.0708 ◽

2020 ◽

Vol 17 (162) ◽

pp. 20190708 ◽

Cited By ~ 1

Author(s):

Di Zuo ◽

Stéphane Avril ◽

Haitian Yang ◽

S. Jamaleddin Mousavi ◽

Klaus Hackl ◽

...

Keyword(s):

Wound Healing ◽

Damage Mechanics ◽

Healing Process ◽

Three Dimensional ◽

Biological Tissues ◽

Collagen Fibres ◽

Length Scales ◽

Constrained Mixture ◽

Proposed Model ◽

Intrinsic Length

Healing of soft biological tissues is the process of self-recovery or self-repair after injury or damage to the extracellular matrix (ECM). In this work, we assume that healing is a stress-driven process, which works at recovering a homeostatic stress metric in the tissue by replacing the damaged ECM with a new undamaged one. For that, a gradient-enhanced continuum healing model is developed for three-dimensional anisotropic tissues using the modified anisotropic Holzapfel–Gasser–Ogden constitutive model. An adaptive stress-driven approach is proposed for the deposition of new collagen fibres during healing with orientations assigned depending on the principal stress direction. The intrinsic length scales of soft tissues are considered through the gradient-enhanced term, and growth and remodelling are simulated by a constrained-mixture model with temporal homogenization. The proposed model is implemented in the finite-element package Abaqus by means of a user subroutine UEL. Three numerical examples have been achieved to illustrate the performance of the proposed model in simulating the healing process with various damage situations, converging towards stress homeostasis. The orientations of newly deposited collagen fibres and the sensitivity to intrinsic length scales are studied through these examples, showing that both have a significant impact on temporal evolutions of the stress distribution and on the size of the damage region. Applications of the approach to carry out in silico experiments of wound healing are promising and show good agreement with existing experiment results.

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The Impact of Covariance Localization for Radar Data on EnKF Analyses of a Developing MCS: Observing System Simulation Experiments

Monthly Weather Review ◽

10.1175/mwr-d-12-00203.1 ◽

2013 ◽

Vol 141 (11) ◽

pp. 3691-3709 ◽

Cited By ~ 25

Author(s):

Ryan A. Sobash ◽

David J. Stensrud

Keyword(s):

System Simulation ◽

Three Dimensional ◽

Radar Data ◽

Convective System ◽

State Variables ◽

Simulation Experiments ◽

Length Scales ◽

Convective Scale ◽

The Impact ◽

Prior State

Abstract Several observing system simulation experiments (OSSEs) were performed to assess the impact of covariance localization of radar data on ensemble Kalman filter (EnKF) analyses of a developing convective system. Simulated Weather Surveillance Radar-1988 Doppler (WSR-88D) observations were extracted from a truth simulation and assimilated into experiments with localization cutoff choices of 6, 12, and 18 km in the horizontal and 3, 6, and 12 km in the vertical. Overall, increasing the horizontal localization and decreasing the vertical localization produced analyses with the smallest RMSE for most of the state variables. The convective mode of the analyzed system had an impact on the localization results. During cell mergers, larger horizontal localization improved the results. Prior state correlations between the observations and state variables were used to construct reverse cumulative density functions (RCDFs) to identify the correlation length scales for various observation-state pairs. The OSSE with the smallest RMSE employed localization cutoff values that were similar to the horizontal and vertical length scales of the prior state correlations, especially for observation-state correlations above 0.6. Vertical correlations were restricted to state points closer to the observations than in the horizontal, as determined by the RCDFs. Further, the microphysical state variables were correlated with the reflectivity observations on smaller scales than the three-dimensional wind field and radial velocity observations. The ramifications of these findings on localization choices in convective-scale EnKF experiments that assimilate radar data are discussed.

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THREE-DIMENSIONAL PHONON TRANSPORT SIMULATION FOR NANO/MICROSTRUCTURED MATERIALS

International Journal of Nanoscience ◽

10.1142/s0219581x08005262 ◽

2008 ◽

Vol 07 (02n03) ◽

pp. 103-112 ◽

Cited By ~ 2

Author(s):

A. SAKURAI ◽

S. MARUYAMA ◽

A. KOMIYA ◽

K. MIYAZAKI

Keyword(s):

Radiative Transfer ◽

Heat Transport ◽

Characteristic Length ◽

Transport Phenomena ◽

Three Dimensional ◽

Phonon Transport ◽

Discrete Ordinates ◽

Complex Geometries ◽

Transport Mechanisms ◽

Length Scales

The Discrete Ordinates Radiation Element Method (DOREM), which is radiative transfer code, is applied for solving phonon transport of nano/microscale materials. The DOREM allows phonon simulation with multi-dimensional complex geometries. The objective of this study is to apply the DOREM to the nano/microstructured materials. It is confirmed that significant changes of the heat transport phenomena with different characteristic length scales and geometries are observed. This study also discusses further variations for understanding of heat transport mechanisms.

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STUDIES ON SHELL FORMATION

The Journal of Cell Biology ◽

10.1083/jcb.9.4.761 ◽

1961 ◽

Vol 9 (4) ◽

pp. 761-771 ◽

Cited By ~ 28

Author(s):

Norimitsu Watabe ◽

Karl M. Wilbur

Keyword(s):

Crystal Growth ◽

Dendritic Growth ◽

Three Dimensional ◽

Outer Part ◽

Organic Matrix ◽

Transitional Zone ◽

Homogeneous State ◽

Concentration Gradients ◽

Strong Concentration ◽

Small Crystals

Details of crystal growth in the calcitostracum of Crassostrea virginica have been studied with the purpose of analyzing the formation of the overlapping rows of oriented tabular crystals characteristic of this part of the shell. Crystal elongation, orientation, and dendritic growth suggest the presence of strong concentration gradients in a thin layer of solution in which crystallization occurs. Formation of the overlapping rows can be explained by three processes observed in the shell: a two-dimensional tree-like dendritic growth in which one set of crystal branchings creeps over an adjacent set of branchings; three-dimensional dendritic growth; and growth by dislocation of crystal surfaces. Multilayers of crystals may thus be formed at one time. This is favored by infrequent secretion of a covering organic matrix which would inhibit crystal growth. The transitional zone covering the outer part of the calcitostracum and the inner part of the prismatic region is generally characterized by aggregates of small crystals with definite orientation. Growth in this zone appears to take place in a relatively homogeneous state of solution without strong concentration gradients. Thin membranes and bands of organic matrix were commonly observed in the transitional zone bordering the prismatic region. The membrane showed a very fine oriented network pattern.

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Requirements for the Manufacturing of Scaffold Biomaterial With Features at Multiple Scales

Manufacturing Engineering and Materials Handling, Parts A and B ◽

10.1115/imece2005-82515 ◽

2005 ◽

Author(s):

I. M. Sebastine ◽

D. J. Williams

Keyword(s):

Tissue Engineering ◽

Multiple Scales ◽

Cell Attachment ◽

Structural Parameters ◽

Complex Function ◽

Three Dimensional ◽

Cell Orientation ◽

Length Scales

Tissue engineering aims to restore the complex function of diseased tissue using cells and scaffold materials. Tissue engineering scaffolds are three-dimensional (3D) structures that assist in the tissue engineering process by providing a site for cells to attach, proliferate, differentiate and secrete an extra-cellular matrix, eventually leading cells to form a neo-tissue of predetermined, three-dimensional shape and size. For a scaffold to function effectively, it must possess the optimum structural parameters conducive to the cellular activities that lead to tissue formation; these include cell penetration and migration into the scaffold, cell attachment onto the scaffold substrate, cell spreading and proliferation and cell orientation. In vivo, cells are organized in functional tissue units that repeat on the order of 100 μm. Fine scaffold features have been shown to provide control over attachment, migration and differentiation of cells. In order to design such 3D featured constructs effectively understanding the biological response of cells across length scales from nanometer to millimeter range is crucial. Scaffold biomaterials may need to be tailored at three different length scales: nanostructure (<1μm), microstructure (<20–100μm), and macrostructure (>100μm) to produce biocompatible and biofunctional scaffolds that closely resemble the extracellular matrix (ECM) of the natural tissue environment and promote cell adhesion, attachment, spreading, orientation, rate of movement, and activation. Identification of suitable fabrication techniques for manufacturing scaffolds with the required features at multiple scales is a significant challenge. This review highlights the effect and importance of the features of scaffolds that can influence the behaviour of cells/tissue at different length scales in vitro to increase our understanding of the requirements for the manufacture of functional 3D tissue constructs.

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