scholarly journals Description of Nonlinear Vortical Flows of Incompressible Fluid in Terms of a Quasi-Potential

Physics ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 799-813
Author(s):  
Andrei Ermakov ◽  
Yury Stepanyants
Keyword(s):  
Fluid Flows ◽  
Scalar Function ◽  
Governing Equations ◽  
Vorticity Field ◽  
Spherical Coordinate ◽  
Coordinate Frames ◽  
Practical Applications ◽  
3 Dimensional ◽  
Component Velocity ◽  
3D Flows

As it was shown earlier, a wide class of nonlinear 3-dimensional (3D) fluid flows of incompressible viscous fluid can be described by only one scalar function dubbed the quasi-potential. This class of fluid flows is characterized by a three-component velocity field having a two-component vorticity field. Both these fields may, in general, depend on all three spatial variables and time. In this paper, the governing equations for the quasi-potential are derived and simple illustrative examples of 3D flows in the Cartesian coordinates are presented. The generalisation of the developed approach to the fluid flows in the cylindrical and spherical coordinate frames represents a nontrivial problem that has not been solved yet. In this paper, this gap is filled and the concept of a quasi-potential to the cylindrical and spherical coordinate frames is further developed. A few illustrative examples are presented which can be of interest for practical applications.

scholarly journals An Assessment of the Reliability of the NIGNET Data

2019 ◽  
Vol 3 (1) ◽  
pp. 18-29
Author(s):  
E. G. Ayodele ◽  
C. J. Okolie ◽  
O. A. Mayaki
Keyword(s):  
National Development ◽  
Accurate Information ◽  
Positional Accuracy ◽  
Data Archiving ◽  
Practical Applications ◽  
3 Dimensional ◽  
Gnss Network ◽  
High Level ◽  
Gnss Data ◽  
Geodetic Reference Frame

The Nigerian Geodetic Reference Frame is defined by a number of Continuously Operating Reference Stations (CORS) that constitute the Nigerian GNSS Network (NIGNET). NIGNET is essential for planning and national development with the main goal of ensuring consistency in the geodetic framework both nationally and internationally. Currently, the strength of the network in terms of data reliability has not been adequately studied due to the fact that research into CORS in Nigeria is just evolving, which constitutes a limitation in its applications. Therefore, the aim of this research is to explore the reliability of the 3-dimensional coordinates of NIGNET to inform usability and adequacy for both scientific and practical applications. In particular, this study examines if the 3-dimensional coordinates of NIGNET are equally reliable in terms of positional accuracy. Accordingly, this study utilised GNSS data collected over a period of six years (2011 – 2016) from the network to compute the daily geocentric coordinates of the stations. Exploratory and statistical data analysis techniques were used to understand the magnitude of the errors and the accuracy level in the 3-dimensional coordinates. For this purpose, accuracy metrics such as standard deviation (𝜎), standard error (𝑆𝐸) and root mean square error (RMSE) were computed. While One-way ANOVA was conducted to explore the coordinate differences. The results obtained showed that SE and RMSE ranged from 13.00 − 56.50𝑚𝑚 and 14.38 − 73.16𝑚𝑚 respectively, which signifies high accuracy. Overall, while 88% of the network showed a high level of positional accuracy, the reliability has been compromised due to excessive gaps in the data archiving. Therefore, due attention must be given to NIGNET to achieve its purpose in the provision of accurate information for various geospatial applications. Also, any efforts directed at understanding the practical implications of NIGNET must be well-embraced for the realization of its set objectives.

scholarly journals Axisymmetric simulation of viscoelastic filament thinning with the Oldroyd-B model

2018 ◽  
Vol 851 ◽  
Author(s):  
Emre Turkoz ◽  
Jose M. Lopez-Herrera ◽  
Jens Eggers ◽  
Craig B. Arnold ◽  
Luc Deike
Keyword(s):  
Stress Component ◽  
Fluid Flows ◽  
Theoretical Description ◽  
Slender Body ◽  
Complex Materials ◽  
Two Phase ◽  
Practical Applications ◽  
Numerical Studies ◽  
Fundamental Understanding ◽  
The One

A fundamental understanding of the filament thinning of viscoelastic fluids is important in practical applications such as spraying and printing of complex materials. Here, we present direct numerical simulations of the two-phase axisymmetric momentum equations using the volume-of-fluid technique for interface tracking and the log-conformation transformation to solve the viscoelastic constitutive equation. The numerical results for the filament thinning are in excellent agreement with the theoretical description developed with a slender body approximation. We show that the off-diagonal stress component of the polymeric stress tensor is important and should not be neglected when investigating the later stages of filament thinning. This demonstrates that such numerical methods can be used to study details not captured by the one-dimensional slender body approximation, and pave the way for numerical studies of viscoelastic fluid flows.

Simulation of cancer prognosis

2020 ◽  
Vol 05 (01) ◽  
pp. 2050004
Author(s):  
Hao Sun ◽  
James D. Lee
Keyword(s):  
Finite Element ◽  
Pressure Field ◽  
Growth Dynamics ◽  
Cancer Prognosis ◽  
Governing Equations ◽  
Poroelastic Medium ◽  
3 Dimensional ◽  
Biological Growth ◽  
Dynamic Finite Element ◽  
Innovative Model

Most mechanobiology phenomena commonly involve biological growth and deformation. In this work, we propose an innovative model of cancerous growth which posits that an expandable tumor can be described as a poroelastic medium consisting of solid and fluid components. In our biologically informed mechanical description of tumor growth dynamics, we derive the governing equations of the tumor’s growth and incorporate them with large deformation and materially nonlinear constitutive equations to improve the accuracy and efficiency of our simulation. Meanwhile, the dynamic finite element equations (DFE) for coupled displacement field and pressure field are formulated and solved. The 3-dimensional porous model is introduced. Numerical results are presented and discussed.

Use of 3D Prints to Compare the Efficacy of Three Different Calcaneal Osteotomies for the Correction of Heel Varus

2018 ◽  
Vol 39 (5) ◽  
pp. 591-597 ◽  
Author(s):  
Glenn B. Pfeffer ◽  
Max P. Michalski ◽  
Tina Basak ◽  
Joseph C. Giaconi
Keyword(s):  
Lateral Displacement ◽  
Varus Deformity ◽  
Coordinate Frames ◽  
3 Dimensional ◽  
Studentized Range ◽  
Neurologic Disorders ◽  
Reconstruction Image ◽  
Complex Procedure ◽  
Coronal Rotation ◽  
Range Test

Background: Cavovarus deformity of the hindfoot is typically caused by neurologic disorders. Multiple osteotomies have been described for the correction of varus deformity but without clinical comparison. In this study, we used 18 identical 3-dimensional (3D) prints of a patient with heel varus to compare the operative correction obtained with Dwyer, oblique, and Z osteotomies. Methods: A computed tomography (CT) scan of a patient with heel varus was used to create 18 identical 3D prints of the talus, calcaneus, and cuboid. Coordinate frames were added to the talus and calcaneus to evaluate rotation. The prints were then divided into 3 groups of 6 models each. A custom jig precisely and accurately replicated each osteotomy. Following the simulated operations, cut models were CT scanned and compared with 6 uncut models. Measurements were calculated using multiplanar reconstruction image processing. An analysis of variance (ANOVA) was performed on the initial data to determine significant differences among the measured variables. A Tukey Studentized range test was run to compare variables that showed statistically significant differences using the ANOVA. Results: The coronal angle of the Dwyer and oblique osteotomies was significantly less than that of the Z osteotomy ( P < .05). The axial angle, lateral displacement, and calcaneal shortening of the uncut model and Z osteotomy were significantly less than the Dwyer and oblique osteotomies. Conclusions: Dwyer, oblique, and Z osteotomies did not create either lateral translation or coronal rotation without the addition of a lateralizing slide or rotation of the posterior tuberosity. Clinical Relevance: Dwyer and oblique osteotomies would be best suited for mild deformity, yet the amount of calcaneal shortening must be acknowledged. A Z osteotomy is a complex procedure that has the capability of correcting moderate-severe coronal plane rotation but fails to provide lateralization of the pull of the Achilles insertion.

Miscible rectilinear displacements with gravity override. Part 1. Homogeneous porous medium

2000 ◽  
Vol 420 ◽  
pp. 225-257 ◽  
Author(s):  
MICHAEL RUITH ◽  
ECKART MEIBURG
Keyword(s):  
Flow Characteristics ◽  
Point Of View ◽  
Governing Equations ◽  
Vorticity Field ◽  
Miscible Displacements ◽  
Homogeneous Porous Medium ◽  
Combined Action ◽  
Parameter Ranges ◽  
Impermeable Boundary ◽  
Upper Boundary

Rectilinear homogeneous miscible displacements with gravity override are analysed by means of direct numerical simulations on the basis of the vorticity–streamfunction formulation of the governing equations. The vorticity-based point of view offers the advantage of clearly attributing the dominant flow characteristics to the effects of viscosity contrast, density difference, impermeable boundary conditions, or interactions among the above. Basic considerations regarding the vorticity field show that in an integral sense the coupling between viscosity and gravity vorticity is predominantly one way in nature, in that the gravity vorticity can amplify the viscous vorticity, but not vice versa. In particular, the vorticity point of view provides an explanation for the formation of the gravity tongue in terms of a focusing mechanism, which results from the combined action of the unfavourable viscosity gradient and the potential flow field generated by the interaction of the gravitational vorticity with the horizontal boundaries. This potential velocity field locally enhances the uniform global displacement velocity near the upper boundary, and thereby amplifies the viscous fingering instability along this section of the interface. In some parameter ranges, the gravity tongue exhibits interesting interactions with the viscous fingers next to it, such as pinching and partial merging. The influence of the Péclet number, the viscosity and density contrasts, and the aspect ratio on the dynamic evolution of the displacement is investigated quantitatively.

scholarly journals Some geometric properties of magneto-fluid flows

1982 ◽  
Vol 5 (2) ◽  
pp. 385-392
Author(s):  
S. S. Gangwar ◽  
Ram Babu
Keyword(s):  
Fluid Flows ◽  
Governing Equations ◽  
Geometric Properties ◽  
Normal Congruence ◽  
Stream Lines

By employing an anholonomic description of the governing equations, certain geometric results are obtained for a class of non-dissipative magnetofluid flows. The stream lines are geodesics on a normal congruence of the surfaces which are the Maxwellian surfaces.

Rational Drug Design

2014 ◽  
Vol 4 (1) ◽  
pp. 59-85 ◽  
Author(s):  
Khaled H. Barakat ◽  
Michael Houghton ◽  
D. Lorne Tyrrel ◽  
Jack A. Tuszynski
Keyword(s):  
Drug Design ◽  
Rational Drug Design ◽  
Dimensional Structure ◽  
Computational Tools ◽  
Structure Based Drug Design ◽  
Practical Applications ◽  
3 Dimensional ◽  
Drug Candidates ◽  
The Past ◽  
Rational Drug

For the past three decades rationale drug design (RDD) has been developing as an innovative, rapid and successful way to discover new drug candidates. Many strategies have been followed and several targets with diverse structures and different biological roles have been investigated. Despite the variety of computational tools available, one can broadly divide them into two major classes that can be adopted either separately or in combination. The first class involves structure-based drug design, when the target's 3-dimensional structure is available or it can be computationally generated using homology modeling. On the other hand, when only a set of active molecules is available, and the structure of the target is unknown, ligand-based drug design tools are usually used. This review describes some recent advances in rational drug design, summarizes a number of their practical applications, and discusses both the advantages and shortcomings of the various techniques used.

scholarly journals Fluid Flow in Composite Regions Past a Solid Sphere

2021 ◽  
Vol 12 (4) ◽  
pp. 4755-4769
Keyword(s):  
Fluid Flow ◽  
Similarity Transformation ◽  
Solid Sphere ◽  
Transformation Method ◽  
Normal Velocity ◽  
Governing Equations ◽  
Spherical Coordinate ◽  
Brinkman Equations ◽  
Porous Region ◽  
Parabolic Velocity Profile

A steady, 2-D, incompressible, viscous fluid flow past a stationary solid sphere of radius 'a' has been considered. The flow of fluid occurs in 3 regions, namely fluid, porous and fluid regions. The governing equations for fluid flow in the clear and porous regions are Stokes and Brinkman equations, respectively. These governing equations are written in terms of stream function in the spherical coordinate system and solved using the similarity transformation method. The variation in flow patterns by means of streamlines has been analyzed for the obtained exact solution. The nature of the streamlines and the corresponding tangential and normal velocity profiles are observed graphically for the different values of porous parameter 'σ'. From the obtained results, it is noticed that an increase in porous parameters suppresses the fluid flow in the porous region due to less permeability; as a result, the fluid moves away from the solid sphere. It also decreases the velocity of the fluid in the porous region due to the suppression of the fluid as 'σ' increases. Hence the parabolic velocity profile is noticed near the solid sphere.

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