Three-dimensional problem on the stability of a row of fibers perpendicular to the free boundary of a matrix

1994 ◽  
Vol 30 (12) ◽  
pp. 919-926 ◽  
Author(s):  
A. N. Guz' ◽  
Yu. N. Lapusta
Keyword(s):  
Free Boundary ◽  
Three Dimensional ◽  
Dimensional Problem ◽  
The Stability ◽  
Row Of Fibers

scholarly journals The stability of thermally stratified plane Poiseuille flow

1968 ◽  
Vol 33 (1) ◽  
pp. 21-32 ◽  
Author(s):  
K. S. Gage ◽  
W. H. Reid
Keyword(s):  
Poiseuille Flow ◽  
Richardson Number ◽  
Three Dimensional ◽  
Complete Analysis ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Plane Poiseuille Flow ◽  
Spiral Flow ◽  
Tollmien Schlichting ◽  
The Stability

In studying the stability of a thermally stratified fluid in the presence of a viscous shear flow, we have a situation in which there is an important interaction between the mechanism of instability due to the stratification and the Tollmien-Schlichting mechanism due to the shear. A complete analysis has been carried out for the Bénard problem in the presence of a plane Poiseuille flow and it is shown that, although Squire's transformation can be used to reduce the three-dimensional problem to an equivalent two-dimensional one, a theorem of Squire's type does not follow unless the Richardson number exceeds a certain small negative value. This conclusion follows from the fact that, when the stratification is unstable and the Prandtl number is unity, the equivalent two-dimensional problem becomes identical mathematically to the stability problem for spiral flow between rotating cylinders and, from the known results for the spiral flow problem, Squire's transformation can then be used to obtain the complete three-dimensional stability boundary. For the case of stable stratification, however, Squire's theorem is valid and the instability is of the usual Tollmien—Schlichting type. Additional calculations have been made for this case which show that the flow is completely stabilized when the Richardson number exceeds a certain positive value.

On the stability of rotating compressible and inviscid fluids

1980 ◽  
Vol 99 (2) ◽  
pp. 433-448 ◽  
Author(s):  
Knut S. Eckhoff ◽  
Leiv Storesletten
Keyword(s):  
Shear Flow ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
Expansion Method ◽  
Inviscid Fluid ◽  
Dimensional Problem ◽  
External Force Field ◽  
Inviscid Fluids ◽  
Steady Shear Flow ◽  
The Stability

Necessary conditions for linear stability of a rotating, compressible and inviscid fluid are found by the generalized progressing wave expansion method. The full three-dimensional problem involving an arbitrarily given rotational symmetric external force field is considered for an arbitrary steady shear flow with vanishing axial velocity. The results obtained are compared with previously known results.

ON THE EXISTENCE OF SPATIALLY PATTERNED DORMANT MALIGNANCIES IN A MODEL FOR THE GROWTH OF NON-NECROTIC VASCULAR TUMORS

2001 ◽  
Vol 11 (04) ◽  
pp. 601-625 ◽  
Author(s):  
AVNER FRIEDMAN ◽  
FERNANDO REITICH
Keyword(s):  
Free Boundary ◽  
Free Boundary Problems ◽  
Three Dimensional ◽  
Radial Symmetry ◽  
Vascular Tumors ◽  
Free Boundaries ◽  
Dimensional Problem ◽  
Boundary Problems ◽  
Equilibrium Configurations ◽  
Growth Equilibrium

Despite their great importance in determining the dynamic evolution of solutions to mathematical models of tumor growth, equilibrium configurations within such models have remained largely unexplored. This was due, in part, to the complexity of the relevant free boundary problems, which is enhanced when the process deviates from radial symmetry. In this paper, we present the results of our investigation on the existence of non-spherical dormant states for a model of non-necrotic vascularized tumors. For the sake of clarity we perform the analysis on two-dimensional geometries, though our techniques are evidently applicable to the full three-dimensional problem. We rigorously show that there is, indeed, an abundance of steady states that are not radially symmetric. More precisely, we prove that at any radially symmetric stationary state with free boundary r=R0 (which we first show to exist), there begin infinitely many branches of equilibria that bifurcate from and break the symmetry of that radial state. The free boundaries along the bifurcation branches are of the form [Formula: see text], where ℓ=2,3,… and |ε|<ε0; each choice of ℓ and ε determines a non-radial steady configuration.

A Liquid Metal Flow Between Two Coaxial Cylinders System

2019 ◽  
Vol 11 (1) ◽  
pp. 79-86
Author(s):  
Abdelkrim Merah ◽  
Ridha Kelaiaia ◽  
Faiza Mokhtari
Keyword(s):  
Couette Flow ◽  
Metal Flow ◽  
Three Dimensional ◽  
Liquid Sodium ◽  
Taylor Vortex ◽  
Turbulent Regime ◽  
Coaxial Cylinders ◽  
Concentric Cylinders ◽  
Ideal Tool ◽  
The Stability

Abstract The Taylor-Couette flow between two rotating coaxial cylinders remains an ideal tool for understanding the mechanism of the transition from laminar to turbulent regime in rotating flow for the scientific community. We present for different Taylor numbers a set of three-dimensional numerical investigations of the stability and transition from Couette flow to Taylor vortex regime of a viscous incompressible fluid (liquid sodium) between two concentric cylinders with the inner one rotating and the outer one at rest. We seek the onset of the first instability and we compare the obtained results for different velocity rates. We calculate the corresponding Taylor number in order to show its effect on flow patterns and pressure field.

Handheld Laser Scanner Research

2019 ◽  
Vol 952 (10) ◽  
pp. 47-54
Author(s):  
A.V. Komissarov ◽  
A.V. Remizov ◽  
M.M. Shlyakhova ◽  
K.K. Yambaev
Keyword(s):  
Point Cloud ◽  
Three Dimensional ◽  
Laser Scanner ◽  
Test Site ◽  
Optical Systems ◽  
Advantages And Disadvantages ◽  
Site Survey ◽  
Laser Scanners ◽  
Three Dimensional Models ◽  
The Stability

The authors consider hand-held laser scanners, as a new photogrammetric tool for obtaining three-dimensional models of objects. The principle of their work and the newest optical systems based on various sensors measuring the depth of space are described in detail. The method of simultaneous navigation and mapping (SLAM) used for combining single scans into point cloud is outlined. The formulated tasks and methods for performing studies of the DotProduct (USA) hand-held laser scanner DPI?8X based on a test site survey are presented. The accuracy requirements for determining the coordinates of polygon points are given. The essence of the performed experimental research of the DPI?8X scanner is described, including scanning of a test object at various scanner distances, shooting a test polygon from various scanner positions and building point cloud, repeatedly shooting the same area of the polygon to check the stability of the scanner. The data on the assessment of accuracy and analysis of research results are given. Fields of applying hand-held laser scanners, their advantages and disadvantages are identified.

scholarly journals Gum Tragacanth (GT): A Versatile Biocompatible Material beyond Borders

Molecules ◽  
2021 ◽  
Vol 26 (6) ◽  
pp. 1510 ◽  
Author(s):  
Mohammad Ehsan Taghavizadeh Yazdi ◽  
Simin Nazarnezhad ◽  
Seyed Hadi Mousavi ◽  
Mohammad Sadegh Amiri ◽  
Majid Darroudi ◽  
...  
Keyword(s):  
Tissue Engineering ◽  
Food Packaging ◽  
Three Dimensional ◽  
Great Promise ◽  
Anionic Polymer ◽  
Gum Tragacanth ◽  
New Horizons ◽  
Tissue Healing ◽  
The Stability ◽  
Therapeutic Substance

The use of naturally occurring materials in biomedicine has been increasingly attracting the researchers’ interest and, in this regard, gum tragacanth (GT) is recently showing great promise as a therapeutic substance in tissue engineering and regenerative medicine. As a polysaccharide, GT can be easily extracted from the stems and branches of various species of Astragalus. This anionic polymer is known to be a biodegradable, non-allergenic, non-toxic, and non-carcinogenic material. The stability against microbial, heat and acid degradation has made GT an attractive material not only in industrial settings (e.g., food packaging) but also in biomedical approaches (e.g., drug delivery). Over time, GT has been shown to be a useful reagent in the formation and stabilization of metal nanoparticles in the context of green chemistry. With the advent of tissue engineering, GT has also been utilized for the fabrication of three-dimensional (3D) scaffolds applied for both hard and soft tissue healing strategies. However, more research is needed for defining GT applicability in the future of biomedical engineering. On this object, the present review aims to provide a state-of-the-art overview of GT in biomedicine and tries to open new horizons in the field based on its inherent characteristics.

scholarly journals Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
András L. Szabó ◽  
Bitan Roy
Keyword(s):  
Fixed Points ◽  
Chiral Symmetry ◽  
Rotational Symmetry ◽  
Three Dimensional ◽  
Spatial Dimension ◽  
Dirac Fermions ◽  
Electronic Interactions ◽  
Emergent Phenomena ◽  
Ordered Phases ◽  
The Stability

Abstract We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1) ⊗ SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a small parameter ϵ with ϵ = d−1, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings ∼ ϵ. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the s-wave and p-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of weak rotational symmetry breaking on the stability of various RG fixed points.

Mathematical Theory of Transversally Isotropic Shells of Arbitrary Thickness at Static Load

2019 ◽  
Vol 968 ◽  
pp. 496-510
Author(s):  
Anatoly Grigorievich Zelensky
Keyword(s):  
Mathematical Theory ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Elastic Plates ◽  
Dimensional Problem ◽  
Boundary Problems ◽  
Complex Boundary ◽  
Plates And Shells ◽  
Basic Equations

Classical and non-classical refined theories of plates and shells, based on various hypotheses [1-7], for a wide class of boundary problems, can not describe with sufficient accuracy the SSS of plates and shells. These are boundary problems in which the plates and shells undergo local and burst loads, have openings, sharp changes in mechanical and geometric parameters (MGP). The problem also applies to such elements of constructions that have a considerable thickness or large gradient of SSS variations. The above theories in such cases yield results that can differ significantly from those obtained in a three-dimensional formulation. According to the logic in such theories, the accuracy of solving boundary problems is limited by accepted hypotheses and it is impossible to improve the accuracy in principle. SSS components are usually depicted in the form of a small number of members. The systems of differential equations (DE) obtained here have basically a low order. On the other hand, the solution of boundary value problems for non-thin elastic plates and shells in a three-dimensional formulation [8] is associated with great mathematical difficulties. Only in limited cases, the three-dimensional problem of the theory of elasticity for plates and shells provides an opportunity to find an analytical solution. The complexity of the solution in the exact three-dimensional formulation is greatly enhanced if complex boundary conditions or physically nonlinear problems are considered. Theories in which hypotheses are not used, and SSS components are depicted in the form of infinite series in transverse coordinates, will be called mathematical. The approximation of the SSS component can be adopted in the form of various lines [9-16], and the construction of a three-dimensional problem to two-dimensional can be accomplished by various methods: projective [9, 14, 16], variational [12, 13, 15, 17]. The effectiveness and accuracy of one or another variant of mathematical theory (MT) depends on the complex methodology for obtaining the basic equations.

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