Elastic Boundary Layers in Two-Dimensional Isotropic Lattices

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
A. Srikantha Phani ◽  
Norman A. Fleck
Keyword(s):  
Boundary Layer ◽  
Relative Density ◽  
Boundary Layers ◽  
Hexagonal Lattice ◽  
Free Edge ◽  
Two Dimensional ◽  
Kagome Lattice ◽  
Kagomé Lattice ◽  
Elastic Boundary ◽  
Lattice Boundary

The phenomenon of elastic boundary layers under quasistatic loading is investigated using the Floquet–Bloch formalism for two-dimensional, isotropic, periodic lattices. The elastic boundary layer is a region of localized elastic deformation, confined to the free edge of a lattice. Boundary layer phenomena in three isotropic lattice topologies are investigated: the semiregular Kagome lattice, the regular hexagonal lattice, and the regular fully triangulated lattice. The boundary layer depth is on the order of the strut length for the hexagonal and the fully triangulated lattices. For the Kagome lattice, the depth of boundary layer scales inversely with the relative density. Thus, the boundary layer in a Kagome lattice of low relative density spans many cells.

Elastic Boundary Layers in Two-Dimensional Isotropic Lattices

2007 ◽  
Author(s):  
A. Srikantha Phani ◽  
Norman A. Fleck
Keyword(s):  
Boundary Layer ◽  
Relative Density ◽  
Boundary Layers ◽  
Hexagonal Lattice ◽  
Free Edge ◽  
Two Dimensional ◽  
Kagome Lattice ◽  
Kagomé Lattice ◽  
Elastic Boundary ◽  
Lattice Boundary

The phenomenon of elastic boundary layers under quasistatic loading is investigated using the Floquet-Bloch formalism for two-dimensional, isotropic, periodic lattices. The elastic boundary layer is a region of localised elastic deformation, confined to the free-edge of a lattice. Boundary layer phenomena in three isotropic lattice topologies are investigated: the semi-regular Kagome lattice, the regular hexagonal lattice and the regular fully-triangulated lattice. The boundary layer depth is on the order of the strut length for the hexagonal and the fully-triangulated lattices. For the Kagome lattice, the depth of boundary layer scales inversely with the relative density. Thus, the boundary layer in a Kagome lattice of low relative density spans many cells.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

Effects of Curvature on Laminar Boundary Layers in Sink-Type Flows

1969 ◽  
Vol 91 (3) ◽  
pp. 353-358 ◽  
Author(s):  
W. A. Gustafson ◽  
I. Pelech
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Momentum Equation ◽  
Similarity Solutions ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Thickness Increase ◽  
Laminar Boundary Layers ◽  
Converging Channel ◽  
Special Case

The two-dimensional, incompressible laminar boundary layer on a strongly curved wall in a converging channel is investigated for the special case of potential velocity inversely proportional to the distance along the wall. Similarity solutions of the momentum equation are obtained by two different methods and the differences between the methods are discussed. The numerical results show that displacement and momentum thickness increase linearly with curvature while skin friction decreases linearly.

A Reference Temperature Method for Compressible Laminar Boundary Layers

1973 ◽  
Vol 2 (4) ◽  
pp. 201-204
Author(s):  
R. Camarero
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Reference Temperature ◽  
Integral Approach ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Laminar Boundary Layers ◽  
Temperature Method ◽  
Compressibility Effects

A calculation procedure for the solution of two-dimensional and axi-symmetric laminar boundary layers in compressible flow has been developed. The method is an extension of the integral approach of Tani to include compressibility effects by means of a reference temperature. Arbitrary pressure gradients and wall temperature can be specified. Comparisons with experiments obtained for supersonic flows over a flat plate indicate that the method yields adequate results. The method is then applied to the solution of the boundary layer on a Basemann inlet.

scholarly journals Kagome van-der-Waals Pd3P2S8 with flat band

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Seunghyun Park ◽  
Soonmin Kang ◽  
Haeri Kim ◽  
Ki Hoon Lee ◽  
Pilkwang Kim ◽  
...  
Keyword(s):  
Diamagnetic Susceptibility ◽  
Van Der Waals ◽  
Localized States ◽  
Flat Band ◽  
Two Dimensional ◽  
Kagome Lattice ◽  
Kagomé Lattice ◽  
Localized State ◽  
Low Dimensional ◽  
Important Structure

AbstractWith the advanced investigations into low-dimensional systems, it has become essential to find materials having interesting lattices that can be exfoliated down to monolayer. One particular important structure is a kagome lattice with its potentially diverse and vibrant physics. We report a van-der-Waals kagome lattice material, Pd3P2S8, with several unique properties such as an intriguing flat band. The flat band is shown to arise from a possible compact-localized state of all five 4d orbitals of Pd. The diamagnetic susceptibility is precisely measured to support the calculated susceptibility obtained from the band structure. We further demonstrate that Pd3P2S8 can be exfoliated down to monolayer, which ultimately will allow the possible control of the localized states in this two-dimensional kagome lattice using the electric field gating.

Criteria for Boundary Layer Transition

2011 ◽  
Author(s):  
Stefan Becker ◽  
Donald M. McEligot ◽  
Edmond Walsh ◽  
Eckart Laurien
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Boundary Layer Flow ◽  
Leading Edge ◽  
Boundary Layer Transition ◽  
Turbulence Level ◽  
Two Dimensional ◽  
Freestream Turbulence ◽  
Layer Transition ◽  
Layer Flow

New results are deduced to assess the validity of proposed transition indicators when applied to situations other than boundary layers on smooth surfaces. The geometry employed utilizes a two-dimensional square rib to disrupt the boundary layer flow. The objective is to determine whether some available criteria are consistent with the present measurements of laminar recovery and transition for the flow downstream of this rib. For the present data — the proposed values of thresholds for transition in existing literature that are based on the freestream turbulence level at the leading edge are not reached in the recovering laminar run but they are not exceeded in the transitioning run either. Of the pointwise proposals examined, values of the suggested quantity were consistent for three of the criteria; that is, they were less than the threshold in laminar recovery and greater than it in the transitioning case.

scholarly journals Pinwheel valence-bond solid and triplet excitations in the two-dimensional deformed kagome lattice

2010 ◽  
Vol 6 (11) ◽  
pp. 865-869 ◽  
Author(s):  
K. Matan ◽  
T. Ono ◽  
Y. Fukumoto ◽  
T. J. Sato ◽  
J. Yamaura ◽  
...  
Keyword(s):  
Valence Bond ◽  
Two Dimensional ◽  
Kagome Lattice ◽  
Kagomé Lattice ◽  
Valence Bond Solid
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