Directional asymmetry of the nonlinear wave phenomena in a three-dimensional granular phononic crystal under gravity

Owing to their thermal insulating properties, superlattices have been extensively studied. A breakthrough in the performance of thermoelectric devices was achieved by using superlattice materials. The problem of those nanostructured materials is that they mainly affect heat transfer in only one direction. In this paper, the concept of canceling heat conduction in the three spatial directions by using atomic-scale three-dimensional (3D) phononic crystals is explored. A period of our atomic-scale 3D phononic crystal is made up of a large number of diamond-like cells of silicon atoms, which form a square supercell. At the center of each supercell, we substitute a smaller number of Si diamond-like cells by other diamond-like cells, which are composed of germanium atoms. This elementary heterostructure is periodically repeated to form a Si/Ge 3D nanostructure. To obtain different atomic configurations of the phononic crystal, the number of Ge diamond-like cells at the center of each supercell can be varied by substitution of Si diamond-like cells. The dispersion curves of those atomic configurations can be computed by lattice dynamics. With a general equation, the thermal conductivity of our atomic-scale 3D phononic crystal can be derived from the dispersion curves. The thermal conductivity can be reduced by at least one order of magnitude in an atomic-scale 3D phononic crystal compared to a bulk material. This reduction is due to the decrease of the phonon group velocities without taking into account that of the phonon average mean free path.

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Three-dimensional, nonlinear wave interaction in water of constant depth

Nonlinear Analysis ◽

10.1016/0362-546x(81)90035-3 ◽

1981 ◽

Vol 5 (3) ◽

pp. 303-323 ◽

Cited By ~ 36

Author(s):

John Reeder ◽

Marvin Shinbrot

Keyword(s):

Nonlinear Wave ◽

Three Dimensional ◽

Wave Interaction ◽

Constant Depth ◽

Nonlinear Wave Interaction

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Three-dimensional phononic crystal with ultra-wide bandgap at megahertz frequencies

Applied Physics Letters ◽

10.1063/5.0033615 ◽

2021 ◽

Vol 118 (6) ◽

pp. 063507

Author(s):

Julio Andrés Iglesias Martínez ◽

Johnny Moughames ◽

Gwenn Ulliac ◽

Muamer Kadic ◽

Vincent Laude

Keyword(s):

Phononic Crystal ◽

Three Dimensional ◽

Wide Bandgap

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Symmetric Boundary Condition for Laplacian on Net of Regular Hexagons

Journal of Mathematics Research ◽

10.5539/jmr.v9n3p46 ◽

2017 ◽

Vol 9 (3) ◽

pp. 46

Author(s):

Daniel Lee

Keyword(s):

Boundary Condition ◽

Matrix Theory ◽

Three Dimensional ◽

Cardiac Tissues ◽

Energy Product ◽

Symmetric Boundary Condition ◽

Almost All ◽

Wave Phenomena ◽

Dimensional Cell ◽

Theory Series

Hexagonal grid methods are found useful in many research works, including numerical modeling in spherical coordinates, in atmospheric and ocean models, and simulation of electrical wave phenomena in cardiac tissues. Almost all of these used standard Laplacian and mostly on one configuration of regular hexagons. In this work, discrete symmetric boundary condition and energy product for anisotropic Laplacian are investigated firstly on general net of regular hexagons, and then generalized to its most extent in two- or three-dimensional cell-center finite difference applications up to the usage of symmetric stencil in central differences. For analysis of Laplacian related applications, this provides with an approach in addition to the M-matrix theory, series method, functional interpolations and Fourier vectors.

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Towards More Realistic Leaf Shapes in Functional-Structural Plant Models

Symmetry ◽

10.3390/sym10070278 ◽

2018 ◽

Vol 10 (7) ◽

pp. 278 ◽

Cited By ~ 5

Author(s):

Dominik Schmidt ◽

Katrin Kahlen

Keyword(s):

Fluctuating Asymmetry ◽

Leaf Shape ◽

Three Dimensional ◽

Directional Asymmetry ◽

The Novel ◽

Shape Model ◽

Plant Model ◽

Virtual Plant ◽

Perfect Symmetry

Fluctuating asymmetry in plant leaves is a widely used measure in geometric morphometrics for assessing random deviations from perfect symmetry. In this study, we considered the concept of fluctuating asymmetry to improve the prototype leaf shape of the functional-structural plant model L-Cucumber. The overall objective was to provide a realistic geometric representation of the leaves for the light sensitive plant reactions in the virtual plant model. Based on three-dimensional data from several hundred in situ digitized cucumber leaves comparisons of model leaves and measurements were conducted. Robust Bayesian comparison of groups was used to assess statistical differences between leaf halves while respecting fluctuating asymmetries. Results indicated almost no directional asymmetry in leaves comparing different distances from the prototype while detecting systematic deviations shared by both halves. This information was successfully included in an improved leaf prototype and implemented in the virtual plant model L-Cucumber. Comparative virtual plant simulations revealed a slight improvement in plant internode development against experimental data using the novel leaf shape. Further studies can now focus on analyses of stress on the 3D-deformation of the leaf and the development of a dynamic leaf shape model.

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Nonlinear Wave Phenomena in Dense Conglomerate of Flux Tubes

Physics of Magnetic Flux Tubes - Astrophysics and Space Science Library ◽

10.1007/978-3-319-96361-7_9 ◽

2018 ◽

pp. 239-259

Author(s):

Margarita Ryutova

Keyword(s):

Nonlinear Wave ◽

Flux Tubes ◽

Wave Phenomena

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The influence of mean shear on Alfvén-internal wave propagation

Journal of Plasma Physics ◽

10.1017/s0022377800019735 ◽

1976 ◽

Vol 15 (2) ◽

pp. 197-222

Author(s):

R. J. Hartman

Keyword(s):

Three Dimensional ◽

Dimensional System ◽

Linear Wave ◽

Mean Flow ◽

Wave Processes ◽

Initial Value ◽

Initial Wave ◽

Wave Phenomena ◽

Three Dimensional System

This paper uses the general solution of the linearized initial-value problem for an unbounded, exponentially-stratified, perfectly-conducting Couette flow in the presence of a uniform magnetic field to study the development of localized wave-type perturbations to the basic flow. The two-dimensional problem is shown to be stable for all hydrodynamic Richardson numbers JH, positive and negative, and wave packets in this flow are shown to approach, asymptotically, a level in the fluid (the ‘isolation level’) which is a smooth, continuous, function of JH that is well defined for JH < 0 as well as JH > 0. This system exhibits a rich complement of wave phenomena and a variety of mechanisms for the transport of mean flow kinetic and potential energy, via linear wave processes, between widely-separated regions of fluid; this in addition to the usual mechanisms for the absorption of the initial wave energy itself. The appropriate three-dimensional system is discussed, and the role of nonlinearities on the development of localized disturbances is considered.

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