Spectro-Spatial Wave Features in Nonlinear Metamaterials: Theoretical and Computational Studies

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Mohammad Bukhari ◽  
Eshagh Farzaneh Joubaneh ◽  
Oumar Barry
Keyword(s):  
Spatial Analysis ◽  
Multiple Scales ◽  
Computational Study ◽  
Nonlinear Phenomena ◽  
Long Wavelength ◽  
Finite Element Software ◽  
Nonlinear Metamaterials ◽  
A Cell ◽  
Processing Techniques ◽  
Computational Analyses

Abstract Considerable attention has been given to nonlinear metamaterials because they offer some interesting phenomena such as solitons, frequency shifts, and tunable bandgaps. However, only little is known about the spectro-spatial properties of a wave propagating in nonlinear periodic chains, particularly, a cell with multiple nonlinear resonators. This problem is investigated here. Our study examines both hardening and softening nonlinearities in the chains and in the local resonators. Explicit expressions for the nonlinear dispersion relations are derived by the method of multiple scales. We validate our analytical results using numerical simulations. The numerical simulation is based on spectro-spatial analysis using signal processing techniques such as spatial-spectrogram and wave filtering. The spectro-spatial analysis provides detailed information about the interactions of dispersive and nonlinear phenomena of waveform in both short- and long-wavelength domains. Furthermore, we validate and demonstrate the theoretically obtained bandgaps, wave distortion, and birth of solitary waves through a computational study using finite element software, ansys. The findings, in both theoretical and computational analyses, suggest that nonlinear resonators can have more effect on the waveform than the nonlinear chains. This observation is valid in both short and long wavelength limits.

On the Spectro-Spatial Wave Features in Nonlinear Metamaterials With Multiple Local Resonators

2019 ◽  
Author(s):  
Mohammad A. Bukhari ◽  
Oumar R. Barry
Keyword(s):  
Spatial Analysis ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Nonlinear Phenomena ◽  
Long Wavelength ◽  
Spatial Properties ◽  
Nonlinear Metamaterials ◽  
A Cell ◽  
Processing Techniques ◽  
Signal Processing Techniques

Abstract Considerable attention has been given to nonlinear metamaterials because they offer some interesting phenomena such as solitons, frequency shifts, and tunable bandgaps. However, only little is known about the spectro-spatial properties of a wave propagating in nonlinear periodic chains, particularly, a cell with multiple nonlinear resonators. This problem is investigated here. Our study examines both hardening and softening nonlinearities in the chains and in the local resonators. Explicit expressions for the nonlinear dispersion relations are derived by the method of multiple scales. We validate our analytical results using numerical simulations. The numerical simulation is based on spectro-spatial analysis using signal processing techniques such as spatial-spectrogram and wave filtering. The spectro-spatial analysis provides detailed information about the interactions of dispersive and nonlinear phenomena of waveform in both short and long-wavelength domains. The findings suggest that nonlinear resonators can have more effect on the waveform than the nonlinear chains. This observation is valid in both short and long wavelength limits.

Multimode Dynamics of Inextensional Beams on the Elastic Foundation With Two-to-One Internal Resonances

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Lianhua Wang ◽  
Jianjun Ma ◽  
Minghui Yang ◽  
Lifeng Li ◽  
Yueyu Zhao
Keyword(s):  
Chaotic Dynamics ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Continuation Methods ◽  
Nonlinear Phenomena ◽  
Modal Interactions ◽  
Internal Resonances ◽  
Modulation Equations ◽  
Nonlinear Responses ◽  
Methods Numerical

The modal interactions and nonlinear responses of inextensional beams resting on elastic foundations with two-to-one internal resonances are investigated and the primary resonance excitations are considered. The multimode discretization and the method of multiple scales are applied to obtain the modulation equations. The equilibrium and dynamic solutions of the modulation equations are examined by the Newton–Raphson, shooting, and continuation methods. Numerical simulations are performed to investigate the chaotic dynamics of the beam. It is shown that the nonlinear responses may undergo different bifurcations and exhibit rich nonlinear phenomena. Finally, the effects of the foundation models on the nonlinear interactions of the beam are examined.

scholarly journals Computations of Film Cooling From Holes With Struts

1999 ◽  
Author(s):  
T. I-P. Shih ◽  
Y.-L. Lin ◽  
M. K. Chyu ◽  
S. Gogineni
Keyword(s):  
Film Cooling ◽  
Computational Study ◽  
Three Dimensional ◽  
Protective Layer ◽  
Navier Stokes ◽  
Time Stepping ◽  
Cooling Hole ◽  
A Cell ◽  
Volume Method ◽  
Film Cooling Holes

Computations were performed to study the three-dimensional flow and heat transfer on a flat plate cooled by jets, injected from a plenum through one row of film-cooling holes in which each hole is fitted with a strut in the form of a circular cylinder. Three different configurations of the film-cooling hole were investigated: without strut, with streamwise strut, and with spanwise strut. For all configurations, the film-cooling holes are inclined at 35°, and the coolant-to-mainflow density and mass-flux ratios are 1.6 and 0.5, respectively. The focus of this study is to understand how struts in holes affect film cooling jets and their interactions with the mainflow in forming a protective layer of cooler fluid over the plate. This computational study is based on the ensemble-averaged conservation equations of mass, momentum (compressible Navier-Stokes), and energy. Effects of turbulence was modeled by a low Reynolds number k-ω closure known as the shear-stress-transport (SST) model. Solutions were generated by a cell-centered finite-volume method that uses third-order accurate flux-difference splitting of Roe with limiters, multigrid acceleration of a diagonalized ADI scheme with local time stepping, and patched/overlapped structured grids. In the computations, the flow is resolved not just in the cooling-jet/mainflow interaction region, but also inside the film-cooling holes and in the plenum. Computed results for adiabatic effectiveness for the case without struts were compared with experimental data, and reasonably good agreements were obtained.

Mechanics of Microtubule Buckling Supported by Cytoplasm

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
Hanqing Jiang ◽  
Jiaping Zhang
Keyword(s):  
Evolution Equations ◽  
Compressive Force ◽  
Cylindrical Tube ◽  
Long Wavelength ◽  
Euler Buckling ◽  
In Vivo Experiments ◽  
Critical Wavelength ◽  
A Cell

The cytoskeleton provides the mechanical scaffold and maintains the integrity of cells. It is usually believed that one type of cytoskeleton biopolymer, microtubules, bears compressive force. In vitro experiments found that isolated microtubules may form an Euler buckling pattern with a long-wavelength for very small compressive force. This, however, does not agree with in vivo experiments where microtubules buckle with a short-wavelength. In order to understand the structural role of microtubules in vivo, we developed mechanics models that study microtubule buckling supported by cytoplasm. The microtubule is modeled as a linearly elastic cylindrical tube while the cytoplasm is characterized by different types of materials, namely, viscous, elastic, or viscoelastic. The dynamic evolution equations, the fastest growth rate, the critical wavelength, and compressive force, as well as equilibrium buckling configurations are obtained. The ability for a cell to sustain compressive force does not solely rely on microtubules but is also supported by the elasticity of cytoplasm. With the support of the cytoplasm, an individual microtubule can sustain a compressive force on the order of 100pN. The relatively stiff microtubules and compliant cytoplasm are combined to provide a scaffold for compressive force.

TUTORIAL ON CONTINUATION

1991 ◽  
Vol 01 (01) ◽  
pp. 3-11 ◽  
Author(s):  
R. SEYDEL
Keyword(s):  
Computational Study ◽  
Nonlinear Phenomena ◽  
Essential Tool ◽  
Predictor Corrector

A computational study of most nonlinear phenomena is based on equations that involve a parameter. Solutions to the equations vary with the parameter. An essential tool for generating such solutions is continuation. This paper presents a tutorial on continuation, and explains the principles of predictor–corrector methods.

Metabolite Transport Inside Channeled Porous Scaffolds for Haematopoietic Stem Cell Culture: A Computational Study

2008 ◽  
Author(s):  
Marco Cantini ◽  
Gianfranco B. Fiore ◽  
Alberto Redaelli ◽  
Monica Soncini
Keyword(s):  
Fluid Dynamics ◽  
Cell Culture ◽  
Computational Study ◽  
Three Dimensional ◽  
Polymeric Materials ◽  
Haematopoietic Stem Cell ◽  
Porous Scaffolds ◽  
A Cell ◽  
Definition Of

Porous polymeric materials play a key role in regenerative medicine, serving as three-dimensional scaffolds for cell culture. Hence, the definition of their micro-architecture should be regarded as a pivotal design issue, that has to be wittingly addressed while engineering a cell culture system. Computational fluid dynamics techniques (CFD) appear to be very valuable in this respect, since they have been appreciably applied in recent literature as a means to analyze fluid dynamics and mass transport inside scaffold or bioreactor models [1]; moreover, leading researchers in tissue engineering have acknowledged the role of numerical methodology in the issue of defining optimal flow conditions for three-dimensional dynamic culture systems.

Generalization and multiscale structure of subsurface structural maps

2018 ◽  
Vol 6 (4) ◽  
pp. T1045-T1054 ◽  
Author(s):  
Simon A. Stewart
Keyword(s):  
Multiple Scales ◽  
Original Data ◽  
Sampling Theory ◽  
Geologic Structure ◽  
Grid Sampling ◽  
Long Wavelength ◽  
Standard Mapping ◽  
Yield Structure ◽  
Mapping Process ◽  
Process Controls

Subsurface structural maps are stored as spatially referenced numeric grids. The spatial sampling density of these grids is a critical parameter in the mapping process because the sampling and aliasing that occurs when transforming from original data sources during the gridding process controls the information content and aesthetics of the final map. New results from upscaling experiments and sampling theory indicate that it is possible to specify gridding parameters that remove noise while retaining key geologic structure — an optimized generalization procedure. Furthermore, geologic structure may exist at multiple scales. Sampling theory can again be applied, in a multiscale curvature analysis, to yield structure at a range of scales via decomposition of a gridded surface. These products can be analyzed further for indications of short-wavelength, high-curvature features that may correspond to fault or fracture zones, and long-wavelength, prospect, and field-scale structure. These results combine to inform a discussion on sampling, smoothing, and geologic information, as well as provide a quantitative alternative to rules of thumb for grid sampling that balance signal and noise in standard mapping schemes.

Numerical Modeling of Nanostructure-Enhanced Solar Cells

2014 ◽  
Author(s):  
Rongheng Li ◽  
Ben Q. Li
Keyword(s):  
Thin Film ◽  
Solar Cells ◽  
Maxwell Equations ◽  
Light Propagation ◽  
Model Simulation ◽  
Computational Study ◽  
Light Trapping ◽  
Ag Nanoparticle ◽  
Long Wavelength ◽  
Embedded Particles

This paper presents a computational study of nanostructure-enhanced solar cells. The computer model is developed based on the FDTD solution of the Maxwell equations describing the light propagation in thin film solar cells. With the model, a combination of Ag nanoparticle arrays at the top, Ag nanoparticle embedded into absorption layer and nanograting structures at the bottom of a thin film solar cell is studied. Each nanostructure is known to be capable of enhancing the solar light absorption to a certain degree, with the effect of metal particles coming primarily from the light scattering, the embedded particles from the reflection and that of back reflector from light trapping and reflection. The preliminary data from model simulation illustrate that with an appropriate combination and arrangement of these nanostructures, an increase in both short and long wavelength range can be achieved, thereby overcoming the shorting comings of each of the nanostructures when applied alone.

Computational Study of High Temperature Liquid Metal Infusion

2017 ◽  
Author(s):  
Arturo Schiaffino ◽  
Ashesh Chattopadhyay ◽  
Shaikh Tanveer Hossain ◽  
Vinod Kumar ◽  
V. M. K. Kotteda ◽  
...  
Keyword(s):  
Porous Media ◽  
Liquid Metal ◽  
Molten Metal ◽  
Multiple Scales ◽  
Computational Study ◽  
Interface Energy ◽  
Network Simulator ◽  
Void Space ◽  
Infiltration Process ◽  
Viscous Forces

Liquid metal infiltration, or liquid method infusion, consists of impregnating porous media composed of woven, ceramic particles, or fibers with a molten metal matrix, which fills the pores and occupies the void space within. Understanding the infiltration process is crucial to optimize the properties of the recently formed material and avoid or minimize the formation of fabrication defects. Given the fact that the flow of molten metal differs from organic flows, since molten metal possess a higher interface energy than organic flows, and modifies the wetting dynamics of the molten metal over surfaces, creating a flow driven by capillary and viscous forces. In addition, flow through porous media presents an extraordinary challenge to simulate efficiently, due to the presence of multiple scales far apart participating in the governing dynamics. For this reason, an in-house pore network simulator (EXPNS) was used. EXPNS was designed on a next generation computing framework using Sandia National Lab’s Trilinos and Kokkos library to perform high-resolution computing to generate data for the infiltration model and improve the general understanding of this process.

A COMPUTATIONAL STUDY TO INVESTIGATE DEBONDING IN COATED BIORESORBABLE STENTS

2015 ◽  
Vol 15 (02) ◽  
pp. 1540015 ◽  
Author(s):  
WEI WU ◽  
MASSIMILIANO MERCURI ◽  
CHIARA PEDRONI ◽  
FRANCESCO MIGLIAVACCA ◽  
LORENZA PETRINI
Keyword(s):  
Finite Element ◽  
Degradation Rate ◽  
High Strain ◽  
Computational Study ◽  
Two Dimensional ◽  
Finite Element Analyses ◽  
Bioresorbable Scaffold ◽  
Polymer Properties ◽  
Coating Delamination ◽  
Computational Analyses

A new trend in the treatment of atherosclerosis foresees the exploitation of bioresorbable materials for stents. Magnesium alloys are good candidates since they are completely biocorrodible in human body. To overcome the limitation of very fast degradation, the bioresorbable scaffold can be coated with a polymer having lower degradation rate and taking advantages by coupling metal and polymer properties. However, the coating has a risk of debonding due to the high strain the stent undergoes during the expansion. In this paper two-dimensional (2D) finite element analyses are performed to provide a greater understanding of coating delamination and to show how computational analyses can be usefully employed in the design of coated bioresorbable stents.

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