scholarly journals Part 2: Spatially Dispersive Metasurfaces - IE-GSTC-SD Field Solver with Extended GSTCs

2021 ◽  
Author(s):  
Tom J. Smy ◽  
Joao Guilherme Nizer Rahmeier Rahmeier ◽  
jordan dugan ◽  
Shulabh Gupta
Keyword(s):  
Simulation Framework ◽  
Fourier Decomposition ◽  
Full Wave ◽  
Unit Cells ◽  
Conducting Wire ◽  
Spatial Derivatives ◽  
The Difference ◽  
Scattered Fields ◽  
Spatially Dispersive ◽  
Derivatives Of

<div>An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of Part-</div><div>1 [1], which proposed the basic methodology of representing spatially dispersive metasurface structure in the spatial frequency domain, k. By representing the angular dependence of the surface susceptibilities in k as a ratio of two polynomials, the standard Generalized Sheet Transition Conditions (GSTCs) have been extended to include the spatial derivatives of both the difference and average fields around the metasurface. These extended boundary conditions are successfully integrated here into a standard IE-GSTC solver, which leads to the new IEGSTC-SD simulation framework presented here. The proposed IE-GSTC-SD platform is applied to various uniform metasurfaces, including a practical short conducting wire unit cell, as a representative practical example, for various cases of finite-sized flat and curvilinear surfaces. In all cases, computed field distributions are successfully validated, either against the semi-analytical Fourier decomposition method or the brute-force full-wave simulation of volumetric metasurfaces in the commercial Ansys FEM-HFSS simulator.</div>

scholarly journals Part 2: Spatially Dispersive Metasurfaces - IE-GSTC-SD Field Solver with Extended GSTCs

2021 ◽  
Author(s):  
Tom J. Smy ◽  
Joao Guilherme Nizer Rahmeier Rahmeier ◽  
jordan dugan ◽  
Shulabh Gupta
Keyword(s):  
Simulation Framework ◽  
Fourier Decomposition ◽  
Full Wave ◽  
Unit Cells ◽  
Conducting Wire ◽  
Spatial Derivatives ◽  
The Difference ◽  
Scattered Fields ◽  
Spatially Dispersive ◽  
Derivatives Of

<div>An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of Part-</div><div>1 [1], which proposed the basic methodology of representing spatially dispersive metasurface structure in the spatial frequency domain, k. By representing the angular dependence of the surface susceptibilities in k as a ratio of two polynomials, the standard Generalized Sheet Transition Conditions (GSTCs) have been extended to include the spatial derivatives of both the difference and average fields around the metasurface. These extended boundary conditions are successfully integrated here into a standard IE-GSTC solver, which leads to the new IEGSTC-SD simulation framework presented here. The proposed IE-GSTC-SD platform is applied to various uniform metasurfaces, including a practical short conducting wire unit cell, as a representative practical example, for various cases of finite-sized flat and curvilinear surfaces. In all cases, computed field distributions are successfully validated, either against the semi-analytical Fourier decomposition method or the brute-force full-wave simulation of volumetric metasurfaces in the commercial Ansys FEM-HFSS simulator.</div>

scholarly journals Surface Susceptibilities as Compact Full-Wave Simulation Models of Fully-Reflective Volumetric Metasurfaces

2021 ◽  
Author(s):  
Ville Tiukuvaara ◽  
Tom J. Smy ◽  
Karim Achouri ◽  
Shulabh Gupta
Keyword(s):  
Computational Cost ◽  
Simulation Models ◽  
Arbitrary Field ◽  
Simulation Techniques ◽  
Full Wave ◽  
Unit Cells ◽  
Scattered Fields ◽  
Two Sides ◽  
Model Structures ◽  
High Computational Cost

<p>While metasurfaces (MSs) are constructed from deeply-subwavelength unit cells, they are generally electrically-large and full-wave simulations of the complete structure are computationally expensive. Thus, to reduce this high computational cost, non-uniform MSs can be modeled as zero-thickness boundaries, with sheets of electric and magnetic polarizations related to the fields by surface susceptibilities and the generalized sheet transition conditions (GSTCs). While these two-sided boundary conditions have been extensively studied for single sheets of resonant particles, it has not been shown if they can correctly model structures where the two sides are electrically isolated, such as a fully-reflective surface. In particular, we consider in this work whether the fields scattered from a fully reflective metasurface can be correctly predicted for arbitrary field illuminations, with the source placed on either side of the surface. In the process, we also show the mapping of a PEC sheet with a dielectric cover layer to bi-anisotropic susceptibilities. Finally, we demonstrate the use of the susceptibilities as compact models for use in various simulation techniques, with an illustrative example of a parabolic reflector, for which the scattered fields are correctly computed using a integral equation (IE) based solver.<br></p>

scholarly journals Surface Susceptibilities as Compact Full-Wave Simulation Models of Fully-Reflective Volumetric Metasurfaces

2021 ◽  
Author(s):  
Ville Tiukuvaara ◽  
Tom J. Smy ◽  
Karim Achouri ◽  
Shulabh Gupta
Keyword(s):  
Computational Cost ◽  
Simulation Models ◽  
Arbitrary Field ◽  
Simulation Techniques ◽  
Full Wave ◽  
Unit Cells ◽  
Scattered Fields ◽  
Two Sides ◽  
Model Structures ◽  
High Computational Cost

<p>While metasurfaces (MSs) are constructed from deeply-subwavelength unit cells, they are generally electrically-large and full-wave simulations of the complete structure are computationally expensive. Thus, to reduce this high computational cost, non-uniform MSs can be modeled as zero-thickness boundaries, with sheets of electric and magnetic polarizations related to the fields by surface susceptibilities and the generalized sheet transition conditions (GSTCs). While these two-sided boundary conditions have been extensively studied for single sheets of resonant particles, it has not been shown if they can correctly model structures where the two sides are electrically isolated, such as a fully-reflective surface. In particular, we consider in this work whether the fields scattered from a fully reflective metasurface can be correctly predicted for arbitrary field illuminations, with the source placed on either side of the surface. In the process, we also show the mapping of a PEC sheet with a dielectric cover layer to bi-anisotropic susceptibilities. Finally, we demonstrate the use of the susceptibilities as compact models for use in various simulation techniques, with an illustrative example of a parabolic reflector, for which the scattered fields are correctly computed using a integral equation (IE) based solver.<br></p>

scholarly journals Part 1: Spatially Dispersive Metasurfaces: Zero Thickness Surface Susceptibilities & Extended GSTCs

2021 ◽  
Author(s):  
Joao Guilherme Nizer Rahmeier Rahmeier ◽  
Tom J. Smy ◽  
jordan dugan ◽  
Shulabh Gupta
Keyword(s):  
Temporal Frequency ◽  
Simple Method ◽  
Spatial Frequencies ◽  
Short Dipole ◽  
Unit Cells ◽  
Spatial Boundary ◽  
Spatio Temporal ◽  
The Difference ◽  
Frequency Behavior ◽  
Spatially Dispersive

<div>A simple method to describe spatially dispersive metasurfaces is proposed where the angle-dependent surface susceptibilities are explicitly used to formulate the zero thickness sheet model of practical metasurface structures. It is shown that if the surface susceptibilities of a given metasurface are expressed as a ratio of two polynomials of tangential spatial frequencies, k<sub>||</sub>, with complex coefficients, they can be conveniently expressed as spatial derivatives of the difference and average fields around the metasurface in the space domain, leading to extended forms of the standard Generalized Sheet Transition Conditions (GSTCs) accounting for the spatial dispersion. Using two simple examples of a short electric dipole and an all-dielectric cylindrical puck unit cells, which exhibit purely tangential surface susceptibilities and reciprocal/symmetric transmission and reflection characteristics, the proposed concept is numerically confirmed in 2D. A single Lorentzian has been found to describe the spatio-temporal frequency behavior of a short dipole unit cell, while a multi-Lorentzian description is developed to capture the complex multiple angular resonances of the dielectric puck. For both cases, the appropriate spatial boundary conditions are derived.</div>

scholarly journals Part 1: Spatially Dispersive Metasurfaces: Zero Thickness Surface Susceptibilities & Extended GSTCs

2021 ◽  
Author(s):  
Joao Guilherme Nizer Rahmeier Rahmeier ◽  
Tom J. Smy ◽  
jordan dugan ◽  
Shulabh Gupta
Keyword(s):  
Temporal Frequency ◽  
Simple Method ◽  
Spatial Frequencies ◽  
Short Dipole ◽  
Unit Cells ◽  
Spatial Boundary ◽  
Spatio Temporal ◽  
The Difference ◽  
Frequency Behavior ◽  
Spatially Dispersive

<div>A simple method to describe spatially dispersive metasurfaces is proposed where the angle-dependent surface susceptibilities are explicitly used to formulate the zero thickness sheet model of practical metasurface structures. It is shown that if the surface susceptibilities of a given metasurface are expressed as a ratio of two polynomials of tangential spatial frequencies, k<sub>||</sub>, with complex coefficients, they can be conveniently expressed as spatial derivatives of the difference and average fields around the metasurface in the space domain, leading to extended forms of the standard Generalized Sheet Transition Conditions (GSTCs) accounting for the spatial dispersion. Using two simple examples of a short electric dipole and an all-dielectric cylindrical puck unit cells, which exhibit purely tangential surface susceptibilities and reciprocal/symmetric transmission and reflection characteristics, the proposed concept is numerically confirmed in 2D. A single Lorentzian has been found to describe the spatio-temporal frequency behavior of a short dipole unit cell, while a multi-Lorentzian description is developed to capture the complex multiple angular resonances of the dielectric puck. For both cases, the appropriate spatial boundary conditions are derived.</div>

Energy Approximation

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Main Lemma ◽  
The Other ◽  
Coarse Scale ◽  
Continuous Solutions ◽  
Material Derivative ◽  
Energy Variation ◽  
Energy Approximation ◽  
The Difference ◽  
Derivatives Of

This chapter presents the equations and calculations for energy approximation. It establishes the estimates (261) and (262) of the Main Lemma (10.1) for continuous solutions; these estimates state that we are able to accurately prescribe the energy that the correction adds to the solution, as well as bound the difference between the time derivatives of these two quantities. The chapter also introduces the proposition for prescribing energy, followed by the relevant computations. Each integral contributing to the other term can be estimated. Another proposition for estimating control over the rate of energy variation is given. Finally, the coarse scale material derivative is considered.

MODIFICATION OF CASIMIR FORCES DUE TO BAND GAPS IN PERIODIC STRUCTURES

2002 ◽  
Vol 17 (06n07) ◽  
pp. 798-803 ◽  
Author(s):  
C. VILLARREAL ◽  
R. ESQUIVEL-SIRVENT ◽  
G. H. COCOLETZI
Keyword(s):  
Density Of States ◽  
Casimir Force ◽  
Periodic Structures ◽  
Local Density ◽  
Band Gaps ◽  
Basic Unit ◽  
Local Density Of States ◽  
Casimir Forces ◽  
Unit Cells ◽  
The Difference

The Casimir force between inhomogeneous slabs that exhibit a band-like structure is calculated. The slabs are made of basic unit cells each made of two layers of different materials. As the number of unit cells increases the Casimir force between the slabs changes, since the reflectivity develops a band-like structure characterized by frequency regions of high reflectivity. This is also evident in the difference of the local density of states between free and boundary distorted vacuum, that becomes maximum at frequencies corresponding to the band gaps. The calculations are restricted to vacuum modes with wave vectors perpendicular to the slabs.

Vibration attenuation of a two-link flexible arm carried by a translational stage

2018 ◽  
Vol 24 (23) ◽  
pp. 5650-5664 ◽  
Author(s):  
Shang–Teh Wu ◽  
Shan-Qun Tang ◽  
Kuan–Po Huang
Keyword(s):  
Feedback Loop ◽  
Control Method ◽  
Flexible Manipulator ◽  
Closed Loop System ◽  
Flexible Arm ◽  
Vibration Attenuation ◽  
Shaft Encoder ◽  
High Frequency Vibrations ◽  
Spatial Derivatives ◽  
Derivatives Of

This paper investigates the vibration control of a two-link flexible manipulator carried by a translational stage. The first and the second links are each driven by a stage motor and a joint motor. By treating the joint motor as a virtual spring, the two-link manipulator can be regarded as an integral flexible arm driven by the stage motor. A noncollocated controller is devised based on feedback from the deflection of the virtual spring, which can be measured by a shaft encoder. Stability of the closed-loop system is analyzed by examining the spatial derivatives of the modal functions. By including a bandpass filter in the feedback loop, residual vibrations can be attenuated without exciting high-frequency vibrations. The control method is simple to implement; its effectiveness is confirmed by simulation and experimental results.

Effects of avertin versus xylazine-ketamine anesthesia on cardiac function in normal mice

2001 ◽  
Vol 281 (5) ◽  
pp. H1938-H1945 ◽  
Author(s):  
Chari Y. T. Hart ◽  
John C. Burnett ◽  
Margaret M. Redfield
Keyword(s):  
Cardiac Function ◽  
Diastolic Pressure ◽  
Systolic Function ◽  
Pressure Rise ◽  
Left Ventricular ◽  
Lv Function ◽  
Ketamine Anesthesia ◽  
The Difference ◽  
And Function ◽  
Derivatives Of

Anesthetic regimens commonly administered during studies that assess cardiac structure and function in mice are xylazine-ketamine (XK) and avertin (AV). While it is known that XK anesthesia produces more bradycardia in the mouse, the effects of XK and AV on cardiac function have not been compared. We anesthetized normal adult male Swiss Webster mice with XK or AV. Transthoracic echocardiography and closed-chest cardiac catheterization were performed to assess heart rate (HR), left ventricular (LV) dimensions at end diastole and end systole (LVDd and LVDs, respectively), fractional shortening (FS), LV end-diastolic pressure (LVEDP), the time constant of isovolumic relaxation (τ), and the first derivatives of LV pressure rise and fall (dP/d t max and dP/d t min, respectively). During echocardiography, HR was lower in XK than AV mice (250 ± 14 beats/min in XK vs. 453 ± 24 beats/min in AV, P < 0.05). Preload was increased in XK mice (LVDd: 4.1 ± 0.08 mm in XK vs. 3.8 ± 0.09 mm in AV, P < 0.05). FS, a load-dependent index of systolic function, was increased in XK mice (45 ± 1.2% in XK vs. 40 ± 0.8% in AV, P < 0.05). At LV catheterization, the difference in HR with AV (453 ± 24 beats/min) and XK (342 ± 30 beats/min, P < 0.05) anesthesia was more variable, and no significant differences in systolic or diastolic function were seen in the group as a whole. However, in XK mice with HR <300 beats/min, LVEDP was increased (28 ± 5 vs. 6.2 ± 2 mmHg in mice with HR >300 beats/min, P < 0.05), whereas systolic (LV dP/d t max: 4,402 ± 798 vs. 8,250 ± 415 mmHg/s in mice with HR >300 beats/min, P < 0.05) and diastolic (τ: 23 ± 2 vs. 14 ± 1 ms in mice with HR >300 beats/min, P < 0.05) function were impaired. Compared with AV, XK produces profound bradycardia with effects on loading conditions and ventricular function. The disparate findings at echocardiography and LV catheterization underscore the importance of comprehensive assessment of LV function in the mouse.

The effect of microscale random Alfvén waves on the propagation of large-scale Alfvén waves

1983 ◽  
Vol 29 (2) ◽  
pp. 243-253 ◽  
Author(s):  
Tomikazu Namikawa ◽  
Hiromitsu Hamabata
Keyword(s):  
Large Scale ◽  
Ponderomotive Force ◽  
Collisionless Plasma ◽  
Alfven Waves ◽  
Velocity Fields ◽  
Velocity Shear ◽  
Alfvén Waves ◽  
Spectrum Function ◽  
Spatial Derivatives ◽  
Derivatives Of

The ponderomotive force generated by random Alfvén waves in a collisionless plasma is evaluated taking into account mean magnetic and velocity shear and is expressed as a series involving spatial derivatives of mean magnetic and velocity fields whose coefficients are associated with the helicity spectrum function of random velocity field. The effect of microscale random Alfvén waves through ponderomotive and mean electromotive forces generated by them on the propagation of large-scale Alfvén waves is also investigated.

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