$20 Bonus + 25% OFF
Securing Higher Grades Costing Your Pocket?
Book Your Assignment at The Lowest Price
Now!
Students Who Viewed This Also Studied
PHYS97066 Plasmonics and Metamaterials
Question:
(MEM)design from the literature
Identify the factors that determine its performance and investigate the effect of these factors on its relevant performance by developing a mathematical model and applying appropriate techniques analysis and simulation I need to achieve the aim as describe earlier from either one of these designs which ever is easy to approach and also need guidance to write literature on passive and active metamaterials if possible.
Viscoelastic locally resonant double negative metamaterials with controllable effective density and elasticity
Materials with a subwavelength structure and which have properties allowing the concept of negative refraction to be realised, were first investigated for electromagnetic waves [1–4]. The refractive index (n) of a homogeneous electromagnetic material is a function of its permittivity εr and permeability μr (n = ±√εrμr ). When both parameters are positive, the refractive index is positive real. When a wave transitions between two materials with positive real refractive indices, the change of direction across the boundary is as would be expected for conventional refraction, i.e. the incident and refracted waves lie on opposite sides of the boundary normal. When the parameters have opposite signs, the refractive index is complex and the medium partially blocks the propagation of the incident wave. Veselago [5] concluded that if both of these parameters could be made negative simultaneously, a negative refractive index material could result, i.e. n is negative real.
When a wave transitions between mediums with opposite signed real refractive indices, Snell’s law leads to a refracted wave which lies on the same side of the boundary normal as the incident wave. Pioneering work has shown that double negative materials can be constructed by combining two materials, one with the ability to provide negative permittivity and the other negative permeability [3]. The negative values for both parameters result from low frequency resonances built into a periodic structure. More recently metamaterials have been extended to pressure waves [6–18]. The mechanical analogues of permittivity and permeability are respectively, the modulus of elasticity and density. It follows that the refractive index for a pressure wave in a homogeneous medium is a function of density ρ and modulus of elasticity κ (n = ±√ρ/κ ). Thus negative refraction for a pressure wave in a homogeneous elastic medium occurs when the modulus of elasticity and density are simultaneously negative. For acoustics, a material with the properties of negative density and modulus of elasticity can be constructed using either a single resonant structure [16] or a combination of two different structural units [17,18]. An array of Helmholtz resonators connected to a one-dimensional transmission medium is described by Fig. 1a. An array of Helmholtz resonators connected to a transmission medium has previously been shown to provide negative effective modulus of elasticity in a designed frequency band [8,12].
These relationships have been derived through analogy with earlier work on electromagnetic metamaterials. Other arrangements have been shown to posses either a negative effective modulus of elasticity [6,13] or density [14,15]. In the single negative band these systems thus have a complex refractive index which acts to partially block the propagation of a pressure wave through the medium. In these studies the Helmholtz resonator has been modelled as a mass connected to a stationary reference point through a stiffness element and to the transmission medium through a damping element.
Theory
An array of Helmholtz resonators connected to a transmission medium can be approximated by the lumped parameter spring–mass– damper system illustrated in Fig. 1b. By applying D’Alembert’s principle to the individual masses and assuming a harmonic signal, this system can be represented by a homogeneous effective system consisting of a simple cascade of masses connected by parallel stiffness and damping elements, such as is described by:
Eq. (1). −Mexnω2 = (Ce iω + Ke)(xn−1 + xn+1 − 2xn) + fn (1)
The mass and stiffness of the effective homogeneous system are derived as Eqs. (2) and (3) respectively.
Me = m − (−mrω2 + chiω + kh)(criω + kr) ω2(−mrω2 + (ch + cr)iω + kh + kr) (2) Ke = k (3)
The mass term is a complex function, which can be divided into its real and imaginary terms. The real part (4) acts as the actual effective mass of the system and the imaginary term (5) acts as an additional loss term, which is effectively equivalent to a damper attached to a stationary point, i.e. this loss term is only a function of the motion of the respective point in the transmission system. The other dispersive loss term is given by Eq. (6) and is equal to the loss factor of the original transmission system.
An active metamaterial with a controllable negative effective mass The stationary reference point intrinsic to acoustic Helmholtz resonators, results from the motion of the fluid mass in the connecting neck, against the compressible fluid contained within the attached volume. If the volume is encased in a rigid shell, the motion of the shell can be ignored, resulting in the stationary connection. In solid materials the equivalent modulus of elasticity of the transmission material is generally much higher than the equivalent modulus for most fluids and properties such as the Poisson effect become significant. Under these conditions the creation of this rigid connection is difficult, particularly in three-dimensional structures. However, a mass with a single elastic connection to the transmission medium can be relatively easily introduced into a solid material.
An active metamaterial with a controllable negative effective mass and stiffness The Skyhook controlled system described by Fig. 1c is adaptable but still only capable of providing a single negative effective parameter. To create an adaptable system with double negative properties the control system is extended to include the motion of the (n − 1)th and (n + 1)th transmission masses. This modified control force fcn = kc (xn−1 + xn+1 − 2xrn ) + cc (x˙n−1 + x˙n+1 − 2x˙rn ) leads to Eqs. (9) and (10) for the mass and combined damping–stiffness of the effective system.
Fig. 2. The displacement transmission across the first and fourth masses (m) which form part of a series of four units connected by stiffness and damping elements (a), i.e. an ambient system with no LR structures (red line); and for the ambient system with the addition of actively controlled masses (mr) attached in parallel and designed to emulate Helmholtz resonators (black line). The sign of the real part of the dispersion curve for the effective mass of the actively controlled system is plotted in (b). The grey regions mark the single negative region, i.e. the region where the real part of the effective mass of the controlled system is negative. The model parameters are: m = 0.01 kg, mr = 0.1 kg, k = 3000 N/m, kr = 1000 N/m, kc = 2100 N/m, c = 0.1 Ns/m, cr = 0.002 N s/m, cc = 0.02 N s/m.
(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.) Both the effective mass (11) and stiffness (14) are dispersive and can become negative in a prescribed frequency band for certain mass, stiffness and damping combinations. For a homogeneous system of the form described by Eq. (1), the equation for the refractive index of an elastic medium can be generalised to a function of the mass and stiffness of the discrete elements. For such a system a negative refractive index occurs when the effective mass and stiffness are simultaneously negative. An array of actively controlled masses connected to a transmission medium described in a lumped parameter form thus constitutes a potential material with a negative refractive index in a prescribed frequency band, i.e. a double negative metamaterial.
PHYS97066 Plasmonics and Metamaterials
Answer in Detail
Solved by qualified expert
Get Access to This Answer
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Hac habitasse platea dictumst vestibulum rhoncus est pellentesque. Amet dictum sit amet justo donec enim diam vulputate ut. Neque convallis a cras semper auctor neque vitae. Elit at imperdiet dui accumsan. Nisl condimentum id venenatis a condimentum vitae sapien pellentesque. Imperdiet massa tincidunt nunc pulvinar sapien et ligula. Malesuada fames ac turpis egestas maecenas pharetra convallis posuere. Et ultrices neque ornare aenean euismod. Suscipit tellus mauris a diam maecenas sed enim. Potenti nullam ac tortor vitae purus faucibus ornare. Morbi tristique senectus et netus et malesuada. Morbi tristique senectus et netus et malesuada. Tellus pellentesque eu tincidunt tortor aliquam. Sit amet purus gravida quis blandit. Nec feugiat in fermentum posuere urna. Vel orci porta non pulvinar neque laoreet suspendisse interdum. Ultricies tristique nulla aliquet enim tortor at auctor urna. Orci sagittis eu volutpat odio facilisis mauris sit amet.
Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Hac habitasse platea dictumst vestibulum rhoncus est pellentesque. Amet dictum sit amet justo donec enim diam vulputate ut. Neque convallis a cras semper auctor neque vitae. Elit at imperdiet dui accumsan. Nisl condimentum id venenatis a condimentum vitae sapien pellentesque. Imperdiet massa tincidunt nunc pulvinar sapien et ligula. Malesuada fames ac turpis egestas maecenas pharetra convallis posuere. Et ultrices neque ornare aenean euismod. Suscipit tellus mauris a diam maecenas sed enim. Potenti nullam ac tortor vitae purus faucibus ornare. Morbi tristique senectus et netus et malesuada. Morbi tristique senectus et netus et malesuada. Tellus pellentesque eu tincidunt tortor aliquam. Sit amet purus gravida quis blandit. Nec feugiat in fermentum posuere urna. Vel orci porta non pulvinar neque laoreet suspendisse interdum. Ultricies tristique nulla aliquet enim tortor at auctor urna. Orci sagittis eu volutpat odio facilisis mauris sit amet.
Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Hac habitasse platea dictumst vestibulum rhoncus est pellentesque. Amet dictum sit amet justo donec enim diam vulputate ut. Neque convallis a cras semper auctor neque vitae. Elit at imperdiet dui accumsan. Nisl condimentum id venenatis a condimentum vitae sapien pellentesque. Imperdiet massa tincidunt nunc pulvinar sapien et ligula. Malesuada fames ac turpis egestas maecenas pharetra convallis posuere. Et ultrices neque ornare aenean euismod. Suscipit tellus mauris a diam maecenas sed enim. Potenti nullam ac tortor vitae purus faucibus ornare. Morbi tristique senectus et netus et malesuada. Morbi tristique senectus et netus et malesuada. Tellus pellentesque eu tincidunt tortor aliquam. Sit amet purus gravida quis blandit. Nec feugiat in fermentum posuere urna. Vel orci porta non pulvinar neque laoreet suspendisse interdum. Ultricies tristique nulla aliquet enim tortor at auctor urna. Orci sagittis eu volutpat odio facilisis mauris sit amet.
Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.
34 More Pages to Come in This Document. Get access to the complete answer.
Throw away your coursework related worries into the sea when MyAssignmenthelp.com is here. Our brand is backed by 3000+ PhD expert writers to provide online assignment help for coursework. Our writers have graduated from prestigious international universities and have been providing assignment help services since the past several years. Students from UK, US and Australia can avail our academic assignment help especially when it is related to coursework. Our talented writers provide professional help regarding any type of coursework like custom essay writing, dissertation writing and so on. You can clear all your coursework related queries though our 24×7 online chat facility anytime. We provide plagiarism-free coursework and all sorts of assignment help material to students.
More PHYS97066 PHYS97066 Plasmonics and Metamaterials: Questions & Answers
Management
This assessment is designed to test your achievement of selected learning objectives of Modules 2 to 5. In particular, the assignment involves flood frequency analyses and working with historical streamflow and rainfall data. The assignment is intended to reinforce and extend your knowle …
View Answer
Business Management
a) Produce a detailed analysis of the policies to achieve stated corporate objectives of one or more companies, and an examination of the problem of resource acquisition and deployment relevant to those policies.b) Provide a relevant literature review on the probl …
View Answer
Statistics and Business Research
Using the mean field approximation of the 2 D Ising model on a square lattice we found that the avarage spin s satisfied an equation s-=tanh (B(4es + h))Find the temperature dependence of the average spin s when T 0 …
View Answer
Management
Go through the assignment brief thoroughly and also the lecture notes on the students portal to see the requirements . Kindly follow the assignment brief as specified. Also there will be need for Appendixes of some marketing strategies which the expert will be discussing in the main body of the assi …
View Answer
Content Removal Request
If you are the original writer of this content and no longer wish to have your work published on Myassignmenthelp.com then please raise the
content removal request.
Choose Our Best Expert to Help You
Still in Two Minds? The Proof is in Numbers!
33845 Genuine Reviews With a Rating of 4.9/5.
English
Essay: 1.6 Pages, Deadline:
11 hours
I like how they help me. They are easy honest and always on time. I recommend them.
User ID: 8***35 United States
Civil Law
Home Work: 12 Pages, Deadline:
15 days
Thank you so much! It was a well-written and organized paper. Great job Thank you so much! Great job,Well written, but hoped for better grade, but i w …
User ID: 3***07 Cork, Ireland
Accounting
Assignment: 1400 Pages, Deadline:
8 days
It was very accurate. The research was done very well and I got nice marks . They really helped me with my work as I was struggling
User ID: 5***57 Sydney, Australia
Business Law
Assignment: 8 Pages, Deadline:
9 days
it was great assignment according to what was important, without mistakes, great
User ID: 8***11 Lincoln, Great Britain
Business Law
Assignment: 6.4 Pages, Deadline:
10 days
The assignment done by professional way and I got more than 85 marks for this subject. Thanks for the whole Nerddz team.
User ID: 2***65 Deepdene, Australia
Psychology
Assignment: 6.8 Pages, Deadline:
10 days
Great work done by the Team Nerddz. I got marks more than 85 for the subject. Thank you…
User ID: 2***65 Deepdene, Australia
Management
Assignment: 6 Pages, Deadline:
4 days
It was nice work and written in a good way. It helped me to increase my final grades for the same course and instructor praised me. Got good grades ov …
User ID: 5***29 Calgary, Canada
Economics
Assignment: 3.5 Pages, Deadline:
2 days
It was nice work and written in a good way. It helped me to increase my final grades for the same course and instructor praised me. 1 star less for im …
User ID: 5***29 Calgary, Canada
Management
Home Work: 3 Pages, Deadline:
1 day
This instructor was really very strict but still gave good marks. Abcdefghijklmno
User ID: 5***29 Calgary, Canada
Management
Thesis: 3 Pages, Deadline:
1 day
Amazing work on this! Got good marks excellent work by the writer. I did not expect so much marks
User ID: 5***29 Calgary, Canada
English
Essay: 1.6 Pages, Deadline:
11 hours
I like how they help me. They are easy honest and always on time. I recommend them.
User ID: 8***35 United States
Civil Law
Home Work: 12 Pages, Deadline:
15 days
Thank you so much! It was a well-written and organized paper. Great job Thank you so much! Great job,Well written, but hoped for better grade, but i w …
User ID: 3***07 Cork, Ireland
Accounting
Assignment: 1400 Pages, Deadline:
8 days
It was very accurate. The research was done very well and I got nice marks . They really helped me with my work as I was struggling
User ID: 5***57 Sydney, Australia
Business Law
Assignment: 8 Pages, Deadline:
9 days
it was great assignment according to what was important, without mistakes, great
User ID: 8***11 Lincoln, Great Britain
Business Law
Assignment: 6.4 Pages, Deadline:
10 days
The assignment done by professional way and I got more than 85 marks for this subject. Thanks for the whole Nerddz team.
User ID: 2***65 Deepdene, Australia
Psychology
Assignment: 6.8 Pages, Deadline:
10 days
Great work done by the Team Nerddz. I got marks more than 85 for the subject. Thank you…
User ID: 2***65 Deepdene, Australia
Management
Assignment: 6 Pages, Deadline:
4 days
It was nice work and written in a good way. It helped me to increase my final grades for the same course and instructor praised me. Got good grades ov …
User ID: 5***29 Calgary, Canada
Economics
Assignment: 3.5 Pages, Deadline:
2 days
It was nice work and written in a good way. It helped me to increase my final grades for the same course and instructor praised me. 1 star less for im …
User ID: 5***29 Calgary, Canada
Management
Home Work: 3 Pages, Deadline:
1 day
This instructor was really very strict but still gave good marks. Abcdefghijklmno
User ID: 5***29 Calgary, Canada
Management
Thesis: 3 Pages, Deadline:
1 day
Amazing work on this! Got good marks excellent work by the writer. I did not expect so much marks
User ID: 5***29 Calgary, Canada