If you should be considering applying for an internship, however you're unsure whether a program is most effective for you, have a look at our testimonials. Thinking about howto write If you are searching for an internship or need to learn more London offers with their own website. Internships and volunteer work outside the classroom reveals admissions officials that you're excited encourage that a workforce and to work hard and what you are thinking about.
Every grad is currently fighting with their CV. By composing it specific to the project, especially if you are a graduate you are able to generate your instruction your benefit! Most scholars acquire their CVs wrong. What many graduates don't know is that specialist experience's deficiency isn't a challenge at all if you are searching to an entry-level location. They frequently worry about locating work due to their deficiency of work experience. Don't be scared to really go around and contend together with individuals who have pro experiences if you a fresh graduate. At the centerfield of that which, becoming truly a fresh college graduate is regarded as Over the terms of a expert globe.
For that reason don't worry if your CV appears different no arrangement that is crucial, and there's. You need a CV format that is certainly OPTIMIZED for your own present recruitment program. You'll find assorted formats of CV.
It is important to get a unique resume portraying your job particulars In making positive effect on the recruiter. A employment cover letter example for people that are currently searching work . Keep in mind in the occasion that you understand that you could do the task, there is no rationale to never make an effort to employ. For example, you may well be asking for work in a dynamic, collaborative job atmosphere. Afterward, when you are asking to get a specific job, you are going to possess the opportunity to customise the CV to fit employer and your job. Another thing in regards to the job and the company info, if any, need to go cited.
Your own CV supplies a synopsis of that you are and exactly what you've got to offer an organization. Make certain that there is. Even the CV makes it possible for you to center about the skills you might have grown in a lot of elements of your own life.
Make certain the CV represents YOU! Make certain your CV conveys this. It's quite crucial to organize your CV prior to starting creating it. You also needs to mention that your CV and covering correspondence are all attached. Your CV is simple to scan through and readable'. CVs are intended to get an extremely special audience. Deciding the acceptable CV to highlight your abilities and experiences is very important.
Additionally, there certainly are a lot of different CVs utilised in the united kingdom today and whilst it's correct which you find it possible to have distinct formats of CV, you also has to think about the sort of career which you're searching for, your organisation's culture, your own experience and the manner in which you wish to sell yourself to the company. A CV can change from 2 pages. Your CV won't get you a job, however nevertheless, it may offer you a increased probability of having a meeting. A graduate CV should be pretty small. Assembling the right CV may possibly look like an overwhelming endeavor, but it is something which you are able to easily study. It is necessary to keep in your mind the the trick to generating excellent CVs instead of only excellent ones is to cause them to become as achievement-based as you can.
Make an extensive collection of these info which you'll need to include, as a way to compile your CV, and use it. Your CV can be an, and so do not dismiss its relevance. A fantastic CV can allow you to get lots of interviews and responses, whereas an insufficient CV will receive ignored. Moreover, in case you have not already written an instructional CV, now is the time in your career to achieve that.
Tailoring your CV is essential and hence the more effort which you put into it that the better. What you are hoping for is your CV is what they really want at the second. The CV is perfect for academic or healthcare professions and it is a whole lot more extensive. Your CV must shout you are the very best candidate for the organization. Producing your own initially CV immediately after graduating may be tricky, particularly if you should be browsing for the own first professional position. Thus, it's important that your application add a sturdy CV.
You want to modify your work character. The truth is, it had to be carried out. It is which you need not go all out when it comes to freelancing. Consistently attempt to recognize your crowd, regardless of what you're doing. If anything negative occurred to you , try and do something that certainly will make you get happy and is favorable. You must also have a look at their cover letter tutorial.
Bear in your mind the decision on how best to create your letter would be your own pick. Resignation letter is equally as crucial as the application form correspondence for virtually any project. Here are some ideas on the best way to compose a letter for resignation. Also it needs to supply information about your very last moment, although A resignation letter perhaps not just must inform an employer that you're leaving. Therefore it is imperative prior to making job that you simply compose an resignation letter.
Organize your reason for resignation if you are feeling likely to accomplish this, even though it is maybe not required. The reason behind the resignation is relocation for a other community. The resignation should be supplied carefully. Let us focus on exactly what the resignation was about.
When people are departing a small business or perhaps a position, usually they aren't certain how to compose a resignation letter. When it is you are browsing for is hopeless currently company, attempt to locate some thing acceptable for you in the job industry. Completely anticipate the enterprise In the event you make an effort to quit whenever there's tons of organization. You have to discover what afterward locate the software and guidance and you really need to achieve in your business. By just starting to have the bases set up, you're one-step ahead for if you are ready to establish your business. Also, just in case you left as you are going on your own to begin a fresh firm, be sure what's set up for you to present your whole attention into.
If you're an warn CEO or manager, you'll be in a position to see the signs of disengagement and accept therapeutic measures. Disengagement doesn't happen over night. In the event you are not positive concerning your yield date, then notice that you'll reevaluate your capability to work in that moment and it is sti should request a duration. If you should be contemplating quitting your work toohere certainly are some suggestions that may permit one to express goodbye together with style.
If you've been unhappy with work, a statement like I've settled to go after various decisions for particular causes" is adequate. So it's possible you will need to transform tasks to acquire a raise, but in addition, it's possible that you can locate a reasonably major increase by playing your cards right and staying put. Propose a training session for a direct employee who might be in a position to carry control the job you do. Some people are incredibly painful and sensitive to this job. You can find more than a couple reasons why an employee may leave work. It truly is by no means simple todo exactly what they do, and also stopping your job for a means to stop leading to evil is. There are capabilities and values which you must develop so the endeavors you would like Even though a great deal of the things that you perform within your organization endeavor will likely be helpful as you transition to a freelance work.
State the position you are thinking about, and also you would love to meet it. You might decide to read these strategies, In the event you understand that you are in place of experiencing to compose a letter to resign by your instruction occupation. Before it's way far too late When you armed to spot the signs and're alert, you're able to quit the slip. Are all supplied below.
The Typical is popularly Known as the Warrior Monk for a motive. You see, in any off ice we all usually speak about brand. Typically in order that it's wise to become prepared your Manager is going to be caught offguard. No matter how good of the manager you're employees will leave. An employee make an effort to get the most useful you can from your own job, As you are still . If you're in a position to be receptive with your employer on your job search, sit back together with your superiors and enable them to be aware which you're searching for work everywhere. Or when it is truly hopeless due to the workplace that is present, go.
Because it's only going to restrict your choices In the event you are not specific regarding the task which you're targeting, then do not use objects. The job in the banking business is of accountability that is wonderful as the individual needs to deal with economic transactions and translate the reports. Illustrate that you know the task you've applied to get and warrant why you ought to find that job. Hence, it's important to talk about the job expertise in detail.
If you're trying to be given a job lately, you're informed the existing labour market is competitive. As you would like to make cash, maybe not to invest it 20, after all, you're looking for employment! Added it shows you're interested and educated in a particular job rather than only casting a broad net and seeing what you may land.
Similar to one other resumes, it's imperative to list the occupation certain particulars from the restart. If you are interested in locating a great occupation It is. In the event you want to execute a really exceptional endeavor, when you have completed your outline, then you should go back and analyze the first article a single second that is last. Usually do not increase the length of resume by including irrelevant information, but include things that you experience can support you in work. New projects will help ex felons to become a part of the modern society.
Where you'll find quite a few posts and suggestions In the event you prefer to find more information regarding creating resumes that get interviews, then go to a blog such as Top job Resumes. Resumes are made to emphasize the best side of someone. The thing about simplifying your initial resume would be that when you've done it, then you never should start off out from scratch and will update it needed across the course of your livelihood. Unfortunately resumes contain ineffective or overused words which usually do not add value. All the expert resumes share characteristics. The restart, after all, isn't an autobiography, however, a summary of qualifications and one's experience. Every thing on your resume should be to comprehend and simple to read.
People looking for work ought to be aware when they will need to obtain an updated restart plus it needs to be employer-ready. Wherever possible for the results, they will need to locate advantages. Job seekers must move throughout the meeting phase.
Do not be vague or your company might be unable to to detect what you are after. The other difficulty is that employers assume that you want to find a position that is challenging and rewarding. To start with, companies assume which you're currently browsing for a posture which is both challenging and rewarding. As a result of sheer volume of software, recruiters and companies just don't have enough opportunity to carefully examine the very first time approximately of each of resume.
Something to bear in your mind when producing a specific railroad jobs resume is it is crucial that you find more out for. Over a clean sheet of paper write every accomplishment or credential you are going to have the ability to believe of that applies towards the sort of location you are browsing for. You ascertain the location that you are searching for.
The resume aim must be. Creating a intriguing and distinguishing resume aim is not likely to become a job. The Career Objective is intended to provide the potential employer a rationale to keep in reading your resume.
You will see that they employ clear paragraphs which get if you have a close look at of our complimentary resume writing examples. This illustration can reveal the way the dates that you have spent can be managed by you. It's vital to provide an example that illustrates the way in which the candidate is actually a team player, compared to generating the blanket remark. It is possible to refer that the resume objective examples to find out how to present your career targets and draw employers.
Career purpose element in restart will probably incorporate the truth of your future accomplishments that you would like to accomplish working in the position within the company. Where your statement should be placed, the 2nd paragraph of one's resume cover letter is. Offers a succinct introduction to this intent supporting the restart and also the form of work which you want to get.
With the help of the template it's possible to come up with a resume that is flawless. You are able to select at the appropriate template and then design your own resume. The template can be selected by you for the position you would love to apply.
With just a couple of clicks you decide exactly the period of time and may check out what is accessible you desire to enter customizing just one or more just go in what is already there. After you pick it's enough time for implementing biometric authentication, then you must do so in a way that's not very likely to create unhappiness among your own employees. You need to take the opportunity to develop some easy web design capabilities, buy ready-made templates, or apply a person to designing a website for you personally. You have to decide, realistically you will have to accomplish your goals. You are able to conserve money and time whilst enhancing. For instance, in case you have got employment, you may need to perform overtime. There's nothing for a job for life anymore.
At the mean time is have the term Out! So to be successful you will need, as some additional business, an suitable small business program in an identical way. You definitely will be in a position to own to conduct a institution or company .
It is possible to make the home a source of additional income once that you don't own it. If you have your house you can put it to use as a way to generate more money. Save to get the own mortgage deposit or pension, for a very long run, dependent on where you are in daily living. Marketing your self is your secret to your own success. Furthermore, you'll be able to acquire assistance from sample ethnographies for assistance and guidance. You pay when you submit your purchase, therefore take the time you must receive it precisely all the direction you want it. If it seems to be good, we'll submit an all cash deal.
You will not need to write the important points repeatedly. Free Templates to Make Holiday Cards lists lots of diverse sources that offer great latitude in the variety and theme of card you might need to send. Business Cards Business cards support to put to a enterprise in an expert appeal. They can be quite costly. You will provide card and key to the do or to every one.
For the lack of updated information the site receives a B. It's rather challenging to remember to copy and paste the info across and upgrade points on either my sales funnel and also my client database spreadsheet, also that I may wind up having a small clear out one time a month to guarantee everything on the website's true, nonetheless it's actually a handy matter to get! In the event that you can provide us with all of the current information and any vision and logos you would like to set inside your style. You are able to easily view. Pages on free MP3 internet sites and completely free domain names usually don't supply you with a professional picture. For instance, in the event that you like listening, then make an effort to come across the text in audio book format, or record yourself reading passages that are vital so that you are able to engage in with them to yourself whenever you need to reassess the content.
Basically, you merely select the design you want and you then are told what to accomplish with it. Free of fee timecard templates it is likely to print and download. You can locate ready-made templates on the net or programs for your mobile phone. The template is also remarkably straightforward. Free of any time you're looking for it, as an extra incentive to companies, you can use the moment card template.
Other folks believe such tools to become tricky to use. No actions are split into parts. The procedure offers you a few important tips for you to sell your house in order to anyone you are pick. But the control process that is expert is, it is crucial that you create organizational coverages to help managers or payroll and employees personnel in processing and completing time-sheets in an beneficial and accurate way. Possessing an excellent system to track exactly how you are spending time, also provide you with a small nudge when you would like it, is still quite favorable. The pc might well not be eliminated on. The procedure should be enrolled from by every person .
Worker Attendance sheet is beneficial in keeping a watch out and also boost the organization's functioning. If merely 1 cell selected it believes you'd like to restore that the worksheet that is throughout. In case you own Microsoft Excel you will download a template which will help you track your spending above month or a week. A spreadsheet is in fact simply a calculator, but with more flexibility. It can boost your accuracy. By contrast, that you never need to make a time keeping and payroll system which consists of components. With many customization and saving alternatives to select from, it definitely can turn to a Revenue employee's new preferred software.
Excel will allow it to be an breeze. It is but one of the most popular softwares in the digital environment of today. Spreadsheets generally are tremendously versatile means of storing info. Timesheets, Simply allow you to track project cost, and which means you know exactly in which your real money funds is moving! Possessing a member of staff time-sheet will enable one to observe exactly just how a number of individual hours each project necessitates. You have to send a statement to the customer.
2 templates may be sufficient when your organization is large, if you think it. The templates at our department can help relieve quite a few of those stress which comes with a buy. Once you are attempting to reduce or keep your present weight, they can be valuable reduction. Out-of-the-box templates allow you to start immediately away with whichever strategy is appropriate for the team best. It is likely to personalize the templates so they can fit your customer's demands. Men and women are able to get and utilize it for their businesses. On occasion you may run into the best templates to the most sites.
Bill templates won't will need to become tedious. If you've got Template Docs allows you to contribute your quite happy with an choice to market your merchandise or services. You receive it into several minutes and may search for an invoice template online.
Dashboards grew to become common. For example, your app can offer coupons to purchase a product in your site, forcing persons there to get longer information. If you are in possession of a program that is free, assume about exactly how many users that you expect you'll get. Or, if you have many apps you'll look at a program bundle. Much like freemium programs, paymium programs need participation to continue being up-to-date appropriate and engaging as a means to entice users to reunite and also make more purchases.
We analyzed both the negative and beneficial facets of every tool to ensure it is simpler that you identify which application to test. This tool lets you find every issue in one opinion, regardless of which job it belongs to. In general, it is sometimes a very simple and strong pest monitoring tool together with the appropriate setup.
By employing pre-built templates with surgeries that are common people can contact undertaking their job rather than wanting to figure out. In truth, it might be utterly one of the section of the project application treatment. Instead, it is an easy procedure for setting authentication and fast installation. It will also benefit only see a activity at one time, In case you're single-tasking. From the dash board it will be possible to write exactly what special task you are most very likely decide on the task, to use and begin the timer. It is tough to keep focused if you are switching between several exceptional types of activities for any range of projects. You will place tasks, projects, your customers and hourly rates in a simple to use interface.
Utilizing a tactical tool like Beeye allows you control pursuits like administrative tasks and therefore to continue to keep tabs at some time spent on each form of activity. You will find various kinds of applications that may significantly help you with timing and labour management. Maintaining all of your associates to the identical page will make sure that you are releasing applications with confidence. The power handling application may let you differentiate phases of childbirth in which you are likely to be in a place to assign tools that are currently habituated to endeavors. Trello's workforce cooperation tools ensure your teams continue to be in sync at just about every stage of your project.
Construction jobs could be high priced and more rather complicated, depending on temperament and the dimensions of this plus so they're always catchy to calculate. Planning future projects will become easier, and without needing to disrupt ongoing projects, you are definitely going to own head aches. Particularly whenever you own your own billable work to contend with. The graphical time reporting and overviews of unbilled perform will prevent you in controlling your own company. With time-sheets could be challenging getting the companies started. It is critical to review functions and also prices to better decide on the one that is perfect for you personally along with your own organization.
Your business is dependent on its technology. Any business should be in a posture. In the event you contribute the form of firm which cares about results as opposed templates that are easy-to-read are certain to get the job.
The templates would undoubtedly be more convenient. Business proposal templates are perfect so you can get started out read onto track down the best kinds for your proposition. You'll find about 1-5 templates out there to client projects, that may help to make your company proposal organized and straightforward to learn.
It is likely to download templates for suggestions from our principal website at no cost in order save your time and to simplify the procedure. Templates could possibly be altered at any moment. There are a lot of varieties of project suggestion templates and job proposal formats from that firm people can take assistance that is critical. The ideal way to accomplish so would be always to use an job proposal template.
You'll find many sorts of templates out there to be hint creating that is effective in addition to efficient. You may possibly find which you find yourself preserving templates from a couple of the a variety of internet sites previously-mentioned . Now that you can find tons of templates created, it's manageable and very simple to produce a job suggestion. Make sure that you uncover the best template. There really are still an range of sample templates readily available, which means you're most likely to find the one that will utilize your field or market. The reason for employing sample proposal template will be to get a thought in regards to the perfect way to start the habit of making a fantastic deal that offers a certain shot endorsement by the possibility to you. The 36-page expert proposal template includes a clean structure that is nominal.
Click Download" to pick the template that you want touse. The templates arrive with customization tools. A proposition template is really just a template utilized anyplace in the site as long as you have acquired an accessibility. Even the 20-page suggestion template contains an invoice, meaning that your branding stays consistent across their undertaking's life span. Clean Web design template has a slick design which is sure to help you distinguish oneself in the competition.
Once you have uploaded a record, it's going to appear from the list of one's document folder. On the Envato Market web site, you can find tons of documents needed for inventive endeavors. The absolute documents and templates may be seen below.
In case the proposal is to get utilization, then you can consist of repayment terms for customers to check. A project proposal has a format that is certain. Project proposals frequently have a format that you want to follow. Making use of Sinnaps job planning tool every thing demanded is included by your suggestions. You have to know just how to properly create an endeavor suggestion if you're tasked to develop a new job proposal which you are able to present to pertinent parties who are involved on your job. If you also wish to write project suggestions that are effective, it is wise to get into job suggestion templates out of our website that is chief.
Bear in mind, the list is that the very first part of the suggestion, and it may be the part they see. Now before it's likely to start composing a proposal a sales persons has to get the precise info. You could fancy on all of worries you to possess made a decision. Professional suggestions ought to be more computer-generated on business letterhead, even though service industry forms can be pre-printed. An everyday proposal is the very first step within a project. ContractsEven it requires a contract. An contractor proposal to develop a bridge should begin with an announcement of need.
The proposition comprises the programs for the organization and provides an outstanding outline to get an small business application. Project suggestion may be an essential business document for one that ought to be accomplished. A project proposal contains elements.
The suggestion is targeted at partners or possible investors in the small business. A business proposal is utilized to provide assistance or your own product to buyer or a customer. On the reverse side, you might pose the organization proposal unsolicited. Make and an unsolicited small business proposition meant to make a business option follows the exact same arrangement nevertheless anticipates questions that the client might have.
All suggestions experience deliberation before it skilled for understanding. What's more not quite all proposals adhere to a template that is very related. Project suggestions contain key information regarding your own endeavor. Funding challenge Proposals should contain in depth advice regarding the job where the fundraising event has to be arranged.


text:
Q: streaming of two cameras to two outputs
*

*How can I send two separate camera streams with one command? (The image from two cameras is sent to the same address but with different ports)

ffmpeg -stimeout 5000000 -rtsp_transport tcp -i
"rtsp://admin:password@192.168.0.14:554/Streaming/Channels/101/"
-c:v copy -c:a aac -f mpegts udp://176.xxx.xxx.126:91?pkt_size=1316

ffmpeg -stimeout 5000000 -rtsp_transport tcp -i
"rtsp://admin:password@192.168.0.15:554/Streaming/Channels/101/"
-c:v copy -c:a aac -f mpegts udp://176.xxx.xxx.126:92?pkt_size=1316

If I connect it this way, I receive the same image from the first camera on the two output channels.

ffmpeg -stimeout 5000000 -rtsp_transport tcp -i
"rtsp://admin:password@192.168.0.14:554/Streaming/Channels/101/"
-c:v copy -c:a aac -f mpegts udp://176.xxx.xxx.126:91?pkt_size=1316 -i
"rtsp://admin:password@192.168.0.15:554/Streaming/Channels/101/"
-c:v copy -c:a aac -f mpegts udp://176.xxx.xxx.126:92?pkt_size=1316

*How can I overlay the logo on the camera image while forwarding it in the same camera streaming?

*How can I upload a music file in the same camera streaming and loop it?

A: Since you actually asked 3 questions, let's go through it one after the other.

*

*If you want two separate outputs containing different streams, you need to explicitly map them. Your command starts just like your example, but after setting the input, you map everything that's supposed to go into your first output (stream or file doesn't matter) and set the target (file or stream), then map the streams for your 2nd output and set the target.

*To overlay a logo, you set your logo image as source and then add it to the video with the overlay filter. This is really easy with just one video stream, but since you have two video streams, and I guess you want the logo in both, you need a complex filter. See FFmpeg Documentation for overlay filter for more details.

*

*The use of complex filters alters the way you need to map your streams. Basically you map the input streams not to your files, but to your filters instead. Then you map your filters' output to your files. In the command below I'll use labelled pads for that, see ffmpeg filters documentation for details.

*Also using any kind of video filter conflicts with streamcopying (the option -c:v copy from your question). You need to set an encoder for this type of streaming. In the following example I'll use libx264 as this is widely compatible with most devices and shouldn't be too much in terms of hardware requirements. In terms of efficiency and bandwidth of course libx265 would be better, but will be too much to encode in real time on many devices. Even better would be a hardware encoder, but to answer this, you need to know on what device exactly the code will be run. Impossible to tell that with a generic command.

*You can set an audio file as 3rd source and loop it infinitely with -stream_loop -1 -i your_audio_file_here
All together you command will look like this, placing the logo in the top left corner:
ffmpeg -stimeout 5000000 -rtsp_transport tcp /
    -i "rtsp://admin:password@192.168.0.14:554/Streaming/Channels/101/" /
    -stimeout 5000000 -rtsp_transport tcp /
    -i "rtsp://admin:password@192.168.0.15:554/Streaming/Channels/101/" /
    -i your_logo_image_here -stream_loop -1 -i your_audio_file_here /
    -filter_complex "[0:v:0][2]overlay[video1]; [1:v:0][2]overlay[video2]" /
    -map "[video1]" -map 3 -c:v libx264 -preset faster -c:a aac -f mpegts udp://176.xxx.xxx.126:91?pkt_size=1316 /
    -map "[video2]" -map 3 -c:v libx264 -preset faster -c:a aac -f mpegts udp://176.xxx.xxx.126:92?pkt_size=1316

redpajama_set_name: RedPajamaStackExchange


Ms. Maria Dyulgerova works as a legal assistant at the law firm "Ruskov and Colleagues" in Sofia.
Mrs. Maria Dyulgerova works as a Legal assistant at the law firm "Ruskov and Colleagues" in Sofia.
From July 2018- Legal assistant at the Law firm "Ruskov and Colleagues" in Sofia.


text:
Regional Report Western August 2012
Regional Report Western August 20122012-08-152012-08-15https://businessnc.com/wp-content/uploads/2021/09/businessnc_2021_logo_orange.jpgBusiness North Carolinahttps://businessnc.com/wp-content/uploads/2021/09/businessnc_2021_logo_orange.jpg200px200px
Back to August 2012 home page
REGIONALREPORT Western
A smaller share makes goods
The Western North Carolina Vitality Index, released in June, reports on the natural, social, built and economic environments in 26 counties. It found, among other things, that while the portion of the goods-production workforce in the state and region is higher than in the nation, those leads have shrunk during the past 20 years. The study came to this conclusion by using an economic measure called a location quotient, which in North Carolina is 1.15 — meaning its portion of employment in goods-producing industries is 1.15 times higher than the nation's. In the 23 counties that make up Business North Carolina's Western region, the location quotient decreased from 1990 to 2010 in every county except Graham and McDowell.
WEST JEFFERSON — The Office of the Comptroller of the Currency designated LifeStore Bank in "troubled condition" and gave it several rules as part of a consent order, including that it submit a "profit plan" to the regulator and not issue a dividend without written approval. The bank says it is well-capitalized and has made progress on nonperforming assets and loan-loss reserves.
FRANKLIN — Mission Health named James Bross president and CEO of Angel Medical Center. He was senior director of client services at Temple, Texas-based Applied Revenue Analytics, where he specialized in improving hospitals using financial analytics. Before that he was chief operating officer at Rutherford Hospital in Rutherfordton.
ASHEVILLE — State lawmakers passed legislation establishing Asheville Regional Airport as an independent authority no longer controlled by the city. The airport's board will have more influence from Henderson County, with two of seven members required to be from there.
airport, Angel Medical Cener, Asheville, Asheville Regional Airport, board members, CEO, economy, Franklin, General Assembly, James Bross, LifeStore Bank, Mission Health, troubled bank, troubled condition, West Jefferson, Western North Carolina
Lawmakers hear economic growth projections for NC in 2022
Round table: Western North Carolina, rising higher
NC Trend: Health care and takeovers
Raytheon plans 800-employee plant near Asheville

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Sina Weibo feeds in Wordpress? I did days of research and tried nearly every available wp plugin. But it seems to me like in English there's no way to find a solution.
I need a way to show the latest Sina Weibo feeds on my Wordpress website. If there's any way to get the weibo feeds as RSS, that will help me a lot already!
A reason is that many plugins are outdated since Sina changed the oauth to oauth2.0 and I can't read and write Chinese a lot, but speak.
Thanks a lot

A: Might be too late, but if you still need a solution, you can try http://sinacn.weibodangan.com/
Among other things it provides you with the option of pulling an RSS from any Weibo account. Search for your Weibo username, and then you will see towards the top of the page the link "RSS订阅TA的消息". Copy that URL and you will have the RSS feed.
Hope this helps!

A: I have found an alternative Weibo to RSS solution which is http://github.com/diygod/Weibo2RSS
It is an open source project written by nodejs. You can use the service the author provided or you can deploy one for your self.

A: This tool below is very cool:
https://rssfeed.today/weibo/


text:
require 'spec_helper'
require 'fileutils'

RSpec.describe DataSourcePipeline do
  describe '#process' do
    let(:zip_file_name) { 'loopholes.zip' }
    let(:file_name) { 'test' }
    let(:source_name) { 'loopholes' }
    let(:file_content) { File.read("spec/fixtures/#{zip_file_name}") }
    let(:passphrase) { '' }
    let(:tmpdir) { Dir.mktmpdir }

    before do
      stub_request(:get, /#{Terminal::DOMAIN}.*/).
        to_return(status: 200, body: file_content)
    end

    subject do
      described_class.new(
        source_name: source_name,
        passphrase: passphrase,
        destination_dir: tmpdir
      )
    end

    after do
      FileUtils.rm_r(tmpdir)
    end

    it 'loads data' do
      records_set = subject.process
      expect(records_set).to_not be_empty
    end
  end
end

redpajama_set_name: RedPajamaGithub


text:
Celebrity News, Photos, Styles and Videos
Facebook Twitter Google_plus RSS
DCMA/Privacy Policy
Sarcheshmeh
Persian TOP Models
Persian TV
Persian Music
Kim Kardashian posed beside an airplane on board the USS San Diego in Dubai
Kimberly "Kim" Kardashian West (کیم کارداشیان) (Kimberly Noel Kardashian) is an American television and social media personality, socialite, fashion designer, businesswoman, model, and actress. Born and raised in Los Angeles, California, Kardashian first came to prominence after a 2003 sex tape with her then-boyfriend Ray J that was leaked in 2007. In the same year, she and her family were commissioned to star in the reality television series Keeping Up with the Kardashians. Its success has led to the creation of spin-offs including Kourtney and Kim Take New York and Kourtney and Kim Take Miami. In 2010, Kardashian was named the highest-paid reality television personality, with estimated earnings of $6 million.
Born: October 21, 1980, Los Angeles, California, United States
Siblings: Khloé Kardashian, Kourtney Kardashian, Rob Kardashian, Brody Jenner, Brandon Jenner, Kendall Jenner, Kylie Jenner,
Spouse: Kanye West (m. 2014), Kris Humphries (m. 2011–2013), Damon Thomas (m. 2000–2004)
Parents: Robert Kardashian, Kris Jenner
Children: North West
Darn you, Kim Kardashian.
We really can't crack any jokes at your expense for this article.
That's because the reality star recently paid a visit to Abu Dhabi, stopping by the USS San Diego navy ship at one point to meet armed service members and show her support.
"Of course I need a selfie!" Kardashian captioned the picture above, as three sailors stood around and undoubtedly imagined Kim Kardashian nude in their minds.
Another image depicted Kim giving one of the men a kiss, along with the message:
"Kisses to the troops! Thank you for all you do! Was an honor to meet you all."
Kardashian was in Abu Dhabi last month prior to returning home for Thanksgiving.
She was joined their by many friends, including French Montana... sort of.
The rapper snapped a couple pictures with Kardashian, but then didn't see much of her at all. This led some to question his motives for visiting Dubai and to warn Khloe Kardashian that Montana may be cheating on her.
We have no comment on that possible scandal, but we must make a comment regarding Kim and her visiting of the troops, as much as it pains us:
Job well done, Kim Kardashian.
Publishd on Wednesday, December 03, 2014
Labels: Kim Kardashian Photos
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September 9, 2011 ipad, iPhone, Mobile, News No comments
SNK Releases Free Additional Content for Hit iPhone Game: King of Fighters-i
iPhone/iPad Game News: SNK Releases Free Additional Content for Hit iPhone Game: King of Fighters-i. More details after the jump.
SNK PLAYMORE Announces Special One Week Sale and Free Additional Content for "THE KING OF FIGHTERS-i" iPhone / iPod Touch Application Starting September 9th, 2011
SNK PLAYMORE CORPORATION also announces the worldwide release of free additional content for "THE KING OF FIGHTERS-i" on iPhone / iPod touch from September 9th, 2011. 6 new characters join the battle!.
"THE KING OF FIGHTERS-i" is the newest installment in THE KING OF FIGHTERS 2D versus fighting series on iPhone / iPod touch, which has been enjoying great success worldwide from July 7th, 2011. "THE KING OF FIGHTERS-i" faithfully recreates the gorgeous graphics of SNK PLAYMORE's world-famous KOF 2D versus fighting series, while its touch screen "tapping-based" controls allow players to easily perform various special moves and combos, so that even novice players will enjoy this new KOF play-feeling.
Via this free additional content, "Iori Yagami", "Mature", "Vice", "ElisabethBranctorche", "ShenWoo", and "DuoLon" join the original cast of 14 characters in "THE KING OF FIGHTERS-i"for a total of 20 fighters available! These 6 new entries will increase the number of possible teams, allowing you to create a lineup that suits your fighting style / strategy.In addition to these new characters, a "Challenge Mode" in which your brain will be required, and more trading cards and illustrations for"Gallery Mode" have also been added!
In addition, in order to celebrate this upgrade, "THE KING OF FIGHTERS-i" will be available at the incredibly low price of $4.99, for a limited one week period between September 9th and September 16th, 2011! Don't miss it!
Title: THE KING OF FIGHTERS-i
Release Date: Available Now
(*The additional content is scheduled to be released from September 9th, 2011)
Compatible Systems: iPhone 3GS (iOS4.1 and later), iPhone 4, iPod touch (3rd generation and later)
Qualifying Age: 12+
Price:$7.99⇒ $4.99 (limited time sales between September 9th and September 16th, 2011)
(*The additional content is free to download for those who have previously purchased this application)
"THE KING OF FIGHTERS-i" Official (English) Web Site:
http://iphone.snkplaymoreusa.com/kof-i/
"THE KING OF FIGHTERS-i" Official Facebook Fan Page:
KING OF FIGHTERS-i Facebook Page
SNK PLAYMORE Official Game Web Site: (Japanese only): http://game.snkplaymore.co.jp/
SNK PLAYMORE USA Official Web Site:http://www.snkplaymoreusa.com/
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One third to die by plague or famine; one third will fall by the sword; one third to be scattered to every wind
by Mike Adams, the Health Ranger
Tags: Biblical plague, famine, infectious disease
(NaturalNews) Many believe that Biblical signs of famine and pestilence have begun to appear in our world, and that's why the title of this article quotes Ezekiel 5:12.
In what is now admitted by all the top infectious disease experts to be a "post-antibiotics era" where Big Pharma's drugs are useless, we are now facing unprecedented outbreaks of Ebola, Chikungunya and even the Plague.
Diseases are spreading out of control in many regions while at the same time the Centers for Disease Control (CDC) is recklessly exposing its own scientists to Anthrax and other deadly agents. (1)
Here's a frightening update on some of the most dangerous infectious diseases that are now spreading out of control:
Ebola outbreak out of control; 600 dead and counting
From The Extinction Protocol blog (2):
Ebola has spread through several West African countries, including Sierra Leone, Liberia and Guinea, since its latest outbreak in February. The death toll from the virus has surpassed 600 despite efforts by regional and international health experts to contain the epidemic. There is currently no known cure for Ebola, a form of hemorrhagic fever whose symptoms are diarrhea, vomiting and bleeding.
Deadly airborne plague strikes four in Denver, Colorado
From Bloomberg.com (3):
A rare airborne form of the plague that can spread through coughing and sneezing has infected a Colorado man, and state health officials are searching for other possible cases.
Following that story, Bloomberg went on to report that the airborne disease had already begun to spread to other victims: (4)
Three more plague cases were found in Colorado, a week after the first infection of the deadliest form of the disease was reported in the state in a decade. The man initially reported with pneumonic plague on July 11 is hospitalized. Two of the new cases also had pneumonic plague, while the third had a milder form.
Chikungunya explodes across 35 U.S. states
From the New York Daily News: (13)
There is no vaccine and no treatment. The Centers for Disease Control has listed a total of 497 cases in the U.S. in 35 states, Puerto Rico and the Virgin Islands, 197 locally transmitted. "The arrival of chikungunya virus, first in the tropical Americas and now in the United States, underscores the risks posed by this and other exotic pathogens," Roger Nasci, a mosquito expert at the Centers for Disease Control and Prevention, said in a statement.
Drug-resistant infections explode 500% across U.S. hospitals
From Natural News: (5)
Drug-resistant superbug infections have reached near-epidemic levels across U.S. hospitals, with an alarming 500% increase now documented in a study just published in the August issue of Infection Control and Hospital Epidemiology (the journal of the Society for Healthcare Epidemiology of America).
Lead author of the study, Dr. Joshua Thaden, warned "This dangerous bacteria is finding its way into healthcare facilities nationwide... A CRE epidemic is fast approaching... Even this marked increase likely underestimates the true scope of the problem given variations in hospital surveillance practices."
MERS mutates into airborne pathogen
From TheWeek.com: (6)
Middle East Respiratory Syndrome (MERS) may be airborne... "These data show evidence for the presence of the airborne MERS in the same barn that was owned by the patient and sheltered the infected camels," the study authors said in a statement.
Sierra Leone's chief Ebola doctor contracts Ebola
As yet more evidence that medical staff are some of the first people who tend to become infected with deadly diseases, a top Ebola doctor has himself contracted Ebola.
From Reuters: (7)
The head doctor fighting the deadly tropical virus Ebola in Sierra Leone has himself caught the disease, the government said.
The 39-year-old Sheik Umar Khan, hailed as a "national hero" by the health ministry, was leading the fight to control an outbreak that has killed 206 people in the West African country. Ebola kills up to 90 percent of those infected and there is no cure or vaccine.
Chinese government quarantines entire city after outbreak of bubonic plague
To the shock of international observers, an entire city in China has been quarantined by the government following an outbreak of the plague.
From Fox News: (8)
A city in China has reportedly been sealed off after one resident died from bubonic plague... Plague is an infectious disease caused by the bacteria Yersinia pestis that is carried by rodents, and can be transmitted to people through flea bites or by direct contact with the tissues or fluids of an animal with plague, according to the Centers for Disease Control and Prevention. The disease is known for killing millions of people in Europe in the 1300s, in a pandemic called the Black Death.
Insect plague reaches Biblical proportions in Wisconsin
As reported in TheWeek.com: (9)
This year's mayfly hatch in the Mississippi River reached Biblical proportions. Wisconsin residents captured some stunning -- read: horrifying -- images of the mayfly emergence, which happened on Sunday night. Check out the swarm below.
One third to die by the sword
Beyond the plague and pestilence now emerging, we are also witnessing what may be the start of World War IIi with recent events in Ukraine.
The U.S. and Russia are in a tense standoff over trying to assign blame for the downing of MH17, a passenger jet with hundreds of innocent civilians on board. The U.S. government says Russia did it, but when the State Department was pressed on what evidence they might have to prove it, they could only point to tweets and Youtube videos as their "intelligence sources." Wow.
As explained on LewRockwell.com: (10)
Tuesday the US government admitted it had been bluffing about its certainty that Russia was behind the downing of Malaysian Air Flight MH-17 over Ukraine. This dramatic turn of events started with State Department Spokeswoman Marie Harf claiming Monday that the State Department's certainty of Russian involvement in the apparent downing of the plane was primarily based on "social media" evidence.
Many observers believe these events may be the spark that leads to war. Already, 1 in 10 Americans now believes America should launch an all-out war on Russia due to current events.
As reported by CNN: (11)
...one in 10 say the United States should take military action if there is clear evidence that Russia is responsible for the shooting down of the plane, which killed all 298 passengers and crew.
Infowars' Steve Watson added this all-important analysis comment: "The number may at first seem low, but it translates to one in every ten Americans believing that a war with a nuclear super power is a good idea." (12)
One third scattered to every wind
Wrapping up the Biblical quote, "one third scattered to the wind" could very easily describe the aftermath of a grid-down scenario in which masses of homeless refugees flee U.S. cities in an effort to survive.
We already know that the vast majority of Americans now depend almost entirely on the government for their survival: housing, health insurance, food stamps, unemployment checks, disability benefits, retirement checks, social security checks, Medicare coverage, housing subsidies and more. Yet, at the same time, the U.S. government is beyond bankrupt. It's trillions of dollars in debt and the enormity of that debt is multiplying at an alarming rate.
It doesn't take a mathematical genius to figure out that the U.S. government's financial default is only a matter of time, and when it happens, all the business sectors kept afloat by government payments and entitlements will crumble: Big Pharma and the health care system, Big Food manufacturers, large agricultural producers, weapons manufacturers, universities, public services (including law enforcement) and more.
When that happens, the cities will rapidly become uninhabitable due to crime waves that spread faster than Ebola. No honest citizen will be safe in an urban area, and residents will attempt to flee into lower-density population areas, scattering them all "to every wind."
Humanity is one event away from a global wipeout
What can you do against all this? Keep your head on straight and prepare for uncertain times. A wave of disease and pestilence has already begun, and the "health authorities" openly admit all their vaccines, antibiotics and pharmaceutical drugs are worthless against these new pandemics. Humanity right now stands just one event away from a global wipeout from infectious disease.
All it takes is a simple laboratory mistake, the release of an intentional bioweapon, or a random mutation of a virus that becomes a global killer. Humanity is largely defenseless against pandemics and infectious disease, yet we keep packing people into high-density urban areas as if we were all magically immune.
We aren't. And the pandemic wave may have only just begun.
(1) http://www.theguardian.com/world/2014/jul/23...
(2) http://theextinctionprotocol.wordpress.com/2...
(3) http://www.bloomberg.com/news/2014-07-13/dea...
(4) http://www.bloomberg.com/news/2014-07-18/fou...
(5) https://www.naturalnews.com/046041_cre_superb...
(6) http://theweek.com/speedreads/index/265151/s...
(7) http://www.reuters.com/article/2014/07/23/uk...
(8) www.foxnews.com/health/2014/07/23/chinese-of...
(10) http://www.lewrockwell.com/2014/07/daniel-mc...
(11) http://politicalticker.blogs.cnn.com/2014/07...
(12) http://www.infowars.com/insane-1-in-10-ameri...
(13) http://www.nydailynews.com/life-style/health...
More news on Biblical plague
These emergency foods have helped millions survive famine
Catastrophic famine could cause society to collapse within four decades, scientists say
The coming oil collapse will lead to global famine followed by food revolution and renewal
Government officials plan emergency meeting to address persistent drought, potential famine conditions
Computer models: Even a small nuclear war would cause global famine and wipe out billions of people
Global famine could destroy society if Ebola outbreak isn't stopped, United Nations warns
History proves that Western governments have already used food as a weapon of genocide
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Dear Donald Trump: Blockade the lying mainstream media and recognize the independent media as America's real free press
Kellogg's found to have financial ties to the money man for cop-killing left-wing HATE groups: George Soros


text:
The Pulse: Behind The Scenes at Traverse City Film Festival With Kendall and Katie
Brighid Driscoll,
The sound of phones ringing and computer keys clicking is the running background noise at the Traverse City Film Festival Office. I went to the eclectic office on the second floor of the Arcade building to interview Kendall Kotcher and Katie Zwick for a Rocky Horror Picture Show story, but upon arriving to the office and seeing the duo working so hard I realized that they are a story of their own.
Kendall, Katie and I sat in the middle of the TCFF office and we aren't even a minute into the interview before Kendall has to pause to answer a co-worker's question.
"There's a person who wants to volunteer at The Franklin where we're hosting the producers and directors and stuff. Are we doing that this year?" the young man asked Kendall.
Kendall fields questions like this all day long in her role as TCFF's office manager. Kendall is from Clarkston and Katie is from Mount Pleasant, but the two spend their summers here in Traverse City to be a part of the driving force behind the film festival.
"I was brought on in May, Katie in June," Kendall said.
Katie Zwick is a returning intern working in film traffic for her second year. She enjoys the work experience she gets and the collaborative community that working for TCFF brings. She keeps track of and organizes all of the films that come through the office
"It's about knowing how to do your job, but it's also about knowing how to do a little bit of everything and to jump in and help people out when needed."
At any given moment between the months of May and July there is a lot going on in the office, and Kendall's job is to make sure it's all running smoothly. Her day is filled with answering questions from co-workers, answering emails and overseeing interns, among a host of other projects.
"Lots of emails, lots of phone calls" Kendall said. "In terms of intern projects, they're filming promos, they're creating social media posts, they're editing, taking pictures. It's a lot of project management type things."
The TCFF office is incredibly youthful which correlates to many of the staff being hired from the TCFF internship program. Credits are available for students who get hired on as an intern. Kendall was a former intern in the communications and media department.
"I interned and then they were looking for an office manager so I applied for that. They see how you work."
Katie, currently a college student at Central Michigan University, interned at TCFF for the first time last summer when managing director of the festival Susan Fisher came to the university to recruit interns. Katie was asked back this year.
"It's definitely not a normal internship. Before working here when I heard the word 'internship', and with working in media and film, I just assumed it would be getting coffee and doing grunt work, but I'm actually managing projects. I have a lot of responsibility and freedom."
Both Katie and Kendall have formed a friendship through their time working the film festival together. The pair have bonded through a love of film and theatre, macaroni and cheese and cats.
"Last year if both of us were having a case of the Mondays we would send each other cat pictures," Kendall said.
"I feel like that's when our relationship started," Katie responded with a laugh.
It's not just Kendall and Katie who have bonded, the entire TCFF team all seem to have bond with each other and having an open, collaborative workspace helps. The space is filled with light streaming through a row of windows, movie posters and not many walls at all. Team members ask questions to each other without having to get up and weave through a maze of gray cubicles.
"It used to be Hocus Pocus costume shop," Kendall said. "It's also a dance studio. It's a very creative and fun space."
It's easy to see the passion that both women have for not only their working roles at the film festival, but also for the film festival itself. Katie enjoys that TCFF is thoughtful with their film selections and that their selections give a voice and power to marginalized groups and area relevant to current culture and society. Kendall's favorite thing about TCFF?
"It sounds cliché, but the films. This year's theme is Cinema Saves The Word. All the films that I've seen at film festivals have inspired me in some way, changed me in some way."
Kendall and Katie are the kind of creative, down to earth, cool girls that I always wanted to be friends with. The talent and work ethic of these two ladies and the rest of the TCFF team is something to admire, and something to remember when we're all out enjoying this year's film festival.
Categories: GTPulse
Glen Lake Couple To Open Part Salon, Part Home Decor Store in Suttons Bay
GTPulse: Sunshine and Punchlines - Traverse City Woman Dazzles In Comedy
GTPulse: New Traverse City Nonprofit Will Spotlight Diverse Artists


Annie Vincent Interiors: Happy Easter!
I have been busy lately! Remember the mass amounts of people I hosted for Thanksgiving? Well they are coming again!! But it's okay, I love to have my family in my home it just causes me to be a little busier.
I hope you all enjoy this wonderful time of year.
Make sure to come back on Monday for some tips on healthy eating!


text:
\section{Introduction}

Metamaterials, which are typically regular arrays of
sub-wavelength resonant particles, offer us a new degree of
freedom in controlling the electromagnetic response of matter.
Thus we are no longer completely constrained by the properties of
existing materials, but can tailor the response in an almost
arbitrary fashion, for example achieving very high \cite{Silveirinha2008c}, very low
\cite{Ziolkowski2004}, and negative\cite{Pendry1999} values of refractive index,
permittivity and/or permeability.
Because of the inherently strong dispersion of
resonant metamaterials, they must be modified in order to operate in a
different frequency band. Therefore,
there is a significant push to have a further degree of control
over these materials --- tunability of their response.

Fortunately, the engineered nature of metamaterials allows their
properties to be controlled externally, either by dynamically
modifying their structure, or by adding some nonlinear inclusion
and controlling with external fields~\cite{Gorkunov2004prb}.
Examples of the latter approach include the introduction of
varactor diodes~\cite{Shadrivov2006a}, ferroelectrics~\cite{Hand2008} and photo-conductive
semi-conductors~\cite{Degiron2007}. On the other hand,
even without resorting to such exotic (and often lossy)
constituents, there is a great deal of freedom to manipulate the
structure itself, and this is the approach we take here. We
consider specifically the split ring resonator (SRR) as one of the
most important metamaterial elements, noting that whilst the
fine details of near-field interaction are structurally specific,
our approach can be applied to a wide variety of structures.

An analytical model for the magnetic response of a sub-wavelength array
of identically oriented wire loops loaded with
a capacitance~\cite{Gorkunov2002} takes
into account the mutual interaction of all the elements in the
lattice, which is essential for deriving the effective
permeability correctly. Although that analysis is limited to the
quasi-static case accounting only for magnetic near-field
interactions, it is crucial for revealing the consequence of
lattice changes. These tend to be overlooked by
otherwise rigorous approaches which include spatial dispersion but
develop Lorentz local field approaches,
based on nearest-neighbor interaction~\cite{Baena2008}
or point-dipole approximation~\cite{Simovski2008mm}.

In particular, it was pointed out in
Ref.~\onlinecite{Gorkunov2002} that the resonant frequency of the
metamaterial permeability can be altered by varying the lattice
constants without changing the structural units. This scheme is
illustrated in Fig.~\ref{fig:lattice-tuning-schemes}(a), and has
been verified by experiments in Ref.~\onlinecite{Shadrivov2007a}.
However, a practical consequence of this change in lattice
constant is that the sample size also changes correspondingly.
More recently, an alternative approach was suggested in
Ref.~\onlinecite{Lapine2009}: introducing a shift between layers
in order to create a monoclinic lattice, with the shift increasing
linearly between layers, as shown in
Fig.~\ref{fig:lattice-tuning-schemes}(b). This configuration keeps
the density of elements within the metamaterial constant, and can
tune the coupling between neighboring particles to modify the
response of the complete metamaterial. However, for finite size
samples, this shift inevitably results in a significant change in
sample shape. Thus, for practical purposes, we have proposed a
super-lattice type of geometry, whereby only every second layer is
shifted by the same amount, as shown in
Fig.~\ref{fig:lattice-tuning-schemes}(c). This tuning scheme
proved to be robust, and allows significant manipulation of the
resonant frequency with only a small change in the sample
geometry~\cite{Lapine2009}. Therefore, the sample geometry and its
effective properties can be engineered {\em almost independently} to
achieve the desired manipulation of electromagnetic waves.

\begin{figure}
\includegraphics[width=0.8\columnwidth]{lattice-tuning-schemes.pdf}\caption{(Color online)
Several approaches to modify the lattice for metamaterial tunability:
(a) a change of the lattice constant~\cite{Shadrivov2007a}, (b)
a continuous shift of the layers~\cite{Lapine2009}; and
(c) a super-lattice of alternating shifts of layers~\cite{Lapine2009}.
\label{fig:lattice-tuning-schemes}}
\end{figure}

However, as we demonstrate below, this structural tuning of
metamaterials depends very strongly on the nature of the near-field interactions.
Since metamaterial elements such as split ring
resonators are usually not highly symmetric, \emph{the relative
orientation of particles within the lattice is of key importance}.
This effect is not described by existing circuit theory models,
and can give rise to some surprising experimental results, which
we present here.

In order to understand the coupling mechanisms and how they are
affected by the lattice shift, it is useful to start with the
simplest geometry --- a pair of split ring resonators. Several authors have
conducted numerical and experimental investigations of coupling
between metamaterial elements for different types of elements and
relative orientation between them,
in microwave~\cite{Garcia-Garcia2005,Gay-Balmaz2002}
and optical frequency ranges.(see the overview in Ref.~\onlinecite{Liu2009b} and references therein,
as well as Refs.~\onlinecite{Li2009a,Kante2010,Zhou2009a,Decker2009,Singh2009a,Liu2008}.)
A detailed study has previously been undertaken on tailoring the geometric arrangement
of a pair of coupled one-dimensional SRR arrays to engineer the dispersion
curves of magneto-inductive waves \cite{Sydoruk2006}.

As we have shown recently~\cite{Lapine2009}, a rough qualitative
understanding of the structural tuning can be achieved by using
circuit theory with purely inductive coupling between SRRs.
However, this approximation fails to provide a quantitative
understanding of the metamaterial tuning in question and, most
importantly, does not explain the observed strong influence of the
relative SRR orientation.
Therefore, below we develop {\em a new model} based on the calculation of
the fundamental mode of a single resonator. The knowledge of
the current and charge distributions within the mode allows
calculating the coupling constants of a pair of split rings. These
constants are then used to explain the experimentally observed
tuning response of our metamaterial samples.

In \prettyref{sec:theory}, we develop our approach to calculate the metamaterial coupling,
including a discussion of the limitations of other purely analytical methods.
In \prettyref{sec:pair}, we apply our approach to the study of
interaction between a pair of split ring resonators which are shifted
laterally relative to each other, and explain quantitatively how the shift affects
the position of the fundamental resonance. In \prettyref{sec:slab}, we
apply these results to a bulk metamaterial and identify the
mechanisms at work in the experimental tuning of a metamaterial
slab in a waveguide. Finally, \prettyref{sec:concl} concludes the
paper with further discussions and outlook.

\section{Near-field interaction in metamaterials\label{sec:theory}}

Considering a single SRR, it is known\cite{Garcia-Garcia2005}
that it possesses a discrete set of
eigenmodes (standing waves) with corresponding eigenfrequencies.
In an arbitrarily excited SRR, the currents and charges can be
represented as a superposition of the eigenmodes. The fundamental mode with
the lowest frequency is relevant for the
magnetic resonance in SRRs. On the frequency scale this mode is well
isolated from the higher-order modes, and we can restrict
ourselves to the single-mode approximation neglecting the
excitation of higher modes.

The time dependent charge density $\rho$ and current density
$\mathbf{J}$ in a resonant element with excited fundamental mode
can be written in the most general form of a standing wave:
\begin{equation}\label{eq:Qwave}
\rho(\mathbf{x},t)=Q(t)q(\mathbf{x}),
\end{equation}
\begin{equation}\label{eq:Iwave}
\mathbf{J}(\mathbf{x},t)=I(t)\mathbf{j}(\mathbf{x}),
\end{equation}
where $q$ and $\bf J$ describe the charge and current distribution
in space. In SRRs, the variation of the current distribution across the
width of the conductive track could be neglected, however
for generality our approach takes into account the complete
3-dimensional surface-current distribution.

To satisfy the conservation of charge
\begin{equation}
\nabla \cdot \mathbf{J}=-\frac{\partial \rho(\mathbf{x},t)}{\partial t}
\end{equation}
we imply that
\begin{equation}\label{eq:QI}
I(t)=\dot{Q}(t),
\end{equation}
\begin{equation}\label{eq:qj}
\nabla \cdot \mathbf{j}(\mathbf{x})=-q(\mathbf{x}).
\end{equation}
Thus if the the current is known, it is easy to find the charge
distribution and vice-versa. The mode profile obtained numerically
for our SRR geometry is shown in Fig.~\ref{fig:current_charge}.
The current $\mathbf{j}$ is symmetric and reaches its maximum at
the point opposite to the gap. In accordance with
Eq.~\eqref{eq:qj}, the charge distribution $q(\mathbf{x})$ is
antisymmetric and goes through zero where $\mathbf{j}(\mathbf{x})$
is maximal. We see that $q(\mathbf{x})$ reaches its maximum magnitude near the gap.

\begin{figure}[t]
\includegraphics[width=\columnwidth]{current_charge.pdf}
\caption{Numerically calculated (a) current and (b) charge distribution across an SRR at resonance\label{fig:current_charge}}
\end{figure}

In the single mode approximation, the dynamics of the SRR can be
fully described by the time-dependent amplitude $Q(t)$, and we may
write the SRR Lagrangian as a sum of terms quadratic in $Q$ and
$\dot{Q}$:
\begin{equation}
\mathcal{L}=A\dot{Q}^2-BQ^2,
\end{equation}
where $A$ and $B$ are constants which will be discussed below.
Accordingly, the SRR energy reads:
\begin{equation}
E=\dot{Q}\frac{\partial \mathcal{L}}{\partial\dot{Q}}-\mathcal{L}= AI^2+BQ^2,
\end{equation}
and is nicely separated into inductive (magnetic) and capacitive
(electric) parts. Clearly, for a passive SRR we require $A \geqslant 0$,
$B \geqslant 0$.

The Lagrangian equation of motion
\begin{equation}
\frac{\mathrm d}{\mathrm d t} \frac{\partial \mathcal{L}}{\partial\dot{Q}} =
\frac{\partial \mathcal{L}}{\partial Q}
\end{equation}
yields that the dynamics of a single SRR is described by the
oscillator equation for the charge amplitude:
\begin{equation}
\ddot{Q}(t)+\omega_0^2Q(t)=0,
\end{equation}
and the fundamental mode resonance occurs at the frequency
$\omega_0=\sqrt{B/A}$.

Note that in contrast to the known modifications of the Lagrangian
formalism for metamaterials (see e.g.\ Ref.~\onlinecite{Liu2006c}), here
we do not rely on an equivalent circuit model. Although one might
identify the parameters $2A$ and $1/2B$ as effective inductance
and capacitance respectively, below we evaluate them explicitly
from the known fundamental mode shape. In fact, the strongly
inhomogeneous mode profile (see Fig.~\ref{fig:current_charge})
suggests that it is unlikely that the correct values of the
parameters would agree with those calculated from a circuit
analysis. Additionally, to find the resonant frequency, we do not
need to calculate $A$ and $B$ explicitly, only their ratio.

For the purposes of our analysis, it is sufficient to consider the
case of a pair of SRRs, and it will subsequently be shown that
this explains all of the important features observed in our
experiments with a bulk metamaterial. In this case, the Lagrangian
can be written as a sum of the single SRR Lagrangians and coupling
terms, which we also write as quadratic in currents and charges:
\begin{equation}\label{eq:L12}
\mathcal{L}=A(\dot{Q}_1^2+\dot{Q}_2^2+2\alpha
\dot{Q}_1\dot{Q}_2)-B(Q_1^2+Q_2^2+2\beta Q_1Q_2).
\end{equation}
The parameters $\alpha$ and $\beta$ are the dimensionless
constants of magnetic and electric near-field interaction
respectively.

The corresponding Lagrangian equations of motion yield the system
of ODEs for the time-dependent amplitudes $Q_{1,2}$:
\begin{eqnarray}\label{eq:Q1Q2}
\ddot{Q}_1+\omega_0^2 Q_1=-\alpha \ddot{Q}_2-\beta \omega_0^2 Q_2,\\
\ddot{Q}_2+\omega_0^2 Q_2=-\alpha \ddot{Q}_1-\beta \omega_0^2 Q_1,
\end{eqnarray}
Solving these equations one finds that a pair of resonators
exhibits two resonances: symmetric and antisymmetric. For the
symmetric resonance, $Q_1=Q_2$, which yields the resonant
frequency
\begin{equation}\label{eq:omega_s}
\omega_{S}=\omega_0\sqrt{\frac{1+\beta}{1+\alpha}},
\end{equation}
while the antisymmetric mode with $Q_1=-Q_2$ has the frequency
\begin{equation}\label{eq:omega_as}
\omega_{AS}=\omega_0\sqrt{\frac{1-\beta}{1-\alpha}}.
\end{equation}

The described resonance splitting is well known in the theory of
harmonic oscillators. Generally, bringing together two oscillators
of the same resonant frequency introduces coupling between them,
which results in splitting into two modes. Examples have been
shown of SRR resonant frequency as a function of some coupling
parameter, e.g.\ mutual orientation\cite{Hesmer2007} or twist
angle\cite{Liu2009}, and typically demonstrate a splitting or
hybridization of modes.

As we see, the direction and strength of the resonance shift are
determined by the coupling constants $\alpha$ and $\beta$. To
evaluate them, we use the expression for the
electromagnetic energy following from the Lagrangian \eqref{eq:L12}:
\begin{equation}\label{eq:E}
E=A(I_1^2+I_2^2+2\alpha I_1I_2)+B(Q_1^2+Q_2^2+2\beta Q_1Q_2).
\end{equation}
The first group of terms gives the magnetic energy and the second
group describes the electric energy.

A possible route to calculate $\alpha$ and $\beta$
is to approximate the electric and magnetic response of each ring
by a few terms of the multipole expansion.
The problem with this approach is that it is based on the
assumption that the observer (i.e.\ the second SRR) is at a large
distance compared to the dimensions of the source.  This
requirement is strongly violated in our metamaterial samples,
where the separation between rings is actually much smaller than
the outer ring diameter. This is essential for achieving strong
tuning by lattice manipulation.

Therefore we have chosen to calculate $\alpha$ and $\beta$
numerically from the known charge and current distributions,
$q(\mathbf{x})$ and $\mathbf{j}(\mathbf{x})$, of the fundamental
mode in a single SRR. Indeed, in the single mode approximation,
the energy of a pair of SRRs reads
\begin{multline}\label{eq:EW}
E = Q_1^2W_{E,11} + Q_2^2W_{E,22}+ 2Q_1Q_2W_{E,12} +\\
I_1^2W_{H,11} + I_2^2W_{H,22} + 2I_1I_2W_{H,12},
\end{multline}
where the parameters:
\begin{equation} \label{eq:WE}
W_{E,mn} = \int_{V_m}\!\!\!\mathrm{d}^3x\int_{V_n}\!\!\!\mathrm{d}^3x'\frac{q(\mathbf{x})q(\mathbf{
x'})}{4\pi\epsilon_0|\mathbf{x} - \mathbf{x'}|},
\end{equation}
\begin{equation} \label{eq:WH}
W_{H,mn} = \int_{V_m}\!\!\!\mathrm{d}^3x\int_{V_n}\!\!\!\mathrm{d}^3x'\frac{\mu_0\ \mathbf{j}(\mathbf{
x})\cdot \mathbf{j}(\mathbf{x}')}{4\pi|\mathbf{x} - \mathbf{x}'|}.
\end{equation}
The integrals can be easily evaluated once the charge and current
distributions are known. The integrations over $\mathbf{x}$ and
$\mathbf{x}'$ are over the same ring if $m=n$ or over different
rings otherwise. Accordingly, $V_1$ is a volume containing only
the first ring, and $V_2$ is a volume containing only the second.
The singular terms at $x=x'$ are handled using the analytical formulas
given in Ref.~\onlinecite{Arcioni1997}.

Comparing Eqs. \eqref{eq:E} and \eqref{eq:EW} shows that the coupling
parameters can be evaluated as
\begin{equation} \label{eq:coefficients_energy}
\alpha = \frac{W_{H,12}}{W_{H,11}}, \ \ \beta =
\frac{W_{E,12}}{W_{E,11}}.
\end{equation}

For comparison purposes, when inductive coupling is the dominant interaction mechanism
between the SRRs in a metamaterial, we are able to consider an array
of split rings as an array of current loops with some mutual
inductance between them. This approach can then be used to define the effective
permeability of a metamaterial sample\cite{Gorkunov2002}.
In particular, for thin wire loops with their axes oriented in the same
direction, the mutual inductance can be found\cite{Landau} by numerical integration:
\begin{multline*}
 L_{nn'}(\mathbf{r})=\frac{\mu_{0}r_{0}^{2}}{4\pi} \intop_{0}^{2\pi} \intop_{0}^{2\pi} \mathrm{d} \varphi_{1} \mathrm{d} \varphi_{2}
 \cos(\varphi_{1}\text{\textminus}\varphi_{2}) \times \\
 \left[\rho^{2}\text{+}z^{2}\text{+}2r_{0}^{2}(1\text{\textminus} \cos(\varphi_{1}\text{\textminus}\varphi_{2})) + 2\rho r_{0}(\cos\varphi_{2}\text{\textminus\ensuremath{\cos\varphi_{1}}})\right]^{-\frac{1}{2}},
\end{multline*}
where the distance vector $\mathbf{r}$ between the ring centers has
been decomposed into a radial component $\rho$ and axial component
$z$, $r_{0}$ is the ring radius and $\varphi_{1}$ and
$\varphi_{2}$ represent the angle about each ring.
We can use the calculated mutual inductance
to define an equivalent magnetic interaction parameter
\begin{equation} \label{eq:inductance}
\alpha_L = L_{nn'}/L
\end{equation}
(where $L$ denotes the self-inductance of one element)
which should approximate the interaction energy calculated from \eqref{eq:coefficients_energy}.
Asymptotically this interaction decays as $1/r$, so in a large
array the nearest neighbors provide the strongest contribution, but
do not necessarily dominate over all others. Clearly, this
interaction is highly anisotropic\cite{Sydoruk2006}, being positive
for rings on the same axis, but negative for rings in the same plane.

It is also possible to develop equivalent circuit models to calculate
the electric interaction between rings. For a pair of
coaxial rings, the total interaction can be reliably modeled as
a circular parallel conductor transmission line, as for
broadside-coupled split ring resonators \cite{Marques2003} or,
alternatively, with an extended circuit model accounting for the
distributed capacitance and inductance \cite{Shamonin2005}.
However, once we introduce some offset between the rings, these approaches
are not applicable and so we do not consider them here.

\section{Tuning interaction between a pair of split ring resonators\label{sec:pair}}

Having developed an approach for calculating near-field interaction
between a pair of rings, we now apply it to a canonical system
which has the basic properties of our experimental arrangement.
We consider a pair of SRRs, either identically (gap-to-gap) oriented or
rotated by 180\textdegree{} with respect to each other (as in the
broadside-coupled SRR), and subject to a lateral offset $\delta a$.
The geometry and incident polarization are shown in
Fig.~\ref{fig:2rings-geometry}. The rings have average radius $r_0 = 2.25$mm,
track width of 0.5mm, metal thickness of 0.03mm, gap width of 1mm,
and are separated in the transverse direction by 1.5mm. The resulting resonant frequency is 10.6GHz

\begin{figure}[tb]
\includegraphics[width=1\columnwidth]{2rings-geometry.pdf}
\caption{Geometry of the pair of rings (a) broadside-coupled
and (b) gap-to-gap orientation\label{fig:2rings-geometry}}
\end{figure}

\begin{figure}
\includegraphics[width=\columnwidth]{interaction-energy.pdf}
\caption{(Color online) Magnetic ($\alpha$) and electric ($\beta$) coupling parameters for broadside coupled ($bc$)
and gap-to-gap ($gtg$) orientation of a pair of shifted SRRs. The magnetic interaction calculated from
the mutual inductance is given as $\alpha_L$.
\label{fig:interaction_energy}}
\end{figure}

We plot the interaction energy calculated from Eq.~\eqref{eq:coefficients_energy} in Fig.~\ref{fig:interaction_energy},
for different offsets between the rings.
It can be seen that the electric coupling parameter $\beta$ is nearly
symmetric between the two configurations. This can be understood from Fig. \ref{fig:current_charge},
where we see that the charge distribution has a strong dipole component oriented
in the $x$ direction. For the symmetric mode of the broadside-coupled orientation the charges accumulated on the
closest sides of the SRRs have opposite signs, the total charge distribution has the nature of
a pair of anti-parallel dipoles, thus $W_{E,12}<0$, and $\beta$ is also negative.
In contrast, in the gap-to-gap orientation, the closest charges are of the same sign,
the total charge distribution becomes like a pair of parallel dipoles and the
parameter $\beta>0$.

At an offset of about one ring radius ($\delta a \approx r_0$), the charge on one ring is
approximately equidistant from both positive and negative charges
on the opposite ring, thus the net coupling
passes through zero. At larger offsets, the electric coupling
changes its sign but remains smaller, since only the nearest halves of the SRRs
are effectively interacting, with this interaction decaying towards zero as the offset increases.

The magnetic interaction energy is also quite different for
the two orientations, with the magnetic interaction $\alpha_L$ calculated
by Eq. \eqref{eq:inductance} lying between the gap-to-gap and broadside curves. For the broadside-coupled case, the
situation is qualitatively similar to the analytical result $\alpha_L$.
At low offset, the magnetic field of one ring cuts through
the other ring in the same direction to the surface normal, thus
reinforcing the magnetic field and increasing the total energy. As
the offset is increased, the situation gradually shifts to become like a pair of
loops in the same plane, where the field from one ring cuts
through the other in the opposite direction with respect to the
surface normal. Hence, $\alpha_{bc}$ undergoes a change in sign.
However, in comparison to the ring with uniform current, the coupling
is substantially more negative. This is due to the current maxima
being on opposite sides of the rings, and hence further away from each other.

For the gap-to-gap orientation the magnetic interaction is much
stronger for low $\delta a$.  This is due to the current maxima
being located near each other which produces a
stronger contribution to the integral in $W_{H,12}$ thus
increasing $\alpha$. As the rings are further separated from each
other, the interaction energy reduces, but \emph{does not undergo
a change of sign}. We can intuitively understand this by
neglecting the small contributions of the current in the region
near the gaps, thus we effectively have two linear current
elements in the same plane which always interact with the same
sign. However, this balance is not universal and is determined by
the specific geometry and parameters. To check this, we studied a
geometry with a very small gap, so that the current distribution
was much more homogeneous, with lower resonance frequency. In this
simulation (not shown) the magnetic coupling did change sign and
both values of $\alpha$ converged closely to $\alpha_L$.

\begin{figure}[tb]
\includegraphics[width=1\columnwidth]{2rings-tuning.pdf}
\caption{(Color online) Numerical results.  Transmission
spectrum for a pair of (a) broadside-coupled and (b) gap-to-gap oriented rings.
Solid line: $\omega_{S}$ from Eq.~\eqref{eq:omega_s}, broken line: $\omega_{AS}$ from Eq.~\eqref{eq:omega_as}
\label{fig:freq-2rings}}
\end{figure}

In order to verify that the calculated coupling correctly
describes the frequency splitting of this system, we compare the
frequency shift predicted by Eq.~\eqref{eq:omega_s} and
\eqref{eq:omega_as} with that obtained from the full numeric
simulations.
For consistency with our
interaction energy approach we assume a homogeneous free-space background.
We use the frequency domain solver of the
commercial software package CST Microwave Studio\cite{CST} to
model a pair of rings, in a unit cell with periodic boundary
conditions in the directions transverse to the propagation
direction. This periodic system enables us to define a transmission coefficient,
and the boundaries are 10mm from the rings. This value is chosen
to be large enough so that there is no significant interaction
with periodic neighbors, yet small enough to avoid significant scattering
into higher order diffraction modes. Thus we can consider this the limiting
case of a highly dilute metamaterial slab.

The transmission spectrum as a function of offset is plotted in
Fig.~\ref{fig:freq-2rings}. We see that all the important features
of the mode splitting are represented correctly by our single-mode
theory of coupled SRRs. Expansion of Eqs.~\eqref{eq:omega_s} and
\eqref{eq:omega_as} for small coupling predicts frequency splitting of
$\Delta \omega = \pm(\beta-\alpha)/2$, hence the curves are approximately
symmetric about $\omega_0$.

The strong splitting observed for the broadside-coupled orientation
is due to the opposite signs of the electric and magnetic coupling.
At $\delta a/r_0 \approx 1.1$ both $\alpha_{bc}$ and $\beta_{bc}$ change signs,
hence the crossing of the symmetric and anti-symmetric modes is observed.
In contrast, we see that for the gap-to-gap orientation, for small offset
$\alpha_{gtg}$ and $\beta_{gtg}$ are of the same sign, and thus they have an
opposing effect, resulting in small frequency splitting. Since
$\beta$ decreases much faster and changes sign, the result in maximum
frequency splitting for $\delta a/r_0$ between 1.1 and 1.5.
We note that in
Ref.~\onlinecite{Lapine2009} the resonant frequency based on
$\alpha_L$ was compared with experimental results for the gap-to-gap
orientation, and strong disagreement was found.

It can be seen that the calculated transmission through the cell
exhibits different depths of the resonance for the symmetric
and antisymmetric modes. This is due to the different efficiency of
coupling between the modes and the incident plane wave. For
instance, it is impossible to excite the anti-symmetric mode
with a normally-incident plane wave for $\delta a = 0$, since both rings
are excited in-phase. As the offset is increased, some retardation between
the rings occurs, and excitation of the anti-symmetric mode is allowed.

There are several reasons for the small quantitative disagreement
between the exact  calculations and those based on the calculated
interaction energy. Firstly, the minimum of
transmission occurs at a frequency slightly different from the
resonant frequency, due to coupling effects (impedance matching) between the incident
wave and the ring. Secondly,
there may be some small contribution of higher SRR eigenmodes due
to perturbation of the charge and current distributions. Thirdly, there may still be
some small influence of the periodic boundaries. Finally, our developed relations neglect retardation,
which is strictly valid in the sub-wavelength limit, whereas the
the outer radius of the rings is $0.18\lambda$ at $\omega_0$.
Retardation has previously been shown to modify the interaction
between SRRs through its influence on the dispersion of magneto-inductive
waves in arrays\cite{Radkovskaya2006,Zhuromskyy2009,Decker2009b}.

We emphasize that our approach developed in \prettyref{sec:theory}
is advantageous over the direct numerical calculation. Firstly, once
the mode profile is known, calculation of the frequencies in Fig. \ref{fig:freq-2rings}
takes approximately 30 seconds on a single CPU, whereas the direct
calculation of the full spectrum takes several hours on a multi-core
machine. Secondly, we are clearly able to demonstrate the nature of
the coupling, which yields insight into the tuning behavior.

\section{Tuning interaction in a bulk metamaterial \label{sec:slab}}

\begin{figure}[tb]
\includegraphics[width=1\columnwidth]{experimental.pdf}
\caption{(Color online) Experimental transmission while tuning $\delta a$ for split ring
resonator slab in waveguide, for (a) broadside-coupled and (b) gap-to-gap
orientation of adjacent layers.
\label{fig:experimental-tuning}}
\end{figure}

\begin{figure}[tb]
\includegraphics[width=1\columnwidth]{experimental-reflection.pdf}
\caption{(Color online) Experimental reflection while tuning $\delta a$ for split ring
resonator slab in waveguide, for (a) broadside-coupled and (b) gap-to-gap
orientation of adjacent layers.
\label{fig:experimental-reflection}}
\end{figure}

We now apply our approach to explain experimental results for tuning the response of a slab
of metamaterial. The metamaterial is fabricated using photolithography
to etch copper tracks onto FR4 printed circuit board, using the same
geometry as in our numerical simulation of a pair of rings. The fabricated
sample has 30 layers, each with 5 rings in the propagation direction
and is only one ring in height (i.e.\ a $5\times30\times1$ array).
The longitudinal period of the sample is 7mm, the transverse period is
dictated by the sample thickness (1.5mm) as there is no spacing between boards.
As with the pair of rings, we have assembled slabs with two relative orientations
of the split rings in adjacent planes --- gap-to-gap and broadside-coupled.
The sample is placed in the center of a WR229 rectangular metallic waveguide, with
dimensions 58.17$\times$29.08mm, excited at its dominant TE$_{10}$ mode.
We removed the influence of the coaxial adapters and feeding waveguide sections
by performing a TRL (through-reflect-line) calibration \cite{Engen1979}.
In Fig.~\ref{fig:experimental-tuning}
we show the experimentally obtained transmission through each slab of
closely coupled SRRs, with the corresponding reflection shown in
Fig.~\ref{fig:experimental-reflection}.
\begin{figure}[tb]
\includegraphics[width=1\columnwidth]{super-lattice.pdf}
\caption{Schematic of the effective super-lattice geometry corresponding to
the waveguide measurement for (a) broadside-coupled and (b) gap-to-gap
orientation. Dashed lines show planes of reflection
symmetry, and the shaded region shows the super-cell with
4 SRRs.\label{fig:superlattice-geometry}}
\end{figure}

The shift of resonant frequency shows good qualitative
agreement with the results for a pair of rings presented in \prettyref{sec:pair},
with very similar changes in the spectrum observed (noting that $\delta a /a = 0.5$
corresponds to $\delta a/r_0 = 1.56$).
However, for the gap-to-gap orientation, numerical simulation of a system of two boards
with 5 rings each, and \emph{periodic boundaries} in both transverse
directions (not shown), is qualitatively similar to the experimentally
observed results but quantitatively highly inaccurate.
The reason turns out to be the loss of symmetry when the system is
placed inside the waveguide, because
the upper and lower waveguide walls do not correspond to
periodic boundaries, but instead represent planes of mirror reflection.
Therefore, this system must be described as having a super-lattice arrangement in the vertical
as well as horizontal planes, with each super-cell consisting of four SRRs.
This cell has alternating orientation of the SRRs in the vertical direction
corresponding to the planes of mirror symmetry,
as shown in Fig.~\ref{fig:superlattice-geometry}(b).
Once this unit cell is taken into account, numerical simulations are in a good agreement with
the experiment (Fig.~\ref{fig:freq-waveguide}(b)).

Naturally, numerical simulations for the broadside-coupled orientation also
agree well with the experiment (Fig.~\ref{fig:freq-waveguide}(a)).
In this case a very similar result is provided with simple
periodic boundary conditions (not shown). For this orientation the super-lattice effectively formed by
the waveguide shown in Fig.~\ref{fig:superlattice-geometry}(a)
does not have an essentially different symmetry to the original super-lattice.

\begin{figure}[tb]
\includegraphics[width=1\columnwidth]{waveguide-tuning.pdf}\caption{(Color online)
Numerically obtained transmission spectrum of metamaterial in waveguide,
(a) broadside-coupled and (b) gap-to-gap orientation. The white line indicates experimentally obtained resonant frequencies.
\label{fig:freq-waveguide}}
\end{figure}

We can conclude that in
both cases the dominant mode of the slab corresponds to the dominant
symmetric mode of a pair of rings, with a similar pattern
of resonant frequency \emph{vs.}\ offset occurring.
The weaker coupling to the modes for the gap-to-gap orientation is due
to the shape of the symmetric mode. Its magnetic field has a large component
parallel to that of the waveguide mode, however its electric field
is primarily longitudinal, in contrast to the transverse electric field
of the waveguide mode.

In Fig.~\ref{fig:freq-waveguide}(b), we see two higher order modes,
which most likely correspond to the higher order resonances observed in
the experimental results in Fig.~\ref{fig:experimental-tuning}(b). From
the numerical simulations we observe that the current distributions of
these modes are symmetric, thus they correspond to higher-order modes of
the metamaterial slab, and not to the anti-symmetric mode of a pair of rings.
In contrast, in Fig.~\ref{fig:freq-waveguide}(a) there is a weakly coupled
anti-symmetric mode, which we verified by inspection of the currents.
This mode also qualitatively agrees with the corresponding mode of the
pair of rings, with somewhat weaker coupling due to the increased mismatch
to the incident waveguide mode.
This mode may correspond to some of the smaller features observable in
Fig.~\ref{fig:experimental-tuning}(a), however due to the size of these
features this cannot be reliably determined.

We do not consider offsets greater
than $0.5a$, since in an infinite lattice only shifts between 0 and 0.5
are unique, while in a finite structure, larger shifts result
in very irregular boundaries. Note that in the simulations we have neglected
the effect of the mode profile of the rectangular waveguide, which
would correspond to an effective variation of the angle of incidence
of the plane wave as a function of frequency, which can result in
a different response due to the anisotropy and non-negligible
spatial dispersion of the medium\cite{Simovski2008mm}.

Clearly the coupling in the complete lattice is much more complicated than
in the simple two-ring system, as the interactions between a large number of rings
must be taken into account.  In principle it is possible to extend the analysis of
 \prettyref{sec:pair} to an arbitrary number of rings.  However the
qualitative agreement between the experimental results and the modelled pair of rings
suggests that the phenomenology developed for the two rings is
generally applicable and leads to correct predictions.

Clearly, the coupling in the metamaterial lattice is much more complicated
than in the simple two-ring system, as the interactions between a large
number of rings must be taken into account. The qualitative agreement
between the experimental results and the modelled pair of rings suggests
that the phenomenology developed in \prettyref{sec:pair} for the two rings can be
extended to an arbitrary number of rings.

Although an accurate generalization of our modelling approach to a bulk system lies beyond the scope of this paper, it is clear that the resulting homogenized effective metamaterial  parameters will
exhibit similar tuning pattern due to the resonance shift. Note that the
introduction of the effective parameters is justified when the ratio of the
unit cell size to the incident wavelength is small. Therefore, when
considering modifications of the lattice which create a super-lattice
structure, the size of the super-cell should be smaller than the wavelength.
There are homogenisation approaches in the literature (e.g. Ref.~\onlinecite{Petschulat2008}) which
include unknown parameters for interaction between resonant elements and our
semi-analytical approach would make an ideal tool for evaluating these
constants.

\section{Conclusion\label{sec:concl}}

We have analyzed the near-field coupling within metamaterials, considering both
the relative orientation and the offset between the centers of two neighboring resonators.
Using a pair of split ring resonators as a simple model, we have shown the coupling mechanisms
at work in our recently proposed tuning scheme, based on the direct calculation of the interaction
energy. We have confirmed that these mechanisms can predict qualitatively the performance of a realistic
metamaterial structure. This paves a road towards a reliable design and development of
tunable metamaterials for various applications.

We note that the specific geometry of the split rings can have a very
significant influence on the qualitative nature of the coupling,
including cases which run counter to our intuitive understanding
of current loops interacting magnetically.

Finally, we point out that the approach developed here for modeling
near-field effects is particularly promising for metamaterials
scaled down to operate at optical frequencies. In the visible, the
paradigm of ideally conducting metal fails and the area of
applicability of circuit models is rather limited. In contrast,
the consideration in terms of excitation and interaction of
plasmonic standing waves will provide a clear physical picture.

\section*{Acknowledgments}

The authors are grateful to Dr.~Lukas Jelinek and Prof.~Ricardo Marqu{\'e}s
(University of Seville) for helpful discussions.
This work was supported by the Australian Research Council.
M.L. acknowledges hospitality of Nonlinear Physics Center and
support of the Spanish Junta de Andalusia Project P06-TIC-01368.
M.G. acknowledges support from the Russian Academy of Sciences,
BPS Program \textquotedblleft{}Physics of new materials and
structures\textquotedblright{}.

redpajama_set_name: RedPajamaArXiv


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