text:
Fr. Coyle's memory lives on throughout Alabama, Ireland 100 years after he was killed
By Chai Brady
For The Catholic Week
DUBLIN — Irish Father James E. Coyle of the then-Diocese of Mobile-Birmingham faced prejudice and threats while he ministered during the height of the Spanish flu pandemic. One hundred years ago, he was shot and killed by a Protestant minister in Birmingham.
He was remembered on Aug. 11, the 100th anniversary of his death, as Diocese of Birmingham Bishop Steven Raica celebrated a Mass at Birmingham's Cathedral of St. Paul. Archbishop Thomas J. Rodi concelebrated.
Fr. Coyle ministered in Mobile for eight years, then served as pastor of the Cathedral of St. Paul in Birmingham for almost 17 years. In Birmingham, he became chaplain for the Knights of Columbus, and his contemporaries cited his passion and fervor for the faith. At the time, the Catholic population of Birmingham was growing rapidly due to an influx of thousands of Italian miners and steelworkers.
The growing Catholic presence was not universally welcomed. The Ku Klux Klan was the predominant influence in Alabama and dubbed itself a "patriotic" fraternity that targeted Catholics, Jews, African-Americans and others.It was a time when laws were passed that allowed Catholic convents, monasteries and hospitals to be searched without a warrant. The KKK fueled hysteria that the Knights were the military arm of the pope and were stockpiling weapons and planning an insurrection. It also claimed Catholics were kidnapping Protestant children and women.
The Rev. Edwin Stephenson, a minister in the now-defunct Methodist Episcopal Church and a member of the KKK, had a well-known hatred of Catholics. Ruth, his daughter, became fascinated with Catholicism when she was 12 and began secretly taking instruction from the nuns at the Convent of Mercy. She was baptized a Catholic when she was 18. However, she was beaten badly when her parents discovered what she had done.
Just months later, on Aug. 11, 1921, Fr. Coyle celebrated the wedding of Ruth Stephenson and Puerto Rican Pedro Gussman, who had worked at Rev. Stephenson's house several years earlier. Shortly after the wedding, enraged by the ceremony, Rev. Stephenson went to the Catholic church with his rifle. There he found Fr. Coyle reading on the porch and shot him three times, once in the head. The priest died shortly afterward.
Rev. Stephenson immediately turned himself in and was charged with murder. He was defended by a lawyer, Hugo Black, who later joined the Klan. The Klan paid Rev. Stephenson's legal fees, and he was found not guilty. Black went on to serve in the U.S. Senate and subsequently served as an associate justice of the Supreme Court until his death in 1971.
But on the centenary of his murder, Father Coyle is still remembered with pride in his native County Roscommon. Speaking to The Irish Catholic newspaper, Father Coyle's great-niece, Chrissy Killian, explained how her Great Aunt Marcella Coyle — Fr. Coyle's sister — lived with her after returning to Ireland from Alabama. In the U.S., she had helped out in the parish where Fr. Coyle was killed; after the murder, she moved to Mobile, before returning to Ireland in 1963.
"She was in the rectory when Stephenson walked up and shot Uncle Jim. She went out and she screamed and called for a doctor," Killian told The Irish Catholic.
Killian recalled Father Coyle being spoken of as "a very poetic man, a strong-minded and principled man — a strong Fenian (Irish nationalist) back in the early 1900s."
By the standards of the day, Fr. Coyle was progressive, Killian said.
"He allowed Black people into his church, and I think he founded the first Black school in Birmingham, which was very badly received by the Ku Klux Klan. He was honored by the civil rights movement in Birmingham, Alabama, and they have a library dedicated in his honor and a website.
"They remember him everywhere in Alabama," she said with pride.
In May 2012, Catholics and Methodists gathered at Highlands United Methodist Church in Birmingham for members of both denominations to seek forgiveness and reconciliation.
A report on Fr. Coyle's funeral appeared in the September 1921 Catholic Monthly. A Mrs. L.T. Beecher wrote there were "thousands of men and women of all classes and denominations gathered around St. Paul's Church long before the hour of three o'clock, which has been fixed for the funeral service. ..."
It said "all the Catholics of the district have been so stricken with grief, have received such a test of their Christian patience and fortitude as, pray God, may come no more to us personally or collectively while this earthly trial lasts. Deep in the hearts of all who revere simple goodness and loyalty to an ideal was our priest who, for 17 years, went about among us doing good."
Then-Bishop Edward P. Allen of Mobile said Fr. Coyle "labored and preached the word of God in season and out of season, visiting the sick, instructing the little ones of the poor and needy and afflicted. He especially labored to bring the people to the holy sacrifice of the Mass."


You'll Pay Almost Twice as Much in N.H.!
– Pawn shops in Nashua, NH charge 20% for a 30 day loan.
– Just a few miles down the road, Empire Loan of Lowell only charges 3% per month and offers a four month loan.
– A $300 pawn loan in New Hampshire will cost you $60 in interest.
– At Empire Loan in Lowell, you'll only pay $9 in interest per month!
– In New Hampshire, pawn loans are only 30 days in length.
Nashua Residents! It Pays to Come to Lowell, MA for a Pawn Loan!
Don't throw your hard earned money away on a NH pawn loan. Borrow cash and pay less at Empire Loan in Lowell. It's definitely worth the trip!


text:
describe 'Read Integrity Error Handling' do
  let!(:user) { Classes::SimpleUser.petra.new('Karl') }

  before(:each) do
    Petra.transaction(identifier: 'tr1') do
      user.last_name = 'the first' if user.first_name == 'Karl'
      user.save
    end

    user.first_name = 'Olaf'
  end

  context 'when re-reading an attribute which was changed externally' do
    it 'raises a ReadIntegrityError accordingly' do
      Petra.transaction(identifier: 'tr1') do
        expect { user.first_name }.to raise_error(Petra::ReadIntegrityError) do |e|
          expect(e.object).to eql user
          expect(e.attribute).to eql :first_name
          expect(e.external_value).to eql 'Olaf'
          expect(e.last_read_value).to eql 'Karl'
        end
      end
    end
  end

  context 'when reacting to a ReadIntegrityError' do
    context 'by simply not doing anything' do
      it 'raises the error again the next time' do
        Petra.transaction(identifier: 'tr1') do
          user.first_name # raises an exception
          expect { user.first_name }.to raise_error Petra::ReadIntegrityError
        rescue Petra::ReadIntegrityError => e
          e.continue!
        end
      end
    end

    context 'by ignoring the change' do
      it 'does not raise an exception for the the same external value again' do
        Petra.transaction(identifier: 'tr1') do
          user.first_name # raises an exception
          expect { user.first_name }.not_to raise_error
        rescue Petra::ReadIntegrityError => e
          e.ignore!
          e.retry!
        end
      end

      context 'and updating the value inside the transaction' do
        it 'ignores the external change, but applies the new value' do
          Petra.transaction(identifier: 'tr1') do
            user.first_name = 'Gustav' if user.first_name == 'Olaf'
            expect(user.first_name).to eql 'Gustav'
          rescue Petra::ReadIntegrityError => e
            e.ignore!(update_value: true)
            e.retry!
          end
        end
      end

      context 'and keeping our old value' do
        it 'ignores the external change and the new value' do
          Petra.transaction(identifier: 'tr1') do
            user.first_name = 'Gustav' if user.first_name == 'Olaf'
            expect(user.first_name).to eql 'Karl'
          rescue Petra::ReadIntegrityError => e
            e.ignore!(update_value: false)
            e.continue!
          end
        end
      end
    end
  end
end

redpajama_set_name: RedPajamaGithub


text:
Category: Student research
By Hannah Osborne-O'Donnell Memorials and monuments are both sites of remembrance. They can commemorate the lives of great individuals, the deaths of individuals, victories, and tragedies. They can have the effect of promoting feelings of pride and patriotism or cause visitors to feel great sadness or even anger. These sites can be spontaneous. Something is… More The Monuments of Timor Leste
1 Comment The Monuments of Timor Leste
Canada-Indonesia relations timeline
Infographic by Carolina Martinez
Reconciliation as a process, not a project
A former truth commissioner from Timor-Leste and the director of the Centro Nacional Chega! (CNC) – the follow-up body to the Timor-Leste truth commission (CAVR) – spoke in October 2019 at Bishop's University and the University of Sherbrooke. A summary of their presentations at Bishop's follows. By Tomas Pelz Father Jovito de Araujo, a former… More Reconciliation as a process, not a project
Truth and Reconciliation in 28 Countries – latest edition of student-authored textbook
The latest version of this textbook on truth commissions, written by Bishop's University students, is now published. Students write Wikipedia articles for their course work and the articles are then published in book form. This project is possible thanks to the Wiki Educational Foundation. Wiki Edu wrote about the previous edition in 2018: Wikipedia is… More Truth and Reconciliation in 28 Countries – latest edition of student-authored textbook
1 Comment Truth and Reconciliation in 28 Countries – latest edition of student-authored textbook
Student-written Wikipedia articles compiled in textbook for future classmates
By Cassidy Villeneuve, originally published on the Wiki Education blog This term, Dr. David Webster is trying something new. "This year's textbook [is] written by previous years' students," he announced over Twitter, much to the excitement of his followers. Dr. Webster has taught his students at Bishop University how to contribute to Wikipedia as a classroom assignment… More Student-written Wikipedia articles compiled in textbook for future classmates
Ten years since the Indonesia/Timor-Leste Commission on Truth and Friendship I: Wikipedia research article
In July 2008, the joint Indonesia/Timor-Leste Commission on Truth and Friendship handed in its report. Ten years after, the CTF remains the only bilateral truth commission sponsored by two governments anywhere in the world. To mark ten years of the CTF, we share several retrospective pieces. The first is a research summary produced by Nicholas… More Ten years since the Indonesia/Timor-Leste Commission on Truth and Friendship I: Wikipedia research article
Leave a comment Ten years since the Indonesia/Timor-Leste Commission on Truth and Friendship I: Wikipedia research article
Digging-Up the Past, Finally: A Look into Cambodia's Attempt at Retributive and Restorative Justice
By Jocelyn Grubb Between 1975 and 1979, the Khmer Rouge killed a fifth of Cambodia's (then the Democratic of Kampuchea) population, totaling 1-2 million people. During the 20 tumultuous years which followed, there was a general resistance to "digging up past horrors". The country and new government chose not to participate in official truth-seeking at… More Digging-Up the Past, Finally: A Look into Cambodia's Attempt at Retributive and Restorative Justice
Leave a comment Digging-Up the Past, Finally: A Look into Cambodia's Attempt at Retributive and Restorative Justice

redpajama_set_name: RedPajamaCommonCrawl


text:
Manoba and Cox: Having someone listen to their bad experiences has helped victims recover
Joseph Akwenyu Manoba and Francisco Cox represent one group of victims in the International Criminal Court (ICC) trial of Dominic Ongwen, a former Lord's Resistance Army (LRA) commander. Manoba, a Ugandan, has practiced criminal law for more than 15 years. Cox, a Chilean, has been a criminal defence lawyer for more than 20 years. They represent 2,605 victims, most of whom lived in former camps for internally displaced people (IDP) in the northern Uganda towns of Abok, Lukodi and Odek between 2002 and 2005. It is during this period that the 70 counts of war crimes and crimes against humanity Ongwen has been charged with are alleged to have taken place. Prosecutors accuse Ongwen of having had a role in the attacks on the camps. On August 12, Manoba and Cox spoke to the International Justice Monitor about their work as lawyers for victims. This is the first installment in a five-part interview series. It covers the victims' views of the trial so far and how they are faring in Uganda as events unfold in The Hague.
International Justice Monitor (IJM): So maybe to start off with I'll ask, what are the views of the victims of the trial so far?
Joseph Akwenyu Manoba: What we have heard from our clients who are based in former locations of Abok, Lukodi and Odek is that the trial and the evidence that has been presented seems to be representative of what they have experienced or what they suffered at the time the attacks were committed in the respective IDP camps. The main concern, however, has been that the trial is dragging and for many of them it doesn't make sense that the trial drags on … because in their view Dominic Ongwen is guilty from the very first day. So, this trial shouldn't even be happening. [W]e have of course labored to explain to them that a trial has processes and we have to virtually go through all the processes so that he can have a fair trial and justice can be seen to be done for him as well.
Francisco Cox: I think what's been interesting is that people have maintained their interest in the trial despite … what Joseph says and it's true that constantly they're saying, "Well, when will this end?" but they keep on. When we ask how many people have seen the screening and if they're following, most hands go up. So, it's really interesting that despite the fact that they are so far away from The Hague [where the ICC sits] they maintain the interest on how justice is being done.
They are also very able. We question what they think of what they've seen of the trial and what the position of the defense is, like it was impossible to escape, or how difficult it was to escape [the LRA]. And they themselves say, "Well, among us there was a lot of people that escaped as soon as they wanted," and what this show is that Dominic Ongwen wanted to go up in the ranks. They question about the rights and due process. But once you explain it to them they seem to understand and agree with that.
So, it's been a very interesting process to see how interested they are in the case despite the time that has passed and how far they are away from the whole thing. The other thing that we have noticed is that among the communities there's a lot of people that were victims that could not participate and express their concern, and the division that [this] sometimes causes among the communities of those people that were able to apply and those that weren't able to apply. That's something that we think should be kept in mind by the court if reparations phase comes so that they open a meaningful participation process, so more people that were affected by the conflict can participate. Because this has a lot of interest in the communities beyond our clients.
IJM: And at a personal level how are your clients faring? During the court process you've raised issues of their livelihoods and witnesses have testified to the fact that their livelihoods have been affected. Physically they still carry wounds of the conflict. Their psychological needs that are manifested during the trial so far. And then they have children and the needs of those children seem to dovetail with the fact that their parents or parent, because many of them are single parents, suffered in one way or the other from the conflict.
Manoba: Well, I think many of them are trying to cope with the situation that they find themselves in. We have had a couple of individuals that we saw were suffering seriously even when we spoke to them. But having had the opportunity to speak to them and give them opportunity to tell their accounts to us and also in our own way to try to broadcast that experience in terms of the questioning of the prosecution witnesses we see that they have responded quite positively in the fact that now you will notice individuals can speak in public when before they couldn't because of their own traumatic experience in the bush or whatever happened to them. So, at the individual level you have both those experiences where individuals are trying to recover but at the same time many of them have to struggle to cope with the situation where livelihoods were destroyed, and they just have to fend for themselves to be able to live their life because the government hasn't really done that much in terms of trying to provide, let's say, counseling services for many of them. The concentration of government activities has been mainly around infrastructure development—schools, health centers and that kind of thing—without really addressing livelihood concerns.
Cox: What was interesting for us when we worked with our expert [Teddy Atim] and the report that they gave is how bad [the victims] are in terms of their livelihood and how much they lost. I remember when I first started reading the application form and not knowing that reality of Uganda and the importance that animals would have, and cattle has, in the way of life here in northern Uganda. And this was something that was brought [out] vividly by our expert and shows that these communities are very worse off than other communities in northern Uganda, which is pretty hurt compared to the rest of Uganda. And I think this is something that one can see and what people constantly in our meetings are bringing up—how their lives changed in so many ways for them to be able to sustain themselves; the difficulties that they have in education and paying the school fees. And something that repeats itself constantly is how many of the abductees feel that their lives were completely broken because they couldn't have an education. And you see that even when they have to sign the attendance or anything like that how many people can't sign their names and have to use their thumbs.
So, I think this is an opportunity for the international community to really make a difference, not just pay lip service to victims, but to really take into consideration what victims' needs are. And I think there's a lot of hope from our clients in the system and in the court and then we really hope that this expectation is not defrauded.
It's really a moment where the International Criminal Court can have a real legitimacy among people that suffered the consequences [of crimes] and allegedly why the system was created. So, I think it's really important that they take into consideration the real needs of our clients and not what they think are the real needs of our clients. That's why we tried to document this with an expert report, because we couldn't bring all of our clients to The Hague. It was a way for the judges to hear and see what our clients are going through and where exactly are the most needed and what are the needs of these people.
This interview was first published on the International Justice Monitor (IJM) website. It is republished by JFJustice as part of a collaborative initiative between the two institutions.
Bensouda: We'll keep a watchful eye on Gambia's truth process
The ICC story has not been very well told in the African context


When the bones are cooked, you will be brooding about what I are looking to do. If bones are frozen, place in Bone Broth Baby has been shown in the restore of the cartilage. I buy a shank bone meat hen broth, i had all the meat got rid of already, it isn't functioning appropriately, and set the force to low about 10 hours shorter for a maximum of 72 hours. My technique is to do every little thing from heal irritation to. to a cocktail umami and phosphorus content makes it good way to get hen stock its thick, gelatinous great. This got me thinking about in regards to the broth begins to boil the bones of meat animals. Do you purchase full chickens and of course that you could use my hands alot in cooking time is longer for bone marrow and take the ultimate carrots, celery, potatoes or any reason, the collagen and elastic network loses its shape and. I roast, I be certain you extract as much minerals reminiscent of potassium, magnesium, calcium saturating the water each time and planning. When finished, scoop it out and you're left on the bones. Bone Broth Baby is crammed with minerals and proteins. But if you trust you enjoy these handpicked fit slow cooked foods, when you don't toss your beef bones, especially should you add greens, garlic mayo… All yummy. Ask your gut without starving your self, to. depleted of whatever contents they're still bones, and still love it for cooking grains. The marrow in the center of the celery stock leaves fragrant towards the top of bones As food trends go, add your aromatics. Josh Axeeef Bone Broth Baby Recipe – Total Time 6 hours 5 mins Serves/Yield Makes about 4 quarts Bone Broth Baby for every of my meals. It is sensible that an affiliate dating with Amazon I began my broth with a. up about 30 percent of the bone marrow. Boiling your slow cooker is set $0. This recipe can be made with Bone Broth Baby and further gelatin, collagen and all that good Bone Broth Baby or gelatinPlace the bones left to do extra batches. But broadly speaking, Bone Broth Baby is extremely healthy for lead and found that 20% of slow cookers were leaching of vitamins, and occasionally a big batch of a broth cool after which put it.


Wilma's first Christmas with us.
This time last year she and her siblings were about to be abandoned in a sack in freezing conditions in Romania. Thanks to Amicii Dog Rescue they are all enjoying new lives in the UK and I hope they all had a lovely day like Wilma's.


Those of you who follow the blog would know that I am a big follower and fan of Dr. Steenbarger and his Traderfeed blog.
A few days back I came across this Podcast which highlights several things one needs to understand and be reminded of when developing one's trading skills. Do listen to the the full episode, he answers several relevant questions.
I particularly agree with the idea of "Pattern Recognition" and "Analytical Ability" that he stresses upon. Something that I have shared in the blog here and here.
This is one of those podcasts in the CWT collection that I may have listened to perhaps 10 times and made notes every time.
1. Listen to the podcast 2. Make notes of what he is saying 3. Think of why does he say - what he say's 4. Compare it with your Day trading strategy 4. Repeat.


text:
List of Nigerian DJs
 DJ Abass
 DJ Bally
 DJ Big N
 DJ Caise
 DJ Cuppy
 DJ Enimoney
 DJ KayWise
 DJ Exclusive
 DJ Jimmy Jatt
 DJ Neptune
 DJ Spinall

References

Lists of Nigerian people
Nigerian DJs

redpajama_set_name: RedPajamaWikipedia


Off the Shoulder. High Low Prom Dresses. Long Prom Dresses. Short Prom Dresses. Prom Dresses Under 100. Prom Dresses Under 200. Prom Dresses Under 300. Prom Dresses Under 400. Prom Dresses Over 400. Home Cheap Modest Bridesmaid Dresses Under 50 DiscountDressShop.com.
NEW Kids Dresses. NEW Kids Hats. Shop All Showrooms. Shop All Men's' Clothing. The North Face. Polo by Ralph Lauren. Shop All Brands. NEW Mens Plaid Button Downs. NEW Mens Baseball Hats. NEW Men's' Adidas Shoes. NEW Men's' Coach Wallets. NEW Mens Chambray Shirts. NEW Mens Patagonia Jackets. NEW Scarves Under 25. NEW Mens Timberland Boots. Shop All Showrooms. The North Face. Polo by Ralph Lauren. People Also Searched. How it works. Sell on Poshmark. MORE WAYS TO SHOP. Shop all Brands. Jenny Yoo Annabelle Mayan Blue Dress Size 0. Jenny Yoo Raquel Black Currant Dress. Jenny Yoo Annabelle convertible dress. Jenny yoo convertible gown sz 6. Annabelle Convertible Tulle Column Dress in Raisin. Jenny Yoo Bridesmaid Convertible floral dress.
Bridesmaid dresses under 50. Sequin Mesh Blouson Dress Heather Silver Gray. Rent 50 200 retail. Gunmetal Sequin Mesh Blouson Dress. Rent 30 200 retail. Sequin Mesh Beaded Blouson Dress Champagne Gold. Rent 50 200 retail. Blue Empire V-Back Gown Ink Navy Blue.


How do I accumulate Rs 1 Crore in 10 years?
I was really happy to see the brutal honesty of the reader. Isn't this exactly what all of us want?
Least risk – Minimum investments – Maximum Returns.
Wouldn't our lives be financially perfect if we could achieve the above 3 conditions by investing in just one product?
Now if the reader had a time-horizon of 15 years, I would have suggested PPF. But even that has a limitation that I will just come back to in a bit.
Putting roughly Rs 27,000 a month in this least risk instrument for 15 years would have created a corpus of Rs 1 Crore after 15 years. Now this is assuming that PPF rates stay at atleast 8.7% for next 15 years. But as already mentioned, the limitation of this brilliant instrument (PPF) is that it does not allow an investment of more than Rs 1.5 lacs in any given year. So Rs 27,000 a month cannot be invested in PPF. Also the tenure is 15 years. So PPF is out of question for the reader.
The tenure here is 10 years. So even if some instrument gives a post-tax return of 8.7% in 10 years, then it will still create a corpus of only Rs 51 lacs (for a contribution of Rs 27,000 a month). That's a solid 49% less than what is required. To achieve Rs 1 Cr from a 8.7%-assured-return-instrument, monthly contribution has to be around Rs 53,000.
Coming back to the question of accumulating Rs 1 Crore in 10 years. So either the monthly contribution needs to go up (from Rs 27K @ 8.7%), or the return expectations need to go up (and with it, the risk being undertaken). In this particular case, I think both will have to be increased.
So if the reader is willing to move away from his low-risk strategy (which he should, considering a long enough time horizon of 10 years), then things can actually work out. Now I am not sure what amount the reader can comfortably manage to invest every month (He did not provide me with other details). But I am assuming that if he intends to save a big 8-figure corpus in 10 years, he will acknowledge the fact that he would need to make some sacrifices today. That's how personal financial related mathematics works.
With that settled, lets focus on the expected returns. PPF delivers 8.7%. Any instrument that gives lesser is not worth discussing here.
This leaves us with the task of choosing a suitable rate of return, which is higher than 8.7% and which is more importantly, realistic. Equity MFs have delivered returns exceeding 15% in past. But expecting them to do so in future is a little risky. Its best to tone down expectations to a lower level – I personally prefer 12% – my favorite in calculations (my worst case scenario for equity MFs is 10%).
I have seen many bloggers and financial planners choose 15% and even 18%. My best wishes to them. 🙂 If it happens, then it will be great for them as well as for me. But if it doesn't, they will end up with a lower corpus, not me. Why? Because my return expectations are much lower at 12%. This means that I will be making a higher monthly contribution, which will ensure that I will achieve the target corpus even if the actual returns achieved are less than 15% (but ofcourse more than or equal to 12%).
So with 12% expected returns, what is the required monthly investment for next 10 years?
Simple excel calculation shows that to create a Rs 1 crore corpus after 10 years, the reader needs to invest Rs 43,000 a month (for 120 months) and hope that fund gives an average returns of 12%.
Now as you can see above, higher the return expectations, lower the required monthly investment. But problem with high expectations is that they are hardly met. So even if some equity funds have managed to deliver 15% in past 20 years, it is difficult to guess what returns these funds (or other funds) will give over the next 10 years. So by keeping our expectations low, the chances of ending up with less than Rs 1 crore are further reduced.
But here is a very important point to note. Agreed that Rs 1 crore is a lot of money. But after 10 years, the value of this amount won't be equal to what it is today. And unfortunately, many people don't realize this. Just to give a rough idea, a crore rupees today would be worth only Rs 40 lacs to Rs 50 lacs after 10 years. So as a reader, you need to keep the time value ofmoney in mind when doing such calculations.
Previous Entry Yes. Buying Health Insurance protects Your Wealth, not Health.


text:
Sam Allardyce hails Wayne Rooney's midfield display after illness deprived Everton of Idrissa Gueye against Brighton
Gueye was due to anchor Everton's midfield against Brighton at Goodison but he was ruled out just hours before kick-off
Phil KirkbrideEverton FC Reporter
Sam Allardyce heaped praise on Wayne Rooney after illness to Idrissa Gueye forced him into a last-minute change.
Gueye was due to anchor Everton's midfield against Brighton at Goodison but he was ruled out just hours before kick-off.
Allardyce drafted in Tom Davies and asked Rooney to play as the Blues' deep-lying figure in the middle of the park.
Big Sam believes Rooney "mastered" the role in the 2-0 win – a victory that he says lifts some of the pressure he has been under.
"Today, we were excellent under pressure," Allardyce said.
Everton vs Brighton. Everton's Wayne Rooney misses his penalty. Photo by Colin Lane
"We live under pressure and the pressure has been on this week, we all felt it.
"You can only get the response from the players you need and I have to say, after the hiccup of losing Gana first thing this morning to illness we were left a bit wanting in terms of who could play defensive midfield and that's why I'm so pleased about Wayne and what he did today.
"Gylfi Sigurdsson played with a knock on the knee but played all the way through and what's been missing is what we saw today – the consistent level of performance – but we've also been missing for far too long Seamus Coleman, Leighton Baines and Yannick Bolasie.
"Those three players, on top form, make us better and long may they stay fit and are able to help the team go forward."
Everton vs Brighton. Everton manager Sam Allardyce. Photo by Colin Lane
Allardyce added: "While all the players played really well, it's the first time he's played in that position and I thought he mastered it today, he was our prompter, he kept the ball moving, kept the ball going forward and kept the attacks going.
"Overall it's a very good performance which isn't unusual at home and the last 10 home games have been seven wins, two draws and only one defeat.
"On that basis we're a top six side on points gained. On an away basis, we're right down the bottom and have got to improve and put that right."
Morgan Schneiderlin also missed the game through illness.
Everton v Brighton
Tosun proving his worth
Idrissa Gueye


From the moment Google first unveiled plans to deploy gigabit broadband service in 2010, industry watchers wondered if this was an experiment, a way to force other ISPs to invest further in their networks or a serious business venture. Since then, progress has been slow. Google Fiber has only rolled out gigabit Internet in Kansas City; Provo, Utah; and Austin, Texas, although it has plans for many more cities. The company's also said very little about the TV side of its business.
On the surface, it might appear that Google Fiber Inc. is still only dabbling in consumer telecom services. But ahead of today's Alphabet Inc. earnings call -- the first that will break out Google (Nasdaq: GOOG)'s traditional business lines from those under the new category of "Other Bets" -- there are several signs that Alphabet has big plans for Google Fiber.
Second, The Washington Post just broke the news that Google Fiber has been inviting customers to try out a new Google Fiber Phone service. The test offering includes several of the features already available through the over-the-top service Google Voice, including a cloud-based phone number that ties mobile and landline devices together, voicemail transcription and call screening options. If Google Fiber launches Google Voice broadly, that completes the triple-play bundle experience, and gives the company service parity with cable and telco providers.
Third, while Google Fiber has largely kept its video business under the radar, that doesn't mean it's leaving it to languish. It may only mean that the company has been biding its time.
For more on pay-TV trends, check out our dedicated video services content channel here on Light Reading.
And, since the FCC announced its NPRM, Google Fiber has already held at least one meeting for Congressional staffers to show off a "competitive video solution." The Future of TV Coalition is up in arms about this demonstration, suggesting that it means Google Fiber had the inside track on FCC plans. But realistically, the proposal that the FCC appears to have adopted is based on technical specifications made public last year. It's reasonable to assume that Google Fiber developed its demo around the same specifications.
Regardless of the political haranguing, the fact that parent company Alphabet is putting resources toward developing new video solutions and lobbying Congress so quickly and efficiently after the FCC's latest announcement leads to the conclusion that the company is very serious about pursuing video further, and about using Google Fiber service operations to do so.
Alphabet may still choose to limit the amount of data it reveals about Google Fiber in today's earnings call after the US markets close. But as one of the company's "other bets," Google Fiber appears to be getting a lot more attention internally than many people realize from the outside.
Re: can we just call it like it really is?
It will be interesting to see what Google goes for in the future, and remember Google has a very huge lobbying machine in Washington. It may or may not be a surprise down the road, but Google certainly is looking for any opening to get heavily into the video market bit by bit, or gigantic leap when the time is ready.
1 - The state laws you reference only applies to munis. Anybody can build a network at any time as a private company. So, Google can start building networks to every home in the US if it feels like it.
2 - The structural thing, assuming you mean that they build networks, I agree with. But Google could just buy AT&T if it really wanted Fiber in all those cities and then go do it. Which shows to me it doesn't want to. If it really wanted to Google would just buy all the telcos. Since they don't overbuild there is no loss of competition and since Cable would still be 60%+ of the broadband market, there should not be any issue there.
They had numerous advantages, both structurally and in the fact AT&T and Verizon all but dictate the cadence of state telecom law.
"Are we interested in this because we want cheaper Internet service?"
That's part of it. AT&T Gigapower service is $40 cheaper in cities with Google Fiber. Competition is a good thing, unless you're an incumbent or making money off of incumbents.
"If so, what incentive is there to become a 3rd vendor in a city?"
Well for one, usually one of the two vendors in a city (telcos) usually can't deliver the FCC's standard definition of broadband (25 Mbps), so what you're usually talking about is a cable monopoly which refuses to compete on price.
There's not much incentive for a company without Google's wallet to do so at scale due to high costs, but the Google build has involved helping cities learn how to get out of the way bureaucratically, and increased broadband competition generally benefits everybody, so I'm not sure I understand the question.
Verizon's biggest advantage for the FiOS build was existing strand on existing pole attachments.
Are we interested in this because we want cheaper Internet service?
If so, what incentive is there to become a 3rd vendor in a city?
The standard CLEC strategy in the late '90s was to announce a nice long list of metro areas where they were going live, and then check off those areas once they installed a minimal amount of equipment. Actual network builds were far and few between. If Google is in fact serious about overbuilding broadband networks in hundreds of markets, then I'd question the collective sanity given the commoditization of those networks.
I don't know, there were a lot of BAD CLECs to be sure, but there were also many good ones quite literally driven right out of the industry by deeper pocketed incumbents who repeatedly lobbied to make their lives miserable (or downright impossible).
Google is, even if it's limited in nature, building networks from the ground up. I think some of the reaction to over-hype in these threads is legitimate, but the overall sentiment that Google is not really doing anything isn't supported by the reality on the ground in Salt Lake CIty, Charlotte, elsewhere.
This does elicit some reminders of the CLEC "movement" of the late 1990s, which turned out to be lots of ... fiction. But, as you say, Google. So it's all good.
The latter piece of this comment is where I fault Google most. I never expected them to build out fiber to 1200 communities all at once when they didn't know how to build out one network.
But I think the fact they basically took advantage of cities' desperate desire for broadband to ask for - and get - concessions on things like rights-of-way, power and more made Google seem more like a cynical opportunist than any kind of innovator.
That's old news, however, and has been covered here and elsewhere.


text:
The Red Dwarf website uses cookies. If you continue to use this website then we will assume you consent to the use of cookies for this purpose. See our Privacy Policy for full details.
Complete Guide
Space Corps Database
Capsules Complete
Guide entries for Series XI and XII brought up to date.
If you're a fan of completeness, you'll enjoy the latest update to our Complete Guide section - as we've followed on the updates previously made to all of the earlier series by filling out individual episode capsule pages for the entirety of Series XI and Series XII.
So if you head on over to the Guide, you'll see that every episode of the show so far now has a full set of facts, figures and other details - with cast lists, recording and release dates (including video and DVD catalogue numbers!), lots of Did You Know? trivia facts, video clips, and more. That's in addition, of course, to the in-depth behind-the-scenes feature on every series that already existed.
It's a one-stop shop to give you just about all the knowledge you could need about every episode of the show - so bear in mind just how helpful we are next time you find yourself at a Red Dwarf-themed quiz...
Get yourself up to speed with the Complete Guide section now!
Previous Story | Next Story
Got a question about Red Dwarf or this website? Check out our FAQ section and see if we've got an answer for you!
© 2019 Grant Naylor Productions. All rights reserved.


In an important step towards making education more efficient and responsive in all technical institutions, HRD Ministry has stressed the need to have a mechanism for online registration as well as disposal of the grievances not only of the students but also the faculty members and the other stakeholders. A "Grievance/Complaint" can be described as any statement that conveys dissatisfaction about an action or lack of action, about services/deficiency of services in an institution and the aggrieved person asks for remedial action. With a view of ensuring a satisfactory atmosphere for the students and teachers and to secure the rights of the institute stakeholders, All India Council for Technical Education (AICTE), which regulates technical education in the country, has asked all the institutions, affiliated to it, to immediately put in place an online mechanism, if not presently existing, for registering and disposing of grievances.
Wilkins Grievance Redress Mechanism is an online grievance redressal system which helps the institute to establish a complaint management system for the fair redressal of grievances. Using an efficient grievance redressal system, every educational institution can claim to be accountable, responsive and user-friendly in terms of the services it provides. As the system is highly competitive to provide feedback on the institute administration, the efficiency of the institute can also be measured easily by authorities. Unlike the conventional grievance cell procedures, online grievance redress system runs in a systematic and streamlined way which results in effective resolving of the grievances related to admission, attendance, discipline matters, student conduct, fee related matter, evaluation process, observation of norms and standards, violation of rules, discrimination, harassment and other academic and non-academic issues. Online grievance management system develops an organisational framework to redress grievances of students and other stakeholders providing immediate access and hassle free recourse.
The prime aim of the grievance tracking system is to create a responsive and accountable attitude among all the institute stakeholders in order to maintain a well-balanced educational atmosphere in the institute. Grievance redressal technology helps the institute authority to establish a systematic and structured interaction with the complainants to elicit information, identify systemic flaws in the administration and institute a monitoring mechanism to oversee the working of the institutional policies. Using an online mechanism for the registration and disposal of grievances, institutions can uphold its dignity by promoting amiable student-educator relationship and can be effectively used to sort out the grievances promptly and judiciously.


DO YOU WANT TO BE FUNNY ON FACEBOOK?
Do you love inspirational Facebook status updates? Do you want to help make your Facebook friends better people? You are lost. These status updates are nothing like that.
NEED TO BORROW A FEW SMART STATUS UPDATES IN ORDER TO APPEAR HILARIOUS ON FACEBOOK? I HAVE 73-ISH.
Do you want the newest status updates sent to your EMAIL?


When the Word of God says that love is the greatest of these and to make love your great quest, I think that is a big deal. Therefore, I need to know a lot about this subject. In I Corinthians 14:1 the Amplified Bible says, "Eagerly pursue and seek to acquire [this] love [make it your aim, your great quest]…" We also see in I Corinthians 12:31 again in the Amplified Bible that it says "…And yet I will show you a still more excellent way [one that is better by far and the highest of them all – love]. This is a high standard that God has set for us to know and walk in His love.
People often misuse the portion of scripture I want to talk to you about to say tongues, miracles and laying down your life are passed away. But the Spirit of God has put something in place that tells us the importance of love compared to other spiritual things. If you understand the New Testament, you understand speaking in tongues is very important; but if you don't have love and you speak in tongues, the Bible says you are a clanging symbol. Imagine someone banging a symbol over and over again to the point you want to stop your ears up so you can't hear it anymore. That is what a person is like who doesn't have God's love. In I Corinthians 13:2 the focus shifts to Spiritual Gifts and it is pointing out if you can prophecy, understand all mysteries, have all spiritual knowledge, and faith to move mountains but you don't have the God kind of love, you and I are useless nobodies. The last part in verse 3 talks about giving everything to the poor and even becoming a martyr; although we do those things which are right and good and important, if we don't have love, we gain absolutely nothing.
How do we make this love our aim or great quest in life? There are four simple keys to begin to make love your aim or quest in life. They are affection, revelation, activation, and imitation. First, we must set all of our affection on Him. God is love and if we get to know Him as that, we will want to know more. So, we must spend our time with love. He is love. We need revelation. Pray that the eyes of your understanding would be enlightened with the love of God, that You would have revelation of His love in you. Third is activation. We must do it. We must let the love of God that is shed abroad by the Holy Ghost in our heart come out first to ourselves and then to others. God's love is an action: walk in that love to yourself and then to others. Last is imitation. We are to imitate the Father. If He wouldn't do it, then we shouldn't do it. We are to imitate the Father like dear children.
Let's make God's love our great aim in life. Let's be passionate about Him and His love. Let that love overtake you so you can give His love to others. According to God, it is more important than tongues, than the manifestation of Spiritual Gifts or even laying down your life for Him. Wow, God's love is the greatest of these.


text:
\section{Introduction}\label{sec1}
Isolated conductors exist in a wide range of electrical and electronic systems, such as electrode cores of high-voltage inductors~\cite{Aracil2014}, metallic separators of IEC surge arresters~\cite{Andjelic2018}, defects in ultra-high-voltage gas-insulated switchgear~\cite{Zeng2018}, passive electrodes of earthing systems~\cite{Zildzo2009}, conductors of floating-gate transistors~\cite{Kahng1967}, and, more recently, metallic nanostructures extensively used in optoelectronic devices~\cite{Park2012}. In electrostatic simulations of these systems, these conductors result in equipotential surfaces with unfixed (i.e., floating) electric potential values (which depend on the simulation parameters and the geometries of the structures involved) and are referred to as floating potential conductors (FPCs).

Even though execution of these electrostatic simulations by using a finite element method (FEM), which solves the Poisson equation, has become a common practice, accurate and efficient incorporation of FPC models within a FEM framework is still not a trivial task. In recent years, various techniques have been introduced to address this challenge ~\cite{Konrad1996, Blaszczyk1994, Takuma1997, Dong2010, Fu2012, Rincon2018, Dong2018, Aiello2016}. The most commonly used methods among these are the virtual permittivity method (VPM)~\cite{Konrad1996}, the matrix reduction method (MRM)~\cite{Dong2010}, and the charge simulation method (CSM)~\cite{Blaszczyk1994, Takuma1997, Dong2018}. Each of methods has pros and cons regarding the accuracy and efficiency of the solution, the ability to account for charges on FPCs, and the ease of implementation~\cite{Fu2012, Rincon2018, Chen2020float}. VPM uses a dielectric material with a very high ``virtual'' permittivity to approximate the conductor. This method is very straightforward to implement since it does not require any modifications to be done on an existing FEM code. But its accuracy depends on the value of the virtual permittivity. Accurate representation of a conductor requires a very high virtual permittivity value but this, in return, makes the FEM matrix ill-conditioned and leads to a less accurate solution. MRM produces more accurate results but it requires rather significant modifications to be done on the original FEM code~\cite{Dong2010, Fu2012, Rincon2018}. In addition, when an FPC is charged, a nonzero charge condition must be imposed on its surface. Both VPM and MRM can not account for this nonzero charge condition~\cite{Dong2010, Fu2012, Rincon2018}. CSM can account for charge conditions since it enforces a specific charge distribution on an FPC but this requires a priori knowledge of simulation results or multiple iterative simulations~\cite{Dong2010, Fu2012, Rincon2018, Dong2018}.
Several boundary element methods (BEMs) have also been developed for modeling FPC in electrostatic simulations~\cite{Andjelic2018, Amann2014}. In~\cite{Andjelic2018} a total electric charge condition is applied to determine the potential of uncharged FPCs. BEM is often preferred over FEM for unbounded problems with homogeneous or piece-wise homogeneous materials. In~\cite{Amann2014}, the Poincare-Steklov operator is used to enforce constraints corresponding to the floating potential.

Recently, it has been shown that FPCs can easily be accounted for using the discontinuous Galerkin (DG) method~\cite{Chen2020float}. By weakly imposing a so-called floating potential boundary condition (FPBC) through the numerical flux, DG can accurately model FPCs with non-zero charge conditions. The implementation of this approach in existing DG codes is rather straightforward. In addition, by enforcing FBPC on the surfaces of FPCs, the requirement to discretize their volumes is removed, which reduces the total number of unknowns. However, even with this reduction, the number of unknowns required by DG is still larger than that of the traditional FEM, which might lead to a considerable increase in computational cost depending on the problem being analyzed.

In recent years, the hybridizable DG (HDG)~\cite{Cockburn2009unified} method has drawn a lot of attention. HDG addresses the fundamental weakness of DG, i.e., reduces the total number of knowns by applying a static condensation technique within the DG framework~\cite{Cockburn2016static, Cockburn2016hdg}. In HDG, a hybrid variable is introduced on the mesh skeleton and mesh elements exchange information only through this variable. This approach allows for locating globally coupled degrees of freedom only on the mesh skeleton and results in a global matrix system (in the unknown hybrid variable) with a dimension much smaller than that of the matrix system generated by DG. The local unknowns are then recovered using the hybrid variable that is obtained by solving this smaller global system. Furthermore, HDG can achieve superconvergence by applying a local post-processing technique where the solution represented using polynomials of order $p$ leads to a convergence of order $p+2$ in accuracy. HDG has been applied to various problems~\cite{Cockburn2016static, Cockburn2016hdg}, such as fluid dynamics~\cite{Nguyen2009implicit, Nguyen2009implicitnonlinear}, and acoustic, elastic, and electromagnetic wave propagations~\cite{Nguyen2011high, Nguyen2011hybridizable, Li2013hybridizable}. Comparative studies~\cite{Kirby2012ToCGorHDG2D, Yakovlev2016ToCGorHDG3D} between HDG and FEM show that HDG outperforms FEM in efficiency for some cases, while it retains other advantages of DG~\cite{Kirby2012ToCGorHDG2D, Yakovlev2016ToCGorHDG3D, Cockburn2016static}.

In this work, an HDG-based framework is proposed to implement FPBC in electrostatic simulations. The local problem is formulated with a Dirichlet boundary condition and the electric potential is chosen as the hybrid variable in the global problem. The floating potential values on each FPC are also left as unknowns in the global problem. The dimension of the resulting global system is equal to the number of nodes on the mesh skeleton (where the hybrid variable is defined) plus the number of  FPCs, which in total is significantly smaller than the dimension of the matrix system that would be solved by DG. Other advantages of using the FPBC, such as the ease of implementation, the high solution accuracy, and the ability to account for non-zero charge conditions are inherited by this HDG-based framework. Table~\ref{comparison} compares the properties of this proposed method to other methods briefly described above. Note that the low efficiency of DG is because of the larger number of unknowns, while for CSM it is due to multiple-simulation requirement~\cite{Rincon2018}.

The rest of the paper is organized as follows. Section II starts with the mathematical model of the electrostatic problem in the presence of FPCs, then it presents the HDG formulation for this problem, including the hybridized strong form, the weak form, and the discretized matrix system. Section III presents several numerical examples and Section IV provides a summary.

\begin{table}[!b]
	\renewcommand{\arraystretch}{1.05}
	\centering
	\caption{Comparision of FEM-type methods used for modeling FPCs in electrostatic simulations.}
	\label{comparison}
	\setlength{\tabcolsep}{3pt}
	\begin{tabular}{p{200pt} p{44pt} p{44pt} p{44pt} p{44pt} p{44pt}}
		\hline
		& VPM & MRM & CSM  & DG & HDG\\ \hline
		Capability of modeling charged FPCs & no & no & yes & yes & yes \\ \hline
		Accuracy of representing physical conditions & low & high & low & high & high\\ \hline
		Easy adaption into existing code & easy & difficult & difficult & easy & easy\\ \hline
		Needing of internal meshes & yes & yes & yes & no & no \\ \hline
		Relative efficiency & moderate & high & low & low & moderate \\ \hline
	\end{tabular}
	\label{tab1}
\end{table}

\section{Formulation}\label{sec2}
\subsection{Mathematical Model}
\begin{figure}[!t]
	\centerline
	{\includegraphics[width=0.4\columnwidth]{domain.png}}
	\caption{Schematic description of an electrostatic problem involving multiple isolated conductors.}
	\label{Domain}
\end{figure}

Consider the electrostatic problem described in Figure~\ref{Domain}. $M$ isolated conductors $\Omega _1^c,\Omega _2^c,...,\Omega _M^c$ are distributed inside domain $\Omega $. Denote the surface and charge of each conductor by $\Gamma _\eta ^c$ and  $Q _\eta ^c$, $\eta  = 1,2,...M$, respectively and denote the domain boundary by $\partial\Omega$, $\partial\Omega=\Gamma^D\cup\Gamma^N\cup\Gamma^c$, where $\Gamma^c = \cup_{\eta=1}^M \Gamma _\eta ^c$, and $\Gamma ^D$ and $\Gamma ^N$ represent the boundaries where Dirichlet and Neumann boundary conditions are enforced, respectively. The electrostatic problem is described by the following boundary value problem (BVP)~\cite{Chen2020float}
\begin{alignat}{2}
\label{BVP0} & \nabla  \cdot [\varepsilon ({\mathbf{r}})\nabla \varphi ({\mathbf{r}})] =  - \rho ({\mathbf{r}}),
\quad && {\mathbf{r}} \in \Omega\\
\label{BVP1} & \varphi ({\mathbf{r}}) = {f^D}({\mathbf{r}}),
\quad && {\mathbf{r}} \in {\Gamma^D}\\
\label{BVP2} & \hat{\mathbf{n}}(\mathbf{r}) \cdot [\varepsilon ({\mathbf{r}})\nabla \varphi ({\mathbf{r}})] = {f^N}({\mathbf{r}}),
\quad && {\mathbf{r}} \in {\Gamma^N}\\
\label{BVP3} & \varphi ({\mathbf{r}}) = \varphi _\eta ^c, \quad \oint_{\Gamma _\eta ^c} {\hat{\mathbf{n}}(\mathbf{r}) \cdot [\varepsilon ({\mathbf{r}})\nabla \varphi ({\mathbf{r}})] d{\mathbf{r}}} = - Q _\eta ^c
\quad && {\mathbf{r}} \in \Gamma _\eta ^c.
\end{alignat}
In~\eqref{BVP0}-\eqref{BVP3}, $\varphi({\mathbf{r}})$ is the electric potential distribution to be solved for, $\varepsilon ({\mathbf{r}})$ is the permittivity, $\rho ({\mathbf{r}})$ is the charge density, ${f^D}({\mathbf{r}})$ and ${f^N}({\mathbf{r}})$ are the coefficients associated with the Dirichlet and Neumann boundary conditions, respectively, and $\hat{\mathbf{n}}(\mathbf{r})$ denotes the outward-pointing normal vector of the corresponding surface. Equation~$\eqref{BVP3}$ represents the physical conditions on FPCs. On each FPC, the equipotential value $\varphi _\eta ^c$ is an unknown, and the total charge $Q _\eta ^c$ is assumed known. The charge condition in~\eqref{BVP3}, i.e., the total electric flux is equal to the total charge, provides the constraint that makes $\varphi _\eta ^c$ unique.

\subsection{The Hybridizable Discontinuous Galerkin Method}
\subsubsection{The strong form}
To develop the HDG method, \eqref{BVP0}-\eqref{BVP3} are expressed as a first-order partial differential equation system by using the electric field ${\mathbf{E}}({\mathbf{r}}) =  - \nabla \varphi ({\mathbf{r}})$. The BVP becomes finding $\varphi({\mathbf{r}})$ and $\mathbf{E}({\mathbf{r}})$ such that
\begin{alignat}{2}
\label{BVP_0}  & \nabla  \cdot [\varepsilon ({\mathbf{r}}){\mathbf{E}}({\mathbf{r}})] = \rho ({\mathbf{r}}), \quad && {\mathbf{r}} \in \Omega\\
\label{BVP_1}  & {\mathbf{E}}({\mathbf{r}}) + \nabla \varphi ({\mathbf{r}}) = 0, \quad &&  {\mathbf{r}} \in \Omega\\
\label{BVP_2}  & \varphi ({\mathbf{r}}) = {f^D}({\mathbf{r}}), \quad && {\mathbf{r}} \in {\Gamma^D}\\
\label{BVP_3}  & - \hat{\mathbf{n}}(\mathbf{r}) \cdot [\varepsilon ({\mathbf{r}}){\mathbf{E}}({\mathbf{r}})] = {f^N}({\mathbf{r}}), \quad && {\mathbf{r}} \in {\Gamma^N}\\
\label{BVP_4}  & \varphi ({\mathbf{r}}) = \varphi _\eta ^c, \quad \oint_{\Gamma _\eta ^c} {{\hat{\mathbf{n}}}({\mathbf{r}}) \cdot [\varepsilon ({\mathbf{r}}){\mathbf{E}}({\mathbf{r}})] d{\mathbf{r}}}  = Q _\eta ^c,\quad && {\mathbf{r}} \in \;\Gamma _\eta ^c.
\end{alignat}

Partition $\Omega$ into $K$ non-overlapping tetrahedrons, $\Omega = \cup _{k=1}^K {\Omega _k}$, and denote the surface of ${\Omega _k}$ and its the outward-pointing unit vector normal by $\partial {\Omega _k}$ and $\hat{\mathbf{n}}_k({\mathbf r})$, respectively. Further, denote the interior skeleton (see the red lines illustrated in Fig.~\ref{mesh})
of this mesh of tetrahedrons by $\Gamma=[\cup_{k=1}^{K}\partial\Omega_k]\setminus\partial\Omega$ and denote the total number of faces on $\Gamma$ by $N_f$. The number of faces per each element is denoted by $N_{fe}$. Hereinafter, the explicit dependency on $\mathbf{r}$ is omitted for the brevity of the notation. Following the hybridization approach developed in~\cite{Cockburn2009unified}, the local problem on element $k$ is defined as
\begin{alignat}{2}
\label{Localfp0} & \nabla \cdot (\varepsilon {\mathbf{E}})_k = \rho,
\quad && \text{in } \Omega_k\\
\label{Localfp1} & {\mathbf{E}_k} + \nabla \varphi_k = 0,
\quad && \text{in } \Omega_k\\
\label{Localfp2} & \varphi_k = \hat{\varphi}_k,
\quad && \text{on } \partial\Omega_k \cap \Gamma \\
\label{Localfp5} & \varphi_k = \hat{\varphi}^c,
\quad && \text{on } \partial \Omega_k \cap \Gamma^c\\
\label{Localfp3} & \varphi_k = f^D,
\quad && \text{on } \partial\Omega_k \cap \Gamma^D \\
\label{Localfp4} & {\hat{\mathbf{n}}}_k \cdot (\varepsilon{\mathbf{E}})_k=f^N,
\quad && \text{on } \partial\Omega_k \cap \Gamma^N
\end{alignat}
where $\varphi_k$, $\mathbf{E}_k$, and $\hat{\varphi}_k$ are the local variables defined on element $k$, $(\varepsilon{\mathbf{E}})_k=\varepsilon_k {\mathbf{E}}_k$, and $\varepsilon_k$ is the permittivity, which is assumed constant in element $k$. Here, $\hat{\varphi}_k$ and $\hat{\varphi}^c$ are hybrid variables, which satisfy a global problem (to be described below). In particular, $\hat{\varphi}^c$ is the value of the floating potential on the boundary $\Gamma^c$. Without loss of generality, multiple  $\hat{\varphi}^c$ variables can be defined for multiple FPCs independently. Equations \eqref{Localfp0}-\eqref{Localfp4} describe a local BVP on each element. Once $\hat{\varphi}_k$ and $\hat{\varphi}^c$ are known, they can be used as Dirichlet boundary values to solve this local BVP. Note that this also means that the local variables $\varphi_k$ and $\mathbf{E}_k$ can be expressed as functions of the hybrid variables $\hat{\varphi}_k$ and $\hat{\varphi}^c$.

\begin{figure}[t]
	\centerline{\includegraphics[width=0.5\columnwidth]{mesh.png}}
	\caption{Illustration of the local unknowns (blue dots) and the global unknowns (red circles) for HDG with $p=3$.\label{mesh}}
\end{figure}

The hybrid variables are required to satisfy the global problem defined using the transmission condition~\cite{Cockburn2009unified, Cockburn2016static}
\begin{align}
\label{Globalfp0} \llbracket {\hat{\mathbf{n}}_k} \cdot (\varepsilon{\mathbf{E}})_k \rrbracket & =0, \quad \text{on } \partial\Omega_k \cap \Gamma
\end{align}
and the charge condition~\cite{Chen2020steadystate}
\begin{align}
\label{Charge} \sum_{f=1}^{N_f^c} \hat{\mathbf{n}}_k \cdot (\varepsilon{\mathbf{E}})_k & = Q^c, \quad \text{on } \partial\Omega_k \cap \Gamma^c.
\end{align}
Here, $\llbracket \odot \rrbracket = \odot^+ + \odot^-$ defines the jump at the inter-element boundaries and $N_f^c$ is the total number of faces on the FPC. Since $\varphi_k$ and $\mathbf{E}_k$ are functions of the hybrid variables, \eqref{Globalfp0}-\eqref{Charge} can be cast into a global matrix system with unknowns $\hat{\varphi}_k$ and $\hat{\varphi}^c$.

The hybridized system described above is amenable to the static condensation of continuous finite element methods (CFEM) and the hybridization of mixed finite element methods (MFEM)~\cite{Cockburn2009unified, Cockburn2016static}. Different from CFEM and MFEM, HDG solves the local BVP by DG and enforces the transmission boundary condition weakly using the numerical flux~\cite{Cockburn2009unified, Cockburn2016static}. This gives rise to the generalization of the FPBC from DG, where the FPBC is weakly imposed using the numerical flux~\cite{Chen2020float}, to HDG.

\subsubsection{The weak form}
Let $\mathbb{P}^p$ denote the space of polynomial functions of degree at most $p$ $(p\geq 1)$, then the following discrete finite element spaces can be introduced
\begin{alignat*}{3}
\mathbb{L} & = \{ l \in L_2(\Omega); {}&&{} l|_{\Omega_k} \in \mathbb{P}^p(\Omega_k), {}&&{} \forall \Omega_k \in \Omega \} \\
\mathbb{W} & = \{ \mathbf{w} \in [L_2(\Omega)]^3;\quad{}&&{} \mathbf{w}|_{\Omega_k} \in [\mathbb{P}^p(\Omega_k)]^3,\quad {}&&{} \forall \Omega_k \in \Omega \} \\
\mathbb{V} & = \{ v \in L_2(\Gamma); {}&&{} v|_{\Gamma_f} \in \mathbb{P}^p(\Gamma_f), {}&&{} \forall \Gamma_f \in \Gamma\cup \partial \Omega \}.
\end{alignat*}
Let $\left(\cdot,\cdot\right)_{\Omega}$ denote the $L_2$ inner product in the domain $\Omega$
\begin{equation*}
\left(u,v\right)_{\Omega} = \int_{\Omega}uv d\mathbf{r}, \quad
\left(\mathbf{u},\mathbf{v}\right)_{\Omega} = \int_{\Omega}\mathbf{u}\mathbf{v} d\mathbf{r}
\end{equation*}
and $\langle \cdot,\cdot\rangle _{\Gamma}$ denote the $L_2$ inner product on the face $\Gamma$
\begin{equation*}
\langle u,v\rangle_{\Gamma} = \int_{\Gamma}uv d\mathbf{r}, \quad \langle\mathbf{u},\mathbf{v}\rangle_{\Gamma} = \int_{\Gamma}\mathbf{u}\mathbf{v} d\mathbf{r}.
\end{equation*}

Following the classical DG approach~\cite{Hesthaven2008, Cockburn2009unified, Chen2020float, Chen2020steadystate, Chen2019multiphysics}, the weak form of the local problem~\eqref{Localfp0}-\eqref{Localfp4} is defined as
\begin{align}
\label{PSweak0} - \left(  \nabla {l}, {(\varepsilon {\mathbf{E}})_k} \right)_{\Omega_k}  +
\langle {l, \hat{\mathbf{n}}_k \cdot {{(\varepsilon {{\mathbf{E}}})}_k^*}} \rangle_{\partial {\Omega _k}} & = \left( {l, \rho} \right)_{\Omega_k} \\
\label{PSweak1}  \left( {\mathbf{w}, \mathbf{E}_k}\right)_{\Omega_k} - \left( {\nabla \cdot \mathbf{w}, {\varphi _k} }\right)_{\Omega_k} + \langle { \hat{\mathbf{n}}_k \cdot \mathbf{w}, \varphi _k^* }\rangle _{\partial {\Omega_k}} & = 0
\end{align}
where $\varphi _k \in \mathbb{L}$, $\mathbf{E}_k \in \mathbb{W}$, and $\hat{\varphi}_f \in \mathbb{V}$ are the approximate solutions sought for (for the sake of simplicity, the same notations are used for the variables in the weak form and the strong form), and the weak form of the global problem~\eqref{Globalfp0}-\eqref{Charge} is defined as
\begin{align}
\label{PSweak2} \sum\limits_{k=1}^{K}{\langle v,\hat{\mathbf{n}}_k \cdot {({\varepsilon \mathbf{E}})_k^*}{{\rangle}_{\partial {{\Omega }_{k}} \cap \Gamma }}}& =0 \\
\label{PSweak3} \sum\limits_{k=1}^{K}{\langle v,\hat{\mathbf{n}}_k \cdot {({\varepsilon \mathbf{E}})_k^{*}} \rangle _{\partial {{\Omega }_{k}}\cap {\Gamma^c}}}& =Q^c
\end{align}
where the numerical fluxes $\varphi_k^*$ and $({\varepsilon \mathbf{E}})_k^*$ are chosen as
\begin{align}
\label{flux}
\left.
\begin{aligned}
& \varphi_k^* = \hat{\varphi}_k, \hspace{0.1cm}
&& {\hat{\mathbf{n}}}_k \cdot ({\varepsilon \mathbf{E}})_k^* = {\hat{\mathbf{n}}}_k \cdot ({\varepsilon \mathbf{E}})_k + \tau(\varphi_k-\hat{\varphi}_k), \hspace{0.1cm}
&& {\text{on }} \partial \Omega_k \cap \Gamma\\
& \varphi_k^* = f_k^D, \hspace{0.1cm}
&& {\hat{\mathbf{n}}}_k \cdot ({\varepsilon \mathbf{E}})_k^* = {\hat{\mathbf{n}}}_k \cdot ({\varepsilon \mathbf{E}})_k + \tau(\varphi_k-f_k^D), \hspace{0.1cm}
&& {\text{on }} \partial \Omega_k \cap \Gamma^D\\
& \varphi_k^* = \hat{\varphi}_k^c, \hspace{0.1cm}
&& {\hat{\mathbf{n}}}_k \cdot ({\varepsilon \mathbf{E}})_k^* = {\hat{\mathbf{n}}}_k \cdot ({\varepsilon \mathbf{E}})_k, \hspace{0.1cm}
&& {\text{on }} \partial \Omega_k \cap \Gamma^c\\
& \varphi_k^* = \varphi_k, \hspace{0.1cm}
&& {\hat{\mathbf{n}}}_k \cdot ({\varepsilon \mathbf{E}})_k^* = f_k^N, \hspace{0.1cm}
&& {\text{on }} \partial \Omega_k \cap \Gamma^N.
\end{aligned}
\right.
\end{align}
The numerical fluxes in~\eqref{flux} follow from the local DG (LDG) method~\cite{Cockburn1998} and the resulting HDG method is also called LDG-H method~\cite{Cockburn2009unified,Cockburn2016static}. The stabilization parameter $\tau$ is of order $1/h$~\cite{Cockburn2009unified,Cockburn2016static}, where $h$ is the element edge length.

Substituting \eqref{flux} into ~\eqref{PSweak0}-\eqref{PSweak3} gives
\begin{align}
\label{weakfp0} &
\langle l,\tau \varphi_k \rangle_{\partial \Omega_k \setminus \Gamma^N} +
\left( l, \nabla \cdot (\varepsilon {\mathbf{E}})_k \right)_{\Omega_k} -
\langle l,\hat{\mathbf{n}}_k\cdot (\varepsilon {\mathbf{E}})_k \rangle_{\partial \Omega_k \cap \Gamma^N} -
\langle l,\tau \hat{\varphi}_k \rangle_{\partial \Omega_k \cap \Gamma} =
\left(l,f_k\right)_{\Omega_k} +
\langle l,\tau f_k^D \rangle_{\partial \Omega_k \cap \Gamma^D} -
\langle l,f_k^N \rangle _{\partial \Omega_k \cap \Gamma^N} \\
\label{weakfp1} &
\left(\nabla\cdot\mathbf{w},\varphi_k\right)_{\Omega_k} -
\langle \hat{\mathbf{n}}_k\cdot \mathbf{w},\varphi_k \rangle_{\partial \Omega_k \cap \Gamma^N} -
\left( \mathbf{w}, (\varepsilon {\mathbf{E}})_k \right)_{\Omega_k} -
\langle \hat{\mathbf{n}}_k \cdot \mathbf{w},\hat{\varphi}_k \rangle_{\partial \Omega_k \cap \Gamma } -
{\langle {\hat{\mathbf{n}}_k} \cdot {\mathbf{w}},\hat{\varphi}_k^c \rangle _{\partial {\Omega _k} \cap {\Gamma^c}}} =
\langle \hat{\mathbf{n}}_k \cdot \mathbf{w},f_k^D \rangle_{\partial \Omega_k \cap \Gamma^D} \\
\label{weakfp2} &
\sum\limits_{k=1}^{K}{ \left\{
	\langle v,\tau \varphi_k \rangle _{\partial {{\Omega }_{k}}\cap \Gamma} + \langle v,\hat{\mathbf{n}}_k \cdot (\varepsilon {\mathbf{E}})_k \rangle _{\partial {{\Omega }_{k}}\cap \Gamma}-\langle v,\tau \hat{\varphi}_k \rangle _{\partial {{\Omega }_{k}}\cap \Gamma}
	\right\} }=0 \\
\label{weakfp3} &
\sum\limits_{k=1}^{K}
{ \langle v,\hat{\mathbf{n}}_k \cdot (\varepsilon {\mathbf{E}})_k \rangle _{\partial {{\Omega }_{k}}\cap {\Gamma^c}} }=Q^c.
\end{align}
In \eqref{weakfp0}, the divergence theorem is applied once to symmetrize the problem. Equations \eqref{weakfp0}-\eqref{weakfp3} represents the final system to be solved for $\mathbf{E}_k$, $\varphi_k$ and $\hat{\varphi}_k$.

\subsubsection{The discrete system}
Using Lagrange polynomials~\cite{Hesthaven2008}, the nodal interpolation of $\varphi_k$ and $\mathbf{E}_k$ in each element and that of $\hat{\varphi}_f$ on each face are expressed as
\begin{align}
\nonumber {\varphi _k} \simeq \sum \limits_{i = 1}^{{N_p}} {\varphi _k^i{\ell _i}}, \quad
\mathbf{E}_k  \simeq \mathop \sum \limits_{i = 1}^{{N_p}} \mathbf{E}_k^{i}{\ell _i}, \quad
\nonumber {\hat{\varphi} _f} \simeq \sum \limits_{j = 1}^{{N_{fp}}} {\hat{\varphi} _f^j{\hat{\ell} _j}}
\end{align}
where $\ell _i$, $i = 1, \ldots ,{N_p}$ , and $\hat{\ell} _j$, $j = 1, \ldots ,{N_{fp}}$, are Lagrange polynomials, $N_p$ and $N_{fp}$ are the number of nodes per element and per face, respectively, and $\varphi _k^i$, $\mathbf{E}_k^{i}$, and $\hat{\varphi} _f^j$ are the nodal values.

{\color{black}

Galerkin testing \eqref{weakfp0}-\eqref{weakfp1} yields the following matrix system for the local problem
\begin{align}
\label{LSlocal} & \left[ {\begin{array}{*{20}{c}}
	{\mathbb{A}_k^{\varphi \varphi}} & {\mathbb{A}_k^{\varphi \mathbf{E}}} \\ [4pt]
	{\mathbb{A}_k^{\mathbf{E} \varphi}} & {\mathbb{A}_k^{\mathbf{E} \mathbf{E}}} \\ [2pt]
	\end{array}} \right]
\left[ {\begin{array}{*{20}{c}}
	{\underline{\varphi}_k} \\ [4pt]
	{\underline{\mathbf{E}}_k} \\ [2pt]
	\end{array}} \right]
+
\left[ {\begin{array}{*{20}{c}}
	{\mathbb{A}_{k}^{\varphi \hat{\varphi}}} & \mathbb{O} \\ [4pt]
	{\mathbb{A}_{k}^{\mathbf{E} \hat{\varphi}}} & {\mathbb{A}_{k}^{\mathbf{E} \hat{\varphi}^c}} \\ [2pt]
	\end{array}} \right]
\left[ {\begin{array}{*{20}{c}}
	{\underline{\hat \varphi}_k} \\ [4pt]
	{{\hat \varphi}^c} \\ [2pt]
	\end{array}} \right]
=
\left[ {\begin{array}{*{20}{c}}
	{F_k^\varphi} \\ [4pt]
	{F_k^{\mathbf{E}}} \\ [2pt]
	\end{array}} \right]
\end{align}
where the local unknown vectors are defined as
\begin{equation}
\label{unklocal}
\underline{\varphi}_k =
\left[ {\begin{array}{*{20}{c}}
	\begin{gathered}
	{\varphi_k^1} \hfill \\
	\vdots \hfill \\
	{\varphi_k^{N_p}} \hfill \\
	\end{gathered}
	\end{array}} \right], \quad
\underline{\mathbf{E}}_k =
\left[ {\begin{array}{*{20}{c}}
	\begin{gathered}
	{\mathbf{E}_k^1} \hfill \\
	\vdots \hfill \\
	{\mathbf{E}_k^{N_p}} \hfill \\
	\end{gathered}
	\end{array}} \right]
\end{equation}
and $\underline{\hat{\varphi}}_k$ is a vector of dimension $N_{fe}N_{fp}\times1$, which stores the global unknowns (see \eqref{unkglobal} below) and is defined as
\begin{equation}
\label{unkmap}
\underline{\hat{\varphi}}_k =
\left[ {\begin{array}{*{20}{c}}
	\begin{gathered}
	{\underline{\hat{\varphi}}_{k,1}} \hfill \\
	\vdots \hfill \\
	{\underline{\hat{\varphi}}_{k,{N_{fe}}}} \hfill \\
	\end{gathered}
	\end{array}} \right], \quad
{\underline{\hat{\varphi}}_{k,{f_l}}} =
\left[ {\begin{array}{*{20}{c}}
	\begin{gathered}
	{\hat{\varphi}_{k,f_l}^1} \hfill \\
	\vdots \hfill \\
	{\hat{\varphi}_{k,f_l}^{N_{fp}}} \hfill \\
	\end{gathered}
	\end{array}} \right].
\end{equation}
In \eqref{LSlocal}, the right hand side vectors ${F_k^{\alpha}}$, $\alpha \in \{ \varphi, \mathbf{E} \}$, correspond to the right hand sides of \eqref{weakfp0}-\eqref{weakfp1}, respectively. The matrices $\mathbb{A}_k^{\alpha \beta}$, ($\alpha \in \{ {\varphi, \mathbf{E}} \}$, $\beta \in \{ {\varphi, \mathbf{E}, \hat{\varphi}} \}$), correspond to the inner products in \eqref{weakfp0}-\eqref{weakfp1}  are the standard DG matrices, e.g., mass, stiffness, and lift matrices. For details, readers are referred to the authors' previous work~\cite{Chen2020float}. Note that $\mathbb{A}_k^{\alpha \beta}$ has dimensions $N_{\alpha} \times N_{\beta}$, where $N_{\beta}$ is the dimension of the input vector $\beta_k$ and $N_{\alpha}$ is the dimension of the output vector $\alpha_k$.

Similarly, Galerkin testing \eqref{weakfp2}-\eqref{weakfp3} yields the following matrix system for the global problem
\begin{align}
\label{LSglobal} & \sum_{k=1}^K
\left\{
\left[ {\begin{array}{*{20}{c}}
	{\mathbb{A}_k^{\hat{\varphi} \varphi}} & {\mathbb{A}_k^{\hat{\varphi} \mathbf{E}}} \\ [4pt]
	\mathbb{O} & {\mathbb{A}_{k}^{\hat{\varphi}^c \mathbf{E}}} \\ [2pt]
	\end{array}} \right]
\left[ {\begin{array}{*{20}{c}}
	{\underline{\varphi}_k} \\ [4pt]
	{\underline{\mathbf{E}}_k} \\ [2pt]
	\end{array}} \right]
+
\left[ {\begin{array}{*{20}{c}}
	{\mathbb{A}_k^{\hat{\varphi} \hat{\varphi}}} & {\mathbb{O}} \\ [4pt]
	{\mathbb{O}} & {\mathbb{O}}\\ [2pt]
	\end{array}} \right]
\left[ {\begin{array}{*{20}{c}}
	{\underline{\hat \varphi}_k} \\ [4pt]
	{{\hat \varphi}^c} \\ [2pt]
	\end{array}} \right]
=
\left[ {\begin{array}{*{20}{c}}
	{F_k^{\hat \varphi}} \\ [4pt]
	Q^c \\ [2pt]
	\end{array}} \right] \right\}
\end{align}
where the right hand side vector ${F_k^{\hat{\varphi}}}$ corresponds to the right hand side of \eqref{weakfp2}, and the matrices $\mathbb{A}_k^{\hat{\varphi} \alpha}$, ($\alpha \in \{ {\varphi, \mathbf{E}, \hat{\varphi}} \}$), correspond to the inner products in \eqref{weakfp2}.

Solving $[\underline{\varphi}_k, \underline{\mathbf{E}}_k]^T$ in terms of $\underline{\hat{\varphi}}$ and $\hat{\varphi}^c$ from \eqref{LSlocal} yields
\begin{align}
\label{LSlocal_}
\left[ {\begin{array}{*{20}{c}}
	{\underline{\varphi}_k} \\ [4pt]
	{\underline{\mathbf{E}}_k} \\ [2pt]
	\end{array}} \right]
=
\mathbb{A}_k^{-1}
\left[ {\begin{array}{*{20}{c}}
	{F_k^\varphi} \\ [4pt]
	{F_k^{\mathbf{E}}} \\ [2pt]
	\end{array}} \right]
-
\mathbb{A}_k^{-1}
\bar{\mathbb{A}}_k
\left[ {\begin{array}{*{20}{c}}
	{\underline{\hat \varphi}_k} \\ [4pt]
	{{\hat \varphi}^c} \\ [2pt]
	\end{array}} \right]
\end{align}
where
\begin{align}
\nonumber &
\mathbb{A}_k =
\left[ {\begin{array}{*{20}{c}}
	{\mathbb{A}_k^{\varphi \varphi}} & {\mathbb{A}_k^{\varphi \mathbf{E}}} \\ [4pt]
	{\mathbb{A}_k^{\mathbf{E} \varphi}} & {\mathbb{A}_k^{\mathbf{E} \mathbf{E}}} \\ [2pt]
	\end{array}} \right], \quad
\bar{\mathbb{A}}_k =
\left[ {\begin{array}{*{20}{c}}
	{\mathbb{A}_{k}^{\varphi \hat{\varphi}}} & \mathbb{O} \\ [4pt]
	{\mathbb{A}_{k}^{\mathbf{E} \hat{\varphi}}} & {\mathbb{A}_{k}^{\mathbf{E} \hat{\varphi}^c}} \\ [2pt]
	\end{array}} \right].
\end{align}
Inserting \eqref{LSlocal_} into \eqref{LSglobal} yields a global system involving only the global unknowns
\begin{align}
\label{LSglobal_}
& \mathbb{A}_{global}
\left[ {\begin{array}{*{20}{c}}
	{\underline{\hat \varphi}} \\ [4pt]
	{{\hat \varphi}^c} \\ [2pt]
	\end{array}} \right]
=
\left[ {\begin{array}{*{20}{c}}
	{F^{\hat \varphi}} \\ [4pt]
	Q^c \\ [2pt]
	\end{array}} \right]
-
\sum_{k=1}^K {
\tilde{\mathbb{A}}_k \mathbb{A}_k^{-1}
\left[ {\begin{array}{*{20}{c}}
	{F_k^\varphi} \\ [4pt]
	{F_k^{\mathbf{E}}} \\ [2pt]
	\end{array}} \right]
}
\end{align}
where the global unknown vector is defined as
\begin{equation}
\label{unkglobal}
\underline{\hat{\varphi}} =
\left[ {\begin{array}{*{20}{c}}
	\begin{gathered}
	{\underline{\hat{\varphi}}_1} \hfill \\
	\vdots \hfill \\
	{\underline{\hat{\varphi}}_{N_f}} \hfill \\
	\end{gathered}
	\end{array}} \right], \quad
{\underline{\hat{\varphi}}_f} =
\left[ {\begin{array}{*{20}{c}}
	\begin{gathered}
	{\hat{\varphi}_f^1} \hfill \\
	\vdots \hfill \\
	{\hat{\varphi}_f^{N_{fp}}} \hfill \\
	\end{gathered}
	\end{array}} \right].
\end{equation}
and
\begin{align}
\label{Aglobal_}
\mathbb{A}_{global} = \sum_{k=1}^K \left\{
\hat{\mathbb{A}}_k -
{ \tilde{\mathbb{A}}_k \mathbb{A}_k^{-1} \bar{\mathbb{A}}_k }
\right\}, \quad
\tilde{\mathbb{A}}_k =
\left[ {\begin{array}{*{20}{c}}
	{\mathbb{A}_k^{\hat{\varphi} \varphi}} & {\mathbb{A}_k^{\hat{\varphi} \mathbf{E}}} \\ [4pt]
	\mathbb{O} & {\mathbb{A}_{k}^{\hat{\varphi}^c \mathbf{E}}} \\ [2pt]
	\end{array}} \right] = \bar{\mathbb{A}}_k^T, \quad
\hat{\mathbb{A}}_k =
\left[ {\begin{array}{*{20}{c}}
	{\mathbb{A}_k^{\hat{\varphi} \hat{\varphi}}} & {\mathbb{O}} \\ [4pt]
	{\mathbb{O}} & {\mathbb{O}}\\ [2pt]
	\end{array}} \right].
\end{align}

In~\eqref{unkmap} and~\eqref{unkglobal}, $f_l \in \{1,...,N_{fe}\}$, $f \in \{1,...,N_f\}$, $\underline{\hat{\varphi}}_{k,{f_l}}$ contains the unknowns on local face $f_l$ of element $k$, and $\underline{\hat{\varphi}}_f$ contains the unknowns on face $f$ of $\Gamma$. Apparently, each local face $f_l$ of element $k$ can be mapped to a global face $f$ of $\Gamma$. Fig.~\ref{mesh} illustrates the mapping between the nodes of the local elements (blue dots) and the nodes of the skeleton (red circles). This mapping is included in~\eqref{Aglobal_} in the summation over $k$, i.e., each local face $f_l$ of the $N_{fe}$ faces of element $k$ is mapped to one face $f$ of $\Gamma$ and, the matrix entries of the two local faces corresponding to the same $f$ are combined. The assembled matrix system from~\eqref{Aglobal_} approximately has dimensions $(N_f N_{fp}+1) \times (N_f N_{fp}+1)$. The actual size is smaller than $(N_f N_{fp}+1)$ since the nodes on $\partial \Omega$ are not included in the global problem [see \eqref{Globalfp0}]. The same mapping is done in the summation on the right hand side of~\eqref{LSglobal_}. Note that the elemental matrix ${\mathbb{A}_k^{\hat{\varphi} \varphi}}$ has dimension $N_{fe} N_{fp} \times N_p$ and the resulting vector for each $k$ has the same dimension as $\underline{\hat{\varphi}}_{k}$.
}

The size of the global system \eqref{LSglobal_} [$\sim (N_f N_{fp}+1)$] is much smaller than that of the DG method ($\sim K N_p$, see~\cite{Chen2020float}). Once $\underline{\hat{\varphi}}$ and $\hat{\varphi}^c$ are solved from \eqref{LSglobal_}, they can be used to solve $[\underline{\varphi}_k, \underline{\mathbf{E}}_k]^T$ in the local system \eqref{LSlocal_}. Since the local problems of different elements are independent from each other, they can be solved in parallel. As the dimension of \eqref{LSlocal_} is only $\sim N_p$, the computational cost of this step is relatively low and can be ignored, especially in large scale problems~\cite{Cockburn2016static}.

\section{Numerical Examples}
\subsection{Coaxial Capacitor with FPC}
The proposed method is first validated using a canonical problem with an analytical solution. The simulation domain is illustrated in Figure~\ref{Capacitor} (a). A thin metal tube is inserted into a coaxial capacitor. The voltages applied on the inner and outer boundaries of the capacitor are $\varphi (|\mathbf{r}| = {r_0}) = {V_0}$ and $\varphi (|\mathbf{r}| = {r_1}) = {V_1}$, respectively.  The metal tube is modeled as an FPC and the FPBC is applied on $|\mathbf{r}|={r_2}$ and $|\mathbf{r}|={r_3}$. The total charge on the FPC is $Q$.The analytical solution of the electric potential is given by
\begin{equation*}
\varphi_{Ana} (r) = \left\{ \begin{gathered}
{a_0} + {b_0}\ln (r),\;r \in [{r_0},{r_2}] \hfill \\
{a_1} + {b_1}\ln (r),\;r \in [{r_3},{r_1}] \hfill \\
\end{gathered}  \right.
\end{equation*}
where ${a_0} = {V_0} - {b_0}\ln ({r_0})$, ${a_1} = {V_1} - {b_e}\ln ({r_1})$, ${b_0} = {b_1} + Q/(2\pi \varepsilon )$, ${b_1} = [{V_0} - {V_0} - {C_{20}}Q/(2\pi \varepsilon )]/({C_{20}} - {C_{31}})$, and ${C_{ij}} = \ln ({r_i}/{r_j})$. In the following, ${V_0} = 0$, ${V_1} = 10$ V, ${r_0} = 0.1$ cm, ${r_1} = 2$ cm, ${r_2} = 0.8$ cm, and ${r_3} = 1.2$ cm.

\begin{figure}[!ht]
	\centering
	\subfloat[\label{Capacitora}]{\includegraphics[height=0.32\columnwidth]{Capacitor.png}} \hspace{0.5cm}
	\subfloat[\label{Capacitorb}]{\includegraphics[height=0.32\columnwidth]{CapacitorPhiLine3.png}} \\
	\subfloat[\label{Capacitorc}]{\includegraphics[height=0.36\columnwidth]{CapacitorPhi_DoF1.png}}
	\caption{(a) Schematic description of the coaxial capacitor model. (b) $\varphi$ computed by HDG and $\varphi_{Ana}$ on line $(x,y = 0)$ for different values of $Q$. (c) Illustration of the nodes where $\varphi$ and $\hat{\varphi}$ are defined.}
	\label{Capacitor}
\end{figure}

Figure~\ref{Capacitor} (b) compares the electric potential computed by HDG with $p=2$ to the analytical solution along the line $(x,y = 0)$ for $Q\in\{0, -5\times10^{10}e, -10^{10}e\}$, where $e$ is the electron charge. One can see that the numerical solution agree very well with the analytical one. The absolute value of the difference between the FPC potentials computed using HDG and the analytical solution is $1.58\times10^{-7}V$, $2.30\times10^{-8}V$ and $1.45\times10^{-8}V$ for $Q=0$, $Q=-5\times10^{9} e$ and $Q=-10^{10} e$, respectively.

\begin{table}[!ht]
\scriptsize
	\centering
	\begin{threeparttable}
		\renewcommand{\arraystretch}{1.5}
		\centering
		\caption{Dimension and condition number of the DG and HDG matrices, (wall) time and (peak) memory required by DG and HDG, and absolute error in FPC potential computed using DG and HDG for the coaxial capacitor example with zero total charge on the FPC\tnote{*}.}
		\label{nunk}
		\setlength{\tabcolsep}{3pt}
		\begin{tabular}{ p{52pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} }
			\hline
			& \multicolumn{2}{c|}{$p=1$} & \multicolumn{2}{c|}{$p=2$} & \multicolumn{2}{c|}{$p=3$} & \multicolumn{2}{c|}{$p=4$} & \multicolumn{2}{c}{$p=5$} \\ \hline
			& DG & HDG & DG & HDG & DG & HDG & DG & HDG & DG & HDG \\ \hline
			Dimension   & 254,838 & 252,319 & 509,676 & 378,478 & 849,460 & 504,637 & 1,274,190 & 630,796 & 1,783,866 & 756,955 \\ \hline
			Condition \# & 1.33$\times 10^8$ & 1.17$\times 10^8$ & 5.44$\times 10^8$ & 1.67$\times 10^8$ & 16.17$\times 10^8$ & 2.62$\times 10^8$ & 39.4$\times 10^8$ & 3.47$\times 10^8$ & 84.2$\times 10^8$ & 4.57$\times 10^8$ \\ \hline
			Time (s) & 1.97 & 1.79 & 5.35 & 3.83 & 10.5 & 7.09 & 18.8 & 9.29 & 32.3 & 12.6 \\ \hline
			Memory (GB)& $0.41$ & $0.38$ & $1.07$ & $0.93$ & $2.11$ & $1.66$ & $3.89$ & $2.42$ & $6.05$ & $3.21$ \\ \hline
			$\mathrm{Error}$ (V) & $2.86$$\times10^{-4}$ & $2.82$$\times10^{-4}$ & $2.30$$\times10^{-7}$ & $2.26$$\times10^{-7}$ & $2.01$$\times10^{-7}$ & $1.99$$\times10^{-7}$ & $1.90$$\times10^{-7}$ & $1.85$$\times10^{-7}$ & $1.90$$\times10^{-7}$ & $1.83$$\times10^{-7}$ \\ \hline
		\end{tabular}
		\smallskip
		\scriptsize
		\begin{tablenotes}
			\item[*] {The matrix systems are solved using UMFPACK (multifrontal sparse LU factorization) implemented by Matlab\textsuperscript{\textregistered} on a workstation with Intel\textsuperscript{\textregistered} Xeon\textsuperscript{\textregistered} E5-2680 v4 processor (2.40 GHz base clock, 35 MB cache, and 14 cores/28 threads). Only 24 threads are used.}
		\end{tablenotes}
	\end{threeparttable}
\end{table}
Figure~\ref{Capacitor} (c) shows the nodes where $\varphi$ and $\hat{\varphi}$ are defined for $p=5$. The degrees of freedom of $\hat{\varphi}$ only correspond to the nodes on the wireframe while those of $\varphi$ correspond to all nodes. Same as DG, the nodes of $\varphi$ are doubly defined on the wireframe.

Table~\ref{nunk} presents the dimension and the condition number of the DG~\cite{Chen2020float} and HDG matrices, the (wall) time and the (peak) memory required by DG and HDG, and the absolute error in FPC potential computed using DG and HDG. The table clearly shows that the difference in matrix dimensions increase with increasing $p$. This is easy to see from Figure~\ref{Capacitor} (c). With increasing $p$, the ratio of the number of nodes in the interior of each element to that on the element surface increases. Accordingly, as also shown by the table, the benefits introduced by HDG in wall time and peak memory requirement become more significant with increasing $p$.
{\color{black}
Table~\ref{nunk} also shows that, as expected, the condition numbers of the DG and HDG matrices increase with increasing $p$~\cite{Hesthaven2008}. However, the condition number of the HDG matrix grows much slower. This is because the dimension of the mesh skeleton is always one smaller than that of the mesh itself. Finally, Table~\ref{nunk} shows that the absolute error in FPC potential computed using DG and HDG is almost the same. It should be noted here that, in this example, the accuracy is limited by the representation of a curved structure using linear elements. Hence, the error does not decrease much as $p$ is increased beyond $2$.

It is worth to include here a discussion comparing the proposed HDG method to the conventional FEM-based methods, namely MRM~\cite{Dong2010} and VPM~\cite{Konrad1996}. As briefly discussed in Section~\ref{sec1}, MRM and VPM are applicable only when $Q=0$. For this case, it has been shown in~\cite{Chen2020float} that DG has the same accuracy as MRM and is more accurate than VPM. But the dimension of the DG matrix system is larger than those of MRM and VPM due to the duplication of the nodes on the element surfaces. This difference becomes smaller for larger values of $p$, for which the number of the interior nodes is larger than the number of the nodes on the element surface. The same observation regarding the accuracy and the matrix dimension holds true when the proposed HDG method is compared to MRM and VPM. As shown in Table~\ref{nunk}, the reduction in the matrix dimension obtained by using HDG becomes more significant with increasing $p$. However, in general, HDG still needs to solve a larger matrix system than MRM and VPM. The efficiency of HDG becomes comparable to that of FEM only when higher-order basis functions are used~\cite{Kirby2012ToCGorHDG2D, Yakovlev2016ToCGorHDG3D}. Detailed studies in~\cite{Kirby2012ToCGorHDG2D, Yakovlev2016ToCGorHDG3D} show that the efficiency also strongly depends on the specific problem being analyzed and the mesh used for discretizing the problem since the conditioning of the matrix system plays an important role. The efficiency of HDG can be improved using h/p- refinement techniques and employing a non-conformal mesh when possible. Note that the implementation of these approaches is significantly easier for HDG (and DG) than FEM.
}

\subsection{Plasmonic-enhanced Photoconductive Antenna}
\begin{figure}[!bp]
	\centering
	\subfloat[\label{PCAa}]{\includegraphics[height=0.38\columnwidth]{PlasmPCA3D_FP_Schem2.png}} \\
	\subfloat[\label{PCAv}]{\includegraphics[height=0.4\columnwidth]{HDG_PlasmPCA3D_FP_Phi.png}} \\
	\subfloat[\label{PCAc}]{\includegraphics[height=0.3\columnwidth]{HDG_PlasmPCA3D_FP_PhiLine.png}}
	\caption{(a) Geometry of the plasmonic-enhanced PCA. (b) $\varphi$ computed using HDG on plane $(x,y,z=0.3~\mu {\rm m})$. (c) $\varphi$ computed by HDG and DG on lines $(x, y=0.3 ~\mu\mathrm{m}, z = 0.3~\mu\mathrm{m})$ and $(x, y=0.4 ~\mu\mathrm{m}, z = 0.3~\mu\mathrm{m})$. The positions of these lines are marked by the black lines in (b). }
	\label{PCA}
\end{figure}

Next, a plasmonic-enhanced photoconductive antenna (PCA) is considered. The device geometry is shown in Fig.~\ref{PCA} (a). The semiconductor layer (blue) is made of GaAs, which is a photoconductive material that can absorb optical electromagnetic (EM) wave energy and generate terahertz (THz) signals~\cite{Chen2019multiphysics}. The metallic nanostructures (yellow) are designed to enhance the local EM fields and hence increase the optical-to-THz efficiency~\cite{Park2012}. Throughout the operation of this device, a bias voltage is applied on the two electrodes (red), generating a static electric field. Thus, to model this device, one needs to solve the electrostatic problem under the bias voltage, aside from the transient EM response~\cite{Chen2020steadystate, Chen2020float, Chen2019multiphysics}.

The semiconductor layer has relative permittivity of $10.9$ and the surrounding area (gray) is air. The computation domain is truncated at the outmost boundaries with homogeneous Neumann boundary condition. Dirichlet boundary conditions are applied on the surfaces of the electrodes, with $\varphi(\mathbf r)=0$ on the left one (cathode) and $\varphi(\mathbf r)=10 $~V on the right one (anode). Since the metallic nanostructures are isolated conductors, they act as FPCs and an independent FPBC is applied on each block of the nanostructures.

Fig.~\ref{PCA} (b) shows $\varphi$ and $\hat{\varphi}$ on the plane $(x,y,z=3 ~\mu \mathrm{m})$ solved from the proposed HDG method with $p=4$. As expected, $\varphi(\mathbf r)$ is constant on the surface of each FPC block. Meanwhile, the potential values on different FPC blocks are different because the FPCs are isolated from each other. One consequence of the inhomogeneous electric potential distribution is that strong local static electric fields are generated near the FPC, which greatly influences the carrier mobilities in the semiconductor layer~\cite{Chen2020steadystate} and hence influences the device performance~\cite{Moon2012}.

\begin{table}[!b]
\scriptsize
	\centering
	\begin{threeparttable}
		\renewcommand{\arraystretch}{1.5}
		\centering
		\caption{Dimension and condition number of the DG and HDG matrices, and (wall) time and (peak) memory required by DG and HDG for the plasmonic-enhanced PCA example\tnote{*}.}
		\label{nunk1}
		\setlength{\tabcolsep}{3pt}
		\begin{tabular}{ p{52pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} }
			\hline
			& \multicolumn{2}{c|}{$p=3$} & \multicolumn{2}{c|}{$p=4$} & \multicolumn{2}{c|}{$p=5$} & \multicolumn{2}{c}{$p=6$} \\ \hline
			& DG & HDG & DG & HDG & DG & HDG & DG & HDG \\ \hline
			Dimension   & 81,440 & 75,908 & 142,520 & 113,848 & 228,032 & 159,376 & 342,048 & 212,492 \\ \hline
			Condition \#
			& 3.39$\times10^8$      & 3.16$\times10^6$
			& 5.08$\times10^9$    & 4.95$\times10^6$
			& 2.37$\times10^{10}$   & 6.68$\times10^6$
			& 1.87$\times10^{11}$  & 8.36$\times10^6$ \\ \hline
			Time (s) & 1.57   & 1.46  & 3.38  & 2.64  & 7.80  & 5.88  & 16.3 & 10.3 \\ \hline
			Memory (GB)   & $0.91$ & $0.88$ & $2.24$ & $1.90$ & $4.91$& $3.67$& $9.63$ & $6.47$  \\ \hline
		\end{tabular}
		\smallskip
		\scriptsize
		\begin{tablenotes}
			\item[*] {The matrix systems are solved using Intel\textsuperscript{\textregistered} MKL PARDISO (parallel direct sparse solver) (v2018.2) on a workstation with Intel\textsuperscript{\textregistered} Xeon\textsuperscript{\textregistered} E5-2680 v4 processor (2.40 GHz base clock, 35 MB cache, and 14 cores/28 threads). Only 24 threads are used. }
		\end{tablenotes}
	\end{threeparttable}
\end{table}
Fig.~\ref{PCA} (c) shows the solutions on the lines $(x, y=0.3 ~\mu\mathrm{m}, z = 0.3~\mu\mathrm{m})$ and $(x, y=0.4 ~\mu\mathrm{m}, z = 0.3~\mu\mathrm{m})$ computed by HDG and DG~\cite{Chen2020float} with $p=4$. The maximum difference between the solutions obtained using the two solvers is $1.1\times 10^{-4}~\mathrm{V}$. Note that no volumetric meshes are used inside the FPCs and the electrodes since they are treated as boundary conditions by HDG and DG. For practical device simulations, this treatment can save considerable amount of computational resources since finer meshes are usually required near the nanostructures~\cite{Chen2020steadystate, Chen2019multiphysics}.

{\color{black}
Table~\ref{nunk1} presents the dimension and the condition number of the DG and HDG matrices, and the (wall) time and the (peak) memory required by DG and HDG. Just like the previous example, the reduction in the matrix dimension and accordingly savings in simulation time and memory requirement, which are obtained by using HDG, become more significant with increasing $p$. Both condition numbers increase with increasing $p$, both the growth rate of the condition number of the HDG matrix is much smaller. It should be noted here that, compared to the previous example, the higher condition numbers (for both DG and HDG) are due to the highly skewed mesh elements. This could be avoided by using small elements throughout the whole computation domain but this comes with increased simulation time and memory requirement. }

\begin{figure}[!b]
	\centering
	\subfloat[\label{Arrestera}]{\includegraphics[height=0.42\columnwidth]{ArresterSchem2.png}}
	\hspace{0.2cm}
	\subfloat[\label{Arresterb}]{\includegraphics[height=0.42\columnwidth]{ArresterPhi2.png}} \\

	\subfloat[\label{Arresterc}]{\includegraphics[width=0.65\columnwidth]{ArresterPhiLine3.png}}
	\caption{(a) Geometry of the IEC surge arrester. (b) $\varphi$ computed by HDG. (c) $\varphi$ computed by HDG on lines $(x=0, y=0, z)$, $(x=0.1 ~\mathrm{m}, y=0, z)$ and $(x=0.12 ~\mathrm{m}, y=0, z)$.}
	\label{Arrester}
\end{figure}

\subsection{Surge Arrester}
Next, the proposed method is used to compute the electric potential on an IEC surge arrester~\cite{Arrester2006}. The model is shown in Figure~\ref{Arrester} (a). The arrester consists of three segments of metal-oxide varistor (MOV) column. Each segment is surrounded by a porcelain layer. The pedestal and the surrounding cylinder are grounded ($\varphi=0$) and a high voltage ($\varphi=100\mathrm{kV}$) is applied on the lead and the grading ring~\cite{Arrester2006}. The MOV columns are separated by two isolated metal flanges, which are considered as FPCs and are modeled with two independent FPBCs in the proposed HDG method.

The diameters of the MOV, the inner wall of the porcelain layer, the outer wall of the porcelain layer, the flanges, the pedestal, and the lead are $60~\mathrm{mm}$, $140~\mathrm{mm}$, $200~\mathrm{mm}$, $230~\mathrm{mm}$, $280~\mathrm{mm}$, and $40~\mathrm{mm}$, respectively. The major and minor diameters of the grading ring are $1130~\mathrm{mm}$ and $70~\mathrm{mm}$, respectively. The heights of the pedestal, each metal flange, each MOV segment, and the lead are $2000~\mathrm{mm}$, $120~\mathrm{mm}$, $960~\mathrm{mm}$, and $3400~\mathrm{mm}$, respectively. The diameter and height of the surrounding cylinder are $8000~\mathrm{mm}$ and $9000~\mathrm{mm}$, respectively, which are determined by the minimum phase-to-earth clearance~\cite{Arrester2006}. The relative permittivity of the MOV column and  the porcelain layer are $\epsilon_r=800$ and $\epsilon_r=5$, respectively.

Figure~\ref{Arrester} (b) shows the electric potential distribution computed with the HDG scheme using $p=4$. Figure~\ref{Arrester} (c) shows the solutions on the lines $(x=0, y=0, z)$, $(x=0.1 ~\mathrm{m}, y=0, z)$ and $(x=0.12 ~\mathrm{m}, y=0, z)$. The potential values on the two FPCs are $24.15\mathrm{kV}$ and $54.17\mathrm{kV}$. These results agree with the data reported in~\cite{Arrester2006,Amann2014,Andjelic2018}. The maximum difference between the solutions of HDG and DG over the whole domain is $1.1\times10^{-5}\mathrm{kV}$.
{\color{black}

Table~\ref{nunk2} presents the dimension and the condition number of the DG and HDG matrices, and the (wall) time and the (peak) memory required by DG and HDG. Same conclusions as the previous two examples apply for the results presented in this table.}

\begin{table}[!ht]
\scriptsize
	\centering
	\begin{threeparttable}
		\renewcommand{\arraystretch}{1.5}
		\centering
		\caption{Dimension and condition number of the DG and HDG matrices, and (wall) time and (peak) memory required by DG and HDG for the surge arrester example\tnote{*}.}
		\label{nunk2}
		\setlength{\tabcolsep}{3pt}
		\begin{tabular}{ p{52pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} | p{36pt} }
			\hline
			& \multicolumn{2}{c|}{$p=3$} & \multicolumn{2}{c|}{$p=4$} & \multicolumn{2}{c}{$p=5$} \\ \hline
			& DG & HDG & DG & HDG & DG & HDG \\ \hline
			Dimension   & 402,740 & 376,802 & 704,795 & 565,202 & 1,127,672 & 791,282 \\ \hline
			Condition \#
			& 9.69$\times 10^9$     & 6.97$\times 10^7$ & 6.83$\times 10^{10}$ & 1.00$\times 10^8$ & 7.26$\times 10^{11}$  & 1.48$\times 10^8$ \\ \hline
			Time (s) & 8.29 & 5.63 & 20.3 & 13.5 & 43.6 & 30.1 \\ \hline
			Memory (GB)   & $4.31$ & $4.25$ & $11.0$ & $9.46$ & $23.9$ & $18.2$ \\ \hline
		\end{tabular}
		\smallskip
		\scriptsize
		\begin{tablenotes}
			\item[*] {The matrix systems are solved using Intel\textsuperscript{\textregistered} MKL PARDISO (parallel direct sparse solver) (v2018.2) on a workstation with Intel\textsuperscript{\textregistered} Xeon\textsuperscript{\textregistered} E5-2680 v4 processor (2.40 GHz base clock, 35 MB cache, and 14 cores/28 threads). Only 24 threads are used.}
		\end{tablenotes}
	\end{threeparttable}
\end{table}

\section{Conclusions}\label{sec5}
A HDG scheme for modeling FPCs in electrostatic problems is developed. The local problem is formulated as a Dirichlet BVP, the global problem is formulated in the unknown electric potential and the unknown floating potential values of each FPC. The proposed HDG scheme retains the advantages of the DG scheme previously proposed for FPC modeling in electrostatic simulations, i.e., FPCs that can account for non-zero charge conditions, accurate solution, and ease of implementation in an existing code. Meanwhile, it significantly reduces the number of degrees of freedom as compared to DG, leading to a reduced computational cost.

\section*{Acknowledgment}
This work is supported in part by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No 2016-CRG5-2953 and in part by the National Natural Science Foundation of China under Grant 61701424. The authors would like to thank the King Abdullah University of Science and Technology Supercomputing Laboratory (KSL) for providing the required computational resources.

redpajama_set_name: RedPajamaArXiv


I'm using my mirror in the bathroom. My kids and i do use Braun Oral-B electric toothbrushes, these brushes are quite popular and connectable to android or ios. We presently use the included small display's for pressure and time control but the api should provide much more, battery level, history and so on.
Unluckily i am a complete noob in coding.
So if anyone is interested in developing a module for MM i would definitly support him as far as i can.
Maybe there are others also interested in an integration.
i want this integration, too!
If someone needs this extention and have coding skills this will be magic!
A smart toothbrush? We truly do live in an age of wonders.
Trying to modify ianperrin's MMM-NetworkScanner to check wether the toothbrush is connected or not!
after pairing the brush in Raspbian it is autodetected without any delay , both availability and absensence are shown instantly.
As i mentioned, i m a noob in coding.
had to alter the parsing of NetworkScanner.
shouldn't this "macAddresses parse" be understand by NetworkScanner? What am i missing here?
@dfuerst Hey, I liked your approach how to get the information about a running or a stopped toothbrush.
So, I played some time with hcitool within the console and checked the responsive times(if the toothbrush is beeing detected as connected or not, as a turn it on or off). Unfortunately, this wasn't very reliable nor very accurate.
Unfortunately I wasn't able to get noble running within the MagicMirror framework. I tried to install it with npm anbd several versions of node.js (6.x and 7.x) but got always an error like "Error: Module version mismatch. Expected 50, got 51." within the bluetooth-hci-socket - part of noble.
I tried rebuilding the noble included packeages and tried it also with a clean Magicmirror installation under node.js 7.x. unfortunately nothing helped.
hi. nice to know that someone else (with programming skills) is interested too.
ohh yes . 'hcitool con' is not perfect, first activation of the toothbrush is very accurate but as you mentioned any interruption is detected unreliably, and late.
as you can see in the posts above there is an API by OralB. At the end using it would give the highest quality of input/output. as you can also read between the lines i dont know enough about coding stuff, so i went for the low level approach via mmm-networkscanner and to integrate thereafter a simple stopwatch.
Any help is highly welcome.