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Home Indigenous Operation NANOOK: Towards a new North
Operation NANOOK: Towards a new North
Lynne Brown
With a harsh climate and fascinating wildlife, the North is a noteworthy region of Canada. The vast region—almost 4 million square kilometres large—is the home of many Indigenous communities. It is also a blossoming business landscape. It carries an abundance of minerals and fossil fuels and its unique environment attracts tourists and adventurers. All this paired with the fact that it spans three territories and claims one of Canada's coasts emphasizes the importance of the North in Canada's defence system. The Canadian Armed Forces (CAF) maintains a strong, permanent presence in the North through several channels. These include Canadian Forces Station Alert, Joint Task Force North (JTFN) and the Canadian Rangers. The CAF also runs northern operations.
Operation NANOOK takes place each year across Yukon, the Northwest Territories, Nunavut, and Labrador. It features up to five deployments throughout the year.
Canada is an Arctic nation which guards its sovereignty and defends the country against threats in the region. The Canadian Armed Forces (CAF) plays a key role in this. Further, the CAF is adapting to environmental changes and enhancing its ability to operate in the Arctic.
A Royal Canadian Air Force CC-138 Twin Otter aircraft arrives at 5 Wing Goose Bay, Newfoundland and Labrador August 14, 2017 for Operation NANOOK. Photo: Mona Ghiz, MARLANT PA
During Operation NANOOK, the CAF guards Canada's sovereignty over its northernmost regions, improves the way it operates in Arctic conditions, improves coordination with Indigenous, federal and territorial governments and northern partners, and works with mission partners to best respond to safety and security issues in the North.
Deployed members from Operation NANOOK practice moving their centre of gravity while driving on steep terrain during an all-terrain vehicle driver safety course in the training area in Rankin Inlet, NU on August 15, 2017. Photo: Cpl Dominic Duchesne-BeaulieuOperation
NANOOK involves sailors, soldiers, air women and air men. The number and makeup of CAF members changes from year to year based on planned activities and exercises.
About 300 CAF members deployed on Operation NANOOK from August 8, 2018 to September 4, 2018. They participated in a maritime domain defence and security exercise in Northern Labrador, Nunavut and Greenland areas.
HMCS Charlottetown and HMCS Kingston visited a number of communities in the Arctic. This gave the sailors an opportunity to connect with and strengthen relationships with northern communities.
CAF members worked alongside governmental partners and departments as well as international partners, including the Danish Navy.
During Operation NANOOK, the CAF works and trains with a variety of partners. Focusing on working with key allies and partners makes the CAF more effective in the North.
These partners include international military partners, and other Canadian federal departments and agencies, territorial and Indigenous governments, and local organizations. Canada's contributions to Arctic security are a key part of the Canada-United States defence relationship.
Approximately 270 CAF members participated in a major air disaster exercise in Yellowknife, NT from September 17 to 21, 2018.
Search and Rescue Technicians tend to simulated causalities during Exercise READY SOTERIA, an exercise designed to evaluate the Canadian Armed Forces response to a major air disaster, on September 17, 2018 in Yellowknife, Northwest Territories. Photo: AB Erica Seymour, 4 Wing Imaging
While the CAF has the primary responsibility for aeronautical SAR—that is, searching for downed aircraft—a major air disaster would require a coordinated response. So, during the exercise, CAF members worked alongside other government departments, Non-Governmental Organizations, and private companies.
The exercise involved soldiers, airwomen and airmen, including medical professionals and support personnel. The following aircraft were involved:
CC-130 Hercules
CH-146 Griffon
CH-149 Cormorant
Members of 1 Canadian Ranger Patrol Group demonstrate how to make an emergency shelter during survival skills training near Rankin Inlet, Nunavut during Operation NANOOK 2016 on August 28, 2016. Photo: Petty Officer Second Class Belinda Groves, Task Force Imagery Technician
As part of the scenario, SAR technicians and health services personnel conducted a number of training activities, including initial triage, stabilization, medical treatment, and preparation for onward movement.
Indigenous communities are at the heart of Canada's North. The CAF works to deepen its relationships with these communities, particularly through collaborative and continuous discourse throughout the year. The CAF continues to build on mutual understanding with northern community leaders.
There are a number of important international issues in the Arctic: climate change, international trade and global security. The Arctic is becoming more accessible because of climate change and new technology. For example, there were fewer than 1,000 flights on polar routes in Canadian airspace in 2003. In 2016, there were over 14,000 flights.
A crewmember from Her Majesty's Canadian Ship MONCTON, transports members of the Royal 22e Régiment back to Rankin Inlet, Nunavut on August 27, 2016 during Operation NANOOK. Photo: Petty Officer Second Class Belinda Groves, Task Force Imagery Technician
State and commercial actors from around the world are interested in the long-term benefits from operating in the Arctic. There are also large reserves of fossil fuels and minerals. These factors are expected to lead to increased commercial activity, research, and tourism in and around Canada's northern region.
The increase in traffic brings new safety and security risks. Canada must be ready to respond to search and rescue cases, as well as natural or man-made disasters.
From September 21 to 28, 2018, CAF members are working with partners in and around Yellowknife and Behchokǫ̀, Northwest Territories. They are practicing how military and civilian organizations would respond to emergencies and natural disasters in Canada's north.
The training focuses on helping the Government of the Northwest Territories and a number of local municipal and Indigenous government partners exercise their emergency management plans.
Together, they will go through a series of escalating scenarios. The CAF's focus is to exercise how it would evacuate people in the event of a forest fire.
Canada's sovereignty
Canadian Armed Forces
HMCS Charlottetown
HMCS Kingston
Operation NANOOK
The Canadian Armed Forces (CAF)
the Northwest Territories
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Algoma writer and reporter. Has written for special editions Thunder Bay Chronicle Journal. In the 80's, Lynne worked for AutoTrader Magazine in rural Southwestern Ont. Trudging through farmers' fields for a picture of a 56 Dodge Custom Royale was considered a very good day. Special interests include issues relating to rural life, seniors, travel, history, community development and indigenous peoples. email to [email protected] Twitter: @dlynnebrown.
Trudeau offers condolences as search called off for sailor missing off California
Ottawa launches independent review of Canada's beleaguered military-justice system


Over the past 10 weeks our Fast Facts series has explored the various worldviews that have influenced Western culture over the past two centuries.
The primary lesson to be learned in humanity's spiritual journey these past two hundred years is that apart from an embrace of God's revealed truth in Scripture, societies are destined for disaster. This is the lesson we learn from history, but it's also what God's word has revealed to us for over 2,000 years (Romans 1:18-32).
Culture is simply worldview externalized. What an individual, a nation, or society thinks and believes about God will directly impact all areas of life. Thus, for true societal transformation to take place, it must begin with heart transformation.
For us as believers who are concerned with the direction our culture is heading today, what this means is that our primary motivation must be for declaring the Gospel and calling people to repentance and making Christ the Lord of their lives. Apart from genuine heart transformation, all of our other social ministry endeavors will simply be temporary band-aids masking humanity's true need.
The most important message we can share with the world today is that single most important truth expressed by Jesus Christ, himself, "I am the way and the truth and the life. No one comes to the Father except through me" (John 14:6).
For more information on sharing the Gospel with those caught up in false worldviews, please check out the book "Apologetics For A New Generation", available in our online store.


Perfect way to hit all those smoothie-choc-fruit cravings in one! Love making one of these mid morning to give me a great energy lift for the day. The Maca powder I use in my smoothies has a long list of beautiful benefits (it's one of my fave health ingredients at the moment) some include, increased energy levels, supplying iron and restoring red blood cells, supplying the body with Vitamins B, C + E as well as providing the body with plenty of calcium, zinc, iron, magnesium, phosphorous and amino acids. It's also great for the skin! You can add any fruit combo you like.
Pop everything in a Vitamix, or any blender, mix well and drink through a straw with a big smile on your face making lots of 'mmmmm' sounds.


The Similarities & Differences Between The Catch It & Tahitian Mini Boats?
What's The Difference Between The Catch It and The Tahitian Boats?
Each and every year literally millions of people around the world, like yourself, take to their local waterways, rivers, and coastlines on their personal watercraft. They do this for a variety of reasons, including for relaxation, recreation, and also serious fishing. While people like you spend time on boats for a variety of reasons, you probably have something in common with your fellow boating enthusiasts: You doubtless want to spend your time on the best, most affordable watercraft that you can get your hands on. If you are trying to decide whether to select between Catch-It or Tahitian mini boats, read below to help you make the decision process easier.
Luckily, a company that builds such affordable and well-built watercraft exists, and it's called CraigCat. This iconic firm builds a variety of exciting and popular watercraft, including two that are known as the Catch-It and the Tahitian Compact Boat. These popular vessels have in common the fine engineering that this firm is known for, but they also have differences that are optimized for specific situations. This article will help to inform you about some of the differences between the Tahitian Compact and its counterpart, thus helping you to decide which model of boat best fits your unique needs and tastes.
The boat design known as the catamaran has been around for thousands of years, and is known to have been a staple of the Polynesians. The engineers at CraigCat have taken this age old design and have added a slew of mouthwatering modern features that have to be experienced to be believed.
TheTahitian Mini Boats and its counterpart have many important differences, being that they are made for different purposes. The Tahitian Mini Boats are popular among people like you who just like to cruise the ocean blue on beautiful, sunny days. The Catch-It tends to be more popular among people who also like to cruise waterways, but also enjoy the challenge of serious fishing.
That said, these watercraft do have some similarities which will now be explored.
Full Remote Capability. This includes electric key start and electric tilt functionalities that have the power to make your days on the water trouble-free.
Specialized Deluxe Bucket Seats. This feature includes high-backed, waterproof deluxe bucket seats that will allow you to ride in comfort as well as in style.
Beverage Holders. Let's face it, you'll get thirsty from time to time on the open water, but the removable, polished stainless steel beverage holders will have you covered when you do.
Dynamic Sport Tuned Suspension (DSTS). The DSTS feature allows your watercraft to perform well at high speeds.
Evinrude Motors. The experts at Evinrude are responsible for the powerful motors that can have you zipping across the waves at a healthy 30 miles per hour.
Practically Unsinkable. Both the Tahitian and its partner are made with foam-filled polyurethane pontoons that will give you peace of mind on the high-seas.
As you can see, there are many great features that these two models have in common. Here are some differences.
Minnkota Trolling Motor. The Catch-It includes a trolling motor to make your fishing expeditions a piece of cake.
Removable Raised Fishing Seat. The Catch-It also includes a specialized removable fishing seat that you can deploy while fishing and stow when you aren't.
As you can see, there is much to be appreciated from both varieties of watercraft. If you are a lover of maneuverable, comfortable, and safe watercraft, you'll do well to take a closer look at these excellent selections.
If you are ready to enjoy the waters in one of the most loved boats in the industry, contact CraigCat today!


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Reading the riots
UK riots 2011
Were the riots about race?
Some commentators were quick to call them 'race riots', but the true picture was more complicated
Hugh Muir and Yemisi Adegoke
Thu 8 Dec 2011 11.00 EST First published on Thu 8 Dec 2011 11.00 EST
Amid the chaos and confusion of this summer's riots, a few commentators felt the benefit of certainty. "These riots were about race. Why ignore the fact?" chided the Telegraph columnist Katharine Birbalsingh. Abroad, there seemed no need for deeper reflection. "Over 150 arrested after London hit by huge race riots," said one US business website. "Let's talk about those race riots in London," urged talkshow hosts in New Zealand. Those on the other side of the debate could appear just as certain. "This is not about race at all," Max Wind-Cowie of the left-leaning thinktank Demos told the Huffington Post.
Who was right? All and none. Race played its part – that much is clear from our conversations with many of those involved in the riots. But its role in terms of who took part and why is difficult to categorise in a manner simplistic enough to give anybody certainty.
The first point worth making is that these were not disturbances resulting from conflict between races.
The far right turned up to complicate the situation in Liverpool. In Eltham, groups of white men coalesced, claiming to be defending "the area" from looters. "It's going to kick off. A nigger is going to get it tonight," one was overheard predicting. There was similar activity in Enfield, where a group of middle-aged men were seen shouting "get the blacks" as they chased some local teenagers.
And in Birmingham, there were skirmishes between black and Asian residents, including one that left three people dead, although it is probably more accurate to view these as clashes between looters and people defending local shops.
But such instances were rare. For the most part, there was no obvious significance attached by rioters to the ethnicity of others taking part in the disorder. Researchers from the Guardian and the London School of Economics interviewed 270 participants for the Reading the Riots project, being published this week in the Guardian.
"Normally we don't get along, we have our own turf, we have our own area and fight with other gangs," said one who took part in disturbances in Birmingham. "But the other gangs there like, we all together one day, we weren't fighting each other, we were fighting the police. That one day, we all got together, the Asians, the blacks, the whites, we all got together, it felt like one, you get me? It felt like we were like one big gang … We took over Birmingham."
Even in London, where the rioting spread following the police shooting of the mixed-race suspect Mark Duggan, there was no conflict between the white people involved in the disturbances and ethnic minorities. It is hard to dispute the findings of the government panel set up to receive evidence from communities and victims of the riots, which announced last week: "We do not believe these were race riots."
If anything, the ethnic mix said something about the way various communities coexist in the capital. One young black man who joined the melee in Tottenham described what he saw. "Originally it started off, it was like, yes it was a group of black people … but I seen Hasidic Jews from Stamford Hill who were down there. I seen lots of white people. I seen guys from shops – Turkish, it turned out. It was like the whole neighbourhood came out. The neighbourhood knew it was all wrong. But sadly it was the neighbourhood that got trashed. They were all out in support." Another was also struck by the diversity. "I can't even count the numbers, yeah, of different ethnicities that I saw there," he said.
The police came under attack. Shops and offices and stores came under attack. But they appear to have been targeted as symbols of the establishment rather than as part of any kind of racial statement.
Witness statements aside, can we be more precise about the races of the rioters? The police have released figures on those who were arrested, but even that cannot be a completely reliable account, as studies repeatedly indicate that minorities are more likely to be arrested than others.
An estimate from the Ministry of Justice (MoJ) says that 42% of those brought before the courts were white, and 46% black or of mixed heritage. A total of 7% were from an Asian or mixed Asian background.
But the proportions, as noted by the MoJ, varied significantly around the country. In Haringey – including Tottenham, where the rioting began – 34% were white, 55% from a black or mixed background. In Nottingham, 32% were white and 62% from a black or mixed background.
In Birmingham, 46% were from a black background, 33% white and 15% were Asian. In Salford, those taken to court were 94% white; with 6% from a black or mixed background.
Of the 270 rioters interviewed by the Guardian and the LSE, 50% were black, 27% were white, 18% of mixed race and 5% Asian.
Does this mean that people of some races were more likely to join the disorder than others? Possibly. But why? Behind these figures lie a whole range of determinants: poverty, affluence, class, geography.
But it is indisputable that a great many black Britons were involved in the disturbances. And a surprising number of the black people interviewed by Guardian/LSE researchers made stark and impassioned complaints about unfairness and inequality; attributable, they said, to the colour of their skin.
It was not a main driver. Racial protest does not completely explain their decisions to take part in the disorder. But it cropped up again and again as part of a wider disillusionment that led people on to the streets, as observers and participants; part of a mindset.
For the vast majority of us, comfortable in the notion that the UK has made significant strides towards racial equality, the accounts of those who feel left behind make troubling reading.
"If you're black or coloured skin, basically, you're at the bottom sort of thing," said one interviewee in the capital. "And then white people, they start off in the middle and then can get to the top. But black people always start from the bottom."
Another interviewee, an 18-year-old man of mixed race from Birmingham, directly linked those who took to the streets to people's concerns about inequality. "If they give us, the black people, the opportunities like they give the white community, then that wouldn't have happened," he said. "If people had jobs on the line … if people had college on the line … if they had something to look forward to or getting a decent income, do they want to ruin it by going to the riots?"
One young black man said he viewed the police and government as the enemy. "No matter how much they say they are with black people … no they ain't … they don't give a fuck about us," he said. "It's still the same way it was many years ago. Many moons. We're still being held down … still getting bullshitted."
Another participant saw an element of community fightback in the disorder, saying: "One young black man gets killed every month at the hands of the police in the UK. I was glad that we're doing something about it now." Doing what? One 19-year-old interviewee, a student from south London, said he was using the limited avenues available to protest about the Duggan shooting and more besides.
"We found, like, no other way to express how we felt about it, so we felt fucking up, well, doing that to their environment would be like, make up for half of the pain that the blacks felt," he said.
Black Britons have made great strides in many areas in recent years and there is a burgeoning black middle class. And yet, given the opportunity to voice their concerns, some black interviewees spoke of a continuing alienation, of continuing struggles for acceptance that might seem more relevant to Britain as it was in the 1960s and 1970s.
And a dispiriting hopelessness. "They section you out, Jamaicans, Caribbeans, so you don't really feel like a part of society," said one man, 22, from north London. "I never feel like this is my home really. Not at all … if they want to move us out of this area quickly they could … it's their land at the end of the day … we've only been here … you can count how much years we've been here … so wherever you go they're always going to look at you like a nigger.
"If I go anywhere I'm [treated like] a black man that came here 60 years ago so if anything they see me as an immigrant and you can feel the subconscious racism everywhere. You can feel it and you see the way they look at you … it is what it is. There's nothing you can do."
He said the pressure only lifts when he visits the Caribbean. "When I go Jamaica, I feel more at home before I even open my mouth. In 50 years' time, [Turkish and Polish people] will be more part of this society than we ever will."
At the intersection of race and class, said another man from Brixton, lies community stratification. "At the end of the day you understand it's still backra [the system imposed by white plantation owners], field slaves and house slaves and that's what it is," he said, "and I believe this is what people are clicking on to why they feel like they have to rise, they had to rise up at that time."
Will things change? Not in the immediate future, according to a 26-year-old from Edmonton. "I can have children and raise them with my views," he said. "They know how the system's shaped against them. They know how hard it is for them to pursue a successful life legitimately, against everyone's discrimination against them."
Some people interviewed for the study declined to answer a question about their racial or ethnic background – arguing the available categories were restrictive or flawed. Others smiled, and gave false answers.
The rioters' discussions of race give us a glimpse of different lives, different perspectives, and different value systems – some of it cause for hope, even amid disorder, some cause for despair. And much of it inexplicable to those in Britain who live more comfortably.
A fire lit in Tottenham that burned Manchester: the rioters' story
Rioters from across England describe how it felt to be caught up in the chaos that engulfed the country last summer
'It was like Christmas': a consumerist feast amid the summer riots
The women who rioted
The morality of rioters
Don't blame our parents, say rioters

redpajama_set_name: RedPajamaCommonCrawl


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CASPER UPDATE: July 29, 2008
BUSH has again stopped deliveries.
The Chinese and Japanese Ambassadors to the United States in Washington had obtained the codes to our accounts and were attempting on behalf of BUSH and themselves to access our accounts. Security personnel from their respective countries arrived and arrested the Ambassadors. BUSH had to have those codes which are now useless.
The accounts were blocked and the codes again changed. The World Court says they "will take action". How many times have those wimps said that?
BUSH has gone berserk in the Whitehouse, stark raving mad WE hear, and has ordered the execution of those who have foiled his most recent attempt to steal the funds. Not to worry about that, he can't reach our allies.
Now he is having his traitorous flunky's at the CIA put out word that a contract has been let on him (BUSH) which is an abominable LIE being used to try to cover this latest scam.
The situation is being handled. More when available. He can delay but he can not stop.
casper 7-29-08


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Scholarly Commons Home
Home > Journals and Magazines > Journals > JDFSL > Vol. 7 (2012) > No. 2
Technology Corner Automated Data Extraction Using Facebook
Nick V. Flor, Technology Corner Automated Data Extraction Using FacebookFollow
The Association of Digital Forensics, Security and Law (ADFSL)
Because of Facebook's popularity, law enforcement agents often use it as a key source of evidence. But like many user digital trails, there can be a large amount of data to extract for analysis. In this paper, we explore the basics of extracting data programmatically from a user's Facebook via a Web app. A data extraction app requests data using the Facebook Graph API, and Facebook returns a JSON object containing the data. Before an app can access a user's Facebook data, the user must log into Facebook and give permission. Thus, this approach is limited to situations where users give consent to the data extraction.
Carioli, C. (2012, April 6). When the Cops Subpoena your Facebook Information, Here's what Facebook Sends the Cops. Retrieved June 30, 2012, from The Boston Phoenix: http://blog.thephoenix.com/blogs/phlog/archive/2012/04/06/when-policesubpoena-your-facebook-information-heres-what-facebook-sends-cops.aspx
Crockford, D. (2006, July). The Application/JSON Media Type for JavaScript Object Notation (JSON). Retrieved June 30, 2012, from The Internet Engineering Task Force (IETF): http://www.ietf.org/rfc/rfc4627.txt
Facebook. (2012, March). Key Stats. Retrieved June 30, 2012, from Facebook: http://newsroom.fb.com/content/default.aspx?NewsAreaId=22
Facebook. (2012a). Download Your Information. Retrieved June 30, 2012, from Facebook: https://www.facebook.com/help/?page=116481065103985
Facebook. (2012b). Information for Law Enforcement Authorities. Retrieved June 30, 2012, from Facebook: https://www.facebook.com/safety/groups/law/guidelines/
Facebook. (2012c). Graph API. Retrieved June 2012, 30, from Facebook: https://developers.facebook.com/docs/reference/api/
Fielding, R. T., & Taylor, R. N. (2002). Principled Design of the Modern Web Architecture. ACM Transactions on Internet Technology, 2, 115-150.
Recordon, D., & Hardt, D. (2012, June 8). The OAuth 2.0 Authorization Framework. Retrieved June 30, 2012, from The Internet Engineering Task Force (IETF): http://tools.ietf.org/html/draft-ietf-oauth-v2-28
https://doi.org/10.15394/jdfsl.2012.1124
Flor, Nick V. (2012) "Technology Corner Automated Data Extraction Using Facebook," Journal of Digital Forensics, Security and Law: Vol. 7 : No. 2 , Article 9.
DOI: https://doi.org/10.15394/jdfsl.2012.1124
Available at: https://commons.erau.edu/jdfsl/vol7/iss2/9
Computer Engineering Commons, Computer Law Commons, Electrical and Computer Engineering Commons, Forensic Science and Technology Commons, Information Security Commons
Indexing/Databases
All Issues Vol. 13, No. 4 Vol. 13, No. 3 Vol. 13, No. 2 Vol. 13, No. 1 Vol. 12, No. 4 Vol. 12, No. 3 Vol. 12, No. 2 Vol. 12, No. 1 Vol. 11, No. 4 Vol. 11, No. 3 Vol. 11, No. 2 Vol. 11, No. 1 Vol. 10, No. 4 Vol. 10, No. 3 Vol. 10, No. 2 Vol. 10, No. 1 Vol. 9, No. 4 Vol. 9, No. 3 Vol. 9, No. 2 Vol. 9, No. 1 Vol. 8, No. 4 Vol. 8, No. 3 Vol. 8, No. 2 Vol. 8, No. 1 Vol. 7, No. 4 Vol. 7, No. 3 Vol. 7, No. 2 Vol. 7, No. 1 Vol. 6, No. 4 Vol. 6, No. 3 Vol. 6, No. 2 Vol. 6, No. 1 Vol. 5, No. 4 Vol. 5, No. 3 Vol. 5, No. 2 Vol. 5, No. 1 Vol. 4, No. 4 Vol. 4, No. 3 Vol. 4, No. 2 Vol. 4, No. 1 Vol. 3, No. 4 Vol. 3, No. 3 Vol. 3, No. 2 Vol. 3, No. 1 Vol. 2, No. 4 Vol. 2, No. 3 Vol. 2, No. 2 Vol. 2, No. 1 Vol. 1, No. 4 Vol. 1, No. 3 Vol. 1, No. 2 Vol. 1, No. 1
ISSN: (Print) 1558-7215
ISSN: (Online) 1558-7223


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2019 Employees of the Month
Past Employees of the Month
Nominate an Employee of the Month
Customer Service Impact Award
Vincent Jones: June 2013 Employee of the Month
Vincent Jones, Employee of the Month for June, is a police officer at Holland Middle School, a position he has held since he first joined Team HISD in 2002. Before that, Jones served as a deputy constable in Harris County for six years. He obtained his law enforcement degree from the University of Houston-Downtown, and currently holds an advanced police officer's certification.
As a campus police officer, Jones' main duties consist of patrolling the school grounds, preparing incident reports, and working with other campus personnel to keep all students, teachers, staff, and visitors safe. He is also a member of the Shared Decision-Making Committee, the Safety and Security Committee, and the Police Officers Association, and he has run a weight-lifting program on campus for at-risk students for the past two years.
A native Houstonian, Jones is a proud member of Yates High School's Class of 1983. He lives in Fresno with his wife, Sytiria, and daughter, Chevaria. When not working, he enjoys working out, cooking, and spending time with his family and friends.
"Safety is our number-one priority," says Holland Middle School Principal Tarrynce Robinson, "and Officer Jones is a part of that plan. He exemplifies the characteristics of a team player, and he reminds the students daily that the decisions they make in the next four years will directly affect the next 40 years of their lives. His weight-lifting program contributed to an undefeated football season this past year, as many of our boys dominated on the field. But more importantly, his training program emphasized mental strengthening and decision-making skills."
"Supervising Officer Jones has been a joy," adds Sergeant Sabrina Naulings. "'Safety First' is what he lives by, and he works very well with the administration and staff and is highly respected by students and parents. He is an asset to HISD and to the police department."
"I have known Vince for more than 40 years," said METRO Police Lieutenant Kevin Williams. "He has always been the same person—someone you can depend on. He is one of the most dedicated officers that I have seen. He really cares about the kids and is always available to help with anything he can."


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MARTY & THE BAD PUNCH - Walk A Straight Line
product: Marty & The Bad Punch
label: Enghardt Media/ Edel
PR territory: Europe
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Marty Punch returns after his successful debut album "Moon Over Baskerville", which was awarded with four awards at the German Rock & Pop Awards in 2015. The brilliant follow-up double album is called "Marty And The Bad Punch – Walk A Straight Line" (EnghardtMedia) and will be released on February 21st, 2020. Also featured on the new release is frontman & singer David Cagle (JK Northrup/ David Cagle "That's Gonna Leave A Mark", MelodicRock Records).
"Walk A Straight Line" is a time travel through the most beautiful time of Melodic & AOR Rock – the 80's. In addition to beautiful ballads you can also find incredible AOR Rock songs and country anthems!
The album includes the 3 singles "Zakopane" (#1 Hit in Poland!) with Tommy Denander on lead guitar, the melodic rock anthem "Universe" with Frank Pané (Bonfire) on guitar and "My Demons" with Bruce Kulick (ex-Kiss / Grand Funk Railroad) on lead guitar (to be released Dec 13, 2019 as single).
Many international stars such as David Cagle, Sarah Straub, Robert Karasek, Martin Motnik, Carsten Enghardt, JK Northrup, Tommy Denander, Frank Panè and Bruce Kulick can be heard on "Walk A Straight Line". The recording and mix was handled by Carsten Enghardt, and the final touches were given to the album by mastering engineer Dennis Ward.
Right now, Marty is working with Tommy Denander on a re-recording of the track "Better Be Strong" from his first album – with Robert Tepper, David Cagle, Steph Honde and Mick White as singers amongst others. This recording will be released for charity in the near future.
Line-up: Marty Punch (Guitars), David Cagle (Vocals), Carsten Enghardt (Drums), Martin Motnik (Bass), Robert Karasek (Keyboards)
Guests: Sarah Straub (vocal duet on "Feels Like Heaven"); Tommy Denander (lead guitar & solo on "Zakopane"), JK Northrup (guitar solo on "Southbound Train", Voice over on "The Story Of The Making…), Frank Pané (guitar solo "Universe"), Bruce Kulick (lead guitar & solo "My Demons"


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Yami and Lolita kawaii clothes
December 11, 2022 December 12, 2022 by lovegoyal lovegoyal
Yume kawaii
Yami kawaii clothes is a popular ตอนนี้ทางเว็บไซต์ จีคลับ รองรับอุปกรณ์พกพาส่วนใหญ่ สล็อตเว็บตรงแตกง่าย ดังนั้นผู้เล่นจึงสามารถพกพาติดตัวไปได้ทุกที่ ไม่จำเป็นต้องดาวน์โหลดแอพใดๆ เพิ่มเติม ผู้เล่นสามารถเข้าสู่ระบบหรือลงทะเบียนผ่านเบราว์เซอร์บนมือถือได้ทันที แต่ต้องใช้บัญชีเดียวเท่านั้นในการเล่นทั้งบนเว็บและเวอร์ชั่นมือถือ style of Japanese fashion. Unlike the more pastel-based Yume kawaii, Yami kawaii uses darker themes. These styles are often inspired by Japanese anime characters. These outfits usually feature headbands and other accessories that are whimsical.
Yami kawaii clothing can be found in women's and men's clothing. These outfits usually feature headbands, ribbons, and fluffy materials. They can also include loose socks, platform shoes, and feathers. This subculture is often seen in a wide range of colors and sizes.
This style is often associated with the Japanese manga series Sailor Moon. Many artists have drawn inspiration from this aesthetic. For example, Kato Rei has released her first artbook, Girl Friend.
In addition to the fantasy-based themes, Yami kawaii also involves dark motifs. During this time, mental illness is a taboo in Japan. Yami kawaii clothes and accessories sometimes feature images of death and sickness.
Yami kawaii is the newest subculture of the kawaii fashion world. It shares a lot of characteristics with Yume kawaii. Its motifs can include clouds, animals, fairytales, and sailor collars. The dark themes are juxtaposed with the fantasy playfulness of Yume kawaii.
Yami kawaii wearers can choose to wear pink or red eyeshadow. They may also wear headbands or other accessories that are reminiscent of Sanrio.
Yami kawaii accessories can be bought from any cute brand. They are never overwhelming. They always add to the look of the outfit. Yami kawaii accessories are a fun way to show off your personality. Whether you are a kawaii fan or not, they are a great addition to any wardrobe.
Yume kawaii was first made popular by Japanese model AMO. She was a popular Harajuku-style figure. In 2013, AMO coined the term Yume Kawaii. Although AMO is no longer a part of the kawaii scene, her dreamy pastel look inspired a generation of young Japanese fashionistas.
Today, Yume kawaii is a popular subculture. It is often seen in music videos and anime. It has also inspired many other fashions. It is often seen in Harajuku street fashions.
Known as "Lolita" in Japan, Lolita is a kawaii clothing culture originating in Japan. It is a self-focused subculture that emphasizes clothing, accessories, and other aesthetics. There are a number of different brands of Lolita fashion.
Lolita is a Japanese style of clothing that has gained a strong foothold outside of Japan. It is characterized by frills, lace, and ribbons. The aesthetic is based on Victorian era fashions from the 1800s. Its designs have been influenced by Chinese, Korean, European, and North American designers. The styles vary greatly, and each is based on specific motifs.
Lolita was born out of a desire for young women to dress for themselves. It is also associated with a youthful doll-like appearance. The outfits are usually decorated with ribbons, lace, and other embellishments. The headdresses, including bows, bonnets, and berets, are also very popular. The tops are made of jersey fabric, and sleeves are normally covered with wrist cuffs.
Many brands of Lolita apparel and accessories are manufactured by the Lolita community. They may be purchased from specialty stores or online. The majority of the merchandise comes from China, but there are small shops in other countries.
The Lolita subculture has a large online presence, with many members using social media sites to discuss Lolita fashion. This includes discussion boards on 4chan's /cgl/ board. Its members include both self-proclaimed Lolitas and those who are accused of sexual predatory behaviors. It also includes groups on Facebook and LiveJournal.
The style is very expensive because of the intricate construction of the garments. Some of the larger fashion houses are influenced by the style. They sometimes follow the Lolita stylistic principles, but they also offer more affordable alternatives.
Although a popular clothing brand has a great deal of influence over the aesthetic of Lolita, there are indie brands that have appeared all over the world. Some of the most prominent indie brands are Baby, The Stars Shine Bright, and Angelic Pretty. These brands operate stores in San Francisco, Paris, and other locations. They also have an online store that ships to the US and Canada.
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Dr. Pedrozo holds a Doctorate degree in Animal Physiology & Cell and Structural Biology. He is an Associate Professor of Biology at St Edwards University in Austin, Texas, and Founder of Orthobiomedical, LLC, a consulting and technology incubation company. Prior to this Dr. Pedrozo worked in various capacities in orthobiologics and tissue engineering for companies like DePuy, a Johnson and Johnson Company, Calcitec Inc, Kinetic Concepts Inc (KCI), and SpineSmith LLP. He has been part of the orthopedic industry since 1995 and contributed to the improvement in the treatment of patients by making significant contributions to the research and development of orthobiologic products for the regeneration of musculoskeletal tissues. Some of these products include: CellectTM, alpha-BSM®, ConduitTM TCP granules, Symphony PCS®; and technologies such as OsteoFix, OsteoFix plus BMP2, SISTM Patch plus GDF-5, VicrylTM plus GDF-5, among others.
Dr. Pedrozo is knowledgeable and experienced in working with autologous or patient-derived regenerative tissues such as human marrow-derived stem cells, mesenchymal stem cells, blood-derived products, such as platelet rich plasma (PRP), platelet lysates and releasates, autologous growth factors, activated plasma, leukocyte-poor platelet rich plasma and autologous growth factors.


text:
1946-1958 - L.A. Success
Los Angeles Memorial Coliseum: Memories galore for the Rams
Five former Los Angeles Rams that had more success after leaving the Rams
The Los Angeles Rams trade WR Brandin Cooks to Houston Texans for 2020 2nd round pick
2019 L.A. Rams preview: The biggest questions at every position
L.A. Rams' Goff, Gurley, Donald and Littleton Selected to the 2019 Pro Bowl
Being selected to the Pro Bowl is an annual honor that every player in the NFL aspires to during the course of...
News: Los Angeles Rams release KR Pharoh Cooper, sign RB C.J. Anderson
The Los Angeles Rams shook up their roster with the surprise release of All-Pro kick returner Pharoh Cooper on Tuesday, December 18....
Butting Heads Ep. 15 – Undefeated L.A. Rams prepare for Green Bay
Steve Rebeiro and Norm Hightower discuss lingering thoughts from the victory over the 49ers, expectations for Marcus Peters and the Los Angeles...
Son of Bum's No-Name Linebackers
Defenses, even parts of defenses are known by nicknames. Teams of lore like the Purple People Eaters, the Steel Curtain, and even...
Truth and Lies: Sammy Watkins and the L.A. Rams
The Los Angeles Rams traded a second round pick and a promising cornerback for Sammy Watkins in August 2017. He was expected...
L.A. Rams made the right decision to renegotiate with WR Tavon Austin
The Los Angeles Rams surprised the rest of the league by renegotiating with wide receiver Tavon Austin earlier this week. Most experts...


text:
Connacht Rugby extend partnership with Murray Timber Group
We are pleased to announce a four-year extension of Connacht Rugby's partnership with Murray Timber Group.
The province have been official partners with the family-run business for the past three years. As part of the new deal, the Murray Timber Group name will continue to be displayed on the Connacht Rugby home, away and European playing jerseys.
Established in Ballygar, Galway and now based in both Galway and Carlow, Murray Timber Group is one of the largest, most progressive and flexible providers of timber in the country. The Group's products can be seen in Builders Merchants throughout Ireland and the UK under their own distinctive trademarked SNR (Sustainable Natural Resource) brand.
They have their own dedicated and professional forestry division to offer free forestry management advice and thinning and clear-fell services to forestry growers throughout the country.
Connacht Rugby Head of Commercial & Marketing, Brian Mahony, said:
"We are very happy to extend our deal with Murray Timber Group up to 2021. This partnership, which has been in place since the summer of 2014, has proven a great success.
"With the newly-expanded PRO14 Championship, a position on our playing jersey has become an even more valuable asset and we look forward to showcasing the Murray Timber Group name on our jerseys for the next four years."
Commenting on the new deal, Patrick Murray, Director of Murray Timber Group, said:
"We are very proud to be extending our partnership with Connacht Rugby. It has been fantastic to be part of the journey over the past three years and to witness the growth of the club both on and off the field.
"Connacht Rugby is an ambitious club with very similar values to our family-run business and we look forward to supporting new Head Coach Kieran Keane and all of the team in the seasons ahead."
Connacht Rugby announce three-year catering partnership with Tribe Hospitality Group
SeniorSquad
Connacht Rugby and BLK Sport Launch New Home Jersey
Bank of Ireland announced as Connacht Rugby Sponsor
ABrowne
Connacht Rugby announce Four Star Pizza as an official partner


text:
GBR: SB20 Class helps drive change at Aberdeen Asset Management Cowes Week
Cowes Week Limited is always keen to listen carefully to what competitors want from Aberdeen Asset Management Cowes Week. Together with input from the classes involved, CWL has come up with a tweaked format this year that is already starting to prove popular with an influx of additional entries writes Sue Pelling.
SB20 at Aberdeen Asset Management Cowes Week, 2012
The most significant change for 2013 is the introduction of two races a day for the SB20 and J/70 sportsboats. The SB20s are using the regatta as the third event in their European Grand Slam tour, which means turnout should be good.
Jerry Hill Director of Sportsboatworld who is racing at the event says the format change is really important: "In general the SB20 fleet felt they were not getting enough races or sailing in exchange for a weeks holiday – some only wanted to do the first weekend too.
"This format allows our sailors to get eight races in for four days, and they either have the option of getting back to work for Wednesday or carrying on with the more traditional race format for the rest of the week, which is more attractive if they've travelled from further afield. We have visitors from France, Holland, Russia all coming on the back of the Grand Slam format, and potentially more UK sailors coming who wouldn't otherwise attend."
Ian Atkins from boats.com who is racing a new J/70 endorsed Hill's view, commenting: "The new, condensed four-day format offering two shorter races each day, but including the unique experience of both starting and finishing on the Squadron line is a tremendous step forward that is bound to increase the popularity of Cowes Week in years to come. Well done to all concerned for the effort involved in making this option available."
Sportsboat sailors may also be interested in the news, announced last week, that Aberdeen Asset Management Cowes Week is a qualifying event the 2014 EFG Pan American Sport Boat Championship to be held in March in Miami.
Other format changes to the Week include the repositioning of the Black Group start line. The line, which will be known as the Bramble Line, will be positioned approximately 400 metres to the east of where it was previously, at the mouth of Southampton Water. This has been done primarily to move the line further from the Thorn Channel and also so that it can be used as a finish line.
CWL are also introducing a new race format on the final Saturday (10 August), aimed predominantly at cruisers who want a taste of the racing action at Aberdeen Asset Management Cowes Week for just one day. Cowes Week Limited CEO, Stuart Quarrie, said the aim is to give newcomers a soft introduction. "The plan is to keep it relaxed with a late start, a simple course and a condensed set of sailing instructions."
Quarrie added: "Before launching the idea we canvassed opinion on the concept and had an overwhelmingly positive response. We hope that those who give one day a go this year may come back and spend a bit more time with us in future years".
SB20 Solent Series 3 & 4 & Class Training
GBR: SB20 Open Championships PRELIMINARY Sailing Instructions


text:
\section{Introduction}
\label{intro}
Graphene is a gapless semiconductor made of a single layer of carbon
atoms arranged into a honeycomb hexagonal lattice. Around the Dirac points,
it has, as first approximation, a conical band structure, so electrons have a zero
effective mass and they exhibit a photon-like behavior.
A physically accurate model for charge transport is given by a semiclassical Boltzmann
equation whose scattering terms have been deeply analyzed in the last decade.
Quantum effects has also been included in the literature but for  Fermi energies high enough, as those considered in this paper,
the interband tunneling effect is practically negligible and the semiclassical approach reveals satisfactory \cite{KaLaMau}.
The aim of this work is to simulate a monolayer graphene on a substrate, as, for
instance, considered in \cite{Hirai}  (see
Figure \ref{gr_sh}), at variance with the case of suspended graphene studied in
\cite{RoMaCo}.
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=0.5\textwidth]{Graphene_on_subs.eps}
\caption{The graphene sheet over a substrate. The spheres represents the impurities.
\label{gr_sh}}
\end{center}
\end{figure}
\\
Usually the available solutions are
obtained with direct Monte Carlo simulations.  The peculiar band structure of graphene requires that the Pauli exclusion principle must be taken into account but  the standard Monte Carlo
approaches suffer from a violation of such a principle because they predict a  maximum occupation number grater than one.  In \cite{RoMaCo} a new Direct Simulation Monte Carlo (DSMC) procedure has been devised in order to overcome such a difficulty and successfully applied to charge transport in suspended monolayer graphene. Comparison with  direct solutions of the electron Boltzmann equation obtained with Discontinuous Galerkin (DG)  methods \cite{Cockburn} have confirmed the validity of the approach \cite{CoMajRo}.

 Apart from the scatterings already present in the suspended case, now  also the effects of the remote phonons  and the impurities of the substrate must be included. The scattering rate between the electrons and the phonons of the substrate is similar to that of the suspended case while the interaction with the impurities adds noticeable additional difficulties, mainly due to the rather involved expression of the dielectric function which is itself a source of theoretical debates \cite{Hwang2007b,Hwang2007}.

We will assume the model proposed in \cite{Hwang2007b}  for the charge-impurities scattering. A crucial parameter is the depth $d$ of the remote impurities. It is of the order of a few angstroms but the exact value can vary from a specimen to another. In \cite{CoMajRo} $d$ has considered constant and the results for several values of $d$ have been compared.

Here we take into account the randomness of the impurities location, related also to the roughness of the interface of the oxide, by considering $d$ a random variable. Various  distributions have been analyzed: uniform and chi-square with several degrees of freedom.

Two different substrates have been tackled: SiO$_2$ and hexagonal boron nitride (h-BN).  In  \cite{Hirai}   HfO$_2$ has been also considered but the analysis at low fields  reveals that it is not an adequate  material because the strong degradation of the mobilities.
Our analysis confirms that the h-BN is a better material than SiO$_2$  on account of the reduced degradation of the mobility and the stability  with respect to the fluctuations of the parameter $d$, even if significant quantitative differences are found with respect to \cite{Hirai}. h-BN assures the higher mobility and its performance  is robust with respect to the randomness of $d$.

The plan of the paper is as follows. In section 2 the semiclassical kinetic model for charge transport in graphene on a substrate is outlined. In section 3 the DSMC is discussed and in the last section  the numerical results are presented and commented.

\section{Semiclassical charge transport in graphene on a substrate}
\label{sec:2}
In a semiclassical kinetic setting, the charge transport in graphene is described by
four Boltzmann equations, one for electrons in the valence ($\pi$) band and one for
electrons in the conductions ($\pi^*$) band, that in turn can belong to the $K$ or $K'$
valley,
\begin{equation}
\frac{\partial f_{\ell,s}(\mathrm{t},\mathbf{x},\mathbf{k}) }{\partial \mathrm{t}} + {\bf v}_{\ell,s} \cdot
\nabla_{{\mathbf{x}}}
f_{\ell,s}(\mathrm{t},\mathbf{x},\mathbf{k})  - \frac{e}{\hbar} {\bf E} \cdot \nabla_{\mathbf{k}}
f_{\ell,s}(\mathrm{t},\mathbf{x},\mathbf{k})
= \left( \dfrac{df_{\ell,s}}{d \mathrm{t}}(\mathrm{t},\mathbf{x},\mathbf{k}) \right)_{coll} ,
\label{transport}
\end{equation}
where $f_{\ell,s}(\mathrm{t},\mathbf{x},\mathbf{k})$ represents the distribution function of charge carriers in
the valley $\ell$  ($K$ or  $K'$), band  $\pi$ or $\pi^*$ ($s = -1$ or $s=1$) at position
${\mathbf{x}}$, time $\mathrm{t}$ and wave-vector ${\mathbf{k}}$.
We denote by $\nabla_{\mathbf{x}}$ and $\nabla_{\mathbf{k}}$ the gradients with respect to the position
and wave-vector, respectively.
The microscopic velocity ${\bf v}_{\ell,s}$ is related to the energy band $\varepsilon_{\ell,s}$
by
$$
{\bf v}_{\ell,s} = \dfrac{1}{\hbar} \, \nabla_{\mathbf{k}} \, \varepsilon_{\ell,s} \, .
$$
With a very good approximation \cite{CaNe} a linear dispersion relation holds for the
energy bands  $\varepsilon_{\ell,s}$ around the equivalent Dirac points; so that
$\varepsilon_{\ell,s} = s \,  \hbar \, v_F \left| \mathbf{k} -\mathbf{k}_{\ell} \right| $, where $v_F$ is the
(constant) Fermi velocity, $\hbar$ is the Planck constant divided by $2 \, \pi$, and
$\mathbf{k}_{\ell}$ is the position of the Dirac point $\ell$ in the first Brillouin zone.
The elementary (positive) charge is denoted by $e$, and ${\bf E}$ is the electric field,
here assumed to be constant.
The right hand side of Eq.~\eq{transport} is the collision term representing the
interaction of electrons with impurities and phonons, the latter due to both the
graphene crystal and substrate \cite{Fang}.
Acoustic phonon scattering is intra-valley and intra-band. Optical phonon scattering is intra-valley
and can be  longitudinal optical ($LO$) and transversal optical ($TO$); it can be intra-band or
inter-band. Scattering with optical phonons of type $K$  pushes electrons from a valley to the other
one (inter-valley scattering).
In addition to the interactions already present in the suspended case, surface optical phonon scattering and charged impurity
(imp) scattering
induced by the substrate are also included.

We assume that phonons are at thermal equilibrium.
The general form of the collision operator can be written as
\begin{eqnarray*}
\left( \dfrac{d f_{\ell,s}}{d \mathrm{t}}(\mathrm{t},\mathbf{x},\mathbf{k}) \right)_{coll}
&=& \sum_{\ell', s'} \left[
\int S_{\ell', s', \ell, s}(\mathbf{k}', \mathbf{k}) \,
f_{\ell',s'}(\mathrm{t},\mathbf{x},\mathbf{k}') \left( 1 - f_{\ell,s}(\mathrm{t},\mathbf{x},\mathbf{k}) \right) d \mathbf{k}'  \right.
\\
&&
\left.  -
\int S_{\ell, s, \ell', s'}(\mathbf{k}, \mathbf{k}') \,
f_{\ell,s}(\mathrm{t},\mathbf{x},\mathbf{k}) \left( 1 - f_{\ell',s'}(\mathrm{t},\mathbf{x},\mathbf{k}') \right) d \mathbf{k}' \right]
\end{eqnarray*}
where the transition rate $\displaystyle S_{\ell', s', \ell, s}(\mathbf{k}', \mathbf{k})$ is given by the sum of
terms of kind
\begin{eqnarray}
&&
\left| G^{(\nu)}_{\ell', s', \ell, s}(\mathbf{k}', \mathbf{k}) \right|^{2} \left[
\left( n^{(\nu)}_{\mathbf{q}} + 1 \right)
\delta \left( \varepsilon_{\ell,s}(\mathbf{k}) - \varepsilon_{\ell',s'}(\mathbf{k}') + \hbar \, \omega^{(\nu)}_{\mathbf{q}}
\right) \right. \nonumber
\\
&&
\left. \mbox{} \hspace{100pt} + n^{(\nu)}_{\mathbf{q}} \,
\delta \left( \varepsilon_{\ell,s}(\mathbf{k}) - \varepsilon_{\ell',s'}(\mathbf{k}') - \hbar \, \omega^{(\nu)}_{\mathbf{q}}
\right) \right]   \label{Scatt}
\end{eqnarray}
related to electron-phonon scatterings and other terms corresponding to the scatterings with
the impurities.

The index $\nu$ labels the $\nu$th phonon mode, $G^{(\nu)}_{\ell', s', \ell, s}(\mathbf{k}', \mathbf{k})$
is the kernel, which describes the scattering mechanism, due to phonons $\nu$, of
electrons belonging to valley $\ell'$ and band $s'$, and electrons belonging to valley $\ell$ and
band $s$.
The symbol $\delta$ denotes the Dirac distribution, $\omega^{(\nu)}_{\mathbf{q}}$ is the
$\nu$th phonon frequency, $n^{(\nu)}_{\mathbf{q}}$ is the Bose-Einstein distribution for the
phonon of type $\nu$
$$
n^{(\nu)}_{\mathbf{q}} = \dfrac{1}{e^{\hbar \, \omega^{(\nu)}_{\mathbf{q}} /k_B T} - 1} \, ,
$$
$k_B$ is the Boltzmann constant and $T$ the constant graphene lattice temperature.
When, for a phonon $\nu_{*}$, $\hbar \, \omega^{(\nu_{*})}_{\mathbf{q}} \ll k_B T$, the
scattering with the phonon $\nu_{*}$ can be assumed elastic.
In this case, we eliminate in Eq.~\eq{Scatt} the term
$\hbar \, \omega^{(\nu_{*})}_{\mathbf{q}}$ inside the delta distribution and we use the
approximation
$n^{(\nu_{*})}_{\mathbf{q}} \approx k_B T / \hbar \, \omega^{(\nu)}_{\mathbf{q}} - \frac{1}{2}$.

We will describe the terms of the collision operator concerning the scatterings with the impurities
in the sequel.
\subsection{The model with only one distribution function}

By applying a gate voltage transversal with respect to the graphene sheet, it is possible to modify the Fermi energy $\varepsilon_F$ and therefore the charge density.
If a high positive value of the
Fermi energy is considered, the electrons responsible for the current are those belonging to the conduction band. Therefore, only the transport equation for electrons in the
conduction band is considered and interband electron transitions are neglected.  Moreover
the valleys $K$ and $K'$ are considered as equivalent.
A reference frame centered in the $K$-point  will be used.
Of course, we simplify the notation, omitting the indexes $s$ and $\ell$ and denoting by $f$ the only relevant distribution function.

The expressions of the electron-phonon scattering matrices  used in our simulations are as follows.
\\
For acoustic phonons, usually one considers the elastic approximation, and therefore
\begin{equation}
\left( 2 \, n^{(ac)}_{\mathbf{q}} + 1 \right)
\left| G^{(ac)}(\mathbf{k}', \mathbf{k}) \right|^{2} = \dfrac{1}{(2 \, \pi)^{2}} \,
\dfrac{\pi \, D_{ac}^{2} \, k_{B} \, T}{2 \hbar \, \sigma_m \, v_{p}^{2}}
\left( 1 + \cos \vartheta_{\mathbf{k} \, , \mathbf{k}'} \right) ,
\label{transport_acoustic}
\end{equation}
where $D_{ac}$ is the acoustic phonon coupling constant, $v_{p}$ is the sound speed in graphene,
$\sigma_m$ the graphene areal density,
and $\vartheta_{\mathbf{k} \, , \mathbf{k}'}$ is the convex angle between $\mathbf{k}$ and ${\mathbf{k}'}$.
\\
There are three relevant optical phonon scatterings: the longitudinal optical ($LO$), the transversal
optical ($TO$) and the ${K}$  phonons.
The electron-phonon scattering matrices are
\begin{eqnarray}
\left| G^{(LO)}(\mathbf{k}', \mathbf{k}) \right|^{2} & = &
\dfrac{1}{(2 \, \pi)^{2}} \, \dfrac{\pi \, D_{O}^{2}}{\sigma_m \, \omega_{O}}
\left( 1 - \cos ( \vartheta_{\mathbf{k} \, , \mathbf{k}' - \mathbf{k}} + \vartheta_{\mathbf{k}' \, , \mathbf{k}' - \mathbf{k}} ) \right)
\label{GLO}
\\
\left| G^{(TO)}(\mathbf{k}', \mathbf{k}) \right|^{2} & = &
\dfrac{1}{(2 \, \pi)^{2}} \, \dfrac{\pi \, D_{O}^{2}}{ \sigma_m \, \omega_{O}}
\left( 1 + \cos ( \vartheta_{\mathbf{k} \, , \mathbf{k}' - \mathbf{k}} + \vartheta_{\mathbf{k}' \, , \mathbf{k}' - \mathbf{k}} ) \right)
\label{GTO}
\\
\left| G^{(K)}(\mathbf{k}', \mathbf{k}) \right|^{2} & = &
\dfrac{1}{(2 \, \pi)^{2}} \, \dfrac{2 \pi \, D_{K}^{2}}{\sigma_m \, \omega_{K}}
\left( 1 - \cos \vartheta_{\mathbf{k} \, , \mathbf{k}'} \right) ,
\label{GK}
\end{eqnarray}
where $D_{O}$ is the optical phonon coupling constant, $\omega_{O}$ is the optical phonon frequency,
$D_{K}$ is the K-phonon coupling constant and $\omega_{K}$ is the $K$-phonon frequency.
The angles $\vartheta_{\mathbf{k} \, , \mathbf{k}' - \mathbf{k}}$ and $\vartheta_{\mathbf{k}' \, , \mathbf{k}' - \mathbf{k}}$ denote
the convex angles between $\mathbf{k}$ and $\mathbf{k}' - \mathbf{k}$  and between $\mathbf{k}'$ and  $\mathbf{k}' - \mathbf{k}$,
respectively. \\
Due to the presence of  the substrate, we must also include the interactions between the electrons of
the graphene sheet and the remote phonons and impurities of the substrate.
The electron-phonon scattering matrices  have the same form of \eq{GLO} and
\eq{GTO}.
Regarding the remote impurity scattering, we assume that they stay in a plane at distance
$d\, \, $ from the graphene sheet.
The definition of the transition rate for electron-impurity scattering is highly complex; so many
approximate models are proposed.
Following \cite{Hwang2007b}, we adopt the transition rate
\begin{equation}
S^{(imp)}(\mathbf{k}, \mathbf{k}') = \dfrac{2 \pi}{\hbar}  \, \dfrac{n_{i}}{(2 \, \pi)^{2}}
\left| \dfrac{V_{i}(|\mathbf{k} - \mathbf{k}'|, d)}{\epsilon(|\mathbf{k} - \mathbf{k}'|)} \right|^{2}
\dfrac{\left(1 + \cos \vartheta_{\mathbf{k} \, , \mathbf{k}'} \right)}{2}
\delta \left( \varepsilon(\mathbf{k}') - \varepsilon(\mathbf{k}) \right) ,
\end{equation}
where
\begin{itemize}
\item[a)]
$n_{i}$  is the number of impurities per unit area.
\vskip 0.3cm
\item[b)]
$\displaystyle V_{i}(|\mathbf{k} - \mathbf{k}'|, d) = 2 \, \pi e^{2} \,
\dfrac{\exp(- \, d \, |\mathbf{k} - \mathbf{k}'|)}{\tilde{\kappa} \, |\mathbf{k} - \mathbf{k}'|}$
\begin{itemize}
\vskip 0.3cm
\item
$d$ is the location of the charged impurity measured from the graphene sheet
\item
$\displaystyle \tilde{\kappa}$ is the effective dielectric constant, defined by
$\displaystyle 4 \pi  \epsilon_{0} \left( \kappa_{top} + \kappa_{bottom}  \right) / 2$, where $\epsilon_{0}$
is the vacuum dielectric constant and $\kappa_{top}$ and $\kappa_{bottom}$ are the relative
dielectric constants of the medium above and below the graphene layer.
For example, if the materials are SiO$_{2}$ and air one has
$\displaystyle \tilde{\kappa} = 4 \pi  \epsilon_{0}  \left( 1 + \kappa_{SiO_{2}} \right) / 2 \approx 4 \pi \times 2.45 \,
\epsilon_{0}$. For the other material see Table  \ref{Cost_fis_sub}.
\end{itemize}
\vskip 0.3cm
\item[c)]
\begin{small}
$\displaystyle \epsilon(|\mathbf{k} - \mathbf{k}'|) = \left\{
\begin{array}{ll}
 1 + \dfrac{q_{s}}{|\mathbf{k} - \mathbf{k}'|} - \dfrac{\pi \, q_{s}}{8 \, k_{F}} \hfill
  \mbox{if  \,\,} |\mathbf{k} - \mathbf{k}'| < 2 \, k_{F} &
\\[15pt]
 1 + \dfrac{q_{s}}{|\mathbf{k} - \mathbf{k}'|} -
 \dfrac{q_{s} \sqrt{|\mathbf{k} - \mathbf{k}'|^{2} - 4 \, k_{F}^{2}}}{2 \, |\mathbf{k} - \mathbf{k}'|^{2}} -
 \dfrac{q_{s}}{4 \, k_{F}} \, \mbox{asin} \left( \dfrac{2 \, k_{F}}{|\mathbf{k} - \mathbf{k}'|} \right)
 \hfill \mbox{otherwise}&
\end{array}
\right.
$
\end{small}
\vskip 0.3cm
is the 2D finite temperature static random phase approximation (RPA) dielectric (screening) function appropriate for
graphene;
\begin{itemize}
\item
$\displaystyle q_{s} = \dfrac{4 \, e^{2} \, k_{F}}{\tilde{\kappa} \, \hbar \, v_{F}}$
is the effective Thomas-Fermi wave-vector for graphene; it can be rewritten in terms of the dimensionless Wigner-Seitz radius $ r_S$ as
$\displaystyle q_{s} = 4 r_S k_F$;
\item
$\displaystyle k_{F} = \dfrac{\varepsilon_F}{\hbar v_F}$  is the Fermi wave-vector.
\end{itemize}
\end{itemize}
$d$ is usually fixed once for all in each simulation. However, it is more realistic to assume that $d$ can vary because the impurities are implanted with a certain degree of uncertainty in their location.
As already shown in \cite{CoMajRo}, $d$ is crucial for a correct prediction of the electron velocity, and therefore, in turn, of the electron  mobilities. In the present paper we assume that $d$ is a random variable. A uniform distribution and chi-square distributions with several degree of freedom will be considered. The choice of the latter ones is due to their flexibility
to model the distance of the impurities with a realistic unlikely value of $d$ close to zero.

We close this section evaluating the transition rates (collision frequencies) associated to the scattering mechanisms introduced above.
For the $A$th type of scattering the  transition rate is defined as
$$
\Gamma_A (\mathbf{k}) =  \int S_A (\mathbf{k}, \mathbf{k}') \: d \mathbf{k}'
$$
and depends on $\mathbf{k}$ only through the energy, that is indeed $\Gamma_A (\mathbf{k}) = \Gamma_A  (\varepsilon)$.

For the acoustic phonon scattering we get
\begin{eqnarray*}
\Gamma_{ac}  (\varepsilon) = \dfrac{ D_{ac}^{2} \, k_{B} \, T}{4 \hbar^3  \,  v_F^2 \, \sigma_m \, v_{p}^{2}} \,\, \varepsilon \label{rate_ac}
\end{eqnarray*}
while for the total optical phonon scattering, given by the sum of the longitudinal and transversal contribution,  we have
\begin{eqnarray*}
\Gamma_{op}  (\varepsilon) = \dfrac{D_{O}^{2}}{ \sigma_m \, \omega_{O} \hbar^2 \, v_F^2} \left[\left(\varepsilon -   \hbar \, \omega_{O} \right) \left( n^{(O)}_{\mathbf{q}} + 1 \right) H (\varepsilon  +   \hbar \, \omega_{O}) +        \left(\varepsilon + \hbar \, \omega_{O} \right) \, n^{(O)}_{\mathbf{q}} \right], \label{rate_op}
\end{eqnarray*}
where the fact that the coupling constants are the same for  both the longitudinal and the transversal optical phonons has been used. In Eq.~\eq{rate_op} $H$ is the Heaviside function and $n^{(O)}_{\mathbf{q}} $ the equilibrium optical phonon distribution.

The expression of the transition rate for the $K$ phonon scattering is the same as for the optical phonon
\begin{eqnarray*}
\Gamma_{K}  (\varepsilon) = \dfrac{D_{K}^{2}}{ \sigma_m \, \omega_{K} \hbar^2 \, v_F^2} \left[\left(\varepsilon -   \hbar \, \omega_{K} \right) \left( n^{(K)}_{\mathbf{q}} + 1 \right) H (\varepsilon -   \hbar \, \omega_{K}) +        \left(\varepsilon + \hbar \, \omega_{K} \right) \, n^{(K)}_{\mathbf{q}} \right]. \label{rate_K}
\end{eqnarray*}
Above $n^{(K)}_{\mathbf{q}} $ is the equilibrium $K$ phonon distribution.
At last the transition rate for the impurity scattering, due to the rather involved expression, has to be evaluated numerically. Following a standard procedure, the following correction is adopted
\cite{Lund}
\begin{eqnarray}
\Gamma_{imp}  (\mathbf{k}) = \int S^{(imp)}   (\mathbf{k}, \mathbf{k}') \left( 1 - \cos \vartheta_{\mathbf{k} \, , \mathbf{k}'} \right)  \: d \mathbf{k}'.
\end{eqnarray}
The physical parameters for the scattering rates are summarized in Tables \ref{tabella}, \ref{Cost_fis_sub} and are the same as in \cite{Hirai}.
\begin{table}[h]
\caption{Physical parameters for the scattering rates in pristine graphene.}
\label{tabella}
\centering
\begin{tabular}{||l|c||l|c||}
\hline & & & \\[-10pt]
$v_{F}$ & $10^{8}$ cm/s & $v_{p}$ & $2 \times 10^{6}$ cm/s \\[2pt]
\hline & & & \\[-10pt]
$\sigma_{m}$ & $7.6 \times 10^{-8}$ g/cm$^{2}$ & $D_{ac}$ & $6.8$ eV \\[2pt]
\hline & & & \\[-10pt]
$\hbar \, \omega_{O}$ & $164.6$ meV & $D_{O}$ & $10^{9}$ eV/cm \\[2pt]
\hline & & & \\[-10pt]
$\hbar \, \omega_{K}$ & $124$ meV & $D_{K}$ & $3.5 \times 10^{8}$ eV/cm \\[2pt]
\hline
\end{tabular}

\end{table}

\begin{table}[!ht]
\centering
\caption{Physical parameters for the scattering rates related to the substrates.}
\label{Cost_fis_sub}
\begin{tabular}{||c||cc||}
\cline{2-3}
\multicolumn{1}{c||}{} & \multicolumn{1}{c}{SiO$_2$} & \multicolumn{1}{c||}{h-BN} \\
\hline
$\hbar\omega_{op-ac}$ & 55 meV  & 200 meV \\ [2pt]
\hline
$D_f$ & 5.14 $\times 10^7$ eV/cm  & 1.29 $\times 10^9$ eV/cm \\ [2pt]
\hline
$n_i$ & 2.5 $\times 10^{11} $ cm$^{-2}$ & 2.5 $\times 10^{10} $ cm$^{-2}$ \\
\hline
$\kappa_{bottom}$  & 3.9 &  3\\[2pt]
\hline
\end{tabular}
\end{table}
We look for spatially homogeneous solutions to Eq.~\eq{transport} under  a constant applied electric field.
In such a case the transport equation reduces to
\begin{eqnarray}
&&
\dfrac{\partial f(\mathrm{t},\mathbf{k})}{\partial \mathrm{t}} -
\dfrac{e}{\hbar} \, \mathbf{E} \cdot \nabla_{\mathbf{k}} f(\mathrm{t},\mathbf{k}) =
\int S(\mathbf{k}', \mathbf{k}) \, f(\mathrm{t},\mathbf{k}') \left( 1 - f(\mathrm{t},\mathbf{k}) \right) d \mathbf{k}' \nonumber
\\
&&
\hspace{106pt} -
\int S(\mathbf{k}, \mathbf{k}') \, f(\mathrm{t},\mathbf{k}) \left( 1 - f(\mathrm{t},\mathbf{k}') \right) d \mathbf{k}' \, .
\label{bulk}
\end{eqnarray}
As initial condition, we take a Fermi-Dirac distribution,
$$
f(0, \mathbf{k}) = \dfrac{1}{1 + \exp \left( \dfrac{\varepsilon(\mathbf{k}) - \varepsilon_F}{k_{B} \, T} \right)} ,
$$
where $T = 300\, \, $ K is the room lattice temperature which will be kept constant.

\section{DSMC method}
We have  also used,  for solving the transport equation \eq{transport}, the ensemble DSMC method recently proposed in \cite{RoMaCo}.
The $\mathbf{k}$-space is approximated by the set $[-k_{x \, max}, k_{x \, max}] \times [-k_{y \, max}, k_{y \, max}]$ with $k_{x \, max}$ and $k_{y\, max}$ such that the number of electrons  with a wave-vector $\mathbf{k}$ outside such a set is practically negligible. The  $\mathbf{k}$-space  is partitioned into a uniform rectangular grid. We shall denote by $C_{ij}$ the generic cell of the grid centered at the
$\mathbf{k}_{ij}$ wave-vector.

The distribution function is approximated with a piecewise constant function in each cell. Initially the $n_P$ particles used for the simulation are distributed in each cell according to the equilibrium Fermi-Dirac distribution.

The motion of each particle alternates free-flight and scattering. The latter is the most involved and delicate part and in graphene it is particularly important to include the PEP. This implies a heavy computational cost and, more importantly, requires a continuous update of the distribution function.

In the standard approach the free-flight is performed  according to the semiclassical equation of motion
\begin{eqnarray}
\hbar \dot{\mathbf{k}} = - e \,  \mathbf{E}.
\end{eqnarray}

The time interval $\Delta \mathrm{t}$ is chosen for each particle in a random way by
\begin{eqnarray}
\Delta \mathrm{t} = - \frac{\ln \xi}{\Gamma_{tot}}, \label{time_free_flight}
\end{eqnarray}
$\xi$ being a random number with uniform distribution in the interval $[0,1]$ and
$\Gamma_{tot}$ being the total scattering rate (see for example \cite{JacLug})
$$
\Gamma_{tot}  = \Gamma_{ac} (\varepsilon (\mathrm{t}) ) + \Gamma_{op} (\varepsilon (\mathrm{t}) ) + \Gamma_{K} (\varepsilon (\mathrm{t}) ) + \Gamma_{imp} (\varepsilon (\mathrm{t}) ) + \Gamma_{ss} (\varepsilon (\mathrm{t}) ).
$$
$\Gamma_{ss}$, called {\em self-scattering rate},  is the scattering rate associated to a fictitious scattering that does not change the state of the electron. It is introduced so that    $\Gamma_{tot}$ is constant leading to the simple relation (\ref{time_free_flight}). To fix the value of $\Gamma_{tot}$ one considers the range of the energy involved in the simulation and takes the maximum value $ \Gamma_M$ of the sum
$\Gamma_{ac} + \Gamma_{op} + \Gamma_{K} +  \Gamma_{imp}$. $\Gamma_{tot}$ is then set equal to $\alpha \Gamma_M$ with $\alpha > 1$ a tuning parameter, e.g. $\alpha = 1.1$.

Since the range of  $\Gamma_{ac}$,  $\Gamma_{op}$,  $\Gamma_{K}$, $ \Gamma_{imp}$  can be very large, in order to reduce the  computational cost,
a good variant is to use a variable  $\Gamma_{tot}$ which depends on the energy $\varepsilon (\mathrm{t})$ of the considered  particle at the current  time $\mathrm{t}$
$$
\Gamma_{tot} = \alpha \left(\Gamma_{ac} (\varepsilon (\mathrm{t}) ) + \Gamma_{op} (\varepsilon (\mathrm{t}) ) + \Gamma_{K} (\varepsilon (\mathrm{t}) ) \right).
$$
 We will use this procedure and set $\alpha = 1.1$ in our simulations.

After the free-flight the scattering is selected randomly according to the values of the transition rates, and PEP  is taken into account as in \cite{Lugli}. Once the state after the scattering has been determined, let us denote  by $\mathbf{k}'$ its wave-vector, the initial state is changed or left the same with a rejection technique:  a random number $\xi$ is generated uniformly in $[0, 1]$ and if $\xi < 1 - f(\mathbf{k}')$ the transition is accepted,  otherwise it is rejected. Then,
according to the angular distribution of the scattering rate, a rejection method allows to select the angular dependence of the wave-vector after the scattering event.

At  fixed times the momentum, velocity, energy of each electron are recorded and the mean values are evaluated along with the distribution of electrons among the cells in the $\mathbf{k}$-space in order to follow the time evolution of the system.

The maximum number $n_{ij}^{*}$ of simulated particles accommodated in each cell  is easily evaluated (see \cite{Lugli}). Let $N_{ij}$ be the number of real particles in the cell $C_{ij}$ and let $n_{ij}$ be the number of simulated particles in the  same cell.  Let $A$ be the area of the sample and  let $N$ be the number of real particles
in the sample, $N = \rho A$. By observing that $N/n_p$ is the statistical weight of each particle entering the simulation and taking into account the condition
$0 \le f \le 1$, one has
\begin{eqnarray}
n_{ij} &=& \frac{N_{ij}}{N} n_P = \frac{n_P}{N }\frac{2}{(2 \pi)^2} A \int_{C_{ij}} f \, d\, {\bf k} \le \frac{n_P}{N } \frac{2}{(2 \pi)^2} A \int_{C_{ij}} d\, {\bf k} \nonumber\\
& = &\frac{2}{(2 \pi)^2} \mbox{meas} ({C_{ij}}) \frac{n_P}{N} A = \frac{2}{(2 \pi)^2} \mbox{meas} ({C_{ij}}) \frac{n_P}{\rho} = n_{ij}^{*},
\end{eqnarray}
where  $\mbox{meas} ({C_{ij}})$ is the measure of the cell $C_{ij}$. Of course $n_{ij}^{*}$ is not in general an integer, therefore rounding errors are introduced. Usually the problem is solved by using a number of simulated particles $n_P$ great enough to make  such errors negligible. The convergence of the procedure is often checked just by comparing the results with different $n_P$.

The main concern with the procedure delineated above is that, according to the semiclassical approximation, the compatibility with Pauli's exclusion principle of the positions occupied during the free flight is not checked. {\em It may occur that the particle at the end of the free-flight reaches a cell in the $\mathbf{k}$-space already fully occupied making the occupation number greater than one} (see \cite{RoMaCo}).

The fact that, for high values of the Fermi energy, the maximum occupation number can greatly exceed the maximum one is of course unphysical, although the average quantities could be acceptable according to the large number law.
Even if the scattering can redistribute  the particles among  the cells, in general it is not  possible to eliminate the presence of anomalous occupation numbers.

For overcoming the problem, in \cite{Reggiani} it has been proposed to apply the rejection technique not only to the scattering event but also at the end of each free-flight. However,  even implementing this  variant, the same drawbacks are still present as shown in \cite{RoMaCo}.

In order to avoid such a difficulty,  in  \cite{RoMaCo} the following approach has been proposed.   The crucial point in the previous procedure is the  step concerning the free-flight. If we go back to the original transport equation, we can use a splitting scheme to avoid unphysical results. The basic idea is to reformulate the splitting method in terms of a particle method.

In  a time interval $\Delta \mathrm{t}$, first we solve  the drift part of the equation corresponding to the free-flight  in the analogous DSMC approach,
\begin{equation}
\frac{\partial f (\mathrm{t},\mathbf{x},\mathbf{k}) }{\partial \mathrm{t}}   - \frac{e}{\hbar} {\bf E} \cdot \nabla_{\mathbf{k}} f (\mathrm{t},\mathbf{x},\mathbf{k})
= 0,
\label{transport_drift}
\end{equation}
taking as initial condition the distribution at time $\mathrm{t}$,
and then the collision part
\begin{equation}
\frac{\partial f (\mathrm{t},\mathbf{x},\mathbf{k}) }{\partial \mathrm{t}} = \left. \dfrac{d f}{d \mathrm{t}}(\mathrm{t},\mathbf{x},\mathbf{k}) \right|_{coll} \, ,
\label{transport_coll}
\end{equation}
taking as initial condition the solution of Eq.~\eq{transport_drift}. The global procedure gives a numerical approximation of $f (\mathrm{t} + \Delta \mathrm{t},\mathbf{x},\mathbf{k})$ up to first order in $\Delta \mathrm{t}$.
The solution of Eq.~\eq{transport_drift} is just a {\em rigid} translation of the distribution function along the characteristics and can be reformulated from a particle point of view as a free-flight of the same duration for each electron. In this way, the cells in the $\mathbf{k}$-space are moved of the displacement vector $\hbar \Delta \mathbf{k} = - e \,  \mathbf{E} \, \Delta \mathrm{t}$ but without changing the occupation number of the cells themselves. To avoid  considering a computational domain as too large,  we adopt a Lagrangian approach and  move the grid by adapting it to the new position of the cells instead of moving the cells.

Eq.~\eq{transport_coll} is solved by considering a sequence of collision steps for each particle during the time interval $[\mathrm{t}, \mathrm{t} + \Delta \mathrm{t}]$ in a standard way: choice of the scattering, including also the self one, and selection of the final state. Since the collision mechanisms take into account PEP, the occupation number cannot exceed the maximum occupation number  in this second step as well.
Hence, neither the drift nor the collision step give rise to the possibility of having,  in a single cell, more particles than the maximum occupation number.

The overall scheme  is a hybrid approach which furnishes a first order in time approximation of the distribution function. Average quantities can be evaluated as well by taking the mean values of the quantities of interest, e.g. velocity and energy.

\section{Numerical results}

We consider a surface impurity density according to Table \ref{Cost_fis_sub}.
 The simulations are performed at several values of the electric field and Fermi energy.

 In order to validate the simulation approach, we numerically solve, in the case of constant $d$, the Boltzmann equation by using also a discountinuos Galerkin (DG) method (see \cite{CoMajRo} for the details) obtaining an excellent agreement.

 $d$ should of the order of few angstroms. In the literature a range from 0 to 1 nm is considered. At variance with \cite{CoMajRo} $d$ is considered a random variable. Therefore in the simulation whenever a  scattering with impurities occurs $d$ is generated according to the chosen distribution. For comparison, the cases with fixed $d$ are also shown along with the solutions obtained by the DG-method.

 Mass conservation implies that the charge density $\rho$, given by
\begin{eqnarray}
\rho  =  \dfrac{2}{(2 \, \pi)^{2}} \int f(\mathrm{t}, \mathbf{k})  \, \: d \mathbf{k} \, ,
\end{eqnarray}
 is constant in time.

We choose a reference frame  such that only the $x-$component of the
electric field is different from $0$; therefore only the $x-$component of the mean velocity is relevant.
10$^{5}$  particles have been used for the DSMC.

In Figs.~\ref{confronto3_5kV}-\ref{confronto2_dvar_1}, we show the numerical results of the average velocity
$\mathbf{v}$ defined as
\begin{equation}
\mathbf{v}(\mathrm{t}) = \dfrac{2}{(2 \, \pi)^{2} \, \rho} \int f(\mathrm{t}, \mathbf{k}) \dfrac{1}{\hbar} \, \nabla_{\mathbf{k}}
\, \varepsilon(\mathbf{k}) \: d \mathbf{k} \, ,
\end{equation}
The velocity is related to the current $\mathbf{J}$ by the relation
$$
\mathbf{J} = - e  \rho \mathbf{v}
$$
and, in turn, $\mathbf{v}$ is related to the mobility $\mu (\mathbf{E})$ as follows
$$
\mathbf{v} = \mu (\mathbf{E} ) \mathbf{E}.
$$
Therefore, from the analysis of the average velocity it is possible to estimate the effect of the impurities on the mobility.
It is expected that the scattering with the remote impurities leads to a degradation of the mobility depending on the specific material.

First we have assessed the general performance of the different materials, by a comparison of the average velocity for three different values of $d$ kept constant. \begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{Velocity_5KV_04eF_0dimp.eps}\\[10pt]
\includegraphics[width=0.5\textwidth]{Velocity_5KV_04eF_05dimp.eps}\\[10pt]
\includegraphics[width=0.5\textwidth]{Velocity_5KV_04eF_1dimp.eps}
\caption{
Comparison of the average velocity  versus time for $d =0$ (top) , $0.5$, $1$ (bottom) nm
 in the case of an applied
electric field of 5 kV/cm and Fermi energy $\varepsilon_F = 0.4$ eV.
\label{confronto3_5kV}}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{Velocity_10KV_04eF_0dimp.eps}
\includegraphics[width=0.5\textwidth]{Velocity_10KV_04eF_05dimp.eps}\\[10pt]
\includegraphics[width=0.5\textwidth]{Velocity_10KV_04eF_1dimp.eps} t
\caption{
Comparison of the average velocity  versus time for $d =0$ (top) , $0.5$, $1$ (bottom) nm
 in the case of an applied
electric field of 10 kV/cm and Fermi energy $\varepsilon_F = 0.4$ eV.
Both the results obtained by using the Monte Carlo (MC) and the discontinuous Galerkin methods (DG)  are reported.
\label{confronto3_10kV}}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{Velocity_10KV_04eF_uniform-dimp.eps}\includegraphics[width=0.5\textwidth]{Velocity_10KV_04eF_2_05gamma-dimp.eps} \\[10pt]
\includegraphics[width=0.5\textwidth]{Velocity_10KV_04eF_3_05gamma-dimp.eps}\includegraphics[width=0.5\textwidth]{Velocity_10KV_04eF_4_05gamma-dimp.eps}
\caption{
Comparison of the average velocity versus time in the case of an applied
electric field of 10 kV/cm and Fermi energy $\varepsilon_F = 0.4$ eV by considering different distribution for $d$:
uniform (top left), $\Gamma(2,0.5)$  (top right),  $\Gamma(3,0.5)$ (bottom left),
$\Gamma(4,0.5)$ (bottom right). In the results obtained with the discontinuous Galerkin methods (DG)  we have assumed $d$ equal to the mean values of the corresponding distribution rescaled by the factor 0.2 nm.
\label{confronto2_dvar_1}}
\end{center}
\end{figure}

We can observe that the values of the average velocity and energy become  lower by reducing the distance  $d$ from the impurities in the oxide,  confirming the degradation of the mobility due to the substrate as  a direct consequence of the additional scatterings with the remote  impurities. For the higher value of $d$,  which is very close to the pristine case, both SiO$_2$ and h-BN produce of course the same effect with a comparable electron velocity. For the intermediate value of $d$
h-BN performs better than  SiO$_2$ and this behaviour is even more evident for $d=1$. Therefore,  h-BN gives a better high-field mobility, in  qualitative agreement with the low field analysis in \cite{Hirai}.

The previous results, however, do not take into account the intrinsic noise in the location of the impurities. In order to assess its effect on the high-field mobility, we have performed some simulations with a random $d$ generated, in each scattering involving impurities, according to a prescribed probability distribution (see Fig. \ref{confronto2_dvar_1}). First we have considered a uniform distribution in the interval $[0, 1]$ (in nm). The results are similar to the case with constant  $d = 0.5$ nm and this can be explained by observing that 0.5 is the expectation value. Then we have considered a $\Gamma (\alpha, \lambda)$ distribution
$$
f(x) = \left\{
\begin{array}{ll}
\dfrac{1}{\lambda \Gamma (\alpha)} x^{\alpha - 1} e^{x/ \lambda} & x > 0\\
0 & x \le 0
\end{array}
\right.
$$
where $\Gamma (\alpha)$ is the Euler gamma function. We have used the values $\lambda = 0.5$ and $\alpha = 2, 3, 4$  (see Fig. \ref{chi2})  and rescaled $d$ by a factor 0.5 nm in order to have a values less than 1 with very high probability, as confirmed by the simulation.

In order to validate our findings, the results obtained by using the DG-method in \cite{CoMajRo} but with a valued of $d$ set equal to the mean values of the considered distribution ($\alpha \lambda$ for the $\Gamma (\alpha, \lambda)$ one) rescales by the factor 0.2 nm. The agreement is still excellent.

We would like to conclude by observing that both the materials
 seem only slightly  influenced by the stochastic effect related to the randomness of the impurity positions.
\begin{figure}
\begin{center}
\includegraphics[width=0.6\textwidth]{Prob_gamma.eps}
\caption{ Plot of the $\Gamma (\alpha, \lambda)$ distribution with  $\lambda = 0.5$ and $\alpha = 2, 3, 4$. Note that the probability to generate a number greater than 5 is practically
zero.
\label{chi2}}
\end{center}
\end{figure}

\section{Conclusions}
An analysis of the high-field mobility has been performed in graphene on a substrate by a new DSMC approach which properly takes into account the Pauli exclusion principle. The same substrates as in \cite{Hirai} have been considered but with the  more elaborate model for the charge-impurities scattering proposed in  \cite{Hwang2007b}.  Moreover, also the random distribution of the depth of the impurities implanted in the oxide has been taken into account
and described with several theoretical probability distributions.

The differences among the average velocities for the considered substrates  are in agreement with the expected effects and confirm a degradation of the mobility.  As already found out in \cite{Hirai} for the low field mobility, h-BN reveals a better substrate than SiO$_2$ because produce a smaller degradation also in the high-field mobility.

redpajama_set_name: RedPajamaArXiv


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text:
Tags: church and state, Education, Religious Freedom, The Year in Quotes
The Year in Quotes: Religious Freedom
Threats to religious freedom — and the constitutional protections for that freedom — were evident in much of the far right's political rhetoric in 2010. Some right-wing politicians even sought to turn religion and government into enemies by using faith as a political weapon. You can read more of our review of what the far right had to say in 2010 here and here.
"Our country was founded on religious principles … and our students will know that. . . . I think the [Founding Fathers] fully intended that our government would not separate church and state."
— Gail Lowe, chair of the Texas State Board of Education, talking about new social studies curriculum standards for public schools, North Texas Daily, September 20, 2010
"The exact phrase 'separation of church and state' came out of Adolf Hitler's mouth. That's where it comes from. So next time your liberal friends talk about the separation of church and state, ask them why they're Nazis."
— Glen Urquhart, Republican congressional candidate from Delaware, Washington Post, April 2010
"WE [sic] elected a house [sic] with Christian, conservative values. We now want a true Christian, conservative running it."
— John Cook, an elected State Republican Executive Committee member, explaining his opposition to current Texas House of Representatives Speaker Joe Straus, R-San Antonio, who happens to be Jewish, Texas Observer, November 30, 2010
"That's the question: Who do you worship? Do you believe in the primacy of unrestrained federal government? Or do you worship the God of the universe, placing our trust in him?"
— Texas Governor Rick Perry, painting the upcoming election as a religious crusade to take back the soul of the country during a Thursday night speech to Republican faithful and delegates to the Texas Republican state convention, Dallas Morning News, June 10, 2010
"And these programs that you mentioned — that Obama has going with Reid and Pelosi pushing them forward — are all entitlement programs built to make government our God. And that's really what's happening in this country is a violation of the First Commandment. We have become a country entrenched in idolatry, and that idolatry is the dependency upon our government. We're supposed to depend upon God for our protection and our provision and for our daily bread, not for our government."
— Nevada U.S. Senate candidate Sharron Angle, a Tea Party favorite claiming that Democrats are violating the Bible's First Commandment by trying to turn government into a god, Las Vegas Sun, August 4, 2010
"If we do not do something, we will not have any Protestants in government."
— Oklahoma state Rep. Todd Russ, R-Cordell, sponsor of a bill on Bible classes in the state's public schools. Cordell's statement came after it was pointed out that only one member of the current U.S. Supreme Court is a Protestant Christian — the others are Roman Catholic and Jewish, Tulsa World, April 8, 2010
"Go back to what our founders and our founding documents meant, they're quite clear that we would create law based on the God of the Bible and the Ten Commandments. . . . What in hell scares people about talking about America's foundation of faith? . . . It is that world view that involves some people being afraid of being able to discuss our foundation, being able to discuss God in the public square, that's the only thing I can attribute it to is some fear of some people."
— Former vice presidential nominee and religious-right idol Sarah Palin, discussing her version of American history and law on Bill O'Reilly's Fox News show, TFN Insider, May 10, 2010
"We have dropout rates. If they get God in school and everything, young people will know they can accomplish anything they want to."
— Roy Brown, a supporter of a bill that would require the Arkansas Department of Education to create a Bible class curriculum for use in the state's schools, WREG-TV (Memphis), December 9, 2010
The Year in Quotes: ScienceThe Year in Quotes: Muslim Bashing
3 thoughts on "The Year in Quotes: Religious Freedom"
james_breck says:
The thing that really ticks me off is that it's no longer possible to correspond with Lowe, Dumbar, McLeroy and the other theocratic scum on the SBOE via email- they no longer have individual SBOE email addresses or any other current email addresses that I can find. I guess they just tired of being fed real, factual, historical information about the Constitutional prohibition on the establishment of religion. And so they had to escape the world of email; they're like a bunch of little kids putting their hands over there ears and chanting "dadadadada I can't hear you." Of course young kids aren't traitors to their country like this bunch of religious right vermin.
Religious freedom. During the past year, I have noted a decided thematic shift on the Religious Right and the extreme radical right. The new theme is: Lost Freedom. Yes, that's the one. The federal government is evil because it takes away our most cherished American freedoms. The key idea here is to weaken the federal government while simultaneously strengthening state and local governments. For example, the federal government would not allow Beverly Baptist Church to take control of your local school system. However, if you invoke the old Confederate principle of "states rights," your town can elect 10 Southern Baptists to the local school board, and Beverly will be given control. Screw every other denomination and religion in town.
I have been pondering this concept of once great American freedoms that have been viciously stolen from the people by a Federal government spinning out of control. Therefore, I thought it might be worthwhile to actually name and illustrate the great freedoms that have been taken from us. Here is the first lost American freedom:
The Freedom to Lie and Mislead Unto Death
http://www.youtube.com/watch?v=gCMzjJjuxQI&feature=related
Very perceptive of you Charles. And isn't it ironic that two of the leading theocratic "family" oriented "Christian" groups, the Family Research Council and the American Family Association, have been officially designed hate groups by the Southern Poverty Law Center due to their incessant bashing of gays. Yes, brothers and sisters, step into the house of mirrors and feel that warm Christian love coming from Tony Perkins and Donald Wildmon for their fellow man.


text:
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Stories from Scotland: Kelvingrove Sets the Tone
By Cassandra Hannahs | January 13, 2016
Cruising Loch Lomond. Credit: Janice Gimbel
There we encountered several classic sites of Scottish memory that had been introduced at Kelvingrove. On the slopes of Glencoe, we remembered the mid-winter massacre of Clan MacDonald in 1692.
At the Battlefield and Visitor Centre of Culloden, we gained firsthand knowledge of the weapons wielded by the Jacobite troops in 1746.
Dunrobin Castle. Credit: Chris Miller
And at Dunrobin Castle, we wandered the rooms, gardens and private museum of the Sutherland family seat. As we'd learned, the Sutherland's treatment of their tenants during the Clearances contrasted sharply with the fairy-tale elegance of their home. But the tragedies evoked at Kelvingrove of Glencoe, Culloden and the Clearances and reinforced on our journey were offset by more positive images. Tassie's portrait medallions and Donald Dewar's bust at the museum called to mind the achievements of the Scottish Enlightenment in the eighteenth century and the return of Scotland's parliament of Edinburgh in the twentieth. And the irreverence we sensed at the museum never flagged during our trip. Everyone we met -- from the falconer at Dunrobin to the shepherd at Kincraig to our whiskey specialists at Pitlochry and Edinburgh -- all seemed to relish a certain very Scottish disregard for conventions. Even the sweet-voiced grandmother in the cèilidh band who sang traditional songs for us had mischief in her eye, relating local plots to topple and demolish the giant statue of the Duke of Sutherland that still stands on Ben Bhraggie.
Shepherd at Kincraig. Credit: Weldon Gimbel
Like Kelvingrove, Scotland also seemed full of unexpected juxtapositions. Christian met Viking at the village of Luss for instance, where the hog-backed memorial we found in the churchyard warned against seeing all Norse in Scotland as virgin-snatching heathens.
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With a Ph.D. in medieval history, Cassandra Hannahs spent most of her academic career at Middlebury College in Vermont, where she was a tenured professor of history. At Middlebury, Cassandra regularly taught courses on Celtic, Viking and Anglo-Norman Studies, as well as more general courses on the Middle Ages, the Renaissance, and the history of Christianity. In her research and lectures, Cassandra explores the cultural and political exchanges that have historically linked Ireland, Scotland, England, and Europe. As Study Leader for the Smithsonian since 2000, she enjoys sharing her love and knowledge of the British Isles and Ireland with travelers on land and sea.


So how did I do? Sleep (not a goal but will post it anyway) = Not so good. Balanced Breathing = did 1 recorded session and practiced the second on my drive home. No sweets and I crushed the steps. More to follow.


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text:
import { Pipe, PipeTransform } from '@angular/core';
import { FiltersService } from '../services/filters.service';
import { Config } from '..';

@Pipe({
  name: 'sort',
})
export class SortPipe implements PipeTransform {
  private defaultArray: any[] = [];

  private static isNaN(aV: any, bV: any): boolean {
    return isNaN(parseFloat(aV)) || !isFinite(aV) || isNaN(parseFloat(bV)) || !isFinite(bV);
  }

  private static compare(a: any[], b: any[], key: string): number {
    const split = key.split('.');
    const aPath = FiltersService.getPath(split, a);
    const bPath = FiltersService.getPath(split, b);
    const aValue = (aPath + '').toLowerCase();
    const bValue = (bPath + '').toLowerCase();
    if (SortPipe.isNaN(aPath, bPath)) {
      return aValue.localeCompare(bValue);
    }
    if (parseFloat(aPath) < parseFloat(bPath)) {
      return -1;
    }
    if (parseFloat(aPath) > parseFloat(bPath)) {
      return 1;
    }

    return 0;
  }

  transform(array: any[], filter: { order: string; key: string }, config?: Config): any[] {
    if (this.defaultArray.length === 0) {
      this.defaultArray = array;
    }
    if (!filter.key || filter.key === '') {
      return array;
    }
    if (filter.order === '') {
      return this.defaultArray;
    }
    if (filter.order === 'asc') {
      return this.sortAsc(array, filter, config);
    }
    return this.sortDesc(array, filter, config);
  }

  private sortAsc(array: any[], filter: { order: string; key: string }, config?: Config): any[] {
    if (config && config.groupRows) {
      return array.map((arr) => arr.sort((a, b) => SortPipe.compare(a, b, filter.key)));
    }
    return array.sort((a, b) => SortPipe.compare(a, b, filter.key));
  }

  private sortDesc(array: any[], filter: { order: string; key: string }, config?: Config): any[] {
    if (config && config.groupRows) {
      return array.map((arr) => arr.sort((a, b) => SortPipe.compare(b, a, filter.key)));
    }
    return array.sort((a, b) => SortPipe.compare(b, a, filter.key));
  }
}

redpajama_set_name: RedPajamaGithub