In October 2013, only a few months after the establishment of Prime Minister Benjamin Netanyahu’s third government, Knesset members Ayelet Shaked (HaBayit HaYehudi) and Yariv Levin (Likud) submitted a series of legislative initiatives to the Knesset. The bills were designed to weaken the power of the Supreme Court and halt the court’s leanings toward judicial activism. Shaked and Levin’s package of bills were supposed to shake up the Israeli judicial system in order to make a major change. These bills included a change in the composition of the Judicial Selection Committee (giving the High Court one representative at the committee instead of three), limits on the High Court’s authority to disqualify bills and the re-legislation of bills it has disqualified. In addition, one of the bills aimed to task the Knesset with the responsibility for choosing the president of the Supreme Court. Traditionally, the position of president was always given to the most senior member of the serving justices.
For Levin, the move was part of his activism to limit the power of what he feels is a left-leaning High Court. In 2011, Levin tried to advance a bill that would subject all judges to a Knesset hearing before they could be appointed to the Supreme Court. Neither round of legislative attempts was successful, but the issues behind them still hover over the Knesset and the judicial system.
These legislative initiatives, which at first seemed marginal and populistic and were sharply challenged even by Likud officials such as Dan Meridor and Benny Begin, eventually morphed into a key agenda. This happened not only because Levin was appointed minister of internal affairs in 2015 and Shaked became justice minister and chairperson of the Judicial Selection Committee. Instead, it mainly happened as a result of the unleashing that has reigned in many spheres of the political system. For example, there is no one in the coalition who has the role of “defender of the rule of law.” True, Kulanu Chairman and Finance Minister Moshe Kahlon took this role upon himself, but his lack of involvement in these processes shows us that he is not the man to halt the tidal waves that have already reached the doors of the High Court.
Last October, Shaked tried to advance a bill that would revoke the veto power of the Supreme Court justices in their appointment process. This attempt led to a bitter argument between her and Supreme Court President Justice Miriam Naor. Naor sent a letter to Shaked, blaming her for “placing a gun on the table.” This background information is important in understanding the confrontation between Naor and Knesset member Robert Ilatov (Yisrael Beitenu), a member of the Judicial Selection Committee. This clash was reported Dec. 14 in the Yedioth Ahronoth newspaper.
The argument erupted after Ilatov demanded that the politicians in the Judicial Selection Committee be permitted to meet with the judges before they are appointed so “as not to be [merely] rubber stamps.” Naor fumed and made it clear that this was a red line as far as she was concerned and would not allow it. She said, “I must protect the judges from politics.” Shaked was also present at the meeting, and her statements show that she supports Ilatov’s position.
Most likely Naor's strong statements were made as the backdrop of Knesset member Nurit Koren’s statements (Likud); Koren is the second representative of the Knesset at the committee who was also present during the same meeting. Last September, Koren made a visit to the Netiv Ha'avot neighborhood in the Gush Etzion settlement (West Bank), following the decision of the High Court to demolish several illegal structures there. In a conversation with Likud activists on the site, the Knesset member boasted that the Likud will soon change the composition of justices on the High Court to conform to the party’s outlook: “In the coming year we are changing five positions in the High Court. One Arab has to be elected, and I'm told that one must be Sephardic. I said, 'Forget about the one Sephardic judge, I want people with our outlook.' Until now they appointed people with their outlook; now they will be from our camp.”
These unrestrained barbs, lacking minimum respect for the judiciary and uttered by a member of the Judicial Selection Committee, are no less than scandalous — even without connection to a specific political position. But Koren’s words were not uttered in a void. Instead, they are part of the overall atmosphere in the right following several judgments rendered by the High Court on the evacuation of houses in the West Bank. HaBayit HaYehudi Chair Naftali Bennett termed the Netiv Ha’avot verdict as “very severe.” In another incident in 2015, faction member Moti Yogev suggested sending a bulldozer to destroy the court (instead of bulldozers destroying Beit El settlement buildings, according to court order).
The verbal assaults on Naor, who grew up and still lives in a right-wing milieu, raise uncomfortable feelings. Miriam Naor’s mother had been a member of Etzel (a far-right paramilitary group that broke off from the Haganah in pre-state Palestine ["pre-state Palestine” refers of course to the British mandate before Israel was founded]). Miriam’s husband, professor Aryeh Naor, is the son of two Etzel members; Aryeh had served as a Cabinet secretary under late Prime Minister Menachem Begin. He even tried to run for a spot on the Likud list. So if Miriam Naor is a red flag for the right, who will ever pass the Koren and Ilatov gauntlet?
The clash between Naor and Ilatov, with Shaked’s backup and Koren’s cheerleading, reveals the extent of alienation between the right and the judicial system. All this is combined with an overall atmosphere of incitement against the left, led by Netanyahu with his high-level ministers as partners. In this atmosphere, if the leftists are traitors, then the High Court justices are their collaborators. As Bennett tweeted Sept. 1 after the Netiv Ha’avot High Court ruling, “The extreme left has despaired of persuading people to establish a Palestinian state in Judea and Samaria. So, it has bypassed public opinion by using the legal system as a tool to enforce the policies of the minority on the majority. … When the High Court helps them, it erodes public trust in the judiciary.”
Accusations of “rule-of-law gang,” as an elitist minority that takes upon itself disproportionate power in running the state, and about the lopsided political composition of justices in the High Court, are not new. High-level jurists like former Justice Minister Daniel Friedman uttered these allegations, and they are important. When these claims are presented in a well-reasoned manner, they challenge the current system and improve it. What has changed lately is the aggressive tone, the disrespect and lack of statesmanship on the part of the highest level of politicians vis-a-vis the judiciary leadership. Israel has no constitution. The High Court of Justice is well-known in the world as an institution symbolizing the robustness of Israeli democracy; it is an institution that protects minority groups, without political considerations. However, nowadays it is clear that the red line has already been crossed. All the signs show that the political and public atmosphere is ripe for infringing on, and restricting, the powers of the High Court of Justice vis-a-vis the politicians. President Naor’s struggle is only rearguard action.


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Before the storm, the prison complex contained close to 7,500 beds and housed city, state and federal prisoners in seven jail facilities.
Orleans Parish Sheriff Marlin N. Gusman originally proposed that a 4,300-bed prison complex be constructed using FEMA funds. The New Orleans City Council agreed in February 2011 to build 1,438 beds at an estimated cost of $78.6 million. The old prison buildings are to be torn down upon completion of the new complex. [See: PLN, June 2011, p.28]. Gusman announced the closure of one of the old buildings, the Orleans Parish Prison House of Detention, on April 10, 2012.
FEMA has committed $50.4 million towards the prison construction project, but there was haggling over cost increases and FEMA’s contribution as the project was redesigned and expanded. Part of the amended plan is a new administration building that will share some of the same walls as the jail.
The four-story “all inclusive administrative facility” will include housing for staff, a television studio, an office for internal affairs and a bail bonds information office, stated Andre Cadogan, deputy director of FEMA’s Louisiana Recovery Office.
Sheriff Gusman said the new complex “will be technologically advanced” as a result of using experts “who considered every aspect of preferred jail design relative to safety of inmates, visitors and deputies.” FEMA is providing the grant money to the Louisiana Governor’s Office of Homeland Security and Emergency Preparedness. As the Sheriff’s Office incurs construction costs, it is reimbursed.
Another project within the jail complex is a 163,000-square-foot kitchen and warehouse facility for the jail and Sheriff’s Office. FEMA agreed to pay the $63.6 million construction cost of that building.
Of course, no one is asking why the Federal Emergency Management Agency considers tens of millions of dollars in funding for a new jail complex to be part of its “emergency management” mission.
Any construction expenses not covered by FEMA will come from a $63 million bond issue for the New Orleans Law Enforcement District, which was renewed by voters in 2008. That bond is funded by a $2.9 million property assessment; it also supports construction costs for municipal and juvenile courts, as well as the coroner, district attorney and clerk of criminal court.
In June 2012, news reports indicated that Sheriff Gusman and city officials were considering the construction of a third jail complex building to house another 600 prisoners. According to emails from Gusman that were obtained via a public records request, the additional building would hold prisoners with medical and mental health needs, as well as minimum-security male prisoners and state prisoners who have been transferred to re-entry programs. A diagram of the third building posted on the city’s website stated the construction costs would be paid by FEMA.
Community advocates have called on city officials to limit the size of the new jail complex to 1,438 beds as originally specified by the City Council. On April 24, 2012, the Micah Project, a faith-based group, held a meeting in New Orleans attended by over 400 church members who urged the city to keep the jail’s population at 1,438 beds. Gusman, however, prefers a larger facility.
“We have to be realistic about the city we live in today,” he stated. “We are engaged in a relentless struggle with violent crime.”
The Orleans Parish Prison system, which currently holds around 2,600 prisoners, is the subject of a lawsuit filed by the Southern Poverty Law Center in April 2012 that alleges high levels of violence and sexual abuse. See: Jones v. Gusman, U.S.D.C. (E.D. LA), Case No. 2:12-cv-00859. The Parish’s jail facilities have also been criticized by the U.S. Department of Justice, which has cited unconstitutional conditions and high rates of sexual assaults. [See: PLN, March 2010, p.3].
Sources: The Times-Picayune, www.
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Jones v. Gusman
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domain: law


Kabul: Russian Foreign Minister Sergey Lavrov announced in a press conference that Russia will inform the Taliban movement about the outcome of the next round of consultative meeting in Moscow regarding Afghanistan.
Earlier Putin’s special representative Zamir Kabulov had announced that delegation or representative of the Taliban interim government would not attend the Moscow meeting.
Regarding the upcoming consultative meeting in Russia about Afghanistan, Lavrov added “We are in regular contact with Taliban officials, they will be aware of what the participants of the Moscow meeting will do.”
He clarified that they certainly do not want to hide any secrets from the representatives of Afghanistan and will provide accurate information to the Taliban and other political forces present in Afghanistan.
Moscow’s consultative meeting on Afghanistan is scheduled to be held in mid-November.
The Ministry of Foreign Affairs of the interim government of the Taliban, in response to not inviting them to attend the aforementioned meeting, had announced that this program is incomplete without the presence of Afghanistan delegation.


Hatteras Pillowtop Hammock in Icon Mystique Specifications:
- Material: Sunbrella and DuraCord
- Material Detail: Two layers of all-weather, solution-dyed synthetic fabric. Top is Sunbrella, bottom is DuraCord
- Color: Icon Mystique multi-colored stripe
- Product Dimensions:
- Length: 13'
- Width: 55"
- Thickness: 3.5", 5" at thickest point
- Bed Length: 6'10"
- Hanging Distance: 13-16 ft.
- Weight: 26 lbs
- Accommodates: 2 people
- USA Made: Yes
- Care: Use Oxyclean or a Mild Detergent, Water, and a Soft Scrub Brush
Overindulgence usually ends badly, however the same can not be said with this Pillowtop Hammock in Icon Mystique from Hatteras Hammocks. With its charming striped coloring and superior construction, this hammock is an extreme joy you won't have to regret later! It features an extremely comfortable bed made of a top layer of Sunbrella fabric and bottom DuraCord fabric lockstitched together with resilient, nonabsorbent polyester hollowfill fiber batting in the center. Large enough for two and designed with long-term comfort in mind, this hammock will provide ample support and cushioning for your back ensuring that you'll get to enjoy long hours lounging luxuriously outdoors.
Hatteras Pillowtop Hammock in Icon Mystique Features:
- Extremely comfortable pillow design
- Made with solution-dyed Sunbrella fabric - colorfast and resistant to rot, mold, mildew and staining
- Polyester fiber fill batting, promising lavish reclining in soft-to-skin comfort
- Duracord Rope is designed specifically to resist mold, mildew and be resilient to weathering
- Cumaru natural finish spreader bars - one of the densest woods on the planet, used for long lasting construction that naturally ages to a stately silver-gray
- Hanging hardware and chain are zinc-plated steel (rust resistant) - safe and able to withstand the elements of the weather.
- Durable lockstitch polyester thread used for tenacity and strength in each seam
- Accommodates 2
- Handcrafted in The Carolinas
- Hammock stand sold separately
Hatteras Pillowtop Hammock in Icon Mystique Includes:
- 1 Hammock
- 2 Zinc-plated chains
- 2 Tree hooks
- 1 Year Limited Manufacturers Warranty


text:
Chicago Artists Coalition welcomes the public to view exhibitions by emerging Chicago artists, join us at opening receptions, or attend education events
Chicago Artists Coalition in partnership with the Gaylord and Dorothy Donnelley Foundation are pleas...
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domain: news


“We love our iconic look,” Joe C said. “It’s classy. It’s timeless. We know who we are. We’re not trying to change that. In no way, shape or form are we abandoning our classic look. Just something we can wear occasionally.”
Schools like Oklahoma State and Oregon and Baylor have made great strides with snazzy uniforms. But again, their uniform changes are popular and trendy because OSU and Oregon and Baylor have reversed their football fortunes and won big. In case you haven’t noticed, Kansas does all kinds of things with its football uniforms and nobody notices or cares.
And OSU and Oregon, particularly, admit they had established no uniform tradition. The uniform craze they’ve embraced is their tradition. And there’s nothing wrong with that. But that is not OU’s tradition.
“There’s just certain things you don’t have to change,” Castiglione said. “Programs like Oklahoma, Alabama or Notre Dame, Michigan, they have uniforms that stand the test of time. You turn on that TV, you know exactly who’s playing. Those are great looks, there’s no reason to deviate from them. By the same token, you’d like something a little bit different.”
If Castiglione and Co. ever decide to scrap the classics, then we’ll talk. Until then, be grateful for the compromise. It could be much worse.
Berry Tramel: Berry can be reached at (405) 760-8080 or at email@example.com. He can be heard Monday through Friday from 4:40-5:20 p.m. on The Sports Animal radio network, including FM-98.1. You can also view his personality page at newsok.com/berrytramel.


text:
Disputes additions and promotions at DentonsLitigation and white-collar hires have added depth to Dentons’ offices in Arizona, Germany and Hong...
Litigation and white-collar hires have added depth to Dentons’ offices in Arizona, Germany and Hong Kong, while there has been a round of partner and counsel promotions in Europe. Dentons has had a busy month of dispute resolution recruitment across a range of offices in the United States, Europe and Asia, while the firm’s European promotions round has made up new partners and counsel in a range of practices. In the US, the decision by Steptoe & Johnson to close its Phoenix office has been to Dentons’ advantage, with the firm hiring nine litigation and white-collar lawyers – four partners, two counsel and three associates – from Washington, DC-headquartered Steptoe.
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domain: geography


text:
Click here for a look at my links to my comprehensive packing list, personal packing list & menu plan.
This summer I decided to plan a week long summer trip on a houseboat. I selected Beaver Creek Marina at Lake Cumberland in Kentucky because it was a very large body of water (1255 miles of shoreline) with plenty of room to explore and it was only about a six hour drive from our home. On the trip were a total of five adults and 12 teenagers so we decided to go for two houseboats that sleep 10 people each. We also wanted a ski boat for daily activities.
While surfing the web I came across a company that seemed to have decent prices but I decided to call a few other places. The company that I chose to rent from had an awesome internet special of about $800 per boat for a Monday PM through Friday AM rental period. This is a great deal because their published rates are about three times as much! The ski boat rental was about the same rate as both boats combined.

domain: travel


The nightgown-as-daywear presents the fantasy of being beholden to no one and simply drifting away from the world and all its messy responsibilities, reports Elle.
I feel like I’m alone in this, though, because when I open my feed these days, it’s filled with people in nightgowns. Brands like Sleeper and Dôen offer their own chic versions. The $125 “nap dress,” the breakout product of the bedding brand Hill House Home, has become an Instagram favorite. Everywhere I look, it seems, there are people lounging in eyelet.elle.com


text:
Traumatic Brain Injury: A Guide for Caregivers of Service Members and Veterans. Welcome
Defense Health Agency/Defense Health Board Falls Church United States
Pagination or Media Count:
Traumatic brain injury TBI is a major public health problem in the United States. In 2006, the Centers for Disease Control and Prevention reported that TBI is more prevalent than cases of multiple sclerosis, HIVAIDS, and breast cancer combined. Due to the present conflicts in Iraq and Afghanistan, members of the United States Armed Forces are one of the largest populations at risk for TBI. Of the service members medically evacuated for battle-related injuries from Iraq and Afghanistan to Walter Reed Army Medical Center, 33 percent had traumatic brain injury as of March 2009. Due to medical and technological advances, we haveseen a decrease in mortality rates for those with severe TBI from the 50 percent range in the 1970s to the 30 percent range at this time. As a result, family members and loved ones like yourself are increasingly being recruited to enlist in the ranks of caregivers to assist in the journey toward the greatest level of recovery possible for your service member. This guide was written to support and empower you along this journey. Individuals who sustain a TBI may experience short- and long-term effects, such as alterations in thinking, sensation, language, behavior, and emotions. Whether the TBI is mild, moderate, or severe, persistent symptoms can have a profound and persisting impact, not only on the injured survivor but also on those who function as caregivers. It is you, the caregiver, who must not only survive the immediate shock when a TBI occurs, but must also learn to support and aid the service member who experiences ongoing effects caused by this injury. A TBI can radically change the lives of the individuals who are closest to those who experience it. In December 2006, Congress took action to support caregivers by passing the National Defense Authorization Act of 2007.
- Medicine and Medical Research

domain: medical


text:
In the graphic below I have extracted a table from a very old study. It highlights the huge increase in lipofuscin aggregation with age. They used acetyl l carnitine has a therapeutic intervention and the results were quite good but only at very high dosages. Other and much more recent research has found that acetyl l carnitine can also play an important role in preventing Age Related Macular Degeneration (AMD). In those studies they created a compound called Phototrop, a combination of acetyl L carnitine, omega 3 fatty acids, and co-enzyme Q10.
Word of warning: you should always use alpha lipoic acid with ALC because ALC increases mitochondrial function and mitochondria are the key region where oxidants are formed.
The table below is from

domain: chemistry


text:
Oneshot Fiber is a macrostructural synthetic fiber designed to improve the durability and
mechanical properties of concrete instead of steel wire and mesh products.
It is recommended to store the product indoors between 5 °C and 30 °C in its original packaging, protected from moisture, water and direct sunlight. Shelf life is 3 years under suitable storage conditions.
On-demand; It is packaged in nylon packages as 3 kg, 4 kg, 5 kg water-soluble bundles. For other packaging options, you can contact the company officials directly.
Fiber bundles are added directly to the aggregate. If it is added to the concrete in the truck mixer, the mixing time should not be less than 5-6 minutes at high speed.


Vail Daily column: Bad news vs. good news — take your pick
The last two weeks have seen some of the wildest fluctuations in mortgage rates I have probably ever seen in my 20 years in the mortgage business.
For the most part, rates have zoomed up, although they have eased slightly the last few days.
But as we all know, when it comes to rates they will come down about half as fast as they go up, and I’m not at all sure they will come down by much.
If you are waiting for 3.5 percent I hope you are young and healthy and have a family history of people making to 100.
What caused this is the fear of investors living in a world without Uncle Ben Bernanke riding in on his white horse to save everyone.
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Recently the Fed Chairman speculated that the Fed would wind down its economic stimulus by mid-2014.
The howls of anguish must have rocked the foundations of the NYSE as investors panicked selling everything in sight. Stocks, bonds and even gold all were unwanted as investors seemed to think a stash of good old fashioned cash wasn’t so boring.
In addition, many investment banks and funds had borrowed cheap money and invested it in the stock market, and investors did not want to be caught holding stock that might take a few years to reach its potential on money they borrowed short term.
This caused a lot of realigning of investments and probably some paying down of lines of credit.
No doubt there were some margin calls as well going on as investors who heavily leveraged their holdings had to suddenly pay back the borrowed money.
Curiously, the historical trend of fleeing stocks and gold to the safety of T-Bills didn’t happen this time around. Almost like clockwork in the past when stocks dropped the money moved to bonds and yields on bonds dropped. I suspect that this is because of the amount of borrowed money out there.
As a result, there was far less cash clamoring for mortgage backed securities, meaning those selling them to raise cash to lend out in the next 30-60 days had to offer a better return to attract buyers.
This caused a run up in rates in a few days of as much as ¾ percent.
Then by Wednesday of this week there was some weak economic news came out, and fueled speculation mid week that perhaps the Fed would ride in again and hand out money like there was no tomorrow.
This cheered stock owners who hope their picks will benefit from economic stimulus.
This also eased bond holders fears about bond rates zooming to 4 percent (which means those who own them today would suffer huge losses if they had to liquidate them any time before maturity).
There aren’t very many economic certainties out there, but one I would bet heavily on is that the Fed will start backing out, and rates will go up.
That means there are going to be some wild swings in rates and that will keep things interesting.
Chris Neuswanger is a mortgage loan originator with Macro Financial Group in Avon and may be reached at 970-748-0342. He welcomes mortgage related inquiries from readers.


More than a billion people have shut themselves after Prime Minister Narendra Modi announced a nationwide lockdown to contain the spread of the virus.
Nearly 700 people have tested positive for the coronavirus infection across the country, with 88 people cases being reported yesterday. The total is now 694 -- including 47 foreigners, 42 people who have been cured or discharged. The virus infection has resulted in the death of 16 people so far.
On Thursday, Union finance minister Nirmala Sitharaman announced a Rs1.7 lakh crore package to help ...
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text: Hi from GDC! I haven't been at the conference in over 4 years, but I guess it feels as crazy and crowded as usual. So far, my best experience has been to try Nintendo's Wii Fit (which now has a US release date of May 19th according to the guy at the booth). I tried the skiing game and the soccer one. My first reaction: the board is incredibly sensitive, so it gets a while to get used to it. But once you do it, it works pretty well. I'm pretty sure the experience is close to using the wiimote the first time: it takes a few minutes to get used to it. I also was able to lift the mat itself and I'm happy to report that it's not heavy at all (I would say the same or less weight than your average scale). As you can see in the pic, players where required to take their shoes off, in the best Japanese tradition. Does it look like a killer app? It certainly does but, you never know. Nintendo has been on a roll lately and certainly can achieve another mass success with the Wii Fit, but of course we will need to wait and see what 3rd party developer come up with. Meanwhile, I'll definitively grab one as soon as they become available.

domain: hobby


Sleepify’s mission is to end mattress waste and make mattresses circular. Currently, 18 million mattresses end up in landfill every year in Europe alone. This is a huge problem, and one which we aim to tackle.
To do so, we are creating a 100% recyclable mattress and providing a fully circular service to our customers, ensuring our mattresses are either resold, reused or recycled at the end of their life cycle.
Sustainability and innovation are at the core of everything we do: from flexible financing, to innovative mattress design to logistics and recycling, we take the hassle of mattress management away for our customers and most importantly, we make mattresses circular.


text:
Viking Truvor Entertainment & Activities
Entertainment onboard Truvor is low-key and limited. A pianist and singer perform in the Panorama or Sky lounges during cocktail hour and after dinner at 9 p.m., as well as on the Sun Deck during sailaway parties from port (where selected cocktails and nibbles are complimentary).
Engaging and informative presentations, delivered daily by the ship's tour escorts or activities director when the ship is cruising between St. Petersburg and Moscow, incorporate slices of Russian history (from the Romanovs to modern day), two Russian language lessons and a laughter-filled, vodka-fueled cooking demonstration on how to make the tiny Russian dumplings known as pelmeni.
But Truvor truly shines with its shore excursions. At least one guided stroll or port tour for each stop is included in the cruise fares, and other tours are offered at an additional cost. Passengers are split into groups and given personal headsets that are recharged back in the cabins each evening.
Among the alternatives are in-depth walking tours of St. Petersburg and Moscow with rides on the cities' subway systems, a musical and dance performance (with passengers invited to join in) at the Governor's Mansion in the "Golden Ring" city of Yaroslavl, and a rendition of Swan Lake at St. Petersburg's opulent Hermitage theater.
Extra options range from a home visit to a St. Petersburg Kommunalka, one of the communal living apartments created after the 1917 revolution, to a session at a Russian banya. The latter, located on the thickly wooded banks of the Svir River in the open-air museum town of Mandrogy, includes time in a traditional steam room and a swatting with birch leaves, followed by an dip in the nippy Svir.


text:
Well here it is. The red cards are little Christmas cards that I made after making the Santa boxes. I cut these cards to use as orniments for my christmas tree. I am doing the traditional red and green this year. The larger cards in the back are cards make from the Cricut Craftroom files that they let you use free for a week. I hope you like them.
Never limit yourself it makes life short
Remember that the sky is not the limit it is the view!!!!

domain: design


text:
Memoirs, Family Stories, and Memorials
Why a memoir? What binds a family together? What are the stories worth remembering and passing from one generation to another? Why do we want to know, understand, and record what happened in the past? Through the process of answering these questions, we can distinguish one story from another. It has been established that the more children know about their family’s history, the stronger their sense of control over their lives. In fact, the single most important thing you can do for your family may be the simplest of all: develop a strong family narrative. And, once you know your story, honor the past, but more importantly, live in the present.
Make new memories for your descendants to talk about and continue to grow your own family tree.
Click on the book titles below for more details.

domain: literature


The midterm elections 2018 are the first real test of Donald Trump's presidency and the results will indicate how well the US public thinks he is doing.
Although Donald Trump’s job is unaffected, his ability to pass bills on issues such as immigration and healthcare could be stunted by Democrat victories.
Should the blue party take ether the Senate or the House of Representatives, they can block future legislation they do not want passed.
And polls running up election day suggest the Democrats have a huge chance of winning the House.
What are the latest updates?
All 435 seats in the House are up for re-election and the latest forecast from polling website Five Thirty Eight shows the Democrats have a 87.9 percent chance of winning control.
To win a majority, the Democrats need to flip 24 Republicans seats and hold onto the 194 seats they already hold.
Former US vice president Joe Biden, who voted earlier today in Delaware, said he would be “dumbfounded” if the Democrats do not win control of the House.
READ MORE: MIDTERM ELECTIONS RESULTS LIVE UPDATES
Will Democrats win midterm elections? President Trump is under pressure to secure good results
He said: “This is the single most important off-year election in my lifetime. It’s about the character of the country.”
And the latest polls agree, with a 87.9 percent chance of the Democrats winning control, says Five Thirty Eight.
Despite Mr Trump placing immigration at the centre of his election campaigning, healthcare remains a top issue for voters.
When a HuffPost/YouGov poll asked 1,000 US adults to pick their top two election issues, 30 percent of voters chose health care.
READ MORE: WHEN WILL RESULTS BE ANNOUNCED?
Nancy Pelosi, the Minority Leader of the United States House of Representatives, also agreed.
She said: “This election is about healthcare.”
But immigration also remains high on the agenda for voters and the Republicans have seized the opportunity to condemn the migrant caravan heading towards the US border in a bid to win votes.
Storms and rain in central and eastern states could dampen turnout for the Democrats, according to some weather experts.
READ MORE: WILL TRUMP WIN THE MIDTERMS?
AccuWeather Data Scientist and Meteorologist Tim Loftus said: “Weather was found to be, on average, nearly 20 percent of the change in voter turnout based on our analysis.
Democrats are more weather sensitive, when compared to Republicans, and among the most weather-sensitive were African-Americans, those 65 and older and 18-24 year olds.”
What about the Senate?
Only 33 seats are up for election in the Senate and here there is far less of a chance of a ‘blue wave’ happening.
Current estimates suggest the Republicans have a 80.9 percent chance of keeping control and the Democrats have a 19.1 percent chance.


In physics, the Navier–Stokes equations are certain partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes).
The Navier–Stokes equations mathematically express conservation of momentum and conservation of mass for Newtonian fluids. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing viscous flow. The difference between them and the closely related Euler equations is that Navier–Stokes equations take viscosity into account while the Euler equations model only inviscid flow. As a result, the Navier–Stokes are a parabolic equation and therefore have better analytic properties, at the expense of having less mathematical structure (e.g. they are never completely integrable).
The Navier–Stokes equations are useful because they describe the physics of many phenomena of scientific and engineering interest. They may be used to model the weather, ocean currents, water flow in a pipe and air flow around a wing. The Navier–Stokes equations, in their full and simplified forms, help with the design of aircraft and cars, the study of blood flow, the design of power stations, the analysis of pollution, and many other things. Coupled with Maxwell's equations, they can be used to model and study magnetohydrodynamics.
The Navier–Stokes equations are also of great interest in a purely mathematical sense. Despite their wide range of practical uses, it has not yet been proven whether smooth solutions always exist in three dimensions—i.e. they are infinitely differentiable (or even just bounded) at all points in the domain. This is called the Navier–Stokes existence and smoothness problem. The Clay Mathematics Institute has called this one of the seven most important open problems in mathematics and has offered a US$1 million prize for a solution or a counterexample.
The solution of the equations is a flow velocity. It is a vector field—to every point in a fluid, at any moment in a time interval, it gives a vector whose direction and magnitude are those of the velocity of the fluid at that point in space and at that moment in time. It is usually studied in three spatial dimensions and one time dimension, although two (spatial) dimensional and steady-state cases are often used as models, and higher-dimensional analogues are studied in both pure and applied mathematics. Once the velocity field is calculated, other quantities of interest such as pressure or temperature may be found using dynamical equations and relations. This is different from what one normally sees in classical mechanics, where solutions are typically trajectories of position of a particle or deflection of a continuum. Studying velocity instead of position makes more sense for a fluid, although for visualization purposes one can compute various trajectories. In particular, the streamlines of a vector field, interpreted as flow velocity, are the paths along which a massless fluid particle would travel. These paths are the integral curves whose derivative at each point is equal to the vector field, and they can represent visually the behavior of the vector field at a point in time.
See main article: Derivation of the Navier–Stokes equations.
The Navier–Stokes momentum equation can be derived as a particular form of the Cauchy momentum equation, whose general convective form isBy setting the Cauchy stress tensor to be the sum of a viscosity term (the deviatoric stress) and a pressure term (volumetric stress), we arrive at
In this form, it is apparent that in the assumption of an inviscid fluid – no deviatoric stress – Cauchy equations reduce to the Euler equations.
Assuming conservation of mass we can use the mass continuity equation (or simply continuity equation),to arrive at the conservation form of the equations of motion. This is often written:
where is the outer product:
The left side of the equation describes acceleration, and may be composed of time-dependent and convective components (also the effects of non-inertial coordinates if present). The right side of the equation is in effect a summation of hydrostatic effects, the divergence of deviatoric stress and body forces (such as gravity).
All non-relativistic balance equations, such as the Navier–Stokes equations, can be derived by beginning with the Cauchy equations and specifying the stress tensor through a constitutive relation. By expressing the deviatoric (shear) stress tensor in terms of viscosity and the fluid velocity gradient, and assuming constant viscosity, the above Cauchy equations will lead to the Navier–Stokes equations below.
A significant feature of the Cauchy equation and consequently all other continuum equations (including Euler and Navier–Stokes) is the presence of convective acceleration: the effect of acceleration of a flow with respect to space. While individual fluid particles indeed experience time-dependent acceleration, the convective acceleration of the flow field is a spatial effect, one example being fluid speeding up in a nozzle.
Remark: here, the Cauchy stress tensor is denoted (instead of as it was in the general continuum equations and in the incompressible flow section).
The compressible momentum Navier–Stokes equation results from the following assumptions on the Cauchy stress tensor:
Since the trace of the rate-of-strain tensor in three dimensions is:
The trace of the stress tensor in three dimensions becomes:
So by alternatively decomposing the stress tensor into isotropic and deviatoric parts, as usual in fluid dynamics:
Introducing the bulk viscosity,
we arrive to the linear constitutive equation in the form usually employed in thermal hydraulics:
Both second viscosity ζ and dynamic viscosity need not be constant – in general, they depend on two thermodynamics variables if the fluid contains a single chemical species, say for example, pressure and temperature. Any equation that makes explicit one of these transport coefficient in the conservation variables is called an equation of state.
The most general of the Navier–Stokes equations becomeApart from its dependence of pressure and temperature, the second viscosity coefficient also depends on the process, that is to say, the second viscosity coefficient is not just a material property. For instance, in the case of a sound wave with a definitive frequency that alternatively compresses and expands a fluid element, the second viscosity coefficient depends on the frequency of the wave. This dependence is called the dispersion. In some cases, the second viscosity can be assumed to be constant in which case, the effect of the volume viscosity is that the mechanical pressure is not equivalent to the thermodynamic pressure: as demonstrated below. Sinceone can introduce a modified pressure to remove the term corresponding to the second viscosity. However, this difference is usually neglected most of the time (that is whenever we are not dealing with processes such as sound absorption and attenuation of shock waves, where second viscosity coefficient becomes important) by explicitly assuming . The assumption of setting is called as the Stokes hypothesis. The validity of Stokes hypothesis can be demonstrated for monoatomic gas both experimentally and from the kinetic theory,; for other gases and liquids, Stokes hypothesis is generally incorrect. With the Stokes hypothesis, the Navier–Stokes equations become
If the dynamic viscosity is also assumed to be constant, the equations can be simplified further. By computing the divergence of the stress tensor, since the divergence of tensor is and the divergence of tensor is, one finally arrives to the compressible (most general) Navier–Stokes momentum equation:
where is the material derivative. The left-hand side changes in the conservation form of the Navier–Stokes momentum equation:Bulk viscosity is assumed to be constant, otherwise it should not be taken out of the last derivative. The convective acceleration term can also be written aswhere the vector is known as the Lamb vector.
For the special case of an incompressible flow, the pressure constrains the flow so that the volume of fluid elements is constant: isochoric flow resulting in a solenoidal velocity field with .
The incompressible momentum Navier–Stokes equation results from the following assumptions on the Cauchy stress tensor:
Dynamic viscosity need not be constant – in incompressible flows it can depend on density and on pressure. Any equation that makes explicit one of these transport coefficient in the conservative variables is called an equation of state.
The divergence of the deviatoric stress is given by:because for an incompressible fluid.
Incompressibility rules out density and pressure waves like sound or shock waves, so this simplification is not useful if these phenomena are of interest. The incompressible flow assumption typically holds well with all fluids at low Mach numbers (say up to about Mach 0.3), such as for modelling air winds at normal temperatures. the incompressible Navier–Stokes equations are best visualised by dividing for the density:
If the density is constant throughout the fluid domain, or, in other words, if all fluid elements have the same density,
where is called the kinematic viscosity.
It is well worth observing the meaning of each term (compare to the Cauchy momentum equation):
The higher-order term, namely the shear stress divergence, has simply reduced to the vector Laplacian term . This Laplacian term can be interpreted as the difference between the velocity at a point and the mean velocity in a small surrounding volume. This implies that – for a Newtonian fluid – viscosity operates as a diffusion of momentum, in much the same way as the heat conduction. In fact neglecting the convection term, incompressible Navier–Stokes equations lead to a vector diffusion equation (namely Stokes equations), but in general the convection term is present, so incompressible Navier–Stokes equations belong to the class of convection–diffusion equations.
In the usual case of an external field being a conservative field:by defining the hydraulic head:
one can finally condense the whole source in one term, arriving to the incompressible Navier–Stokes equation with conservative external field:
The incompressible Navier–Stokes equations with conservative external field is the fundamental equation of hydraulics. The domain for these equations is commonly a 3 or less Euclidean space, for which an orthogonal coordinate reference frame is usually set to explicit the system of scalar partial differential equations to be solved. In 3-dimensional orthogonal coordinate systems are 3: Cartesian, cylindrical, and spherical. Expressing the Navier–Stokes vector equation in Cartesian coordinates is quite straightforward and not much influenced by the number of dimensions of the euclidean space employed, and this is the case also for the first-order terms (like the variation and convection ones) also in non-cartesian orthogonal coordinate systems. But for the higher order terms (the two coming from the divergence of the deviatoric stress that distinguish Navier–Stokes equations from Euler equations) some tensor calculus is required for deducing an expression in non-cartesian orthogonal coordinate systems.
The incompressible Navier–Stokes equation is composite, the sum of two orthogonal equations,where and are solenoidal and irrotational projection operators satisfying and and are the non-conservative and conservative parts of the body force. This result follows from the Helmholtz theorem (also known as the fundamental theorem of vector calculus). The first equation is a pressureless governing equation for the velocity, while the second equation for the pressure is a functional of the velocity and is related to the pressure Poisson equation.
The explicit functional form of the projection operator in 3D is found from the Helmholtz Theorem:
An equivalent weak or variational form of the equation, proved to produce the same velocity solution as the Navier–Stokes equation, is given by,
for divergence-free test functions satisfying appropriate boundary conditions. Here, the projections are accomplished by the orthogonality of the solenoidal and irrotational function spaces. The discrete form of this is eminently suited to finite element computation of divergence-free flow, as we shall see in the next section. There one will be able to address the question "How does one specify pressure-driven (Poiseuille) problems with a pressureless governing equation?".
The absence of pressure forces from the governing velocity equation demonstrates that the equation is not a dynamic one, but rather a kinematic equation where the divergence-free condition serves the role of a conservation equation. This all would seem to refute the frequent statements that the incompressible pressure enforces the divergence-free condition.
Consider the incompressible Navier–Stokes equations for a Newtonian fluid of constant density in a domainwith boundarybeing and portions of the boundary where respectively a Dirichlet and a Neumann boundary condition is applied : is the fluid velocity, the fluid pressure, a given forcing term, the outward directed unit normal vector to, and the viscous stress tensor defined as: Let be the dynamic viscosity of the fluid, the second-order identity tensor and the strain-rate tensor defined as: The functions and are given Dirichlet and Neumann boundary data, while is the initial condition. The first equation is the momentum balance equation, while the second represents the mass conservation, namely the continuity equation. Assuming constant dynamic viscosity, using the vectorial identityand exploiting mass conservation, the divergence of the total stress tensor in the momentum equation can also be expressed as: Moreover, note that the Neumann boundary conditions can be rearranged as:
In order to find the weak form of the Navier–Stokes equations, firstly, consider the momentum equation multiply it for a test function, defined in a suitable space, and integrate both members with respect to the domain :Counter-integrating by parts the diffusive and the pressure terms and by using the Gauss' theorem:
Using these relations, one gets: In the same fashion, the continuity equation is multiplied for a test function belonging to a space and integrated in the domain :The space functions are chosen as follows: Considering that the test function vanishes on the Dirichlet boundary and considering the Neumann condition, the integral on the boundary can be rearranged as: Having this in mind, the weak formulation of the Navier–Stokes equations is expressed as:
With partitioning of the problem domain and defining basis functions on the partitioned domain, the discrete form of the governing equation is
It is desirable to choose basis functions that reflect the essential feature of incompressible flow – the elements must be divergence-free. While the velocity is the variable of interest, the existence of the stream function or vector potential is necessary by the Helmholtz theorem. Further, to determine fluid flow in the absence of a pressure gradient, one can specify the difference of stream function values across a 2D channel, or the line integral of the tangential component of the vector potential around the channel in 3D, the flow being given by Stokes' theorem. Discussion will be restricted to 2D in the following.
We further restrict discussion to continuous Hermite finite elements which have at least first-derivative degrees-of-freedom. With this, one can draw a large number of candidate triangular and rectangular elements from the plate-bending literature. These elements have derivatives as components of the gradient. In 2D, the gradient and curl of a scalar are clearly orthogonal, given by the expressions,
Adopting continuous plate-bending elements, interchanging the derivative degrees-of-freedom and changing the sign of the appropriate one gives many families of stream function elements.
Taking the curl of the scalar stream function elements gives divergence-free velocity elements. The requirement that the stream function elements be continuous assures that the normal component of the velocity is continuous across element interfaces, all that is necessary for vanishing divergence on these interfaces.
Boundary conditions are simple to apply. The stream function is constant on no-flow surfaces, with no-slip velocity conditions on surfaces.Stream function differences across open channels determine the flow. No boundary conditions are necessary on open boundaries, though consistent values may be used with some problems. These are all Dirichlet conditions.
The algebraic equations to be solved are simple to set up, but of course are non-linear, requiring iteration of the linearized equations.
Similar considerations apply to three-dimensions, but extension from 2D is not immediate because of the vector nature of the potential, and there exists no simple relation between the gradient and the curl as was the case in 2D.
Recovering pressure from the velocity field is easy. The discrete weak equation for the pressure gradient is,
where the test/weight functions are irrotational. Any conforming scalar finite element may be used. However, the pressure gradient field may also be of interest. In this case, one can use scalar Hermite elements for the pressure. For the test/weight functions one would choose the irrotational vector elements obtained from the gradient of the pressure element.
The rotating frame of reference introduces some interesting pseudo-forces into the equations through the material derivative term. Consider a stationary inertial frame of reference, and a non-inertial frame of reference, which is translating with velocity and rotating with angular velocity with respect to the stationary frame. The Navier–Stokes equation observed from the non-inertial frame then becomes
Here and are measured in the non-inertial frame. The first term in the parenthesis represents Coriolis acceleration, the second term is due to centrifugal acceleration, the third is due to the linear acceleration of with respect to and the fourth term is due to the angular acceleration of with respect to .
The Navier–Stokes equations are strictly a statement of the balance of momentum. To fully describe fluid flow, more information is needed, how much depending on the assumptions made. This additional information may include boundary data (no-slip, capillary surface, etc.), conservation of mass, balance of energy, and/or an equation of state.
See main article: Continuity equation.
Regardless of the flow assumptions, a statement of the conservation of mass is generally necessary. This is achieved through the mass continuity equation, given in its most general form as:or, using the substantive derivative:
For incompressible fluid, density along the line of flow remains constant over time,
Therefore divergence of velocity is always zero:
Taking the curl of the incompressible Navier–Stokes equation results in the elimination of pressure. This is especially easy to see if 2D Cartesian flow is assumed (like in the degenerate 3D case with and no dependence of anything on), where the equations reduce to:
Differentiating the first with respect to, the second with respect to and subtracting the resulting equations will eliminate pressure and any conservative force. For incompressible flow, defining the stream function throughresults in mass continuity being unconditionally satisfied (given the stream function is continuous), and then incompressible Newtonian 2D momentum and mass conservation condense into one equation:
where is the 2D biharmonic operator and is the kinematic viscosity, . We can also express this compactly using the Jacobian determinant:
This single equation together with appropriate boundary conditions describes 2D fluid flow, taking only kinematic viscosity as a parameter. Note that the equation for creeping flow results when the left side is assumed zero.
In axisymmetric flow another stream function formulation, called the Stokes stream function, can be used to describe the velocity components of an incompressible flow with one scalar function.
The incompressible Navier–Stokes equation is a differential algebraic equation, having the inconvenient feature that there is no explicit mechanism for advancing the pressure in time. Consequently, much effort has been expended to eliminate the pressure from all or part of the computational process. The stream function formulation eliminates the pressure but only in two dimensions and at the expense of introducing higher derivatives and elimination of the velocity, which is the primary variable of interest.
The Navier–Stokes equations are nonlinear partial differential equations in the general case and so remain in almost every real situation.  In some cases, such as one-dimensional flow and Stokes flow (or creeping flow), the equations can be simplified to linear equations. The nonlinearity makes most problems difficult or impossible to solve and is the main contributor to the turbulence that the equations model.
The nonlinearity is due to convective acceleration, which is an acceleration associated with the change in velocity over position. Hence, any convective flow, whether turbulent or not, will involve nonlinearity. An example of convective but laminar (nonturbulent) flow would be the passage of a viscous fluid (for example, oil) through a small converging nozzle. Such flows, whether exactly solvable or not, can often be thoroughly studied and understood.
Turbulence is the time-dependent chaotic behaviour seen in many fluid flows. It is generally believed that it is due to the inertia of the fluid as a whole: the culmination of time-dependent and convective acceleration; hence flows where inertial effects are small tend to be laminar (the Reynolds number quantifies how much the flow is affected by inertia). It is believed, though not known with certainty, that the Navier–Stokes equations describe turbulence properly.
The numerical solution of the Navier–Stokes equations for turbulent flow is extremely difficult, and due to the significantly different mixing-length scales that are involved in turbulent flow, the stable solution of this requires such a fine mesh resolution that the computational time becomes significantly infeasible for calculation or direct numerical simulation. Attempts to solve turbulent flow using a laminar solver typically result in a time-unsteady solution, which fails to converge appropriately. To counter this, time-averaged equations such as the Reynolds-averaged Navier–Stokes equations (RANS), supplemented with turbulence models, are used in practical computational fluid dynamics (CFD) applications when modeling turbulent flows. Some models include the Spalart–Allmaras, –, –, and SST models, which add a variety of additional equations to bring closure to the RANS equations. Large eddy simulation (LES) can also be used to solve these equations numerically. This approach is computationally more expensive—in time and in computer memory—than RANS, but produces better results because it explicitly resolves the larger turbulent scales.
Together with supplemental equations (for example, conservation of mass) and well-formulated boundary conditions, the Navier–Stokes equations seem to model fluid motion accurately; even turbulent flows seem (on average) to agree with real world observations.
The Navier–Stokes equations assume that the fluid being studied is a continuum (it is infinitely divisible and not composed of particles such as atoms or molecules), and is not moving at relativistic velocities. At very small scales or under extreme conditions, real fluids made out of discrete molecules will produce results different from the continuous fluids modeled by the Navier–Stokes equations. For example, capillarity of internal layers in fluids appears for flow with high gradients. For large Knudsen number of the problem, the Boltzmann equation may be a suitable replacement. Failing that, one may have to resort to molecular dynamics or various hybrid methods.
Another limitation is simply the complicated nature of the equations. Time-tested formulations exist for common fluid families, but the application of the Navier–Stokes equations to less common families tends to result in very complicated formulations and often to open research problems. For this reason, these equations are usually written for Newtonian fluids where the viscosity model is linear; truly general models for the flow of other kinds of fluids (such as blood) do not exist.
The Navier–Stokes equations, even when written explicitly for specific fluids, are rather generic in nature and their proper application to specific problems can be very diverse. This is partly because there is an enormous variety of problems that may be modeled, ranging from as simple as the distribution of static pressure to as complicated as multiphase flow driven by surface tension.
Generally, application to specific problems begins with some flow assumptions and initial/boundary condition formulation, this may be followed by scale analysis to further simplify the problem.
Assume steady, parallel, one-dimensional, non-convective pressure-driven flow between parallel plates, the resulting scaled (dimensionless) boundary value problem is:
The boundary condition is the no slip condition. This problem is easily solved for the flow field:
From this point onward, more quantities of interest can be easily obtained, such as viscous drag force or net flow rate.
Difficulties may arise when the problem becomes slightly more complicated. A seemingly modest twist on the parallel flow above would be the radial flow between parallel plates; this involves convection and thus non-linearity. The velocity field may be represented by a function that must satisfy:
This ordinary differential equation is what is obtained when the Navier–Stokes equations are written and the flow assumptions applied (additionally, the pressure gradient is solved for). The nonlinear term makes this a very difficult problem to solve analytically (a lengthy implicit solution may be found which involves elliptic integrals and roots of cubic polynomials). Issues with the actual existence of solutions arise for (approximately; this is not ), the parameter being the Reynolds number with appropriately chosen scales. This is an example of flow assumptions losing their applicability, and an example of the difficulty in "high" Reynolds number flows.
A type of natural convection that can be described by the Navier–Stokes equation is the Rayleigh–Bénard convection. It is one of the most commonly studied convection phenomena because of its analytical and experimental accessibility.
Some exact solutions to the Navier–Stokes equations exist. Examples of degenerate cases—with the non-linear terms in the Navier–Stokes equations equal to zero—are Poiseuille flow, Couette flow and the oscillatory Stokes boundary layer. But also, more interesting examples, solutions to the full non-linear equations, exist, such as Jeffery–Hamel flow, Von Kármán swirling flow, stagnation point flow, Landau–Squire jet, and Taylor–Green vortex. Note that the existence of these exact solutions does not imply they are stable: turbulence may develop at higher Reynolds numbers.
Under additional assumptions, the component parts can be separated.
A steady-state example with no singularities comes from considering the flow along the lines of a Hopf fibration. Let be a constant radius of the inner coil. One set of solutions is given by:
for arbitrary constants and . This is a solution in a non-viscous gas (compressible fluid) whose density, velocities and pressure goes to zero far from the origin. (Note this is not a solution to the Clay Millennium problem because that refers to incompressible fluids where is a constant, and neither does it deal with the uniqueness of the Navier–Stokes equations with respect to any turbulence properties.) It is also worth pointing out that the components of the velocity vector are exactly those from the Pythagorean quadruple parametrization. Other choices of density and pressure are possible with the same velocity field:
Wyld diagrams are bookkeeping graphs that correspond to the Navier–Stokes equations via a perturbation expansion of the fundamental continuum mechanics. Similar to the Feynman diagrams in quantum field theory, these diagrams are an extension of Keldysh's technique for nonequilibrium processes in fluid dynamics. In other words, these diagrams assign graphs to the (often) turbulent phenomena in turbulent fluids by allowing correlated and interacting fluid particles to obey stochastic processes associated to pseudo-random functions in probability distributions.
Note that the formulas in this section make use of the single-line notation for partial derivatives, where, e.g.
A 2022 paper provides a less costly, dynamical and recurrent solution of the Navier-Stokes equation for 3D turbulent fluid flows. On suitably short time scales, the dynamics of turbulence is deterministic.
From the general form of the Navier–Stokes, with the velocity vector expanded as, sometimes respectively named,,, we may write the vector equation explicitly,
Note that gravity has been accounted for as a body force, and the values of,, will depend on the orientation of gravity with respect to the chosen set of coordinates.
The continuity equation reads:
When the flow is incompressible, does not change for any fluid particle, and its material derivative vanishes: . The continuity equation is reduced to:
Thus, for the incompressible version of the Navier–Stokes equation the second part of the viscous terms fall away (see Incompressible flow).
This system of four equations comprises the most commonly used and studied form. Though comparatively more compact than other representations, this is still a nonlinear system of partial differential equations for which solutions are difficult to obtain.
A change of variables on the Cartesian equations will yield the following momentum equations for,, and
The gravity components will generally not be constants, however for most applications either the coordinates are chosen so that the gravity components are constant or else it is assumed that gravity is counteracted by a pressure field (for example, flow in horizontal pipe is treated normally without gravity and without a vertical pressure gradient). The continuity equation is:
This cylindrical representation of the incompressible Navier–Stokes equations is the second most commonly seen (the first being Cartesian above). Cylindrical coordinates are chosen to take advantage of symmetry, so that a velocity component can disappear. A very common case is axisymmetric flow with the assumption of no tangential velocity, and the remaining quantities are independent of :
|In spherical coordinates, the,, and momentum equations are (note the convention used: is polar angle, or colatitude,):
Mass continuity will read:
These equations could be (slightly) compacted by, for example, factoring from the viscous terms. However, doing so would undesirably alter the structure of the Laplacian and other quantities.
The Navier–Stokes equations are used extensively in video games in order to model a wide variety of natural phenomena. Simulations of small-scale gaseous fluids, such as fire and smoke, are often based on the seminal paper "Real-Time Fluid Dynamics for Games" by Jos Stam, which elaborates one of the methods proposed in Stam's earlier, more famous paper "Stable Fluids" from 1999. Stam proposes stable fluid simulation using a Navier–Stokes solution method from 1968, coupled with an unconditionally stable semi-Lagrangian advection scheme, as first proposed in 1992.
More recent implementations based upon this work run on the game systems graphics processing unit (GPU) as opposed to the central processing unit (CPU) and achieve a much higher degree of performance.Many improvements have been proposed to Stam's original work, which suffers inherently from high numerical dissipation in both velocity and mass.
An introduction to interactive fluid simulation can be found in the 2007 ACM SIGGRAPH course, Fluid Simulation for Computer Animation.


text:
A night of stargazing becomes something more when Rion meets a ghost.
This episode was written and produced by Tal Minear. Scarlet was voiced by Ace Corsaira (she/her) and Thea was voiced by Amani (she/her). The voice of Rion was Tal Minear (they/them).
The transcript for this episode can be found here.

domain: entertainment


text:
The following 12 songs will participate in tonight's second semi-final.
The voting will be determined by a 50/50 mix of public televoting and the nine members of the jury.
The six songs that qualified from the first semi-final were;
The final will take place on Saturday the 16th of February in the city of Ventspils.
Stay tuned to eurovision.tv where we will bring you the results of tonight's second semi-final.


text:
President Barack Obama said Saturday his inauguration will be a symbol of U.S. democracy, as well as an “affirmation that we’re all in this together."
Grabbing a paintbrush and pitching in at a volunteer event to spruce up an elementary school in northeast Washington, Obama invoked Martin Luther King – whose birthday is celebrated Monday – the day Obama publicly takes the oath of office for a second term in front of hundreds of thousands on the National Mall.
"I’m always reminded that (King) said everybody wants to be first, everybody wants to be a drum major; but if you’re going to be a drum major, be a drum major for service, be a drum major for justice, be a drum major for looking out for other people,” said Obama, who will take the oath using a Bible that King used, as well as one used by Abraham Lincoln.
Obama was joined Saturday by First Lady Michelle Obama at the Burrville Elementary School event – and by thousands across the country at other events, including Obama Cabinet officials, marking a National Day of Service. The Obamas in 2009 started a tradition of holding a service day the weekend before the swearing-in.
Obama called the volunteer events “really what America is about. This is what we celebrate."
He said his inauguration is will be “a symbol of how our democracy works and how we peacefully transfer power,” but added, “it should also be an affirmation that we’re all in this together and that we’ve got to look out for each other and work hard on behalf of each other."
Vice President Joe Biden, his wife, Jill, and a dozen children and grandchildren joined volunteers at the D.C. Armory for a Unite America in Service event organized by the Points of Light organization, which Biden noted was inspired by former President George Herbert Walker Bush. At his 1989 inaugural address, Bush called on a "thousand points of light” to help others.
Volunteers at the event packed 100,000 care kits filled with necessities for deployed and wounded U.S. service members, veterans and first responders. The kits included lint rollers, dental floss, toothbrush and toothpaste, wipes, bandages and cotton swabs.
Biden called the day “so important” and noted that service members are "not looking for anything, but knowing that we remember is an important piece of the equation."
Biden also invoked King. He said the late civil rights icon instilled "this notion of absolute service." And, he added, “we have to move back to reaching out to people.”
A day before Biden takes the oath for a second term, he declared the U.S. is “on the cusp of doing some really great things.” The country is known for possibilities, he said, “and the possibilities are immense.”
The folksy Biden paused frequently to pose for pictures with volunteers and at one point, apparently unable to resist the temptation, lobbed a bag of cotton swabs at the reporters trailing him.
Volunteers were to participate in events in every state in the country. Outgoing Interior Secretary Ken Salazar was to join department volunteers and youth from the Student Conservation Association to work on beautification projects at the Martin Luther King, Jr., Memorial in Washington.
Though Obama doesn’t officially start his second term until he takes the oath Sunday at a small White House event, his entourage was already sporting a change: three vehicles in the presidential motorcade carried new license plates that say: "Taxation Without Representation." – a nod to the quest for full voting rights in Washington, D.C.
The city had the plates created to protest the fact that district resident don’t have full voting rights in Congress, although they are federal taxpayers.
President Bill Clinton used the plates, though President George W. Bush did not. Obama did not in his first term, but after four years in Washington, “has seen firsthand how patently unfair it is for working families in D.C. to work hard, raise children, and pay taxes without having a vote in Congress," White House spokesman Jay Carney said Thursday.
Though attendance is not expected to rival Obama’s 2009 inauguration – when 1.8 million people crowded into the city to be a part of his historical swearing-in -- there was a festive feel to downtown Washington Saturday. Tourists bundled for the January cold snapped photographs of themselves in front of the inaugural parade viewing stand at the White House, and thousands attended pre-inaugural parties.
Some inaugural celebrants partied in style, such as the several hundred attending a California-centric Presidential Inaugural Luncheon & Fashion Show. Sponsored by the California State Society and the Fashion Institute of Design & Merchandising, the soiree featured models wearing gowns parading before politicians wearing, for the most part, off-the-rack suits.
"We’re on the cutting edge of fashion," declared Rep. Ed Royce, R-Calif., who chairs the House Foreign Affairs Committee.
Michael Doyle of McClatchy’s Washington Bureau contributed to this report.


text:
, New Jersey
Who would have thought that the sleepy Village of Chestnut Ridge would be the place to go when searching for authentic artisan Brick Oven Italian Pizza and French baguettes, batards, and boules? That’s right, Harvest Moon, our well established, local catering service owned and operated by Dave Venitelli, has recently expanded his customers’ options by creating a virtual culinary haven. He and his staff opened a Café, Bakery, and Pizzeria all in one called La Maison du Pain. Here, you will encounter a unique atmosphere teaming with delicacies that will tickle your nose and palate! If you’re looking for bread, I already mentioned baguettes, batards, and boules. They also bake ciabattas and a variety of rolls, both large and small. They sell croissants loaded with butter and/or chocolate, and a variety of pastries, muffins and the Most Amazing Cinnamon Rolls! Once you’ve had one of these, you’ll forget about Cinnabon! These are really the BEST! If you’re looking for French pastries, pies, and cakes, look no further! They even offered little individual Chocolate Mousses last weekend. The best part is you never know what you will find. Oh…did I mention the Biscotti? Orange, Pistachio and Chocolate. Perfetti!

domain: food


White paper from Spee Dee discusses the application of servo controls and a new innovative funnel design to rotary auger fillers for free-flowing and non-free flowing applications. Benefits include dramatic reductions in changeover time and increased efficiencies.
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Spee-Dee's Rotary Auger Filler is designed to accurately fill a broad cross section of products, such as spices, non-dairy creamers, coffee and cornstarch, into a variety of bottles and other rigid containers at rates of 100 to 400 units per minute.
The SATO America S8412, 305dpi print engine partnered with CTM Labeling System's model 3600 printer applicator performs a leading-edge corner wrap. The high-speed, rotary acuator of the CTM 3600 places the label firmly on the case’s leading panel then smoothly wraps the label around the corner and down the side.
Shampoo and conditioner. Peanut butter and jelly. Cleanser and moisturizer. Berry and vanilla yogurt. Swirl filling is the latest packaging technique to visually entice consumers to purchase some of their favorite combinations in a single package.
Fogg Filler, a market leader in the design and manufacture of rotary filling systems for the liquids industry, is continually focused on improving technology that better serves our customers and the environment. Fogg’s new Chemical Supply & Recovery System will help you save 96-98.5% of fluid losses for your new or existing line. This is a savings everyone can appreciate.
The ELECTRO-WRAP SERIES® floor mounted automatic rotary tower stretch wrapper from ARPAC requires no pneumatic hookup, special pneumatic plumbing, or air compressor to stretch wrap unstable pallet loads that are either too light or too heavy to rotate on a turntable wrapper.


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0800 999 69 62
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TThe farming and agriculture sector is a vital part of our economy and one of our oldest industries.
Today, there’s a wealth of new machinery and technology available to help farms maximise their potential for growth and improve efficiency.
Our team has vast knowledge of the farming industry and extensive experience of delivering top funding for agricultural businesses. We can help you find a way to spread the cost of the agriulturaal machinery, vehicles and technology you need, through a tailored agricultural hire purchase, lease or refinance packages
Our expertise – as experts in the agricultural industry, we understand your challenges and have the experience to fund the assets you require.
Cash flow management – you can keep funds to reinvest in your business and benefit from tax efficiencies.
Funding assets – we can fund almost any business asset.
Providing one-stop-finance – we bring the best terms in a seamless, hassle free process, and can continue to offer asset funding solutions as your business develops and grows.

domain: agronomy


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The Bielefeld Academic Search Engine contains more than 30 million scientific
documents, full texts and references of books and articles, most of which are freely
accessible. This search engine offers intellectually selected resources, and includes only
document servers that comply with the specific requirements of academic quality and
relevance. It provides "Refine your search result" opinions (by author, subject, DDC, year of publication, content provider, language, document type, access and terms of re-use).

domain: library


Sesame Access is one of the most reliable places to locate affordable stairlifts, and you can also find bespoke lifts that will meet your specific needs. The website offers a broad selection of lifts and also offers a no-cost home consultation. There is a staircase lift for you, no matter if you need one for one floor or for the entire home.
Sesame Access manufactures and installs stairs lifts that are affordable and simple to operate. They are designed to meet the needs of people of different ages and physical abilities. Charlie Lyons founded the company after becoming frustrated by the inaccessibility of the London Art Gallery for wheelchairs. He began sketching out ideas and constructed a prototype in his Staines shed.
Sesame Access offers stairlifts that can be installed in different types of buildings at varying prices. They also offer custom solutions for famous buildings. They are able to meet all DDA requirements and can easily be installed to existing architectural features. Stairlifts can be a great investment that can enhance mobility and can be affordable. Sesame Access also offers a one-year guarantee and service every six months.
AmeriGlide is an stairlift which gives you easy access to every level of your house. This stairlift allows for easy entry and departure. It features a 180-degree swinging seat and high-tech nylon wheels.
A stairlift could be an ideal solution for someone who is unable to climb stairs. It can be set up both outdoors and indoors and be positioned over existing staircases or stairs. The cladding may be made from a variety materials, including marble and glass. These aren’t obvious accessibility solutions for disabled persons, but they provide accessibility and independence.
You can purchase a stairlift from an authorized dealer on the internet. There are many kinds of stairlifts on the market. stairlifts prices is important to choose the appropriate one for you. While most stairlifts come with a seatbelt, a few manufacturers offer a retractable option for those who want it. The retractable seatbelt is simple to secure and hold. An ‘Immobilizer” seatbelt can also be used, which will stop the stairlift from working until the seatbelt is engaged. A lap-diagonal seatbelt provides additional protection over your shoulders. A five-point harness belt provides extra security between your legs.
Handicare has a variety models for straight and curving stairways. Some models feature powered seats and tracks with hinges on the top models. The company also offers an unique outdoor/indoor staircase lift. The company also provides low-cost stairs lifts that have curve rails.
The company also offers free installation and delivery which makes it a cost-effective alternative for those who are on a tight budget. It does not provide financing. Most stairlift companies do not offer financing in store, but they do offer no- or low-interest credit cards as well as local and state-wide grants.


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BMR GROUP WELCOMES ANDRÉ LAVOIE AS VICE PRESIDENT, FINANCE
Boucherville, January 28, 2021— BMR Group is proud to announce that as of February 3, André Lavoie will join the company’s management team as Vice President, Finance.
Throughout his career, Mr. Lavoie has contributed to the growth and business success of numerous companies, including some 17 years at the Caisse de dépôt et placement du Québec, where he was Senior Director, Investments, Private Equity, since 2016.
Graduate of HEC Montréal in finance and senior manager in corporate finance, strategy and investment, André Lavoie is a leader with integrity and passion, known as much for his business acumen and rigour as for his leadership and his ability to listen. There is no doubt that he will be a key player in the implementation of BMR Group’s most recent strategic plan, which will serve as the foundation for the continued growth of the company’s activities across Canada.


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A MUM who still breastfeeds her five-year-old daughter has been slammed by horrified Good Morning Britain viewers, who say her decision is "wrong".
Emma Shardlow-Hudson, from Grimsby, breastfeeds daughter Alex, five, and son Ollie, two, in between meals - and sometimes even nurses them at the same time.
Appearing on GMB this morning, the 29-year-old said her kids "didn't know any different", and have friends who are also self-weaning.
Emma claims breastfeeding stops Alex picking up germs at school and getting ill - but viewers think she's setting her kids up for "bullying" and "abuse from others".
Speaking to Richard Madeley and Charlotte Hawkins, Emma insisted the reaction from people she knows is normally positive.
When asked if she continues nursing Alex to "keep her a baby", Emma said: "No gosh not at all I am quite happy for her to grow up."
But viewers were horrified, with one tweeting: "5 years old is taking the whole breast fed thing too long!
"Opening her up for abuse from others! Theres no health benefits at this age!"
Julie Kelly added: "#breastfeeding At 5 is just wrong the child will be #stigmatised and bullied".
While Natalie Smith wrote: "If you want to feed your kids breast milk at age 5 pump it! There is no reason to continue to feed from the breast."
Tracey Morgin tweeted: "I think about the kids, they are going to remember breast feeding.
"Surely no child should be able to remember something like that.
"Funny how these women who breast feed their children past school age always seem to end up on TV talking about it. Do you think they enjoy the attention".
And Broken Angel asked: "sorry why is she posting pics of her children breastfeeding .
"The children will be embrassed in their teens something should remain in the comfort of their own homes not plastered on tv".
MOST READ IN FABULOUS
But others backed Emma's decision, saying "fair play to her".
One viewer, Rebekah, insisted breastfeeding was "the most natural thing in the world, and it should be encouraged and supported more!"
While some were more distracted by Richard Madeley supposedly telling Emma "you’ve got great t**s". Here's what he ACTUALLY said...

domain: sociology


- RC027P Gas Regulator Designed for use with Calor 5kg Propane Patio Gas and 13kg Propane Patio Gas Cylinders.
- Capacity 1.5kg/hr Max Inlet Pressure 16bar
- Nozzle outlet to suit 8mm ID hose
- Operating pressure 37mbar Inlet 27mm clip on connection
- Nozzle outlet to suit 8mm ID hose Approved to EN16129
- 37mbar PROPANE GAS REGULATOR STANDARD SCREW IN TYPE
- Outlet pressure: 37 mbar max , Cylinder connection standard propane screw , Outlet 8mm nozzle , Rating 1.5 kg per hr ,
- This regulator can be used on any brand of screw in type propane cylinder
- Ideal for use with Bbq, Patio heater, Cookers, Caravans & camping stoves.
- FITS: CALOR GAS 47kg 19kg 13kg 11kg 6kg 3.9kg CYLINDERS , FLOGAS 47kg 19kg 11kg 6kg 3.9kg CYLINDERS
- 27mm PATIO / BBQ Regulator 2m Hose Kit & 2 x Mikalor W2 Stainless Band Hose Clips
- To fit 27mm clip on GREEN Patio cylinders , Calor gas 13kg and 5kg green patio gas , Flogas 11kg and 9kg green patio gas , BP Patio LIght, and any other 27mm clip on propane cylinder
- 1 X 27mm CLIP ON Patio Gas Regulator 1.5 kgh 37mbar might be either one of the two regulators shown in the pictures
- This Regulator Will Not Fit Standard Propane Screw On Gas Cylinders
- 2m High Pressure 8mm Hose BS3212/2 , 2 x Mikalor Stainless Band hose clips
- CE & CSA Approved Unit ,Weak Current FD4 Dump Safety Switch for gas R≤10 mΩ
- Thermocouple wire total 350mm M8*1 Ends
- Special Design for Gas heaters Outdoor heaters Gold plated connectors inside.
- Suitable for Propane gas heaters with Thermoelectric Safety
- This model is suitable for room gas heater, outdoor patio heater and other Thermoelectric gas products
- PROPANE GAS REGULATOR 2m HOSE KIT WITH 2 Stainless Band Hose Clips
- To fit Propane screw in type Cylinders 47kg, 19kg, 13kg, 11kg, 6kg, amd 3.9kg
- This regluator will not fit a green patio gas cylinders
- 1 x propane regulator
- 37mbar propane with pol nut , 2 x hose clips , 2m high pressure 8mm Hose
- Ceramic plaque type heater
- Mounts on the rim of a propane cylinder
- Gas bottle not included
- Fuel: Propane
- Fuel Consumption: 0.22-0.33kg/hr
- Thermoelectric Safety: The patio gas heater dump switch will automatically stop the heater when the heater is tilted or dropped, which can prevent the occurrence of gas leakage when the fire is...
- Wide Compatibility: Suitable for is suitable for propane, patio and thermoelectric gas heaters with thermoelectric safety room gas heater, outdoor patio heater and other thermoelectric gas products.
- Easy Install: The probe is connected to the ignition device, the thermocouple is connected to the valve, and the other two ports are connected to the safety dumping switch, which does not require special...
- Dimensions: Universal thermocouple, thread M 8 x 1, total extension length 353mm/13.9inch.Suitable for weak dump switches with gas R ≤ 10mΩ. Check that it is suitable for your heater before purchasing...
- Thermoelectric Safety: The patio gas heater dump switch will automatically stop the heater when the heater is tilted or dropped, which can preven t the occurrence of gas leakage when the fire is...
- HEAVY DUTY GAS THERMOCOUPLE
- Genuine replacement fan oven heater element for your oven.
- This can fit ovens sold by different manufacturers and brands.
- For a full list of models this part/accessory is suitable for click on “See more product details” and then click “See all product details”.
- This is a genuine product.
- Take safety precautions when repairing all appliances. Repairs to gas appliances should only be made by a Gas Safe Registered engineer.
Last update on 2021-09-29 / Affiliate links / Images from Amazon Product Advertising API
Best Goodman Gas Furnaces Buying Guide
Are you shopping for great Goodman Gas Furnaces? Are you looking for a bargain, the best value, or the top-of-the-range model? Are you finding research to be stressful?
We know the feeling, which is exactly why we’ve done all the research for you. We’ve looked at all the options when it comes to Goodman Gas Furnaces, and we’ve come up with what we think are the greatest Goodman Gas Furnaces on the market today. Also, we’ve covered all the questions you might have, so you know you’re getting a great deal.
When it comes to buying the best, we can anticipate many of the questions you might have, and we know exactly what features you’re looking for when it comes to Goodman Gas Furnaces. To meet your requirements, we think you might need to know the answers to the following questions:
- Should I buy Goodman Gas Furnaces?
- What will Goodman Gas Furnaces do for me?
- What should I look for when shopping for quality Goodman Gas Furnaces?
- What’s the difference between good Goodman Gas Furnaces and the best ones?
- Which models or manufacturers are currently leading the market?
- Where should I go if I want to learn more about Goodman Gas Furnaces?
While the above questions are far from comprehensive, and you probably have far more concerning Goodman Gas Furnaces. This buying guide and recommendations should help arm you with the knowledge you need to get a great deal. If you have any other additional questions please feel free to reach out to us and we’ll get back to you as soon as we can.
If you’d like to do your research elsewhere, then there are near endless buying guides for Goodman Gas Furnaces available online, through specialist reviewers, subject matter experts, as well as word of mouth reviews. Getting a great deal and one of the best performing Goodman Gas Furnaces is not difficult, look at our guide and review our recommendations.
Our Goodman Gas Furnaces buying guide is 100 percent unbiased and based on real experiences, market data, user feedback, and authenticity. Our suite of tools includes machine learning AI, augmented big data analytics, as well as good old-fashioned research, testing, and understanding.
Combined together this allows us to put together a comprehensive top 10 best available Goodman Gas Furnaces.
Our processes and procedures that allow us to make buying recommendations are based on a scientific process that includes but is not limited to the following:
1. Brand Recognition and Value: Every manufacturer and brand of Goodman Gas Furnaces has its own distinct set of values. Most offer something unique, but that doesn’t necessarily equate to good. We look at these factors when making our guides and recommendations.
2. Selling Points: When stripped back to be basics, what matters when it comes to Goodman Gas Furnaces?
3. What’s included: Are they packed with every feature and made to meet our stringent criteria?
4. Value for money: Are you getting a great deal when you buy Goodman Gas Furnaces?
5. Customer Satisfaction: Are customers consistently rating the product well above average?
6. Long-term value: Is the buying experience short-lived? Have we found that some users are having a bad experience? What does that tell us about Goodman Gas Furnaces?
7. Field Tested Quality: When we tested the Goodman Gas Furnaces in real-world scenarios, did it live up to expectations? Was it lacking in a particular area or was there an area in which it exceeded?
8. Reliability: If the Goodman Gas Furnaces are well made with a professional finish, then it can be an indication of a product that is expected to last longer than most.
We know that new Goodman Gas Furnaces might be released any day, which is why we are constantly updating our top 10 list to ensure we have the latest information. Check back regularly to find updates, new reviews, and changes made to our list.
If you find that any of our information is incorrect, biased, wrong, or no longer accurate, then please do reach out to us and let us know. You can always reach out to us via our contact form. If you would like more information on our website’s purpose, then take a look at our vision statement here.