when does the hunger games mockingjay part 2 come out

The Hunger Games: Mockingjay – Part 2 is a 2015 American dystopian science fiction adventure film directed by Francis Lawrence, with a screenplay by Peter Craig and Danny Strong. It is the fourth and final installment in The Hunger Games film series, and the second of two films based on the novel Mockingjay, the final book in The Hunger Games trilogy by Suzanne Collins. Produced by Nina Jacobson and Jon Kilik, and distributed by Lionsgate, the film features an ensemble cast that includes Jennifer Lawrence, Josh Hutcherson, Liam Hemsworth, Woody Harrelson, Elizabeth Banks, Julianne Moore, Philip Seymour Hoffman, and Donald Sutherland. Hoffman died in February 2014, making Mockingjay – Part 2 his final film role. Principal photography on both parts of the film began on September 23, 2013 in Atlanta, before moving to Paris for two weeks of back-to-back filming and officially concluding on June 20, 2014, in Berlin and at Babelsberg Studios, Germany.[6]

The Hunger Games: Mockingjay – Part 2

The story continues from The Hunger Games: Mockingjay – Part 1 with Katniss Everdeen (Jennifer Lawrence) preparing to win the war against President Snow (Donald Sutherland) and the tyrannical Capitol. Together with Peeta, Gale, Finnick, and others she travels to the Capitol to kill Snow. However, President Coin (Julianne Moore), the leader of District 13 and the rebellion, hides a bigger agenda that could not only jeopardize Katniss' life, but the future of Panem.

Mockingjay â€“ Part 2 was released on November 20, 2015 in the United States, in 2D and IMAX, and internationally in 2D, 3D, RealD Cinema, and IMAX 3D in select territories; it is the only film in the series widely released in 3D. Falling below expectations internationally and domestically with a $102.7 million gross during its opening weekend in North America, the film had the sixth-biggest opening in 2015, but held at number one at the international box office for four consecutive weekends. The film grossed over $653 million worldwide, making it the ninth highest-grossing film of 2015 and the lowest-grossing of the four films in the franchise,[5] but still a commercial success.[7]

Part 2 was positively received by critics for its performances, screenplay, and action sequences, though it was criticized for splitting the final adaptation into two separate parts. The film had garnered a nomination for Best Fantasy Film at the 42nd Saturn Awards. For her part, Jennifer Lawrence was awarded as the Favorite Movie Actress at the 2016 Kids' Choice Awards and Best Hero at the 2016 MTV Movie Awards.

Katniss Everdeen is recovering after being attacked by Peeta Mellark, who has been brainwashed by the Capitol.

Despite her intention to kill President Snow, Katniss' request is declined by Alma Coin, as she is too valuable to risk losing. However, Katniss volunteers to be sent to District 2, the final district still controlled by the Capitol. 13’s air force launches a full-scale bombing on a mountain nicknamed The Nut, which houses the Capitol’s main weaponry and air force, with few survivors. Although Katniss manages to convince the district to join the rebellion, she is shot by the one of the survivors who is then gunned down; Katniss survives the gunshot wound due to her bulletproof Mockingjay costume.

At the wedding of Finnick Odair and Annie Cresta, Katniss is convinced by Johanna Mason to sneak aboard a supply ship leaving for the Capitol. Unable to bring her back, Coin has her assigned to the “Star Squad”, which is led by Boggs and includes Gale, Finnick, Cressida, Messalla, Castor, Pollux, Leegs 1 and 2, Mitchell, and Homes. They will follow in relative safety behind the actual invasion of the Capitol, providing video of their incursion for propaganda purposes. Boggs carries a holographic map (the “Holo”) to help them evade known booby-trapped “pods” which line the streets of the Capitol. Coin also sends Peeta to join the squad, even though he has not fully recovered from the Capitol’s conditioning.

As they venture deeper into the Capitol, Boggs accidentally triggers a land mine and is fatally wounded, giving the Holo to Katniss before dying. The squad triggers another pod which releases a flood of lethal black tar. Peeta momentarily succumbs to his conditioning and attacks Katniss, killing Mitchell in the process. The group takes shelter in an abandoned building, where Jackson, the second-in-command, attempts to commandeer the Holo, until Katniss says that she is under secret orders from Coin to kill Snow. Katniss and most of the group escape just before a squad of Peacekeepers arrive and destroy the building, killing the Leegs twins after they had earlier stayed behind. The Capitol then broadcasts a message with Caesar Flickerman announcing Katnissâ€™s death before Snow starts to make a speech against the rebellion, which is interrupted by Coin, who delivers an impassioned eulogy for her to rally the rebels.

Castor decides to have them go through the sewers to avoid getting detected by the Capitol's forces, having Pollux show the way down. The team manages to avoid further pods, but they are attacked by a horde of genetically engineered creatures called “mutts” when Snow finds out that they are still alive. Jackson, Castor, and Homes are killed as the squad flees through the sewers. Finnick fights off the mutts with his trident and pocket-knife to allow the rest of the team to escape, but they overwhelm him and Katniss is forced to set the Holo’s self-destruct, killing Finnick and the remaining mutts. While running from pursuing Peacekeepers, Messalla is melted by a pod. The surviving team members reach the surface and take refuge in a shop, where Tigris, a former Hunger Games stylist and rebel sympathizer, hides them in her basement.

As rebel forces gain ground, Snow invites fleeing Capitol citizens into his mansion for protection. Katniss and Gale join the crowd, posing as refugees. As rebels arrive and attack, Peacekeepers capture Gale and herd Capitol children toward the palace gates. A hovercraft with Capitol markings flies overhead and drops small parcels into the crowd. The parcels explode, killing and injuring many people. A team of rebel medics attempt to help the injured, including Katnissâ€™s sister Prim. As Katniss rushes forward, a second wave of bombs detonate, killing Prim and knocking Katniss unconscious.

Upon recovering, Katniss learns the Capitol has been conquered and that Snow is captured. When Katniss confronts Snow in his greenhouse, he explains that Coin orchestrated the bombing using a Capitol hovercraft to make it look like he would kill their children and to turn his soldiers against him. Katniss disbelieves Snow until he reminds her that they promised not to lie to each other. She realizes that the incident resembles a trap that Gale had developed earlier. When Gale doesn't deny that it may have been based on his idea, Katniss becomes heartbroken and cuts all ties with him. Coin declares herself as the interim President of Panem and invites the remaining Hunger Games victors to vote on a proposal to have another Hunger Games using the children of the Capitol as a symbolic gesture to satisfy the districts. Peeta, Beetee and Annie disagree with the idea, while Johanna and Enobaria agree. Katniss votes yes in exchange for the right to publicly execute Snow and to avenge her sisterâ€™s death, having realized that Snow was telling the truth about Coin in the process. Haymitch considers the situation and then swings the vote in favor.

At the execution, Katniss kills Coin instead of Snow, thus avenging Prim. A riot ensues and, after Peeta stops her from committing suicide via pills, Katniss is taken into custody while witnessing Snow get beaten to death by charging rebels. Once it is all over, Katniss receives a letter from Plutarch Heavensbee on her actions and is assured that she will eventually be pardoned by the newly appointed President of Panem for her crime and will be able to return to District 12 once the dissension quiets. At District 12 she is joined by Peeta, who has recovered from his condition. Commander Paylor is elected the new President of Panem, and Katniss, Peeta, and Haymitch bond over their shared trauma.

In the epilogue years later, Katniss and Peeta play with their two children, and Katniss realizes she made the right choice when she tells her infant that "there are much worse games to play."

On July 10, 2012, Lionsgate announced that the film adaptation of Mockingjay would be split into two parts; The Hunger Games: Mockingjay – Part 1, released on November 21, 2014, and The Hunger Games: Mockingjay – Part 2, released November 20, 2015.[33] On November 1, 2012, Francis Lawrence, director of The Hunger Games: Catching Fire, announced that he would return to direct both final films in the series.[34] Talking about direction for last two parts Francis explains, "I felt a different kind of pressure," he explains. "[On 'The Hunger Games: Catching Fire'], I had to prove myself a little bit as the new guy in the game. It was a relief that it was received well by the fans. Even though I was relieved, it was only momentary; it sort of set the bar higher for the next one!."[35]

On December 6, 2012, Danny Strong announced that he would write the third and fourth films.[36] On February 15, 2013, Lionsgate approved the script for Part 1 and gave Strong permission to write that of Part 2.[37] In August, Hemsworth confirmed that shooting of the film would begin the following month.[38]

The film's production began on September 16, 2013, in Boston, Atlanta, and Los Angeles.[39] Studio Babelsberg co-produced and oversaw production services for the film.[40] On November 13, 2013, producer Nina Jacobson revealed that Peter Craig was also hired to write the adaptations.[1] The film carried a production budget of $160 million with a further $55 million spent on promotion and advertisements, and $13.9 million in television advertisements.[41]

All the principal cast such as Jennifer Lawrence as Katniss, Josh Hutcherson as Peeta, Liam Hemsworth as Gale, Woody Harrelson as Haymitch, Donald Sutherland as President Snow, Elizabeth Banks as Effie, Willow Shields as Prim, Paula Malcomson as Mrs Everdeen and Stanley Tucci as Caesar,[42] return to reprise their roles.[29] Julianne Moore also returned to reprise her role as President Alma Coin, along with Philip Seymour Hoffman, who died during the filming in February 2014, as Plutarch. He had nearly completed his scenes,[43] and his two remaining scenes were rewritten to compensate for his absence.[44] Regarding Hoffman's scenes, Lawrence commented that, "He had two substantial scenes left and the rest were appearances in other scenes. We had no intention of trying to fake a performance, so we rewrote those scenes to give to other actors… The rest, we just didn’t have him appear in those scenes. There’s no digital manipulation or CG fabrication of any kind."[45] One of the changed scenes saw the character of Plutarch sending Katniss a letter in prison, read by Haymitch, rather than coming himself to talk to her after her arrest for assassinating President Coin, explained as him being unable to see her for political reasons after her actions, which he nonetheless supports.

On August 26, 2013, it was announced that actress Stef Dawson had joined the cast to portray Annie Cresta.[26] Lionsgate announced on September 13, 2013, that Julianne Moore joined the cast to play President Alma Coin.[12] The same month, Lily Rabe, Patina Miller, Mahershala Ali, Wes Chatham, and Elden Henson were announced to have joined the cast.[21][24][22] to reprise their roles of Commander Lyme, Commander Paylor, Boggs, Castor, and Pollux, respectively.[46] During this time, there was also a casting call for extras.[47] Rabe subsequently had to leave the film due to a scheduling conflict with the 2014 Shakespeare in the Park production of Much Ado About Nothing.[48] On April 4, 2014, it was announced that she would be replaced by Gwendoline Christie to portray Lyme.[29]

Principal photography began on September 23, 2013, in Atlanta, and concluded on June 20, 2014, in Berlin, Germany;[49] the two parts were filmed back-to-back.[6] In October 2013, filming took place in Rockmart, Georgia.[50] After the cast and crew took a break to promote The Hunger Games: Catching Fire, filming resumed on December 2, 2013. On December 14, 2013, shooting was held at the Marriott Marquis in Atlanta.[51] On December 18, shooting began at Caldwell Tanks in Newnan, Georgia.[52]

Philip Seymour Hoffman, who plays Plutarch Heavensbee, died on February 2, 2014. He had completed filming his scenes for Part 1 and had a week left of shooting for Part 2; Lionsgate thereafter released a statement affirming that since the majority of Hoffman's scenes had been completed, the release date for Part 2 would not be affected.[53][54] It was initially announced that Hoffman would be digitally recreated for a major scene involving his character that had not been shot,[55][56] but Francis Lawrence later stated that he had rewritten Hoffman's two remaining scenes to compensate for the actor's absence, and there would be "no digital manipulation or CG fabrication of any kind".[57] In a scene near the end of the film which was to have shown Plutarch speaking with Katniss in detention, Woody Harrelson's character instead reads her a letter from him.[58]

Filming in Atlanta completed in mid-April 2014,[59] and production moved to Europe.[60][61] On May 9, filming took place in Noisy le Grand, Paris.[62] It is the same location where Brazil (1985) was filmed 30 years earlier.[63] Toward the end of May, the cast and crew shot scenes at several locations in Berlin and Brandenburg, Germany. In Rüdersdorf, Brandenburg, the crew shot scenes for the portrayal of District 8 in an old cement factory. Hemsworth was injured on the set and was brought to a doctor in the Berlin borough Mitte.[64] Scenes for District 2 were shot at Berlin Tempelhof Airport.[65] Scenes for the underground approach on the Capitol were filmed in the Metropolitan Area Outer Underground Discharge Channel in Japan. A German casting agency sought 1,000 ethnically diverse extras (African, Asian, Southern-European, and Turkish) and "lived faces" to shoot scenes at the Babelsberg Film Studio.[66]

The film score was released on December 4, 2015. James Newton Howard returned to compose the film score; unlike the previous films in the series, there is no additional pop companion album with songs inspired by the film.[68] Jennifer Lawrence performed "Deep in the Meadow",[69] a lullaby that she sang in the first film.[70]

Along with the film's first teaser poster,[71] Lionsgate released a teaser trailer on March 18, 2015, titled The Hunger Games Franchise Logo — Remember, featuring the transformation of the Mockingjay, along with notable quotes from the previous three movies, as well as a quote from the new film.[72] The teaser was also played at screenings of Lionsgate's The Divergent Series: Insurgent. Scott Mendelson of Forbes noted the similarity of the teaser with that of The Dark Knight's (2008) teaser, which also features just an animated logo of the film and select dialogue.[73] On June 1, a new teaser poster for the film, featuring a vandalised statue of President Snow, was revealed on the viral site TheCapitol.PN. On June 9, the teaser trailer for the film was released.[74] A series of different posters, featuring the main cast with red Mockingjays painted on their faces, was released in July by Lionsgate.

Later in July 2015, Lionsgate released a motion and teaser poster and propaganda video, followed by the film's official trailer. In August, a poster was released stating "100 days until The Hunger Games: Mockingjay - Part 2". However, it was taken down shortly thereafter, as the text on the poster appeared to resemble a swear word due to layout.[75] However, another "bold and beautiful" poster was released depicting Katniss standing on the shoulder of a fallen President Snow statue.[76]

In October 2015, the first official clip and the final trailer were released,[77] followed by the film's theatrical posters.[78][79] In October, fan sites revealed the first two TV spots.

"The Mockingjay App" was revealed on October 20.

In certain parts of Israel, the poster which depicted the image of Katniss (Lawrence) aiming her bow and arrow was removed over concerns her image would offend ultra-conservative Jewish audiences. Instead, a fiery mockingjay in the poster's background replaced Lawrence in marketing materials in multiple locations in Israel including Bnei Brak and West Jerusalem. Lionsgate did not comment on the Israeli marketing campaign.[80] In Jerusalem, public posters with the image of a female are often torn down, while Bnei Brak does not allow posters with female images.[81]

The Hunger Games: Mockingjay – Part 2 premiered in Los Angeles, at the L.A. Live, complex on November 16, and in New York City on November 18. It premiered internationally in Berlin on November 4, in London November 5, in Paris November 9, in Madrid November 10, and in Beijing November 12.[82][83][84] Due to the terrorist attacks in Paris on November 13, Lionsgate scaled down its L.A. premiere, cancelling press interviews on the red carpet (which was scheduled to last two hours). The stars mostly greeted fans and took a few photos before heading into the screening in Downtown Los Angeles.[82] Mockingjay – Part 2 was released on November 20, 2015 in the United States and Canada.[85] The film was originally scheduled to be released in 2D, Digital 3D, RealD 3D, and IMAX 3D, which would have made it the only film of the series to be globally released in 3D formats; the previous film was released in 3D in China.[86] It is the third film in the franchise to be released in IMAX, following the first and the second film with the exception of the third film.[87] However, the decision to release the film in 3D and IMAX 3D in North America was revoked. Director Francis Lawrence discussed the decision, stating, "I love the 3D format and I know that Mockingjay Part 2 will play perfectly in 3D and 2D internationally – but I'm pleased that we're maintaining the 2D only (and IMAX) formats domestically. It is the best of all worlds!". It was nevertheless released in 3D formats in overseas markets, including China.[88] The film was also released in the Dolby Vision format in Dolby Cinemas, which is the first ever for Lionsgate.[89][90]

Internationally, it was released day-and-date across 87 countries, starting from November 18, in certain markets like Belgium, Brazil, France and the Netherlands and on November 19 in Australia, Germany, Russia, Italy, and the United Kingdom, followed by China, Mexico, Japan, the United States, Canada, and 19 other markets, on November 20, as part of the biggest movie rollout ever by Lionsgate.[91] The only big territories where the film did not open on the same weekend are Spain, Greece and India, which released the movie on November 27.[92]

The Hunger Games: Mockingjay â€“ Part 2 was released on Digital HD on March 8, 2016, and was followed by a Blu-ray and DVD release on March 22, 2016.[93] It topped the home video sales chart for the week ending on March 27, 2016.[94]

The Hunger Games: Mockingjay – Part 2 fell short of expectations at the box office.[95] It grossed a total of $281.7 million in the USA & Canada and $371.7 million in other countries for a worldwide total of $653.4 million.[5] Its worldwide opening of $247.2 million is the twenty-seventh-biggest of all time.[96] It is the lowest-grossing film in The Hunger Games film series,[97] and the ninth highest-grossing film of 2015,[98] Lionsgate's co-chairman Rob Friedman blamed the impact of the November 2015 Paris attacks as well as Star Wars: Episode VII – The Force Awakens for the film's underwhelming performance in certain European countries and in the U.S. and Canada, further blaming the latter for cutting the film's North American gross by as much as $50–100 million.[99] However, according to Deadline.com, this is untrue given how Mockingjay – Part 2 had the lowest opening among the series and was already grossing behind Mockingjay – Part 1 by $32.7 million or 12% before The Force Awakens even opened.[100] Thus, the November attacks in Paris did not noticeably affect the European release of Mockingjay — Part 2.[101] And notably in China (where the film grossed a dismal $21.5 million), the studio blamed The Martian and Spectre for the film's underperformance there after facing competition with the two films along with Taiwanese film Our Times.[99][102] Deadline.com calculated the net profit of the film to be $134.3 million, when factoring together all expenses and revenues for the film.[7]

In North America, according to pre-release trackings, The Hunger Games: Mockingjay – Part 2 was initially projected to earn around $120–125 million in its opening weekend.[103][104] However, estimates decreased to a mid-$110 million range once the film approached its opening day.[105][106] It made $16 million from its Thursday night preview which is the lowest among the franchise but the third-biggest of 2015,[107] and $45.5 million on its opening day.[108] In its opening weekend, the film grossed $102.7 million, finishing first at the box office but fell below expectations and becoming the lowest opening among the franchise.[109] Sources attributed to the franchise-low opening to heavy winter weather hitting areas such as South Dakota, Michigan, and Chicago as well as Lionsgate's decision to split the last novel into two separate pictures.[110] Still, it is the fourth film in the Hunger Games film series to open with more than $100 million, and is 2015's sixth-biggest opening, behind Star Wars: The Force Awakens, Jurassic World, Avengers: Age of Ultron, Furious 7, and Minions.[111] IMAX comprised $8.5 million of the opening gross from 384 IMAX locations.[110] The low opening of the film led to the decline of Lionsgate stock the day after its opening weekend.[112] The film retained the top spot at the box office in the second weekend, declining 49.3% and grossing $52 million.[113] It topped the box office for the third consecutive weekend despite facing competition with the animated movie The Good Dinosaur and the horror comedy Krampus in its second and third weekend, respectively.[114] In total, it held the No. 1 spot in the North American box office for four consecutive weekends (even after facing competition with In the Heart of the Sea in its fourth weekend), becoming the first film since Furious 7 to top the box office for four straight weekends and the second film in The Hunger Games film series after 2012's The Hunger Games to achieve this feat.[115][116] Mockingjay – Part 2 grossed a total of $281 million, 17% less than Mockingjay – Part 1 and when compared with its two other prequels is the lowest.[5][117]

Outside North America, the film was released in a total of 92 countries.[118][119] It was projected by many box office analysts to surpass the openings of all the previous Hunger Games film, considering it was the last installment, and that its release date was the same in 87 markets, including China (the latter being a rare phenomenon). It was projected to gross around $165â€“185 million.[92] However, it ended up earning $144.5 million across 32,500 screens from 87 markets opening at No. 1 in 81 of them.[120][121] The underperformance was attributed to the 2015 Paris terror attacks which affected many parts of Europe and the rising value of the U.S. dollar.[122] Earning $62 million (down 57%) and $30.05 million (down 49%) in its second and third weekend, respectively, it topped the international box office for four consecutive weekends.[118][119][123]

The United Kingdom posted the highest opening with $17.1 million followed by China with $15.8 million, Germany ($15 million), Mexico ($8.9 million) France ($7.1 million), Australia ($6.8 million), Brazil ($6.8 million), Russia ($6.7 million), Venezuela ($5.6 million), and Italy ($4.3 million).[120] In China, it opened at No. 1 despite facing competition with Taiwanese film Our Times, and the continued run of Spectre and having an underperforming opening.[111][120] It fell precipitously by 88.6% in its second weekend, which is the worst second-weekend drop for any major Hollywood release in China of 2015.[124][125] Notably in France, the opening was above expectations considering cinemagoers being affected by the Paris terror attacks and the heightened state of alert in Belgium at that time.[120] It topped the United Kingdom and Ireland box office for four consecutive weekends which is a rare achievement and thereby becoming the first film since Les Misérables in 2013 to have four straight weeks of win at the UK box office.[126] It is the highest-grossing film of 2015 in Colombia with $36 million.[127] In terms of total earnings its largest markets are Germany ($43.7 million) and the United Kingdom ($43.1 million), and Colombia ($36 million).[128][129]

The Hunger Games: Mockingjay – Part 2 received generally positive reviews from critics, with praise for action sequences and performances but criticism for splitting the book into two separate adaptations.[130] On review aggregator website Rotten Tomatoes, the film has an approval rating of 70%, based on 235 reviews, with an average rating of 6.5/10. The site's critical consensus reads, "With the unflinchingly grim Mockingjay Part 2, The Hunger Games comes to an exciting, poignant, and overall satisfying conclusion."[131] On Metacritic, the film has a weighted average score of 65 out of 100, based on 44 critics, indicating "generally favorable reviews".[132] Audiences polled by CinemaScore gave the film an average grade of "A–" on an A+ to F scale.[133]

Manohla Dargis from The New York Times praised Lawrence's character saying, "Katniss is the right heroine for these neo-feminist times."[134] Stephen Whitty from New York Daily News said, "'Remember that line from the first 'Hunger Games' film: "May the odds be ever in your favor"? Yeah, well, that luck has run out'."[135] Lawrence, Hutcherson, and Sutherland received praise for their performances. The supporting cast's performances, particularly Harrelson, Claflin, and Malone's, were also highly praised, but critics felt their appearances were too brief. Several critics also commented on the film's dark tone, even by comparison to its predecessors.[131][132]

Leah Greenblatt of Entertainment Weekly remarked, "With its political power struggles and prodigious body count, all rendered in a thousand shades of wintry greige, the movie feels less like teen entertainment than a sort of Hunger Games of Thrones."[136] Robbie Collin awarded the film four out of five stars and called the film "scorchingly tense". In his review for The Telegraph, he praised the film for "being intense" and lauded the performances of Lawrence and Hoffman."[137]

Benjamin Lee, writing for The Guardian, felt that "the decision to split the final chapter of the dystopian saga into two chapters looms large over a frustratingly-paced mixture of thrilling action and surprisingly dark drama." He praised Jennifer Lawrence's acting and Francis Lawrence's direction and commented, "The decision to turn a 390-page book into over four hours' worth of screen time (and a bonus payday) has resulted in a patchy end to a franchise that started so promisingly."[138] Tom Huddleston of Time Out gave the film four out of five stars. He praised the ending of the film as "genuinely powerful", and commented that "this might be the most downbeat blockbuster in memory, a film that starts out pitiless and goes downhill from there, save for a fleeting glimmer of hope in the final moments. It's a bold statement about the unforgiving nature of war, unashamedly political in its motives and quietly devastating in its emotional effect."[139]


what is a retarder on a semi truck

A retarder is a device used to augment or replace some of the functions of primary friction-based braking systems, usually on heavy vehicles. Retarders serve to slow vehicles, or maintain a steady speed while traveling down a hill, and help prevent the vehicle from "running away" by accelerating down the hill. They are not usually capable of bringing vehicles to a standstill, as their effectiveness diminishes as vehicle speed lowers. They are usually used as an additional "assistance" to slow vehicles, with the final braking done by a conventional friction braking system. As the friction brake will be used less, particularly at higher speeds, their service life is increased, and since in those vehicles the brakes are air-actuated helps to conserve air pressure too.

Retarder (mechanical engineering)

Friction-based braking systems are susceptible to "brake fade" when used extensively for continuous periods, which can be dangerous if braking performance drops below what is required to stop the vehicle â€“ for instance if a truck or bus is descending a long decline. For this reason, such heavy vehicles are frequently fitted with a supplementary system that is not friction-based.

Retarders are not restricted to road motor vehicles, but may also be used in railway systems. The British prototype Advanced Passenger Train (APT) used hydraulic retarders to allow the high-speed train to stop in the same distance as standard lower speed trains, as a pure friction-based system was not viable.

Diesel engine vehicles do not have a throttle. Diesel engines regulate power output purely by the volume and timing of fuel injected into the combustion chambers. The engine braking generated by creating partial vacuum with a closed throttle at each intake stroke in petrol/gasoline engines does not apply to diesel engined vehiclesâ€”diesel engines are quite "free-running". However Clessie L. Cummins, founder of Cummins Engine Company, realized that by opening the cylinder exhaust valves when the piston reached top dead centre, rather than at the end of the power stroke, the accumulated compressed air in the cylinder could be vented before it could act as a "spring" to drive the piston back down again. By doing this, the engine acts as an air compressor, with the energy coming from the transmission used to compress the air, hence slowing the vehicle. The amount of power extracted from the transmission can be up to 90% of the rated power of the engine for certain engines.[citation needed]

In a compression release engine braking system for a turbocharged internal combustion engine, excessive stress associated with opening the exhaust valves of the engine near top dead center of engine compression strokes when the engine is turning at high speed is prevented by reducing the intake manifold pressure from what it otherwise would be at that high speed. This is done by retarding the turbocharger so that its speed is less than it otherwise would be at high engine speed.[1]

This type of retarder is known as Jake brake or compression release brake. A disadvantage of this system is that it becomes very noisy in operation, particularly if the exhaust muffler is faulty; its use is therefore banned in some locales.

Exhaust brakes are simpler in operation than an engine brake. Essentially, the exhaust pipe of the vehicle is restricted by a valve. This raises the pressure in the exhaust system, forcing the engine to work harder on the exhaust stroke of its cylinders, so again the engine is acting as an air compressor, with the power required to compress the air being withheld from the exhaust pipe, retarding the vehicle. Turbocharger retarders that restrict the flow of exhaust gas can also help in increasing the exhaust pressure to achieve the same objective.[2]

A disadvantage of this system is that the exhaust pipe has to be engineered to accommodate the high pressure generated. The retarding horsepower available from this system is significantly lower than other systems.[citation needed] It can cause a marked increase in engine oil carry-over out the crankcase ventilation system.[citation needed]

Hydraulic retarders use the viscous drag forces between dynamic and static vanes in a fluid-filled chamber to achieve retardation. There are several different types which can use standard transmission fluid (gear oil), a separate oil supply, water, or a mix of oil and magnetic retardation.[3] Magnetic retarders are similar to the electric retarder discussed below.

A simple retarder uses vanes attached to a transmission driveshaft between the clutch and roadwheels. They can also be driven separately via gears off a driveshaft. The vanes are enclosed in a static chamber with small clearances to the chamber's walls (which will also be vaned), as in an automatic transmission. When retardation is required, fluid (oil or water) is pumped into the chamber, and the viscous drag induced will slow the vehicle. The working fluid will heat, and is usually circulated through a cooling system. The degree of retardation can be varied by adjusting the fill level of the chamber.

Hydraulic retarders are extremely quiet, often inaudible over the sound of a running engine, and are especially quiet in operation compared to engine brakes.[4]

Electric retarders use electromagnetic induction to provide a retardation force. An electric retardation unit can be placed on an axle, transmission, or driveline and consists of a rotor attached to the axle, transmission, or drivelineâ€”and a stator securely attached to the vehicle chassis. There are no contact surfaces between the rotor and stator, and no working fluid. When retardation is required, the electrical windings in the stator receive power from the vehicle battery, producing a magnetic field through which the rotor moves. This induces eddy currents in the rotor, which produces an opposing magnetic field to the stator. The opposing magnetic fields slows the rotor, and hence the axle, transmission or driveshaft to which it is attached. The rotor incorporates internal vanes (like a ventilated brake disk) to provide its own air cooling, so no load is placed on the vehicle's engine cooling system. The operation of the system is extremely quiet.

A hybrid vehicle drivetrain uses electrical retardation to assist the mechanical brakes, while recycling the energy. The electric traction motor acts as a generator to charge the battery. The power stored in the battery is available to help the vehicle accelerate.

Regenerative braking and eddy current braking are separate types of electric braking. Regenerative braking might not be classified as a retarder as it uses no extra physical hardware in addition to the existing rotor/stator pair of the motor. It effectuates braking by using the electric field created by the rotational inertia in the rotor/stator that is delivered into the rotor by the momentum of the vehicle(wheels). Additional circuitry in the controller is used to manage this current flow from the stator windings into the battery, some of which dissipates as heat within the circuitry of the controller.

In contrast, eddy current retarder brakes comprise a distinct and purpose-built static armature and rotor that are explicitly made and added to a vehicle for braking and dissipation of heat and not for motive power; it is a purpose-built system distinct from the motor.

Finally, "dynamic" braking is a term used to describe a complex use of controller braking where the controller can be used either for regenerative braking or by switching the circuit to feed the current to resistors. In this latter way "rheostatic" braking can be achieved. Whereas an eddy brake relies on eddy currents to create magnetic resistance some of which is incidentally dissipated as heat, rheostatic braking relies on controller circuitry resistors which directly dissipate current-borne electric energy as heat. Some dynamic braking vehicles describe the rheostatic braking as "plug" braking. In particular, forklift dynamic braking has been developed to take advantage of combining this type of braking with controllers specialized to quickly reverse vehicle direction.

Dynamic and regenerative braking, when used on electric or diesel-electric railroad locomotives, means that the electric motors which usually are used to drive the road wheels are instead use as generators being driven by the wheels on a downslope. In regenerative braking, the electric current created is typically fed back into the power supply (i.e. overhead catenary, third rail), and can be used by other locomotives or stored for later use. In this way a locomotive will receive current while on level ground or traveling uphill, but acts as a current supply when braking, transforming the kinetic energy created from traveling downhill (or less often, converting forward momentum from travel on level ground) into electricity. In a diesel-electric, rather than being generated remotely and collected from a power source, the power supply is generated directly by the onboard prime mover (engine) and transmitted to the motors; there is presently rarely any way of storing electricity up for later use, so instead, the motors are used as generators, retarding the wheel rotation, and the generated power is routed through resistors mounted on the roof of the locomotive, where it is transformed into heat energy (much like an electric heating element) and dissipated into the atmosphere with large fans. While this has the drawback of not re-utilizing the energy created while traveling downhill, it does create a powerful and safe retarding system that isn't prone to brake fade or wearing out like mechanical brakes.


what is the difference between a patu and a mere

These types of short-handled clubs were mainly used as a striking weapon. The blow administered with this weapon was a horizontal thrust straight from the shoulder at the enemyâ€™s temple. If the foe could be grasped by the hair then the patu would be driven up under the ribs or jaw. Patu were made from hardwood, whale bone, or stone. The most prestigious material for the patu was pounamu (greenstone). Patu made from pounamu were generally called "mere". Maori decorated the patu by carving into the wood, bone or stone.

Patu

A patu is a generic term for a club or pounder used by the M훮ori, the indigenous people of New Zealand. The word patu in the M훮ori language means to strike, hit, beat, or subdue.[1]

Types of patu include:

Less traditional is the rare patu pora, made from iron[2] and the hatchet (patiti).[3]

Types of nonweapon patu include:


where did they film the beach leonardo dicaprio

The beach seen in the film is not the same as in real life. There is a gap between mountains on the actual beach in Thailand. The special effects crew digitally added some of the surrounding mountains during the post-production phase. The actual beach was also transformed from its natural look. It is reported that crew members flattened the beach with a tractor, much to the locals' dismay. The tsunami of 2004, however, has reshaped the beach to its natural look.[citation needed]

The Beach (film)

The Beach is a 2000 English-language drama film directed by Danny Boyle and based on the 1996 novel of the same name by Alex Garland, which was adapted for the film by John Hodge. The film stars Leonardo DiCaprio, Tilda Swinton, Virginie Ledoyen, Guillaume Canet, and Robert Carlyle. It was filmed on the Thai island Koh Phi Phi.

Richard, a young American seeking adventure in Bangkok, meets the eccentric Daffy, who tells him of a pristine, uninhabited island in the Gulf of Thailand with a beautiful hidden beach and lagoon. Daffy explains that he and other travelers settled there in secret several years earlier, but difficulties arose and he chose to leave. Daffy commits suicide, leaving Richard a map to the island. Richard convinces a young French couple, Françoise and Étienne, to accompany him to the island, and the three travel to Ko Samui. Richard meets two Americans who have heard rumors of the island, including that huge amounts of cannabis supposedly grow there. Before departing, Richard leaves them a copy of the map.

En route to the island, Richard becomes infatuated with Françoise. After swimming to the island from a neighboring one, they find a large cannabis plantation guarded by armed Thai farmers. Avoiding detection, they make their way across the island and are welcomed into the secret beach settlement. The community's leader, Sal, explains that the farmers allow them to stay so long as they keep to themselves and do not allow any more travelers to come to the island. Richard lies that they have not shown the map to anyone else, which satisfies Sal. The trio become integrated into the largely self-sufficient and leisurely community. The relationship between Richard and Françoise becomes romantic, and Étienne says he will not stand in their way if Françoise is happier with Richard when everyone finds out about their relationship. Tensions rise between Richard and Sal's boyfriend Bugs; when Richard gains celebrity by killing a shark, Bugs mocks him over the shark's small size.

When Sal selects Richard to accompany her on a supply run to Ko Pha Ngan, Bugs warns him to keep his hands off her. While there they encounter the Americans Richard met in Ko Samui, who are preparing to search for the island and mention Richard's map. Richard lies to Sal that he did not give them a copy, and she readily talks him into having sex with her. On their return to the island, Richard lies to Françoise about having had sex with Sal. Things return to normal until a shark attack kills one of the community's fishermen and leaves another, Christo, severely injured. Sal refuses to compromise the community's secrecy by bringing medical help, and Christo is unable to travel to the mainland. His worsening condition affects the group's morale, so they isolate him in a tent despite Étienne's objections.

When the Americans from Ko Pha Ngan turn up on the neighboring island, Sal sees that they have a map, confronts Richard for lying about it, and orders him to camp alone to observe them until they cross over, then intercept them and destroy it. She also tells everyone that she and Richard had sex, which leaves Françoise angry and heartbroken. Isolated from the group, Richard begins to lose his sanity, stalking the cannabis farmers, stealing some of their personal items while they sleep, and imagining that he is conversing with the deceased Daffy. The Americans reach the island but are discovered and killed by the farmers. Shocked at witnessing their deaths, Richard tries to gather Françoise and Étienne to leave the island. Étienne refuses to leave Christo, whose leg has become gangrenous, so Richard euthanizes Christo by suffocation.

The series of events propagated by Richard come to a head. He is captured by the farmers, who know that he has been stalking them, and brought before the community. The farmers have also found the map that Richard had given the (now dead) Americans, furious with the community for breaking their deal to not allow anymore newcomers. Richard's part in the sexual betrayals of Françoise, Étienne and Bugs has already frayed the community's cohesion. The lead farmer gives Sal a gun loaded with a single bullet and orders her to make a choice: kill Richard and the group will be allowed to stay, or else they must all leave immediately. Sal pulls the trigger, but the chamber is empty. Shocked by her willingness to commit murder, the community abandons Sal, leaving the island and going their separate ways.

Later, Richard receives an email at an Internet cafe from FranÃ§oise with a group photograph of the beach community in happier times.

Additional beach community members are played by Myriam Acharki, Andrew Carmichael, Josh Cole, Hélène de Fougerolles, Stacy Hart, Nina Jacques, Sheridan Jones, Gunilla Karlson, Sian Martin, Isabella Seibert, Elizabeth Thomas, Michael Thorpe, Timothy Webster, and Ramon Woolfe.

Additional cannabis farmers are portrayed by Sanya 'Gai' Cheunjit, Kaneung 'Nueng' Kenia, Somchai Santitarangkul, Seng Kawee, and Somkuan 'Kuan' Siroun.

Ewan McGregor was cast as the main character before leaving due to disputes with the director. It was speculated that Boyle was offered additional funding under the condition that DiCaprio be cast and his character made American.[2]

Real-life drama unfurled on set one day when the cast and crew were involved in a boating accident during production. It was reported that the incident involved both Boyle and DiCaprio. No one was injured.[3]

Boyle has been cited saying that the look of the jungle scenes in the film was inspired by the Rare/Nintendo game Banjo-Kazooie.[citation needed]

The waterfall scene, where DiCaprio and others jump from a high cliff to the water below, was filmed in Khao Yai National Park in central Thailand, at the Haew Suwat Waterfall.

The map in the film was illustrated by the author of the book that The Beach was based upon, Alex Garland. He received credit for this as the cartographer.

Controversy arose during the making of the film due to 20th Century Fox's bulldozing and landscaping of the natural beach setting of Ko Phi Phi Leh to make it more "paradise-like". The production altered some sand dunes and cleared some coconut trees and grass to widen the beach. Fox set aside a fund to reconstruct and return the beach to its natural state; however, lawsuits were filed by environmentalists who believed the damage to the ecosystem was permanent and restoration attempts had failed.[4] Following shooting of the film, there was a clear flat area at one end of the beach that was created artificially with an odd layout of trees which was never rectified, and the entire area remained damaged from the original state until the tsunami of 2004.

The lawsuits dragged on for years. In 2006, Thailand's Supreme Court upheld an appellate court ruling that the filming had harmed the environment and ordered that damage assessments be made. Defendants in the case included 20th Century Fox and some Thai government officials.[5]

After the film premiered in Thailand in 2000, some Thai politicians were upset at the way Thailand was depicted in the film and called for it to be banned. The depiction of the drug culture was said to give Thailand a bad image and having a statue of Buddha in a bar was cited as "blasphemous".[6]

The soundtrack for the film, co-produced by Pete Tong, features the international hits "Pure Shores" by All Saints and "Porcelain" by Moby, as well as tracks by New Order, Blur, Underworld, Orbital, Faithless, Sugar Ray, and others. Leftfield's contribution to the soundtrack, "Snakeblood", was found to have sampled Orchestral Manoeuvres in the Dark's "Almost" without permission, leading to a lawsuit; band member Neil Barnes said he forgot to remove the sample from the finished track.[7] The songs "Synasthasia" by Junkie XL, "Out of Control" by The Chemical Brothers, "Fiesta Conga" by Movin' Melodies, "Redemption Song" by Bob Marley, "Neon Reprise" by Lunatic Calm and "Smoke Two Joints" by Chris Kay and Michael Kay were also included in the movie but omitted from the soundtrack. The teaser trailer for the film featured "Touched" by VAST.

The film score was composed by Angelo Badalamenti, and a separate album containing selections of his score was released as well.

On Rotten Tomatoes the film holds an approval rating of 20% based on 117 reviews, and an average rating of 4.4/10. The website's critical consensus reads, "The Beach is unfocused and muddled, a shallow adaptation of the novel it is based on. Points go to the gorgeous cinematography, though."[8] On Metacritic, the film has a weighted average score of 43 out of 100, based on 34 critics, indicating "mixed or average reviews".[9]

Critics suggested that DiCaprio's fame post-Titanic might have contributed to the financial success of this film, which came out less than three years after the James Cameron blockbuster. CNN's Paul Clinton said "Leonardo DiCaprio's main fan base of screaming adolescent girls won't be disappointed with The Beach. The majority of the film displays the titanic-sized young heartthrob sans his shirt in this story about the pseudo-angst and alienation of a young man from the United States escaping civilization and his computer-obsessed generation." He agreed with most others that The Beach was "nothing to write home about". DiCaprio was nominated for a Razzie Award for Worst Actor for his work on the film.

The budget of the film was US$50 million. Global takings totaled over US$144 million, of which US$39 million was from the USA.[10]

Director Boyle has spoken negatively of the film, telling a Philadelphia audience in 2017 that he realized halfway through filming that he "didn't like any of the characters."

The film has been released on VHS and DVD. The standard DVD release included nine scenes that were deleted from the movie, including an alternative opening which to a degree resembles the one in the novel, were later included in a Special Edition DVD release, along with Danny Boyle's commentary on what might have been their purpose. There is also an alternative ending which depicts Sal committing suicide and everyone loading up on a boat from the raft.


how many cities in india has metro train

There are currently 11 operational rapid transit (also called'metro') systems in ten cities in India. As of November 2017, India has 425 kilometres (264 miles) of operational metro lines and 347 stations. A further 500+Â km of lines are under construction. Metro rail lines in India are composed of mainly standard gauge. Projects like the Kolkata Metro and Delhi Metro used broad gauge for their earliest lines but all new projects in India are on standard gauge as rolling stock imported is of standard gauge.

Urban rail transit in India

Urban rail transit in India consists of suburban rail, rapid transit, monorail, light rail, and tram systems.

Suburban rail plays a major role in the public transport system of many major Indian cities. Suburban rail is a rail service between a central business district and the suburbs, a conurbation or other locations that draw large numbers of people on a daily basis. The trains are called suburban trains. These trains are also referred to as "local trains" or "locals". The suburban rail systems in Hyderabad, Pune, Barabanki–Lucknow, Lucknow–Kanpur and Bengaluru do not have dedicated suburban tracks but share tracks with long distance trains. The suburban rail system of Chennai and Mumbai have both dedicated tracks and tracks shared with long distance trains

The first suburban rail system in India is Mumbai Suburban Railway which started operations in 1853. The Kolkata Suburban Railway has the largest network in the entire country.

Suburban trains that handle commuter traffic are all electric multiple units (EMUs). They usually have nine or twelve coaches, sometimes even fifteen to handle rush hour traffic. One unit of an EMU train consists of one power car and two general coaches. Thus a nine coach EMU is made up of three units having one power car at each end and one at the middle. The rakes in the suburban rails run on 25kV AC.[1] Ridership on India's suburban railways has risen from 1.2 million in 1970–71 to 4.4 million in 2012–13. The suburban railways of Mumbai, Kolkata and Chennai account for about 7.1% of the Indian Railways 20819.3  million train kilometres but contribute 53.2% of all railway passengers.[2] In some cities of India, the opening of rapid transit systems have led to a decline in the use of the suburban rail system.

The first rapid transit system in India is Kolkata Metro, which started operations in 1984. The Delhi Metro has the largest network in the entire country. The newest metro opened in Hyderabad Metro on 29 November 2017.

In 2006, the National Urban Transport Policy proposed the construction of a metro rail system in every city with a population of 20 lakh (2 million).[3] On 11 August 2014, Union Government announced that it would provide financial assistance, for the implementation of a metro rail system, to all Indian cities having a population of more than 1 million.[4][5] In May 2015, the Union Government approved the Union Urban Development Ministry's proposal to implement metro rail systems in 50 cities. The majority of the planned projects will be implemented through special purpose vehicles, which will be established as 50:50 joint ventures between the Union and respective State Government. The Union Government will invest an estimated ₹5 lakh crore (US$77 billion).[6][7] In a new draft policy unveiled in March 2017, the Central Government stated that it wanted state governments to consider metro rail as the "last option" and implement it only after considering all other possible mass rapid transit systems. The decision was taken due to the high cost of constructing metro rail systems.[8] In August 2017, the Union Government announced that it would not provide financial assistance to new metro rail project, unless some sort of private partnership is involved.[9][10][11]

The Mumbai Monorail, which opened on 2 February 2014 is the first operational monorail system used for rapid transit in independent India.[76] Many other Indian cities have monorail projects, as a feeder system to the metro, in different phases of planning.

Like monorail, light rail is also considered as a feeder system for the Metro systems. Two light rail projects have been proposed respectively in Delhi and Kolkata. There would be a total number of 68 stations of light rail in India.

In addition to trains, trams were introduced in many cities in late 19th century, though almost all of these were phased out. The Trams in Kolkata is currently the only tram system in the country. The Calcutta Tramways Company (Now under WBTC) is in the process of upgrading the existing tramway network at a cost of ₹240 million (US$3.7 million).[89]

There are three metro rolling stock manufacturers in India. Bharat Earth Movers is the only Indian rolling stock manufacturer. The other manufacturers are the Indian subsidiaries of Canadian firm Bombardier and French company Alstom. Under the Union Government's Make in India program, 75% of the rolling stock procured for use on Indian metro systems are required to be manufactured in India.[90]

Bharat Earth Movers

Bharat Earth Movers manufactures of Rolling Stock consortium with Hyundai Mitsubishi Rotem.

Bombardier built a Â£26m factory in Savli, Gujarat after it won a contract to supply 614 cars to the Delhi Metro.[91] Production at Savli began in June 2009.[92] In June 2012, the plant won an order to supply semi-finished bogies to Australia.[92]

In 2013, Alstom built a factory in Sri City, Andhra Pradesh after it won a â‚¬243 million contract to supply 168 cars to the Chennai Metro.[93] The 156-acre plant will be used to supply trains to cities in India and abroad.[94]

Integral Coach Factory

Integral Coach Factory manufactures Rolling Stock, ICF has manufactured "Medha Rakes" and is in the process of supplying them to various metro systems.

Chinese firm CRRC is planning to set up a manufacturing plant in Nagpur, Maharashtra

The subject of Railways is in the Union List of the Seventh Schedule of the Constitution, giving Parliament the exclusive power to enact legislation concerning it. According to former Minister of Urban Development Kamal Nath, "Since the Metro rail is a central subject, it has been decided that all such projects in the country, whether within one municipal area or beyond, shall be taken up under the Central Metro Acts."[95]

Construction of metros in India is governed by the centrally enacted The Metro Railways (Construction of Works) Act, 1978 which defines itself as an act to provide for the construction of works relating to metro railways in the metropolitan cities and for matters connected therewith.[96] Operation and maintenance of metros are governed by The Delhi Metro Railway (Operation and Maintenance) Act, 2002. Both laws were amended in 2009 with the passing of The Metro Railways (Amendment) Act, 2009.[97] The amendment expanded the coverage of both the acts to all metropolitan areas of India.

Initially, state governments attempted to implement metro rail projects through various Tramways Act. However, the Commissioner of Railways Safety (CRS), who operates under the Ministry of Civil Aviation, is tasked with providing safety certification for metro rail projects. The CRS refused safety certification unless the projects were implemented under a Metro Act enacted by the state government and published in The Gazette of India.[98] Research Design and Standards Organization (RDSO), another railway entity, also refused certification to projects not implemented under the criteria. Subsequently, several state governments have enacted their own Metro Acts.[98]


what are the characteristics of a maritime tropical air mass

Tropical and equatorial air masses are hot as they develop over lower latitudes. Those that develop over land (continental) are drier and hotter than those that develop over oceans, and travel poleward on the western periphery of the subtropical ridge.[6] Maritime tropical air masses are sometimes referred to as trade air masses.[7] Monsoon air masses are moist and unstable. Superior air masses are dry, and rarely reach the ground. They normally reside over maritime tropical air masses, forming a warmer and drier layer over the more moderate moist air mass below, forming what is known as a trade wind inversion over the maritime tropical air mass. Continental Polar air masses (cP) are air masses that are cold and dry due to their continental source region. Continental polar air masses that affect North America form over interior Canada. Continental Tropical air masses (cT) are a type of tropical air produced by the subtropical ridge over large areas of land and typically originate from low-latitude deserts such as the Sahara Desert in northern Africa, which is the major source of these air masses. Other less important sources producing cT air masses are the Arabian Peninsula, the central arid/semi-arid part of Australia and deserts lying in the Southwestern United States. Continental tropical air masses are extremely hot and dry. [8]

Air mass

In meteorology, an air mass is a volume of air defined by its temperature and water vapor content. Air masses cover many hundreds or thousands of square miles, and adapt to the characteristics of the surface below them. They are classified according to latitude and their continental or maritime source regions. Colder air masses are termed polar or arctic, while warmer air masses are deemed tropical. Continental and superior air masses are dry while maritime and monsoon air masses are moist. Weather fronts separate air masses with different density (temperature and/or moisture) characteristics. Once an air mass moves away from its source region, underlying vegetation and water bodies can quickly modify its character. Classification schemes tackle an air mass' characteristics, as well as modification.

The Bergeron classification is the most widely accepted form of air mass classification, though others have produced more refined versions of this scheme over different regions of the globe.[1] Air mass classification involves three letters. The first letter describes its moisture properties, with c used for continental air masses (dry) and m for maritime air masses (moist). The second letter describes the thermal characteristic of its source region: T for Tropical, P for Polar, A for arctic or Antarctic, M for monsoon, E for Equatorial, and S for superior air (an adiabatically drying and warming air formed by significant downward motion in the atmosphere). For instance, an air mass originating over the desert southwest of the United States in summer may be designated "cT". An air mass originating over northern Siberia in winter may be indicated as "cA".[2]

The stability of an air mass may be shown using a third letter, either "k" (air mass colder than the surface below it) or "w" (air mass warmer than the surface below it).[2] An example of this might be a polar air mass blowing over the Gulf Stream, denoted as "cPk". Occasionally, one may also encounter the use of an apostrophe or "degree tick" denoting that a given air mass having the same notation as another it is replacing is colder than the replaced air mass (usually for polar air masses). For example, a series of fronts over the Pacific might show an air mass denoted mPk followed by another denoted mPk'.[2]

Another convention utilizing these symbols is the indication of modification or transformation of one type to another. For instance, an Arctic air mass blowing out over the Gulf of Alaska may be shown as "cA-mPk". Yet another convention indicates the layering of air masses in certain situations. For instance, the overrunning of a polar air mass by an air mass from the Gulf of Mexico over the Central United States might be shown with the notation "mT/cP" (sometimes using a horizontal line as in fraction notation).[3]

Arctic, Antarctic, and polar air masses are cold. The qualities of arctic air are developed over ice and snow-covered ground. Arctic air is deeply cold, colder than polar air masses. Arctic air can be shallow in the summer, and rapidly modify as it moves equatorward.[4] Polar air masses develop over higher latitudes over the land or ocean, are very stable, and generally shallower than arctic air. Polar air over the ocean (maritime) loses its stability as it gains moisture over warmer ocean waters.[5]

A weather front is a boundary separating two masses of air of different densities, and is the principal cause of meteorological phenomena. In surface weather analyses, fronts are depicted using various colored lines and symbols, depending on the type of front. The air masses separated by a front usually differ in temperature and humidity. Cold fronts may feature narrow bands of thunderstorms and severe weather, and may on occasion be preceded by squall lines or dry lines. Warm fronts are usually preceded by stratiform precipitation and fog. The weather usually clears quickly after a front's passage. Some fronts produce no precipitation and little cloudiness, although there is invariably a wind shift.[9]

Cold fronts and occluded fronts generally move from west to east, while warm fronts move poleward. Because of the greater density of air in their wake, cold fronts and cold occlusions move faster than warm fronts and warm occlusions. Mountains and warm bodies of water can slow the movement of fronts.[10] When a front becomes stationary, and the density contrast across the frontal boundary vanishes, the front can degenerate into a line which separates regions of differing wind velocity, known as a shearline.[11] This is most common over the open ocean.

Air masses can be modified in a variety of ways. Surface flux from underlying vegetation, such as forest, acts to moisten the overlying air mass.[12] Heat from underlying warmer waters can significantly modify an air mass over distances as short as 35 kilometres (22 mi) to 40 kilometres (25 mi).[13] For example, southwest of extratropical cyclones, curved cyclonic flow bringing cold air across the relatively warm water bodies can lead to narrow lake-effect snow bands. Those bands bring strong localized precipitation since large water bodies such as lakes efficiently store heat that results in significant temperature differences (larger than 13 °C or 23 °F) between the water surface and the air above.[14] Because of this temperature difference, warmth and moisture are transported upward, condensing into vertically oriented clouds (see satellite picture) which produce snow showers. The temperature decrease with height and cloud depth are directly affected by both the water temperature and the large-scale environment. The stronger the temperature decrease with height, the deeper the clouds get, and the greater the precipitation rate becomes.[15]


who was the prime minister of the undivided bengal

The Congress party boycotted the office due to its anti-British policy. The office was held by three Muslims. The first premier was A. K. Fazlul Huq, the leader of the anti-feudalist Krishak Praja Party. Huq formed his first government with the All India Muslim League in 1937.[citation needed] The League withdrew support in 1941, after which Huq forged a coalition with the Hindu Mahasabha led by Syama Prasad Mukherjee. The Huq-Syama coalition lasted till 1943. Huq was succeeded by a Muslim League ministry led by Sir Khawaja Nazimuddin. An unpopular conservative, the Nazimuddin ministry lasted till 1945,[2][3] when governor's rule was imposed. The next election saw H. S. Suhrawardy lead the Muslim League to a majority. Suhrawardy sought an undivided Bengal with support from Hindu leaders and the British governor; but faced challenges like the Noakhali riots and Direct Action Day.

Prime Minister of Bengal

The Prime Minister of Bengal was the head of government and the Leader of the House in the Bengal Legislative Assembly in British India. The position was dissolved upon the Partition of Bengal in 1947.

The office was created under the Government of India Act 1935, which granted Bengal a bicameral legislature, including the Bengal Legislative Council and the Bengal Legislative Assembly. The Prime Minister was in charge of the executive branch.[1] The Prime Minister of Bengal played an important role in pan-Indian politics, including proclaiming the Lahore Resolution and dealing with Japanese attacks during World War II.

When Bengal was partitioned, the office was succeeded by the Chief Minister of West Bengal and the Chief Minister of East Bengal.

All three Bengali premiers moved to East Bengal, where they continued to be influential statesmen. Nazimuddin and Suhrawardy became Prime Ministers of Pakistan, while Huq served as East Bengal's chief minister, and later as East Pakistan's governor. The three premiers are considered the forerunners of politics in modern Bangladesh.


why are coordinate systems useful when formulating a solution to a problem

The chief advantage of non-Cartesian coordinates is that they can be chosen to match the symmetry of the problem. For example, the pressure wave due to an explosion far from the ground (or other barriers) depends on 3D space in Cartesian coordinates, however the pressure predominantly moves away from the center, so that in spherical coordinates the problem becomes very nearly one-dimensional (since the pressure wave dominantly depends only on time and the distance from the center). Another example is (slow) fluid in a straight circular pipe: in Cartesian coordinates, one has to solve a (difficult) two dimensional boundary value problem involving a partial differential equation, but in cylindrical coordinates the problem becomes one-dimensional with an ordinary differential equation instead of a partial differential equation.

Orthogonal coordinates

In mathematics, orthogonal coordinates are defined as a set of d coordinates q = (q1, q2,..., qd) in which the coordinate surfaces all meet at right angles (note: superscripts are indices, not exponents). A coordinate surface for a particular coordinate qk is the curve, surface, or hypersurface on which qk is a constant. For example, the three-dimensional Cartesian coordinates (x, y, z) is an orthogonal coordinate system, since its coordinate surfaces x = constant, y = constant, and z = constant are planes that meet at right angles to one another, i.e., are perpendicular. Orthogonal coordinates are a special but extremely common case of curvilinear coordinates.

While vector operations and physical laws are normally easiest to derive in Cartesian coordinates, non-Cartesian orthogonal coordinates are often used instead for the solution of various problems, especially boundary value problems, such as those arising in field theories of quantum mechanics, fluid flow, electrodynamics and the diffusion of chemical species or heat.

The reason to prefer orthogonal coordinates instead of general curvilinear coordinates is simplicity: many complications arise when coordinates are not orthogonal. For example, in orthogonal coordinates many problems may be solved by separation of variables. Separation of variables is a mathematical technique that converts a complex d-dimensional problem into d one-dimensional problems that can be solved in terms of known functions. Many equations can be reduced to Laplace's equation or the Helmholtz equation. Laplace's equation is separable in 13 orthogonal coordinate systems, and the Helmholtz equation is separable in 11 orthogonal coordinate systems.[1][2]

Orthogonal coordinates never have off-diagonal terms in their metric tensor. In other words, the infinitesimal squared distance ds2 can always be written as a scaled sum of the squared infinitesimal coordinate displacements

where d is the dimension and the scaling functions (or scale factors)

equal the square roots of the diagonal components of the metric tensor, or the lengths of the local basis vectors

e

k

{\displaystyle \mathbf {e} _{k}}

 described below. These scaling functions hi are used to calculate differential operators in the new coordinates, e.g., the gradient, the Laplacian, the divergence and the curl.

A simple method for generating orthogonal coordinates systems in two dimensions is by a conformal mapping of a standard two-dimensional grid of Cartesian coordinates (x, y). A complex number z = x + iy can be formed from the real coordinates x and y, where i represents the imaginary unit. Any holomorphic function w = f(z) with non-zero complex derivative will produce a conformal mapping; if the resulting complex number is written w = u + iv, then the curves of constant u and v intersect at right angles, just as the original lines of constant x and y did.

Orthogonal coordinates in three and higher dimensions can be generated from an orthogonal two-dimensional coordinate system, either by projecting it into a new dimension (cylindrical coordinates) or by rotating the two-dimensional system about one of its symmetry axes. However, there are other orthogonal coordinate systems in three dimensions that cannot be obtained by projecting or rotating a two-dimensional system, such as the ellipsoidal coordinates. More general orthogonal coordinates may be obtained by starting with some necessary coordinate surfaces and considering their orthogonal trajectories.

In Cartesian coordinates, the basis vectors are fixed (constant). In the more general setting of curvilinear coordinates, a point in space is specified by the coordinates, and at every such point there is bound a set of basis vectors, which generally are not constant: this is the essence of curvilinear coordinates in general and is a very important concept. What distinguishes orthogonal coordinates is that, though the basis vectors vary, they are always orthogonal with respect to each other. In other words,

These basis vectors are by definition the tangent vectors of the curves obtained by varying one coordinate, keeping the others fixed:

where r is some point and qi is the coordinate for which the basis vector is extracted. In other words, a curve is obtained by fixing all but one coordinate; the unfixed coordinate is varied as in a parametric curve, and the derivative of the curve with respect to the parameter (the varying coordinate) is the basis vector for that coordinate.

Note that the vectors are not necessarily of equal length. The useful functions known as scale factors of the coordinates are simply the lengths

h

i

{\displaystyle h_{i}}

 of the basis vectors

e

^

i

{\displaystyle {\hat {\mathbf {e} }}_{i}}

 (see table below). The scale factors are sometimes called LamÃ© coefficients, but this terminology is best avoided since some more well known coefficients in linear elasticity carry the same name.

The normalized basis vectors are notated with a hat and obtained by dividing by the length:

A vector field may be specified by its components with respect to the basis vectors or the normalized basis vectors, and one must be sure which case is meant. Components in the normalized basis are most common in applications for clarity of the quantities (for example, one may want to deal with tangential velocity instead of tangential velocity times a scale factor); in derivations the normalized basis is less common since it is more complicated.

The basis vectors shown above are covariant basis vectors (because they "co-vary" with vectors). In the case of orthogonal coordinates, the contravariant basis vectors are easy to find since they will be in the same direction as the covariant vectors but reciprocal length (for this reason, the two sets of basis vectors are said to be reciprocal with respect to each other):

this follows from the fact that, by definition,

e

i

⋅

e

j

=

δ

i

j

{\displaystyle \mathbf {e} _{i}\cdot \mathbf {e} ^{j}=\delta _{i}^{j}}

, using the Kronecker delta. Note that:

We now face three different basis sets commonly used to describe vectors in orthogonal coordinates: the covariant basis ei, the contravariant basis ei, and the normalized basis Ãªi. While a vector is an objective quantity, meaning its identity is independent of any coordinate system, the components of a vector depend on what basis the vector is represented in.

To avoid confusion, the components of the vector x with respect to the ei basis are represented as xi, while the components with respect to the ei basis are represented as xi:

The position of the indices represent how the components are calculated (upper indices should not be confused with exponentiation). Note that the summation symbols Î£ (capital Sigma) and the summation range, indicating summation over all basis vectors (i = 1, 2,..., d), are often omitted. The components are related simply by:

There is no distinguishing widespread notation in use for vector components with respect to the normalized basis; in this article we'll use subscripts for vector components and note that the components are calculated in the normalized basis.

Vector addition and negation are done component-wise just as in Cartesian coordinates with no complication. Extra considerations may be necessary for other vector operations.

Note however, that all of these operations assume that two vectors in a vector field are bound to the same point (in other words, the tails of vectors coincide). Since basis vectors generally vary in orthogonal coordinates, if two vectors are added whose components are calculated at different points in space, the different basis vectors require consideration.

The dot product in Cartesian coordinates (Euclidean space with an orthonormal basis set) is simply the sum of the products of components. In orthogonal coordinates, the dot product of two vectors x and y takes this familiar form when the components of the vectors are calculated in the normalized basis:

This is an immediate consequence of the fact that the normalized basis at some point can form a Cartesian coordinate system: the basis set is orthonormal.

For components in the covariant or contravariant bases,

This can be readily derived by writing out the vectors in component form, normalizing the basis vectors, and taking the dot product. For example, in 2D:

where the fact that the normalized covariant and contravariant bases are equal has been used.

The cross product in 3D Cartesian coordinates is:

The above formula then remains valid in orthogonal coordinates if the components are calculated in the normalized basis.

To construct the cross product in orthogonal coordinates with covariant or contravariant bases we again must simply normalize the basis vectors, for example:

which, written expanded out,

Terse notation for the cross product, which simplifies generalization to non-orthogonal coordinates and higher dimensions, is possible with the Levi-Civita tensor, which will have components other than zeros and ones if the scale factors are not all equal to one.

Looking at an infinitesimal displacement from some point, it's apparent that

By definition, the gradient of a function must satisfy (this definition remains true if Æ’ is any tensor)

It follows then that del operator must be:

and this happens to remain true in general curvilinear coordinates. Quantities like the gradient and Laplacian follow through proper application of this operator.

From dr and normalized basis vectors Ãªi, the following can be constructed.[3][4]

d

ℓ

=

h

i

d

q

i

e

^

i

=

∂

r

∂

q

i

d

q

i

{\displaystyle d{\boldsymbol {\ell }}=h_{i}dq^{i}{\hat {\mathbf {e} }}_{i}={\frac {\partial \mathbf {r} }{\partial q^{i}}}dq^{i}}

d
ℓ
=

d

r

⋅
d

r

=

(

h

1

d

q

1

)

2

+
(

h

2

d

q

2

)

2

+
(

h

3

d

q

3

)

2

{\displaystyle d\ell ={\sqrt {d\mathbf {r} \cdot d\mathbf {r} }}={\sqrt {(h_{1}\,dq^{1})^{2}+(h_{2}\,dq^{2})^{2}+(h_{3}\,dq^{3})^{2}}}}

d

S

=
(

h

i

d

q

i

e

^

i

)
×
(

h

j

d

q

j

e

^

j

)

=
d

q

i

d

q

j

(

∂

r

∂

q

i

×

∂

r

∂

q

j

)

=

h

i

h

j

d

q

i

d

q

j

e

^

k

{\displaystyle {\begin{aligned}d\mathbf {S} &=(h_{i}dq^{i}{\hat {\mathbf {e} }}_{i})\times (h_{j}dq^{j}{\hat {\mathbf {e} }}_{j})\\&=dq^{i}dq^{j}\left({\frac {\partial \mathbf {r} }{\partial q^{i}}}\times {\frac {\partial \mathbf {r} }{\partial q^{j}}}\right)\\&=h_{i}h_{j}dq^{i}dq^{j}{\hat {\mathbf {e} }}_{k}\end{aligned}}}

d

S

k

=

h

i

h

j

d

q

i

d

q

j

{\displaystyle dS_{k}=h_{i}h_{j}\,dq^{i}\,dq^{j}}

d
V

=

|

(

h

1

d

q

1

e

^

1

)
⋅
(

h

2

d

q

2

e

^

2

)
×
(

h

3

d

q

3

e

^

3

)

|

=

|

e

^

1

⋅

e

^

2

×

e

^

3

|

h

1

h

2

h

3

d

q

1

d

q

2

d

q

3

=
J

d

q

1

d

q

2

d

q

3

=

h

1

h

2

h

3

d

q

1

d

q

2

d

q

3

{\displaystyle {\begin{aligned}dV&=|(h_{1}\,dq^{1}{\hat {\mathbf {e} }}_{1})\cdot (h_{2}\,dq^{2}{\hat {\mathbf {e} }}_{2})\times (h_{3}\,dq^{3}{\hat {\mathbf {e} }}_{3})|\\&=|{\hat {\mathbf {e} }}_{1}\cdot {\hat {\mathbf {e} }}_{2}\times {\hat {\mathbf {e} }}_{3}|h_{1}h_{2}h_{3}\,dq^{1}\,dq^{2}\,dq^{3}\\&=J\,dq^{1}\,dq^{2}\,dq^{3}\\&=h_{1}h_{2}h_{3}\,dq^{1}\,dq^{2}\,dq^{3}\end{aligned}}}

is the Jacobian determinant, which has the geometric interpretation of the deformation in volume from the infinitesimal cube dxdydz to the infinitesimal curved volume in the orthogonal coordinates.

Using the line element shown above, the line integral along a path

P

{\displaystyle \scriptstyle {\mathcal {P}}}

 of a vector F is:

An infinitesimal element of area for a surface described by holding one coordinate qk constant is:

Similarly, the volume element is:

where the large symbol Π (capital Pi) indicates a product the same way that a large Σ indicates summation. Note that the product of all the scale factors is the Jacobian determinant.

As an example, the surface integral of a vector function F over a q1 = constant surface

S

{\displaystyle \scriptstyle {\mathcal {S}}}

 in 3D is:

Note that F1/h1 is the component of F normal to the surface.

Since these operations are common in application, all vector components in this section are presented with respect to the normalised basis:

F

i

=

F

⋅

e

^

i

{\displaystyle F_{i}=\mathbf {F} \cdot {\hat {\mathbf {e} }}_{i}}

.

The above expressions can be written in a more compact form using the Levi-Civita symbol, defining

H
=

h

1

h

2

h

3

{\displaystyle H=h_{1}h_{2}h_{3}}

, and assuming summation over repeated indices:

Besides the usual cartesian coordinates, several others are tabulated below.[5] Interval notation is used for compactness in the coordinates column.

(
r
,
θ
,
ϕ
)
∈
[
0
,
∞
)
×
[
0
,
π
]
×
[
0
,
2
π
)

{\displaystyle (r,\theta,\phi )\in [0,\infty )\times [0,\pi ]\times [0,2\pi )}

(
r
,
ϕ
,
z
)
∈
[
0
,
∞
)
×
[
0
,
2
π
)
×
(
−
∞
,
∞
)

{\displaystyle (r,\phi,z)\in [0,\infty )\times [0,2\pi )\times (-\infty,\infty )}

(
u
,
v
,
z
)
∈
(
−
∞
,
∞
)
×
[
0
,
∞
)
×
(
−
∞
,
∞
)

{\displaystyle (u,v,z)\in (-\infty,\infty )\times [0,\infty )\times (-\infty,\infty )}

(
u
,
v
,
ϕ
)
∈
[
0
,
∞
)
×
[
0
,
∞
)
×
[
0
,
2
π
)

{\displaystyle (u,v,\phi )\in [0,\infty )\times [0,\infty )\times [0,2\pi )}

(
u
,
v
,
z
)
∈
[
0
,
∞
)
×
[
0
,
2
π
)
×
(
−
∞
,
∞
)

{\displaystyle (u,v,z)\in [0,\infty )\times [0,2\pi )\times (-\infty,\infty )}

(
ξ
,
η
,
ϕ
)
∈
[
0
,
∞
)
×
[
0
,
π
]
×
[
0
,
2
π
)

{\displaystyle (\xi,\eta,\phi )\in [0,\infty )\times [0,\pi ]\times [0,2\pi )}

(
ξ
,
η
,
ϕ
)
∈
[
0
,
∞
)
×

[
−

π
2

,

π
2

]

×
[
0
,
2
π
)

{\displaystyle (\xi,\eta,\phi )\in [0,\infty )\times \left[-{\frac {\pi }{2}},{\frac {\pi }{2}}\right]\times [0,2\pi )}

(
λ
,
μ
,
ν
)

λ
<

c

2

<

b

2

<

a

2

,

c

2

<
μ
<

b

2

<

a

2

,

c

2

<

b

2

<
ν
<

a

2

,

{\displaystyle {\begin{aligned}&(\lambda,\mu,\nu )\\&\lambda <c^{2}<b^{2}<a^{2},\\&c^{2}<\mu <b^{2}<a^{2},\\&c^{2}<b^{2}<\nu <a^{2},\end{aligned}}}

where

(

q

1

,

q

2

,

q

3

)
=
(
λ
,
μ
,
ν
)

{\displaystyle (q_{1},q_{2},q_{3})=(\lambda,\mu,\nu )}

(
u
,
v
,
z
)
∈
[
0
,
2
π
)
×
(
−
∞
,
∞
)
×
(
−
∞
,
∞
)

{\displaystyle (u,v,z)\in [0,2\pi )\times (-\infty,\infty )\times (-\infty,\infty )}

(
u
,
v
,
ϕ
)
∈
(
−
π
,
π
]
×
[
0
,
∞
)
×
[
0
,
2
π
)

{\displaystyle (u,v,\phi )\in (-\pi,\pi ]\times [0,\infty )\times [0,2\pi )}

(
λ
,
μ
,
ν
)

ν

2

<

b

2

<

μ

2

<

a

2

λ
∈
[
0
,
∞
)

{\displaystyle {\begin{aligned}&(\lambda,\mu,\nu )\\&\nu ^{2}<b^{2}<\mu ^{2}<a^{2}\\&\lambda \in [0,\infty )\end{aligned}}}