document_title: List of The Facts of Life characters

question_text: what was blair's last name on facts of life

question_tokens: what was blair 's last name on facts of life

text: List of The Facts of Life characters

text: Characters table[edit]

text:
Actor
Character
Seasons

1
2
3
4
5
6
7
8
9

Charlotte Rae
Edna Garrett
Main
Guest
Absent

Lisa Whelchel
Blair Warner
Main

Kim Fields
Tootie Ramsey
Main

Mindy Cohn
Natalie Green
Main

Nancy McKeon
Jo Polniaczek
Absent
Main

John Lawlor
Steven Bradley
Main
Absent

Jenny O'Hara
Emily Mahoney[note 1]
Main
Absent

Felice Schachter
Nancy Olsen
Main
Recurring
Absent
Guest
Absent

Julie Piekarski
Sue Ann Weaver
Main
Recurring
Absent
Guest
Absent

Julie Anne Haddock
Cindy Webster
Main
Recurring
Absent
Guest
Absent

Molly Ringwald
Molly Parker
Main
Guest
Absent

Pamela Segall
Kelly Affinado
Absent
Main
Absent

Mackenzie Astin
Andy Moffett
Absent
Recurring
Main

George Clooney
George Burnett
Absent
Main
Recurring
Absent

Cloris Leachman
Beverly Ann Stickle
Absent
Main

Sherrie Krenn
Pippa McKenna[note 2]
Absent
Main

text: Edna Garrett[edit]

text:
Edna Garrett

Diff'rent Strokes, The Facts of Life character

First appearance
"Movin' In" (Diff'rent Strokes)
"Rough Housing" (The Facts of Life)

Last appearance
The Facts of Life Reunion

Portrayed by
Charlotte Rae

Information

Aliases
Mrs. Garrett, Mrs. G

Occupation
Housekeeper, housemother, dietitian, businesswoman

Spouse(s)
Robert Garrett (divorced)
Dr. Bruce Gaines (1986–, widowed before 2001 reunion)

Children
Alex Garrett (son)
Raymond Garrett (son)

Relatives
Beverly Ann Stickle (sister)
Andy Moffett (adoptive nephew)

text: Edna Ann Garrett Gaines, known as Mrs. Garrett or Mrs. G, was played by actress Charlotte Rae from 1978 to 1986.

text: Garrett was the youngest child in a large family, born and raised on a farm near Appleton, Wisconsin. Her exact age was never disclosed during the series, but on several occasions, it was hinted or implied that she was somewhere in her fifties. On Diff'rent Strokes, she was the housekeeper to the Drummond family in New York City after Willis and Arnold's mom Lucy (the Drummonds' original housekeeper) died. In 1979, she took a job as house mother at the Eastland School for Girls in Peekskill, New York (Kimberly Drummond attended Eastland). Over the years, Mrs. Garrett's role on The Facts of Life changed. At first she was merely a live-in supervisor for the girls of Eastland; in the second season she became their in-house dietitian who managed the school's cafeteria.

text: Garrett was married twice, divorced (first marriage), and widowed (second marriage); one early episode showed Mr. Garrett coming to town to woo her and reconcile, but he was unsuccessful because Edna felt that his gambling problem would always be an obstacle. She had two sons, a singer/songwriter/carpenter named Alex (Tom Fitzsimmons) (born 1953) and an accountant named Raymond (Joel Brooks). Raymond helped her raise funds and secure commercial space so she could open her own gourmet food shop, Edna's Edibles, in the fall of 1983. The girls, who had previously lived with Mrs. Garrett at Eastland, and worked with her in the kitchen to pay off various restitution-related expenses (see below), moved into an apartment above "Edna's Edibles" and continued to work for Mrs. Garrett in the shop (this time on the payroll). In the fall of 1985, Edna's Edibles was extensively damaged by fire; it was rebuilt as a gift shop called "Over Our Heads." Since the insurance on Edna's Edibles had lapsed by the time of the fire, the girls contributed their insurance claim checks to help rebuild, effectively making Mrs. Garrett and the girls equal partners in the business.

text: Edna Garrett was a mentor to the girls at Eastland, functioning in loco parentis. At times the girls would take her for granted, and forget that Edna herself had problems. Many times Edna would lash out at the girls when they got careless with her. In one episode, she actually fires them from "Edna's Edibles" when their irresponsible behavior ends up costing her $500 in fines after a dismal health inspection. She hires them back the next day when the girls promise her that they will be more responsible at their jobs. She also fires George, when he falls behind on his work constructing "Over Our Heads," but they later make up. Mrs. Garrett is a Democrat. She is also against censorship, such as book banning.

text: Mrs. Garrett remarried in 1986. She and her new husband, Dr. Bruce Gaines (Robert Mandan), rejoined the Peace Corps to work in eastern Africa. (Charlotte Rae did not want to continue with the series). Edna was replaced by her sister, Beverly Ann Stickle (Cloris Leachman). However, in the reunion movie that aired in 2001, Mrs. Garrett reunited with the three girls (Blair, Natalie, and Tootie) at a hotel owned by Blair and which was run by Mrs. Garrett's son Raymond. It was also revealed that Mrs. Garrett and Tootie were widows. It's revealed that she was in a romantic relationship with a ship captain.

text: Mrs. Garrett also appears on the Hello, Larry episode "The Trip", the first of three crossovers between Diff'rent Strokes and Hello, Larry.

text: In an episode of Halt and Catch Fire, a man fencing computers refers to married mother Donna Clark ( played by Kerry Bishe ) as Mrs. Garrett, in reference to her conservative appearance and critical opinion of him.

text: Natalie Green[edit]

text:
Natalie Green

First appearance
"Rough Housing" (The Facts of Life)

Last appearance
The Facts of Life Reunion

Portrayed by
Mindy Cohn

Information

Occupation
Student

Relatives
Dr. Sy Green (father; deceased)
Evelyn "Evie" Green (mother)
Ellen Manheim (biological mother)

text: Natasha Letisha Sage "Natalie" Green was played by Mindy Cohn. Natalie's best friend on the show was Tootie, as they were close in age. Natalie's age was 12 at the series' beginning.

text: Natalie's most defining physical attribute was that she was large-figured, but she had a healthy self-image, once quoted as saying, "Who wants to be a skinny pencil? I'd rather be a happy Magic Marker!"

text: Natalie is Jewish, as Mindy Cohn is in real life; and her faith was featured in several episodes. In one, she celebrated Hanukkah while the others celebrated Christmas. Her heritage was highlighted when her father, Dr. Green, died unexpectedly; Natalie's bottled-up grief was a continuing storyline.

text: Although she wasn't a mold-fitting "traditional beauty," Natalie was involved in many storylines regarding sex. In an early episode, she dated a boy who spread a rumor that Natalie was easy. In another episode, she was almost sexually assaulted on the way back from a costume party. In the controversial episode "The First Time," toward the series' end, she became the first of the girls to have sex when she slept with her boyfriend Snake on their first anniversary as a couple. A budding writer, she wrote for the Eastland School newspaper.

text: Natalie graduated from Eastland in 1985, in the Season 6, Episode 25, "Bus Stop," and took a year off before college to travel across the country in a bus, leaving family and friends dismayed because she was postponing Princeton. At the year's end, she decided to attend Langley College, and she became a reporter for the local newspaper in Peekskill. She went to New York City towards the end of the series and decided to stay and pursue her writing career. The episode in which she checks out the SoHo loft she will eventually call home features Richard Grieco and David Spade as her future roommates. (The episode, which aired in 1988, was originally set up for Mindy Cohn to transition into a spinoff series, but the plans never materialized.) In the TV-movie, The Facts of Life Reunion, she is revealed to be a television news producer at CNN and is also involved with two different men; none of whom knew of the other. Her boyfriends Robert and Harper were willing, for a short time, to compete for her heart. Though her friends deemed Robert the winner, Natalie eventually choose Harper. While her now ex, Robert accepted this and parted with Natalie on good terms.

text: Natalie was the only one of the girls who was adopted. In one episode, Blair successfully tracked down Natalie's birthmother, but Natalie—who realized that her adoptive parents were her true parents, even though they weren't biologically related to her—refused to answer the phone and hear the results of the search, instead inviting her friends to taste the cake "my mother made." However, thanks in part to an argument with her adoptive mother during a 1982 episode, the subject arose again, and it was her adoptive mother who finally told Natalie who her biological mother was. Natalie tracked her down and met her, but as before, she still considered the mother who had reared her to be her mother.

text: Natalie also appears in two episodes of Diff'rent Strokes: "The Slumber Party" and "The Older Men".

text: Jo Polniaczek[edit]

text:
Jo Polniaczek

First appearance
The New Girl, pt. 1

Last appearance
The Beginning of the Beginning

Portrayed by
Nancy McKeon

Information

Occupation
Student

Relatives
Charlie Polniaczek (father)
Rose Polniaczek (mother)
Josef Polniaczek (paternal grandfather)

text: Joanna Marie "Jo" Polniaczek was played by Nancy McKeon. Jo was first introduced in the second season in 1980, at 14 years old, arriving at the Eastland Academy on her motorcycle. She almost immediately formed a dislike for Blair Warner; Jo found Blair stuck-up, and Blair found Jo short-tempered, bossy, classless, and manly. In a memorable introduction, Blair introduced herself to Jo, to which Jo replied, "Charmed; I'm Gloria Vanderbilt." Jo was Polish American.

text: Jo convinced the gang to steal the school van and use fake IDs to buy drinks at a bar. The van was wrecked and the girls were forced to work in the Eastland cafeteria to make up the repair costs; this was from the second season two-part premiering in November 1980 "The New Girl Part 1". In the second episode "The New Girl Part 2", the girls were also placed on house probation and were forced to live in a room adjoining Mrs. Garrett's for a year; when the punishment expired, all four girls found other living arrangements, but were responsible for cleaning and painting their former room. While painting, their friendship began to rekindle culminating into an all-out paint fight, which severely damaged the hardwood floor requiring expensive repairs. The girls decided to move back in together and continued to work in the kitchen to pay off the bill for the damaged floor.

text: Blair's attitude toward Jo worsened when Blair's boyfriend asked Jo to a country club dance. However, Blair stood up for Jo when her would-be love interest tried to assault and humiliate her on the ninth green. When asked why Blair stood up for Jo, Blair stated, "At least when I insult you, I know what I'm talking about!" Another problem for Jo came when she shoplifted a blouse for Mrs. Garrett's birthday; Mrs. Garrett was subsequently arrested when she went to exchange the blouse for the smaller size, not knowing the garment was stolen.

text: Early on, Jo's sailor boyfriend, Eddie Brennan (actor Clark Brandon), came to Eastland and convinced her to marry him. They planned to elope to West Virginia, where the marriage age was lower, but Mrs. Garrett and Blair tracked her down at a nearby motel to stop her. Jo had by that point already begun to change her mind when she realized just how difficult teenage marriage would be. Jo returned to Peekskill without Eddie. Eddie visited again the following season but things had changed between them. They were moving in different directions and keeping the long distance relationship going was proving to be very difficult, so they decided to see other people for the time being. Eddie returned late in the fifth season, now an officer in the Navy but Tootie discovered he was married to a girl in Italy. Clark Brandon's last appearance was in the 5th season's 23rd episode "Seems Like Old Times".

text: In the 15th episode of the 4th season called "Teacher's Pet", Jo developed a friendship with her 26-year-old English teacher, Miss Gail Gallagher (played by Deborah Harmon), who was raised in a similar environment to that of Jo. Gail inspired Jo to think about becoming a teacher herself and Jo went as far as to calling her by her first name. When Jo learned from Blair that Gail was quitting Eastland, she became very disappointed believing that the reason was for a higher-paying job. She was crushed when she found out from Mrs. Garrett that it was because of something unthinkable – terminal illness. Jo was so shocked that she stopped going to Gail's class and shunned her completely. She tried to keep herself busy with things that would distract her from thoughts of Gail and went as far as breaking her evening curfew. When Mrs. Garrett and Tootie confronted her about her strange behavior, she managed to overcome the shock and fear and come to terms with Gail. Jo associated the fact that Gail's dying with her friend Gloria's death.

text: Many of Jo's stories revolved around her tomboyish ways. Jo got into verbal spars with girls who didn't think she was "feminine enough," and boys (including some of her boyfriends) were threatened by her mechanical aptitude, which she displayed by getting a job at a local garage.

text: In the later seasons, Jo's tomboyish image softened considerably, as she and the girls were growing up and was rarely raised as an issue again. Her relationship with Blair became more friendly as time went on (Jo would even refer to Blair as her best friend by the last season), although the two still argued, traded wisecracks and made fun of each other from time to time. Jo graduated from Eastland as valedictorian of her class, and attended Langley College with Blair, graduating with a degree in education. In one flashback-heavy episode; the ninth sixth-season episode "Dear Apple", Jo relayed her latest ongoing spat with Blair to a computer, which analyzed the data and concluded that Jo should stop being friends with Blair. At the end of the episode, Jo quietly threw the computer's printout away. During Season 6, Jo met and was romanced by a young rock singer named Flyman (played by Michael Damian) in the two-part episode, "Gone With the Wind". She was reunited with him in Season 7, where it was revealed he now had a lounge act in Las Vegas. In the last season, Jo married Rick Bonner, a concert musician, and she asked Blair to be her maid of honor.

text: Jo did not appear at the reunion TV special because it was stated that she was now a police officer and was working; however, Rick and their daughter Jamie did attend. This also coincided with Nancy McKeon's role as a policewoman in the drama series The Division since the reason she couldn't participate in the reunion was a conflict in her working schedule.

text: Tootie Ramsey[edit]

text:
Tootie Ramsey

First appearance
The Girls School (Diff'rent Strokes)
"Rough Housing" (The Facts of Life)

Last appearance
The Facts of Life Reunion

Portrayed by
Kim Fields

Information

Occupation
Student

Relatives
Harrison "Rifle" Ramsey (father)
Paula/Diane Ramsey (mother)
Marshall Ramsey (brother)
Ethel (maternal grandmother)

text: Dorothy "Tootie" Ramsey was played by Kim Fields. She was the youngest of the main characters at the age of 11, and the only African-American girl. She and her family hailed from Washington, D.C.. She attended Eastland Academy for most of the show's run. Tootie's most-remembered attributes were her penchant for rollerskates (at first used by Facts of Life producers to mask Fields' short stature), her gossipy nature, and her braces. In real life, Kim Fields had to wear braces for three years, finally having them removed in 1984, after the show begins the sixth season. A lot of Tootie's gossip got her and her friends in trouble, and she was noted for her catch phrase, "We are in trou-ble!"

text: Tootie was involved in many issue-based storylines. For example, Tootie befriended a boy named Fred who insisted that she only associate with black people, in an attempt to realize "her true roots." In another episode, Tootie was chosen by a photographer to model for newspaper advertisements but was instead lured into a borderline kiddie porn operation and was saved by Mrs. Garrett at the last minute. During a trip to New York City, Tootie was almost strong-armed into prostitution before Mrs. Garrett found her and took her home. In another episode, she struggled with the race issue again when her best friend Natalie dated a relative of hers and Tootie intervened, causing conflict between Natalie and herself. Tootie's favorite singer is Michael Jackson's older brother Jermaine Jackson.

text: Tootie helped Mrs. Garrett with her bakery, Edna's Edibles, after school and then worked full-time at the gift shop Over Our Heads after she graduated from high school in 1986.

text: In the 2001 The Facts of Life Reunion TV movie, Tootie had attended the Royal Academy of Dramatic Arts in London to pursue an acting career, was a Hollywood-based talk show host, and was the single mother of Tisha, a 10-year-old (fathered by her longtime boyfriend and later deceased husband, Jeff Williams). After her visit, Tootie (who now preferred to be called "Dorothy") decided to quit her talk show, Waking Up with Dorothy, and move to New York to take up the theater, but not before becoming the co-owner of the Peekskill Playhouse. Tisha Williams remained behind to attend Eastland Academy and continue the family tradition.

text: In addition to the Diff'rent Strokes episode "The Girls School" that serves as the pilot for The Facts of Life, Tootie also appears in "The Slumber Party", "The Bank Job", "First Day Blues" and "The Team".

text: Blair Warner[edit]

text:
Blair Warner

First appearance
The Girls School (Diff'rent Strokes)
"Rough Housing" (The Facts of Life)

Last appearance
The Facts of Life Reunion

Portrayed by
Lisa Whelchel

Information

Occupation
Student

Relatives
David Warner, Jr. (father)
Monica Warner Eloise Hoffdale, neé Blair (mother)
Meg Warner (half-sister)
Bailey Hoffdale-Warner (sister)
Geri Warner (cousin)
Hon. Carlton Blair (maternal grandfather; deceased)
David Warner, Sr. (paternal grandfather)

text: Blair Warner was played by Lisa Whelchel. She was 14 at the series' beginning; an episode in the 1985–1986 season centered on her 21st birthday.

text: At the series' beginning in 1979, Blair was portrayed as a very rich and very rebellious girl from a blue blood background. She was seen smoking cigarettes, drinking beer, and enjoying great popularity with boys; unlike many of her classmates, she was looking to lose her virginity. When the show was retooled in 1980, all instances of her rebellion were either dropped or given to the new character of Jo Polniaczek, and Blair was rewritten as an unashamedly spoiled "daddy's girl".

text: Blair was vain, arrogant, egotistical, and shallow, but she is also funny, kind-hearted, and loving to Mrs. Garrett and her friends, especially Jo Polniaczek. She also got good grades, won school awards, was crowned Harvest Queen for 3 straight years, and even convinced a guy to move from Switzerland to attend school near her (when asked about it, Blair dryly remarked, "I've done it before.") Blair's delusions of grandeur were usually played for laughs when Natalie, Tootie or Jo would make sarcastic remarks about her "beauty", "perfect" personality, or "naturally blonde hair". Blair felt she was more important than "regular" people because she was the heiress to her father's multimillion-dollar business, Warner Textile Mills. Any crisis at Eastland would usually prompt a suggested solution from Blair, preceded by her catch phrase: "I just had another one of my brilliant ideas!" More often than not, though, her "brilliant ideas" were actually quite the opposite, although on at least two occasions they turned out to actually be brilliant. In the episode Growing Pains, it was her idea to have Mrs Garrett punish them after Tootie gets drunk on wine that Blair, Jo, and Natalie were responsible for, and in The Four Muskateers it was her idea to move back into the room and work in the kitchen to pay off the debt incurred when she and the other girls get into a paint fight while painting the room. She eventually developed a more down-to-earth attitude, especially after she suffered a car accident (after falling asleep at the wheel) that left her slightly scarred, spoiling her "perfect" beauty.

text: Blair's parents (played by Nicolas Coster and Marj Dusay) were divorced on June 14, 1973, and although she didn't usually show it, Blair wished that she had a nuclear family like all of her friends. Later in the series, her mother remarried (for the fourth time) and gave birth to a baby girl (Bailey). Blair had misgivings about her mother's pregnancy but fell in love with baby Bailey as soon as she saw her.

text: Another secret Blair kept from her friends was that her cousin Geri (played by comedian Geri Jewell) had cerebral palsy. She was not embarrassed by her cousin, but rather jealous of her, since Blair was used to being the center of attention. Mrs. Garrett told Blair not to lash out against Geri because of her jealousy, and Blair joined Geri, a successful comedian, onstage at an impromptu comedy show Geri threw at the Eastland Academy. Blair's big sister Meg visited Eastland to tell her little sister that she's going to become a nun in "Best Sister Part 1" and in "Best Sister Part 2" it's revealed that Blair is an atheist because she asked God to not allow her parents' divorce to become final in 1973, but her parents split up nevertheless.

text: Blair attended Eastland, and upon graduating in 1983, attended nearby Langley College. She worked with Mrs. Garrett at Edna's Edibles and, later, Over Our Heads. After graduating from Langley, she enrolled in law school. In the series finale, she purchases the financially troubled Eastland Academy and turns it into a co-educational school.

text: Blair's chief foil was Jo. The two made no secret of their mutual dislike: Jo found Blair spoiled and snobbish; Blair thought Jo was classless and crude. However, more than once Blair stuck up for and stood by Jo in her time of need (and vice versa), and eventually the two developed a much friendlier relationship. In one episode, Jo even declared Blair as her official best friend.

text: In the episode "Legacy," Blair, initially enthusiastic about a library being built with her family's funds and named after her late maternal grandfather, Judge Carlton Blair, thus immortalizing the name "Blair", was horrified to learn her grandfather had been a member of the Ku Klux Klan. The revelation devastated Blair and made her question all her assumptions about her supposed "superiority," even though Jo assured her "You're not prejudiced; you're a snob." She almost withdrew the library funding to avoid commemorating her grandfather but finally agreed to let it be built so long as it was not given the "Blair" name.

text: In addition to the Diff'rent Strokes episode "The Girls School" that serves as the pilot for The Facts of Life, Blair appears in "The Older Man".

text: In the 2001 TV movie The Facts of Life Reunion, Blair, who became a lawyer, is wealthier than ever and owns a hotel empire (Warner Enterprises) with her husband Tad Warner (no relation), managed by Mrs. Garrett's son Raymond; she and Tad have no children. At end of the movie, she and Tad decided to adopt a child.

text: Note: Actress Geri Reischl ("fake Jan" of The Brady Bunch Hour) was given the role of Blair Warner in the television pilot Garrett's Girls (later renamed The Facts of Life), but was forced to give it up due to her contract with General Mills.[1]

text: Cindy Webster[edit]

text:
Cindy Webster

First appearance
"Rough Housing"

Last appearance
The Little Chill

Portrayed by
Julie Anne Haddock

Information

Occupation
Student

text: Cindy Webster was played by Julie Anne Haddock. She was around 12 years old at the beginning of The Facts of Life. Cindy was an athletic tomboy, who, at the start of the series, was worried she wasn't "normal". The first episode of The Facts of Life, which aired in summer 1979, focused on Cindy, who was concerned that she might like girls, after hearing disparaging remarks from snobby Blair. The episode tackled a sensitive issue during an era when lesbianism was rarely talked about on television, although reaction from modern-day critics has been mixed. Stephen Tropiano, writing in 2002, wrote: "While the episode is not really about homosexuality per se, it seems to deliver a contradictory message. On the one hand, wise Mrs. Garrett dispenses Cindy some good advice when she explains the value of being yourself [...] yet there is a sense of relief that Cindy is heading down the road to heterosexuality because she's fallen for a guy she met at the dance."[2]

text: On the series, Cindy's best friend and roommate was Sue Ann Weaver, and the pair appeared together frequently in many early episodes, including in an episode where the two girls fight over a racing competition ("Running", 1980). Cindy also does gymnastics and tries out for Harvest Queen at Eastland. She attends journalism class with Blair, Jo and Sue Ann. The character of Cindy Webster was gradually written out of the show between summer 1980 and winter 1982, with the character making only a few appearances during seasons two and three. However, she reappeared in the 1986 reunion episode "The Little Chill"; it was revealed in that episode that Cindy had become a model, and was now known professionally as Cindy Baker.

text: Beverly Ann Stickle[edit]

text:
Beverly Ann Stickle

First appearance
"Out of Peekskill"

Last appearance
"The Beginning of the End: Part 1"

Portrayed by
Cloris Leachman

Information

Gender
Female

Occupation
Businesswoman

Spouse(s)
Frank Stickle (divorced)

Children
Andy Moffet (adopted son)

Relatives
Edna Garrett (sister)

text: Beverly Ann Stickle was played by Cloris Leachman.

text: Beverly Ann was first seen in the fall of 1986, after Mrs. Garrett married and moved to Africa to serve in the Peace Corps. In reality, actress Charlotte Rae's contract had expired, and she did not want to continue with the series. At the time, The Facts of Life was still lucrative for NBC, and NBC president Brandon Tartikoff chose to renew, but only with a new mother figure at the helm.

text: Beverly Ann, Mrs. Garrett's divorced sister, moved in with the girls as Mrs. Garrett wanted someone to keep an eye on them as she had. She became the property owner for Mrs. Garrett's house and the boutique store, Over Our Heads. Beverly Ann's role expanded from confidante to mother when she legally adopted Over Our Heads worker Andy (Mackenzie Astin), who was being shuffled from foster home to foster home.

text: She mentioned that she was named after her grandfather, Boris Ann.

text: Notes[edit]

text:
Jump up ^ O'Hara's character was dropped after the fourth episode, "I.Q."
Jump up ^ Krenn was introduced in "Up from Down Under", the sixth episode of season 9, as a recurring character. She was promoted to the main cast beginning with the episode "Something in Common".

tag: ol


document_title: Burn card

question_text: when do you burn cards in texas holdem

question_tokens: when do you burn cards in texas holdem

root

text: Burn card

text: This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (February 2013) (Learn how and when to remove this template message)

tag: table

text: In card games, a burn card is a playing card dealt from the top of a deck, and discarded ("burned"), unused by the players. Burn cards are almost always placed face down next to the discard pile without being revealed to the players.

tag: p

text: Burning is most often performed in casinos to deter a form of cheating known as card marking. In poker, for example, the top card of the deck stub is burned at the beginning of each betting round, so that players who might have been able to read markings on that card during the previous round are less able to take advantage of that information. Knowledge of a burn card might be marginally useful, such as knowing there is one fewer Ace in the deck, but far less so than having it in play.[1]

text: Two other uses for burning are: to prevent second dealing and to provide extra cards for use when an irregularity of play occurs. Sometimes a misdealt card (such as one of the down cards in poker that has flashed during the deal) will be used as the burn card—in those cases, the card should be immediately placed face up on the deck after the deal is complete.

text: In Texas hold 'em (as well as in Omaha hold 'em), a card is burned before the flop, before the turn, and before the river.[1]


document_title: Diffusion

question_text: what is one condition for diffusion to take place

question_tokens: what is one condition for diffusion to take place

text: Diffusion

text: Diffusion vs. bulk flow[edit]

text: An example of a situation in which bulk motion and diffusion can be differentiated is the mechanism by which oxygen enters the body during external respiration known as breathing. The lungs are located in the thoracic cavity, which expands as the first step in external respiration. This expansion leads to an increase in volume of the alveoli in the lungs, which causes a decrease in pressure in the alveoli. This creates a pressure gradient between the air outside the body at relatively high pressure and the alveoli at relatively low pressure. The air moves down the pressure gradient through the airways of the lungs and into the alveoli until the pressure of the air and that in the alveoli are equal i.e. the movement of air by bulk flow stops once there is no longer a pressure gradient.

text: The air arriving in the alveoli has a higher concentration of oxygen than the “stale” air in the alveoli. The increase in oxygen concentration creates a concentration gradient for oxygen between the air in the alveoli and the blood in the capillaries that surround the alveoli. Oxygen then moves by diffusion, down the concentration gradient, into the blood. The other consequence of the air arriving in alveoli is that the concentration of carbon dioxide in the alveoli decreases. This creates a concentration gradient for carbon dioxide to diffuse from the blood into the alveoli, as fresh air has a very low concentration of carbon dioxide compared to the blood in the body.

text: The pumping action of the heart then transports the blood around the body. As the left ventricle of the heart contracts, the volume decreases, which increases the pressure in the ventricle. This creates a pressure gradient between the heart and the capillaries, and blood moves through blood vessels by bulk flow down the pressure gradient. As the thoracic cavity contracts during expiration, the volume of the alveoli decreases and creates a pressure gradient between the alveoli and the air outside the body, and air moves by bulk flow down the pressure gradient.

text: Diffusion in the context of different disciplines[edit]

text: The concept of diffusion is widely used in: physics (particle diffusion), chemistry, biology, sociology, economics, and finance (diffusion of people, ideas and of price values). However, in each case, the object (e.g., atom, idea, etc.) that is undergoing diffusion is “spreading out” from a point or location at which there is a higher concentration of that object.

text: There are two ways to introduce the notion of diffusion: either a phenomenological approach starting with Fick's laws of diffusion and their mathematical consequences, or a physical and atomistic one, by considering the random walk of the diffusing particles.[2]

text: In the phenomenological approach, diffusion is the movement of a substance from a region of high concentration to a region of low concentration without bulk motion. According to Fick's laws, the diffusion flux is proportional to the negative gradient of concentrations. It goes from regions of higher concentration to regions of lower concentration. Sometime later, various generalizations of Fick's laws were developed in the frame of thermodynamics and non-equilibrium thermodynamics.[3]

text:
From the atomistic point of view, diffusion is considered as a result of the random walk of the diffusing particles. In molecular diffusion, the moving molecules are self-propelled by thermal energy. Random walk of small particles in suspension in a fluid was discovered in 1827 by Robert Brown. The theory of the Brownian motion and the atomistic backgrounds of diffusion were developed by Albert Einstein.[4]
The concept of diffusion is typically applied to any subject matter involving random walks in ensembles of individuals.

text: Biologists often use the terms "net movement"  or "net diffusion" to describe the movement of ions or molecules by diffusion. For example, oxygen can diffuse through cell membranes so long as there is a higher concentration of oxygen outside the cell. However, because the movement of molecules is random, occasionally oxygen molecules move out of the cell (against the concentration gradient). Because there are more oxygen molecules outside the cell, the probability that oxygen molecules will enter the cell is higher than the probability that oxygen molecules will leave the cell. Therefore, the "net" movement of oxygen molecules (the difference between the number of molecules either entering or leaving the cell) is into the cell. In other words, there is a net movement of oxygen molecules down the concentration gradient.

text: History of diffusion in physics[edit]

text: In the scope of time, diffusion in solids was used long before the theory of diffusion was created. For example, Pliny the Elder had previously described the cementation process, which produces steel from the element iron (Fe) through carbon diffusion. Another example is well known for many centuries, the diffusion of colors of stained glass or earthenware and Chinese ceramics.

text: In modern science, the first systematic experimental study of diffusion was performed by Thomas Graham. He studied diffusion in gases, and the main phenomenon was described by him in 1831–1833:[5]

text: "...gases of different nature, when brought into contact, do not arrange themselves according to their density, the heaviest undermost, and the lighter uppermost, but they spontaneously diffuse, mutually and equally, through each other, and so remain in the intimate state of mixture for any length of time.”

text: The measurements of Graham contributed to James Clerk Maxwell deriving, in 1867, the coefficient of diffusion for CO2 in the air. The error rate is less than 5%.

text: In 1855, Adolf Fick, the 26-year-old anatomy demonstrator from Zürich, proposed his law of diffusion. He used Graham's research, stating his goal as "the development of a fundamental law, for the operation of diffusion in a single element of space". He asserted a deep analogy between diffusion and conduction of heat or electricity, creating a formalism that is similar to Fourier's law for heat conduction (1822) and Ohm's law for electric current (1827).

text: Robert Boyle demonstrated diffusion in solids in the 17th century[6] by penetration of zinc into a copper coin. Nevertheless, diffusion in solids was not systematically studied until the second part of the 19th century. William Chandler Roberts-Austen, the well-known British metallurgist and former assistant of Thomas Graham studied systematically solid state diffusion on the example of gold in lead in 1896. :[7]

text: "... My long connection with Graham's researches made it almost a duty to attempt to extend his work on liquid diffusion to metals."

text: In 1858, Rudolf Clausius introduced the concept of the mean free path. In the same year, James Clerk Maxwell developed the first atomistic theory of transport processes in gases. The modern atomistic theory of diffusion and Brownian motion was developed by Albert Einstein, Marian Smoluchowski and Jean-Baptiste Perrin. Ludwig Boltzmann, in the development of the atomistic backgrounds of the macroscopic transport processes, introduced the Boltzmann equation, which has served mathematics and physics with a source of transport process ideas and concerns for more than 140 years.[8]

text: In 1920–1921, George de Hevesy measured self-diffusion using radioisotopes. He studied self-diffusion of radioactive isotopes of lead in the liquid and solid lead.

text: Yakov Frenkel (sometimes, Jakov/Jacob Frenkel) proposed, and elaborated in 1926, the idea of diffusion in crystals through local defects (vacancies and interstitial atoms). He concluded, the diffusion process in condensed matter is an ensemble of elementary jumps and quasichemical interactions of particles and defects. He introduced several mechanisms of diffusion and found rate constants from experimental data.

text: Sometime later, Carl Wagner and Walter H. Schottky developed Frenkel's ideas about mechanisms of diffusion further. Presently, it is universally recognized that atomic defects are necessary to mediate diffusion in crystals.[7]

text: Henry Eyring, with co-authors, applied his theory of absolute reaction rates to Frenkel's quasichemical model of diffusion.[9] The analogy between reaction kinetics and diffusion leads to various nonlinear versions of Fick's law.[10]

text: Basic models of diffusion[edit]

text: Diffusion flux[edit]

text:
Each model of diffusion expresses the diffusion flux through concentrations, densities and their derivatives. Flux is a vector

J

{\displaystyle \mathbf {J} }

. The transfer of a physical quantity

N

{\displaystyle N}

 through a small area

Δ
S

{\displaystyle \Delta S}

 with normal

ν

{\displaystyle \nu }

 per time

Δ
t

{\displaystyle \Delta t}

 is

text:
where

(

J

,
ν
)

{\displaystyle (\mathbf {J} ,\nu )}

 is the inner product and

o
(
⋯
)

{\displaystyle o(\cdots )}

 is the little-o notation.
If we use the notation of vector area

Δ

S

=
ν

Δ
S

{\displaystyle \Delta \mathbf {S} =\nu \,\Delta S}

 then

text:
The dimension of the diffusion flux is [flux] = [quantity]/([time]·[area]).
The diffusing physical quantity

N

{\displaystyle N}

 may be the number of particles, mass, energy, electric charge, or any other scalar extensive quantity. For its density,

n

{\displaystyle n}

, the diffusion equation has the form

text:
where

W

{\displaystyle W}

 is intensity of any local source of this quantity (the rate of a chemical reaction, for example).
For the diffusion equation, the no-flux boundary conditions can be formulated as

(

J

(
x
)
,
ν
(
x
)
)
=
0

{\displaystyle (\mathbf {J} (x),\nu (x))=0}

 on the boundary, where

ν

{\displaystyle \nu }

 is the normal to the boundary at point

x

{\displaystyle x}

.

text: Fick's law and equations[edit]

text: Fick's first law: the diffusion flux is proportional to the negative of the concentration gradient:

text: The corresponding diffusion equation (Fick's second law) is

text:
where

Δ

{\displaystyle \Delta }

 is the Laplace operator,

text: Onsager's equations for multicomponent diffusion and thermodiffusion[edit]

text:
Fick's law describes diffusion of an admixture in a medium. The concentration of this admixture should be small and the gradient of this concentration should be also small. The driving force of diffusion in Fick's law is the antigradient of concentration,

−
∇
n

{\displaystyle -\nabla n}

.

text:
In 1931, Lars Onsager[11] included the multicomponent transport processes in the general context of linear non-equilibrium thermodynamics. For
multi-component transport,

text:
where

J

i

{\displaystyle \mathbf {J} _{i}}

 is the flux of the ith physical quantity (component) and

X

j

{\displaystyle X_{j}}

 is the jth thermodynamic force.

text: The thermodynamic forces for the transport processes were introduced by Onsager as the space gradients of the derivatives of the entropy density s (he used the term "force" in quotation marks or "driving force"):

text:
where

n

i

{\displaystyle n_{i}}

 are the "thermodynamic coordinates".
For the heat and mass transfer one can take

n

0

=
u

{\displaystyle n_{0}=u}

 (the density of internal energy) and

n

i

{\displaystyle n_{i}}

 is the concentration of the ith component. The corresponding driving forces are the space vectors

text:
where T is the absolute temperature and

μ

i

{\displaystyle \mu _{i}}

 is the chemical potential of the ith component. It should be stressed that the separate diffusion equations describe the mixing or mass transport without bulk motion. Therefore, the terms with variation of the total pressure are neglected. It is possible for diffusion of small admixtures and for small gradients.

text: For the linear Onsager equations, we must take the thermodynamic forces in the linear approximation near equilibrium:

text:
where the derivatives of s are calculated at equilibrium n*.
The matrix of the kinetic coefficients

L

i
j

{\displaystyle L_{ij}}

 should be symmetric (Onsager reciprocal relations) and positive definite (for the entropy growth).

text: The transport equations are

text:
Here, all the indexes i, j, k = 0, 1, 2, ... are related to the internal energy (0) and various components. The expression in the square brackets is the matrix

D

i
k

{\displaystyle D_{ik}}

of the diffusion (i,k > 0), thermodiffusion (i > 0, k = 0 or k > 0, i = 0) and thermal conductivity (i = k = 0) coefficients.

text:
Under isothermal conditions T = constant. The relevant thermodynamic potential is the free energy (or the free entropy). The thermodynamic driving forces for the isothermal diffusion are antigradients of chemical potentials,

−
(
1

/

T
)

∇

μ

j

{\displaystyle -(1/T)\,\nabla \mu _{j}}

, and the matrix of diffusion coefficients is

text: (i,k > 0).

text:
There is intrinsic arbitrariness in the definition of the thermodynamic forces and kinetic coefficients because they are not measurable separately and only their combinations

∑

j

L

i
j

X

j

{\displaystyle \sum _{j}L_{ij}X_{j}}

 can be measured. For example, in the original work of Onsager[11] the thermodynamic forces include additional multiplier T, whereas in the Course of Theoretical Physics[12] this multiplier is omitted but the sign of the thermodynamic forces is opposite. All these changes are supplemented by the corresponding changes in the coefficients and do not affect the measurable quantities.

text: Nondiagonal diffusion must be nonlinear[edit]

text: The formalism of linear irreversible thermodynamics (Onsager) generates the systems of linear diffusion equations in the form

text:
If the matrix of diffusion coefficients is diagonal, then this system of equations is just a collection of decoupled Fick's equations for various components. Assume that diffusion is non-diagonal, for example,

D

12

≠
0

{\displaystyle D_{12}\neq 0}

, and consider the state with

c

2

=
⋯
=

c

n

=
0

{\displaystyle c_{2}=\cdots =c_{n}=0}

. At this state,

∂

c

2

/

∂
t
=

D

12

Δ

c

1

{\displaystyle \partial c_{2}/\partial t=D_{12}\,\Delta c_{1}}

. If

D

12

Δ

c

1

(
x
)
<
0

{\displaystyle D_{12}\,\Delta c_{1}(x)<0}

 at some points, then

c

2

(
x
)

{\displaystyle c_{2}(x)}

 becomes negative at these points in a short time. Therefore, linear non-diagonal diffusion does not preserve positivity of concentrations. Non-diagonal equations of multicomponent diffusion must be non-linear.[10]

text: Einstein's mobility and Teorell formula[edit]

text: The Einstein relation (kinetic theory) connects the diffusion coefficient and the mobility (the ratio of the particle's terminal drift velocity to an applied force)[13]

text: where D is the diffusion constant, μ is the "mobility", kB is Boltzmann's constant, T is the absolute temperature.

text:
Below, to combine in the same formula the chemical potential μ and the mobility, we use for mobility the notation

m

{\displaystyle {\mathfrak {m}}}

.

text: The mobility—based approach was further applied by T. Teorell.[14] In 1935, he studied the diffusion of ions through a membrane. He formulated the essence of his approach in the formula:

text: This is the so-called Teorell formula. The term "gram-ion" ("gram-particle")  is used for a quantity of a substance that contains Avogadro's number of ions (particles). The common modern term is mole.

text: The force under isothermal conditions consists of two parts:

text:
Diffusion force caused by concentration gradient:

−
R
T

1
n

∇
n
=
−
R
T

∇
(
ln

(
n

/

n

eq

)
)

{\displaystyle -RT{\frac {1}{n}}\,\nabla n=-RT\,\nabla (\ln(n/n^{\text{eq}}))}

.
Electrostatic force caused by electric potential gradient:

q

∇
φ

{\displaystyle q\,\nabla \varphi }

.

text: Here R is the gas constant, T is the absolute temperature, n is the concentration, the equilibrium concentration is marked by a superscript "eq", q is the charge and φ is the electric potential.

text: The simple but crucial difference between the Teorell formula and the Onsager laws is the concentration factor in the Teorell expression for the flux. In the Einstein–Teorell approach, If for the finite force the concentration tends to zero then the flux also tends to zero, whereas the Onsager equations violate this simple and physically obvious rule.

text: The general formulation of the Teorell formula for non-perfect systems under isothermal conditions is[10]

text:
where μ is the chemical potential, μ0 is the standard value of the chemical potential.
The expression

a
=
exp

(

μ
−

μ

0

R
T

)

{\displaystyle a=\exp \left({\frac {\mu -\mu _{0}}{RT}}\right)}

 is the so-called activity. It measures the "effective concentration" of a species in a non-ideal mixture. In this notation, the Teorell formula for the flux has a very simple form[10]

text:
The standard derivation of the activity includes a normalization factor and for small concentrations

a
=
n

/

n

⊖

+
o
(
n

/

n

⊖

)

{\displaystyle a=n/n^{\ominus }+o(n/n^{\ominus })}

, where

n

⊖

{\displaystyle n^{\ominus }}

 is the standard concentration. Therefore, this formula for the flux describes the flux of the normalized dimensionless quantity

n

/

n

⊖

{\displaystyle n/n^{\ominus }}

:

text: Teorell formula for multicomponent diffusion[edit]

text: The Teorell formula with combination of Onsager's definition of the diffusion force gives

text:
where

m

i

{\displaystyle {\mathfrak {m_{i}}}}

 is the mobility of the ith component,

a

i

{\displaystyle a_{i}}

 is its activity,

L

i
j

{\displaystyle L_{ij}}

 is the matrix of the coefficients,

X

j

{\displaystyle X_{j}}

 is the thermodynamic diffusion force,

X

j

=
−
∇

μ

j

T

{\displaystyle X_{j}=-\nabla {\frac {\mu _{j}}{T}}}

. For the isothermal perfect systems,

X

j

=
−
R

∇

n

j

n

j

{\displaystyle X_{j}=-R{\frac {\nabla n_{j}}{n_{j}}}}

. Therefore, the Einstein–Teorell approach gives the following multicomponent generalization of the Fick's law for multicomponent diffusion:

text:
where

D

i
j

{\displaystyle D_{ij}}

 is the matrix of coefficients. The Chapman–Enskog formulas for diffusion in gases include exactly the same terms. Earlier, such terms were introduced in the Maxwell–Stefan diffusion equation.

text: Jumps on the surface and in solids[edit]

text: Diffusion of reagents on the surface of a catalyst may play an important role in heterogeneous catalysis. The model of diffusion in the ideal monolayer is based on the jumps of the reagents on the nearest free places. This model was used for CO on Pt oxidation under low gas pressure.

text:
The system includes several reagents

A

1

,

A

2

,
…
,

A

m

{\displaystyle A_{1},A_{2},\ldots ,A_{m}}

 on the surface. Their surface concentrations are

c

1

,

c

2

,
…
,

c

m

.

{\displaystyle c_{1},c_{2},\ldots ,c_{m}.}

 The surface is a lattice of the adsorption places. Each
reagent molecule fills a place on the surface. Some of the places are free. The concentration of the free places is

z
=

c

0

{\displaystyle z=c_{0}}

. The sum of all

c

i

{\displaystyle c_{i}}

 (including free places) is constant, the density of adsorption places b.

text:
The jump model gives for the diffusion flux of

A

i

{\displaystyle A_{i}}

 (i = 1, ..., n):

text: The corresponding diffusion equation is:[10]

text:
Due to the conservation law,

z
=
b
−

∑

i
=
1

n

c

i

,

{\displaystyle z=b-\sum _{i=1}^{n}c_{i}\,,}

 and we
have the system of m diffusion equations. For one component we get Fick's law and linear equations because

(
b
−
c
)

∇
c
−
c

∇
(
b
−
c
)
=
b

∇
c

{\displaystyle (b-c)\,\nabla c-c\,\nabla (b-c)=b\,\nabla c}

. For two and more components the equations are nonlinear.

text: If all particles can exchange their positions with their closest neighbours then a simple generalization gives

text:
where

D

i
j

=

D

j
i

≥
0

{\displaystyle D_{ij}=D_{ji}\geq 0}

 is a symmetric matrix of coefficients that characterize the intensities of jumps. The free places (vacancies) should be considered as special "particles" with concentration

c

0

{\displaystyle c_{0}}

.

text: Various versions of these jump models are also suitable for simple diffusion mechanisms in solids.

text: Diffusion in porous media[edit]

text: For diffusion in porous media the basic equations are:[15]

text: where D is the diffusion coefficient, n is the concentration, m > 0 (usually m > 1, the case m = 1 corresponds to Fick's law).

text: For diffusion of gases in porous media this equation is the formalisation of Darcy's law: the velocity of a gas in the porous media is

text:
where k is the permeability of the medium, μ is the viscosity and p is the pressure. The flux J = nv and for

p
∼

n

γ

{\displaystyle p\sim n^{\gamma }}

 Darcy's law gives the equation of diffusion in porous media with m = γ + 1.

text: For underground water infiltration, the Boussinesq approximation gives the same equation with m = 2.

text: For plasma with the high level of radiation, the Zeldovich–Raizer equation gives m > 4 for the heat transfer.

text: Diffusion in physics[edit]

text: Elementary theory of diffusion coefficient in gases[edit]

text:
The diffusion coefficient

D

{\displaystyle D}

 is the coefficient in the Fick's first law

J
=
−
D

∂
n

/

∂
x

{\displaystyle J=-D\,\partial n/\partial x}

, where J is the diffusion flux (amount of substance) per unit area per unit time, n (for ideal mixtures) is the concentration, x is the position [length].

text: Let us consider two gases with molecules of the same diameter d and mass m (self-diffusion). In this case, the elementary mean free path theory of diffusion gives for the diffusion coefficient

text:
where kB is the Boltzmann constant, T is the temperature, P is the pressure,

ℓ

{\displaystyle \ell }

 is the mean free path, and vT is the mean thermal speed:

text: We can see that the diffusion coefficient in the mean free path approximation grows with T as T3/2 and decreases with P as 1/P. If we use for P the ideal gas law P = RnT with the total concentration n, then we can see that for given concentration n the diffusion coefficient grows with T as T1/2 and for given temperature it decreases with the total concentration as 1/n.

text: For two different gases, A and B, with molecular masses mA, mB and molecular diameters dA, dB, the mean free path estimate of the diffusion coefficient of A in B and B in A is:

text: The theory of diffusion in gases based on Boltzmann's equation[edit]

text:
In Boltzmann's kinetics of the mixture of gases, each gas has its own distribution function,

f

i

(
x
,
c
,
t
)

{\displaystyle f_{i}(x,c,t)}

, where t is the time moment, x is position and c is velocity of molecule of the ith component of the mixture. Each component has its mean velocity

C

i

(
x
,
t
)
=

1

n

i

∫

c

c
f
(
x
,
c
,
t
)

d
c

{\displaystyle C_{i}(x,t)={\frac {1}{n_{i}}}\int _{c}cf(x,c,t)\,dc}

. If the velocities

C

i

(
x
,
t
)

{\displaystyle C_{i}(x,t)}

 do not coincide then there exists diffusion.

text: In the Chapman–Enskog approximation, all the distribution functions are expressed through the densities of the conserved quantities:[8]

text:
individual concentrations of particles,

n

i

(
x
,
t
)
=

∫

c

f

i

(
x
,
c
,
t
)

d
c

{\displaystyle n_{i}(x,t)=\int _{c}f_{i}(x,c,t)\,dc}

 (particles per volume),
density of momentum

∑

i

m

i

n

i

C

i

(
x
,
t
)

{\displaystyle \sum _{i}m_{i}n_{i}C_{i}(x,t)}

 (mi is the ith particle mass),
density of kinetic energy

tag: ul

text: The kinetic temperature T and pressure P are defined in 3D space as

text:
where

n
=

∑

i

n

i

{\displaystyle n=\sum _{i}n_{i}}

 is the total density.

text:
For two gases, the difference between velocities,

C

1

−

C

2

{\displaystyle C_{1}-C_{2}}

 is given by the expression:[8]

text:
where

F

i

{\displaystyle F_{i}}

 is the force applied to the molecules of the ith component and

k

T

{\displaystyle k_{T}}

 is the thermodiffusion ratio.

text: The coefficient D12 is positive. This is the diffusion coefficient. Four terms in the formula for C1-C2 describe four main effects in the diffusion of gases:

text:
∇

(

n

1

n

)

{\displaystyle \nabla \,\left({\frac {n_{1}}{n}}\right)}

 describes the flux of the first component from the areas with the high ratio n1/n to the areas with lower values of this ratio (and, analogously the flux of the second component from high n2/n to low n2/n because n2/n = 1 – n1/n);

n

1

n

2

(

m

2

−

m

1

)

n
(

m

1

n

1

+

m

2

n

2

)

∇
P

{\displaystyle {\frac {n_{1}n_{2}(m_{2}-m_{1})}{n(m_{1}n_{1}+m_{2}n_{2})}}\nabla P}

 describes the flux of the heavier molecules to the areas with higher pressure and the lighter molecules to the areas with lower pressure, this is barodiffusion;

m

1

n

1

m

2

n

2

P
(

m

1

n

1

+

m

2

n

2

)

(

F

1

−

F

2

)

{\displaystyle {\frac {m_{1}n_{1}m_{2}n_{2}}{P(m_{1}n_{1}+m_{2}n_{2})}}(F_{1}-F_{2})}

 describes diffusion caused by the difference of the forces applied to molecules of different types. For example, in the Earth's gravitational field, the heavier molecules should go down, or in electric field the charged molecules should move, until this effect is not equilibrated by the sum of other terms. This effect should not be confused with barodiffusion caused by the pressure gradient.

k

T

1
T

∇
T

{\displaystyle k_{T}{\frac {1}{T}}\nabla T}

 describes thermodiffusion, the diffusion flux caused by the temperature gradient.

text: All these effects are called diffusion because they describe the differences between velocities of different components in the mixture. Therefore, these effects cannot be described as a bulk transport and differ from advection or convection.

text: In the first approximation,[8]

text:
D

12

=

3

2
n
(

d

1

+

d

2

)

2

[

k
T
(

m

1

+

m

2

)

2
π

m

1

m

2

]

1

/

2

{\displaystyle D_{12}={\frac {3}{2n(d_{1}+d_{2})^{2}}}\left[{\frac {kT(m_{1}+m_{2})}{2\pi m_{1}m_{2}}}\right]^{1/2}}

 for rigid spheres;

D

12

=

3

8
n

A

1

(

ν

)
Γ
(
3
−

2

ν
−
1

)

[

k
T
(

m

1

+

m

2

)

2
π

m

1

m

2

]

1

/

2

(

2
k
T

κ

12

)

2

ν
−
1

{\displaystyle D_{12}={\frac {3}{8nA_{1}({\nu })\Gamma (3-{\frac {2}{\nu -1}})}}\left[{\frac {kT(m_{1}+m_{2})}{2\pi m_{1}m_{2}}}\right]^{1/2}\left({\frac {2kT}{\kappa _{12}}}\right)^{\frac {2}{\nu -1}}}

 for repulsing force

κ

12

r

−
ν

.

{\displaystyle \kappa _{12}r^{-\nu }.}

text:
The number

A

1

(

ν

)

{\displaystyle A_{1}({\nu })}

 is defined by quadratures (formulas (3.7), (3.9), Ch. 10 of the classical Chapman and Cowling book[8])

text: We can see that the dependence on T for the rigid spheres is the same as for the simple mean free path theory but for the power repulsion laws the exponent is different. Dependence on a total concentration n for a given temperature has always the same character, 1/n.

text: In applications to gas dynamics, the diffusion flux and the bulk flow should be joined in one system of transport equations. The bulk flow describes the mass transfer. Its velocity V is the mass average velocity. It is defined through the momentum density and the mass concentrations:

text:
where

ρ

i

=

m

i

n

i

{\displaystyle \rho _{i}=m_{i}n_{i}}

 is the mass concentration of the ith species,

ρ
=

∑

i

ρ

i

{\displaystyle \rho =\sum _{i}\rho _{i}}

 is the mass density.

text:
By definition, the diffusion velocity of the ith component is

v

i

=

C

i

−
V

{\displaystyle v_{i}=C_{i}-V}

,

∑

i

ρ

i

v

i

=
0

{\displaystyle \sum _{i}\rho _{i}v_{i}=0}

.
The mass transfer of the ith component is described by the continuity equation

text:
where

W

i

{\displaystyle W_{i}}

 is the net mass production rate in chemical reactions,

∑

i

W

i

=
0

{\displaystyle \sum _{i}W_{i}=0}

.

text:
In these equations, the term

∇
(

ρ

i

V
)

{\displaystyle \nabla (\rho _{i}V)}

 describes advection of the ith component and the term

∇
(

ρ

i

v

i

)

{\displaystyle \nabla (\rho _{i}v_{i})}

 represents diffusion of this component.

text: In 1948, Wendell H. Furry proposed to use the form of the diffusion rates found in kinetic theory as a framework for the new phenomenological approach to diffusion in gases. This approach was developed further by F.A. Williams and S.H. Lam.[16] For the diffusion velocities in multicomponent gases (N components) they used

text:
Here,

D

i
j

{\displaystyle D_{ij}}

 is the diffusion coefficient matrix,

D

i

(
T
)

{\displaystyle D_{i}^{(T)}}

 is the thermal diffusion coefficient,

f

i

{\displaystyle f_{i}}

 is the body force per unite mass acting on the ith species,

X

i

=

P

i

/

P

{\displaystyle X_{i}=P_{i}/P}

 is the partial pressure fraction of the ith species (and

P

i

{\displaystyle P_{i}}

 is the partial pressure),

Y

i

=

ρ

i

/

ρ

{\displaystyle Y_{i}=\rho _{i}/\rho }

 is the mass fraction of the ith species, and

∑

i

X

i

=

∑

i

Y

i

=
1.

{\displaystyle \sum _{i}X_{i}=\sum _{i}Y_{i}=1.}

text: Diffusion of electrons in solids[edit]

text: When the density of electrons in solids is not in equilibrium, diffusion of electrons occurs. For example, when a bias is applied to two ends of a chunk of semiconductor, or a light shines on one end (see right figure), electron diffuse from high density regions (center) to low density regions (two ends), forming a gradient of electron density. This process generates current, referred to as diffusion current.

text: Diffusion current can also be described by Fick's first law

text: where J is the diffusion current density (amount of substance) per unit area per unit time, n (for ideal mixtures) is the electron density, x is the position [length].

text: Diffusion in geophysics[edit]

text: Analytical and numerical models that solve the diffusion equation for different initial and boundary conditions have been popular for studying a wide variety of changes to the Earth's surface. Diffusion has been used extensively in erosion studies of hillslope retreat, bluff erosion, fault scarp degradation, wave-cut terrace/shoreline retreat, alluvial channel incision, coastal shelf retreat, and delta progradation[17]. Although the Earth's surface is not literally diffusing in many of these cases, the process of diffusion effectively mimics the holistic changes that occur over decades to millennia. Diffusion models may also be used to solve inverse boundary value problems in which some information about the depositional environment is known from paleoenvironmental reconstruction and the diffusion equation is used to figure out the sediment influx and time series of landform changes[18].

text: Random walk (random motion)[edit]

text: One common misconception is that individual atoms, ions or molecules move randomly, which they do not. In the animation on the right, the ion on in the left panel has a “random” motion, but this motion is not random as it is the result of “collisions” with other ions. As such, the movement of a single atom, ion, or molecule within a mixture just appears random when viewed in isolation. The movement of a substance within a mixture by “random walk” is governed by the kinetic energy within the system that can be affected by changes in concentration, pressure or temperature.

text: Separation of diffusion from convection in gases[edit]

text: While Brownian motion of multi-molecular mesoscopic particles (like pollen grains studied by Brown) is observable under an optical microscope, molecular diffusion can only be probed in carefully controlled experimental conditions. Since Graham experiments, it is well known that avoiding of convection is necessary and this may be a non-trivial task.

text: Under normal conditions, molecular diffusion dominates only on length scales between nanometer and millimeter. On larger length scales, transport in liquids and gases is normally due to another transport phenomenon, convection, and to study diffusion on the larger scale, special efforts are needed.

text: Therefore, some often cited examples of diffusion are wrong: If cologne is sprayed in one place, it can soon be smelled in the entire room, but a simple calculation shows that this can't be due to diffusion. Convective motion persists in the room because of the temperature [inhomogeneity]. If ink is dropped in water, one usually observes an inhomogeneous evolution of the spatial distribution, which clearly indicates convection (caused, in particular, by this dropping).[citation needed]

text: In contrast, heat conduction through solid media is an everyday occurrence (e.g. a metal spoon partly immersed in a hot liquid). This explains why the diffusion of heat was explained mathematically before the diffusion of mass.

text: Other types of diffusion[edit]

text:
Anisotropic diffusion, also known as the Perona–Malik equation, enhances high gradients
Anomalous diffusion,[19] in porous medium
Atomic diffusion, in solids
Eddy diffusion, in coarse-grained description of turbulent flow
Effusion of a gas through small holes
Electronic diffusion, resulting in an electric current called the diffusion current
Facilitated diffusion, present in some organisms
Gaseous diffusion, used for isotope separation
Heat equation, diffusion of thermal energy
Itō diffusion, mathematisation of Brownian motion, continuous stochastic process.
Kinesis (biology) is an animal's non-directional  movement activity in response to a stimulus.
Knudsen diffusion of gas in long pores with frequent wall collisions
Levy flights and walks
Momentum diffusion ex. the diffusion of the hydrodynamic velocity field
Photon diffusion
Plasma diffusion
Random walk,[20] model for diffusion
Reverse diffusion, against the concentration gradient, in phase separation
Rotational diffusion, random reorientations of molecules
Surface diffusion, diffusion of adparticles on a surface
Turbulent diffusion, transport of mass, heat, or momentum within a turbulent fluid


document_title: Leonard Hofstadter

question_text: what is leonard's job on big bang theory

question_tokens: what is leonard 's job on big bang theory

text: Leonard Hofstadter

text: Creation and casting[edit]

text: Leonard is named after actor/producer Sheldon Leonard,[5] and Nobel Prize in Physics Laureate Robert Hofstadter.[6] Johnny Galecki was originally asked to play the role of Sheldon Cooper, but thought he would be "better suited" for the character of Leonard. Leonard is one of four characters to appear in every episode of the series, along with Sheldon, Howard Wolowitz and Raj Koothrappali.

text: Personality[edit]

text: Originally from New Jersey and a graduate of Princeton University, Leonard works as a Caltech experimental physicist, mainly working with lasers, and shares an apartment with colleague Sheldon Cooper in Pasadena, California. He is usually seen wearing his characteristic black thick-framed glasses, low-cut black Converse All Stars sneakers, pastel hoodies or neutral-colored sweat jackets (i.e. jackets with integrated hoodies) or a combination of the two, brown or red trousers (or, less frequently, jeans), and physics-themed T-shirts. His various girlfriends have tried to change his outfits: Penny had no success while Stephanie got him to wear dress shirts and sweaters (which he found uncomfortable), and Priya got him to briefly switch to dress shirts, waistcoats and dark slacks; he reverted to his original outfits after she left for India, but started eschewing his hoodies in favor of button-down shirts and non-hooded jackets towards the end of the seventh season, a trend that continued into successive seasons.

text: Although Leonard feels at home with his geek colleagues, he wants to be more social. Among the main characters, he has little to no difficulty interacting with "non-geek" individuals. He is instantly captivated by Penny, and from the beginning sets out to date her.[7]

text: In early episodes, Leonard is reluctant to let Penny know about his recreational activities (such as Klingon Boggle), as he does not want her to see him as a geek. While certainly a geek by most definitions, he is far less socially inept than Sheldon (who is unable to grasp social norms and is often even dismissive of them), Raj (who was unable to talk to women unless he was under the influence of alcohol or anti-anxiety prescription drugs, and even after getting over his handicap still tended to speak inappropriately), and Howard (who was often seen as "creepy" when flirting with women, including Penny).

text: Leonard is also musically inclined, as he can play the cello, although he holds the bow upside down and plays on the finger board. As seen in the season 1 episode "The Hamburger Postulate", he and Leslie Winkle practice their instruments and then leave to have intercourse, which Leonard calls "a little musical foreplay".

text: Despite his attempts to not appear to be a geek, Leonard owns, among other things, Star Wars hygiene products, a prop of the One Ring, Star Trek and Star Trek: The Next Generation officer's uniforms, an expansive Superman comic book collection (and wears Clark Kent-type glasses) and a Battlestar Galactica Colonial warrior's flight suit. Early in the series, Leonard tried to get rid of his collectables to impress Penny with his maturity. However, he changed his mind when he saw that Penny was already dating another man.[8]

text: Because he has lived with Sheldon for several years, Leonard knows him better than his other colleagues: this has led Sheldon to believe (slightly erroneously) that Leonard is his best friend. Nevertheless, Leonard often finds himself explaining Sheldon's behavior or serving as a mediator between him and other people in many situations. For instance, when Penny and Sheldon engaged in a fierce dispute, Leonard gave Penny Sheldon's mother's phone number so she would call her son and scold him for his behavior, thus ending the fight.[9] "The Staircase Implementation" features a flashback to when Leonard first moved in with Sheldon. Leonard explains to Penny that he moved in despite the difficulty of living with Sheldon because the rent was so reasonable. Shortly after moving in, during a rocketry experiment Leonard, Raj and Howard conducted, Sheldon observed miscalculations Leonard made in mixing the rocket fuel and managed to avert disaster by grabbing the fuel and placing it in their apartment building's elevator. The resulting explosion disabled the elevator, thus explaining why the elevator is out of order for the duration of the series. Leonard explains that Sheldon, despite his tendency to alienate others, kept quiet about Leonard's destruction of the elevator. (Leonard cites: "He didn't rat me out to the landlord, or the police.... or Homeland Security.")

text: Despite Leonard's reasonable nature and friendly personality, he occasionally demonstrates a mean streak. These include deliberately triggering Sheldon's obsessive compulsive problems, mocking Howard and Raj whenever they slip up, and making sniping comments when Penny's commitment issues flare up. In addition, he is often shown to be quite jealous, often feeling insecure and defensive whenever Penny interacts with another guy, and on one occasion trying to frighten off a British college student she was doing a project with, because Penny commented positively on his accent.

text: Leonard's primary health concern is his lactose intolerance: his consuming melon or any dairy products (and according to the pilot episode, even corn) results in flatulence. Leonard wears eyeglasses because of astigmatism, and cannot see without them. On one occasion, when his glasses were broken at the movie theater, he had to surreptitiously return to his apartment and retrieve his backup glasses. In order to avoid detection by a sick Sheldon and Penny, who was nursing him, Howard and Raj helped him to navigate through the living room by using a helmet camera.[10] Leonard states in one episode that he suffers from sleep apnea. During his relationship with Leslie Winkle, he tells her that many members of his family have died from heart disease and thus he has a genetic disposition to the condition.

text: Family[edit]

text: All of the members of Leonard's family are accomplished scientists, except for his younger brother Michael, who is a tenured law professor at Harvard University.

text: Leonard's mother, Dr. Beverly Hofstadter, is a psychiatrist and neuroscientist. She has a personality almost identical to Sheldon's, including strict speech patterns, lack of social conventions, and attention to detail, and she is principally responsible for Leonard's difficult childhood. Sheldon and Beverly have a friendly relationship where they share details of each other's lives, with Sheldon often failing to pass on significant information to Leonard such as Leonard's parents divorcing and the family dog Mitsy's death. Leonard is upset with the fact that she tells Sheldon more than she tells him. After a night out of bonding and drinking with Penny in which she notices an attractive busboy, Beverly kisses Sheldon but realizes she "would rather have the busboy".

text: Due to his mother's views, Leonard never celebrated his birthday when he was a child,[11] and when she visited him she was not impressed with his unoriginal research. Leonard revealed to Penny that he built a "hugging machine" when he was young in order to compensate for the lack of affection from his mother. He further stated that his father used to borrow it. Beverly also belittles Leonard by pointing out that his brother and sister are more successful in their respective fields than he is. Leonard's brother, Michael, is a Harvard law professor and is engaged to the youngest appellate court judge in New Jersey history, and his older sister, Hayley, is a cutting-edge medical researcher working with gibbons to cure diabetes.[12] However, Beverly admits in season 11 that Leonard married the best out of his siblings, after she develops a genuine friendship with Penny. Leonard also dislikes Christmas because instead of gifts the Hofstadter kids had to turn in papers to "Santa" which were graded the next day. Over the course of six years he never got over a "C minus", which according to Sheldon was a true gift, because by Sheldon's lights he never deserved anything better. Leonard had two childhood pets, a cat named Dr. Boots Hofstadter and a dog named Mitsy.

text: Leonard's father is briefly mentioned as an anthropologist. Sheldon reveals that Leonard's middle name, "Leakey", comes from famed archaeologist Louis Leakey, with whom Leonard's father had worked.[13] Leonard is embarrassed by his middle name and its humorous connotations, and rarely mentions it, as the name is an obvious embarrassment. Apparently his father was not very affectionate towards him either; he mentions that he had to compete with the bones of an Etruscan boy for his father's attention. However, they seem to have developed a good, affectionate rapport by the time of Leonard and Penny's second wedding ceremony in the season 9 finale.

text: Though little is known about Leonard's extended family, a few references to it have been made. In the first episode, Sheldon and Leonard discuss Leonard's grandmother, who had visited them on Thanksgiving the year before. She has Alzheimer's disease and apparently "had an episode" during her visit, which resulted in her stripping off her clothes and carving the turkey. On Beverly's first visit, she tells Leonard that his uncle Floyd has died, which greatly upsets him (according to him, Floyd was the only family member he really liked). Leonard also has several other uncles, whom Sheldon says are all very bald; when they gather together, they look "like a half carton of eggs."[14] Leonard describes his aunt, however, as "one of the hairiest women you'll ever meet".[15] He also mentioned an Aunt Nancy, apparently a "crazy cat lady" who had 25 cats, died, and was eaten by them.[16]

text: Work[edit]

text: Leonard has an IQ of 173,[7][10] and was 24 years old when he received his PhD from Princeton University.[17] Leonard also received a dissertation of the year award for his doctoral paper on experimental particle physics.[18]

text: Leonard has been established to have been a child prodigy, and a gifted scientist with an impressive knowledge of theoretical physics. His work as an experimental physicist often includes the use of lasers, such as a helium–neon laser or free-electron laser, and his research topics have varied from Bose–Einstein condensates and foundations of quantum mechanics to soft cosmic rays at sea level and development of novel rocket propellants. Leonard designs experiments in order to test theories but, according to Sheldon, his work is mostly derivative and thus unimportant.[19]

text: Although Leonard's attempts to disprove the existence of dark matter were made moot by the work of another physicist, Leonard helped to solidify proof of the hypothetical matter's existence with a photomultiplier, and was invited as keynote speaker to a topical conference by the Institute of Experimental Physics for his successful research on super solids.[20]

text: From the season 6 finale, The Bon Voyage Reaction" Leonard heads to the United Kingdom to work on a physics project seeking the hydrodynamics equivalent of the Unruh effect, sponsored by Professor Stephen Hawking, for three months on a ship in the North Sea.

text: Relationships[edit]

text: Leonard became interested in Penny almost immediately after seeing her for the first time.[7] His infatuation with Penny becomes the major force that drives the series during the first few seasons. By the end of the first season, Leonard finally manages to ask Penny out, and they have their first date.[21] Subsequently, they break up because Penny felt she was not as smart as Leonard would like.[19]

text: Besides Penny, Leonard has been involved with only a few other women. One of Leonard's former girlfriends who is mentioned on several occasions is Joyce Kim, who did not appear until the third season. Leonard's friends recalled on many occasions that they were together for only 27 days, after which Joyce, later revealed to be a spy, defected to North Korea.[22]

text: Initially, after feeling that Penny was not for him, Leonard turned his attention to fellow scientist Leslie Winkle. The first time Leonard asks Leslie out, she rejects him,[23] and his further relationships with her proved to be only short-lived casual sexual encounters that only happened to satisfy Leslie's libido.[24][25] Leslie briefly started dating Leonard in Season 2, but when he failed to back her up in an argument with Sheldon, she dumped him.

text: In the second season, Leonard began a stable relationship with a physician named Stephanie Barnett.[26] Although the relationship went well, even earning Sheldon's approval, Leonard felt uncomfortable with Stephanie moving in with him, and the relationship ended.[27]

text: On another occasion, when Leonard's mother was visiting, he and Penny came very close to having sex, but Leonard ruined the moment by suggesting that they were burying their lifelong issues with their parents by doing so, which offended Penny.[12] In the second-season finale, when Leonard, Sheldon, Howard, and Raj were due to leave for a three-month scientific expedition to the North Pole, Penny privately expresses sadness, and wishes that he would not leave.[28]

text: In the third season premiere, Leonard and Penny finally started a romantic relationship and had intercourse for the first time.[29] However, the relationship ended after eight months,[30] after Leonard told Penny he loved her and took umbrage at her inability to reciprocate, which led to friction that was exploited by guest star Wil Wheaton who appeared as a fictionalized version of himself, who observed and exacerbated it in order to break them up in the middle of a bowling match Wheaton's team was having against Leonard, Penny, Sheldon, Howard and Raj.

text: Shortly after his breakup with Penny, in "The Plimpton Stimulation", Leonard has a one-night stand with Dr. Elizabeth Plimpton (Judy Greer), a physicist he admires, when Sheldon invited her to stay in their apartment for a brief visit. This encounter causes some tension between Leonard and Penny, who is somewhat judgmental of Leonard's doing so. However, the two later resolve their feelings and their friendship continues.

text: In the third-season finale, "The Lunar Excitation", after Penny's failed attempts to move on from her relationship with Leonard, she becomes intoxicated and has sex with him. In the morning, Leonard believes that their relationship has resumed, though Penny tells him that the previous night was a mistake. This causes a strain on their friendship; at the end of the episode, Leonard becomes intoxicated and tries to have intercourse with her, prompting Penny to push him out of her apartment, to which Leonard suspects a double standard. He immediately makes the same advances towards Leslie Winkle, who replies, 'Let me think about it" and slams the door in his face.[31]

text: Throughout the fourth season, it becomes obvious that Penny is still in love with Leonard. It is unclear whether or not Leonard has noticed this, though he clearly is still interested in Penny. In "The Benefactor Factor", an older rich woman propositions Leonard in exchange for a large donation to the physics department; he initially resists and she admits that she planned to make the donation anyway, after which they engage in a one-night stand. Leonard arrives home the next morning, whereupon Penny recognizes his "walk of shame" and Sheldon thinks Leonard has a future in becoming a gigolo to rich ladies in exchange for donations.[18]

text: Leonard also has an affair with Raj's younger sister Priya (apparently every time she comes to town), despite a pinky swear with Howard that neither of them would attempt to make a move on her, and Raj giving his strong disapproval.[32] When Priya returns, she and Leonard begin a relationship. Raj strongly opposes this, and Penny is secretly uncomfortable with Leonard dating someone else, eventually breaking down and crying while talking with her friend Amy Farrah Fowler. Once again, Leonard is unaware of Penny's true feelings. Subsequently, Priya pressures Leonard into ending his friendship with Penny, which he attempts with extreme reluctance. Penny complies, though it is clear that she does not want Leonard out of her life.[33] Penny eventually resolves to stay in Leonard's life by ingratiating herself to Priya.[34]

text: In the Season 4 finale, Leonard runs into Penny and Raj as they come out of his room in the morning, just after Leonard and Priya appear to break up upon Leonard's learning that Priya is soon moving back to India. At the start of Season 5, Leonard and Priya are trying to maintain a long-distance relationship via Skype (including a failed attempt at cybersex) with Priya continuing to treat Leonard like a submissive partner. Despite being the most eager to have sex, Leonard proves he is quite awkward in these situations. Leonard later goes to a wedding with Amy, and they seem to take a liking to each other, though Sheldon disapproves, karate-chopping Leonard and saying, "She's not for you...not for you!".[35] Later, despite feeling that he and Priya were in love and might get married, Leonard finds himself attracted to a comic book artist named Alice. The attraction is mutual, and they even share a kiss. Right when they are about to have sex, however, he tells Alice that he has a girlfriend, thus ending the relationship. Leonard then decides to confess his behavior to Priya via Skype, but he is shocked to learn that Priya has also betrayed him, sleeping with her former boyfriend; Priya defends that they both slipped up a little, but Leonard corrects her saying that he slipped a little, while she slipped a lot, bringing the conversation to a strained end. In the next episode, Leonard tells Sheldon that he is single, implying that he and Priya have broken up; his actions since then have confirmed their split occurred.

text: Through the fourth and fifth seasons, Penny was still single and dating, though when intoxicated, she has confessed that she regrets breaking up with Leonard. In "The Ornithophobia Diffusion", Leonard and Penny go to the movies as friends. Leonard decides that since they are no longer dating, he can be honest and does not have to pay for everything or do whatever Penny wants. The two bicker all evening and sabotage each other's attempts to chat up people in the bar. Penny admits that she likes the new, more assertive Leonard. Leonard sees this as another opportunity to grovel and try to get Penny to sleep with him, so she leaves.

text: On the spur of the moment in "The Recombination Hypothesis", Leonard asks Penny out on a date after he imagines what getting back with her might be like. Their real date ends successfully and they agree to take their relationship slow in "The Beta Test Initiation." During their renewed relationship Penny has dismissed comments about him ever leaving or dumping her or about worrying about his unfaithfulness around other women and strippers as in the episode "The Stag Convergence". After Penny suggested having sex in "The Launch Acceleration", Leonard breaks the mood by proposing to her accidentally. They later meet and Penny does have the courage to tell him "no" and not break up with him as she did two years previously when he told her that he loved her. However, their relationship is still obviously strained. In season 5, Leonard and Penny watch Howard being launched into space while holding hands to comfort each other. With the start of season 6, he wants a reluctant Penny to define their relationship in "The Date Night Variable".

text: Penny finally does admit her love to Leonard, in "The 43 Peculiarity". Penny and Leonard awkwardly stare at each other before running off in opposite directions. Leonard, though, is buoyed by optimism over Penny's admission. Alex Jensen asks Leonard out to dinner in "The Egg Salad Equivalency", which boosts Leonard's ego because two beautiful women are interested in him, however, Alex's interest makes Penny insecure. After another dispute with Sheldon, Leonard tries to move in with Penny in "The Spoiler Alert Segmentation", however she is not ready. During their Valentine's Day dinner in "The Tangible Affection Proof", Leonard again tries to propose to Penny and she cuts him off quickly. She admits that she is very happy with him, but she also admits to commitment issues and the thought of being married forever really "freaks" her out. Leonard then tells her that when she is ready to get married, she can propose to him. In the season finale, Leonard leaves for an overseas job for four months and Penny is confident enough in their relationship to wait for him. In "The Gorilla Dissolution", Leonard and Penny become engaged.[4] Throughout season 8, a running gag is their reluctance to decide upon a wedding date. In the season 8 finale, Penny asks Leonard to marry her that night in Las Vegas. Leonard happily accepts, but during the journey, after Penny expresses happiness that they will get married while knowing everything about each other, Leonard confesses to having shared a drunken kiss with another woman while on the boat in Europe, though he adds that the woman started it and he rejected her. Penny becomes hurt by the revelation, and even though she claims to forgive Leonard, there is clearly tension between them, leaving the season ending in a cliffhanger as to whether or not they will go through with the wedding.

text: At the beginning of season 9, Leonard and Penny marry, although not without some initial problems. They both reveal that they were subconsciously trying to sabotage their relationship, feeling unworthy of the other. Leonard, concerned that he was trying to sabotage his relationship with Penny, meets with the woman he kissed on the boat. She barely remembers the incident and quickly grows bored with Leonard's ramblings, taking a sarcastic and dismissive tone toward him. From that meeting Leonard comes to terms with his insecurities and he and Penny are able to become more comfortable in dealing with their mutual fears about their relationship. Leonard seriously tries to move into Penny's apartment though Sheldon has serious objections and makes them compromise to spend multiple nights a week in Leonard's old room. Early in season 10, the couple is very happy to be finally living alone after Sheldon moves in with Amy.


document_title: The Boy in the Striped Pyjamas

question_text: in the book the boy in the striped pajamas where does bruno move to

text: The Boy in the Striped Pyjamas

text:
The Boy in the Striped Pyjamas

Author
John Boyne

Country
Ireland

Language
English

Genre
Historical / post modern

Publisher
David Fickling Books

Publication date

5 January 2006

Media type
Print (hard cover & paper back)

Pages
216

ISBN
0-385-60940-X

OCLC
62132588

Dewey Decimal

823.914 22

LC Class
CS 2006/45764

text: The Boy in the Striped Pyjamas is a 2006[1] Holocaust novel by Irish novelist John Boyne. Unlike the months of planning Boyne devoted to his other books, he said that he wrote the entire first draft of The Boy in the Striped Pyjamas in two and a half days, barely sleeping until he got to the end.[1] As of March 2010, the novel had sold more than five million copies around the world.[2] In both 2007 and 2008, it was the best selling book of the year in Spain, and it has also reached number one on the New York Times bestseller list,[3] as well as in the UK, Ireland, and Australia.[not verified in body] The book was adapted in 2008 as a film of the same name.

text: Plot[edit]

text: Bruno is a 9-year-old boy growing up during World War II in Berlin. He lives with his parents, his 12-year-old sister Gretel and maids, one of whom is called Maria. After a visit by Adolf Hitler, Bruno's father is promoted to Commandant, and the family has to move to 'Out-With' because of the orders of "The Fury" (Bruno's naïve interpretation of the word 'Führer'). Bruno is initially upset about moving to Out-With (never identified, but cf. Auschwitz[4]) and leaving his friends, Daniel, Karl, and Martin. From the house at Out-With, Bruno sees a camp in which the prisoners wear striped pyjamas. One day, Bruno decides to explore the strange wire fence. As he walks along the fence, he meets a Jewish boy named Shmuel, who he learns shares his birthday. Shmuel says that his father, grandfather, and brother are with him on this side of the fence, but he is separated from his mother. Bruno and Shmuel talk and become very good friends, although Bruno still does not understand very much about Shmuel and his side of the fence. Nearly every day, unless it's raining, Bruno goes to see Shmuel and sneaks him food. As the meetings go on, and Shmuel gets more and more skinny, Bruno's naïveté means he never realizes he is living beside a death camp.

text: When lice eggs are discovered in Bruno's hair he is forced to get all of his hair shaved off. Bruno comments that he looks like Shmuel, and Shmuel agrees, except that Bruno is fatter. Bruno's mother eventually persuades his father to take them back to Berlin and stay at Out-With without them.

text: The next day Bruno concocts a plan with Shmuel to sneak into the camp to look for Shmuel's father. Shmuel brings a set of prison clothes (which look to Bruno like striped pyjamas), and Bruno leaves his own clothes outside the fence. As they search the camp, both children are rounded up along with a group of prisoners on a "march". In the gas chamber, Bruno apologizes to Shmuel for not finding his father and tells Shmuel that he is Bruno's best friend for life. Shmuel does not answer, as at that moment the door of the gas chamber is closed, it becomes dark, and all is chaos.

text: Critics' Reviews[edit]

text: Some critics have called the premise of the book and subsequent film – that there would be a child of Shmuel's age in the camp – erroneous. Reviewing the original book, Rabbi Benjamin Blech wrote: "Note to the reader: There were no 9-year-old Jewish boys in Auschwitz – the Nazis immediately gassed those not old enough to work."[5] Rabbi Blech affirmed the opinion of a Holocaust survivor friend that the book is "not just a lie and not just a fairytale, but a profanation". Blech acknowledges the objection that a "fable" need not be factually accurate; he counters that the book trivializes the conditions in and around the death camps and perpetuates the "myth that those [...] not directly involved can claim innocence", and thus undermines its moral authority. Students who read it, he warns, may believe the camps "weren't that bad" if a boy could conduct a clandestine friendship with a Jewish captive of the same age, unaware of "the constant presence of death".[6]

text: Kathryn Hughes, whilst agreeing about the implausibility of the plot, argues that "Bruno's innocence comes to stand for the willful refusal of all adult Germans to see what was going on under their noses".[7]