prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What was the reason given by Governor Rick Scott for not implementing a prescription drug monitoring database in Florida?

Read the following text and answer briefly.

Context 1: How Oxycontin, Florida and the Sackler Family Created the Opioid Crisis In America
Why are the Sacklers worth $13 billion today? Answer: “The Oxy Express Explained”
(MASS TORT NEXUS MEDIA)
A COMPARISON OF OXYCODONE PRESCRIBING
In the first six months of 2010, Ohio doctors and health care practitioners bought the second-largest number of oxycodone doses in the country at just under 1 million pills 
Florida doctors bought 40 8 million in the same period, the comparison is astounding, yet it flew under the DEA, Opioid Big Pharma and everyone elses radar for years and years 
Of the country’s top 50 oxycodone-dispensing clinics, 49 were in Florida  From August 2008 to November 2009, a new pain clinic opened in Broward and Palm Beach counties on average of every three days 
Pharmacies and distributors are at fault as well, pharmacies ordered jaw-dropping numbers of pills from opioid drug distributors, the middlemen between manufacturers and pharmacies 
90 of 100 of the nation’s top 100 oxy-buying doctors in 2010, were in Florida  49 of 50 of the country’s top oxy-dispensing clinics were in Florida  For some reason this didn’t raise an alarm or cause anyone to look further at the time 
Purdue Pharma New What Was Happening In Florida
Purdue and the Sacklers chose to ignore Florida, because apparently nobody there sued them or complained  In 2007, in other states, the infamous drug maker and three of its executives pled guilty in federal court and paid out $634 5 million in fines for purposefully misleading regulators, doctors, and patients about the addictiveness of their opioid painkiller  Around the same time, Purdue was also sued by several states, including Washington, over similar allegations  Purdue agreed to a $19 5 million multi-state settlement  And in 2015, Purdue settled a case with Kentucky, agreeing to pay $24 million 
As part of the state settlements, Purdue was supposed to set up monitoring programs to make sure that its opioid drug didn’t wind up in the wrong hands  It was supposed to watch out for shady pharmacies, unusually large orders, or suspiciously frequent orders  But on this front, Everett alleges that Purdue once again put profits over people 
Obviously, this was ignored as the Florida based “Oxy Expres”; rolled on for years and years with np input, comment or oversight by Purdue Pharma and the Sackler family other than “show me the money” and enjoying a life of luxury on the misery created and managed in the Purdue Pharma boardroom  But, the Purdue boardroom isn’t the only guilty “Opioid Big Pharma” industry player who designed and supported the opioid prescribing crisis 
For the current status of efforts to make Opioid Big Pharma accept responsibility in litigation filed in federal and state courts across the country, see: https://www masstortnexus com/Briefcases/254/OPIOID-CRISIS-BRIEFCASE-INCLUDING-MDL-2804-OPIATE-PRESCRIPTION-LITIGATION
Why Distributors Are Liable
Cardinal Health, one of the nation’s biggest distributors, sold two CVS pharmacies in Sanford a combined 3 million doses of oxycodone, flooding the town of 54,000 with an average of 250,000 oxycodone pills every month 
West of Jupiter, a Walgreens drug distribution center sold 2 2 million tablets to a single Walgreens’ pharmacy in tiny Hudson, a roughly six-month supply for each of its 12,000 residents  It shipped more than 1 1 million pills to each of two Fort Pierce Walgreens pharmacies 
For 40 days starting in late 2010, the distribution center shipped 3,271 bottles of oxycodone — 327,100 doses of the drug — to a Port Richey Walgreens pharmacy, prompting a distribution manager to ask: “How can they even house this many bottles?”
There were 53 million oxycodone prescriptions filled in 2013 by US pharmacies, according to NIDA  This translates to approximately one bottle of this addictive drug for every 6 people in the country  How was this not noticed by those responsible for monitoring narcotics prescribing in the United States?
Charts and Data On Florida’s Oxycontin Gold Mine
https://www documentcloud org/documents/3936665-Purdue-Pharma-1-in-48-Study html
https://www documentcloud org/documents/3534759-uS-Atty-on-Purdue-Settle html#document/p2/a384323
A Boardroom Contrived Opioid Epidemic
This is the pain chart created by the “Opioid Big Pharma Industry” to support massive over-prescribing of opioids across the country to everyone who walked in to a medical treatment facility, this was an effort to increase narcotic prescribing practices in mainstream medical care–and it worked very very well! This chart became a standard treatment assessment protocol tool across the country 
https://www documentcloud org/documents/3936646-DEA-NATL-DRUG-ASSESSMENT-2010 html#document/p51/a383739
HOW WEST VIRGINIA WAS TARGETED
It-Was-Raining-Opiates-How-drug-companies-submerged-West-Virginia-in-opioids-for-years
Reliably red on the political map, Huntington is a West Virginia town with a 182-year-old university, a storied football team and more than 100 churches 
It’s where Will Lockwood graduated from high school  It’s where he enrolled at Marshall University  It’s where he first tried OxyContin  By the time Lockwood entered Marshall, Detroit dealers were trickling into Huntington, selling OxyContin and pills with OxyContin’s active ingredient, oxycodone 
Even though Lockwood could step out his front door and get the drug, Detroit street dealers weren’t the preferred supplier, they were in Florida 
It may have been 1,000 miles away, but to Lockwood, getting OxyContin and oxycodone from Florida’s loosely regulated pain clinics “was legal, in a sense ”
Twice a month, different “crews” from Huntington crowded into vans and headed south to Palm Beach and Broward counties, home to more than 200 pill mills, the pain clinics where anyone with a fake ache and hard cash could walk out with pills and prescriptions 
After hitting a string of clinics, the Huntington crews drove back with “around 500 to 600 pills per person,” said Lockwood 
But it wasn’t just a few hundred pills  It was tens of thousands 
And it wasn’t just Huntington, The West Virginia vans were part of a nationwide caravan heading to South Florida  Cars bearing tags from Kentucky, Tennessee, the Carolinas, Virginia and Ohio crowded into one clinic parking lot after another, loading up on pills and prescriptions 
News stories and law enforcement focused on those “parking lot” states in Appalachia, where dealers and addicts with a tank of gas or a cheap plane ticket traveled the “Oxy Express” to Palm Beach and Broward 
But Florida’s pill pipeline reached far beyond those roadways 
By 2010, Florida was the oxycodone drug dealer of choice for drug users and dealers in the Great Lakes, Northeast and Mid-Atlantic regions as well as the Southeast, DEA records show, an area spanning virtually every state east of the Mississippi  It wasn’t just that Florida guaranteed a flow of cheap oxycodone  For 10 years, key lawmakers and agency heads repeatedly looked the other way as crooked doctors and bogus clinics flooded almost half the nation with the highly addictive drug 
In failing to crack down, Florida extended by years the amount of time highly addictive oxycodone would be available to both first-time experimenters and addicts  It gave criminals the raw materials for trafficking  It gave Will Lockwood the OxyContin needed to feed his growing habit, It paved the way for his eventual jump to heroin 
Jumping state lines
Teenage high-school wrestling buddies in New Port Richey ran oxycodone into Tennessee; they were paid with cash hidden in teddy bears  A Hillsborough County man mailed 17,000 pills to Glen Fork, W Va , a month’s supply for every man woman and child in the tiny town 
A Boston Chinatown crime boss trafficked pills from Sunrise into Massachusetts, New York, Rhode Island and South Carolina  Wellington twins and pill mill kingpins Paul and Phil George, brothers who oversaw one of the largest operations in the country from their five Palm Beach and Broward clinics, pushing oxycodone into Kentucky, Tennessee, Ohio and South Carolina 
A husband and wife team operating out of a Forest Hill Boulevard clinic funneled pills to Delaware  At Palm Beach International Airport, two federal security agents accepted $500 a pop each time they waved through thousands of pillsbound for Connecticut and New York 
A Palm Bay man’s Puerto Rican family bought local pills destined for the working class town of Holyoke, Mass  In Rhode Island, police pulled over a Lauderhill man caught speeding through Providence  They found 903 oxycodone tablets and 56 morphine pills in the car 
Senior citizen and Tulane business graduate Joel Shumrak funneled more than 1 million pills into eastern Kentucky from his South Florida and Georgia clinics, much of it headed for street sales — an estimated 20 percent of the illicit oxycodone in the entire state 
Van loads of pill-seekers organized by “VIP buyers” traveled from Columbus, Ohio, to three Jacksonville clinics, where armed guards handled crowd control (federal indictment) and doctors generated prescriptions totaling 3 2 million pills in six months  In Miami, Vinny Colangelo created 1,500 internet website names to entice drug users throughout the nation to one of his six South Florida pain clinics or pharmacies 
Even the Mafia got in on the Florida oxy express action: A Bonanno crime family associate oversaw a local crew stocking up on Palm Beach and Broward pain clinic oxycodone, upstreaming profits to the New York family 
At times, it seemed almost no section of the country was free of Florida-supplied pills: When Olubenga Badamosi was arrested driving his Bentley Continental in Miami in 2011, the Oregon man was one of two traffickers overseeing a crew smuggling South Florida oxycodone to sell in Salt Lake City, Seattle and Denver as well as Oregon, Nevada, Texas and even Alaska 
Pharmacy delivers oxy ‘pot of gold’
It would be hard to overstate Florida’s role in feeding the country’s voracious appetite for oxycodone  Oxycodone 30-milligram tablets were favored by addicts  And in 2009 and 2010, roughly four of every 10 of those pills were sold in Florida  Small wonder: Of the nation’s top 100 oxycodone-buying doctors, 90 were in Florida 
Pharmacies, too, ordered jaw-dropping numbers of pills from drug distributors, the middlemen between manufacturers and pharmacies 
West of Jupiter, a Walgreens drug distribution center sold 2 2 million tablets to a single Walgreens’ pharmacy in tiny Hudson, a roughly six-month supply for each of its 12,000 residents  It shipped more than 1 1 million pills to each of two Fort Pierce Walgreens pharmacies  By contrast, a single Walgreens pharmacy in the Central Florida townOviedo bought 169,700 doses of oxycodone in 30 days 
People on both sides of the counter knew what was going on: In a letter to the chief executive of Walgreens, Oviedo’s police chief warned that people were walking out of the town’s two Walgreens stores and selling their drugs on the spot, crushing and snorting them, or — still in the pharmacy’s parking lot — injecting them 
Why Pharmacies are LIABLE
In Fort Pierce, a Walgreens pharmacist accidentally provided an extra 120 oxycodone pills to a customer  When the druggist called to ask that the man return the pills, the customer’s girlfriend bluntly responded that he was an addict, that he sold oxycodone and the 120 pills were “a pot of gold,” DEA records show 
That was in September  The same man came back to the same Walgreens in December and January with a prescription in hand, and the pharmacy filled his prescriptions every time 
‘Wild West of Oxycodone Prescribing’
Cincinnati-based Masters Pharmaceuticals Inc  was a middling-sized drug distributor selling oxycodone to Florida pharmacies 
It sold to other customers in other states  But mostly, it sold to Florida: Oxycodone made up more than 60 percent of its drug sales in 2009 and 2010, according to federal records  Of its top 55 oxycodone customers, 44 were in Florida 
Company CEO Dennis Smith worried that the Florida-bound oxycodone was getting in the wrong hands  A trip to Broward did nothing to ease his mind  “It was,” he later testified, “the Wild West of oxycodone prescribing ”
Bus and park benches touted pain clinics  When Smith picked up and thumbed through City Beat, a free magazine, he found pages of ads for pain clinics  “It would show young people sitting around a pool and it named the pain clinic and say (sic) ‘we dispense on site,’ and that really hit home hard ”
Smith stopped selling to pain clinics  But the company continued to shovel millions of oxycodone pills to Florida pharmacies  Masters executives figured the pharmacies would keep an eye out for excessive prescriptions written by pill mill doctors  But not all pharmacies were worrying about doctors at pain clinics, many pharmacies were courting the pill mills prescribers 
A Lake Worth Family Pharmacy
In 2009, the small pharmacy off Lucerne Avenue in Lake Worth had a history  It had been in business for 43 years  The owner and head pharmacist had been there for 32  It had shaded parking and a downtown location, a stone’s throw from the City Hall Annex 
When a Masters inspector visited, he was alarmed to find Tru-Valu Drugs bustling with a long line of young, thin, tattooed customers arriving in groups of 10 to pick up pills  There were signs in the pharmacy warning of limits on the number of oxycodone pills handed out  Even Mallinckrodt Pharmaceuticals, an oxycodone manufacturer, was worried about the volume of its pill sales there 
Of the 300,000 doses of all drugs the small pharmacy dispensed in December 2008, 192,000 were for oxycodone 30 mg, the dosage preferred by traffickers and users alike 
The huge oxycodone volume was no accident  The owner and head pharmacist, unidentified in DEA records, told a Masters inspector that the pharmacy “has pushed for this (narcotic) business with many of the area pain doctors ”
And, despite the torrent of oxycodone going out the door, the pharmacy owner expressed frustration that drug distributors were limiting the amount of narcotics they would sell to his now-closed pharmacy 
Ohio to Florida and Back
Pharmacy after pharmacy benefited from the combination of Masters’ Ohio oxycodone business and Florida’s unregulated pill mills 
In Englewood, north of Fort Myers, the pharmacy owner filled prescriptions for six pain clinics — including clinics an hour’s drive away  A Masters inspector found cars from Tennessee and Kentucky in the parking lot and young men leaving the pharmacy carrying large trash bags 
Superior Pharmacy not only filled oxycodone prescriptions for pain clinics, it shared waiting room space with a pain clinic in a Temple Terrace strip mall outside Tampa  Neither Masters nor Superior had so much as Googled the background of pain clinic doctors writing those prescriptions, the DEA later said 
Had they done so, the DEA dryly noted, they “would likely have come across a press release” announcing one of the doctors had been arrested and charged with trafficking in prescription drugs 
Hundreds of thousands of oxycodone pills were sent from Ohio distributors to Florida pharmacies  Unknown thousands of pills headed right back up to Ohio 
When Ohio police burst into Christopher Thompson’s home outside Columbus, they found an assault rifle, $80,000 in cash and oxycodone from his Florida deals  A construction worker whose own pill habit started at age 14, Thompson oversaw a ring of 15 Ohio buyers who traveled to Florida to pick up oxycodone to resell in Central Ohio 
Two hours to the west in Martin’s Ferry, David L  Kidd orchestrated a ring of buyers traveling to West Palm Beach and Central Florida to pick up oxycodone for resale on the streets of eastern Ohio and West Virginia 
Doctors and pharmacies from Florida were complicit with Kidd’s ring in fueling Ohio’s opioid epidemic, wrote the U S  attorney for West Virginia after Kidd’s 2011 arrest: “The steady flow of pain pills into the Ohio Valley from Florida must stop ”
Driving To Pick Up Death By Rx
With more drugs came more deaths, in January 2010, say police, Fort Lauderdale pathologist Dr  Lynn Averill started a seven-month oxycodone shopping spree, buying 437,880 oxycodone pills from drug distributors 
The same month, Matthew Koutouzis drove from Toms River, N J , to see Averill in her Broward County pain clinic  The 26-year-old collected prescriptions for 390 pills and overdosed two days later  Brian Moore traveled 13 hours from his Laurel County, Ky , home to see Averill  He left with prescriptions for 600 pills and also overdosed within 48 hours 
Kenneth Hammond didn’t make it back to his Knoxville, Tenn , home  He had a seizure after picking up prescriptions for 540 pills and died in an Ocala gas station parking lot 
Keith Konkol didn’t make it back to Tennessee, either  His body was dumped on the side of a remote South Carolina road after he overdosed in the back seat of a car the same day of his clinic visit  He had collected eight prescriptions totaling 720 doses of oxycodone, methadone, Soma and Xanax  Konkol had every reason to believe he would get those prescriptions: In three previous visits to the Plantation clinic, he had picked up prescriptions for 1,890 pills 
An estimated 60 percent of her patients were from out of state, a former medical assistant told the DEA  In 2015, Averill pleaded not guilty to eight manslaughter charges  She is awaiting trial in Broward County  Averill was just one doctor at just one clinic  In 2010, the year Averill’s patients overdosed, Florida received applications to open 1,026 more pain clinics 
An online message board advising drug users summed it up: “Just go anywhere in South Florida and look for a ‘pain management clinic ’ It shouldn’t be too hard; you can’t swing a dead cat without hitting one ” Complain about anything from a back injury to a hangnail, it advised, “and they’ll set you right up ”
By this time, Kentucky had reined in its pill mills  It didn’t matter, Ohio, Delaware, North Carolina, Connecticut acted as well, but other state’s efforts didn’t matter either, Florida continued ignoring the pill mills and rogue doctors feeding the nation’s oxycodone habit, the pills flowed 
“There were folks down there, where if I had an opportunity to, get my hands around their throat, I would have wrung their neck,” said Huntington Mayor Steve Williams  On Florida’s inaction he stated, “There was total evidence as to what was happening  It lays at the foot, in my opinion, of the public officials there that allowed it to continue on ”
Governor Jeb Bush Backed A Solution
One of the first dinners Florida Gov  Jeb Bush hosted after moving into the governor’s mansion in 1999 was a small one  Among those sitting at the table with Bush were Lt  Gov  Toni Jennings, state Sen  Locke Burt and James McDonough, who would become the state’s hard-nosed drug czar  There was an urgent topic on the agenda that night: the explosion of prescription painkillers  For the state’s first family, it may have been personal  Bush had talked publicly about one of his children’s struggle with addiction 
By the time the meal ended, all had agreed on the need for establishing a prescription drug monitoring program that would collect information and track prescriptions written for controlled substances, such as oxycodone 
Absent a prescription drug monitoring database, there was no way to know whether someone was “doctor shopping,” going from doctor to doctor, getting more and more prescriptions to feed their habit 
And there was no way to know whether a doctor was overprescribing, key to pinpointing whether a pill mill was operating, and where  Similar databases had been adopted by more than a dozen states  It was being described as a “silver bullet” to curb overprescribing  Soon enough, $2 million to get the database up and running would be on the table — but it came with a catch 
Florida Attorney General Misfires Against Purdue
In 2001, OxyContin-maker Purdue Pharma was fending off early criticism of its blockbuster painkiller  At issue was whether Purdue’s aggressive marketing campaign had misled doctors and patients alike  Purdue and three top executives later pleaded guilty to federal charges of illegally marketing the drug  Far from being safe and non-addictive, OxyContin carried the same addiction risk as morphine, and was every bit as potent 
But that was six years away  In 2001, towns in Maine reported an alarming uptick in crime tied to OxyContin  The first of several congressional hearings was ramping up  Critics and parents who lost children were piling on  Reporters were starting to write stories 
In November, Florida Attorney General Bob Butterworth appeared poised to take on the company  Calling OxyContin street sales “a major threat to public health,” Butterworth told a state Board of Medicine committee that Purdue should consider temporarily taking the drug off the market  It wasn’t only traffickers concerning Butterworth  It was the sales pitch 
In late 2001, Butterworth called a young assistant attorney general into his office and gave him a magazine article on OxyContin and an assignment: Look into Purdue marketing  Former Florida Attorney General Bob Butterworth and Palm Beach County State Attorney Dave Aronberg  The young lawyer, now-Palm Beach County State Attorney Dave Aronberg, said he knew nothing about OxyContin  But he didn’t like what he read 
During the yearlong inquiry, 589 Floridians died after taking oxycodone  Nothing criminal was found, Aronberg later said  Instead, Butterworth and Purdue struck a settlement  As part of a $2 million deal, Purdue would pay to establish a prescription monitoring database, the same silver bullet sought by Bush  After Florida’s computerized system was up and running, the same system would be free to any other state  The entire country, not just Florida, would benefit 
It could have been a groundbreaking deal  There was one catch  State lawmakers had to vote to create the prescription monitoring program by 2004, or Purdue would keep its money 
Marco Rubio Kills The Anti-Oxy Rx Bill
A political gight killed the program  “And there was one person who was responsible,” said former state Sen  Burt, now an Ormond Beach insurance executive  “And it was Marco Rubio ”
A rising state lawmaker in 2002, now-U S  Sen  Marco Rubio had the clout to make or break the legislation  He had been one of two state House majority whips and was on the fast track to becoming House speaker 
Rubio didn’t kill the 2002 bill out of opposition to prescription monitoring—it was politics “as usual” yet nobody blamed Rubio for the resulting opioid crisis that seems to have started in his political backyard and flourished beyond belief  
U S  Sen  Marco Rubio, R-Fla , was a leader in the Florida House in 2002 when he blocked a vote on prescription monitoring  That year, Rubio favored a bill changing the Miami-Dade County charter, which failed to pass because of a single “no” vote in the Senate  Burt cast the vote 
Angered by what he saw as Burt’s betrayal, Rubio killed the prescription drug monitoring bill  “When I found out he broke his word, it made the choice easy,” Rubio told The Miami Herald 
It’s not certain that the full Legislature would have passed the bill had it made it to a floor vote  Rubio was the first, not the last, in a line of state legislative leaders over years who would refuse to seriously consider the bill  Most cited privacy concerns 
But prescription monitoring databases in Florida and other states free to use Florida’s model would have pinpointed rogue doctors, would-be pill mills and doctor-shoppers across the country, just as all three were beginning to converge  In doing so, it could have curbed a national opioid epidemic when it was just an emerging problem, not the monster it would become 
Only weeks after the 2002 bill was killed, Bush suppressed a sob as he discussed his daughter’s arrest for forging a prescription  Court-ordered to drug treatment and then briefly to jail, Noelle Bush survived her pill addiction  The 2004 deadline for greenlighting a monitoring system passed  So did Purdue’s million-dollar obligation to pay for it 
Between 2002, the year Rubio killed the database that could have identified doctor-shoppers, and late 2011, when the database finally came online, more than 20,800 Floridians died after taking prescription opioids, including OxyContin, annual Florida Medical Examiners’ reports show  “Not getting that bill through the Legislature resulted in Florida becoming the pill mill capital of the United States,” said Burt 
“There was heartache for thousands of families beyond measure and it didn’t have to happen ”
Florida Officials Were Told Of The Oxy Express
The East Kentucky hills and valleys of Greenup County suit Keith Cooper, a long-haired undercover cop-turned-sheriff: “It’s a backwater  I tell people all the time I am a hick sheriff from a hick location, and by 2011, the rural county and its sheriff had big city problems 
Greenup is near the stretch of interstate highways that provided drug traffickers and users with a straight shot to Palm Beach and Broward pill mills  It’s less than an hour’s ride to Huntington Tri-State Airport, where a $27 flight to Fort Lauderdale was a popular draw for dealers hoping to stock up 
Arrests for Florida pills soon eclipsed local arrests for pot 
“When we locked ’em up, we take all their pill bottles and all their paperwork, and we found maps to the doctors offices and everything,” recalled Cooper 
“I called the (Florida) medical board and gave them a big list of doctors,” Cooper said  He called the state pharmacy board, too  He got no response 
“So then I called the Attorney General’s Office and the Governor’s Office  I was calling them all, the whole state  Of course, I was talking to the state police the entire time  “I told them, all of the profits were down there  And all of the pain’s up here ” Nothing happened  Florida’s oxycodone pipeline continued to flow 
On the other side of the law in Greenup, Mikey Frazier was banking on it 
The Oxy Express
Frazier was on a scholarship to play baseball at his junior college in Chicago when he suffered a torn rotator cuff  Doctors prescribed Percocet, a pill containing oxycodone, in 2002  When doctors cut him off, he bought it on the street  In 2006, he moved to OxyContin, nearly pure oxycodone  In 2007, he gave his friends money to go to Florida and bring him back pills 
“My buddy had a minivan and he would actually go down one week and take two to three people with him, and then the following week I’d go,” said Frazier  He still remembers the route: “I’d take 64 East to 77 South to 95 South  And it’s just a straight shot ”
Others followed suit  “What got everyone started was because the doctors around here won’t write a strong enough prescription,” he recalled  OxyContin and generic oxycodone still could be had — just not in Kentucky, which had a prescription drug monitoring database 
In Florida, “there was none of that … stuff that they check and find out what doctor you’ve been to,” said Frazier 
“And one person does it, and then they tell a friend, and then they go do it, and that’s how it all really got started here ”
MEDICAID-MEDICAIRE PAID MILLIONS FOR OXY
Tallahassee wasn’t just ignoring the epidemic, It was financing it 
Before her office was raided by law enforcement in December 2001, Asuncion M  Luyao’s patients would wait in a line in the rain to get prescriptions from the Port St  Lucie internist and acupuncturist  She was one of the most prolific prescribers of OxyContin in the state 
And hundreds of thousands of those pills were being paid for by Medicaid, Florida’s taxpayer-financed health program for the state’s poorest and sickest citizens  Between 1999 and 2001, Medicaid shelled out $935,634 for OxyContin prescriptions written by Luyao  That was just OxyContin  Luyao was prescribing an array of addictive drugs  In the 12 months leading up to the clinic raid, Medicaid paid roughly $1 million for 7,000 prescriptions, only about 17 percent of them for OxyContin 
Nor did the raid slow her down  Between the raid and her arrest on trafficking charges four months later, Luyao wrote another 282 OxyContin prescriptions billed to Medicaid  She was not an outlier  In 24 months, taxpayers footed the bill for more than 49 million doses of pills containing oxycodone, even though there were only 1 36 million Medicaid patients  Half were children 
The sheer volume of pills might have been a tipoff that the drugs were not all intended for legitimate use  So were arrest reports dating to 2001  One man had used his 7-year-old son’s Medicaid number to doctor-shop for OxyContin  A Miramar pharmacist who billed Medicaid $3 7 million for OxyContin pills was charged with paying Medicaid patients $150 each to use their IDs 
Medicaid paid for more than $300,000 to fill Dr  James Graves’ OxyContin prescriptions  The Florida Panhandle physician was the first doctor in the nation convicted of killing patients by overprescribing OxyContin 
Addiction risk for people taking high doses of oxycodone begins climbing after just three days, a recent study concluded  And most people on Florida Medicaid getting oxycodone prescriptions in 2011 were getting much more than a few days worth  They were getting an average of nine months worth of pills, state officials said 
Pill mill doctors prescribed 1 million of those pills:
Doctors working for the George twins’ trafficking empire prescribed at least 102,081 oxycodone pills billed to Medicaid before the ring collapsed in 2010 
Working out of a Delray Beach pain clinic founded by a convicted drug smuggler, Zvi Harry Perper, son of the Broward County medical examiner, was arrested on trafficking charges, but not before he wrote prescriptions to Medicaid patients for 115,977 doses of oxycodone in 90 days 
In Lake Worth, Cesar Deleon was arrestedas part of a DEA pill mill sweep and charged with 55 counts of illegally distributing drugs  Deleon wrote orders for 20,302 oxycodone pills for Medicaid patients 
Miami internist Dr  Selwyn Carrington authorized 32,411 doses of oxycodone for Medicaid patients in just two years  He was busted for signing his name to hundreds of prescriptions 
Further, Florida wasn’t in any hurry to stop doctors linked to pill mills 
Carrington was arrested for overprescribing in March 2011  The state’s emergency order to suspend his license was signed months after he had pleaded guilty in 2012 
Perper was busted at a Delray Beach pill mill operated by a former felon in 2011  The state did not act against his license until 2014 
Joseph M  Hernandez was writing prescriptions from his car, a veritable pill mill on wheels, when he was busted in February 2010 on one count of trafficking in oxycodone 
 Florida’s Department of Health didn’t file paperwork to restrict his license for almost 18 months 
During that time, Hernandez wrote oxycodone prescriptions for Medicaid patients totaling 258,940 doses representing a taxpayer-footed bill of $130,165 
Purdue Pharma’s Profits Before Patients Creed
Kelly Skidmore is exactly the type of person Purdue Pharma’s OxyContin marketing was intended to reach: Diagnosed with juvenile arthritis, the former state legislator’s struggle with chronic pain began at age 4 
Skidmore was wary of opioid painkillers, though, one reason her willingness in 2009 to work with Purdue was surprising  But she did it to get Florida’s dormant drug monitoring database up and running 
Then a state representative in a district straddling Palm Beach and Broward counties, Skidmore recalled that, “They came to me and said, ‘Could you help get it across the finish line?’ ”
OxyContin and prescription opioids, a serious problem in 2002, had evolved into a full-blown crisis in the ensuing seven years  Broward alone had more pain clinics than it had McDonald’s  Deaths tied to oxycodone had exploded, up by 263 percent since the prescription monitoring database had first been proposed and killed  Overdoses from prescription opioids were claiming more than seven lives a day 
“By God, if we had had seven dolphins a day dying and washing up on Florida beaches, we would have been appropriating money and solving it,” Skidmore said 
Skidmore believed a database wasn’t going to resolve the underlying addiction crisis  Still, it was a start  Not a silver bullet, but “maybe silver buckshot,” she said  The database law passed with gaping loopholes  No health care professional would have to report opioid prescriptions or check the database before prescribing more, and the state refused to pay for it 
“Just to get that one little piece … took nine years of filing bills and then it had no teeth,” Skidmore said  “And it should have been the easiest piece ”
Where Was The DEA and Everyone Else?
The DEA all but wrung its hands over Florida’s lethal inaction  The agency ticked off a devil’s brew of regulatory loopholes: Florida’s Health Department regulated health care professionals but not pain clinics  The state’s Agency for Health Care Administration regulated pain clinics that accepted insurance, but pill mills were most often on a cash-only basis  And the prescription monitoring database, mired in a vendor dispute, remained stalled 
In early 2011, when Gov  Rick Scott took office, just one drug — oxycodone — was tied to six fatal overdoses a day  Deaths tied to all drugs claimed 25 a day  In the handful of Appalachian states where traffickers were bringing back South Florida pills, it was worse 
Ohio’s death rate for oxycodone and similar opioids had doubled in 24 months, federal records show  Kentucky’s was up by more than 50 percent  And in West Virginia, home to hard-hit Huntington, death rates tied to pill mill drugs such as oxycodone and Opana had climbed by 341 percent 
The DEA formally pinpointed Palm Beach, Broward and Miami-Dade counties as the nation’s single biggest hub for trafficking pills across state lines  Within weeks of being sworn in, Scott abolished Florida’s Office of Drug Control, eliminating the state drug czar position, announced plans to drive a final stake in the heart of the database and rebuffed Purdue Pharma’s renewed offer to help pay for it 
Scott, a tea party conservative, cited privacy concerns, expressed skepticism the monitoring program would work and raised the possibility taxpayers would be left with a $500,000-a-year bill to operate it 
Attorney General Pam Bondi had also ridden the tea party wave to her position  She shared many of Scott’s conservative convictions  Unlike Scott, the former prosecutor relentlessly lobbied to keep the database alive  Florida’s failure to adopt the drug monitoring database was so out of step with the rest of the country that it began spawning conspiracy theories on both sides of the law 
Everyone knew prescription monitoring was going to kill the pill smuggling business, said a corrupt Florida Highway Patrol trooper as he drove a load of pills out of Florida, according to a federal lawsuit  Talking to the confidential informant in the seat next to him, the trooper speculated someone in Tallahassee must have a piece of the action, “because (Scott) was so adamant about not putting that system in place  Right?”
In Greenup, an infuriated Cooper told a reporter, “In my opinion, (Scott’s) getting money from somewhere  He has to be ” A few days later, recalled Cooper, “A lieutenant with the state police I’d been talking to down there called me, said, ‘Man, just a head’s up: I wouldn’t come to Florida ’” In states on the receiving end of the Florida pill pipeline and among federal officials, Scott’s resistance triggered outrage 
In Kentucky, where as much as 60 percent of the illicit oxycodone in that state flowed from Florida, Lt  Gov  Daniel Mongiardo proposed erecting billboards at the Florida line: “Welcome to the Oxy Tourism Capital of the World ”
U S  House Appropriations Chairman Hal Rogers, also from Kentucky, twice wrote Scott  “Canceling Florida’s prescription drug monitoring program is equal to firing firefighters while your house is ablaze,” he wrote 
Gil Kerlikowske, director of the White House Office of National Drug Control Policy, asked to meet with Scott  So did DEA Administrator Michele Leonhart 
Three U S  senators — New York’s Chuck Schumer, West Virginia’s Joe Manchin and Rhode Island’s Sheldon Whitehouse — joined Florida’s Bill Nelson in pointing out that the pills weren’t just a Florida problem: There were “serious ramifications for the rest of the country,” wrote Nelson of Scott’s reluctance to crack down  This is a perfect example of how political rhetoric, in-fighting and contrived agendas prevented an early stop to the emerging opioid crisis many years ago 
WHY DIDN’T THE DEA, DRUG DISTRIBUTORS AND PHARMACIES TAKE NOTICE BEFORE THE OPIOID CRISIS SPREAD ACROSS THE COUNTRY LIKE WILDFIRE? WAS IT BECAUSE OF THE BILLIONS IN PROFITS, QUARTERLY BONUSES AND DIVIDENDS? STOCK OPTIONS CASHED IN BY BOARDROOMS AT EVERY OPIOID BIG PHARMA COMPANY? STAY TUNED FOR HOW “PROFITS BEFORE PATIENTS” BECAME THE NORM
(article excerpts and quotes have been taken from publicly available media sources and court records)
Context 2: \section{Introduction}\label{sec1}
\setcounter{equation}{0} 

Transport problems with highly forward-peaked scattering are prevalent in a variety of areas, including astrophysics, medical physics, and plasma physics \cite{HGK,aristova,multiphysics} 
For these problems, solutions of the transport equation converge slowly when using conventional methods such as source iteration (SI) \cite{adamslarsen} and the generalized minimal residual method (GMRES) \cite{gmres} 
Moreover, diffusion-based acceleration techniques like diffusion synthetic acceleration (DSA) \cite{alcouffe} and nonlinear diffusion acceleration (NDA) \cite{smithetall} are generally inefficient when tackling these problems, as they only accelerate up to the first moment of the angular flux \cite{JapanFPSA} 
In fact, higher-order moments carry important information in problems with highly forward-peaked scattering and can be used to further accelerate convergence \cite{japanDiss} 

This paper focuses on solution methods for the monoenergetic, steady-state transport equation in homogeneous slab geometry 
Under these conditions, the transport equation is given by
\begin{subequations}\label[pluraleq]{eq1}
\begin{equation}
\label{t1}
\mu\frac{\partial}{\partial x} \psi(x,\mu) + \sigma_t \psi(x,\mu) = \int_{-1}^{1} d\mu' \sigma_s(\mu,\mu') \psi(x,\mu') + Q(x, \mu), \,\,\, x\in [0, X],-1\leq\mu\leq 1  ,\\
\end{equation}
with boundary conditions
\begin{align}
\label{t2}
\psi(0,\mu) &= \psi_L(\mu), \quad \mu > 0,\\
\label{t3}
\psi(X,\mu) &= \psi_R(\mu), \quad \mu < 0 
\end{align}
\end{subequations}
Here, $\psi(x,\mu)$ represents the angular flux at position $x$ and direction $\mu$, $\sigma_t$ is the macroscopic total cross section, $\sigma_s(\mu,\mu')$ is the differential scattering cross section, and $Q$ is an internal source 

New innovations have paved the way to better solve this equation in systems with highly forward-peaked scattering 
For instance, work has been done on modified $P_L$ equations and modified scattering cross section moments to accelerate convergence of anisotropic neutron transport problems \cite{khattab} 
In order to speed up the convergence of radiative transfer in clouds, a quasi-diffusion method has been developed \cite{aristova} 
In addition, the DSA-multigrid method was developed to solve problems in electron transport more efficiently \cite{trucksin} 

One of the most recent convergence methods developed is Fokker-Planck Synthetic Acceleration (FPSA) \cite{JapanFPSA,japanDiss} 
FPSA accelerates up to $N$ moments of the angular flux and has shown significant improvement in the convergence rate for the types of problems described above 
The method returns a speed-up of several orders of magnitude with respect to wall-clock time when compared to DSA  \cite{JapanFPSA} 

In this paper, we introduce a new acceleration technique, called \textit{Nonlinear Fokker-Planck Acceleration} (NFPA) 
This  method  returns  a  modified  Fokker-Planck (FP) equation  that  preserves  the  angular moments of the flux given by the transport  equation 
This preservation of moments is particularly appealing for applications to multiphysics problems \cite{multiphysics}, in which the coupling between the transport physics and the other physics can be done through the (lower-order) FP equation 
To our knowledge, this is the first implementation of a numerical method that returns a Fokker-Planck-like equation that is discretely consistent with the linear Boltzmann equation 

This paper is organized as follows 
\Cref{sec2} starts with a brief description of FPSA 
Then, we derive the NFPA scheme 
In \cref{sec3}, we discuss the discretization schemes used in this work and present numerical results 
These are compared against standard acceleration techniques 
We conclude with a discussion in \cref{sec4} 

\section{Fokker-Planck Acceleration}\label{sec2}
\setcounter{equation}{0} 
In this section we briefly outline the theory behind FPSA, describe NFPA for monoenergetic, steady-state transport problems in slab geometry, and present the numerical methodology behind NFPA 
The theory given here can be easily extended to higher-dimensional problems 
Moreover, extending the method to energy-dependence shall not lead to significant additional theoretical difficulties 

To solve the transport problem given by \cref{eq1} we approximate the in-scattering term in \cref{t1} with a Legendre moment expansion:
\begin{equation}
\label{transport1}
\mu\frac{\partial}{\partial x} \psi(x,\mu) + \sigma_t \psi(x,\mu) = \sum_{l=0}^L \frac{(2l+1)}{2} P_l(\mu) \sigma_{s,l} \phi_l(x) + Q(x, \mu),
\end{equation}
with 
\begin{equation}
\label{transport2}
\phi_l(x) =  \int_{-1}^{1} d\mu P_l(\mu) \psi(x,\mu) 
\end{equation}
Here, $\phi_l$ is the $l^{th}$ Legendre moment of the angular flux, $ \sigma_{s,l}$ is the $l^{th}$ Legendre coefficient of the differential scattering cross section,  and $P_l$ is the $l^{th}$-order Legendre polynomial 
For simplicity, we will drop the notation $(x,\mu)$ in the remainder of this section 

The solution to \cref{transport1} converges asymptotically to the solution of the following Fokker-Planck equation in the forward-peaked limit \cite{pomraning1}:
\begin{equation}
\label{fp1}
\mu\frac{\partial \psi}{\partial x} + \sigma_a \psi = \frac{\sigma_{tr}}{2}\frac{\partial }{\partial \mu} (1-\mu^2) \frac{\partial \psi}{\partial \mu} + Q\,,
\end{equation}
where $\sigma_{tr}= \sigma_{s,0} -\sigma_{s,1}$ is the momentum transfer cross section and $\sigma_a = \sigma_t-\sigma_{s,0}$ is the macroscopic absorption cross section 

Source Iteration \cite{adamslarsen} is generally used to solve \cref{transport1}, which can be rewritten in operator notation:
\begin{equation}
\label{si1}
\mathcal{L} \psi^{m+1} = \mathcal{S} \psi^{m} + Q\,,
\end{equation}
where 
\begin{equation}
\mathcal{L} = \mu \frac{\partial}{\partial x} + \sigma_t,
   \quad
\mathcal{S} = \sum_{l=0}^L \frac{(2l+1)}{2} P_l(\mu) \sigma_{s,l} \int_{-1}^{1}d\mu P_l(\mu) ,
\label{trans1}
\end{equation}
and $m$ is the iteration index 
This equation is solved iteratively until a tolerance criterion is met  The FP approximation shown in \cref{fp1} can be used to accelerate the convergence of \cref{transport1} 

\subsection{FPSA: Fokker-Planck Synthetic Acceleration}\label{FPSA}

In the FPSA scheme \cite{JapanFPSA,japanDiss}, the FP approximation is used as a preconditioner to synthetically accelerate convergence when solving \cref{transport1} (cf  \cite{adamslarsen} for a detailed description of synthetic acceleration) 
When solving \cref{si1}, the angular flux at each iteration $m$ has an error associated with it 
FPSA systematically follows a predict, correct, iterate scheme 
A transport sweep, one iteration in \cref{si1}, is made for a prediction 
The FP approximation is used to correct the error in the prediction, and this iteration is performed until a convergence criterion is met 
The equations used are:
\begin{subequations}
\label{fpsaeq}
\begin{align}
\label{predict}
\mathrm{Predict}&: \mathcal{L} \psi^{m+\frac{1}{2}} = \mathcal{S} \psi^{m} + Q\,,\\
\label{correct}
\mathrm{Correct}&: \psi^{m+1} =  \psi^{m+\frac{1}{2}} + \mathcal{P}^{-1} \mathcal{S} \left( \psi^{m+\frac{1}{2}} -  \psi^{m}\right),
\end{align}
\end{subequations}
where we define $\mathcal{P}$ as
\begin{equation}
\label{FPSAsi1}
\mathcal{P} = \mathcal{A}-\mathcal{F} =\underbrace{\left(\mu\frac{\partial}{\partial x} + \sigma_a\right)}_\mathcal{A} - \underbrace{\left(\frac{\sigma_{tr}}{2}\frac{\partial }{\partial \mu} (1-\mu^2) \frac{\partial }{\partial \mu}\right)}_\mathcal{F},
\end{equation}
In this synthetic acceleration method, the FP approximation is used to correct the error in each iteration of the high-order (HO) equation (\ref{predict})  
Therefore, there is no consistency between the angular moments of the flux in the HO and low-order (LO) equations 

\subsection{NFPA: Nonlinear Fokker-Planck Acceleration}\label{NFPA}

Similar to FPSA, NFPA uses the FP approximation to accelerate the convergence of the solution 
We introduce the additive term $\hat{D}_F$ to \cref{fp1}, obtaining the modified FP equation
\begin{equation}
\label{mfp1}
\mu\frac{\partial \psi}{\partial x} + \sigma_a \psi = \frac{\sigma_{tr}}{2}\frac{\partial }{\partial \mu} (1-\mu^2) \frac{\partial \psi}{\partial \mu} + \hat{D}_F + Q\, 
\end{equation}
The role of $\hat{D}_F$ is to force the transport and modified FP equations to be consistent 
Subtracting \cref{mfp1} from \cref{transport1} and rearranging, we obtain the consistency term
\begin{equation}
\label{dfp}
\hat{D}_F = \sum_{l=0}^L \frac{(2l+1)}{2} P_l \sigma_l \phi_l - \frac{\sigma_{tr}}{2}\frac{\partial}{\partial \mu} (1-\mu^2) \frac{\partial \psi}{\partial \mu} - \sigma_{s,0} \psi\, 
\end{equation}

The NFPA method is given by the following equations:
\begin{subequations}\label[pluraleq]{holocons}
\begin{align}
\label{HO1}
\text{HO}&: \mu\frac{\partial \psi_{HO}}{\partial x} + \sigma_t \psi_{HO} = \sum_{l=0}^L \frac{(2l+1)}{2} P_l \sigma_l \phi_{l, LO} + Q\,,\\
\label{LO11}
\text{LO}&: \mu\frac{\partial \psi_{LO}}{\partial x} + \sigma_a \psi_{LO} = \frac{\sigma_{tr}}{2}\frac{\partial }{\partial \mu} (1-\mu^2) \frac{\partial \psi_{LO}}{\partial \mu} + \hat{D}_F + Q\,,\\
\label{con1}
\text{Consistency term}&: \hat{D}_F = \sum_{l=0}^L \frac{(2l+1)}{2} P_l \sigma_l \phi_{l, HO}^m - \frac{\sigma_{tr}}{2}\frac{\partial }{\partial \mu} (1-\mu^2) \frac{\partial \psi_{HO}}{\partial \mu} - \sigma_{s,0} \psi_{HO}\,,
\end{align}
\end{subequations}
where $\psi_{HO}$ is the angular flux obtained from the HO equation and $\psi_{LO}$ is the angular flux obtained from the LO equation 
The nonlinear HOLO-plus-consistency system given by \cref{holocons} can be solved using any nonlinear solution technique \cite{kelley}  Note that the NFPA scheme returns a FP equation that is consistent with HO transport  
Moreover, this modified FP equation accounts for large-angle scattering which the standard FP equation does not  
The LO equation (\ref{fp1}) can then be integrated into multiphysics models in a similar fashion to standard HOLO schemes \cite{patelFBR}  To solve the HOLO-plus-consistency system above, we use Picard iteration \cite{kelley}:
\begin{subequations}
\begin{align}
\label{H1}
\text{Transport Sweep for HO}&:
\mathcal{L} \psi_{HO}^{k+1} = \mathcal{S} \psi_{LO}^{k} + Q, \\
\label{L1}
\text{Evaluate Consistency Term}&: \hat{D}_F^{k+1} = \left(\mathcal{S} - \mathcal{F} - \sigma_{s,0}\mathcal{I}\right) \psi_{HO}^{k+1}, \\
\label{c1}
\text{Solve LO Equation}&: \psi_{LO}^{k+1} = \mathcal{P}^{-1} \left(\hat{D}_F^{k+1} + Q\right), 
\end{align}
\end{subequations}
where $\mathcal{L}$ and $\mathcal{S}$ are given in \cref{trans1}, $\mathcal{P}$ and $\mathcal{F}$ are given in \cref{FPSAsi1}, $\mathcal{I}$ is the identity operator, and $k$ is the iteration index 
Iteration is done until a convergence criterion is met 

The main advantage of setting up the LO equation in this fashion is that the stiffness matrix for LO needs to be setup and inverted \textit{only once}, just as with FPSA \cite{JapanFPSA, japanDiss}  This has a large impact on the method's performance 
A flowchart of this algorithm is shown in \cref{Nalgorithm} 

\begin{figure}[H]
\centering
\begin{tikzpicture}[node distance = 3cm, auto]
   
    \node [block] (init) {Initial guess of flux moments};
    \node [cloud_HO, right of=init, node distance=4cm] (HOm) {HO};
    \node [cloud_LO, below of=HOm, node distance=2cm] (LOm) {LO};
    \node [HO, below of=init] (transport) {One sweep in transport equation};
    \node [decision, below of=transport,node distance=4cm] (decide) {Flux moments converged?};
    \node [LO, left of=decide, node distance=4cm] (dterm) {Solve for consistency term};
    \node [LO, left of=dterm, node distance=3cm] (MFP) {Solve for FP angular flux};
    \node [LO, above of=MFP, node distance=4cm] (moments) {Convert angular flux to moments};
    \node [block, right of=decide, node distance=4cm] (stop) {Stop};
   
    \path [line] (init) -- (transport);
    \path [line] (transport) -- (decide);
    \path [line] (decide) -- node {no} (dterm);
    \path [line] (dterm) -- (MFP);
    \path [line] (MFP) -- (moments);
    \path [line] (moments) -- (transport);
    \path [line] (decide) -- node {yes}(stop);
\end{tikzpicture}
\caption{NFPA algorithm}
\label{Nalgorithm}
\end{figure}

\section{Numerical Experiments}\label{sec3}

In \cref{sec31} we describe the discretization methods used to implement the algorithms 
In \cref{sec32} we provide numerical results for 2 different choices of source $Q$ and boundary conditions 
For each choice we solve the problem using 3 different scattering kernels, applying 3 different choices of parameters for each kernel 
We provide NFPA numerical results for these 18 cases and compare them against those obtained from FPSA and other standard methods 

All numerical experiments were performed using MATLAB 
Runtime was tracked using the tic-toc functionality \cite{matlab17}, with
only the solver runtime being taken into consideration in the comparisons 
A 2017 MacBook Pro with a 2 8 GHz Quad-Core Intel Core i7 and 16 GB of RAM was used for all simulations 


\subsection{Discretization}\label{sec31}

The Transport and FP equations were discretized using linear discontinuous finite element discretization in space \cite{mpd1}, and discrete ordinates (S$_N$) in angle \cite{landm} 
The Fokker-Planck operator $\mathcal{F}$ was discretized using moment preserving discretization (MPD) \cite{mpd1} 
Details of the derivation of the linear discontinuous finite element discretization can be seen in \cite{japanDiss,martin} 
The finite element discretization for the  Fokker-Planck equation follows the same derivation 

A brief review for the angular discretization used for the FP equation is given below 
First, we use Gauss-Legendre quadrature to discretize the FP equation in angle:
\begin{equation}
\mu_n\frac{\partial \psi_n(x)}{\partial x} + \sigma_a \psi_n(x) - \frac{\sigma_{tr}}{2}\nabla^2_n \psi_n(x) =  Q_n(x),
\end{equation}
for $n=1,  ,N$ 
Here, $\nabla^2_n$ term is the discrete form of the angular Laplacian operator evaluated at angle $n$ 

The MPD scheme is then shown as
\begin{equation}
\nabla^2_n \psi_n = M \psi_n = V^{-1} L V \psi_n,
\end{equation}
where $M$ is the MPD discretized operator defined by
\begin{subequations}
\begin{equation}
V_{i,j} = P_{i-1}(\mu_j)w_j,
\end{equation}
and 
\begin{equation}
L_{i,j} = -i(i-1),
\end{equation}
\end{subequations}
for $i,j=1,   ,N$ 
Here, $P_l(\mu_j)$ are the Legendre polynomials evaluated at each angle $\mu_j$ and $w_j$ are the respective weights 
$M$ is defined as a (N x N) operator for a vector of $N$ angular fluxes $ \psi(x)$, at spatial location $x$  

In summary, if we write the FP equation as
\begin{equation}
\mathcal{H} \frac{\partial \psi}{\partial x}(x) + \sigma_a \psi(x) - \mathcal{F} \psi(x) =  Q(x),
\end{equation}
then $\mathcal{H}$ is Diag$(\mu_n)$ for $n=1,   ,N$, $Q(x)$ is a vector of source terms $Q_n(x)$, and $\mathcal{F}$ is represented by $\frac{\sigma_{tr}}{2}M$ 


\subsection{Numerical Results}\label{sec32}

It is shown that for slowly converging problems, typical convergence methods like $L_\infty$ suffer from false convergence \cite{adamslarsen} 
To work around this issue, the criterion is modified to use information about the current and previous iteration:
\begin{equation}
\label{falseconverge}
\frac{|| \phi^{m}_0(x) - \phi^{m-1}_0(x) ||_2}{1-\frac{|| \phi^{m+1}_0(x) - \phi^{m}_0(x) ||_2}{|| \phi^{m}_0(x) - \phi^{m-1}_0(x) ||_2}} < 10^{-8} 
\end{equation}

Two problems were tested using 200 spatial cells, $X$ = 400, $\sigma_a = 0$, $L$ = 15, and $N$ = 16 
Problem 1 has vacuum boundaries and a homogeneous isotropic source $Q$ for $0 < x < X$ 
Problem 2 has no internal source and an incoming beam at the left boundary  The source and boundary conditions used are shown in \cref{parameters}  
\begin{table}[H]
\begin{center}
\scalebox{0 9}{
\begin{tabular}{c | c | c} \hline 
& Problem 1 & Problem 2 \\ \hline \hline
Q(x) & 0 5 & 0 \\
$\psi_L$ & 0 & $\delta(\mu - \mu_N)$  \\
$\psi_R$ & 0 & 0 \\
\end{tabular}}
\end{center}
\caption{Problem Parameters}
\label{parameters} 
\end{table} 
We consider three scattering kernels in this paper: Screened Rutherford \cite{pomraning1}, Exponential \cite{pomraning2}, and Henyey-Greenstein \cite{HGK} 
Three cases for each kernel were tested 
The results obtained with NFPA are compared with those obtained using GMRES, DSA, and FPSA with the MPD scheme 

\subsubsection{SRK: Screened Rutherford Kernel}

The Screened Rutherford Kernel \cite{pomraning1, JapanFPSA} is a widely used scattering kernel for modeling scattering behavior of electrons \cite{SRK} 
The kernel depends on the parameter $\eta$, such that
\begin{equation}
\sigma^{SRK}_{s,l} = \sigma_s  \int_{-1}^{1} d\mu P_l(\mu) \frac{\eta (\eta+1)}{(1+2\eta-\mu)^2} 
\end{equation}
The SRK has a valid FP limit as $\eta$ approaches 0 \cite{patelFBR}  Three different values of $\eta$ were used to generate the scattering kernels shown in \cref{SRK} 
GMRES, DSA, FPSA, and NFPA all converged to the same solution for problems 1 and 2  \Cref{SRK_plots} shows the solutions for SRK with $\eta = 10^{-7}$ 
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0 1,angle=0]{SRK jpg}
  \caption{Screened Rutherford Kernels}
  \label{SRK}
\end{center}
\end{figure}
\begin{figure}[H]
    \centering
    \subfloat[Problem 1]{{\includegraphics[width=7cm]{s7_iso jpg} }}
    \qquad
    \subfloat[Problem 2]{{\includegraphics[width=7cm]{s7_beam jpg} }}
    \caption{Results for SRK Problems with $\eta = 10^{-7}$}
    \label{SRK_plots}
\end{figure}

\begin{table}[H]
\begin{center}
\scalebox{0 8}{
\begin{tabular}{c || c || c || c} \hline 
Parameter & Solver & Runtime (s) & Iterations \\ \hline \hline
\multirow{4}{*}{$\eta = 10^{-5}$} & GMRES & 98 8 & 12 \\
& DSA & 2380 & 53585 \\
& FPSA & 1 21 & 26 \\
& NFPA & 1 39 & 26 \\ \hline 
\multirow{4}{*}{$\eta = 10^{-6}$} & GMRES & 208 & 84 \\
& DSA & 3040 & 69156 \\
& FPSA & 0 747 & 16 \\
& NFPA & 0 857 & 16 \\ \hline 
\multirow{4}{*}{$\eta = 10^{-7}$} & GMRES & 174 & 124 \\
& DSA & 3270 & 73940 \\
& FPSA & 0 475 & 10 \\
& NFPA & 0 542 & 10 \\ \hline
\end{tabular}}
\end{center}
\caption{Runtime and Iteration Counts for Problem 1 with SRK}
\label{SRKresults1} 
\end{table}
\begin{table}[H]
\begin{center}
\scalebox{0 8}{
\begin{tabular}{c || c || c || c} \hline 
Parameter & Solver & Runtime (s) & Iterations \\ \hline \hline
\multirow{4}{*}{$\eta = 10^{-5}$} & GMRES & 52 4 & 187 \\
& DSA & 1107 & 25072 \\
& FPSA & 0 953 & 20 \\
& NFPA & 1 14 & 20 \\ \hline 
\multirow{4}{*}{$\eta = 10^{-6}$} & GMRES & 108 & 71 \\
& DSA & 1434 & 32562  \\
& FPSA & 0 730 & 14 \\
& NFPA & 0 857 & 14 \\ \hline 
\multirow{4}{*}{$\eta = 10^{-7}$} & GMRES & 94
Context 3: Margaret Way (b  Brisbane d  Cleveland, Queensland, Australia ) was an Australian writer of romance novels and women's fiction  A prolific author, Way wrote more than 120 novels since 1970, many through Mills & Boon, a romance imprint of British publisher Harlequin UK Ltd , owned by Harlequin Enterprises 

Biography
Before her marriage, she was a well-known pianist, teacher, vocal coach and accompanist  She began writing when her son, Laurence Way, was born, a friend took a pile of Mills & Boon books to her, she read all and decided that she also could write these types of novels  She began to write and promote her country with her stories set in Australia  She sold her first novels in 1970  Margaret Way lives with her family in her native Brisbane  Beginning in 2013, Margaret began to self-publish, releasing her first "e-book" mid-July



ground_truth: Privacy concerns and skepticism about its effectiveness.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How do the runtimes and iteration counts of NFPA and FPSA compare to GMRES and DSA in the numerical experiments?

Read the following text and answer briefly.

Context 2: 1 & 185 \\
& DSA & 1470 & 33246 \\
& FPSA & 0 438 & 8 \\
& NFPA & 0 484 & 8 \\ \hline  
\end{tabular}}
\end{center}
\caption{Runtime and Iteration Counts for Problem 2 with SRK}
\label{SRKresults2} 
\end{table}

The results of all solvers are shown in \cref{SRKresults1,SRKresults2} 
We see that NFPA and FPSA tremendously outperform GMRES and DSA in runtime for all cases 
FPSA is a simpler method than NFPA, requiring less calculations per iteration; therefore, it is expected that it outperforms NFPA in runtime 
We see a reduction in runtime and iterations for FPSA and NFPA as the FP limit is approached, with DSA and GMRES requiring many more iterations by comparison as $\eta$ approaches 0 

An advantage that NFPA offers is that the angular moments of the flux in the LO equation will remain consistent with those of the transport equation even as a problem becomes less forward-peaked 
On the other hand, the moments found using only the FP equation and source iteration lose accuracy 
To illustrate this, Problem 1 was tested using different Screened Rutherford Kernels with increasing $\eta$ parameters 
The percent errors (relative to the transport solution) for the scalar flux obtained with the LO equation and with the standard FP equation at the center of the slab are shown in \cref{momcomp} 
It can be seen that the percent relative errors in the scalar flux of the FP solution is orders of magnitude larger than the error produced using the LO equation 
The same trend can be seen when using the exponential and Henyey-Greenstein kernels  

\begin{figure}[H]
\begin{center}
  \includegraphics[scale=0 15,angle=0]{relerrorlog jpg}
  \caption{Log Scale of $\%$ Relative Error vs $\eta$ for Problem 1 at the Center of the Slab with SRK}
  \label{momcomp}
\end{center}
\end{figure}

\subsubsection{EK: Exponential Kernel}

The exponential kernel \cite{pomraning2, JapanFPSA} is a fictitious kernel made for problems that have a valid Fokker-Planck limit \cite{pomraning1} 
The zero$^{\text{th}}$ moment, $\sigma^{EK}_{s,0}$, is chosen arbitrarily; we define $\sigma^{EK}_{s,0}$ as the same zero$^{\text{th}}$ moment from the SRK 
The $\Delta$ parameter determines the kernel: the first and second moments are given by 
\begin{subequations}
\begin{align}
\sigma^{EK}_{s,1} &= \sigma^{EK}_{s,0} (1-\Delta),\\
\sigma^{EK}_{s,2} &= \sigma^{EK}_{s,0} (1-3\Delta+3\Delta^2),
\end{align}
and the relationship for $l\geq 3$ is
\begin{equation}
\sigma^{EK}_{s,l} = \sigma^{EK}_{s,l-2} - \Delta(2l+1) \sigma^{EK}_{s,l-1} 
\end{equation}
\end{subequations}
As $\Delta$ is reduced, the scattering kernel becomes more forward-peaked 

The EK has a valid FP limit as $\Delta$ approaches 0 \cite{patelFBR} 
Three different values of $\Delta$ were used to generate the scattering kernels shown in \cref{EXP} 
The generated scattering kernels are shown in \cref{EXP} 
GMRES, DSA, FPSA, and NFPA all converged to the same solution for problems 1 and 2 
\Cref{EK_plots} shows the solutions for EK with $\Delta = 10^{-7}$ 
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0 1,angle=0]{EXP jpg}
  \caption{Exponential Kernels}
  \label{EXP}
\end{center}
\end{figure}
\begin{figure}[H]
    \centering
    \subfloat[Problem 1]{{\includegraphics[width=7cm]{dta7_iso jpg} }}
    \qquad
    \subfloat[Problem 2]{{\includegraphics[width=7cm]{dta7_beam jpg} }}
    \caption{Results for EK Problems with $\Delta = 10^{-7}$}
    \label{EK_plots}
\end{figure}

The runtimes and iterations for GMRES, DSA, FPSA, and NFPA are shown in \cref{Expresults1,Expresults2} 
We see a similar trend with the EK as seen with SRK 
Smaller $\Delta$ values lead to a reduction in runtime and iterations for NFPA and FPSA, which greatly outperform DSA and GMRES in both categories 

\begin{table}[h]
\begin{center}
\scalebox{0 8}{
\begin{tabular}{c || c || c || c} \hline 
Parameter & Solver & Runtime (s) & Iterations \\ \hline \hline
\multirow{4}{*}{$\Delta = 10^{-5}$} & GMRES & 196 & 142 \\
& DSA & 3110 & 70140 \\
& FPSA & 0 514 & 11 \\ 
& NFPA & 0 630 & 11 \\\hline 
\multirow{4}{*}{$\Delta = 10^{-6}$} & GMRES & 156 & 132 \\
& DSA & 3120 & 70758 \\
& FPSA & 0 388 & 7 \\ 
& NFPA & 0 393 & 7 \\ \hline 
\multirow{4}{*}{$\Delta = 10^{-7}$} & GMRES & 81 & 127 \\
& DSA & 3120 & 70851  \\
& FPSA & 0 292 & 6 \\ 
& NFPA & 0 318 & 6 \\ \hline
\end{tabular}}
\end{center}
\caption{Runtime and Iteration Counts for Problem 1 with EK}
\label{Expresults1} 
\end{table}
\begin{table}[h]
\begin{center}
\scalebox{0 8}{
\begin{tabular}{c || c || c || c} \hline 
Parameter & Solver & Runtime (s) & Iterations \\ \hline \hline
\multirow{4}{*}{$\Delta = 10^{-5}$} & GMRES & 110 & 73 \\
& DSA & 1455 & 33033 \\
& FPSA & 0 492 & 10 \\ 
& NFPA & 0 613 & 10 \\ \hline 
\multirow{4}{*}{$\Delta = 10^{-6}$} & GMRES & 82 7 & 79 \\
& DSA & 1470 & 33309 \\
& FPSA & 0 358 & 7 \\ 
& NFPA & 0 431 & 7 \\ \hline 
\multirow{4}{*}{$\Delta = 10^{-7}$} & GMRES & 56 8 & 90 \\
& DSA & 1470 & 33339 \\
& FPSA & 0 273 & 5 \\ 
& NFPA & 0 319 & 5 \\ \hline  
\end{tabular}}
\end{center}
\caption{Runtime and Iteration Counts for Problem 2 with EK}
\label{Expresults2} 
\end{table}

\subsubsection{HGK: Henyey-Greenstein Kernel}

The Henyey-Greenstein Kernel \cite{HGK,JapanFPSA} is most commonly used in light transport in clouds 
It relies on the anisotropy factor $g$, such that
\begin{equation}
\sigma^{HGK}_{s,l} = \sigma_s g^l 
\end{equation}
As $g$ goes from zero to unity, the scattering shifts from isotropic to highly anisotropic 
\begin{figure}[H]
\begin{center}
  \includegraphics[scale=0 1,angle=0]{HGK jpg}
  \caption{Henyey-Greenstein Kernels}
  \label{HGK}
\end{center}
\end{figure}
\begin{figure}[H]
    \centering
    \subfloat[Problem 1]{{\includegraphics[width=7cm]{g099_iso jpg} }}
    \qquad
    \subfloat[Problem 2]{{\includegraphics[width=7cm]{g099_beam jpg} }}
    \caption{Results for HGK Problems with $g = 0 99$}
    \label{HGK_plots}
\end{figure}


The HGK does not have a valid FP limit \cite{patelFBR} 
The three kernels tested are shown in \cref{HGK} 
GMRES, DSA, FPSA, and NFPA all converged to the same solution for problems 1 and 2 
\Cref{HGK_plots} shows the solutions for HGK with $g = 0 99$ 
The results of each solver are shown in \cref{HGKresults1,HGKresults2}  
\begin{table}[h]
\begin{center}
\scalebox{0 8}{
\begin{tabular}{c || c || c || c} \hline 
Parameter & Solver & Runtime (s) & Iterations \\ \hline \hline
\multirow{4}{*}{$g=0 9$} & GMRES & 9 88 & 76 \\
& DSA & 24 5 & 554 \\
& FPSA & 1 50 & 32 \\ 
& NFPA & 1 39 & 27 \\ \hline 
\multirow{4}{*}{$g=0 95$} & GMRES & 12 2 & 131 \\
& DSA & 47 7 & 1083 \\
& FPSA & 1 75 & 38 \\ 
& NFPA & 1 83 & 35 \\ \hline 
\multirow{4}{*}{$g=0 99$} & GMRES & 40 0 & 27 \\
& DSA & 243 & 5530  \\
& FPSA & 3 38 & 74 \\ 
& NFPA & 3 93 & 73 \\ \hline
\end{tabular}}
\end{center}
\caption{Runtime and Iteration Counts for Problem 1 with HGK}
\label{HGKresults1} 
\end{table}
\begin{table}[h]
\begin{center}
\scalebox{0 8}{
\begin{tabular}{c || c || c || c} \hline 
Parameter & Solver & Runtime (s) & Iterations \\ \hline \hline
\multirow{4}{*}{$g=0 9$} & GMRES & 24 3 & 135 \\
& DSA & 14 8 & 336  \\
& FPSA & 1 15 & 23 \\ 
& NFPA & 1 35 & 24 \\ \hline 
\multirow{4}{*}{$g=0 95$} & GMRES & 31 3 & 107 \\
& DSA & 29 7 & 675 \\
& FPSA & 1 56 & 32 \\ 
& NFPA & 1 90 & 33 \\ \hline 
\multirow{4}{*}{$g=0 99$} & GMRES & 41 4 & 126 \\
& DSA & 146 & 3345 \\
& FPSA & 3 31 & 67 \\ 
& NFPA & 3 99 & 67 \\ \hline  
\end{tabular}}
\end{center}
\caption{Runtime and Iteration Counts for Problem 2 with HGK}
\label{HGKresults2} 
\end{table}

Here we see that NFPA and FPSA do not perform as well compared to their results for the SRK and EK 
Contrary to what happened in those cases, both solvers require more time and iterations as the problem becomes more anisotropic 
This is somewhat expected, due to HGK not having a valid Fokker-Planck limit 
However, both NFPA and FPSA continue to greatly outperform GMRES and DSA 
Moreover, NFPA outperforms FPSA in iteration count for problem 1 


\section{Discussion}\label{sec4}

This paper introduced the Nonlinear Fokker-Planck Acceleration technique for steady-state, monoenergetic transport in homogeneous slab geometry 
To our knowledge, this is the first nonlinear HOLO method that accelerates \textit{all $L$ moments} of the angular flux 
Upon convergence, the LO and HO models are consistent; in other words, the (lower-order) modified Fokker-Planck equation \textit{preserves the same angular moments} of the flux obtained with the (higher-order) transport equation 

NFPA was tested on a homogeneous medium with an isotropic internal source with vacuum boundaries, and in a homogeneous medium with no internal source and an incoming beam boundary 
For both problems, three different scattering kernels were used 
The runtime and iterations of NFPA and FPSA were shown to be similar 
They both vastly outperformed DSA and GMRES for all cases by orders of magnitude 
However, NFPA has the feature of preserving the angular moments of the flux in both the HO and LO equations, which offers the advantage of integrating the LO model into multiphysics models  

In the future, we intend to test NFPA capabilities for a variety of multiphysics problems and analyze its performance 
To apply NFPA to more realistic problems, it needs to be extended to include time and energy dependence  
Additionally, the method needs to be adapted to address geometries with higher-order spatial dimensions 
Finally, for the NFPA method to become mathematically ``complete", a full convergence examination using Fourier analysis must be performed 
However, this is beyond the scope of this paper and must be left for future work 

\section*{Acknowledgements}

The authors acknowledge support under award number NRC-HQ-84-15-G-0024 from the Nuclear Regulatory Commission 
The statements, findings, conclusions, and recommendations are those of the authors and do not necessarily reflect the view of the U S  Nuclear Regulatory Commission 

J ~K  Patel would like to thank Dr ~James Warsa for his wonderful transport class at UNM, as well as his synthetic acceleration codes 
The authors would also like to thank Dr ~Anil Prinja for discussions involving Fokker-Planck acceleration 







ground_truth: NFPA and FPSA greatly outperform GMRES and DSA.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What genre did Margaret Way write in?

Read the following text and answer briefly.

Context 3: 

Margaret died on the 10th of August 2022 in Cleveland, Queensland 

Bibliography

Single Novels
King Country (1970)
Blaze of Silk (1970)
The Time of the Jacaranda (1970)
Bauhinia Junction (1971)
Man from Bahl Bahla (1971)
Summer Magic (1971)
Return to Belle Amber (1971)
Ring of Jade (1972)
Copper Moon (1972)
Rainbow Bird (1972)
Man Like Daintree (1972)
Noonfire (1972)
Storm Over Mandargi (1973)
Wind River (1973)
Love Theme (1974)
McCabe's Kingdom (1974)
Sweet Sundown (1974)
Reeds of Honey (1975)
Storm Flower (1975)
Lesson in Loving (1975)
Flight into Yesterday (1976)
Red Cliffs of Malpara (1976)
Man on Half-moon (1976)
Swan's Reach (1976)
Mutiny in Paradise (1977)
One Way Ticket (1977)
Portrait of Jaime (1977)
Black Ingo (1977)
Awakening Flame (1978)
Wild Swan (1978)
Ring of Fire (1978)
Wake the Sleeping Tiger (1978)
Valley of the Moon (1979)
White Magnolia (1979)
Winds of Heaven (1979)
Blue Lotus (1979)
Butterfly and the Baron (1979)
Golden Puma (1980)
Temple of Fire (1980)
Lord of the High Valley (1980)
Flamingo Park (1980)
North of Capricorn (1981)
Season for Change (1981)
Shadow Dance (1981)
McIvor Affair (1981)
Home to Morning Star (1981)
Broken Rhapsody (1982)
The Silver Veil (1982)
Spellbound (1982)
Hunter's Moon (1982)
Girl at Cobalt Creek (1983)
No Alternative (1983)
House of Memories (1983)
Almost a Stranger (1984)
A place called Rambulara (1984)
Fallen Idol (1984)
Hunt the Sun (1985)
Eagle's Ridge (1985)
The Tiger's Cage (1986)
Innocent in Eden (1986)
Diamond Valley (1986)
Morning Glory (1988)
Devil Moon (1988)
Mowana Magic (1988)
Hungry Heart (1988)
Rise of an Eagle (1988)
One Fateful Summer (1993)
The Carradine Brand (1994)
Holding on to Alex (1997)
The Australian Heiress (1997)
Claiming His Child (1999)
The Cattleman's Bride (2000)
The Cattle Baron (2001)
The Husbands of the Outback (2001)
Secrets of the Outback (2002)
With This Ring (2003)
Innocent Mistress (2004)
Cattle Rancher, Convenient Wife (2007)
Outback Marriages (2007)
Promoted: Nanny to Wife (2007)
Cattle Rancher, Secret Son (2007)
Genni's Dilemma (2008)
Bride At Briar Ridge (2009)
Outback Heiress, Surprise Proposal (2009)
Cattle Baron, Nanny Needed (2009)

Legends of the Outback Series
Mail Order Marriage (1999)
The Bridesmaid's Wedding (2000)
The English Bride (2000)
A Wife at Kimbara (2000)

Koomera Crossing Series
Sarah's Baby (2003)
Runaway Wife (2003)
Outback Bridegroom (2003)
Outback Surrender (2003)
Home to Eden (2004)

McIvor Sisters Series
The Outback Engagement (2005)
Marriage at Murraree (2005)

Men Of The Outback Series
The Cattleman (2006)
The Cattle Baron's Bride (2006)
Her Outback Protector (2006)
The Horseman (2006)

Outback Marriages Series
Outback Man Seeks Wife (2007)
Cattle Rancher, Convenient Wife (2007)

Barons of the Outback Series Multi-Author
Wedding At Wangaree Valley (2008)
Bride At Briar's Ridge (2008)

Family Ties Multi-Author
Once Burned (1995)

Hitched! Multi-Author
A Faulkner Possession (1996)

Simply the Best Multi-Author
Georgia and the Tycoon (1997)

The Big Event Multi-Author
Beresford's Bride (1998)

Guardian Angels Multi-Author
Gabriel's Mission (1998)

Australians Series Multi-Author
7  Her Outback Man (1998)
17  Master of Maramba (2001)
19  Outback Fire (2001)
22  Mistaken Mistress (2002)
24  Outback Angel (2002)
33  The Australian Tycoon's Proposal (2004)
35  His Heiress Wife (2004)

Marrying the Boss Series Multi-Author
Boardroom Proposal (1999)

Contract Brides Series Multi-Author
Strategy for Marriage (2002)

Everlasting Love Series Multi-Author
Hidden Legacy (2008)

Diamond Brides Series Multi-Author
The Australian's Society Bride (2008)

Collections
Summer Magic / Ring of Jade / Noonfire (1981)
Wife at Kimbara / Bridesmaid's Wedding (2005)

Omnibus in Collaboration
Pretty Witch / Without Any Amazement / Storm Over Mandargi (1977) (with Lucy Gillen and Margaret Malcolm)
Dear Caliban / Heart of the Eagle / Swans' Reach (1978) (with Jane Donnelly and Elizabeth Graham)
The Bonds of Matrimony / Dragon Island / Reeds of Honey (1979) (with Elizabeth Hunter and Henrietta Reid)
The Man Outside / Castles in Spain / McCabe's Kingdom (1979) (with Jane Donnelly and Rebecca Stratton)
Winds From The Sea / Island of Darkness / Wind River (1979) (with Margaret Pargeter and Rebecca Stratton)
Moorland Magic / Tree of Idleness / Sweet Sundown (1980) (with Elizabeth Ashton and Elizabeth Hunter)
The Shifting Sands / Portrait of Jaime / Touched by Fire (1982) (with Jane Donnelly and Kay Thorpe)
Head of Chancery / Wild Heart / One-Way Ticket (1986) (with Betty Beaty and Doris Smith)
Heart of the Scorpion / The Winds of Heaven / Sweet Compulsion (1987) (with Janice Gray and Victoria Woolf)
One Brief Sweet Hour / Once More With Feeling / Blue Lotus (1990) (with Jane Arbor and Natalie Sparks)
Marry Me Cowboy (1995) (with Janet Dailey, Susan Fox and Anne McAllister)
Husbands on Horseback (1996) (with Diana Palmer)
Wedlocked (1999) (with Day Leclaire and Anne McAllister)
Mistletoe Magic (1999) (with Betty Neels and Rebecca Winters)
The Australians (2000) (with Helen Bianchin and Miranda Lee)
Weddings Down Under (2001) (with Helen Bianchin and Jessica Hart)
Outback Husbands (2002) (with Marion Lennox)
The Mother's Day Collection (2002) (with Helen Dickson and Kate Hoffmann)
Australian Nights (2003) (with Miranda Lee)
Outback Weddings (2003) (with Barbara Hannay)
Australian Playboys (2003) (with Helen Bianchin and Marion Lennox)
Australian Tycoons (2004) (with Emma Darcy and Marion Lennox)
A Mother's Day Gift (2004) (with Anne Ashley and Lucy Monroe)
White Wedding (2004) (with Judy Christenberry and Jessica Steele)
A Christmas Engagement (2004) (with Sara Craven and Jessica Matthews)
A Very Special Mother's Day (2005) (with Anne Herries)
All I Want for Christmas    (2005) (with Betty Neels and Jessica Steele)
The Mills and Boon Collection (2006) (with Caroline Anderson and Penny Jordan)
Outback Desire (2006) (with Emma Darcy and Carol Marinelli)
To Mum, with Love (2006) (with Rebecca Winters)
Australian Heroes (2007) (with Marion Lennox and Fiona McArthur)
Tall, Dark and Sexy (2008) (with Caroline Anderson and Helen Bianchin)
The Boss's Proposal (2008) (with Jessica Steele and Patricia Thayer)
Island Heat / Outback Man Seeks Wife / Prince's Forbidden Virgin / One Night Before Marriage / Their Lost-and-found Family / Single Dad's Marriage Wish (2008) (with Robyn Donald, Marion Lennox, Carol Marinelli, Sarah Mayberry and Anne Oliver)
Australian Billionaires (2009) (with Jennie Adams and Amy Andrews)
Cattle Baron : Nanny Needed / Bachelor Dad on Her Doorstep (2009) (with Michelle Douglas)

External links
Margaret Way at Harlequin Enterprises Ltd

Australian romantic fiction writers
Australian women novelists
Living people
Year of birth missing (living people)
Women romantic fiction writers



ground_truth: Romance novels and women's fiction.