text:
How to pitch a WIRED UK science story
Matt Reynolds
May 18 · 4 min read
So you're thinking about pitching a science story to WIRED UK. Great! I love hearing exciting ideas from writers I haven't worked with before.
Below are a few pointers about the kind of science stories WIRED UK runs and how to pitch them. These aren't exhaustive by any means, but they're a good guide as to what I'm looking for when I go through pitches.
What WIRED UK does
Our stories run the gamut through politics, science, culture, security, business and a bunch of other sections. But they're always about change — and the people who are altering the world for better or worse.
We hardly ever publish straight news. We only run a handful of stories a day, and always go in-depth and bring something new to our readers. That could mean delving behind the headlines and finding out how Brexit is impacting MP's mental health or bringing something totally surprising to the table that our readers wouldn't find anywhere else.
Usually, our stories are between 1,000 and 1,500 words. Enough to go in-depth on something but not so long that things get boring. If it's a great story that needs more space, however, then we also publish stories all the way up to 5,000 words and beyond.
Three kinds of science story
WIRED UK's science remit is large. It includes just about every science and science-adjacent area you could think of — all the way from food to genetics. And stories about the genetics of food, which I particularly love.
But most stories fall into one of the three following categories. The first two are more urgent and responsive, and require a more timely pitch, while the third is much broader.
1) A science angle on a massive news story happening today. Typically with big UK interest. ie, The physics of fighting the Notre Dame fire, How the London Marathon route slows runners down, Dog DNA tests are helping us make better puppers (tied to Crufts), How Brexit is pushing MPs to the verge of mental breakdown
2) The in-depth version of a big science story. When a massive science story hits, rather than covering it straight we can come at it with a "How they did this" or something like that. This could also include myth-busting style pieces when you know research is likely to be poorly communicated elsewhere. ie, How we imaged the black hole, How we heard the first ever marsquake, Why do we all seem to be having less sex? Blame honesty, Jeff Bezos wants to colonise space, but he's paying for it by destroying Earth
3) This is the most interesting section — and the one where I need the most help from you . Original stories that people just won't have heard elsewhere. ie, The elderly farmers fuelling China's AI revolution, the fight against super-gonorrhoea, The dinosaur trade: how celebrity collectors and glitzy auctions could be damaging science, How China's WeChat became a grim heart of illegal animal trading, The decades-long quest to end drought (and
feed millions) by taking the salt out of seawater, The clean meat industry is racing to ditch its reliance on foetal blood, The unending hunt for Planet Nine, our solar system's hidden world
These can go in-depth on a story that people think they know, but really don't, or introduce something completely new. Often, these run longer than the other two categories.
Some general pointers
Pitch stories, not themes. Tell me a story about the farmers on X farm who are experimenting with genetically-modified strawberries because they think it'll let them replace their workforce with robots — not a story about farming automation or genetically-modified food.
Characters, characters, characters. Science stories can be a bit dry — but that's because we're guilty of overlooking the humans involved and forget to tell the stories of people pursuing their hunch to the ends of the Earth, fighting small battles of huge significance or who are unafraid to push the boundaries of science. Talk to those people, and find them in whatever story you're telling.
Science is culture. Some of the most interesting science stories never see the inside of a scientific journal. I'm interested in wellness, food fads, sleep-hacking and pseudoscience and way more — pitch me stories about these things too.
Timeliness helps. A lot of stories are borderline interesting but have no "why now" about them, and that doesn't give people much of a reason to read them. There doesn't have to be a big news hook, but making your story feel timely can help push it from "interesting" to "we have to publish this".
I'm on mattr [at] wired [dot] co [dot] uk
Send me a headline, plus a paragraph or two outlining your idea, and the general arc of the story. Let me know who you'd speak to as part of it, or where you'd visit. If it requires a timely response, please flag that at the top of the email.
If you've got any questions, drop me an email or find me on Twitter. And if you're passing through London, then feel free to get in touch and we can go for a coffee.


It is very hard not to love this little toy. It looks exactly like in the cartoon. It is just great. My son slept with it for about one week after we received it and still plays with it every single day. Great toy.


text:
New paper finds natural variability accounts for > 50% of long-term temperature change in many regions over past century
A paper published today in Climate Dynamics finds natural multidecadal variability accounts for "more than 30% of long-term temperature variation" in "most regions" and "more than 50% in parts of North America, East Asia, Northern Eurasia, Northern Africa and Greenland" over the past century. The authors find natural ocean oscillations the Atlantic Multidecadal Oscillation [AMO] and Pacific Decadal Oscillation [PDO] account for "more than 40% of the amplitude" of the natural multidecadal variability.
The authors find the well known natural 60-year climate cycle associated with the PDO is present in mid-high-latitude lands, whereas a 20 to 30 year cycle [one-third to one-half the 60 year cycle] is present in low-latitude lands.
The 60-year climate cycle is also related to solar activity and cosmic rays, and many papers have shown that solar activity [in addition to solar and lunar tidal effects] drive the ocean oscillations. Indeed, solar activity alone can explain 95% of climate change over the past 400 years.
Climate Dynamics March 2014
Observed and SST-forced multidecadal variability in global land surface air temperature
L. H. Gao, Z. W. Yan, X. W. Quan
The characteristics of multidecadal variability (MDV) in global land surface air temperature (SAT) are analyzed based on observations. The role of sea surface temperature (SST) variations in generating MDV in land SAT is assessed using atmospheric general circulation model simulations forced by observed SST. MDV in land SAT exhibits regional differences, with amplitude larger than 0.3 °C mainly over North America, East Asia, Northern Eurasia, Northern Africa and Greenland for the study period of 1902–2004. MDV can account for more than 30 % of long-term temperature variation during the last century in most regions, especially more than 50 % in parts of the above-mentioned regions. The SST-forced simulations reproduce the observed feature of zonal mean MDV in land SAT, though with weaker amplitude especially at the northern high-latitudes. Two types of MDV in land SAT, one of 60-year-timescale, mainly observed in the northern mid-high-latitude lands, and another of 20–30-year-timescale, mainly observed in the low-latitude lands, are also well reproduced. The SST-forced MDV accounts for more than 40 % amplitude of observed MDV in most regions. Except for some sporadically distributed regions in central Eurasia, South America and Western Australia, the SST-forced multidecadal variations are well in-phase with observations. The Atlantic Multidecadal Oscillation and Pacific Decadal Oscillation signals are found dominant in MDV of both the observed and SST-forced land SAT, suggesting important roles of these oceanic oscillations in generating MDV in global land SAT.
Posted by MS at 8:53 AM
What is the cause of the ~60 year quasi-cycle? I noticed this just a little while ago.
The Earth's rotation axis is nutatiing with a period of about 18.6 years. However, that is only part of the story. In actual fact, the nutation takes the form of an elliptical cone, as shown here. The distance between the J2000 polar axis and the actual rotation axis looks like this. Its period is necessarily halved, to about 9.3 years.
Thus, the magnitude of the component of the magnetic moment of the Sun along the Earth's rotation axis should have periods of about
T1 = 11*9.3/(11+9.3) = 5 years
T2 = 11*9.3/(11-9.3) = 60 years
Coincidence? Maybe. But, is there not a 5-ish year quasi-periodicity to the major temperature sets? Hard to say for sure, but there surely are several ups and downs which are in the neighborhood of 5 years.
MS March 27, 2014 at 2:36 PM
Thanks Bart for your insights once again.
I wanted to ask you if you had any further thoughts on the comment you made at Tallbloke's site re the spectral "hole" related to the big blue ocean?
Bart,
I elevated your comment to a post, and added a Fourier analysis. Thanks again!
http://hockeyschtick.blogspot.com/2014/03/what-causes-natural-60-year-climate.html
Will take a look.
I didn't really give the "hole" much more thought. Mainly, it just told me I didn't need to worry that the gap invalidated the idea of GHGs as radiators which cool the globe under convection. The gap does not generally indicate atmospheric attenuation because it already exists at the ocean surface. -Bart
Q: data source that the "hole" exists at the ocean surdace?
Doesn't the ocean look blue to you when you look at it from the shore? If it looked yellow at the surface, and looked blue from space, then there would be a definite indication that the atmosphere was taking the red out.
What we would really need to evaluate atmospheric transmission would be the difference between a spectrum at the surface, and at TOA. -Bart
MS March 28, 2014 at 11:45 AM
I'm sure this data exists somewhere - let me know if you find it. Thanks
http://sirena10.blogspot.com/2010/06/day-39-may-force-be-with-you.html
http://scienceofdoom.com/2010/12/27/emissivity-of-the-ocean/
I have been upbraided in another location that the distribution is almost totally in the infrared, and the criticism is apt. The blue of the oceans is reflected sunlight, not thermal emission. It doesn't look blue at night.
So, mea culpa. I was hasty.
It is still true, however, that TOA alone does not tell us the transmission from surface to there. I do not know what the spectrum near the surface is. Maybe I will read over your links and see if they shed any light on this. -Bart
I think that the answer is simply this: a gap in surface to TOA transmission obviously means that some upward bound radiation is being retained. However, that does not mean that the gap is monotonic, i.e., that it is incrementally increasing with an incremental increase in greenhouse gases in all climate states. This leaves the baseline GHE in effect to warm the surface beyond what it otherwise would be, but says that there is a limit to how much it can do so.
I think a lot of problems with climate science result from an overreliance on linearized models. This may be such a case. - Bart
Important new paper finds solar amplification mech...
New paper that selects hockey-stick data finds onl...
The IPCC itself is the biggest threat to future fo...
New paper finds significant increase in plant prod...
New UN IPCC scaremongering on hunger & famine is o...
New paper supports the bipolar seesaw theory of ab...
New paper finds precipitation over Greenland has i...
New paper finds transient climate response to cumu...
New paper finds climate sensitivity to CO2 is ~27%...
New paper finds winters in Poland were warmer in t...
WSJ: Climate Forecast: Muting the Alarm; IPCC exag...
WSJ: Shale gas can free Europe from reliance on Ru...
What causes the natural 60-year climate cycle? A n...
New paper finds climate sensitivity is independent...
New paper finds natural variability accounts for >...
New paper finds no effect of "acidification" on pl...
New paper finds CO2 acts as a huge cooling mechani...
New paper finds "surprisingly, there are many US w...
Can David Appell be humble anymore? Was he ever? W...
New paper finds Arctic sea ice was much less than ...
Study finds Medieval Warm Period in Tibet was warm...
New paper finds global sea level rise has decelera...
IPCC expert reviewer Dr. Vincent Gray: Climate mod...
John Christy: Climate models overcook the planet b...
Dana's unremarkable global warming predictions deb...
How Tesla earns $35,000 additional on every car so...
Mann's latest propaganda: "Global Warming Will Cro...
New paper finds E Australia was significantly warm...
Media claims that "Greenland's ice loss has triple...
New paper attempts to explain ice ages, finds chao...
Review finds CO2 fertilization has increased fores...
New paper finds droughts in China were more severe...
Investor's Business Daily: Dems climate talkathon ...
WSJ: Dems all-nighter climate blabathon was just a...
New paper finds another solar amplification mechan...
Why the ideal gas law, gravity, & atmospheric mass...
IPCC chair denies what the IPCC says about extreme...
Doctor claims no global warming is public health e...
Collection of comments that climate alarmist cowar...
New paper finds "remarkable" growth of glaciers on...
WSJ: "Warren Buffett, Climate-Change Denier"
Newly installed US wind turbines fell 92% in 2013
New renewable energy device generates power from t...
New paper finds 3 more non-hockey-sticks in Eurasi...
New paper in Nature points out warming from 1970's...
Nature editorial says "we must not fall victim to ...
How the journal Nature plays fast & loose with the...
New paper shows climate modelers don't even know w...
New paper falsifies climate model predictions at 9...
New paper finds lows of Arctic sea ice in 2007 and...
New paper shows fire activity at end of 20th centu...
Killing the national bird for the climate scam
WSJ: Why climate-change activists are losing the b...

redpajama_set_name: RedPajamaCommonCrawl


text:
NPFC - DOD D 5136.1
Assistant Secretary of Defense for Health Affairs (ASD(HA))
Organization: NPFC
This Directive, consistent with section 138 of Reference (a):
Reissues Reference (b) under the authority of Reference (c), to update the responsibilities, functions, relationships, and authorities of the ASD(HA), under the Under Secretary of Defense for Personnel and Readiness (USD(P&R)).
Cancels Reference (d) and incorporates the responsibilities and functions assigned to the Special Assistant to the Under Secretary of Defense for Personnel and Readiness for Gulf War Illnesses, Medical Readiness, and Military Deployments.
This Directive applies to OSD, the Military Departments (including the Coast Guard at all times, including when it is a service in the Department of Homeland Security by agreement with that Department), the Office of the Chairman of the Joint Chiefs of Staff and the Joint Staff, the Combatant Commands, the Office of the Inspector General of the Department of Defense, the Defense Agencies, the DoD Field Activities, and all other organizational entities within the Department of Defense (hereafter referred to collectively as the "DoD Components").
This Directive also applies to the Commissioned Corps of the Public Health Service, under agreement with the Department of Health and Human Services, and the Commissioned Corps of the National Oceanic and Atmospheric Administration, under agreement with the Department of Commerce.
DODD 5136.01(D) CE-01
PURPOSE. Pursuant to the authority vested in the Secretary of Defense by sections 113 and 138 of Title 10, United States Code (U.S.C.) (Reference (a)), this directive reissues DoD Directive (DoDD)...
DOD D 5136.1
PURPOSE This Directive, consistent with section 138 of Reference (a): Reissues Reference (b) under the authority of Reference (c), to update the responsibilities, functions, relationships, and...
ASSISTANT SECRETARY OF DEFENSE FOR HEALTH AFFAIRS (ASD(HA)) CFR367
A description is not available for this item.
This document references:
DODD 5105.45 - UNIFORMED SERVICES UNIVERSITY OF THE HEALTH SCIENCES (USU)
Published by DOD on May 30, 2019
Purpose: In accordance with the authority in DoD Directive (DoDD) 5124.02 and pursuant to Chapter 104 of Title 10, United States Code (U.S.C.), this issuance establishes policy, assigns...
DOD D 5124.2 - Under Secretary of Defense for Personnel and Readiness (USD(P&R))
Published by NPFC on June 23, 2008
PURPOSE Under the authority vested in the Secretary of Defense by sections 113 and 136 of Reference (a), this Directive: Reissues Reference (b) to update the responsibilities, functions,...
DODD 5136.12(D) - TRICARE MANAGEMENT ACTIVITY (TMA))
Published by DODD on May 31, 2001
Pursuant to the authority vested in the Secretary of Defense under reference (a) this Directive establishes the TRICARE Management Activity (TMA) with the mission, organization, responsibilities,...
DODD 6205.3(D) - DOD IMMUNIZATION PROGRAM FOR BIOLOGICAL WARFARE DEFENSE
Published by DODD on November 26, 1993
DODD 8910.01 CE-01 - Information Collection and Reporting
Published by DODD on July 8, 2020
PURPOSE. This instruction: a. Reissues DoD Instruction (DoDI) 8910.01 (Reference (a)) in accordance with the authority in DoD Directive (DoDD) 5144.02 (Reference (b)). b. Establishes and reissues...
This document is referenced by:
DODD 1235.12 CE-01 - Accessing the Reserve Components (RC)
Published by DODD on February 28, 2017
PURPOSE. In accordance with the authority in DoD Directive (DoDD) 5124.02 (Reference (a)), this instruction: a. Reissues DoD Instruction (DoDI) 1235.12 (Reference (b)) and incorporates and cancels...
DODD 5101.15 - DoD Medical Materiel Executive Agent (MMEA) Implementation Guidance
Published by DOD on August 31, 2018
PURPOSE. In accordance with the authority in DoD Directive (DoDD) 5134.01 (Reference (a)), this Instruction: a. Implements the policy in DoDD 5101.09E (Reference (b)) by assigning responsibilities...
DODD 1322.24 - Medical Readiness Training (MRT)
Published by DODD on March 16, 2018
Purpose: This issuance: • In accordance with the authority in DoD Directive (DoDD) 5124.02, establishes policy, assigns responsibilities, and provides procedures for governing MRT for Service members...
DODD 3000.10 - Contingency Basing Outside the United States
PURPOSE. This directive establishes policy and assigns responsibilities for DoD contingency basing outside the United States. APPLICABILITY. This directive: a. Applies: (1) To OSD, the Military...
CJCSI 1001.01 - JOINT MANPOWER AND PERSONNEL PROGRAM
Published by NPFC on October 7, 2014
Purpose. This instruction provides policy and establishes responsibilities and procedures for determining, validating, documenting, and maintaining joint manpower requirements. It also provides...


text:
Q: How can I vectorized a function when one parameter is a dataframe that shouldn't be vectorized? I need to vectorize functions manipulating panda Dataframes or Series to decrease processing time.
The problem is that some of the parameters of the vectorized function must not be vectorized.
Let's see an example with the following code. I create a series that will be processed as a vector.
Values = pd.DataFrame(np.random.uniform(0, 1, size=(3, 1)), columns=['V'], index = ['mean', 'std', 'delta'])

Values
        V
mean    0.885185
std     0.262265
delta   0.790134

Then I have a model, it is linked to Values by 'cpt' columns but doesn't have the same shape at all.
Model = pd.DataFrame([['JAVA','mean',10],['Python','std',5],['JS','sqrt',6],['JAVA','dif',3]],
                  columns = ['Language', 'cpt' , 'Id'])

Model
    Language    cpt     Id
0   JAVA        mean    10
1   Python      std     5
2   JS          sqrt    6
3   JAVA        dif     3

I need to find the Id corresponding in the model to the cpt for each value.
I write the function as if I can vectorize it.
def findId(Values, Model):
    return (Model[Model.cpt == Values].Id.values)

The output of the function is then
ValueError: Lengths must match to compare

because the Model parameter is also vectorized.
How can I do to pass the parameter 'Model' to the function and that it will not be considered as the same size parameter?
I could write a loop like that one but it's the initial problem I'm trying to tackle:
def loopfindId(Values, Model):
    ScaleNbrs = []
    for i in range (len(Values)):
        ScaleNbrs.append(findId(Values.index[i], Model))
    return ScaleNbrs

loopfindId(Values, Model)
[array([10], dtype=int64), array([5], dtype=int64), array([], dtype=int64)]

However, even if I get almost the desired result  it is very slow because I have to process that way a lot of times in the algorithm and it has to process it a million times.
I'm not 100% sure of the results I desire from that step but after getting the Id for each Value I will have to check if the value is inside a row of a table depending on the Id.
The DataFrame of the Id will look likes:
Scale = pd.DataFrame([['LevelA', 0, 0.3, 10],['LevelB', 0.3, 1, 10],
                      ['LevelA', 0, 0.2, 3],['LevelB', 0.2, 0.6, 3],['LevelC', 0.6, 1, 3]],
                  columns = ['Level', 'lowerBound', 'upperBound', 'Id'])

      Level     lowerBound  upperBound  Id
0     LevelA    0.0         0.3         10
1     LevelB    0.3         1.0         10
2     LevelA    0.0         0.2         3
3     LevelB    0.2         0.6         3
4     LevelC    0.6         1.0         3

Then I need to know in which level is the Value and also other pieces of information about the row and its position respectively to the other levels available In the Scale DataFrame.
That's why I would like to introduce the DataFrame as a parameter of a function but it may have a better way to do it.

A: You didn't provide an expected output but based on what you wrote I think an index merge is what you want
Model.set_index('cpt').merge(Values, left_index=True, right_index=True)

     Language  Id         V
mean     JAVA  10  0.754550
std    Python   5  0.931809

An isin lookup might work as well if merge is taking too much memory
Model.loc[Model['cpt'].isin(Values.index)]
  Language   cpt  Id
0     JAVA  mean  10
1   Python   std   5

redpajama_set_name: RedPajamaStackExchange


text:
Nigeria LNG awards two LNG carrier time charters to Golar
édité le 19/01/2015 - Plus de news de "Golar LNG" - Voir la fiche entreprise de "Golar LNG"
Golar LNG announced that it has been awarded 2 time charters by Nigeria LNG Ltd ("NLNG") to employ the recently delivered Golar Frost and Golar Crystal. Employment of both vessels under these contracts will commence in January 2015 and will continue for a duration of approximately 12 months for each vessel.
NLNG has elected to retire earlier than planned 3 of its smaller and less efficient LNG Carriers and to replace these with Golar's more modern and technically advanced ships, while NLNG awaits the delivery of its own recently ordered new vessels. Golar's CEO Doug Arnell commented "Golar is delighted to be selected by NLNG for these charters. This new business opportunity provides the clearest possible demonstration of the significant benefits available from the vessels delivered under Golar's existing new-building program. Significant reduction in boil-off and a material improvement in fuel efficiency have contributed to the decision to replace the older vessels with Golar's new buildings".
About Golar LNG
Golar is one of the world's largest independent owners and operators of LNG carriers with over 40 years of industry experience. Golar's innovation delivered the world's first Floating Storage and Regasification Units (FSRU) based on the conversion of existing LNG carriers. The project in Cameroon now demonstrates Golar's latest strategic move to extend its business model further upstream by deploying its floating liquefaction technology (GoFLNG). The objective is to become the industry's leading integrated midstream LNG services provider, supporting resource owners, gas producers and gas consumers.
Origine : Communiqué Golar LNG
Voir la fiche entreprise de "Golar LNG"
Les dernières news de "Golar LNG"
21/07/2021 - Golar, Perenco and SNH agree increased capacity utilisation of FLNG Hilli Episeyo
14/01/2021 - Golar LNG Limited and Stonepeak Infrastructure Partners to Sell 100% of Hygo Energy Transition Ltd. to New Fortress Energy
28/12/2020 - Golar LNG : Acceptance and sale of FSRU LNG Croatia
02/10/2020 - End of FLNG Gimi Force Majeure Events
24/07/2020 - Golar Power takes major step towards one of world's largest GHG reduction initiatives
08/04/2020 - Golar LNG : FLNG Gimi Force Majeure claim
16/03/2020 - Golar Power signs a Protocol of Intentions with the State Government of Pernambuco to develop an LNG import terminal in the Port of Suape, Brazil
19/02/2020 - Golar Power forms Partnership with BR Distribuidora
23/10/2019 - Golar Power awarded PPA for 605MW LNG-to-Power Project in Barcarena, Brazil
16/05/2019 - Golar LNG Limited business update
27/02/2019 - Golar LNG enters into an agreement to supply a FLNG unit to BP for phase 1 of the Greater Tortue / Ahmeyim Project, West Africa
17/12/2018 - Golar LNG receives Limited Notice to Proceed for an FLNG vessel for Phase 1 of the Greater Tortue / Ahmeyim Project, West Africa
01/10/2018 - Stolt-Nielsen Limited, Golar LNG Ltd and Hoegh LNG Holdings Ltd Announce Joint $182 Million Investment in Avenir LNG Ltd
05/06/2018 - Golar LNG: FLNG Hilli Episeyo - Customer Acceptance
20/04/2018 - Golar LNG enters into a Preliminary Agreement and exchanges Heads of Terms for an FLNG vessel for Phase 1A of the Greater Tortue / Ahmeyim Project, West Africa
12/03/2018 - Golar LNG: FLNG Hilli Episeyo and Gandria update
02/10/2017 - FLNG Hilli Episeyo departs Keppel Shipyard
21/08/2017 - Golar LNG Limited: Fortuna FLNG Offtake Awarded to Gunvor
17/08/2017 - Golar LNG Limited - Sale of an Interest in the FLNG, Hilli Episeyo
22/06/2017 - Golar LNG and Delfin Midstream sign agreement to jointly develop the Delfin LNG Project in the US Gulf of Mexico
15/11/2016 - Golar Power enters into long term SPA with Qatar Petroleum Affiliate Ocean LNG Limited
20/06/2016 - Golar and Stonepeak launch Golar Power
02/05/2016 - Golar and Schlumberger reaffirms commitment to Framework Agreement
24/01/2016 - Golar LNG and Schlumberger sign Memorandum of Understanding
04/11/2015 - Golar and West African Gas Limited Agree Ghana FSRU Contract
19/10/2015 - Golar Cameroon FLNG Project Update: Tolling Term Sheet Signed and Executed by Perenco and SNH
01/10/2015 - Golar Cameroon FLNG Project Reaches Major Milestone
18/08/2015 - Dynagas Ltd., GasLog Ltd. and Golar LNG Ltd. have entered into an agreement to establish and operate an LNG Carrier Pool
23/07/2015 - Golar Enters Into Agreements for Third Floating Liquefaction Facility
01/07/2015 - Golar and Perenco agree the material commercial terms for the floating liquefied natural gas export project in Cameroon
11/06/2015 - Golar and Stolt-Nielsen Limited to Jointly Explore Developments within Small-Scale LNG Production and Distribution
05/05/2015 - Golar commences negotiations for the Company's third GoFLNG vessel
05/05/2015 - Ophir Energy plc appoints Golar as Midstream Partner for Fortuna FLNG Project in Equatorial Guinea
05/03/2015 - Golar LNG Limited and Rosneft Oil Company sign a Memorandum of Understanding for cooperation in the area of FLNG
19/01/2015 - Nigeria LNG awards two LNG carrier time charters to Golar
31/12/2014 - Golar Enters Into Agreements for Second Floating Liquefaction Vessel
26/12/2014 - Golar signs Heads of Agreement for the development of a Floating Liquefaction export project in Cameroon
07/08/2013 - Golar LNG Awarded Kuwait FSRU Contract
07/08/2013 - Golar LNG Limited: Jordan FSRU Time Charter Party Execution
27/02/2012 - Golar LNG - Increasing the Company's New Building Investment
14/02/2012 - Golar LNG - Expanding fleet
20/04/2011 - GOLAR LNG LIMITED - Further New Building LNG Carriers
13/04/2011 - Golar LNG Limited announces that it has entered into a firm contract to build four 160,000 m3 LNG carrriers with Samsung


text:
Raimi's Warcraft movie could get iffy
January 18, 2010 By Jacob
With Sam Raimi officially out as the director for the new Spider-Man movie, focus is now on what his next project will be.
If last July's announcement from Blizzard Entertainment and Legendary Pictures will be our basis, then Raimi is going to direct a movie based on the geek-attracting Warcraft universe. Many a geek have lost sleep playing the excellent real time strategy games of Warcraft, and we haven't even touched on the kind of insane obsession people have on World of Warcraft, the MMORPG that has been the cause of many breakups, divorces, and a growing number of 20 year old virgins.
The Warcraft universe would really be perfect for Raimi, whose vision is perfect for the kind of high fantasy world that Warcraft will absolutely require. Even though a screenwriter has also been announced last October (Robert Rodat, who wrote The Patriot) and the film is in the outline/story phase it looks like Raimi actually hasn't made a final decision yet. It seems that the Spider-Man announcement took some of the wind off his sails and he's now reconsidering all of his options before committing fully to a project. Rumblings are that he is leaning towards making a small film first — maybe to take the slimy taste off his mouth after being shafted by a big movie studio — especially since he had a lot of fun making "Drag Me To Hell." But, again, everything's still up in the air.
Spidey 4 and 5 to be shot back to back?
September 5, 2008 By Polly
Rumors are abuzz that director Sam Raimi and Tobey Maguire has signed on to work on Spider-man 4 and Spider-man 5. The plan is that the movies will be shot using a script by James Vanderbilt, which is going to span two films. The first of the two movies is reportedly slated to be released on 2011.
There are no news about Kirsten Dunst but Dunst's Mary Jane Watson character will be featured in the movies. There are no reports though of recasting for the role.
Principal photography for the movies will reportedly begin fall of 2009 and only by then will the villain be determined. The early buzz though is that it will be The Lizard, which is Dylan Baker's character Dr. Curt Connors.
Venom movie eyed
July 31, 2008 By Polly
The prospects of a Spider-Man sequel is still up in the air but Sony Pictures is not willing to wait anymore and has unveiled the possibility of spin-off movies being produced instead.
The first spin-off could be the Venom movie. The plan is to extend the life of the Spider-Man franchise, which is already showing its age. This is the same tactic that's been used on the X-Men franchise with the upcoming Wolverine movie.
A script has already been commissioned and casting is a no-brainer with Topher Grace, who played the role of Venom in the third Spidey sequel. But agents are also eyeing the role for other actors because of the belief that Grace still cannot carry a picture on his own.
Raimi in 'sequel' updates
June 6, 2008 By Polly
If there's one director who is frequently involved in sequel rumors it has got to Sam Raimi. A number of projects he has been involved with have been the constant fodder for speculations of follow-up movies. Fortunately, Raimi has officially spoken and we can now dismiss many of the rumors surrounding his movies.
With regards to the Spider-Man sequel, Raimi said that writer James Vanderbilt is about to finish the script to the next sequel. Raimi has gone on to say that he is excited to read the script and he hopes that it is good enough that he will want to be involved again. he also hopes that Sony will be of the same mind and will want to hire him for a possible sequel. In other words, everything is still up in the air.
The Evil Dead remake, on the other hand, is still stalled. Raimi said that they are interested to do the project but he hasn't been able to do anything with regards to the project. As far as the possibility of having a 30 Days of Night sequel, this project is, for all intents and purposes, dead in the water.


text:
(Lao People's Democratic Republic)
Ground transport infrastructure
Interpretative and visitation facilities
Urban Pressure; Tourism Pressure; Lack of management mechanism (including legislation); Lack of presentation and interpretation.
1999 Preparation of the nomination dossier for Vat Phu ... (Approved) 13,000 USD
The State Party submitted a state of conservation report to the World Heritage Centre, as requested by the World Heritage Committee at its 27th session.
Following decision 27 COM 7B.51, the State Party informed the Secretariat that a consultation meeting with the Ministry of Communications, Transport, Posts and Construction has been organized to decide on the road construction within the World Heritage property. Once the full documentation on the project is received by the Ministry of Information and Culture, a consultation meeting will be convened with UNESCO. The Secretariat was also informed that the transfer of the visitor centre and its parking lot was under study, and the project would be re-examined by the consultant who recommended its relocation out of the buffer zone.
To improve the management and regular monitoring of the property, the Vat Phou Site Management Authority has recruited a new site manager and qualified staff (1 architect, 1 archaeologist, 1 art historian, 1 engineer, etc.), totalling 29 people. The State Party has also reported the coexistence of two committees, the National Inter-ministerial Coordinating Committee (NIMCC) and the Champasak local Committee for Cultural and Natural Heritage, with similar roles, responsibilities and members.
As a follow-up to the Japan International Cooperation Agency (JICA) bilateral grant to improve the state of conservation of the World Heritage property, the maintenance of the fully functioning hydraulic system is ensured by the local staff with the assistance of a Japanese expert, dispatched to the site on a regular basis.
28 COM 15B.65
1. Congratulates the State Party on the actions undertaken to comply with the recommendations of the World Heritage Committee adopted at its 27th session in July 2003;
2. Reiterates the importance of adherence to the government-approved management plan for the property;
3. Encourages the State Party to clarify the distribution of tasks among the different national and provincial authorities involved in the protection and management of the World Heritage property, so as to avoid overlapping of their responsibilities and roles.
Draft Decision: 28 COM 15B.65
Criteria: (iii)(iv)(vi)
WHC-04/28.COM/15B


Shakira concert tickets are on sale. You can find the list of Shakira tour dates here.
Shakira Isabel Mebarak Ripoll, known as Shakira, is a Colombian singer-songwriter, dancer, record producer, choreographer, and model. Born and raised in Barranquilla, she began performing in school, demonstrating Latin, Arabic, and rock and roll influences and belly dancing abilities. In the early 1990s, Shakira emerged in the music industry of Colombia and rose to prominence in Latin America with her official debut studio album Pies Descalzos. Her second album Dónde Están los Ladrones? sold over 7 million copies worldwide. In 2001, Shakira crossed into the English market with her third album Laundry Service, which sold over 15 million copies worldwide; her first English single "Whenever, Wherever" became the best selling single of 2002. Her success was solidified with her fourth and fifth albums Fijación Oral Vol. 1 and Oral Fixation Vol. 2, the latter of which spawned the best-selling song of the 21st century, "Hips Don't Lie". Shakira's sixth album She Wolf gained critical praise for her writing skills, and sold 2 million copies internationally. Her seventh album Sale el Sol returned to styles of her Latin heritage, and sold 4 million copies worldwide. However, Shakira suffered from a strained relationship with her label Epic Records since 2009, which resulted in a lack of promotion and investment towards both of the latter releases. Her official song for the 2010 FIFA World Cup "Waka Waka" became the biggest-selling World Cup song of all time. On YouTube, the English version of the music video is the 7th most watched video of all time with over 500 million views. Since 2013, Shakira has served as a coach on the fourth season of the American version of The Voice.


text:
Evgeny Nagovitsyn
Born in Leningrad in 1986, studied at the Rimsky-Korsakov Music College and Saint-Petersburg Rimsky-Korsakov State Conservatoire (Olga Kondina's class).
In 2007, he joined the Saint-Petersburg Opera theatre where his repertoire included Don Ottavio in Don Giovanni, Alfredo in La Traviata, Beppo in I Pagliacci, Rodolfo in La Bohème, Kochkaryov in Mussorgsky's Marriage, The Tenor in White Nights by Yu. Butzko, Antonio in Prokofiev's Betrothal in a Monastery, Arturo in Lucia di Lammermoor and The Simpleton in Boris Godunov. In the season 2010/11 he worked with the Mikhaylovsky Theatre (Saint-Petersburg) where he sang Lensky (Eugene Onegin), Rodolfo (La Bohème), Lykov (The Tsar's Bride), Vaudémont (Iolanta) and Kudrjáš (Janáček's Káťa Kabanová).
Since 2011, Evgeny is a member of the Young Artist Programme of the Bolshoi Theatre where he debuted as The Prince in Prokofiev's The Love for Three Oranges. His other parts in the Bolshoi are Lykov in The Tsar's Bride and Pong in Turandot.


text:
Q: Spring boot application whitelabel error page I'm getting whitelabel error page 404 with my springboot application. I am hardcoding a list of students and they should pop as firstname basis to the page. I've tried different approaches with the template but nothing seems to work. I also tried to do /* endpoint but didn't have any effect aswell. I couldn't find any relevant questions for this problem that would fix my problems. These are the different classes;
Controller;
public class StudentController {

private List<Student> studentList = new ArrayList<>();

@GetMapping("/hello")
public String friendListing(Model model) {
    Student student1 = new Student("Kate", "Cole");
    studentList.add(student1);
    Student student2 = new Student("Dan", "Brown");
    studentList.add(student2);
    Student student3 = new Student("Mike", "Mars");
    studentList.add(student3);
    model.addAttribute("studentList", studentList);
    return "hello";
}}

Model;
public class Student {

private String firstName;
private String lastName;

public Student(String fn, String ln) {
    this.firstName = fn;
    this.lastName = ln;
}

public String getFirstName() {
    return firstName;
}
public void setFirstName(String firstName) {
    this.firstName = firstName;
}
public String getLastName() {
    return lastName;
}
public void setLastName(String lastName) {
    this.lastName = lastName;
}
@Override
public String toString() {
    return firstName + " " + lastName;
}}

And view;
<!DOCTYPE HTML>
<html xmlns:th="http://www.thymeleaf.org">
    <head>
        <title>Server Programming with Spring Boot</title>
        <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
    </head>
    <body>
        <tr th:each="student: ${studentList}">
        <td  th:text="${student.firstName}"></td>
        </tr>
    </body>
</html>

A: Where is your main application class?

*

*Use @ComponentScan annotation with you controller class package

*Controller class should have @Controller annotation.


Governor Bullock is committed to investing in education, at all levels. He knows that we can maintain Montana's competitiveness through smart targeted investments and that's why he has made funding education one of the pillars of his budget.
Governor Bullock proposes targeted investments in workforce development and educational opportunities, from preschool to adult learning, to maintain Montana's competitiveness nationally. Through these investments, we can prepare Montanans for success in a 21st Century economy and build a more talented and trained workforce to meet growing and changing workforce demands.
Governor Bullock proposes an investment of $30 million over the biennium in high-quality preschool with funding made available to public schools, Head Start programs, and community-based providers to create or expand services for preschool-aged Montana kids. Governor Bullock believes in building on the success of Montana's STARS Preschool pilot program that passed with bipartisan support in the 2017 legislative session to increase access to more high-quality, affordable preschool options in rural and urban communities.
A report on the first year of the pilot program found that in both very rural communities and urban settings, 93% of preschoolers who participated were ready for kindergarten at the end of the year and 94% of teachers were given effective opportunities to grow professionally.
A poll by the Bozeman Daily Chronicle shows that over 64% of Montanans support this investment in Pre-K.
Governor Bullock also proposes to freeze college tuition across the Montana University System and invest in financial aid for students seeking two-or four-year degrees, including returning adult learners. Most jobs in Montana require training beyond a high school diploma, and Montana has set a goal of 60% of Montanans attaining a post-secondary degree or credential, yet for many Montanans, cost is a barrier to get the training they need to get a good job.
Governor Bullock believes in increasing affordable access to post-secondary education and training to ensure students are prepared for jobs in a 21st Century economy. He froze tuition in the 2013 and 2015 legislative sessions, helping to keep Montana with the 4th most affordable college tuition in the nation.
Governor Bullock also proposes to prepare the workforce of tomorrow by investing in professional development for computer science teachers. An increasing number of occupations requires workers to have at least some level of basic technology literacy and proficiency, and computer science occupations are high wage and in high demand across Montana. By increasing training opportunities for teachers, we can ensure that all students gain the skills they need to choose this career pathway.
Governor Bullock's budget also includes an inflationary adjustment for K-12 funding and for special education funding, which is an investment critical to helping districts keep up with the costs of providing intervention and support services for some of our most vulnerable students.
I support the governor's proposal and was glad to see the poll results in the Chronicle. But please note that this poll is NOT scientific. Any reader–actually anyONE–can participate, and I'm not even sure there's a mechanism to insure that respondents are limited to one response per person. The results are encouraging but do not suggest that widespread public support can be taken for granted.


This article is a guide for businesses on how to use the Jobletics application to request shifts.
The holiday season can be quite expensive. Here are some expenses you can keep in mind to save you from the stress this upcoming season.
Jobletics 101: How to Schedule an Interview as a Worker?
This post dives into the steps you need to take to sign up all the way to setting up your interview to start working at Jobletics.
How in the world can a restaurant job prepare me for life? This post dives into the skills that can be learned working in food service.
Uber Drivers are Making Less than Servers: Why Is That?
This post explains the costs of the gig economy and highlights how Uber and Lyft drivers don't make as much money as one would assume.


text:
\section{Introduction}

The nonlinear Schr\"{o}dinger equation (NLSE) and its generalisations have interested researchers for many years, due to the richness of their mathematical structure and the breadth of their applications to fields such as electronics, optics, plasma physics, molecular biophysics, \emph{et cetera} \cite{shabat1972exact,hirota1973exact,kevrekidis2016solitons,davydov1979solitons,luo2018directed}. A natural generalisation is raising the number of spatial dimensions. Exact analytical solutions to the 2D NLSE are known, and relate to the propagation of acoustic disturbances in a static cosmological background \cite{Seadawy2012,kates1988two}. The 3D version, also known as the Gross–Pitaevskii equation, has been studied for the existence and blow-up properties of its solutions, and is a model for Bose-Einstein condensates \cite{holmer2007,holmer2010,duyckaerts2008scattering,dalfovo1999theory,garcia2003quasi}. An $N$-dimensional variant where the cubic nonlinearity is replaced by a $p$\textsuperscript{th}-power nonlinearity, with $ p > 1 + \genfrac{}{}{}1{4}{N} $, has been analysed, its blow-up criteria established \cite{duyckaerts2015going}.

In other developments, a modified NLSE has been proposed as a continuum model of electron self-trapping in an $N$-dimensional lattice, and its stationary solutions have been found \cite{brizhik2001electron,brizhik2003static,Luo2017}. Non-stationary, \textit{soliton} solutions exist for many generalisations or modifications of the NLSE, including ones with higher-power nonlinear terms, trigonometric nonlinear terms or extra derivatives, and studies of these solutions have influenced modern technologies such as optical fibres \cite{hasegawa1973transmission1,biswas2008femtosecond,chen2010formation,hosseininia2018wavelet}, with some solutions having analytical expressions \cite{potasek1991exact,bulut2018optical,benia2019exact,gao2020instability}. However, exact soliton solutions to modified NLSEs remain rare.

In this work, we investigate a novel modified NLSE in two spatial dimensions, and construct an exact analytical solution representing a soliton. We show that the equation has physical origins in the system of an exciton coupled to a collectively oscillating plane lattice, and hence that the soliton solution represents a propagating exciton wavefunction in the lattice. We characterise the soliton's shape and velocity, and detail how they depend on parameters of the physical system. Though we focus on a 2D equation, the method developed herein is readily applicable to higher-dimensional generalisations.

    \section{The equation and soliton solutions}

We consider the equation,
    \begin{align}
    & i \partial_t \psi + \partial_{xx} \psi + \sigma \partial_{yy} \psi + \kappa | \psi |^2 \psi - \lambda ( \partial_{xx} | \psi |^2 ) \psi = 0, \label{eq-GNLSE}
    \end{align}
for a complex-valued function $ \psi $ of $ x \in \mathbb{R} $, $ y \in (-\genfrac{}{}{}1{1}{2},\genfrac{}{}{}1{1}{2}) $, $ t > 0 $, with real constants $ \kappa > 0, \lambda > 0 $, and $ \sigma \neq 0 $. We seek non-trivial solutions with vanishing value and derivatives at $ x \rightarrow \pm \infty $, which are normalised:
    \begin{align}
    \int_{-1/2}^{1/2} \int_{-\infty}^{\infty} | \psi (x,y,t) |^2 ~\d x ~\d y = 1. \label{eq-GNLSE-norm}
    \end{align}
The travelling wave ansatz,
    \begin{align}
    \psi (x,y,t) = f ( \xi ) \exp( i \eta ), \quad \textnormal{where } \xi = x + ay - [ 2 + \sigma b (1+a) ] t, \quad \eta = x + by - Et,
    \end{align}
where $ f $ is a real smooth function and $ a,b,E $ are real constants, transforms \eqref{eq-GNLSE} into
    \begin{align}
    - ( 1 + \sigma b^2 - E ) f + ( 1 + \sigma a ) f'' + \kappa f^3 - \lambda (f^2)'' f = 0, \label{eq-GNLSE-2}
    \end{align}
with $'$ denoting differentiation with respect to $ \xi $.

\subsection*{Case I. $ 1 + \sigma a = 0 $.}

With $ 1 + \sigma a = 0 $, \eqref{eq-GNLSE-2} is significantly simplified. Requiring $f \not \equiv 0$, we deduce $ - ( 1 + \sigma b^2 - E ) + \kappa f^2 - \lambda (f^2)'' = 0 $, which is a linear ODE for $f^2$ with the solution $ f^2 = (1 + \sigma b^2 - E) / \kappa + B \exp ( \xi \sqrt{ \kappa / \lambda } ) + C \exp ( - \xi \sqrt{ \kappa / \lambda } ) $, for some arbitrary constants $ B,C $. It is therefore impossible for a non-trivial $f$ to satisfy vanishing boundary conditions, and so we must require $ a \neq - 1 / \sigma $.

\subsection*{Case II. $ 1 + \sigma a > 0 $.}

With $ 1 + \sigma a > 0 $, we use $ ( f^2 )'' \equiv 2ff'' + 2(f')^2 $ to rewrite \eqref{eq-GNLSE-2} as
    \begin{align}
    - E_0 f + ( 1 - 2 \lambda_0 f^2 ) f''  + \kappa_0 f^3 - 2 \lambda_0 (f')^2 f = 0, \label{eq-GNLSE-caseII}
    \end{align}
where
    \begin{align}
    E_0 = \frac{1 + \sigma b^2 - E}{1 + \sigma a}, \quad \lambda_0 = \frac{\lambda}{1 + \sigma a} > 0, \quad \kappa_0 = \frac{\kappa}{1 + \sigma a} > 0. \label{eq-GNLSE-caseII-consts}
    \end{align}
Noticing that $ f' \d f' / \d f \equiv f'' $ (assuming $f'$ is a well-defined function of $f$), and therefore $ ( 1 - 2 \lambda_0 f^2 ) f''  - 2 \lambda_0 (f')^2 f \equiv \frac{\d}{\d f} [\frac{1}{2} ( 1 - 2 \lambda_0 f^2 ) (f')^2 ] $, we integrate \eqref{eq-GNLSE-caseII} with respect to $f$ to obtain
    \begin{align}
    ( 1 - 2 \lambda_0 f^2 ) (f')^2 = E_0 f^2 - \frac{1}{2} \kappa_0 f^4 + C, \label{eq-GNLSE-caseII-2}
    \end{align}
where $C = 0$ since $ f $ has vanishing value and derivatives at infinity.

Suppose $ 1 - 2 \lambda_0 f^2 $ could vanish at some value of $f$. Then both sides of \eqref{eq-GNLSE-caseII-2} must vanish at that $f$, from which we derive $ 4 E_0 \lambda_0 / \kappa_0 = 1 $, which is a highly restrictive condition on the parameters. To allow for a variety of travelling wave behaviour depending on parameter values, we reject the restrictive condition and require that $ 1 - 2 \lambda_0 f^2 $ never vanishes. Since $f$ is smooth and $ 1 - 2 \lambda_0 f(\infty)^2 = 1 > 0 $, we have $ 1 - 2 \lambda_0 f^2 > 0 $ for all $f$.

If $ E_0 \le 0 $, then the right-hand side of \eqref{eq-GNLSE-caseII-2} is negative whenever $ f \neq 0 $, so it cannot equal the left-hand side; that is, the only $ f $ satisfying \eqref{eq-GNLSE-caseII-2} is identically zero. We therefore require $ E_0 > 0 $, i.e.,
    \begin{align}
    1 + \sigma b^2 - E > 0. \label{eq-GNLSE-caseII-constraint}
    \end{align}
Multiplying \eqref{eq-GNLSE-caseII-2} by $4f^2 / ( 1 - 2 \lambda_0 f^2 )$, we find
    \begin{align}
    (F')^2 = \frac{4 E_0 F^2 - 2 \kappa_0 F^3}{1 - 2 \lambda_0 F} := G(F), \label{eq-GNLSE-caseII-F}
    \end{align}
where we have defined $ F := f^2 $.

Equation \eqref{eq-GNLSE-caseII-F} is invariant under translation and reflection (as is equation \eqref{eq-GNLSE-caseII}), meaning that if $ F(\xi) $ is a solution then so is $ F(const - \xi) $. Therefore we look for solutions which are reflectively symmetric about some point, which we set without loss of generality to $ \xi = 0 $. Then, $ F'(0) = 0 $ implies either $ F(0) = 0 $ or $ F(0) = 2 E_0 / \kappa_0 $. Suppose $ F(0) = 0 $; then, since $ F(\infty) = 0 $ and $F$ is smooth, there must exist some $\xi_0 \in (0,\infty)$ where $F'(\xi_0) = 0$ and $F(\xi_0) = 2 E_0 / \kappa_0 $. We therefore invoke the translational invariance again to set $\xi_0 = 0$ without loss of generality. Thus,
    \begin{align}
    F_0 := F(0) = \frac{2 E_0}{\kappa_0} > 0. \label{eq-GNLSE-caseII-F0}
    \end{align}
We see that $F(\xi)$ cannot exceed $F_0$, since if it did, then there is no greater value of $F$ at which $F'$ can vanish. That is to say, $ \max_{\xi \in \mathbb{R}} F (\xi) = F_0 $. It is easy to check that for all $F \in (0,F_0)$, we have $G(F) > 0$.

Since $F$ must vanish at infinity, we seek $F$ such that
    \begin{align}
    F'(\xi) = - \textnormal{sgn} (\xi) \sqrt{G(F)} , \label{eq-GNLSE-caseII-3}
    \end{align}
where $ \textnormal{sgn} $ is the sign function. Using the change of variable
    \begin{align}
    Z ( \xi ) = \textnormal{arsech} \sqrt{ F(\xi)/F_0 } ,
    \end{align}
and the fact that $ \sqrt{G(F)} = 2 \sqrt{E_0} F \sqrt{\genfrac{}{}{}1{1 - (F/F_0)}{1 - 2 \lambda_0 F}}$, we deduce
    \begin{align}
    Z'(\xi) = \frac{ \textnormal{sgn} (\xi) \sqrt{E_0} }{\sqrt{1 - 2 \lambda_0 F}} = \frac{ \textnormal{sgn} (\xi) \sqrt{E_0} }{\sqrt{1 - 2 \lambda_0 F_0~ \textnormal{sech}^2 Z}}. \label{eq-GNLSE-caseII-4}
    \end{align}
Integrating \eqref{eq-GNLSE-caseII-4} and invoking the vanishing boundary condition, we find
    \begin{align}
    \sqrt{E_0} ~| \xi | = \textnormal{\textnormal{arsinh}} \sqrt{ \frac{1 - \widetilde{F}}{\widetilde{F} - \mu^2 \widetilde{F}} } - \mu ~\textnormal{artanh} \sqrt{\frac{ 1 - \widetilde{F} }{(1/\mu^2) - \widetilde{F}}}, \label{eq-GNLSE-caseII-soln}
    \end{align}
where $ \mu = \sqrt{ 2 \lambda_0 F_0 } $, $ \widetilde{F} = F / F_0 $, and we have used the positivity of $Z$ to write $ \sinh Z = \sqrt{ (1/\widetilde{F}) - 1 } $.

The right-hand side of \eqref{eq-GNLSE-caseII-soln} is a strictly decreasing, unbounded function of $\widetilde{F}$ (setting $\widetilde{F} = 0$ makes the right-hand side blow up as required), so \eqref{eq-GNLSE-caseII-soln} uniquely determines $\widetilde{F}$ given any $\xi$. Re-introducing $x,y,t,\psi$ yields an exact solution to \eqref{eq-GNLSE}:
    \begin{subequations} \label{eq-GNLSE-caseII-soln-re}
    \begin{align}
    &\psi(x,y,t) = f(x+ay - c t) \exp [ i ( x+by - E t ) ] ,\quad \textnormal{where } \sigma b (1+a) = c - 2 \textnormal{ and} \\
    &\sqrt{\frac{ 1 + \sigma b^2 - E }{1 + \sigma a}} ~| x+ay - c t | = \textnormal{\textnormal{arsinh}} \sqrt{ \frac{1 - \widetilde{f}^2}{\widetilde{f}^2 - \mu^2 \widetilde{f}^2} } - \mu ~\textnormal{artanh} \sqrt{\frac{ 1 - \widetilde{f}^2 }{(1/\mu^2) - \widetilde{f}^2}},  \label{eq-GNLSE-caseII-soln-re2} \\
    &\textnormal{with } \mu = \sqrt{ \genfrac{}{}{}1{4 \lambda }{ \kappa ( 1 + \sigma a ) } \left( 1 + \sigma b^2 - E \right)} ,~ \widetilde{f} = f / f_0 \textnormal{ and } f_0^2 = f(0)^2 = \genfrac{}{}{}1{ 2 }{ \kappa } \left( 1 + \sigma b^2 - E \right) .
    \end{align}
    \end{subequations}
The solution \eqref{eq-GNLSE-caseII-soln-re} is parametrised by real constants $a,c,E$ satisfying the constraint [cf. \eqref{eq-GNLSE-caseII-constraint}]:
    \begin{align}
    H(a,c,E) := ( 1 + \sigma b^2 - E )(1+a)^2 \equiv (1 - E) (1+a)^2 + \frac{ (c-2)^2 }{ \sigma } \ge 0 . \label{eq-GNLSE-caseII-constraint2}
    \end{align}
The normalisation condition \eqref{eq-GNLSE-norm} imposes an extra constraint, which we derive as follows. Consider
    \begin{align}
    1 = \int_{-1/2}^{1/2} \int_{-\infty}^{\infty} | \psi (x,y,t) |^2 ~\d x ~\d y = \int_{-\infty}^{\infty} \frac{ f^2 }{ Z'(\xi) } \frac{\d x}{\d \xi} \d Z.
    \end{align}
Note that the $y$-integral is trivial because the $x$-domain is all of $\mathbb{R}$. Using the evenness of $f^2 = f_0^2 \textnormal{sech}^2 Z $, we further deduce
    \begin{align}
    1 = 2 \int_0^{\infty} \frac{ f^2}{ Z'(\xi > 0) } \d Z = 2 \int_0^{\infty} \frac{ ( f_0^2 \textnormal{sech}^2 Z ) \sqrt{ 1 - \mu^2 \textnormal{sech}^2 Z } }{ \sqrt{E_0} } \d Z,
    \end{align}
and hence
    \begin{align}
    \frac{ \sqrt{E_0} }{ 2 f_0^2 } = \frac{1}{2} + \frac{\left( 1 - \mu^2 \right) \textnormal{artanh} (\mu)}{2 \mu} . \label{eq-GNLSE-caseII-tr}
    \end{align}
Multiplying \eqref{eq-GNLSE-caseII-tr} by $ 2 \mu \equiv 2 \sqrt{ 2 \lambda_0 f_0^2 } $ yields a transcendental equation for $\mu$:
    \begin{align}
    \frac{ \sqrt{ \lambda \kappa } }{ 1 + \sigma a } = \mu + ( 1 - \mu^2 ) \textnormal{artanh} (\mu) := I(\mu) . \label{eq-GNLSE-caseII-5}
    \end{align}
By considering the graph of $I(\mu)$ for $\mu \in (0,1)$ [Figure \ref{fig-1}a], we conclude the following. Given any $\kappa,\lambda > 0$ and $\sigma > 0$ ($\sigma < 0$), the left-hand side of \eqref{eq-GNLSE-caseII-5} is a decreasing (increasing) function of $a > -1/\sigma$ ($a <-1/\sigma$), therefore: if $a$ is sufficiently large (small) then \eqref{eq-GNLSE-caseII-5} uniquely determines $\mu$; if $a$ is sufficiently small (large) then no value of $\mu$ satisfies \eqref{eq-GNLSE-caseII-5}; and if $a$ is moderate then \eqref{eq-GNLSE-caseII-5} determines two distinct values of $\mu$. The constant $a$ is therefore constrained by $a \ge a_{\textnormal{c}}(\lambda)$ if $\sigma > 0$ or $a \le a_{\textnormal{c}}(\lambda)$ if $\sigma < 0$, where $a_{\textnormal{c}}$ is such that $\sqrt{\lambda \kappa} / (1+\sigma a_{\textnormal{c}}) = \max I$ [Figure \ref{fig-1}b].
\begin{figure}[t]
\centering
\includegraphics[width=0.75\textwidth]{./fig1.pdf}
\captionsetup{width=\textwidth}
\caption{The existence and uniqueness of $ \mu $ according to \eqref{eq-GNLSE-caseII-5}, depending on the values of $\kappa,\lambda,\sigma,a$. (a) $I(\mu)$ for $\mu \in (0,1)$. To every $I \in (0,1] \cup \{ \max I \approx 1.19968 \} $ there corresponds a unique $\mu$. To every $I \in (1,\max I)$ there corresponds two distinct $\mu$'s. (b) $a_{\textnormal{c}}(\lambda;\sigma)$ and $a_{\textnormal{u}}(\lambda;\sigma)$ are threshold values of $a$ such that $\sqrt{\lambda \kappa} / (1+\sigma a_{\textnormal{c}}) = \max I$ and $\sqrt{\lambda \kappa} / (1+\sigma a_{\textnormal{u}}) = 1$. The vertical scale is unspecified, since it is determined by the arbitrary $\kappa, \sigma $. If $\sigma > 0$ ($\sigma < 0$), then: $a \ge a_{\textnormal{u}}$ ($a \le a_{\textnormal{u}}$) or $a = a_{\textnormal{c}}$ implies unique $\mu$; $a_{\textnormal{c}} < a < a_{\textnormal{u}}$ ($a_{\textnormal{u}} < a < a_{\textnormal{c}}$) implies two distinct $\mu$'s; $-1/\sigma < a < a_{\textnormal{c}}$ ($a_{\textnormal{c}} < a < -1/\sigma$) implies no $\mu$. Given any $\kappa$ and $\sigma$, we always find $\lim_{\lambda \rightarrow 0} a_{\textnormal{c}} (\lambda) = \lim_{\lambda \rightarrow 0} a_{\textnormal{u}} (\lambda) = -1/\sigma$. Given any $\kappa$, we always find that the sign-reversal $\sigma \rightarrow -\sigma$ causes $a_{\textnormal{c}} \rightarrow - a_{\textnormal{c}}$ and $a_{\textnormal{u}} \rightarrow - a_{\textnormal{u}}$.}
\label{fig-1}
\end{figure}

\subsection*{Case III. $ 1 + \sigma a < 0 $.}

If $ 1 + \sigma a < 0 $, then \eqref{eq-GNLSE-2} becomes $ E_1 f + ( 1 + 2 \lambda_1 f^2 ) f''  - \kappa_1 f^3 + 2 \lambda_1 (f')^2 f = 0 $, where $ E_1 = - \frac{1 + \sigma b^2 - E}{1 + \sigma a},  \lambda_1 = - \frac{\lambda}{1 + \sigma a} > 0,  \kappa_1 = - \frac{\kappa}{1 + \sigma a} > 0 $. Defining $ F = f^2 $, we find by analogy to case II that
    \begin{align}
    (F')^2 = \frac{- 4 E_1 F^2 + 2 \kappa_1 F^3}{1 + 2 \lambda_1 F} . \label{eq-GNLSE-caseIII-1}
    \end{align}
Using a similar argument as for \eqref{eq-GNLSE-caseII-F0}, we establish that $ F_0 := F(0) = 2 E_1 / \kappa_1 > 0 $. Now, for all $ F \in (F(\infty)=0,F_0) $, the numerator of the right-hand side of \eqref{eq-GNLSE-caseIII-1} is negative; since the denominator is always positive, we conclude that it is impossible for a non-trivial $F$ to satisfy \eqref{eq-GNLSE-caseIII-1} and therefore reject the case of $ 1 + \sigma a < 0 $ altogether.

\subsection*{Well-posedness and permissible parameter values}

Since \eqref{eq-GNLSE} is a quasilinear PDE, its well-posedness deserves careful consideration. Given $ \kappa $, and $ \sigma > 0 $ without loss of generality, the solution \eqref{eq-GNLSE-caseII-soln-re} is parametrised by $\lambda > 0$ and $a \ge a_{\textnormal{c}}(\lambda)$, with wave speed $c$ determined by [cf. \eqref{eq-GNLSE-caseII-constraint2}]:
    \begin{align}
    &c = c^{(\pm)} = \pm \sqrt{ \sigma [H + (E - 1)(1+a)^2] } + 2.
    \end{align}
We denote by $ \psi^{(\pm)} $ the solution corresponding to $c = c^{(\pm)} $. Then, $ \psi^{(+)} $ and $ \psi^{(-)} $ are solitons with identical waveforms but distinct wave speeds, unless $c^{(+)} = c^{(-)}$. Since $ \psi^{(+)} (x,y,0) = \psi^{(-)} (x,y,0) $, we conclude that \eqref{eq-GNLSE} is well-posed \emph{only if} $H + (E-1)(1 + a)^2 = 0$, since any other case would give rise to non-unique solutions with identical initial data. Therefore,
with $\sigma,\kappa$ and $\lambda$ prescribed for \eqref{eq-GNLSE}, we first choose $a$ such that $\mu$ exists, then find $ \mu $ through \eqref{eq-GNLSE-caseII-5}; invoking $c=2$, we find in turn:
    \begin{subequations} \label{eq-c-pm}
    \begin{align}
    H &= \mu^2 \kappa (1+\sigma a) (1+a)^2 / (4 \lambda) \ge 0, \label{eq-c-pm1} \\
    E &= 1 - \mu^2 \kappa (1+\sigma a) / (4 \lambda) < 1, \label{eq-c-pm2} \\
    b^2 &= \genfrac{}{}{}1{1}{\sigma} \left( \genfrac{}{}{}1{H}{(1+a)^2} + E - 1 \right) = 0 , \label{eq-c-pm3} \\
    f_0^2 &= \mu^2 ( 1 + \sigma a ) / (2 \lambda) > 0. \label{eq-c-pm4}
    \end{align}
    \end{subequations}
In particular, using \eqref{eq-c-pm3}, and the wave speed $ c = 2 $, we simplify the solution \eqref{eq-GNLSE-caseII-soln-re}:
    \begin{subequations} \label{eq-GNLSE-caseII-soln-simp}
    \begin{align}
    &\psi(x,y,t) = f(x+ay - 2 t) \exp [ i ( x - E t ) ] , \textnormal{ and} \\
    &\sqrt{\frac{ 1 - E }{1 + \sigma a}} ~| x+ay - 2 t | = \textnormal{\textnormal{arsinh}} \sqrt{ \frac{1 - \widetilde{f}^2}{\widetilde{f}^2 - \mu^2 \widetilde{f}^2} } - \mu ~\textnormal{artanh} \sqrt{\frac{ 1 - \widetilde{f}^2 }{(1/\mu^2) - \widetilde{f}^2}}, \textnormal{ with }  \widetilde{f} = f / f_0 . \label{eq-GNLSE-caseII-soln-simp2}
    \end{align}
    \end{subequations}
As we will discuss in Section \ref{sec-disc}, the physically relevant quantity is precisely $ | \psi |^2 \equiv f^2 $, which is now computable via \eqref{eq-GNLSE-caseII-soln-simp2}. The restriction of wave speed ensures non-singularity of this solution. Meanwhile, the solution is stable with respect to perturbations in parameter space if and only if $\lambda$ is sufficiently large; we demonstrate this point with the following example.
\begin{figure}[!t]
\centering
\includegraphics[width=0.5\textwidth]{./fig2.pdf}
\captionsetup{width=\textwidth}
\caption{The maximum squared amplitude $f_0^2$ as a function of the anisotropy parameter $\lambda$ and waveform constant $a$, with $\sigma = 0.04, \kappa = 1$ and $E = 1$ fixed. The $f_0^2$ surface is folded sharply along the curve $a = a_{\textnormal{c}}(\lambda)$, so that to each $a \in (a_{\textnormal{c}}(\lambda) , a_{\textnormal{u}}(\lambda))$ there corresponds two distinct values of $f_0^2$, and for $ a = a_{\textnormal{c}} (\lambda) $ or $ a \ge a_{\textnormal{u}}(\lambda) $ there is a unique $f_0^2$. If $(\lambda,a) \rightarrow (0,-1/\sigma)$ along any curve $a(\lambda)$ where $\sqrt{\lambda \kappa} / (1+\sigma a)$ is constant, e.g.~$a = a_{\textnormal{c}}$ or $a_{\textnormal{u}}$, then $f_0^2$ blows up. Since all such $a(\lambda)$ curves unify as $\lambda \rightarrow 0$, we have $f_0^2 \rightarrow \infty$ as $(\lambda,a) \rightarrow (0,-1/\sigma)$.}
\label{fig-2}
\end{figure}
\begin{figure}[!t]
\centering
\includegraphics[width=\textwidth]{./fig3.pdf}
\captionsetup{width=\textwidth}
\caption{Propagation of the solitary wave $ | \psi |^2 $ which solves equation \eqref{eq-GNLSE} with $\sigma = 0.04, \kappa = 1$ and $\lambda = 1$. The solution is parametrised by the waveform constant $a$. (a,b) $a=5$, to which there corresponds a unique waveform. (c,d,e,f) $a=-0.2$, to which there correspond two distinct waveforms; one is represented in (c,d), the other in (e,f). (a,c,e): $ |\psi|^2 $ at $t=0$. (b,d,f): $ |\psi|^2 $ at $t=20$.}
\label{fig-3}
\end{figure}

We consider $ \sigma = 0.04 $ and $ \kappa = 1 $ for the purpose of this illustration; the solution is then parametrised by $\lambda > 0$ and $a \ge a_{\textnormal{c}}(\lambda)$ [Figure \ref{fig-2}]. In the $ a \ge a_{\textnormal{u}}(\lambda) $ region of the $(\lambda,a)$ parameter space, which we call the \textit{uni-waveform} region, $f_0^2(\lambda,a)$ is unique and barely affected by varying $\lambda$; whereas in the $ a_{\textnormal{c}}(\lambda) < a < a_{\textnormal{u}}(\lambda) $ region, which we call the \textit{bi-waveform} region, $f_0^2$ is bi-valued and one branch is more sensitive to variations in $a$ and $\lambda$ than the other branch. As $(\lambda,a) \rightarrow (0,-1/\sigma)$, $f_0^2$ blows up, meaning that the solitary wave asymptotically approaches the delta distribution. Mathematically, the blow-up of $f_0^2$ is predictable from \eqref{eq-c-pm}: if $\kappa$ and $\sqrt{\lambda \kappa} / (1+\sigma a)$ are both held constant, then as $ (\lambda,a) \rightarrow (0,-1/\sigma) $, $\mu$ remains fixed at a finite value, hence $f_0^2 \sim 1/\sqrt{\lambda}$. Since all the $a(\lambda)$ curves hold $\sqrt{\lambda \kappa} / (1+\sigma a)$ constant, and in the limit $\lambda \rightarrow 0$ they unify into $(\lambda,a) \rightarrow (0,-1/\sigma)$, we conclude that $f_0^2 \rightarrow \infty$ as $(\lambda,a) \rightarrow (0,-1/\sigma)$. The blow-up of $f_0^2$ for small $\lambda$ indicates instability of the solution in this region of parameter space.

Some representations of the $|\psi|^2$ waves can be found in Figure \ref{fig-3}, with prescribed parameters $\sigma = 0.04, \kappa = 1$ and $\lambda = 1$. For $a = 5$, there is a unique $\mu$ and hence a unique waveform, initially maximised along the line $x+5y = 0$ [Figure \ref{fig-3}a]. For $a = -0.2$, two distinct waveforms exist: both maximised along the line $x - 0.2y = 0$ initially, but one of them has maximum amplitude $ \approx 0.16 $ [Figure \ref{fig-3}c], whereas the other has maximum amplitude $ \approx 0.49 $ [Figure \ref{fig-3}e].

    \section{Origins in condensed matter physics} \label{sec-disc}

To interpret the solution \eqref{eq-GNLSE-caseII-soln-simp}, we begin by deriving \eqref{eq-GNLSE} as a model of the dynamics of a quantum mechanical exciton when coupled to a lattice. The theoretical principles of exciton-lattice interaction were founded in the 1930s, and have been important in condensed matter physics for their relevance to superconductivity, conducting polymers and bioelectronics \cite{landau1933electron,frohlich1950theory,holstein1959studies,su1979solitons,brizhik2019long}. The method of deriving the NLSE or its variants by taking a exciton-lattice system to a continuum limit was first presented by Davydov \cite{davydov1979solitons}, and has since been employed in many studies; details can be found in some excellent reviews \cite{heeger1988solitons,scott1992davydov}. Since the theory is well established, we present only a brief outline of key steps.

We consider a 2D rectangular lattice whose number of nodes is large in one direction, say $x$, and let the lattice undergo collective stretching oscillations along that direction. An extra exciton, such as an electron, interacts with the lattice and is assumed to undergo no spin-flip. The exciton-lattice system is modelled with a second-quantised Fr\"{o}hlich-Holstein Hamiltonian:
    \begin{align}
	\widehat{H} &= J_0 \sum_{ k = 0 }^{ N_2 } \sum_{ j = 0 }^{ N_1 } \widehat{A}^{\dagger}_{ j , k } \widehat{A}_{ j , k } - J_1 \sum_{ k = 0 }^{ N_2 } \sum_{ j = 0 }^{ N_1 - 1 } \Big( \widehat{A}^{\dagger}_{ j + 1 , k } \widehat{A}_{ j , k } + \widehat{A}^{\dagger}_{ j , k } \widehat{A}_{ j + 1 , k } \Big) \nonumber \\
	& \quad - J_2 \sum_{ k = 0 }^{ N_2 - 1 } \sum_{ j = 0 }^{ N_1 } \Big( \widehat{A}^{\dagger}_{ j , k + 1 } \widehat{A}_{ j , k } + \widehat{A}^{\dagger}_{ j , k } \widehat{A}_{ j , k + 1 } \Big) + \sum_{ k = 0 }^{ N_2 } \sum_{ j = 0 }^{ N_1 } \frac{ \widehat{P}_{ j , k }^2 }{ 2 M } + \sum_{ k = 0 }^{ N_2 } \sum_{ j = 0 }^{ N_1 - 1 } \frac{ K }{ 2 } \left( \widehat{Q}_{ j + 1 , k } - \widehat{Q}_{ j , k } \right)^2 \nonumber \\
	& \quad + \sum_{ k = 0 }^{ N_2 } \left[ \chi_2 \left( \widehat{Q}_{ 1 , k } - \widehat{Q}_{ 0 , k } \right) \widehat{A}^{\dagger}_{ 0 , k } \widehat{A}_{ 0 , k } + \chi_1 \left( \widehat{Q}_{ N_1 , k } - \widehat{Q}_{ N_1 - 1 , k } \right) \widehat{A}^{\dagger}_{ N_1 , k } \widehat{A}_{ N_1 , k } \right] \nonumber  \\
	& \quad + \sum_{ k = 0 }^{ N_2 } \sum_{ j = 1 }^{ N_1 - 1 } \left[ \chi_2 \left( \widehat{Q}_{ j + 1 , k } - \widehat{Q}_{ j , k } \right) + \chi_1 \left( \widehat{Q}_{ j , k } - \widehat{Q}_{ j - 1 , k } \right) \right] \widehat{A}^{\dagger}_{ j , k } \widehat{A}_{ j , k }, \label{eq-ham}
	\end{align}
where $N_1+1$ and $N_2+1$ are the number of nodes in the $x$ and $y$ directions of the lattice, respectively; the remaining notations are explained as follows. The first three terms of the right-hand side of \eqref{eq-ham} constitute the standard tight-binding exciton model, with $J_0$ being the exciton site energy and $J_{1,2}$ the exciton transfer integrals; $\widehat{A}^{\dagger}_{j,k}$ and $\widehat{A}_{j,k}$ are the exciton creation and annihilation operators at the $(j,k)$ node, respectively. The equilibrium distances between lattice nodes are implicitly built into the constants $J_{1,2}$, and we assume $J_1 > 0$; the sign of $J_2 \neq 0$ can vary depending on the type of physical system \cite{scott1982dynamics,zolotaryuk1998polaron}. The next two terms constitute a masses-and-springs model of the lattice, with $M$ being the node mass, $K$ the spring constant, $\widehat{Q}_{j,k}$ the operator for node displacement from equilibrium, and $\widehat{P}_{j,k}$ being the momentum conjugate to $\widehat{Q}_{j,k}$. The remaining terms on the right-hand side of \eqref{eq-ham} model the exciton-lattice interaction, with coupling constants $\chi_{1,2} \ge 0$, not both zero, representing the interaction strengths between a localised exciton and lattice distortions to the small-$j$ and large-$j$ side, respectively. As we shall see, it is precisely this spatial anisotropy in exciton-lattice coupling that leads to the novel $ \partial_{xx} ( | \psi |^2 ) \psi $ term in \eqref{eq-GNLSE}; and it has been argued that an anisotropy of this type is important in modelling molecular-biological systems such as the $\alpha$-helix \cite{Luo2017,georgiev2019quantum}.

Assuming a disentangled exciton-lattice system where the exciton is in a Bloch state and the lattice in a Glauber state:
    \begin{align}
	\ket{ \Psi ( t ) } = \sum_{ k = 0 }^{ N_2 } \sum_{ j = 0 }^{ N_1 } \phi_{ j , k } ( t ) \widehat{A}^{\dagger}_{ j , k } \exp \left( \frac{ i }{ \hbar } \sum_{ k' = 0 }^{ N_2 } \sum_{ j' = 0 }^{ N_1 } \left( \mathcal{P}_{ j' , k' } ( t ) \widehat{Q}_{ j' , k' } - \mathcal{Q}_{ j' , k' } ( t ) \widehat{P}_{ j' , k' } \right) \right) \ket{ 0_\textnormal{e} } \ket{ 0_\textnormal{p} } , \label{eq-state}
	\end{align}
where $ \ket{ 0_\textnormal{e} } $ and $\ket{ 0_\textnormal{p}}$ are the exciton and lattice vacua respectively, we follow the standard Hamiltonian procedure to derive the equations governing the dynamics of the coefficients $ \phi_{j,k}, \mathcal{P}_{j,k} $ and $ \mathcal{Q}_{j,k} $, for the \textit{interior points} $j = 1,2, \dots N_1 - 1, k = 1,2, \dots N_2 - 1$:
    \begin{subequations} \label{eq-disc}
    \begin{align}
	i \frac{ \d \phi_{ j , k } }{ \d t } &= \phi_{ j , k } \left[ \frac{ J_0 }{ J_1 } + \Omega + \frac{ \alpha }{ 2 } ( 1 + \beta ) ( q_{ j + 1 , k } - q_{ j , k } ) + \frac{ \alpha }{ 2 } ( 1 - \beta ) ( q_{ j , k } - q_{ j - 1 , k } ) \right] \nonumber \\
	&\quad - [ \phi_{ j - 1 , k } + \phi_{ j + 1 , k } ] - \rho [ \phi_{ j , k - 1 } + \phi_{ j , k + 1 } ] , \label{eq-disc-phi} \\
	\frac{ \d^2 q_{ j , k } }{ \d t^2 } &= \gamma^2 \left[ ( q_{ j + 1 , k } - 2 q_{ j , k } + q_{ j - 1 , k } ) \right] + \frac{ \alpha }{ 2 } ( 1 - \beta ) \left[ \abs{ \phi_{ j + 1 , k } }^2 - \abs{ \phi_{ j , k } }^2 \right] + \frac{ \alpha }{ 2 } ( 1 + \beta ) \left[ \abs{ \phi_{ j , k } }^2 - \abs{ \phi_{ j - 1 , k } }^2 \right]. \label{eq-disc-q}
	\end{align}
	\end{subequations}
In deriving \eqref{eq-disc}, we have scaled time by $ \hbar / J_1 $, and scaled length by $ \hbar / \sqrt{M J_1} $ so that $ q_{j,k} $ is the non-dimensionalised $ \mathcal{Q}_{j,k} \equiv \braket{\Psi | \widehat{Q}_{j,k} | \Psi} $; we have also defined the dimensionless constants $ \alpha = ( \chi_2 + \chi_1 ) \hbar / \sqrt{M J_1^3} > 0 , \beta = (\chi_2 - \chi_1)/( \chi_2 + \chi_1 ), \rho = J_2 / J_1 \neq 0 , \gamma = \sqrt{ K \hbar^2 / ( M J_1^2 ) } > 0 $, and the dimensionless lattice energy which we assume to be constant:
    \begin{align}
    \Omega = \frac{ \Braket{ \Psi | \sum_k \sum_j \big( \frac{ \widehat{P}_{ j , k }^2 }{ 2 M } + \frac{ K }{ 2 } ( \widehat{Q}_{ j + 1 , k } - \widehat{Q}_{ j , k } )^2 \big) | \Psi } }{ J_1 } .
    \end{align}
Note that $\beta$ encodes the anisotropy of the exciton-lattice interaction, and should take values in $[-1,1]$. However, as we will soon discover, setting $ \beta = 0 $ simply reduces the system to the standard NLSE with a cubic nonlinearity (equivalent to setting $ \lambda = 0 $ in \eqref{eq-GNLSE}). The standard NLSE and its solutions are so well known that we do not consider it here. Furthermore, we assume without loss of generality that $ \chi_2 > \chi_1 $, so that $ \beta \in (0,1] $.

Now we invoke the continuum approximation by introducing smooth functions $ \psi , u $ of the continuous variables $(x,y,t)$ such that $ \phi_{j,k} (t) = \psi (j,k,t) \exp [ - i t (J_0/J_1 + \Omega - 2 - 2 \rho) ]$ and $ q_{j,k} (t) = u(j,k,t) $. Approximating finite differences by derivatives up to the second order \cite{davydov1979solitons}, we find
    \begin{subequations} \label{eq-cont}
    \begin{align}
	i \partial_t \psi &= \psi \times \left( \alpha \partial_x u + \frac{ \alpha \beta }{2} \partial_{xx} u \right) - \partial_{xx} \psi - \rho \partial_{yy} \psi , \label{eq-cont-psi} \\
	\partial_{tt} u &= \gamma^2 \partial_{xx} u + \alpha \partial_x | \psi |^2 - \frac{ \alpha \beta }{ 2 } \partial_{xx} | \psi |^2. \label{eq-cont-u}
	\end{align}
	\end{subequations}
Differentiating \eqref{eq-cont-u} yields $ \partial_{tt} (\partial_x u) - \gamma^2 \partial_{xx} ( \partial_x u ) = \partial_{xx} ( \alpha | \psi |^2 - \genfrac{}{}{}1{ \alpha \beta }{ 2 } \partial_{x} | \psi |^2 )$. We consider a travelling wave ansatz: $ \partial_x u (x,y,t) = v (x-wt) $ for some function $v$ and constant $w$, which leads to $ \partial_{xx} [ (w^2 - \gamma^2 ) v ] = \partial_{xx} ( \alpha | \psi |^2 - \genfrac{}{}{}1{ \alpha \beta }{2} \partial_x | \psi |^2 )$ and therefore enables us to take $ v = ( \alpha | \psi |^2 - \genfrac{}{}{}1{ \alpha \beta }{2} \partial_x | \psi |^2 ) / (w^2 - \gamma^2) $. Substituting this expression for $ \partial_x u $ in \eqref{eq-cont-psi}, we deduce
    \begin{align}
	i \partial_t \psi &= \psi \times \left( \frac{\alpha^2}{w^2 - \gamma^2} | \psi |^2 - \frac{ \alpha^2 \beta^2 }{4 (w^2 - \gamma^2)} \partial_{xx} | \psi |^2 \right) - \partial_{xx} \psi - \rho \partial_{yy} \psi \label{eq-cont-2}.
    \end{align}
Equation \eqref{eq-cont-2} holds over the interior of a finite, rectangular spatial domain, but we scale the $y$ variable so that $ y \in (-\genfrac{}{}{}1{1}{2},\genfrac{}{}{}1{1}{2}) $; and since the lattice is large in the $x$ direction, we let $ x \in \mathbb{R} $. We require that the speed of the $ \partial_x u $ wave is sufficiently small so that $ w^2 < \gamma^2 $ (which we will soon justify). Rearranging \eqref{eq-cont-2}, defining $ \kappa = \alpha^2 / ( \gamma^2 - w^2 ) > 0 $, $ \lambda = \alpha^2 \beta^2 / (4 (\gamma^2 - w^2) ) > 0 $, and combining $\rho$ with the appropriate $y$-scaling into a constant $ \sigma \neq 0 $, we obtain exactly the equation \eqref{eq-GNLSE}.

The normalisation condition \eqref{eq-GNLSE-norm} is imposed because the quantum state $ \ket{ \Psi } $ as per \eqref{eq-state} must be normalised. In the limit $ \beta \rightarrow 0 $, we recover the standard NLSE; that is to say, the exciton-lattice system with spatially isotropic coupling is modelled in the continuum limit by the standard NLSE, as is well known \cite{davydov1979solitons}. We have required $ w^2 < \gamma^2 $ to ensure $\kappa > 0$ and so that, in the limit $\beta \rightarrow 0$, we recover the NLSE that admits \textit{bright} solitons, rather than dark ones, which may not be normalisable. In a realistic system, we expect $ | \rho | \sim 1 $ and hence $ |\sigma| $ to be comparable to the squared reciprocal of the number of lattice nodes in the $y$ direction.

In light of the discussions above, we say that the soliton solution \eqref{eq-GNLSE-caseII-soln-simp} represents the lossless propagation of an exciton wavefunction in a planar lattice with a large aspect ratio, with possible applicability to photonic crystal circuits and Bragg gratings \cite{lonvcar2000waveguiding,gnan2006modelling}. The squared amplitude, $|\psi|^2 \equiv f^2$, is the probability distribution of exciton location. The squared amplitude is a travelling wave with constant speed; it is maximised along a straight line, representing the most probable location of the exciton, and the line advances through the lattice. The parameters $\kappa, \lambda, \sigma$ encode the exciton-lattice coupling strength, the anisotropy of the coupling in the $+x$ versus $-x$ directions, and the anisotropy of exciton hopping energy in the $y$ versus $x$ directions, respectively. If we choose $w$ such that the velocity of the lattice distortion matches the propagation velocity of the exciton, and if the exciton is an electron, then the quasi-particle comprising lattice distortion and electron becomes what is well known in condensed matter physics as a \textit{polaron}.

    \section{Conclusions}

In this study, we have presented a modified nonlinear Schr\"{o}dinger equation in two spatial dimensions, featuring a nonlinear term of the form $ \partial_{xx} ( |\psi|^2) \psi $. We have constructed an exact soliton solution analytically, and characterised its properties, which depend on parameters $ (\sigma,\kappa,\lambda) $ in the equation and a key parameter in the travelling wave ansatz: a waveform constant $a$ determining the gradient of the line of maximum $ | \psi |^2 $. In particular, the waveform constant can only take values in a range $a \ge a_{\textnormal{c}}$ if $\sigma > 0$ or $ a \le a_{\textnormal{c}} $ if $\sigma < 0$, where the threshold $a_{\textnormal{c}}$ depends on $(\sigma,\kappa,\lambda)$ in ways which we have detailed. Another $a$-value threshold, $a_{\textnormal{u}}$, marks the bifurcation between having a unique waveform for each value of $a$, and having two distinct waveforms corresponding to each $a$. The dependence of $a_{\textnormal{u}}$ on $ (\sigma,\kappa,\lambda) $ has been established. The region of parameter space that lies strictly between $a_{\textnormal{c}}$ and $a_{\textnormal{u}}$ is the bi-waveform region. This waveform duality is a novel phenomenon among modified NLSE systems that admit soliton solutions. Crucially, we have found that regardless of the waveform, the wave speed must be $c=2$ in order to ensure the uniqueness of the soliton solution.

From condensed matter theory, we have derived the equation as a model for the propagation of a quantum exciton through a plane lattice to which the exciton is coupled. The lattice is required to be much larger in one direction, say $x$, than in the other, and undergoing collective oscillations (e.g.~by hydrogen bond stretching) in that $x$ direction. The novelty of the model manifests as an anisotropy parameter $ \lambda > 0 $ which encodes the extent to which the exciton-lattice interaction is spatially anisotropic, with the limit $ \lambda \rightarrow 0 $ reducing the model to the standard nonlinear Schr\"{o}dinger equation. We have found that the solution is stable in regions of the parameter space with sufficiently large $\lambda$, representing exciton-lattice systems with highly anisotropic coupling. Furthermore, $ \psi $ is the exciton position wavefunction, and therefore the soliton solution represents the lossless transport of the exciton. If one wishes to consider higher-dimensional slender lattices, then the exciton-lattice system will be suitably modelled by the natural high-dimensional extension of the equation considered here, and the same method of solution will apply. Indeed, in three spatial dimensions this equation becomes a generalisation of the Gross-Pitaevskii model for Bose-Einstein condensates \cite{garcia2003quasi}.

\subsection*{Statement of author contribution(s)}
This work was carried out in full by the sole author.

\subsection*{Declaration}
The author declares no conflict of interest.

\subsection*{Acknowledgement}
The author thanks the University of Birmingham, UK for Fellowship funding.

redpajama_set_name: RedPajamaArXiv


text:
SERI Report: Protest is the "only language government understands"
Protest is the "only language government understands"
Today SERI launched a new research report entitled An Anatomy of Dissent and Repression: The Criminal Justice System and the 2011 Thembelihle Protest.
At the event the author of the report, SERI researcher Michael Clark, explained how in September 2011 residents of Thembelihle informal settlement in Lenasia took to the streets, frustrated by an unaccountable and unresponsive local government. Their demands were dismissed and instead they were met with a forceful police clamp-down. In the aftermath of the protest, arrest and criminal prosecution were used to harass and intimidate community members and to target community leaders.
Bhayiza Miya, former spokesperson of the Thembelihle Crisis Committee (TCC), spoke at the event about how he was arrested by the police during the protest, after visiting the police station on another matter, and charged with public violence and intimidation. Additional charges, on which no further evidence was provided, were also brought against him. He was singled out for his role in the TCC, being the only arrested resident denied immediate bail.
According to Miya "The decision to prosecute me was clearly political and coming from elsewhere."
The prosecution attempted to attribute all of the negative consequences of the protest to Miya personally. They held him in "preventative detention" claiming that his release would result in further protest action at the settlement. The High Court eventually overturned the Magistrate's decision to deny him bail, and ordered Miya's release. By this time, he had spent six weeks in detention at Sun City prison. After an extremely long delay in proceeding with the case, including nine postponements over a period of seven months, his case and was struck off the roll.
Miya also highlighted the frustrations of community residents over their appalling living conditions and the unresponsiveness of government officials and politicians to their plight. According to him, despite what many think "People in informal settlements don't just wake up one day from sleeping and decide to protest." He explained how the government simply ignored issues raised during peaceful protests earlier in the year, putting it bluntly – "Real protest is the only language government understands."
Former deputy editor of the Daily Maverick Phillip de Wet spoke about his experience covering the Thembelihle protest as well as more generally about media coverage of protests. He offered a pessimistic view of the media's appetite or ability to cover protests at all, let alone in a more nuanced manner. Simply put, according to De Wet, "audiences don't care" and are tired of hearing about issues like corruption and protest. He warned that while state responses to protests will most likely become more repressive, with the criminalisation of protestors, "The media may well not be there to cover this."
According to Stuart Wilson, SERI's executive director: "The role of the media in covering issues facing informal settlement communities is critical. Currently much of the media uncritically perpetuates the worst kind of racial and class stereotypes. This needs to change."
· Read the full research report (including the executive summary) here.
· Read more on Bhayiza Miya's criminal case here.
Michael Clark, legal researcher at SERI: michael@seri-sa.org / 011 356 5874 / 082 535 6209


text:
Q: Gekko Python: Memory allocation failed As a follow up to the question:
How can I simplify a large scale NLP model in Gekko Python?
I'm still trying to figure out why gekko gets me this error:

Memory allocation failed
Error: 'results.json' not found. Check above for additional error
details

These are my constraints:
def contraintesPuissance(self):

    Pmin = self.df_donnees_techniques["Puissance min"].to_list()
    Pmax = self.df_donnees_techniques["Puissance max"].to_list()

    self.model.Equations(
    [
        [
            self.on_off_var[ idx + (heure*self.nb_actifs) ] \
                * Pmax[idx] / self.getRendement(idx,heure) \
                - self.variables[ idx + (heure*self.nb_actifs) ] >= 0,

            self.variables[ idx + (heure*self.nb_actifs) ] \
                - self.on_off_var[ idx + (heure*self.nb_actifs) ] \
                * Pmin[idx] / self.getRendement(idx,heure) >= 0
        ]
        for heure in range(self.nb_heure)
        for idx in range(self.nb_actifs)
    ]
    )

def contraintesBesoinsConsommation(self):
    self.model.Equations(
            [
                [
                    sum([self.variables[idx + (heure*self.nb_actifs)]*self.getRendement(idx,heure) for idx in range(self.nb_actifs)])  \
                        - self.Analyse_df['besoins_chaud'][heure] == 0
                ]
                for heure in range(self.nb_heure)
            ]
        )

def contraintesTxENR(self):
    intermed = [self.model.Intermediate(
                    self.variables[ idx + (heure*self.nb_actifs) ] * self.getRendement(idx,heure)
                ) for heure in range(self.nb_heure) for idx in range(self.nb_actifs)
                ]

    numerateur = self.model.sum(
        [intermed[idx + (heure*self.nb_actifs)] * self.getTaux(idx) for heure in range(self.nb_heure) for idx in range(self.nb_actifs)]
    )
    denominateur = self.model.sum(intermed)

    self.model.Equation( numerateur / denominateur - self.Tx_ENR_cible >= 0)

def contrainteEmissions(self):
    self.model.Equation( self.VLE_max_gaz - self.emissions("Gaz_1") >= 0 )
    # !! à arrêter

And this is my objective function:
    def func_cout_NRJV2_gekko(self):

    somme = [
        sum([self.variables[ idx + (heure*self.nb_actifs) ] * self.donnees_prix_NRJ[self.actifs_instancies[idx]][heure] for idx in range(self.nb_actifs)])
    for heure in range(self.nb_heure)]
    [self.model.Minimize(s) for s in somme]
    penalite = self.model.if3(self.Sum_NRJ("Bois") - self.take_or_pay_bois, self.penalite_bois, 0) # Penalité take or pay
    self.model.Minimize(penalite)

If more info is needed, I can provide it, but the code is really big.

A: What OS are you using? The issue with Memory allocation failed may be that the problem is >4 GB. On Local solve: Linux / MacOS and Cloud solve: Linux it isn't a problem because the executables are 64-bit. For Windows, the local executable is still 32-bit so the RAM limitation may be reached. This will likely change in the near future, but it could be the limitation.
Here are a few things to try, even if you are on a 64-bit executable.

*

*Inspect the model by opening the local run folder with m.open_folder(). Open the gk0_model.apm file with a text editor. The variables will have different internal names. They can be changed by naming variables with the name argument such as x = m.Var(value=0,name='x') to make it more readable.

*Convert any Constants or Parameters to just regular Python numbers. This can greatly reduce the memory requirement because they are not added to the automatic differentiation.

*If there are summations that can be np.sum() instead of m.sum(), use that instead so parts of the model are pre-computed before giving it to the solver.

*Use m.options.REDUCE=3 to scan through the model 3 (or more) times to reduce the memory requirements. This eliminates equations such as x==1, y+x==1, and z+y+x==`` by replacing them with x=1, y=0, z=0` as a pre-solve.

*The if3() function creates a few extra variables and equations and can increase the size of the model. If some of the conditions are always greater than zero or less than zero with pre-processing, then try eliminating those.


text:
Filed under Insufficient Talc Containing Evidence, Possible Asbestos Containing Product, Predecessor Liability, Talc, Talc Speculation, triable issue of fact
California Talc Decision Bars Predecessor Liability, and Denies Punitive Damages Absent Scientific Consensus
By Angela Hampton, San Diego on July 29, 2019
When a Los Angeles jury returned an eye-popping $416 million verdict for plaintiff in a closely-watched talcum powder ovarian cancer case in 2017, the world took notice. The trial court granted post-trial motions that dramatically changed the jury's verdict. Recently, in Echeverria v. Johnson & Johnson, the Court of Appeal gave both sides a mixed result, with rulings that will apply to many other product liability cases.
Johnson & Johnson – Former Manufacturer – No Liability
J&J manufactured the product until 1967, when it spun off to subsidiary J&J Consumer Products ("JJCI"). The jury found J&J liable, awarding both compensatory and punitive damages. The trial court granted judgment notwithstanding the verdict ("JNOV"). The Court of Appeal affirmed, applying "the general rule that a manufacturer has no duty to warn of risks posed by another manufacturers product" (citing O'Neil and Taylor, a Gordon & Rees victory). The Echeverria court distinguished the California Supreme Court decision in Novartis, which found such a predecessor manufacturer liable, because that case "concerned continuing liability for a negligent failure to warn in labeling that occurred prior to a manufactured divesting itself of the rights to the" product.
The risk of ovarian cancer from talc use during the time that J&J manufactured the product was speculative. Because of that, J&J did not owe consumers a duty to warn. Later developments, including J&J's active participation in industry groups to defend talc, did not create a duty to warn after the fact. The court ruled that J&J is not responsible for JJCI's later products solely because of the parent-subsidiary relationship.
This part of the decision will aid defendants in future cases where the exposures pre-date certainty of the claimed risk. Manufacturers that spun off, or sold off, product lines should be heartened by the decision. The parent company will not be liable so long as the sub is not controlled by its parent.
The Actual Manufacturer, JJCI, Gets a Split Decision – But All Better than the Jury's Verdict
The jury also found JJCI liable – awarding both compensatory and punitive damages. The trial court granted both JNOV and a new trial. The Court of Appeal reversed the JNOV but affirmed the new trial, essentially holding that while the evidence was sufficient to support the verdict and thus defeat JNOV, there was also enough defense evidence to justify the trial court's discretionary grant of new trial.
Plaintiff's Evidence Enough to Support Verdict
The Court of Appeal reasoned that the evidence showed as of 2007 (when decedent died) JJCI knew, as did the scientific and medical community, that there was a statistically significant association between genital talc use and ovarian cancer. While there has yet to be a scientific consensus that genital talc causes ovarian cancer, as needed to prove causation, it was sufficient to show a risk existed. Thus, JJCI had a duty to warn consumers of the risk. Ultimately, what was known between 1967 and 2007 was significant enough that JJCI failed to act reasonably. JJCI should have issued an appropriate warning.
The trial court found significant weaknesses in plaintiff's causation evidence, particularly relating to the differential diagnosis and relative risk evidence. The defense argued plaintiff's expert's reliance improper because the results failed to stratify patients into well-defined risk groups. Further, the results were not classified by the type of tissue in which decedent's cancer originated. The Court of Appeal found that these weaknesses were not fatal to the plaintiff's case, but merely "affected the weight of the evidence."
The defense argued plaintiff was required to rule out other potential causes of decedent's ovarian cancer, such as unknown etiology, arguing since plaintiff's expert ignored other causes, the opinion was speculative. The Court of Appeal did not find the opinion speculative since the expert "did not ignore idiopathy but instead determined there was in fact a known cause of the cancer." The Court of Appeal also pointed to the failure of the defense to advance evidence of a specific alternative cause stating, "[t]he defendant did not identify any relevant evidence about other causes it claimed the expert overlooked." Had the defense done so, then plaintiff's expert would have had to rule it out. It is not enough to simply discredit plaintiff's theory. Defense counsel should always advance their own narrative.
Defense Evidence Sufficient to Justify New Trial
The trial court granted JJCI's request for a new trial, and the Court of Appeal affirmed, because the evidence supported a defense verdict. "[T]he trial court's ruling granting JNOV to JJCI as to liability must be reversed because the trial court weighed the evidence and made credibility determinations when rejecting and evaluating aspects of [plaintiff's expert] testimony. In ruling on the new trial motion, however, the court was permitted to assess the credibility of witnesses, weigh the evidence, and draw inferences from the evidence different from those the jury may have drawn."
Perhaps the key evidence was that there is no consensus among the scientific and medical community that genital talc use causes ovarian cancer. "[N]o published studies, regulatory agencies, or scientific organizations have concluded talc-based inflammation causes ovarian cancer." The FDA has not found there is "conclusive evidence of a causal association" between talc use and ovarian cancer. Even evidence from the National Cancer Institute in 2017 "concluded the weight of the evidence did not support an association between perineal talc use and ovarian cancer."
"The causation evidence was in significant conflict," and a "reasonable jury" could have found for the defense. For example, "the trial court found [one plaintiff expert] 'cherry picked' the studies without sufficient justification and the weight of the epidemiological evidence undermined her opinion. There was evidence to support this finding." The "trial court also found there was no evidence of inflammation present in Echeverria's tissue, rejecting [another plaintiff expert's] testimony and inferences that could be drawn from it."
No Punitive Damages Before Scientific Consensus Established
Critically, the Court of Appeal held there cannot be an award for punitive damages "when the evidence demonstrated it is not universally accepted in the scientific and medical community that talc is even a significant factor for ovarian cancer." Lack of such consensus is common in cases involving many different products with ingredients alleged to be toxic.
Based on this reasoning, unless the scientific and medical community suddenly comes to a consensus that genital talc use causes ovarian cancer or the California Supreme Court grants the inevitable petition for review and reverses, it seems highly unlikely plaintiff can win punitive damages on retrial.
Filed under Causation, Predecessor Liability, Talc