text:
Douglas Foo
by Subramaniam, Shivaranjani
Feedback on article
Douglas Foo (b. 1969, Singapore–), is the chairman, chief executive officer and founder of Apex-Pal International Ltd., a public listed food and beverage company, which owns and operates Sakae Sushi – one of the leading kaiten (conveyer belt) sushi chains in Singapore.1 The success of Sakae Sushi has won the company numerous accolades such as the Enterprise 50 Award in 2002, Most Promising Brand Award in 2003,2 the Singapore Prestige Brand Award (Regional) in 2006 and the Singapore 1000 Award in 2007. In recognition of his entrepreneurial spirit and philanthropic efforts, Foo was awarded the Rotary-ASME Entrepreneur of the Year in 2002,3 and the Public Service Star in 2013.4
Foo, the eldest of three children, was born in Singapore in 1969. His father, an immigrant from Hainan, China, worked as a mechanical and electrical consultant.5 Foo received his early education at the Red Swastika Primary School, where he was both a prefect and top student.6 He went on to study at Dunman High School, and furthered his education at Victoria Junior College.7 An active sportsman in college, Foo participated in long-distance running, laser sailing and windsurfing.8
Following his GCE "A" Levels, he served his national service with the Singapore Air Force. During his military service, Foo would read up on topics relating to radar and electronics in order to understand the workings of the missile systems. It was then that he discovered that his interest was not in engineering.9
Although Foo had already secured a place with the engineering school at the Nanyang Technological University, he decided to make the switch to study business administration.10 However, his 'A' Level grades did not qualify him for the university's business school. So, aided in part by funds from his parents, Foo enrolled in the Royal Melbourne Institute of Technology in Australia for his degree in business administration (finance),11 where he graduated with distinction in 1994.12
The value of money
Foo was taught the value of money from an early age. Once, when he was 10, Foo, who was running a fever, called his father to ask for a lift home. His father, instead, chided him for wasting 10 cents on the phone call, and told him that he should make his own way home as their house was within walking distance from school.13 Since primary school, Foo was given only a modest monthly allowance of $50 for his food, transport and outings.14
To supplement his allowance , Foo gave tuition on weekends, earning up to $5,000 a month.15 He also worked during the six-month vacation before his enlistment, juggling a number of jobs at the same time. His typical day then involved taking turbine readings at Pulau Seraya in the mornings, relief teaching at Pin Yi Secondary School in the afternoons, and conducting door-to-door market surveys in the evenings.16 He also had a brief stint as a baker at Delifrance, where he met his wife. While studying in Melbourne, Foo continued to earn extra pocket money by selling shoes at the Queen Victoria Market.17
Upon returning from Australia, Foo found employment as a marketing executive with the real estate arm of Tokyu Group in 1995. During the course of his work, he formed friendships with a number of Japanese clients. Through these networks, one of his Japanese business contacts approached him to start a business to manufacture garments in India for sale in Japan.18
Foo took the plunge despite an attractive counter offer from his employer, and his lack of experience in the fashion business.19 He invested $100,000 of his savings and registered Apex-Pal in 1996.20 The trading office was located at International Plaza,21 while a factory with 50 workers and equipped with reconditioned sewing machines from Taiwan was established in India. The business yielded profits in its first year.22
Beginnings of Sakae Sushi
With the success of the garment manufacturing and trading business, Foo began exploring various ways of diversifying the business.23 He studied the basic needs of consumers, and decided that the food industry would be good to venture into. Having learned that Singaporeans were becoming more health conscious and discerning about what they consume,24 Foo ventured into the food and beverage industry in 1997.25
Although, Japanese fare was generally considered to be one of the healthiest among the various cuisines, it was also a relatively expensive dining choice for the masses at the time. Hence, Foo came up with the business proposition to offer Japanese food at affordable prices. By targeting the middle-class masses, the company would be less vulnerable to economic downturns.26 However, with the Japanese economic slump during that period, Foo's business partner was reluctant to take on this new venture.27 In the ensuing months, Foo faced the uphill task of raising funds to buy out his partner's share as well as setting up the sushi business.28
In planning for Sakae Sushi, Foo made frequent trips to Japan and Hong Kong to study the operations of conveyor-belt sushi joints. He decided to implement a single price for all plates (with the exception of delicacies on red plates) because he felt that the various coloured plates (indicating the different prices of sushi dishes) used in Japanese restaurants deterred customers from ordering more. He also created a dining concept unique to Sakae Sushi to differentiate the restaurant from other Japanese dining establishments: the company uses a conveyor belt system that runs on blocks of wheels to deliver sushi to customers, provides hot water taps for customer to make their tea as well as interactive menus for placing orders. Over time, the company added more innovations such as sushi-making robots, and portable conveyor belts for catered dining.29
The first Sakae Sushi outlet opened at the OUB Centre at Raffles Place in the midst of the Asian financial crisis in September 1997.30 Despite the weak economic situation, the business took off. Today, there are over 200 Sakae Sushi outlets in Singapore, Malaysia, Indonesia, Thailand, the Philippines, China, Japan, India, New Zealand and the United States.31
In its efforts to reach out to Muslim consumers, Apex-Pal International went a step ahead by offering halal sushi under the Hei Sushi brand in 1997, and currently operates five outlets around the island.32 Foo, however, did not stop at sushi. He further cemented his foothold in the food and beverage scene by launching Black Tea Box (now defunct), and Crepes & Cream in 2000. The following year, he established Nouvelle Events, an events catering company with its own bakery and butchery.33 Apex-Pal International was listed on the Singapore Stock Exchange in 2003.34
Currently the president of the Singapore Manufacturing Federation,35 Foo also sits on numerous boards for corporate, governmental and non-profit organisations such as MILK (Mainly I Love Kids) Fund,36 Radin Mas Community Club, the ASEAN Business Advisory Council as well as the Lee Kong Chian School of Business Advisory Board at the Singapore Management University.37
Foo received the Public Service Star in 2013 in recognition of his philanthropic efforts. In 2016, he was conferred the Seri Pangeran Temenggong Sultan Mahmud Badaruddin III (S.P.T.M) by His Royal Highness Sultan Mahmud Badaruddin III, Prabu Diraja, Sultan Palembang Darussalam, which carries the title Dato' Seri.38
Personal awards39
2002: Rotary-ASME Entrepreneur of the Year (joint winner).
2002: Top Outstanding Young Person Award, by Junior Chamber of Singapore International.
2002: Merit, Yazhou Zhoukan Chinese Entrepreneur Merit Award.
Hobbies40
2003: Singapore Youth Award.
2004: ASEAN Youth Award (Youth & Entrepreneurship).
2005: Health Leader (Excellence) Award, by the Singapore Human Resource Institute.
2007: Public Service Medal, National Day Award.
2007: International Management Action Award.
2008: Commendation, Singapore Youth Award.
2010: Workforce Skills Qualifications (WSQ) Champion.
2011: ASEAN-China Young Entrepreneur Outstanding Entrepreneur Award.
2012: MCYS Volunteers Award.
2013: Public Service Star (BBM), National Day Award.
2015: Asia Corporate Excellence and Sustainability (ACES) ""Entrepreneur of the Year"" Award.
2016: NTUC May Day Friend of Labour Award.
Wife: Koh Yen Khoon
Children: Donavan, Dominic, Donahue, Donaghan
Shivaranjani Subramaniam
1. Apex-Pal International Ltd. (2004, January 28). The Business Times. p. 29. Retrieved from NewspaperSG; Low, K. T. (Ed.). (2006). Who's who in Singapore 2006. Singapore: Who's Who Pub. p. 141. (Call no.: RSING 920.05957 WHO)
2. People at the peak: The who's who of Singapore. (2006). Singapore: Magazines Incorporated, p. 408. (Call no.: RSING q920.05957 PEO)
3. Long, S. (2003). Grit success II: The guts behind Singapore's top entrepreneurs. Singapore: Prentice Hall, p. 50. (Call no.: RSING 338.0409225957 LON); Low, K. T. (Ed.). Who's who in Singapore 2006. Singapore: Who's Who Pub. p. 141. (Call no.: RSING 920.05957 WHO)
4. Sakae Holdings Ltd. (2016). Personal awards – Douglas Foo, chairman. Retrieved 2016, September 20 from Sakae Holdings website: http://www.sakaeholdings.com/awards-douglas-foo-chairman.html
5. Chew, C. (2009, May 19). Sushi boss serves up recession buster. The Straits Times, p. 10. Retrieved from NewspaperSG; Ang, E., & Chang, P. Y. H. (2004). Winning strokes. Singapore: Nouveau Pub, p. 53. (Call no.: RSING 338.04095957 ANG)
6. Long, S. (2003). Grit success II: The guts behind Singapore's top entrepreneurs. Singapore: Prentice Hall, p. 48. (Call no.: RSING 338.0409225957 LON); Ang, E., & Chang, P. Y. H. (2004). Winning strokes. Singapore: Nouveau Pub, p. 53. (Call no.: RSING 338.04095957 ANG)
7. Chuang, P. M. (2004, February 9). It pays to be crazy sometimes. The Business Times, p. 3. Retrieved from NewspaperSG.
8. Long, S. (2003). Grit success II: The guts behind Singapore's top entrepreneurs. Singapore: Prentice Hall, p. 48. (Call no.: RSING 338.0409225957 LON)
9. Ang, E., & Chang, P. Y. H. (2004). Winning strokes. Singapore: Nouveau Pub, p. 53. (Call no.: RSING 338.04095957 ANG)
10. Ang, E., & Chang, P. Y. H. (2004). Winning strokes. Singapore: Nouveau Pub, p. 53. (Call no.: RSING 338.04095957 ANG)
11. Chuang, P. M. (2004, February 9). It pays to be crazy sometimes. The Business Times, p. 3; Wee, L. (2002, July 10). Recipe for success. The Straits Times, p. 17; Crepes & Cream. (2002, July 10). The Straits Times, p. 17. Retrieved from NewspaperSG.
12. Long, S. (2003). Grit success II: The guts behind Singapore's top entrepreneurs. Singapore: Prentice Hall, p. 51. (Call no.: RSING 338.0409225957 LON)
13. Long, S. (2003). Grit success II: The guts behind Singapore's top entrepreneurs. Singapore: Prentice Hall, p. 50. (Call no.: RSING 338.0409225957 LON); Ang, E., & Chang, P. Y. H. (2004). Winning strokes. Singapore: Nouveau Pub, p. 45. (Call no.: RSING 338.04095957 ANG)
14. Long, S. (2003). Grit success II: The guts behind Singapore's top entrepreneurs. Singapore: Prentice Hall, p. 51. (Call no.: RSING 338.0409225957 LON); Ang, E., & Chang, P. Y. H. (2004). Winning strokes. Singapore: Nouveau Pub. p. 48. (Call no.: RSING 338.04095957 ANG)
19. Long, S. (2003). Grit success II: The guts behind Singapore's top entrepreneurs. Singapore: Prentice Hall. p. 50. (Call no.: RSING 338.0409225957 LON)
20; Ang, E., & Chang, P. Y. H. (2004). Winning strokes. Singapore: Nouveau Pub. p. 51. (Call no.: RSING 338.04095957 ANG)
23. Tan, R. L. (2008, July 27). My McSushi dream. The Straits Times, p. 78. Retrieved from NewspaperSG.
24. Frances, J. (2003, August 25). Teach a man to fish... Today, p. 7. Retrieved from NewspaperSG.
25. Apex-Pal International Ltd. (2004, January 28). The Business Times, p. 29. Retrieved from NewspaperSG.
26. Ang, E., & Chang, P. Y. H. (2004). Winning strokes. Singapore: Nouveau Pub, pp. 42–43. (Call no.: RSING 338.04095957 ANG)
29. Chuang, P. M. (2004, February 9). It pays to be crazy sometimes. The Business Times. p. 3. Retrieved from NewspaperSG.
31. Singapore Management University. (2016). Advisory board member: Douglas Foo. Retrieved 2016, September 20 from Singapore Management University, Lee Kong Chian School of Business website: https://business.smu.edu.sg/business/about/advisory-board/douglas-foo
32. Halal cuisine at Hei Sushi. (2008, December 10). The Straits Times. p. 48. Retrieved from NewspaperSG; Heisushi.com. (2016). Our locations. Retrieved 2016, October 18 from Hei Sushi website: http://www.heisushi.com/outlets.html
33. Wee, L. (2002, July 10). Recipe for success. The Straits Times, p. 17; Crepes & Cream. (2002, July 10). The Straits Times, p. 17. Retrieved from NewspaperSG. Retrieved from NewspaperSG; Sakae Holdings Ltd. (2016). Milestones. Retrieved 2016, October 18 from Sakae Holdings website: http://www.sakaeholdings.com/milestones.html; Apex-Pal International Ltd. (2003, August 18). The innovative F&B people, p. A-21. Retrieved 2016, October 18 from zaobao.sg website: http://ir.zaobao.com.sg/apexpal/pages/doc/apexpal_ipo_prospectus.pdf
35. Singapore Manufacturing Federation (2016). SMF Profile – President's Message. Retrieved 2016, November 2 from Singapore Manufacturing Federation website: http://www.smfederation.org.sg/index.php/profile/presidents-message
36. MILK (2016). Our Team – MILK. Retrieved 2016, September 20 from MILK website: http://www.milk.org.sg/new-index/
37. Singapore Management University. (2016). Lee Kong Chian School of Business – About – Advisory Board – Douglas Foo. Retrieved 2016, September 20 from Singapore Management University, Lee Kong Chian School of Business website: https://business.smu.edu.sg/business/about/advisory-board/douglas-foo; ASEAN Business Advisory Council. (2016). Members. Retrieved 2016, September 20 from ASEAN Business Advisory Council website:http://www.asean-bac.org/members/19-members-profile/79-douglas-foo; Chew, C. (2009, May 19). Sushi boss serves up recession buster. The Straits Times, p. 10; Chew, C. (2009, May 19). Sushi boss serves up recession buster. The Straits Times, p. 10. Retrieved from NewspaperSG.
38. Sakae Holdings Ltd. (2016). Personal awards – Douglas Foo, chairman. Retrieved 2016, September 20 from Sakae Holdings website: http://www.sakaeholdings.com/awards-douglas-foo-chairman.html
39. People at the peak: The who's who of Singapore. (2006). Singapore: Magazines Incorporated. p. 408. (Call no.: RSING q920.05957 PEO); Low, K. T. (Ed.). (2006). Who's who in Singapore 2006. Singapore: Who's Who Pub. p. 141. (Call no.: RSING 920.05957 WHO); Ang, E., & Chang, P. Y. H. (2004). Winning strokes. Singapore: Nouveau Pub. p. 58. (Call no.: RSING 338.04095957 ANG); Sakae Holdings Ltd. (2016). Personal awards – Douglas Foo, chairman. Retrieved 2016, September 20 from Sakae Holdings website: http://www.sakaeholdings.com/awards-douglas-foo-chairman.html
41. Ang, E., & Chang, P. Y. H. (2004). Winning strokes. Singapore: Nouveau Pub, p. 59. (Call no.: RSING 338.04095957 ANG); Tan, R. L. (2008, July 27). My McSushi dream. The Straits Times, p. 78. Retrieved from NewspaperSG.
The information in this article is valid as at 18 October 2016 and correct as far as we are able to ascertain from our sources. It is not intended to be an exhaustive or complete history of the subject. Please contact the Library for further reading materials on the topic.
Foo, Douglas, 1969-
Entrepreneurship--Singapore
Award winners--Singapore--Biography
Businessmen--Singapore--Biography
Business, finance and industry>>Industry>>Services>>Tourism and hospitality
Personalities>>Biographies
~ Recommendations ~
Olivia Lum
Olivia Lum Ooi Lin (b. 1962, Kampar, Perak, Malaysia – ) is the founder, group chief executive officer and president ...
Sakae Sushi
Sakae Sushi is a restaurant chain from Singapore that specialises in affordable Japanese food served to diners via a ...
Jannie Chan
Jannie Chan Siew Lee (Dato' Dr) (b. 7 May 1945, Ipoh, Malaysia–), commonly known by her former matrimonial name, Jannie ...
Charles & Keith
Charles & Keith is a Singapore brand known for its women's footwear and accessories. Established in 1996 by brothers ...
Ip Yiu Tung
Ip Yiu Tung (b. 1949, Hong Kong–) is the former group chairman and chief executive officer of restaurant chain Crystal ...
Rigel Technology
Established in 1991, Rigel Technology is a Singapore-based bathroom supplies manufacturer focused on environmentally ...
Old Chang Kee
Old Chang Kee is a food retail chain best known for its Hainanese-style curry puffs, which were first sold in 1956. ...
Kartar Singh Thakral
Kartar Singh Thakral (b. 22 September 1933, Bangkok, Thailand–) is the chairman of Thakral Group of Companies and executive ...
Goi Seng Hui
Goi Seng Hui (b. 1949, Fuqing, China–) is an entrepreneur and investor nicknamed Singapore's "Popiah King". His company, ...
George Quek
George Quek Meng Tong is the founder and chairman of BreadTalk Group, famous for the BreadTalk bakery chain. He began ...
Incorporated on 28 January 1972, Singapore Airlines (SIA), the national carrier of Singapore, is one of the most successful ...
Bee Cheng Hiang
Bee Cheng Hiang (美珍香) is a Singapore-based company that produces and sells a wide variety of food products, most notably ...
Wee Cho Yaw
Wee Cho Yaw (b. 1930, Jincheng, Quemoy, Taiwan–) is the former chairman and chief executive officer of the United Overseas ...
Adrin Loi
Adrin Loi Boon Sim (b. 1955, Singapore–) is the executive chairman of food and beverage chain Ya Kun International. ...
I have feedback on this infopedia article: Douglas Foo
Community and Social Services
Geography and Travels
Streets and Places


Be sure you don't arch your back! Keep it hollow!
Don't lock out your joints on the positive part of the exercise (the pressing motion). This takes the tension of the chest and that's not what we want.
When pressing the bar over your head, lower your head back down. Don't lock your your elbows when doing this!
Go a little bit past a 90° angle with your elbows!
Grab the bar, your palms facing away from you.
I'm glad you liked it! I'll definitely keep posting!


text:
Q: Creating private chat channels using socketio and laravel Ive implemented this tutorial within a project of mine, and its workin all fine beetween computers in the network, now I just want to know how could I make the user able to comunicate just to 1 person(socket) and not to all.
Ive followed this guide.
https://github.com/oriceon/laravel-5-redis-and-socket.io

A: For emit just to one specific socket you will need his socket.id so you can do:
io.sockets.connected[socketID].emit(....)

redpajama_set_name: RedPajamaStackExchange


Rajasekhar is making a comeback after a very long time and this is the movie that is supposedly one of the most awaited movies for the fans of Rajasekhar.
Directed by Praveen Sattaru and produced by M. Koteswar Raju under Jyostar Enterprises production company, Garuda Vega is a science-fictional movie.
The movie stars Sunny Leone, Rajasekhar, Shraddha Das, Adith Arun and Kishore in lead roles.
Behind the scenes video of Garuda Vega that was uploaded to the web is making rounds around the internet, creating a slow and steady hype.
The music directors of Garuda Vega are Beems Cecirolio and Sricharan Pakala.
Seems like the movie is still a work in progress but it's slated to be released on 6th October 2017.


text:
Своло́та () — художній фільм режисера Олександра Атанесяна, знятий за однойменною повістю Володимира Куніна. Прем'єра фільму відбулася 2 лютого 2006 року.

У ролях
 Андрій Панін — підполковник Антон В'ячеславович Вишневецький, начальник табору
 Андрій Краско — комірник дядько Паша
 Олександр Головін — Кот
 Сергій Риченков — Тяпа
 Володимир Андрєєв — Кот в старості (Чернов Костянтин Аркадійович)
 Володимир Кашпур — Тяпа в старості (Тяпкін Валентин Петрович)
 Микита Єрунов — Бабай
 Олег Буганов — Принц
 Маріус Штандель — Шкет
 Ігор Юртаєв — Окунь
 Олександр Вербицький — Заєць
 Олексій Соболєв — Кучер
 Велімир Русаков — Маестро
 Дмитро Горьовий — Череп
 Семен Сівков — Калуга
 Ілля Сисоєв — Матаня
 Кирило Ємельянов — Студер
 Василь Ликшин — Лаврик
 Микита Панов — Микита
 Ростислав Бершауер — лікар
 Юрій Сошников — замполіт
 Микола Качура — капітан КДБ
 Геннадій Матвєєв — працівник НКВС
 Сергій Неудачин — наглядач у в'язниці
 Олександр Носков — Тимофій
 Дмитро Таланцев — німецький генерал
 Герман Іванов — конвоїр автозаку

Цікаві факти
 На церемонії вручення кінонагород російського філіалу MTV, картина Олександра Атанесяна «Сволота» стала найкращою кінокартиною. Проте Володимир Меньшов, який вийшов вручати премію, відкривши конверт і побачивши назву переможця, кинув пакет на сцену: «Я не вручатиму цю премію фільму, який ганьбить мою країну. Нехай цей приз вручає Памела Андерсон», — заявив він.
 Зйомки фільму відбувалися у Вірменії.
 Вибір постера фільму було проведено за результатами голосування відвідувачів декількох вебсайтів кінематографічної тематики.
 Частину витрат на виробництво фільму — близько $700 000 — сплатило Федеральне агентство з культури та кінематографії, очолюване на той час Михайлом Швидким.
 Фільм «Сволота», поряд з «Батьківщина або смерть» (2007) та «Зозулині діти» (1991), є одним із трьох художніх фільмів, знятих на тему «радянські діти-диверсанти в роки Другої світової війни».
 Крім історичної невідповідності зустрічається незв'язаність сюжету: після підриву бункера Коту відриває ліву кисть, але коли він вмовляє втекти Тяпу він тримає лівою рукою автомат.

Посилання
 «Сволота»   на сайті Internet Movie Database

Фільми-драми Росії
Військові фільми Росії
Фільми про німецько-радянську війну
Фільми про в'язницю

redpajama_set_name: RedPajamaWikipedia


text:
\section{Introduction}
Compact objects such as neutron stars and black holes are formed in collapsing stars some of which eventually end up with supernova explosions.
In general, a fraction of supernova ejecta falls back toward a newborn compact object \citep{1971ApJ...163..221C, 1972SvA....16..209Z, 1988Natur.333..644M}.
The accretion rate and its temporal evolution can be determined by e.g., the strength of the supernova shock and the progenitor structure (e.g., \cite{2016ApJ...818..124E}).
On the other hand, newborn compact objects can continuously deposit energy into the fallback matter via e.g., neutrino emission, pulsar activity and/or accretion-disk wind (e.g., \cite{2011ApJ...736..108P}).
Competition between the fallback accretion onto and the energy deposition from compact objects may result in a variety of outcomes and lead to a diversity of compact objects.

In particular, the dynamics of the fallback accretion may be related to the diversity of relatively young ($\sim 1\mbox{-}10~\rm kyr$) neutron stars;
there are three distinct populations, ordinary pulsars, magnetars, and central compact objects (CCOs)~\footnote{They sometimes show links to another population.
For example, some pulsars underwent soft-gamma repeater like bursts \citep{2010ApJ...711L...1V},
and a CCO was found to exhibit magnetar-like activity \citep{2016MNRAS.463.2394D, 2016ApJ...828L..13R}.}.
Based on the spectral and timing observations, they are considered to have different energy sources,
the rotation, magnetic-field, and thermal energies, respectively.
The most distinctive difference between them is the magnetic-field strength; young pulsars typically have dipole fields of $B_{\rm d} \lesssim 10^{13}$ G~\footnote{http://www.atnf.csiro.au/research/pulsar/psrcat/}.
Magnetars are considered to be powered by decays of stronger fields of $B_* >\mathrm{a~few}\times10^{13}$ G~\citep{2014ApJS..212....6O}
while CCOs have considerably weaker dipole fields of $B_{\rm d} \ll 10^{12}$ G~\citep[and so on]{2001ApJ...559L.131P, 2006ApJ...653L..37P}.
Although the diversity of the magnetic field strength can be attributed to conditions before and during the neutron star formation,
i.e., the magnetic field strength of the iron core of a progenitor (the fossil scenario; \cite{2006MNRAS.367.1323F}) or the magnetic field amplification by a dynamo process~\citep{1992ApJ...392L...9D,2015Natur.528..376M},
it may be also possible to attribute the diversity to conditions after the formation, i.e., various rates of the fallback accretion onto the neutron star.

If the accretion rate is sufficiently high, the fallback matter can compress and bury the magnetic field into the neutron star crust~(e.g., \cite{2010RMxAA..46..309B,2016MNRAS.456.3813T}).
Such a case may correspond to a CCO formation (the hidden magnetic field scenario; \cite{1995ApJ...440L..77M,1995ApJ...442L..53Y}).
For example, \citet{2016MNRAS.456.3813T} obtained the critical accretion rate for burying the magnetic field
by considering the competition between the magnetic pressure of the surface field and the ram pressure of the fallback matter.
In these studies, however, the energy deposition from the neutron star has been neglected.
If the energy deposition rate is sufficiently large, the fallback matter can be repelled before reaching the surface.
The critical conditions can be obtained by considering the competition between the fallback accretion onto and the energy deposition from the neutron star.
This may define additional bifurcations of the neutron star population.

To this end, we here investigate the dynamics of fallback matter being pushed back by an energy deposition from the central object with newly constructed spherically symmetric self-similar solutions.
We consider fallback matter marginally bound by the gravitational field of the central object with a mass $M_{\rm c}$
and a power-law energy deposition rate from the central object;
\begin{equation}\label{eq:edep}
\dot{Q}=L_l t^l.
\end{equation}
Here $L_l$ and $l$ are constants and $t$ is the time measured from the onset of the energy deposition.
Although our solutions are described by a single dimensionless variable
\begin{equation}
\xi=\frac{r}{(GM_{\rm c}t^2)^{1/3}},
\end{equation}
where $r$ is the radial coordinate and $G$ denotes the gravitational constant,
a variety of density and velocity structures can be realized depending on the strength of the deposition and so on,
which, to our knowledge, have not been seen in previous studies.

The structure of the paper is as follows.
The next  section describes our model.
Section 3 presents our self-similar solutions with various values of parameters.
In Section 4, we discuss some applications of our solutions to neutron star formation. Section 5 summarizes the results and discusses relations to previous works.

\begin{figure}
\begin{center}
  \includegraphics[width=0.7\textwidth]{regions.eps}
\end{center}
\label{fig:regions}
\caption{Schematic view of the model consisting of three regions. Region I is adjacent to the central object. The energy from the central object is supposed to be uniformly deposited in this region. Region II contains the shocked fallback matter and is separated from Region I by a contact surface. In Region III, the matter freely falls due to the gravity of the central object. An expanding shock front separates Region II from Region III. The black arrows indicate the direction of the flows while the green and red arrows indicate the propagations of the contact surface and the shock front, respectively. Note that the direction of the flow immediately behind the shock front depends on model parameters. See section \ref{sec:results} for details.}
\end{figure}

\section{Model}\label{sec:model}
We consider the flow of fallback matter affected by the energy deposition from a central object.
Following \citet{2016PASJ...68...22M}, we divide the flow into three distinct regions (see Fig. \ref{fig:regions}):
the innermost region  (Region I) adjacent to the central object where the energy is deposited uniformly,  Region II where the fallback matter is shocked, and the outermost region in which cold matter freely falls due to the gravity of the central object (Region III). Regions I and II are separated by the contact discontinuity specified by the dimensionless variable introduced above as $\xi=\xi_{\rm c}$. The fluid in Region II has a constant adiabatic index $\gamma$ and turns into outflow at a certain point depending on $\xi_{\rm c}$ and $\gamma$.
The shock front divides the fallback matter into Regions II and III at $\xi=\xi_{\rm s}$.
Such a flow structure across Regions I and II has been reproduced by numerical simulations~(e.g., \cite{2016PASJ...68...22M}).

\subsection{Energy deposition region (Region I)}
The central object is assumed to  deposit energy in a uniform spherical region with a radius $R_{\rm c}=\xi_{\rm c}(GM_{\rm c}t^2)^{1/3}$. The internal energy $E_{\rm c}$ and pressure $P_{\rm c}$ in this region evolve with time $t$ according to the first law of thermodynamics as
\begin{equation}\label{eq:eir}
\frac{dE_{\rm c}}{dt}+P_{\rm c}\frac{d}{dt}\left(\frac{4\pi R_{\rm c}^3}{3}\right)=L_l t^l.
\end{equation}
 Here $L_l$ and $l$ are constant. The subscript $l$ of $L_l$ indicates that the dimension of this quantity depends on the value of $l$. This region becomes very hot and the equation of state can be approximated by that for ultra-relativistic gas, that is, $E_{\rm c}=4\pi P_{\rm c} R_{\rm c}^3$.

\subsection{Accreted matter (Regions II and III)}
Accreted matter can be divided into the shocked fallback matter (Region II) and the surrounding accreted matter (Region III). The motion of the surrounding matter is not affected by the energy deposition but controlled solely by the gravity from the central object.  We describe the flow in Region II  by using  a self-similar solution.
We note that the problems treated in this paper involve two constant quantities with physical dimensions $GM_{\rm c}$ and $L_l$.

Here we assume that the spherically symmetric flow depends on time $t$ and $r$ only through $t$ and $\xi(r,\,t)$. Thus the density $\rho$, the velocity $v$, and the pressure $p$ take the forms of
\begin{eqnarray}
&\rho({\xi},{t})=\frac{L_l t^{l-\frac{1}{3}}{D}(\xi)}{\left(GM_{\rm c}\right)^{5/3}},&\label{eq:density} \\
&v({\xi},{t})=\left(\frac{{GM_{\rm c}}}{t}\right) ^{1/3}V(\xi) ,& \label{eq:velocity} \\
& p({\xi},{t})=\frac{L_l  t^{l-1}\Pr (\xi)}{GM_{\rm c} },& \label{eq:pressure}
\end{eqnarray}
as functions of $\xi$ and $t$. Here we have introduced dimensionless functions $D(\xi)$, $V(\xi)$, and $\Pr(\xi)$. The governing equations are described as
\begin{eqnarray}
&\frac{\partial\rho(\xi, t)}{\partial t}+\frac{\partial r^2\rho(\xi, t) v(\xi, t)}{{r^2}\partial r}=0,& \\
&\rho(\xi, t) \left(\frac{\partial v(\xi, t)}{\partial t}+v(\xi, t) \frac{\partial v(\xi, t)}{\partial r}\right)+\frac{GM_{\rm c}\rho(\xi, t)}{r^2}+\frac{\partial p(\xi, t)}{\partial r}=0, &\\
&\left(\frac{\partial }{\partial t}+v(\xi, t) \frac{\partial }{\partial r}\right)\left[\frac{p(\xi, t)}{(\gamma-1)\rho(\xi, t)}\right]+p(\xi, t) \left(\frac{\partial }{\partial t}+v(\xi, t) \frac{\partial }{\partial r}\right)\left[\frac{1}{\rho(\xi, t)}\right]=0. &
\end{eqnarray}
After some manipulations we obtain ordinary differential equations for dimensionless functions $D(\xi)$, $V(\xi)$, and $\Pr(\xi)$ as
\begin{eqnarray}
&\xi (2 \xi-3 V(\xi)) D^\prime(\xi)-D(\xi) \left(3 l \xi+3 \xi V'(\xi)+6 V(\xi)-\xi\right)=0,&\label{eq:ssflc}\\
&D(\xi) \left(\xi^2 (2 \xi-3 V(\xi)) V^\prime(\xi)+\xi^2 V(\xi)-3\right)=3 \xi^2 \Pr ^\prime(\xi),&\label{eq:ssflm}\\
&{\gamma(2 \xi-3 V(\xi)) \frac{D^\prime(\xi)}{D(\xi)}+(3 (1-\gamma) l+\gamma-3)+(3 V(\xi)-2 \xi) \frac{\Pr ^\prime(\xi)}{ \Pr (\xi)}}=0,\label{eq:ssfle}&
\end{eqnarray}
where $^\prime$ denotes the derivative with respect to $\xi$.
Eqs. (\ref{eq:ssflc}-\ref{eq:ssfle}) can be rewritten as
\begin{eqnarray}
&D'(\xi)= \frac{D(\xi) \left(D(\xi)  \left(9-3 \xi V(\xi) ((3 l-4) \xi+6 V(\xi))+(6 l-2) \xi^3\right)\right)}{\xi^2 \left(D(\xi) (2 \xi-3 V(\xi))^2-9 \gamma \Pr (\xi)\right)}&\nonumber \\
&+\frac{ 9 \xi^2 (-3 \gamma l+\gamma+3 l-3) D(\xi)\Pr (\xi)}{\xi^2 (2 \xi-3 V(\xi)) \left(D(\xi) (2 \xi-3 V(\xi))^2-9 \gamma \Pr (\xi)\right)},& \label{eq:ssd}\\
&V'(\xi)= \frac{9 \xi \Pr (\xi) (2 \gamma V(\xi)+(l-1) \xi)-D(\xi) (2 \xi-3 V(\xi)) \left(\xi^2 V(\xi)-3\right)}{\xi^2 \left(D(\xi) (2 \xi-3 V(\xi))^2-9 \gamma \Pr (\xi)\right)},&  \label{eq:ssv}\\
&\Pr '(\xi)= \frac{3 D(\xi) \Pr (\xi) \left(3 \xi V(\xi) (\xi (\gamma-l+1)-2 \gamma V(\xi))+3 \gamma+2 (l-1) \xi^3\right)}{\xi^2 \left(D(\xi) (2 \xi-3 V(\xi))^2-9 \gamma \Pr (\xi)\right)}.  \label{eq:ssp}&
\end{eqnarray}
From the second term of the right hand side of equation (\ref{eq:ssd}), we can find that the derivative of the density diverges at  $\xi_{\rm c}$ where
\begin{equation}\label{eq:contact}
V(\xi_{\rm c})=\frac{2\xi_{\rm c}}{3},
\end{equation}
is satisfied while the other derivatives of the pressure and the velocity do not diverge. Thus this point $\xi=\xi_{\rm c}$ defines the contact surface between Regions I and II.
To obtain a solution, we numerically integrate Eqs.(\ref{eq:ssd}-\ref{eq:ssp}) from $\xi=\xi_{\rm s}$ to $\xi=\xi_{\rm c}$.

The solution for the flow in Region III ($\xi\geq\xi_{\rm s}$) is obtained by ignoring pressure in equations (\ref{eq:ssflc}) and (\ref{eq:ssflm}) (or (\ref{eq:ssd}) and (\ref{eq:ssv})) as
\begin{eqnarray}
&V(\xi)=-\sqrt{\frac{2}{\xi}},& \label{eq:fbv}\\
&D(\xi)=D_{\rm fb}\exp{\left[\int_{\xi_{\rm s}}^\xi dx\frac{2(3l-1)x-9\sqrt{2}x^{-1/2}}{2x(2x+3\sqrt{2}x^{-1/2})}\right]}.& \label{eq:fbd}
\end{eqnarray}
Here a constant $D_{\rm fb}$  denotes $D(\xi_{\rm s})$ in the un-shocked flow (Region III).
It follows from substitutions of these expressions into equations (\ref{eq:density}) and (\ref{eq:velocity}) that the distributions of the density and velocity in the fallback matter evolve as
\begin{eqnarray}
&\rho(r,\,t)=\frac{L_lD_{\rm fb}t^{l-1/3}}{(GM_{\rm c})^\frac{5}{3}}\exp{\left[\int_{\xi_{\rm s}}^\frac{r}{(GM_{\rm c}t^2)^{1/3}} dx\frac{2(3l-1)x-9\sqrt{2}x^{-1/2}}{2x(2x+3\sqrt{2}x^{-1/2})}\right]},& \\
&v(r,\,t)=-\sqrt{\frac{2GM_{\rm c}}{r}} \label{eq:fbvel}, &
\end{eqnarray}
and that the density approaches a power-law function proportional to $r^{(3l-1)/2}$ independent of $t$ in the limit of $r\rightarrow\infty$. Thus the flow approaches a stationary state for a large $r$ ($\xi$).
The velocity expressed by equation (\ref{eq:fbvel}) implies that the fallback matter is initially at rest at  large distances from the center. {Thus the total energy of the flow in Region III is equal to zero while the energy of the flow in Region II becomes positive due to the energy supply from the central source. This  indicates that all the solutions presented here describe the flow eventually repelled by the energy supply.} Because the density distribution depends on the parameter $l$ that specifies the nature of the central energy source, this density distribution is required to lead to a self-similar solution in which the shock front expanding with the radius proportional to $t^{2/3}$ for a given energy source. If the central source is more energetic, which corresponds to larger $L_l$, the fall back matter can be denser, while if the gravity of the central object is stronger, which corresponds to a larger $M_{\rm c}$, then the fallback matter needs to be more sparse to have an expanding shock front.

We ignore physical processes like neutrino heating and cooling, radiative diffusion, photo-disintegration of nuclei, and electron-positron pair production and annihilation, some of which might play crucial roles in the fate of the fallback matter. Instead, we have presented solutions with varying the adiabatic index and the exponent $l$ of $\dot Q$ in equation (\ref{eq:edep}), which mimic some of the effects of these processes.

\subsection{Boundary conditions}
\subsubsection{Contact surface}\label{sec:cs}
We require a condition that the flow has a continuous pressure distribution through the contact surface between Regions I and II where equation (\ref{eq:contact}) holds. From the evolution of the pressure derived from equation (\ref{eq:eir}), this requirement leads to
\begin{equation}\label{eq:pc}
\Pr(\xi_{\rm c})= \frac{3}{4 \pi (5 +3 l) \xi_{\rm c}^3}.
\end{equation}
This boundary condition is equivalent to the condition that the energy deposited by the central source is equal to the total energy of the flow inside the shock front.
Note here that the accreted matter entering into the shock front carries no energy (the sum of the energy densities of the matter is $v^2(r,\,t)/2-GM_{\rm c}/r=0$ from equation \ref{eq:fbvel}).
We found that the self-similar flow around the contact surface behaves as
\begin{eqnarray}
&D(\xi)\sim D_{\rm c}(\xi-\xi_{\rm c})^\frac{3 - \gamma -3 l + 3 \gamma l}{3 ( 2 \gamma -1+ l)},& \label{eq:csd}\\
&V(\xi)\sim\frac{2\xi_{\rm c}}{3} + \frac{3 - 4\gamma - 3 l}{3\gamma} (\xi - \xi_{\rm c}), &
\end{eqnarray}
where $D_{\rm c}$ is a constant. From equation (\ref{eq:csd}), the density distribution near the contact surface drastically changes if $\gamma>3/2$ or not. If $\gamma<3/2$, the density decreases to zero toward the contact surface. If $\gamma>3/2$, solutions with $l=(-3 + \gamma)/[3 ( \gamma-1)]$ give constant densities at the contact surface between Regions I and II. Otherwise the density at the contact surface diverges to infinity ( $l<(-3 + \gamma)/[3 ( \gamma-1)]$) or goes to 0  ( $l>(-3 + \gamma)/[3 ( \gamma-1)]$).

\subsubsection{Shock front}\label{sec:front}
We assume that a strong shock propagates in the accreted matter. The location of the shock front is specified by $\xi=\xi_{\rm s}$, where $\xi_{\rm s}$ is a constant. The Rankine-Hugoniot jump conditions at the shock front can be written as
\begin{eqnarray}
&D(\xi_{\rm s})=\frac{\gamma+1}{\gamma-1}D_{\rm fb},\label{eq:shockd}&\\
&V(\xi_{\rm s})=\frac{1-\gamma}{\gamma+1}\sqrt{\frac{2}{\xi_{\rm s}}}+\frac{4\xi_{\rm s}}{3\left(\gamma+1\right)},&\label{eq:shockv}\\
&\Pr(\xi_{\rm s})=\frac{4D_{\rm fb}\sqrt{\xi_{\rm s}^{3(l-1)}}}{\gamma+1}\left(\frac{\sqrt{2\xi_{\rm s}^3}}{3}+1\right)^2.&
\end{eqnarray}
Here we have used the fact that the dimensionless velocity of the accreted matter in Region III at the shock front is  $-\sqrt{2/\xi_{\rm s}}$ (see eq. \ref{eq:fbv}) and that the dimensionless density at the shock front is denoted by  $D_{\rm fb}$.
The value of  $D_{\rm fb}$ is determined to satisfy the boundary condition (\ref{eq:pc}) at the contact surface for each given $\xi_{\rm s}$.
\begin{figure}
\begin{center}
 \includegraphics[width=0.45\textwidth]{g65l0.eps} \includegraphics[width=0.45\textwidth]{g43l0.eps}
 \includegraphics[width=0.45\textwidth]{g75l0.eps}  \includegraphics[width=0.45\textwidth]{g53l0.eps}
\caption{Relations between some characteristic quantities and $\xi_{\rm c}$ for solutions with four different values of $\gamma$: $6/5$ (top left panel), $4/3$ (top right panel), $7/5$ (bottom left panel),  and $5/3$ (bottom right panel). $l=0$ for all the solutions.}
\label{fig:accretion}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
  \includegraphics[width=0.32\textwidth]{dist_g53_l0_xs1.eps} \includegraphics[width=0.32\textwidth]{dist_g53_l-23_xs2.eps} \includegraphics[width=0.32\textwidth]{dist_g53_l-0.9_xs2.eps}
\caption{Distributions of the density $D$, the pressure $\Pr$, and the velocity $V$ as functions of $\xi$ for solutions with 3 different values of $l$: 0  (left panel), $-2/3$ (middle panel), and $-0.9$ (right panel). $\gamma=5/3$ for all the solutions. The values of $\xi_{\rm s}$ are chosen arbitrarily.}
\label{fig:dist53}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
  \includegraphics[width=0.45\textwidth]{dist_g43_l0_amax.eps} \includegraphics[width=0.45\textwidth]{dist_g65_l0_amax.eps}
\caption{Distributions of the density $D$, the pressure $\Pr$, and the velocity $V$ as functions of $\xi$ for solutions with the maximum accretion rates at the shock front. The left panel shows the solution with $\gamma=4/3$ and the right panel $\gamma=6/5$. $l=0$ for both solutions.}
\label{fig:distlt43}
\end{center}
\end{figure}

{Though it might be possible to extend this shock condition to that with an arbitrary strength as was done  in the context of failed supernovae by \citet{2018ApJ...863..158C}, we take the strong shock limit to simplify the procedure to obtain solutions.}

\section{Results}\label{sec:results}
We can find solutions of equations (\ref{eq:ssflc})-(\ref{eq:ssfle}) satisfying the boundary conditions at the shock front and the contact surface for $l>-1$ and $\gamma>1$.
No solution exists in the other range of these parameters;
the total deposited energy becomes infinite for $l\leq-1$ and the density becomes negative or infinite at the shock front for $\gamma\leq1$ (see eq. \ref{eq:shockd}).
We obtain a solution for any positive value of $\xi_{\rm c}$.
Note that $\xi_{\rm s}$ monotonically increases with $\xi_{\rm c}$ and the solutions in the limit of $\xi_{\rm c}\rightarrow 0$ give the minimum $\xi_{\rm s}$ (denoted by $\xi_{\rm s,\,0}$).
It follows that there are solutions with the maximum possible accretion rates at the shock front when $\gamma\leq 4/3$ for each $l$. Since the central source is supposed to deposit energy at the rate of $\dot{Q}$, it is convenient to normalize the accretion rate $\dot{M}$ at the shock front with $\dot{Q}$ as
\begin{equation}\label{eq:rateE}
\frac{GM_{\rm c}\dot{M}}{r_{\rm s}\dot{Q}}=4\pi D_{\rm fb}\sqrt{\xi_{\rm s}},
\end{equation}
where $r_{\rm s}$ denotes the radius of the shock front and $\dot{M}=4\pi r_{\rm s}^2\rho(\xi_{\rm s},\,t)\sqrt{2GM_{\rm c}/r_{\rm s}}$ is the mass accretion rate at the shock front.
Another normalization is possible by taking account of the dimension as
\begin{equation}\label{eq:rate}
\left(\frac{GM_{\rm c}}{t}\right)^{2/3}\frac{\dot{M}}{\dot{Q}}=4\pi D_{\rm fb}\sqrt{\xi_{\rm s}^3}.
\end{equation}
We show these dimensionless accretion rates, $\xi_{\rm s}$, and $D_{\rm fb}$  as functions of $\xi_{\rm c}$ for solutions with $l=0$ and $\gamma=6/5,\, 4/3,\,7/5$, and $5/3$ in Figure \ref{fig:accretion}. Solutions with $\gamma< 4/3$ have maxima of the dimensionless accretion rates given by equation (\ref{eq:rateE}) or (\ref{eq:rate}) at a finite $\xi_{\rm c}$. For $\gamma=4/3$, solutions in the limit of $\xi_{\rm c}\rightarrow 0$ give the maximum accretion rates. Solutions with $\gamma>4/3$ can sustain any accretion rates. In other words, the accretion rate monotonically increases to infinity as $\xi_{\rm c}\rightarrow 0$ in these solutions. At the same time, the value of $D_{\rm fb}$ becomes infinite in this limit.
These characteristic values are listed in Table 1 for some $\gamma$ and $l$.

\begin{table}[hb]
\tbl{Critical dimensionless quantities in solutions with some $l$ and $\gamma$. For $\gamma=5/3$ and $7/5$, values of $\xi_{\rm s,\,0}$ of the solutions in the limit of $\xi_{\rm c}\rightarrow 0$ are listed. For $\gamma=4/3$, in addition to $\xi_{\rm s,\,0}$, the corresponding eigenvalue of $D_{\rm fb}$ (eq. (\ref{eq:shockd})) as well as the corresponding maximum values of the two accretion rates (eqs. (\ref{eq:rateE}) and (\ref{eq:rate})) are listed.  For $\gamma=6/5$, values of $\xi_{\rm s}$ ($\xi_{\rm s,\,1}$ and $\xi_{\rm s,\,2}$) that give the maximum values of the two accretion rates and the corresponding values of $D_{\rm fb}$. }{%
\begin{tabular}{r|l|l|llll|llllll}\hline
&\multicolumn{12}{c}{$\gamma$}\\ \hline
&\multicolumn{1}{c|}{$5/3$} &\multicolumn{1}{c|}{$7/5$}&\multicolumn{4}{c|}{$4/3$}&\multicolumn{6}{c}{$6/5$} \\ \hline
  $l$ & $\xi_{\rm s,\,0}$  &  $\xi_{\rm s,\,0}$  &$\xi_{\rm s,\,0}$  &$ D_{\rm fb,\,0}$ &  $4\pi\left(D_{\rm fb}\sqrt{\xi_{\rm s}}\right)_0$ &  $4\pi\left(D_{\rm fb}\sqrt{\xi_{\rm s}^3}\right)_0$ & $\xi_{\rm s,\,1}$  &$ D_{\rm fb,\,1}$ &  $4\pi\left(D_{\rm fb}\sqrt{\xi_{\rm s}}\right)_1$ & $\xi_{\rm s,\,2}$  &$ D_{\rm fb,\,2}$ &  $4\pi\left(D_{\rm fb}\sqrt{\xi_{\rm s}^3}\right)_2$  \\ \hline \hline
 $-0.99$ & 3.0 &  1.2& 0.75&5.1&55&41 & 0.3007 &4.180&28.81 & 0.6733 & 1.929&13.39\\
$-0.9$ & 1.7 &  0.80& 0.40&2.3&18&7.2 & 0.2839 & 0.5541& 3.710 & 0.6001 & 0.2714& 1.585\\
$-2/3$ & 1.2&0.57&0.28&1.5&10&2.8 & 0.2309 & 0.2908& 1.756& 0.5168 & 0.1358& 0.6341\\
$-0.5$ & 1.1 &0.49&0.25&1.2&7.8&2.0&0.2129&0.2550& 1.479&0.4766&0.1176&0.4862\\
 0 & 0.80  &0.36& 0.18&1.3&6.9&1.2& 0.1691& 0.2332&1.205 &0.4010 & 0.1003&0.3201\\
 1& 0.57& 0.26&0.13  &1.3&5.8 &0.73 & 0.1191 &0.2471&1.072 &0.3170 & 0.09583&0.2149 \\
2 &0.46& 0.20&0.10 &1.4&6.1 & 0.24 & 0.1000& 0.2588&1.029 & 0.2661 &0.09859& 0.1701\\
\hline
\end{tabular}}
\end{table}

Table 1 shows results of solutions with various $l$. The energy deposition rate usually decreases with time if a single physical process is involved and thus described with negative $l$. Such a deposition rate might mimic the declining phase of a sudden energy release due to a glitch in the crust  followed by the transport of energy toward the surface \citep{1989ApJ...336..360E,1991ApJ...381L..47V}. A positive $l$ may be realized when the central object starts  to deposit energy  from a slight excess of the heating rate compared with the cooling rate. Here we present solutions for the energy depositions with linear and quadratic evolutions for simple examples of positive $l$. On the other hand, the solutions with $l=0$ are of particular importance because the magnetic dipole radiation from a pulsar deposits energy at a nearly constant rate in the early phase.

As mentioned in section \ref{sec:cs}, some solutions have distinct distributions of the density near the contact surface. For example, Figure \ref{fig:dist53} shows solutions with $\gamma=5/3$ and three different values of $l$. The solution with $l=-2/3$ has a finite density at the contact surface, while the density becomes 0 at the contact surface in the solution with $l=0$ and diverges in the solution with $l=-0.9$. The solution with $l=0$ may be subject to the Rayleigh-Taylor instability because the density gradient near the contact surface has a sign opposite to that of the pressure gradient  (see the left panel of Fig. \ref{fig:dist53}). This instability tends to bring dense matter toward the contact surface. Thus the central activity may fail to repel the fallback matter even if $\gamma>4/3$.

Solutions with the maximum accretion rates are shown in Figure \ref{fig:distlt43}. These solutions have negative velocities in some part of Region II because of their small $\xi_{\rm s}$'s.  From equation (\ref{eq:shockv}), the velocity immediately behind the shock front becomes negative when $\xi_{\rm s}<\left[3(\gamma-1)\right]^{2/3}/2$. If $\gamma=4/3$ ($\gamma=6/5$),  this criterion becomes $\xi_{\rm s}<1/2$ ($\xi_{\rm s}<(5/3)^{2/3}/2\sim0.356$).  On the other hand, the solutions with $\gamma=5/3$ presented in Figure \ref{fig:dist53} happen to have large $\xi_{\rm s}$'s that do not satisfy this criterion ($\xi_{\rm s}<1/2^{1/3}$ for $\gamma=5/3$), thus the shocked matter flows outward  while solutions with $\gamma>4/3$ and negative $l$ have $\xi_{\rm s,\,0}$ greater than the upper limit of the criterion as seen in Table 1. Shocked matter in a solution with a positive $l$ tends to flow inward due to the weak central engine in the early phase. Because the contact surface always moves outward in all the solutions (see eq. (\ref{eq:contact})), the pressure increased by the central energy deposition repels the fallback matter somewhere in Region II even for these solutions with great accretion rates.  In solutions with small accretion rates, the energy deposition can repel the fallback at the shock front.

{The kinetic energy $E_{\rm k}(t)$ of the repelled ejecta evolves with time $t$ following the equation
\begin{equation}
E_{\rm k}(t) =2\pi L_lt^{l+1}\int_{\xi_{\rm c}}^{\xi_{\rm s}}D(\xi)V^2(\xi)d\xi.
\end{equation}
Since the value of the dimensionless integral is of the order of unity here, the factor in front of the integral gives a rough amount of the kinetic energy.}

\section{Application to neutron star formation with fallback accretion}
Although the self-similar solutions constructed in the previous sections are valid under limited conditions, they can be practically applicable to some astrophysical phenomena.
Here we mainly focus on supernova fallback pushed back by the energy deposition from a newborn neutron star, in particular, a rotation-powered one.
We discuss the conditions for repelling the fallback accretion by the spin-down luminosity and their implications on properties of associated supernovae and fates of the neutron stars.

After a successful supernova shock propagates through the progenitor star, a bulk of the stellar material is ejected while a minor fraction falls back.
The accretion rate and its temporal evolution can be determined by the strength of the supernova shock and the inner structure of the progenitor.
For example, \citet{2016ApJ...821...69E} estimated the fallback rate based on one-dimensional numerical simulations of neutrino-driven explosions.
The fallback typically starts when the neutrino luminosity significantly decreases, i.e., $t_{\rm fb} \gtrsim 10$ s after the core bounce,
and the accretion rate subsequently decreases as $\propto (t/t_{\rm fb})^{-5/3}$ for $t \gtrsim t_{\rm fb}$.
The total mass $M_{\rm fb}$ of the fallback matter ranges from $ \sim 10^{-4}\,M_\odot$ to $\sim 10^{-2}\,M_\odot$ . More matter falls back in a more massive star.
Correspondingly, the peak mass accretion rate is estimated to be $\dot M_{\rm fb} \lesssim 10^{-(3\mbox{-}5)}\,M_\odot\,\rm s^{-1}$.

In general, the maximum fallback accretion rate that can be repelled by the central energy source is described with
$M_{\rm c}$, $r_{\rm s}$, $(4 \pi D_{\rm fb} \sqrt{\xi_{\rm s}})$, and $\dot Q$ from equation (\ref{eq:rateE}).
Since we consider a fallback accretion onto a neutron star, we take $M_{\rm c} = M_* \sim 1.4 \ M_\odot$ and set the radius of the neutron star as $R_* \sim 12 \ \rm km$.
When the fallback accretion starts, the position of the shock will be $r_{\rm s} \approx \xi_{\rm s} (GM_*t_{\rm fb}{}^2)^{1/3}$, or
\begin{equation}\label{eq:r_s_crit}
r_{\rm s} \sim 4.2 \times 10^{9}\,{\rm cm}~\xi_{\rm s}\,\left(\frac{t_{\rm fb}}{20\,\rm s} \right)^{2/3}.
\end{equation}
In the critical situation corresponding to the maximum mass accretion rate, the radius of the inner contact surface should be set as the neutron star radius, i.e., $\xi_{\rm c, crit} \approx R_*/(GM_*t_{\rm fb}{}^2)^{1/3}$, or
\begin{equation}\label{eq:xi_c_crit}
\xi_{\rm c, crit} \sim 2.8\times 10^{-4}\,\left(\frac{t_{\rm fb}}{20\,\rm s} \right)^{-2/3}.
\end{equation}
The temperature in the shocked region is typically high and the radiation pressure dominates so that the adiabatic index will be slightly larger than $4/3$.
Combining this fact with equation (\ref{eq:xi_c_crit}), we estimate the critical values of $\xi_{\rm s}$ and $(4 \pi D_{\rm fb} \sqrt{\xi_{\rm s}})$ from Figure \ref{fig:accretion} as {
\begin{equation}
\xi_{\rm s, crit} \sim 0.2\ {\rm and}\ (4 \pi D_{\rm fb} \sqrt{\xi_{\rm s}})_{\rm crit} \sim 5.3	.
\end{equation}
}
Hereafter we will assume $l = 0$ which is typically valid for $t \sim t_{\rm fb} \gtrsim 10\,\rm s$ since the timescale $t_{\rm sd}$ of the spin-down is estimated to be much longer than that of the fallback from the following formula:
\begin{equation}\label{eq:sdtime}
t_{\rm sd}=-\left(\frac{\Omega}{\dot\Omega}\right)\sim\frac{6Ic^3}{B_*^2R_*^6\Omega^2}\sim2\times10^9~{\rm s}\left(\frac{B_*}{10^{13}~{\rm G}}\right)^{-2}\left(\frac{P}{10~{\rm ms}}\right)^2,
\end{equation}
where $I$ denotes the moment of inertia of the neutron star, $\Omega(=2\pi/P)$ the angular frequency ($P$ the spin period), $B_*$ the  magnetic field at the magnetic pole on the surface, and $c$ denotes the speed of light.
Finally, the maximum energy deposition rate from a rotating neutron star can be described as $\dot Q_{\rm crit} \approx (\mu^2 \Omega^4/c^3) \times (R_{\rm lc}/R_*)^2$, or
\begin{equation}\label{eq:Q_crit}
\dot Q_{\rm crit} \sim 2.7 \times 10^{45}\,{\rm erg\,s^{-1}}\,\left(\frac{B_*}{10^{13}\,\rm G} \right)^2\left(\frac{P}{10\,\rm ms} \right)^{-2},
\end{equation}
where $\mu = B_*{}R_*{}^3$ is the magnetic dipole moment and $R_{\rm lc} = c/\Omega$ is the light cylinder radius.
We note that the above energy deposition rate is different from the classical dipole spin-down rate, $\dot Q_{\rm dipole} \approx  (\mu^2 \Omega^4/c^3)$.
The additional factor $(R_{\rm lc}/R_*)^2$ represents the enhancement of spin-down luminosity~\citep{2016ApJ...822...33P};
the magnetic fields are maximally open, like a split monopole, due to the accretion.
From equations (\ref{eq:r_s_crit}-\ref{eq:Q_crit}), we obtain the critical accretion rate as {
\begin{equation}\label{eq:Mdot_crit_ns}
\dot M_{\rm crit, repul} \sim 3 \times 10^{-5}\,M_\odot\,{\rm s^{-1}}\,\frac{\xi_{\rm s, crit}}{0.2}\frac{(4 \pi D_{\rm fb} \sqrt{\xi_{\rm s}})_{\rm crit}}{5.3} \left(\frac{B_*}{10^{13}\,\rm G} \right)^2\left(\frac{P}{10\,\rm ms} \right)^{-2}\left(\frac{t_{\rm fb}}{20\,\rm s} \right)^{2/3}.
\end{equation}}
If $\dot M_{\rm fb} \lesssim \dot M_{\rm crit, repul}$, a bulk of the fallback matter will be directly repelled by the spin-down power.
Otherwise, it is accreted on the neutron-star surface.

If $\dot M_{\rm fb} \gtrsim \dot M_{\rm crit, repul}$, the fallback matter reaches the neutron star surface.
If the accretion rate is so large, then the surface magnetic field can be buried and the spin-down power is significantly reduced~(e.g., \cite{2010RMxAA..46..309B,2016MNRAS.456.3813T}).
A necessary condition for burying the magnetic field is set by the balance between the magnetic pressure and the ram pressure at the surface;
\begin{equation}
\frac{B_*{ }^2}{8\pi}\lesssim\rho v^2\sim\frac{\dot M}{4\pi R_*^2}\sqrt{\frac{GM_{\rm c}}{R_*}},
\end{equation}
where $\rho$ and $v$ are the density and velocity of the accreted matter near the surface.  The second equality assumes the steady accretion of freely falling matter. Numerically, this yields the critical accretion rate of
\begin{equation}
\dot M_{\rm crit, bury} \sim 3\times10^{-6}\,M_\odot\,{\rm s^{-1}}\,\left(\frac{B_*}{10^{13}\,{\rm G}}\right)^2.
\end{equation}
Whether the magnetic fields are actually buried into the crust may be addressed by comparing the position of the magnetopause and the crust radius.
In this way, \citet{2016MNRAS.456.3813T}\footnote{There is a typo in their eq. (25).} estimated the threshold value as
\begin{equation}
\dot M_{\rm crit, bury} \sim 10^{-5}\,M_\odot\,{\rm s^{-1}}\,\left(\frac{B_*}{10^{13}\,{\rm G}}\right)^{3/2}.
\end{equation}

In the case of $\dot M_{\rm crit, repul} \lesssim \dot M_{\rm fb} \lesssim \dot M_{\rm crit, bury}$, the situation will be more complicated.
At first, the fallback matter can be accreted on the neutron star; the magnetic fields and spin-down energy are confined in a near surface region.
As the fallback rate decreases with time, large-scale fields emerge and the spin-down power pushes back the fallback matter.
In Figure \ref{fig:cco_psr}, we show how the consequences of a fallback accretion depend on $B_*$ and $P$ for
$\dot M_{\rm fb} = 10^{-6}\,M_\odot\,\rm s^{-1}$(left), $10^{-5}\,M_\odot\,\rm s^{-1}$(center), and $10^{-4}\,M_\odot\,\rm s^{-1}$(right).

\begin{figure}
  \includegraphics[width=0.32\textwidth]{cco_psr_mag_Mfb-6.eps}
  \includegraphics[width=0.32\textwidth]{cco_psr_mag_Mfb-5.eps}
  \includegraphics[width=0.32\textwidth]{cco_psr_mag_Mfb-4.eps}
\caption{
Consequences of fallback accretion onto a neutron star and their dependencies on the magnetic field and rotation.
The left, center, and right panels show the cases of  $\dot M_{\rm fb} = 10^{-6}\,M_\odot\,\rm s^{-1}$, $10^{-5}\,M_\odot\,\rm s^{-1}$, and $10^{-4}\,M_\odot\,\rm s^{-1}$, respectively.
}
\label{fig:cco_psr}
\end{figure}

Let us now discuss possible connection between the diversities of neutron-star formation with fallback accretion and the observed young neutron stars.
From Figure \ref{fig:cco_psr}, the condition $\dot M_{\rm fb} < \dot M_{\rm crit, repul}$ is always satisfied
for fast-spinning strongly-magnetized neutron stars with $B_* \gtrsim 10^{13}\,\rm G$ and $P \lesssim$ a few ms.
Such cases have been proposed as a plausible central engine of extragalactic transients like gamma-ray bursts, superluminous supernovae, and fast radio bursts~(see e.g., \cite{2015MNRAS.454.3311M,2016ApJ...818...94K,2017ApJ...839L...3K,2018MNRAS.475.2659M} and references therein)~\footnote{Also see \citet{2018ApJ...857...95M} for the impact of fallback accretion on the time evolution of spin in the early stage.}.
A similar range of $B_*$ and $P$ has been also considered in the context of Galactic magnetar formation;
the magnetic field amplification can be attributed to the proto-neutron-star convection coupled with a differential rotation~\citep{1992ApJ...392L...9D,1993ApJ...408..194T}
or the magneto-rotational instability~(e.g., \cite{2015Natur.528..376M}).
Note, however, that so far there is no observational support to the dynamo scenario~(e.g., \cite{2006MNRAS.370L..14V}).

Neutron stars with relatively weak magnetic fields ($B_* \lesssim 10^{13}\,{\rm G}\,(\dot M_{\rm fb}/10^{-5}\,M_\odot\,\rm s^{-1})^{2/3}$) and slow spins ($P \gtrsim$ a few 10 ms) satisfy
the condition $\dot M_{\rm fb} > \dot M_{\rm crit, bury}$ .
Both the magnetic field and spin-down power are strongly suppressed by the accreted matter.
As long as the situation continues, the thermal energy stored in the neutron star will be the main source of the emission.
Such neutron stars will be observed as CCOs as proposed by \citet{2016MNRAS.456.3813T}.

The boundary between the former and latter cases is set by  equation (\ref{eq:Mdot_crit_ns}),
i.e., $(B_*/10^{13}\,{\rm G}) \times (P/10\,{\rm ms})^{-1} \sim (\dot M_{\rm fb}/10^{-4}\,M_\odot\,\rm s^{-1})^{1/2}$,
which might correspond to the boundary between rotation-powered pulsars and CCOs.
For example, the initial magnetic field and spin period of the Crab pulsar have been estimated to be $B_* \sim 10^{13}\,\rm G$ and $P =$ a few 10 ms, respectively,
and consistent with the above point if $\dot M_{\rm fb} \lesssim 10^{-5}\,M_\odot\,\rm s^{-1}$.
Such a relatively small fallback accretion rate might be also consistent with a relatively low-mass progenitor inferred for the Crab pulsar.

In the intermediate cases where
$(\dot M_{\rm fb}/10^{-5}\,M_\odot\,\rm s^{-1})^{2/3} \lesssim (B_*/10^{13}\,{\rm G}) \lesssim (P/10\,{\rm ms})\times(\dot M_{\rm fb}/10^{-4}\,M_\odot\,\rm s^{-1})^{1/2}$,
the magnetic field eventually emerges and the energy source of the emission can be either spin-down power or decay of the magnetic-field.
Interestingly, the parameter range of $B_* \sim B_{\rm QED} = 4.4 \times 10^{13}\,\rm G$ and $P \gtrsim$ a few 10 ms, especially for $\dot M_{\rm fb} \gtrsim 10^{-5}\,M_\odot\,\rm s^{-1}$
is somewhat consistent with the so-called fossil scenario of high- and low-field magnetar formation~\citep{2006MNRAS.367.1323F}.
Such a relatively large fallback accretion rate might be expected in relatively high-mass progenitors inferred for magnetars
(e.g., \cite{2005ApJ...622L..49F,2005ApJ...620L..95G,2006ApJ...636L..41M,2014ApJS..212....6O}).

As above, we show that the observed diversity of Galactic neutron stars could be connected to $(B_*, P, \dot M_{\rm fb})$ at their birth.
We speculate that ordinary pulsars, CCOs, and magnetars originate from the blue, red, and yellow shaded regions in Figure \ref{fig:cco_psr}, respectively.
The fact that the three classes have a comparable population (e.g., \cite{2008MNRAS.391.2009K}) can be naturally explained since the typical parameters at their birth, $B_* \sim 10^{13}$ G and $P \sim$ a few 10 ms,
roughly coincide with the intersection of the boundaries of three regions.
We should note, however, that the self-similar solutions in Sec. \ref{sec:results} and calculations by \citet{2016MNRAS.456.3813T} are one dimensional.
Multi-dimensional effects in fallback accretion have to be taken into account consistently to make the above criterions more quantitatively accurate. {For instance, as mentioned in section \ref{sec:results},  solutions with $l=0$ might be subject to the Rayleigh-Taylor instability. Nevertheless, multi-dimensional effects are not expected to change the above criterions because the energy of the shocked flow in Region II is always positive. Of course, one needs to perform multi-dimensional calculations to know detailed outcomes of this instability.}
We should also note that, in order to connect their states at birth to observational properties at $t_{\rm age} \gtrsim $ a few 100 yrs, the long-term evolution of spins and magnetic fields become important.
We will investigate these topics elsewhere.

\section{Summary and Discussion}\label{sec:discussion}
We have presented series of self-similar solutions for fallback matter being shocked and repelled by the energy deposition from a central object.
The behavior of the solutions changes depending on the adiabatic index $\gamma$ in the shocked region.
For $\gamma > 4/3$, we can find a self-similar solution for an arbitrarily high fallback accretion rate by taking the radius of the contact surface correspondingly small.
On the other hand, for $\gamma \leq 4/3$, there are upper-bounds to the accretion rate at the shock front $r = r_{\rm s}$:
\begin{equation}\label{eq:Mdot_crit}
\dot M_{\rm crit} = \frac{r_{\rm s} \dot Q}{G M_{\rm c}} \times (4 \pi D_{\rm fb} \sqrt{\xi_{\rm s}})_{\rm crit}.
\end{equation}
The critical values of $4 \pi D_{\rm fb} \sqrt{\xi_{\rm s}}$, ranging from $\sim 1-100$, are shown in Table 1.
Note that $4 \pi D_{\rm fb} \sqrt{\xi_{\rm s}} = 1$ corresponds to the cases
where the accretion luminosity $G \dot M M_{\rm c}/r_{\rm s}$ is equal to the energy deposition rate from the central object $\dot Q$.
For $\dot M > \dot M_{\rm crit}$, the fallback matter will plunge into the central object.

We have applied the self-similar solution to neutron star formation with fallback accretion when the neutron star deposits energy due to its spin-down power. The solution suggests that the critical mass accretion rate above which the fallback matter can be accreted on the surface is given as a function of  the initial spin rate and surface magnetic filed.  It is shown that this condition together with the criterion that the accreted matter can bury the magnetic field and suppress the spin-down power may determine the fate of the newborn neutron star to become a magnetar, a pulsar, or a CCO.

\subsection{Relation to Previous Works}
We here discuss relations between the self-similar solution constructed in this paper and previous studies on the dynamics of fallback accretion.

The shock propagates outward with the radius proportional to $t^{2/3}$ in our models. A similar behavior of the shock front was obtained from numerical computations for fallback presented in \citet{1972SvA....16..209Z}. Thus our model can capture some features of realistic models that treat the energy source originating from gravitational energy of accreted matter. \citet{1972SvA....16..209Z} discussed the accretion of up to 10$^{-5}$ $M_\odot$ assuming a static power-law density distribution proportional to $r^{-3/2}$ ($r$ denotes the radial coordinate) as the initial condition, which results in a constant accretion rate. They computed hydrodynamics of the fallback matter including radiative diffusion of photons and neutrino emission. \citet{1971ApJ...163..221C} emphasized the role of neutrino emission in driving intense fallback motion.  These investigations focused on the early phase affected by the unknown explosion mechanism of a core collapse supernova.

\citet{1989ApJ...346..847C} discussed the fallback phenomenon after a reverse shock wave reaches the neutron star.  He argued that the accretion rate of the bound debris decreases with time $t$ following a power law as $t^{-5/3}$ provided that the mass fraction of the debris is uniformly distributed in binding energy. This power law evolution of the accretion rate had been already pointed out from a dimensional analysis \citep{1988Natur.333..644M}. Though \citet{1989ApJ...346..847C} started his computations from the uniform motion of uniform matter to obtain this accretion rate,  he pointed out that this situation can be realized if the density $\rho_{\rm d}(r)$ of the debris initially has a static power-law distribution $\rho_{\rm d}(r)\propto r^{-4}$ \citep{1974Ap&SS..31..251S}.  He also discussed the effects of the pulsar activity on the fallback and concluded that the effects are negligible if only the magnetic pressure is considered.

On the contrary, newborn spinning neutron stars should deposit energy in the surrounding matter as a result of the activities originating from rotating strong magnetic fields. This interaction has been discussed with self-similar solutions in 1D spherical symmetry \citep{2005ApJ...619..839C, 2017MNRAS.466.2633S} and numerical simulations in 2D axi-symmetry \citep{2016ApJ...832...73C, 2017MNRAS.466.2633S, 2017ApJ...845..139B} or 3D \citep{2017ApJ...845..139B}. All of these studies have dealt with interactions between pulsar winds and expanding supernova ejecta without fallback matter. In reality, the innermost part of once ejected matter falls back and the  energy deposited by the pulsar wind should affect the motion of the fallback matter, which is important for determining the nature of young neutron stars as discussed in section 4. Our solutions cover some of these aspects though we simplified the situation by introducing the power law energy deposition rate and assuming a specific motion of the fallback matter above the shock front, which is different from the assumptions in the above previous work. Thus our solutions have a different temporal evolution of the mass accretion rate.

\begin{ack}
This work is partially supported by JSPS KAKENHI Grant Number JP17K14248, JP18H04573, 16H06341, 16K05287, 15H02082, MEXT, Japan.
\end{ack}

redpajama_set_name: RedPajamaArXiv


Woodland Fish & Wildlife is a partnership of multiple agencies working in Oregon and Washington. They publish several short guiding documents for private landowners interested in wildlife habitat. Click here to visit their website.


Full factory restore ODIN with radio, kernel and recovery. This will bring you back to the current unrooted 2.2.1 EE4 release of Android for the Droid Charge. Use 7zip to uncompress and flash with ODIN or SamsungPST.
Sent from my Droid Charge!!
Woof. This is a lot better than the ED1 stocker.
has it been tested by anyone yet?


text:
Chile · 8 Items · Anna De Mondey
Handpicked by a Chile Local Expert, we bring you our guide to 'Things to do and visit in Isla de Pascua'.
Things to do and visit in Isla de Pascua Easter & Robinson Crusoe Islands, Rapa Nui
Best Tourist Attractions in Chile Discover the magic of one of the most remote inhabited islands in the world The Moai Easter island is located on the east edge of the Polynesian Triangle, in the south Pacific Ocean, with a latitude of 27° 9′ 10" South, and a longitude of 109° 27′ 17" West. The closest continental point is the coast of Chile at a distance of 3,526 Km. It's l More info
Things to do and visit in Isla de Pascua Easter & Robinson Crusoe Islands, Easter Island
Best Touristic Attractions in Chile Anakena, a paradise beach Anakena is the main beach on Easter Island, it represents the typical picture that you have when you think of a paradise beach. Its white and fine coral sand, crystalline turquoise sea, calm waves and coconut palms (brought from Tahiti several decades ago) make it an ideal place for rest and leisure. Anakena beach in More info
Things to do and visit in Isla de Pascua Easter & Robinson Crusoe Islands, Tongariki
Best Archaeological Tourist Attractions in Chile Ahu Tongariki, the 15 moai statues The contemplation of the imposing Ahu Tongariki with the Pacific Ocean on its back is the fulfilled dream of most travelers who cross the planet to reach Easter Island. The image of Tongariki, together with that of the statues of the nearby Rano Raraku volcano, is the one that has most spread in books, ma More info
Things to do and visit in Isla de Pascua Easter & Robinson Crusoe Islands, Rano Raraku
Best Attractions in Chile Rano Raraku a breath taking Volcano landscape in Chile. Rano Raraku, the quarry of the Moai The Rano Raraku volcano is one of the most incredible and extraordinary archaeological sites on the planet. In this magical place full of mystery, the moai were made, the giant statues that have made Easter Island famous worldwide. The enormous figures and the quarri More info
Things to do and visit in Isla de Pascua Easter & Robinson Crusoe Islands, Rano Kou
Best Tourist Attractions in Chile Rano Kau, an amazing crater Rano Kau, also known as Rano Kao, is the largest volcano and one of the most beautiful and impressive natural settings that can be admired on Easter Island. The sensation of immensity and silence, interrupted only by the wind, the distant sound of the waves and the occasional squawking of seabirds, makes Rano Kau one of the fa More info
Things to do and visit in Isla de Pascua Easter & Robinson Crusoe Islands, Hanga Roa
Best attractions in Chile Visit one of the most touristic and historical urban centers in Easter Island, Chile Hanga Roa Hanga Roa is the only urban center that exists on Easter Island. Here is where the main social, economic and cultural activities of Rapa Nui are developed and where almost all its inhabitants reside. Hanga Roa, which means "wide bay or long bay" in rapanu More info
Best tourist attractions in Chile Welcome to Rapa Nui! One of Chile's National Park in Easter Island. Rapa Nui National Park Easter Island's protected area acquired the status of a National Park on January 16th, 1935 by Supreme Decree No. 103 of the Ministry of Land and colonization, being declared a National Historic Landmark that very same year. The Rapa Nui National Pa More info
Things to do and visit in Isla de Pascua Easter Island
Best tourist attractions in Chile Visit the Easter Island's Museum, a Must-See on the Island. The Anthropological Easter Island Museum (the only museum on the island), is named after the priest Sebastian Englert, a German priest who came to the island in 1935 and spent the last 34 years of his life studying and disseminating the language, traditions and archaeological heritage of More info
Items: 8 · By: Anna De Mondey
UPDATED: Sep 19th 2019

redpajama_set_name: RedPajamaCommonCrawl


text:
# These tests still need to be converted into a proper unit test suite where all tests can easily be ran and verified automatically.
# Currently you need to uncomment the test you want to run, and verify it does what you expect it to. Not ideal, but better than nothing for now.

# Turn on Strict Mode to help catch syntax-related errors.
# 	This must come after a script's/function's param section.
# 	Forces a function to be the first non-comment code to appear in a PowerShell Module.
Set-StrictMode -Version Latest

# Get the directory that this script is in.
$THIS_SCRIPTS_DIRECTORY_PATH = Split-Path $script:MyInvocation.MyCommand.Path

Set-Location -Path $THIS_SCRIPTS_DIRECTORY_PATH

# Clear the screen.
Clear-Host

# Test packing from a project with a NuSpec file.
# .\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -PackOptions "-Build -OutputDirectory ""$THIS_SCRIPTS_DIRECTORY_PATH""" -Verbose
#.\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -VersionNumber "1.1" -ReleaseNotes "Pack project without building and specify version 1.1"

# Test packing from a project without a NuSpec file.
#.\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project Without NuSpec\TestProjectWithoutNuSpec\TestProjectWithoutNuSpec.csproj" -PackOptions "-Build -OutputDirectory ""$THIS_SCRIPTS_DIRECTORY_PATH"""

# Test packing from a nuspec file.
#.\..\New-NuGetPackage.ps1 -NuSpecFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test NuSpec File\StaticNuSpecFileTest.nuspec"
#.\..\New-NuGetPackage.ps1 -NuSpecFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test NuSpec File\StaticNuSpecFileTest.nuspec" -VersionNumber "1.0.0" -ReleaseNotes "Pack nuspec file with version number and release notes specified"

# Test errors to see how they look.
#.\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project With Errors So It Will Not Pack\ProjectWithErrorsSoItWillNotPack\ProjectWithErrorsSoItWillNotPack.csproj" -PackOptions "-Build"
#.\..\New-NuGetPackage.ps1 -NuSpecFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test NuSpec With Errors So It Will Not Pack\NuSpecFileWithErrorsTest.nuspec" -NoPrompt

# Test packing without specifying a file path or any other parameters.
#.\..\New-NuGetPackage.ps1
#.\..\New-NuGetPackage.ps1 -UsePowerShellPrompts -NoPromptForInputOnError

# Test packing using the various different prompt modes.
#.\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -PackOptions "-Build -OutputDirectory ""$THIS_SCRIPTS_DIRECTORY_PATH""" -NoPrompt
#.\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -PackOptions "-Build -OutputDirectory ""$THIS_SCRIPTS_DIRECTORY_PATH""" -NoPromptForVersionNumber
#.\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -PackOptions "-Build -OutputDirectory ""$THIS_SCRIPTS_DIRECTORY_PATH""" -NoPromptForReleaseNotes
# .\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -PackOptions "-Build -OutputDirectory ""$THIS_SCRIPTS_DIRECTORY_PATH""" -NoPromptForPushPackageToNuGetGallery
#.\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -PackOptions "-Build -OutputDirectory ""$THIS_SCRIPTS_DIRECTORY_PATH""" -NoPromptForInputOnError
#.\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -PackOptions "-Build -OutputDirectory ""$THIS_SCRIPTS_DIRECTORY_PATH""" -UsePowershellPrompts

# Test packing without updating the NuSpec file.
#.\..\New-NuGetPackage.ps1 -NuSpecFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test NuSpec File\StaticNuSpecFileTest.nuspec" -DoNotUpdateNuSpecFile
#.\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -PackOptions "-Build -OutputDirectory ""$THIS_SCRIPTS_DIRECTORY_PATH""" -DoNotUpdateNuSpecFile

# Test packing by specifying a custom NuGet.exe path with spaces.
#.\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -VersionNumber "1.2" -ReleaseNotes "Pack project without building and specify version 1.2" -NuGetExecutableFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\NuGet Executable\NuGet.exe"

# Test packing from a relative path.
#.\..\New-NuGetPackage.ps1 -NuSpecFilePath ".\Test Files\Test NuSpec File\StaticNuSpecFileTest.nuspec" -DoNotUpdateNuSpecFile
#.\..\New-NuGetPackage.ps1 -ProjectFilePath ".\Test Files\Test Project\TestProject\TestProject.csproj" -DoNotUpdateNuSpecFile

# Test the NuGet Update switch.
#.\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -VersionNumber "1.3" -ReleaseNotes "Pack project without building and specify version 1.3 and do NOT update the NuGet.exe" -NoPromptForPushPackageToNuGetGallery -NuGetExecutableFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Older Version NuGet Executable\NuGet.exe" -Verbose
#.\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -VersionNumber "1.3" -ReleaseNotes "Pack project without building and specify version 1.3 and update the NuGet.exe" -NoPromptForPushPackageToNuGetGallery -NuGetExecutableFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Older Version NuGet Executable\NuGet.exe" -UpdateNuGetExecutable -Verbose

# Test packing by specifying a custom TF.exe path with spaces.
# .\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -VersionNumber "1.1" -ReleaseNotes "Pack project without building and specify version 1.1" -NoPromptForPushPackageToNuGetGallery -TfExecutableFilePath "C:\Program Files (x86)\Microsoft Visual Studio\2017\Enterprise\Common7\IDE\CommonExtensions\Microsoft\TeamFoundation\Team Explorer\TF.exe"

# Test packing by specifying a custom TF.exe path that does not exist.
# .\..\New-NuGetPackage.ps1 -ProjectFilePath "$THIS_SCRIPTS_DIRECTORY_PATH\Test Files\Test Project\TestProject\TestProject.csproj" -VersionNumber "1.1" -ReleaseNotes "Pack project without building and specify version 1.1" -NoPromptForPushPackageToNuGetGallery -TfExecutableFilePath "C:\Path that does not exist\TF.exe"

# Test pushing NuGet package.
#.\..\New-NuGetPackage.ps1 -PackageFilePath "C:\Users\Dan.Schroeder\Desktop\DansTest\DansTest\bin\Debug\DansTest.1.0.0.0.nupkg" -PushOptions "-Source http://packages2.iqmetrix.net"

#Nuget spec $THIS_SCRIPTS_DIRECTORY_PATH\Test Files\TestProject\TestProject\TestProject.csproj -f
#Nuget spec $THIS_SCRIPTS_DIRECTORY_PATH\Test Files\TestDll\TestDll.dll -f

#Nuget pack $THIS_SCRIPTS_DIRECTORY_PATH\Test Files\TestProject\TestProject\TestProject.csproj -OutputDirectory $thisScriptsDirectory -Build

#cd $THIS_SCRIPTS_DIRECTORY_PATH\Test Files\TestProject\TestProject
#nuget spec -f

#cd $THIS_SCRIPTS_DIRECTORY_PATH\Test Files\TestDll
#nuget spec -f

redpajama_set_name: RedPajamaGithub


We pride ourselves of a network of experienced Close Protection Officers (CPOs), recruited for a wide range of protective tasks in environments characterized by diverse risk levels. We can successfully cater for recruitment needs of our clients in High, Medium, and Low Risk Environments.
–	Communication (Level of English and ability to interact with other team members and crew).


text:
The President Should Not Stand Alone in the Call for Criminal Justice Reform
It's time for Sheriffs also to use their executive authority to address criminal justice reform where it begins, at the county level.
By Charles Rambo
Atlanta, GA — In a passionate speech by President Barack Obama at the NAACP Convention, he stated that criminal justice is an issue America can't afford to ignore. With the sovereign authority that County Sheriffs enjoy in the United States, every Sheriff and even those seeking offices in upcoming elections should also make the clarion call for criminal justice reform. Whether they share party affiliation with the president or not, constitutional law and justice is a non-partisan issue.
As a retired lieutenant commander from the Fulton County Sheriff's Office, I know first-hand what can be done from 27 years of law enforcement, judicial process, corrections, academy instruction, and investigative experience. At the beginning of my career in 1989, I was highly considered for loan-out to the Drug Enforcement (DEA) Task Force. A crucial time when the war on drugs, particularly crack cocaine, was at its pinnacle in Atlanta and surrounding communities. Instead, I continued to work within the scope of the Sheriff's Office law enforcement, corrections, training academy, and judicial process functions. Observing and interacting with offenders as they navigated through the complex Fulton County criminal justice system, I share a balanced view with President Obama on criminal justice reform to police in communities with respect to a person's civil liberties.
Last week when President Obama visited a federal correctional facility to talk with inmates, I reflected back on my own interactions with inmates during the crucial era of government being tough on crime. First hand, I observed the unanticipated consequences of drug sentencing laws on mass incarceration from working in one of the most notorious holding facilities in the southeast region of the United States, the Fulton County Jail. Built in 1989 initially for 1,975 inmates, it reached a boiling point of overcrowding in a relative short time to over 3,900 inmates. I was one of the first Sheriff Deputies to open the facility supervising 300+ inmates in some of the most dangerous housing units consisting of hardcore murderers, drug lords, and notorious street gang leaders.
After their day in court, they had no qualms in being held accountable and responsible for their actions. But, the most resounding complaint I heard from inmates returning to their cells from court hearings, "I don't mind doing the time for what I did, but most of what they (The State) are presenting against me in evidence, statements and witnesses have nothing to do with my case!" This statement has been etched in my mind as I continued my career working in patrol and academy instructor.
Certainly, I make no excuse for offenders who commit crimes. However, the burden of proof is upon the state to prove each element of the offense. In my professional observation, a great number of cases in state courts lack probable cause. The result of hasty efforts at the local level to control crime and influence public opinion. This is why I squarely agrees with President Obama's assessment that criminal justice is an issue America can't afford to ignore. After all, the majority of cases that flow through the criminal justice system originate from the State Courts placing a burden on the state's criminal justice system and taxpayers. And, it's not just for the federal level to resolve, but also actors of state government, particular at the county level.
For that reason, the Constitutions of each state, namely the State of Georgia, have created the Sheriff's Office as an elected constitutional office in a state's governmental hierarchy. The State delegates the discrete functions to Sheriffs that are germane to criminal justice reform: law enforcement, state courts, and corrections. While a Sheriff might share the responsibility of law enforcement with other local agencies, he exercises the most control over persons who are arrested, incarcerated, sentenced and delivered to the state penal system.
Sheriffs, like the United States President, represent the most independent authority as constitutional officers to facilitate real criminal justice reform at the county level. Illustrating the executive authority and power as a constitutional officer, the United States Supreme Court and Georgia Supreme Court rely upon the authority of a Sheriff in A Treatise on the Law of Sheriffs, Coroners and Constables: "… in vindicating the law, and preserving the rights of government, he (the Sheriff) represents the sovereignty of the State, and he has no superior in his county." The most compelling reason for Sheriffs as chief law enforcement officers, now more than ever, to exercise autonomy and influence for reform according to the rule of law. His sovereign authority to speak and act on criminal justice reform should be just as actionable as nationwide Sheriffs who wield their authority on illegal immigration enforcement and protecting the Second Amendment rights of their constituents to bear arms.
As a retired Sheriff's commander, I continue to educate the law enforcement profession and communities as a Senior Instructor certified by the Georgia Peace Officers Standards and Training Council. Thought provoking lectures on criminal justice issues at local law enforcement academies to include: constitutional law, racial profiling prevention, correctional and community oriented policing, media relations, advanced report writing, use of force, courtroom testimony, criminal investigations, etc.. All for the purpose of developing the next generation of law enforcement leaders to enforce the rule of law with competent character in the 21st century.
While the demand for reform is justly placed upon the federal or state government, the real work begins with the quality of governance in homes giving the next generation a pathway to success, outside the criminal justice system.
Charles Rambo is currently a registered candidate for Fulton County Sheriff with the Georgia Secretary State. His expert knowledge of Sheriff public and political policy has been presented before the Georgia General Assembly and mass media interviews. To learn more, please visit www.mysherifframbo.com. He can be reached by cell at 678-438-1195 or email committee@mysherifframbo.com


The Marriott One Cup Coffee Brewer and Brew Tray Kit makes it easy to prepare your daily morning coffee. The rapid brew time helps get you on to the next task quickly, and the one-cup size is perfect for when you need a pick-me-up but don't want to take the time to brew a whole pot. This kit comes complete with the 100 percent Colombian coffee featured in Marriott hotel rooms, and there are both regular and decaffeinated offerings for those who enjoy a cup of coffee in the evenings as an after-dinner treat.


Every business entity offering products and services through its website must select a hosting plan that will meet the company's requirement not just in terms of the basic necessities like disc space, storage capacity, bandwidth, uptime, cost, root access, to name just a few, but it should also be able to upgrade to a higher hosting plan if required in the long run.
Generally speaking, the following points have to be taken into account when you are selecting a web hosting plan. Discussed here are the basic features. Aside from the points that will be highlighted in the paragraphs that follow, you can also zero-in on the right web host by going through online reviews and feedback from users that have already availed the services of the web hosting companies.
However, just remember that not all reviews are authentic and there are many fake ones doing their rounds on the web. So, watch out for such reviews.
To avoid falling into the trap, make sure you visit a website that will give you true information on web hosting plans.
Some of the reliable web hosts that you can bank upon include SiteGround, BlueHost, OVH, GoDaddy, and so on that have established themselves as a reliable brand.
How should good web hosting plans be?
Every web host will offer specific disc space to its clients. But remember, you must go through the terms and conditions to know what exactly will be counted as disc space and how many files you can store.
The amount of data that you can upload and download is usually referred to as amount of bandwidth. It also determines the amount of web traffic that your website can handle at any given point of time. Make sure you have adequate bandwidth assigned to your website so that you don't face downtime too frequently.
You will come across many such web hosts that will offer email accounts. But you have to find out the number of email accounts you will be given or you can set up. Also, find out how many will have Gmail interface.
Find out how easy it is to install the framework. Most of the clients or website owners prefer the so called 'one-click' method that allows them to set up WordPress easily or for that matter any other Content Management System.
Will you be able to access your website administration by means of an app? Not all web hosting companies will offer this privilege but there are handful that offer this incentive.
This is perhaps one of the better points that you ought to take into account. Allowing great storage space and allowing root access is not just enough, find out how well the web hosting firm offers technical support to clients.
Although, you may not require root access presently, but you should keep your options open should you require it in future? So, talk to your web hosting service provider before you settle for any plan.
Find out the number of languages your server will support in the event you want to use any other language for your framework.
Just as the website owners that have hosted their websites on the servers are vulnerable to attack and malware, so can the servers face the problem too. This can be quite frustrating and damaging because it means bulk data will be lost or corrupted not just those belonging to your website but also that of others. Find out what measures your web hosting company has decided upon in the event of an emergency.
The ones that have been mentioned above are just few of them, there are several other parameters that will help you to decide about the right web hosting plans and also the right web hosting service provider.


text:
TELUS Ventures announced as Lead Investor in Alacrity's Planned $70 Million Emend Vision Fund I
Company Profile | Follow Company
Burnaby, BC, October 24, 2022--(T-Net)--Emend Vision Fund (Emend) announced today that its planned $70 million Fund I will be led by TELUS Ventures with a commitment of up to 10 percent of Emend's overall capital.
Emend will focus on investments in technologies that help transform traditional industries, protect critical infrastructure, and maintain food and water security for communities - aligning with TELUS Venture's overall investment thesis.
Emend is an early-stage fund that is working to raise $70M in capital.
Emend is being formed by Alacrity Canada, a not-for-profit established in 2009 with a mandate to support tech entrepreneurship in British Columbia, particularly cleantech. Alacrity will also be committing up to 10 percent of the initial capital closing. The fund will invest in impact technology companies, including some from the Alacrity Canada accelerator which already has strong governmental and academic partnerships.
Owen Matthews, Managing Partner, Emend Vision Fun
"We're delighted to have TELUS Ventures as our anchor investor. Demonstrating their leadership to supporting funds and companies that are introducing technologies that have a positive impact for the environment," said Owen Matthews, Managing Partner of Emend Vision Fund and Board Chair at Alacrity Canada.
"We look forward to supporting these companies who have such a a positive impact for our communities. We have successfully scaled cleantech companies globally with Alacrity Canada already and we want to build on this success story to grow the impact investing ecosystem through the Emend Vision Fund."
Mario Mele, Vice-president, TELUS Ventures
"With Alacrity Canada's demonstrated success in supporting technology based startups, we are excited and looking forward to seeing the growth of the Emend Vision Fund," said Mario Mele, Vice-president, TELUS Ventures. "Emend supports organizations leveraging technology for a more sustainable future which aligns perfectly with our investment thesis at TELUS Ventures."
Led by Owen Matthews, Richard Egli and Todd Tessier, Emend has already garnered interest from corporate, institutional, and family offices. Emend aims to invest in early-stage cleantech companies that can provide game-changing sustainability solutions at a global scale which at the same time can protect the environment while delivering value for investors.
"Our work with the Alacrity Cleantech Program helped many early-stage cleantech companies commercialize their business overseas and helped them to get support from private and government funding programs," said Richard Egli, Managing Partner of Emend Vision Fund. "We were inspired to use this experience to build the Emend Vision Fund to help early-stage impact companies and we are looking forward to the future growth that is to come."
About Emend Vision Fund
Emend Vision Fund is an impact fund dedicated to transforming industry, protecting critical infrastructure and maintaining the safety of our food and water supplies. The Emend Vision Fund seeks to empower the tech ecosystem by funding clean technology companies. Investing in technology companies and aligning their focus with a positive impact, the Fund's vision is to export global solutions for climate action that generate above-market returns for our investors. www.emendfund.com
About TELUS Ventures
As the strategic investment arm of TELUS Corporation (TSX: T ) (NYSE: TU), TELUS Ventures is one of Canada's most active corporate venture capital funds. TELUS Ventures invests globally in companies from Seed to Pre-IPO with a focus on innovative technologies such as AgTech, HealthTech, Connected Consumer, IoT, AI, and Security to actively drive new solutions across the TELUS ecosystem. Led by a team of experienced operators, investors and executives, the Ventures team is passionate about creating positive social impact through financial tools and has invested in more than 90 companies since inception.
These statements are made pursuant to the "safe harbour" provisions of applicable securities laws in Canada and the United States Private Securities Litigation Reform Act of 1995. By their nature, forward-looking statements are subject to inherent risks and uncertainties and are based on assumptions, including assumptions about future economic conditions and courses of action. These assumptions may ultimately prove to have been inaccurate and, as a result, our actual results or events may differ materially from our expectations expressed in or implied by the forward-looking statements.
Burnaby, BC (InfoTech)
8200 Employees In BC (34800 Total)
Founded: 1993 | Revenues: $10 Billion
TELUS is a leading national telecommunications company in Canada, with $10.3 billion of annual revenue and 12.6 million customer connections including 7.2 million wireless subscribers, 3.6 million wireline network access lines
See All News Releases From This Company
Other Recent Company News
TELUS Appoints First Chief Product Officer and Merges Its Mobility and Home Solutions & Customer Excellence Divisions
TELUS Health Signs Deal with Walmart Canada to Provide Over 100,000 Walmart Associates With Comprehensive Virtual Health and Wellbeing Services
TELUS International Announces Agreement to Acquire Full-Service Digital Product Provider WillowTree for $1.2 Billion
Want More TELUS Communications Inc. News? 1 2 3 4 5 6 7 8 9 10
Burnaby, BC (InfoTech & Communications)
News Actions
Hiring Today