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Andrew Rice (Photo Courtesy of the Artist)
Andrew Rice Working It (Photo Courtesy of the Artist)
The Studio (Photo Courtesy of the Artist)
Detail (Photo Courtesy of the Artist)
Setting Up (Photo Courtesy of the Artist)
Work in Progress (Photo Courtesy of the Artist)
Studio Set-up (Photo Courtesy of the Artist)
UMOCA (Photo Courtesy of the Artist)
Jessica McQueen
About One to Watch
Each month, we showcase an emerging artist from around the world who is already garnering attention for their work. "One To Watch" presents some of the most exciting artists on Saatchi Art helping collectors to discover strong emerging talent.
Andrew Rice and the Investigation of the Spaces In-Between
July 27, 2018Posted by Jessica McQueen
Andrew Rice explores space and histories, both personal and collective, in his minimalist works. He is a practiced printmaker, often working in multiple layers and textures to generate a surface with a "history." He likens his experience as a printmaker to that of an architect, building layer upon layer of material and texture, and finds inspiration in the degeneration of older buildings, peeling murals, and dislodged bricks. Playing into this notion of hidden spaces and layers of the past, he employs his printmaking process to create his own architectural spaces and hidden histories.
Andrew received an MFA from the University of Utah and a BFA from the University of Colorado. He is currently an Adjunct Professor at the University of Utah, teaching courses in Intaglio, Screenprint, and Drawing. He has had numerous solo shows in the US, China, New York, and Scotland.
I focus on the idea of space in my work–your own personal space, and the spaces we create as both individuals and groups to call our own. I am interested in how we occupy and define that space. I think the deeper root I get at is how we create spaces for ourselves that on one hand isolate us, but also protect us, whether that is individually or collectively.
How did you first get interested in your medium, and what draws you to it specifically?
My primary medium is printmaking. It is what my degree is in and what I currently teach. I started doing the oil stick drawings as a response to my process of printmaking; building layers of texture up to create richer and more interesting values. I was using these found textures that kind of mimicked chain link fencing in a lot of prints and I brought those same textures to the oil sticks. I thought that if I could get the idea of a rich surface with textural history in the etchings and screen prints using these found textures, why not try to get that actual surface come through on the paper, and that is where the oil sticks came in. Building up multiple layers of the oil medium on the paper, my work is left with a physical and tangible surface that shows the layers of the texture.
How has your style and practice changed over the years?
I've gotten way looser and more abstract. Even in a lot of the work that still lives in the representational realm, I am looser in my approach.
Can you walk us through your process? Do you begin with a sketch, or do you just jump in? How long do you spend on one work? How do you know when it is finished?
My work can start a lot of different ways. For a lot of the printmaking based work, it starts with some really poor sketches and then I will move to photos for source work, most of the time taking my own rather than trying to source them elsewhere. For the oil stick paintings, I jump right in. I will start by planning out areas of negative space, but then just let the work go from there. I have no real ideas of what the piece will look like when it is finished, which, can sometimes be hard to know when it is finished, ha. A lot of times, deadlines will dictate when something gets finished, but if there is nothing on the horizon and I am just working on some pieces, they can grow and build and develop indefinitely. I would say most of the work in oil takes 2, 3, 4 months to finish because of how long it takes the medium to dry before being able to work over top of it.
If you couldn't be an artist, what would you do?
I work with music and don't discriminate on what is on. I will put on any and everything and a lot of times, the music just becomes background noise and not always something I am paying attention. This is why I can't listen to podcasts while I work. I end up having no idea what is being talked about as I'm constantly tuning in and out. I remember listening to that podcast, Serial when it was just coming out and had a big show I was working on in my studio. I ended up having to re-listen to just about every episode 2-3 times just to follow the story! After that, I decided not to put myself through that again and stick to music.
A Richard Serra sculpture, and since this is fantasy, I would want a Serra sculpture I could live inside of.
View Andrew's Portfolio
Jessica McQueen is Associate Curator at Saatchi Art. Need help finding art? Contact her via our free Art Advisory service at saatchiart.com/artadvisory.
Works for Sale by Andrew Rice
Follow Us 2,170
Andrew Rice View artwork
Treasure Map 1,620
Re: The Structure 305
Warming 580
Wandered In 560


A fresh and fruity Champagne from Chartogne-Taillet, Sainte Anne has elegance and poise.
Crushed apple, pine nuts and a herbal edge give the nose a lovely savoury note. On the palate the fruit is vibrant and fresh with elegance and poise.
Crisp apples and lime zest leave your palate wanting more.


Five of Brisbane's last six league matches have had over 2.5 goals which is thanks, in large part, to Brisbane's goalscoring abilities. In four of those five matches theyve scored two or more goals, including in each of their last three matches. In thei last three matches they have scored seven goals.
Beijing Guoan finished second in last season's Chinese Super League and they scored 50 goals in 30 leagues matches, as well as conceding 25 goals, so their games were full of goals. In fact, in the last 11 league matches, eight of them saw over 2.5 goals and prior to the last two games of the season they had a eight game streak of scoring two or more goals in matches.


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About Scribe
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We publish books that matter — narrative and literary nonfiction on important topics, and the best of local, international, and translated fiction.
Scribe Acquires Another Gut
Scribe has acquired world English-language rights in the million-copy bestseller The Diet Compass: the 12-step guide to science-based nutrition for a healthier and longer life.
Scribe's publisher, Henry Rosenbloom, said, 'This is a remarkable and important work, combining memoir and pathfinding popular health in a way that reminds me of Gut by Giulia Enders.
'After collapsing with chest pains when he was only 40, the author, German science journalist and science graduate Bas Kast, embarked on a multi-year quest to investigate the latest worldwide research into ageing and nutrition. The result is an ultra-reliable nutrition compass, comprising 12 proven ways to establish a healthy diet and decrease the risk of acquiring common diseases.'
Scribe acquired rights in The Diet Compass from Random House Germany, which has sold rights in it in 20 other territories. Scribe commissioned David Shaw to carry out the English translation. Scribe will publish the title in July in Australia and New Zealand, and in January 2021 in the UK and North America.
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redpajama_set_name: RedPajamaCommonCrawl


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Sunshine Coast tatts the way we like it, a-ha
Damien Wickham from Ink Attack is one of the best artist in Australia when it comes to tattoos. Photo Patrick Woods / Sunshine Coast Daily Patrick Woods
by nchristian
Natasha Christian Journalist
Young journalist and sane cat lady with a passion for online news and the quirkier things in life. Based in Maroochydore.
28th Mar 2015 6:03 AM
GONE are the days only the roughest and toughest got tattoos - now just about everyone has one.
The traditional skull and dagger tatts have been swapped for beautiful (and expensive) works of art that wearers sport proudly.
Bokarina's Damien Wickham has not only travelled the world to tattoo, he's also had people come from far and wide to have him ink their skin.
Despite only tattooing for seven years, Mr Wickham has fast become a master of photo realism tattooing, a method which demands the artist reproduce a picture as accurately as possible.
"I got into the industry after my father retired; he gave me his equipment. I didn't start until I was 32," he said.
While he may be relatively new to the industry, Mr Wickham's in high demand with fans waiting months to get his work on their body.
But while he's rather good at dishing out the ink, he can't really stand to get it himself.
"I'm the biggest sook out there, it hurts too much... I can dish it but I can't take it," he admitted.
Brianna Anderson
However he warned tattoo fans that photo realism wasn't something all tattoo artists were automatically good at, one of the reasons there were a lot of bad tattoos out there.
"There's a lot of con artists in the industry," he said.
"A lot of artists should stick to their limitations; it takes a lot of time to master photo realism."
While he's constantly surrounded by tattooed people, Mr Wickham's wife doesn't have a single tattoo on her and he admitted he didn't have many either.
"We come from different sides of the railway," he said.
When it came to giving other people their new tattoo, he said he took a responsible approach.
"I don't like tattooing anyone under the age of 20. If someone comes in at a young age and wants to commit to something that's mature, I'm happy to tattoo them. If it's not I'll try and talk them out of it."
While tattoos have become more commonplace in the workplace, Mr Wickham didn't want to be responsible for something that could potentially ruin job prospects.
"I would hate to think I've been a part of anything that would limit someone or allow them to be discriminated against in the future," he said.
Even though he's tattooed hundreds of people, he said he was never 100% happy with his work and always strived to do better.
"I can always do better. I like to always make sure my next tattoo is the best I could be," he said.
"You want it to look good in 15 years time. Tattoos have integrity and they need to be held for a lifetime."
Damien Wickham's shop Ink Attack is located at Thunderbird Dr, Bokarina.
INK ATTACK: Skilled tattooist Damien Wickham admits to being scared of the needle himself. John Mccutcheon
SHOW US YOUR TATTS!
Show us your tatts! Have you got a piece of ink you're proud of? We'd love to know the story behind it. If you've got a...
Posted by Sunshine Coast Daily on Wednesday, March 25, 2015
We asked the Daily's Facebook fans to share their tattoo stories with us. Here's what some of you said:
1. Brianna Anderson: I got this piece on the one year anniversary of my Dad's death. The stem of the poppy says 'Lest We Forget'. He was in the army, SAS and police force when he was well. He passed away after having dementia for 12 years.
2. Jamin Rea: There is no story behind this 9 tentacled octopus. I regret nothing.
3. Lachlan John Downes: This is a memorial piece for my daughter we lost in September last year. Means the world to me and my wife.
Daniel Munro
4. Daniel Munro: Got this Sunny Coast tatt on my butt for free to win the big pineapple festivals competition... and I won.
5. Adam Robert Reynolds: My story started about nine years ago when me and my wife were trying for our second child. After many attempts we found out my wife Anna was expecting. The name we had chosen was Sam either for a boy or girl. We went for our normal scans and everything was awesome, until 13 weeks when we found out there was no more Sam. Crushed we both where after a while we started trying again, which seemed like a life time Anna was pregnant. Nine months later (my son) Mason arrived a healthy baby boy. As I was getting Mason's name done the tattoo artist started with the letter N then O As he continued with the letters S A M I was crying at this stage realising it spelt NO SAM backwards. So Sam is still with us forever.
6. John Hanchard: It is my wife Samantha's. She got it a few weeks ago for our upcoming trip to Gallipoli for the ANZAC ceremony
7. Nath Mackay Portrait of my late father
8. Marie Joan: My grandma's writing from a birthday card. It's the last card I got from both my grandparents for my 21st birthday. I love this tattoo so much as it's like they are with me everyday.
9. Joshua Karlish First tattoo so far. Saw the design and fell in love, am planning on a matching female on the other forearm.
10. Jimmy Haffenden-Carr I got my wife on me. Married over 10 years with five kids. I wanted a pinup girl so why not the one who is the mother to my children and the keeper of my heart?
12. Dusty Gordon Got this done after finishing chemo treatment for cancer last year, just to remind myself how tough I am for getting through chemo and surviving cancer.
13. Jake Woods Portrait of my Grandparents - 50 years together, true love does still exist.
14. Patti Knight I fell in love with this picture as it reminded me of my daughters, so I got it tattooed
15. Miranda King I picked the colours Trista did the rest. My favourite tattoo.
16. Brioni McDonald I've always looked at people with visible tattoos and thought, gee they are gutsy. I always believed I never had the self confidence to pull something like that off. When I turned 24 I thought to myself. I am me. So I got the tattoo.
17. Ben Kawz Moon: In memory of my brother Sam.
18. Kodie Lucas I got this as soon as I was 18. My grandfather and I were very close. He would call me his cheeky monkey. He was diagnosed with alzheimer's and dementia. I went to America for three weeks with my high school and three days after I left he passed away. I missed his funeral. I missed saying goodbye. So I had to do something big for him and to always remember him by. He loved playing golf.
Win may not be blessing for Masters hopeful Kevin Streelman
facebook sunshine coast tattoos


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* Yona, 21st Century Project Hosting SW
*
* Copyright Yona & Yobi Authors & NAVER Corp. & NAVER LABS Corp.
* https://yona.io
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redpajama_set_name: RedPajamaGithub


3. There is a history of commands available as well.
4. The deactivate screen looks a little different.
Commands, in general, will not cause the action to occur immediately. They will trigger the next time the agent checks in. You can run a scan from the computer the agent is installed on in order to force the agent to check in.
It looks pretty good... I do think I will like it.
That looks good! I am very glad to see those improvements in the interface.
BTW - I hate cartoonish looking portals, but can Webroot add a little bit of color to the console?
Thanks Jim for giving us a chance to sniff the new graphic of the console and extended features.
As for myself, I love them all. I can't wait to play with commands. Well done!
I am going to love this, while my wife might not: she never runs system cleaner on our shared computer. When i run it, it clears my cache and temps but not hers.
Want to guess what remote command i am going to use Monday from work?


Share the post "Les Roches Alumnus Appointed to the International Olympic Committee (IOC)"
Les Roches alumnus Panos Tzivanidis, has been appointed to Head of Events & Hospitality at the International Olympic Committee. He will oversee all non-sporting events as well as all hospitality and ticketing services for the IOC family.
He previously served 11 years as Head of Sibos (an annual conference, exhibition and networking event) and events at SWIFT.
An increasing number of professional events of all types are organized every year globally. The events management industry is a significant and highly attractive business area. It is large—approximately $100 billion total revenue across the globe—and it is growing at an average of 6.2% globally since 2003.
Tapping into these trends, Les Roches introduced an event management specialty as part of its Bachelor of Business Administration program in early 2012. The academic content and teaching modules for this concentration were developed in collaboration with professionals in event management. More than 30 students are currently enrolled in this specialty.


ForeignPolicy.com published an opinion piece by CGD research fellow Michael Clemens on brain drain.
"This common idea that skilled emigration amounts to "stealing" requires a cartoonish set of assumptions about developing countries. First, it requires us to assume that developing countries possess a finite stock of skilled workers, a stock depleted by one for every departure. In fact, people respond to the incentives created by migration: Enormous numbers of skilled workers from developing countries have been induced to acquire their skills by the opportunity of high earnings abroad. This is why the Philippines, which sends more nurses abroad than any other developing country, still has more nurses per capita at home than Britain does. Recent research has also shown that a sudden, large increase in skilled emigration from a developing country to a skill-selective destination can cause a corresponding sudden increase in skill acquisition in the source country."


The Biomimicry Guild uses a deep knowledge of biological adaptations to help designers, engineers, architects, and business leaders solve design and engineering challenges sustainable.
The Biomimicry Institute is a not-for-profit organization whose mission is to nurture and grow a global community of people who are learning from, emulating, and conserving life's genius to create a healthier, more sustainable planet.
The Biomimicry Database is intended as a tool to cross-pollinate biological knowledge across discipline boundaries.
Fostering translational research of biomimetic concepts to the point where they are considered commercial candidates.
Biomimetics & Natural Technologies at the University of Bath. Transcript of an interview on Radio 4's "Material World" with Julian Vincent.
Biomimetics (design inspired by nature) is an enabling discipline which looks towards nature for ideas that may be adapted and adopted for solving problems.


Capsicum Gravy is a quick and easy side dish that you can make when you run out of veggies and this gravy has no tomato garlic also so I was quite impressed with this recipe that it pushed me to try it at once.
I also checked with PJ about the taste and she confidently said her lil angel's lunchbox came back empty with this capsicum gravy as sidedish so what more do I need…I was very confident that this gravy would sure be tasty and yes it was.If you love the nutty flavour am sure you are going to love this gravy for sure as we did!
Get all your ingredients ready first.Now dry roast sesame seeds till golden, set aside , then toast peanuts until brown spots appear here and there, set aside to cool.
Then toast coconut till there is no moisture content, do not let the color change,Set aside to cool.Now add cashews and dry roast it 2mins and allow it to cool down.Transfer the ingredients to the mixer.
Add little water and grind it a smooth paste,Set aside.Now in a pan heat oil add capsicum and onion and fry for 3mins,Set aside.Now in the same pan add little more oil and add jeera let it crackle.
Then add the coconut paste , add little water and let it boil for 2mins.Then add red chilli and garam masala powder along with pepper powder.Add required salt.
Add required water as it becomes thick.Check for salt and adjust at this stage.Simmer and let it boil for 5mins. Add toasted onion capsicum stir well.Now garnish with corainder leaves and switch off.
Serve hot with rice or roti(phulka)!
If the gravy tends to thicken add water accordingly.
The gravy thickens even more on resting, just thin it by adding little hot water while serving.
This is very mild in spice as I made it keeping kids lunchox in mind.You can increase red chilli powder if you want a more spicy gravy.
You can even add green chillies while grinding.
You can even add kasoori methi at the final stage.
Instead of capsicum can we add potato?
Add potatoes but with other veggies as with just potatoes it will be bland….
The flavour will change but you can try….
Can you tell me what to add in place of sesame seeds?
You can skip it or add badams…..
I tried it.it was good.hubby liked it.
Wonderful recipe. Tried it. Tasty. Good post Sharmi.
Wonderful recipe. Tried it. Tasty. Good one Sharmi.
Pepper Powder s not mentioned in ingredient s list and also how many badams can we add instead of sesame seeds.
Mam..I have a doubt. You are saying that it will thicken even after cooking. Wat if it becomes thick after putting it in the lunch box ?


Sorry I've been away. Very remiss of me.
The revamped Chequers pub reopened a month or so ago. I've been in a few times; initially just for drinks as they hadn't got their kitchen working.
After being shut for a long time due to the new owners having money problems it is doing very well. They're used a lot of old furniture to create a 'Shabby Chic' look to the place. It actually works and I think adds to making it feel like a venue you can relax in.
They have a good selection of real ales on tap and they clearly focus on London based breweries. The staff are very friendly and welcoming.
My partner and I ate there a couple of weeks ago. It wasn't too busy on a Saturday night, although we left by 9PM. We both had burgers which were lovely and came with 'triple fried chips'. The coleslaw was clearly freshly hand made and tasted delicious.
It is clearly aiming for the 'Village' end of the social spectrum. But as somebody who lives in the North of the 'stow this pub is much more viable for a few beers. I really recommend it; the reborn Chequers deserves to do well.


PINK TINSEL Fragrance Oil - You will love this fabulously fun oil! Certain to be a best seller for the holidays, but perfect for all year! With top notes of pink pomegranate, Valencia orange and tiny hints of coconut; middle notes of Douglas Fir, clove leaf and cinnamon with bottom notes of Frozen Woods and Tonka Bean. You will love this very unique oil!
I love this oil! It is totally different than most holiday oils. It is doing awesome at my shop. It is fantastic in my 50-50 blend tarts. You should really try this - it is awesome!


The nativity stories are at one and the same time utterly familiar (perhaps over familiar) and, in the context in which they were written, political and religious dynamite.
This chapter begins with the oh, so familiar words, 'In those days a decree went out from Emperor Augustus …' With my scientific hat on, I want to know who this Emperor Augustus was, and who Quirinius was, and what evidence we have about them. We know something about Quirinius and his governorship, but we come up against a snag. Luke, otherwise highly accurate, seems not to be quite right about the date of the census. Maybe Quirinius isn't so important after all, if Luke is rather casual about the period of his governorship. Nonetheless, by mentioning the census, Luke gets Mary and Joseph to Bethlehem, where he knows Jesus the Messiah was born – where, indeed, the longed-for Messiah had to be born in accordance with Jewish prophecy.
Providence has ordered all things and is very much interested in our life … giving us Augustus, …, sending him as a saviour, both for us and those after us, … the birthday of the god Augustus was the beginning of the good news [gospel] for the world that came by reason of him.
This gigantic hubris is smashed to pieces by Luke's account of the nativity. Augustus thinks he is in control, but the real Prince of Peace, the real God incarnate, the real promised and longed-for Saviour of the world, is born in an obscure part of his empire. He will conquer by compassion and love, and by suffering an ignominious death under another Roman who thinks he is in control. This is, indeed, political and religious dynamite, but good news for those humble enough to believe in their own weakness and neediness.
The Danish philosopher Soren Kierkegaard tells a story which illustrates the infinite love and humility which God shows through the incarnation. A certain King fell in love with a poor maiden. There were insurmountable barriers to their union, both for the King and for the maiden. If the King commanded the girl to the palace she would have to obey, but would this be love? If he went to her disguised as a peasant, won her love, and then revealed himself, that would be deceitful and not a recipe for trust and happiness. The only way would be for him really to become a peasant himself and lead the life of a humble artisan. So it is with God and humanity, though with an infinitely greater contrast between God's glory and our poverty.
As we ponder these familiar verses once again, let us consider the sheer miracle of it, the gift beyond price of the incarnation. The whole destiny of the human race is bound up with this tiny, vulnerable babe. He was born, not in a palace, not in Rome or Jerusalem, and not of royal parents—except by remote ancestry on his adoptive father's side, Instead he was born in obscurity to a peasant girl engaged to a humble carpenter. He was born in a stable and wrapped in bands of cloth, and yet, despite all that, he is a king. Indeed, he is the King of kings and Lord of lords whose kingdom is 'not from this world' (John 18:36), but a heavenly Kingdom which transcends this earthly realm. His is an eternal Kingdom and he secures our membership of it by his brutal death but mighty resurrection. Praise the Lord for his inestimable gift!
But oh, for thee, for him, hath th' inn no room?
This post was an extract from Rodney Holder, Longing, Waiting, Believing: Reflections for Advent, Christmas and Epiphany (BRF, 2014), pages 127-131, with permission of the publisher.
[i] The Third Letter of Cyril to Nestorius, in E. R. Hardy (ed.), Christology of the Later Fathers, Library of Christian Classics vol. III (London: SCM Press, and Philadelphia: Westminster Press, 1954), p. 350.
[ii] Nativity, in John Donne, The Major Works, Oxford World Classics edition, Oxford: Oxford University Press, 2000, pp. 171-172.


Indore, The City of Food is one of the few places in India where you can savor India's best Poha and Immarti. The capital of Madhya Pradesh is also known as the Food City of India. Travellers not only like to explore the various magnificent sites of the city but also love to savor the exotic delicacies that tantalize their taste buds. There are many budget hotels in the city where one can enjoy these scrumptious delicacies.
Hotel KK is a one of the best budget hotels in Indore. The property is situated at the Siddharth Nagar, Bhanwarkua Chouraha in Indore. The hotel has a close proximity with many tourist destinations such as Khajrana Ganesh Mandir, Sarafa Baazar, Shri Omkareshwar Jyotirling, Gomatgiri and many more. The guests in the hotel are offered with the facilities such as internet access (Wi-Fi), mini fridge, parking, a spacious dining option and newspaper. The rooms are fitted with beautiful décor and premium furnishings. These furnishings are the highlights of the rooms. Every room is spacious and fitted with the range of amenities such as LCD TV, AC, telephone and many more. The attached bathrooms are filled with every necessary amenities and essential toiletries in it. Guests can also avail round the clock hot and cold water facilities in the bathroom. The hotel is 10 km from Devi Ahilyabai Holkar Airport, 4 km from Indore Railway Station and 10 minutes' drive from bus stand.
Hotel Tirupati Palace is also listed among cheap Indore hotels. The property is only at a 10 minutes distance from Devi Ahilyabai Holkar Airport. Many tourist attractions like Lal bagh Palace, Kaancg Mandir, Central Museum and Nehru Park and many more which come as a delight to sightseers. Guests in the hotels can take dining experience by ordering food through room service, which is round the clock available. There are many restaurants situated nearby by the hotel that offers regional and global flavors. The rooms are spacious and air conditioned and fitted with cable TV and direct dial telephone. The historical edifice Rajwada Palace is just 5 minutes away from the hotel. The Rajwada Palace is a perfect amalgamation of Maratha, French and Mughal architectural styles.
There are many more other hotels like hotel south avenue, Prashant Hotel, Samrat Hotel, hotel kanchan tilak and hotel siddhant which are listed among budget Indore hotels. These hotels are standing to give an array of facilities which make the stay of their guests comfortable and relaxing.
Looking for an economy hotel near indore railway station with Room service.?
Hotel Kanchan Tilak 3.5 km from railway station with room service.
Any budget hotel with Bar and retaurant?
Hotel Kalinga and Hotel Somdeep Palace are good budget hotels.Hotels have both facilities.
Please suggest me some good budget hotels they have in house restaurant? My budget is 2500?
Malwa Country ,Hotel Princes Palace ,Golden Gate Hotel these are budget hotels having in-house restaurant.


Geospatial World Forum has a long-standing tradition of hosting a rich set of co-located workshops. It is the perfect avenue for presentation and discussion of geospatial work to a wide and interested audience.
Why organize your workshop at Geospatial World Forum?
Workshop format, i.e. presentation-based, tutorial-based, discussion-based, etc.
Please note, the opportunity to organize a workshop is only open to non-commercial entities – government, academia, NGOs only.
Is there any cost incurred in organizing a workshop?
The fee is inclusive of usage of one hall with 30 pax capacity for 90 minutes. Basic AV is included.
Apart from this, we also require all workshop speakers and participants to register to the conference. Please see our registration options here.
Selected workshops will be featured as part of Geospatial World Forum 2019 program with due promotion on website, newsletters, social media and mobile app.


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Saginaw and Bay City News
SVSU suspending in-person classes amid Michigan coronavirus threat
Saginaw Valley State University is located in Saginaw County's Kochville Township.Kaytie Boomer | MLive.com file
Heather Jordan | heather_jordan@mlive.com
KOCHVILLE TWP, MI — With coronavirus now in Michigan and the World Health Organization declaring the disease it causes, COVID-19, a global pandemic, Saginaw Valley State University has joined a growing list of colleges and universities canceling in-person instruction and moving classes online.
SVSU President Donald J. Bachand sent an email to students just before 5:30 p.m. Wednesday, March 11, notifying them that in-person instruction is to be suspended effective Monday, March 16, through at least Friday, April 17, among other precautionary measures the university is taking. The letter addressed to the campus community reads:
"We care about you, and your health and well-being. The State of Michigan has confirmed two individuals have contracted the COVID-19 virus. We are monitoring the latest guidance from the state and the U.S. Centers for Disease Control.
"The SVSU leadership team meets daily to discuss the status of this outbreak and SVSU's operations. The team had a conference call with the Saginaw County Health Department this morning and is communicating with the department frequently. At this time, the risk for contracting the virus in our area is low, but this is a rapidly developing situation. Please remember that race or ethnicity has no bearing on the likelihood of becoming sick or transmitting disease.
"Effective today (March 11), SVSU is suspending all university-sponsored international travel through at least June 30. We strongly advise faculty, staff and students to avoid personal international travel, as well.
"We strongly discourage SVSU-sponsored domestic travel by faculty, staff and students, as well. Faculty, staff and students should consult with their supervisor prior to any trips. We may further restrict domestic travel with little advance notice, as circumstances warrant.
"We are suspending face-to-face instruction for lecture and discussion classes and moving to online or remote instruction, effective Monday, March 16 and through at least Friday, April 17. All instructors will contact their students no later than Wednesday, March 18 to provide further information about course delivery. We are continuing to work with faculty and staff on laboratory and performance classes, and the university will provide additional guidance.
"We will re-evaluate the need for remote learning before April 15 and will provide further information at that time. During this time period, students doing purely remote work can return to their permanent place of residence but for students who remain on campus, we will maintain operations in our residence halls and dining services. For campus dining, we will be taking steps to increase "grab and go" options and reduce communal dining.
"Academic and student support services, as well as business operations, will remain open.
"At this time, SVSU is evaluating the upcoming public events we are scheduled to host. We are planning to hold events scheduled for this weekend and will make a decision regarding future events later this week. We will continue our enhanced cleaning and sanitation procedures, and we will encourage our visitors to practice good hygiene, as we all should be doing, and to consider their personal health in connection with the implications of large gatherings. Again, this could change with little advance notice.
"Symptoms of the COVID-19 virus include: a cough, a fever greater than 100.4 degrees, and shortness of breath. If you exhibit these symptoms, please call-in sick, avoid contact with others and call your health care provider. It is important to call ahead so that health care agencies can provide appropriate assessment, care and instructions. Please know that many health insurance plans offer tele-medicine services. Individuals who have been sick should remain home until their fever has been gone for at least 24 hours without the use of fever-reducing medicines.
"The health and welfare of our entire campus community is our highest priority. We will continue to update the campus community with the latest information surrounding the COVID-19 virus, and will update our www.svsu.edu/coronavirus webpage."
Elsewhere in Michigan, Central Michigan University and Michigan Technological University officials announced on Wednesday they are suspending in-person classes and moving to online instruction because of coronavirus COVID 19. Both universities are on spring break now, and officials say they're attempting to prevent returning students from bringing coronavirus onto campus. In addition, Michigan State University has cancelled in-person classes and moved to online classes, effective noon Wednesday.
Also on Wednesday, Bay City Public Schools Superintendent Stephen C. Bigelow halted the district's attendance incentives and urged any student or staff member who is ill to stay home.
Gov. Gretchen Whitmer on Tuesday, March 10, announced Michigan's first coronavirus cases and declared a state of emergency. The World Health Organization has declared the coronavirus crisis to be a global pandemic.
"We're going to keep Michigan safe and we're going to be prudent," Whitmer said, adding she intends to meet with officials Wednesday to determine what further measures to take. A related announcement is expected Wednesday afternoon, according to a press release from the governor's office.
Michigan is the 38th state to have a confirmed case of coronavirus COVID-19. Nationwide, there have been nearly 1,000 reported cases and 31 deaths.
COVID-19 symptoms, which include fever, cough and shortness of breath, may appear within two to 14 days of exposure to the virus.
Much like how you would try to prevent the flu, you want to stay away from people who are sick and practice good hygiene, says the CDC.
The latter means thoroughly washing your hands for at least 20 seconds, especially after using the bathroom and before eating. Avoid touching your mouth or face unless your hands are clean.
Use household cleaners to disinfect commonly touched objects and surfaces. Use disinfectant wipes to clean your hands or surfaces such as shopping-cart handles when out in public.
Some people are going the extra step and using smartphone sanitizers as a precaution, but a disinfecting wipe used lightly on the outside will likely work fine, too.
For the latest information, visit Michigan.gov/coronavirus or CDC.gov/coronavirus.
Find more coronavirus coverage from MLive here.
Bay City St. Patrick's Day Parade organizers meeting to discuss coronavirus threat
8 things to know about coronavirus now that it's in Michigan
Michigan Joint Information Center activated to support state's coronavirus response
Coronavirus Q&A, 15 things to know about COVID-19′s spread


text:
Press Releases>Arts & Entertainment>Music>Michael Sanders>
Michael Sanders
Michael Sanders CD Album Release "Don't You Know I Love You"
Kansas City Singer/Songwriter Michael Sanders releases his new CD "Don't You Know I Love You."
Kansas City, MO, March 14, 2016 --(PR.com)-- Michael Sanders wrote "Don't You Know I Love You" for everyone to enjoy and relate too. Through his journey in self discovery working with youth at a boys home in Oklahoma, Michael discovered his creative side in the world of music. His songs all come from experiences he has had through his journey in life while working with those struggling with addictions. This CD was created by him to help inspire others and he was blessed by those around him willing to help see his vision for this project come to life. A few members of his church, the Apostolic Church of Jesus Christ were able to lend their voices to help complete his project. The "Don't You Know I Love You" album was produced by an extremely talented, up and coming producer by the name of Anthony Saunders. The album also featured talented musical artists such as, Lisa Chavis, Bryon Gunn and Rosiland Williams and saxophone by Willie Thorton.
www.michaelsandersmusic.com
www.facebook.com/michaelsandersmusic
www.cdbaby.com/artist/michalsanders
Micheal Sanders Press Release
Press Release for new CD "Don't You Know I Love You"


text:
The Courier-Mail (Brisbane, Qld. : 1933 - 1954)
STEPS TO MEET TEACHERS' WISHES
Protest by the Teachers' Union against some of Its members having been billeted with Italians would result in an early decision
Mon 23 Mar 1942 - The Courier-Mail (Brisbane, Qld. : 1933 - 1954)
Page 3 - STEPS TO MEET TEACHERS' WISHES
STEPS TO MEET
TEACHERS7 WISHES
Protest by the Teachers' Union
against some of its members hav
ing been billeted with Italians
would result in an early decision
to the satisfaction of the teachers,
said the Education Director' (Mr.
L. D. Edwards) yesterday.
The union also had expressed its
opposition to teaching facilities
being provided for children of
aliens of enemy origin. Comment
Ing on that matter, Mr. Edwards
said that these children were at
tending already existing schools.
He could not see that any harm
could be done by teaching the
children, because they, were taught
in English, and through their les
sons were informed of British cul
ture, history, and traditions.
Mr. Edwards added that the
question of Easter holidays for
teachers and children probably
would be decided by the Cabinet
to-day.
STEPS TO MEET TEACHERS' WISHES (1942, March 23). The Courier-Mail (Brisbane, Qld. : 1933 - 1954), p. 3. Retrieved January 20, 2021, from http://nla.gov.au/nla.news-article50116433
"STEPS TO MEET TEACHERS' WISHES" The Courier-Mail (Brisbane, Qld. : 1933 - 1954) 23 March 1942: 3. Web. 20 Jan 2021 <http://nla.gov.au/nla.news-article50116433>.
1942 'STEPS TO MEET TEACHERS' WISHES', The Courier-Mail (Brisbane, Qld. : 1933 - 1954), 23 March, p. 3. , viewed 20 Jan 2021, http://nla.gov.au/nla.news-article50116433
{{cite news |url=http://nla.gov.au/nla.news-article50116433 |title=STEPS TO MEET TEACHERS' WISHES |newspaper=[[The Courier-mail]] |issue=2667 |location=Queensland, Australia |date=23 March 1942 |accessdate=20 January 2021 |page=3 |via=National Library of Australia}}
The Courier-Mail (Brisbane, Qld. : 1933 - 1954), Mon 23 Mar 1942, Page 3 - STEPS TO MEET TEACHERS' WISHES


text:
"What Are You Working On, Jason Schultz?"
September 22, 2010 by MaryKing, posted in Miscellaneous, What Are You Working On Wednesdays
Ever wonder what exciting new projects the many employees at NARA are working on? The "What are You Working On?" blog feature aims to introduce a variety of NARA employees and highlight some of the exciting projects we are working on around the agency. Check for this blog series on Wednesdays!
This week, we introduce Jason Schultz, Archivist at the Richard Nixon Presidential Library.
What is your name and title?
Jason Schultz, Archivist
Where is your job located?
At the Richard Nixon Presidential Library and Museum in Yorba Linda, California.
What is your job in a nutshell?
Along with my fellow archivists, I provide reference services on materials related to the life and political career of Richard Nixon. I also process materials to make them available for public use.
The entire archival staff in Yorba Linda has been busy since July 1 with our newly reopened research room, finally consolidating reference services on all materials related to Richard Nixon. I am passing on to my Yorba Linda colleagues everything I learned in my two years of working with the Presidential materials in College Park; in return they are teaching me the quirks and nuances of the Pre- and Post-Presidential materials.
As time permits, I am processing the White House Central Files materials of David Gergen—the political analyst at CNN who worked for four Presidents, but got his start in the Nixon Administration. Under the Presidential Recordings and Materials Preservation Act of 1974 (which governs these materials), this means reviewing every page for sensitive information, along with the traditional archival preservation activities of refoldering and making any necessary preservation copies.
How long have you been at NARA? Have you worked at any other NARA location?
I began with NARA as a student in November 2005. I spent a year with the Exhibits staff at Archives I and processed State Department records at Archives II for eighteen months before transferring to the College Park Nixon staff in July 2008. In May of this year, I followed the Nixon Presidential materials to California, returning home to Orange County.
What has changed since you started at NARA?
I can think of two changes offhand that have greatly shaped my time at NARA. The first was the ten-year processing initiative to reduce the backlog of unprocessed records. Because of this, I typed up tens of thousands of folder titles and also created many Archival Research Catalog (ARC) entries for State Department records. The second was the Joint Operating Agreement signed by NARA and the Nixon Foundation in July 2007, which created the Federal Nixon Library and got me where I am today.
The College Park move team in front of the first truck of Nixon Presidential Library materials to be loaded and relocated to California. Photo taken on April 5, 2010 at the Archives II loading dock in College Park, Maryland. From left, they are Melissa Heddon, Archivist; Marty McGann, then-Deputy Director; Jason Schultz, Archivist; and Tim Naftali, Director
Working with my colleagues to move the Nixon Presidential materials to California this past spring will always be at the top of my list. We had 35 years of loose ends to tie up before moving the materials and—unlike departing Presidents—we moved the materials without the help of the military.
My favorite research assignment, however, was to investigate the history of two dessicated fingers, part of the General Records of the Department of State. They were submitted as evidence in the 1930s in a claim against the Mexican government for banditry acts committed in the State of Nayarit in 1918. The State Department records are quite dramatic and, at times, gory. (Read more about the story here.)
What are your passions or interests outside of work?
I've been interested in Disneyland history since I was 13. In fact, discovering that there was a Walt Disney Archives was what made me want to become an archivist. My master's thesis on roads and wilderness areas in California, including a section devoted to the proposed Disney ski resort in Mineral King, succinctly captures my chief intellectual interests.
What is the last book you read, or the last book you loved?
Italo Calvino's If on a winter's night a traveler. It's a book about the reading experience, specifically a frustrated Reader who settles in to read a new book only to discover that a misprinting keeps him from getting too far in the book. For the rest of the novel, while seeking to continue the first story, the Reader is led from one compelling story to another wholly unique tale, but never finds more than a part of any one story. I think it's very applicable to archival work because often in the records we only find a partial story, and while searching for additional details we may come across something even more engrossing.
Meet more NARA employees: http://www.archives.gov/careers/employees/
Tagged ARC, archivists, Presidential Libraries
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One thought on ""What Are You Working On, Jason Schultz?""
K. S. says:
Doing a paper on the Nixon Watergate Exhibit for my Graduate degree in Library Science. So fun to see the archivists after reading so much about them.


text:
\section{Introduction}
There are basically two approaches to perturbation theory in general relativity (GR): the Lifshitz's method \cite{lifshitz,lifs_khal} which was rigorously improved by the work of Bardeen \cite{bardeen} and others \cite{kodama, mukh92} and the covariant method given by the Quasi-Maxwellian (QM) equations \cite{jek}, which was first proposed by Hawking \cite{hawking_66} and improved by Olson \cite{olson}, Ellis {\it et al} \cite{ellis_bruni,ellis} and Novello {\it et al} \cite{novello,nbs}. The former includes perturbations of non-observable quantities such as $\delta g_{\mu\nu}$ and it mixes true perturbations with coordinate transformations coming from the gauge freedom due to the arbitrariness of the correspondence between a fictitious background space-time and the physical inhomogeneous one.
In Bardeen's approach gauge-invariant quantities are constructed as combinations of the perturbations of the metric and of the matter content, but no clear physical interpretation can be given to those variables.

On the other hand, the QM equations offer a natural covariant approach to perturbation theory, in which it is possible to find suitable gauge-invariant variables that are directly linked to observational quantities, thus making the physical interpretation clear and providing an elegant description. In this approach, it is possible to find a set of perturbed quantities which are considered as ``good'' ones as their unperturbed counterparts are null in the background and, therefore, Stewart \& Walker's lemma \cite{stewart} ensures that the associated perturbed quantities are gauge-invariant. In \cite{novello} for instance this method was applied to the Friedmann-Lema\^itre-Robertson-Walker (FLRW) models in order to find the minimal closed set of variables necessary to the perturbative analysis, in terms of which all other quantities could be written. Remarkably, this minimal set contained only two of the full set of perturbation variables providing a planar dynamical system, from which all the other quantities could be expressed. The relation between the covariant formalism and Bardeen's approach have been clarified in Refs. \cite{hwang, bruni92}.

In our case, the presence of an anisotropic pressure due to a primordial magnetic field (PMF) removes some symmetries of the FLRW models and makes the analysis a bit more complex. We show that it is possible to construct a minimal set consisting of three gauge-invariant variables contained in the full set we have at our disposal. The latter includes the fractional gradient of the energy density and the gradient of the expansion coefficient, both orthogonal to the fluid flow, which were introduced by Ellis and Bruni \cite{ellis_bruni}. In the special case of large wavelengths, when the equations for the perturbations reduces to a planar system, it is possible to construct a second order equation from which we can analyze the growth of inhomogeneities.

This work is organized as follows. In section \ref{notation} we give the main definitions needed for the description of perturbations in the QM approach. In section \ref{background} we briefly introduce the background model and its important features. In section \ref{basis} we construct the complete basis for the perturbations and derive from them the necessary quantities for the subsequent analysis. Afterwards, in section \ref{set}, we present the set of variables needed to describe the perturbations and their corresponding evolution equations. In section \ref{pert} we perform the perturbative analysis focusing on the large wavelength behavior. Then, we compare our results with the standard FLRW model in order to verify how the growth of perturbations are modified in this new scenario and if the anisotropic pressure could play a role similar to a dark matter component in the standard cosmological model. The full set of the Quasi-Maxwellian equations, the conservation laws for the matter content and the evolution equations for the kinematical quantities are presented in the Appendix.

\section{Definitions and Notation}
\label{notation}

We consider the standard definitions given in \cite{nbs} to introduce the QM approach to General Relativity, except for some conventions (for details see the Appendix). The Weyl conformal tensor is defined as\footnote{Greek indices run from 0 to 3 and latin indices run from 1 to 3.}
\begin{equation}
\nonumber
W_{\alpha\beta\mu\nu}\doteq R_{\alpha\beta\mu\nu} - M_{\alpha\beta\mu\nu} + \fracc{1}{6} R g_{\alpha\beta\mu\nu},
\end{equation}
where the auxiliary tensors are
\begin{equation}
\nonumber
2M_{\alpha\beta\mu\nu} \doteq R_{\alpha\mu}g_{\beta\nu} + R_{\beta\nu}g_{\alpha\mu} - R_{\alpha\nu}g_{\beta\mu} - R_{\beta\mu}g_{\alpha\nu}
\end{equation}
and
\begin{equation}
\nonumber
g_{\alpha\beta\mu\nu}\doteq g_{\alpha\mu}g_{\beta\nu}-g_{\alpha\nu}g_{\beta\mu}.
\end{equation}

The Weyl tensor can be separated into its electric and magnetic parts, defined as
\begin{equation}
\nonumber
\begin{array}{lcl}
E_{\alpha\beta}&\doteq&-W_{\alpha\mu\beta\nu}V^{\mu}V^{\nu},\\[2ex]
H_{\alpha\beta}&\doteq&-^{*}W_{\alpha\mu\beta\nu}V^{\mu}V^{\nu},
\end{array}
\end{equation}
where $^{*}W_{\alpha\mu\beta\nu}$ is the dual Weyl tensor constructed with the skew-symmetric Levi-Civita tensor. The tensors $E_{\alpha\beta}$ and $H_{\alpha\beta}$ are symmetric, traceless and belong to the 3-dimensional space, orthogonal to a class of observers with four-velocity $V^\mu$.

The metric $g_{\mu\nu}$ and the normalized vector field $V^\mu$ (tangent to a timelike congruence of curves $\Gamma$) induce a projector $h_{\mu\nu}$ which splits tensors in terms of quantities defined along $\Gamma$ plus quantities defined on the three-dimensional space orthogonal to $V^\mu$. It is expressed as
\begin{equation}
\label{proj}
h_\mu{}^\nu\doteq\delta_\mu{}^\nu-V_\mu V^\nu.
\end{equation}

We deal here with a Friedmann type of metric which, as such, is written as
\begin{equation}
\label{gen_ds2}
ds^2=dt^2+h_{ij}dx^idx^j,
\end{equation}
where $h_{ij}=-a^2(t)\gamma_{ij}(x^k)$ and the modification with respect to the Friedmann models is encoded in the $\gamma_{ij}$ part, as we shall see.

We introduce the so-called kinematical quantities through the decomposition of the covariant derivative of $V^{\mu}$ into its irreducible parts:
\begin{equation}
V_{\mu;\nu} \doteq \sigma_{\mu\nu} + \omega_{\mu\nu} + \fracc{1}{3}\theta h_{\mu\nu} + a_{\mu}V_{\nu},
\nonumber
\end{equation}
where the expansion coefficient is
$$\theta\doteq V^{\mu}{}_{;\mu},$$
the acceleration is
$$a^{\mu}\doteq V^{\mu}{}_{;\nu}V^{\nu},$$
the traceless and symmetric shear tensor is
$$\sigma_{\mu\nu} \doteq \frac{1}{2} h_{\mu}{}^{\alpha} h_{\nu}{}^{\beta} V_{(\alpha;\beta)} - \frac{\theta}{3} h_{\mu\nu},$$
and the skew-symmetric vorticity tensor is
$$\omega_{\mu\nu}\doteq\frac{1}{2} h_{\mu}{}^{\alpha} h_{\nu}{}^{\beta} V_{[\alpha;\beta]},$$
where $()$ means symmetrization and $[\,]$ means anti-symmetrization.

\section{Friedmann equations in the presence of an anisotropic pressure}
\label{background}

In this section, we briefly review the recent proposal \cite{bitt_salim} in which it is assumed a Friedmann-like geometry
\begin{equation}
\label{fried}
ds^2=dt^2-a^2(t)[d\chi^2+\sigma^2(\chi)d\Omega^2],
\end{equation}
where $t$ represents the cosmic time, $a(t)$ is the scale factor and $\sigma(\chi)$ is an arbitrary function.

We consider as source the linear Lagrangian of Maxwell's theory of electromagnetism
$$L=-\fracc{1}{4}\,F,$$
where $F\equiv\,F^{\mu\nu} F_{\mu\nu} = 2 (B^2-E^2)$.
The energy-momentum tensor corresponding to this Lagrangian is
$$T_{\mu\nu}=F_{\mu}{}^{\alpha}F_{\alpha\nu}-Lg_{\mu\nu},$$
whose decomposition into irreducible parts with respect to a normalized time-like vector field $V^{\mu}$
yields
\begin{equation}
\label{rho_p}
\rho = \frac{1}{2}(E^2+B^2), \hspace{.5cm} p =\frac{\rho}{3},
\end{equation}
\begin{equation}
\label{q}
q^{\alpha} = \eta^{\alpha}{}_{\beta\mu\nu} V^{\beta} E^{\mu} B^{\nu}
\end{equation}
and
\begin{equation}
\label{pi_em}
\pi_{\mu\nu} = -E_{\mu} E_{\nu} -B_{\mu} B_{\nu} - \frac{1}{3} (E^2+B^2) h_{\mu\nu},
\end{equation}
where $\rho$ is the energy density, $p$ is the isotropic pressure, $q^{\alpha}$ is the heat flux and $\pi_{\mu\nu}$ is the anisotropic pressure. It is convenient to assume the cosmic observer $V^{\mu}=\delta^{\mu}_0$. Due to the special symmetries of the metric\ (\ref{fried}), the electromagnetic field can be considered as source of the gravitational field only if an averaging process is performed (cf.\ Ref.\ \cite{tolman2,hind}). The standard way to compute the volumetric spatial average of an arbitrary quantity X at the instant $t=t_0$ is defined by

\begin{equation}
\label{av_def}
\overline{X}\,\equiv \lim_{V \rightarrow V_0} \fracc{1}{V} \int X\sqrt{-g}d^3x^i,
\end{equation}
where we denote $V\equiv\int \sqrt{-g}d^3x^i$ and $V_0$ is a sufficiently large time dependent spatial volume. Therefore, the first and second moments of the electric $E_i$ and magnetic $H_i$ fields are usually given by the so-called Tolman relations:

\begin{equation}
\label{rel_tol_1}
\overline{E_i}=0, \hspace{.3cm} \overline{H_i}=0, \hspace{.3cm} \overline{E_iH_j}=0,
\end{equation}

\begin{equation}
\label{rel_tol_2}
\overline{E^iE_j}=-\frac{1}{3}E^2h^i{}_j,
\end{equation}

\begin{equation}
\label{rel_tol_3}
\overline{B^iB_j}= -\frac{1}{3}B^2h^i{}_j.
\end{equation}
We keep only the magnetic component of this mean field due to the high conductivity of the primordial plasma. Moreover, we do not impose homogeneity of the space-time but keep only the isotropy. Therefore, part of the Tolman relations are preserved [Eq.\ (\ref{rel_tol_1})]. However, our choice leads us to slightly modify the Tolman relation concerning the second moment of the magnetic field (\ref{rel_tol_3}), as follows

\begin{equation}
\label{rel_tol_3_mod}
\overline{B^iB_j}=-\frac{1}{3}B^2h^i_j-\pi^{i}{}_{j},
\end{equation}
where we introduce an arbitrary traceless matrix $\pi^{i}{}_{j}$ that will be identified to an anisotropic pressure term, through Eq.\ (\ref{pi_em}).

In the case of constant spatial curvature $^{(3)}R$, the time evolution of this cosmological model is driven by the usual Friedmann equations and the anisotropic pressure produces a non-vanishing Weyl tensor. The anisotropic pressure components are found to be

\begin{equation}
\label{pi}
\pi^{2}{}_{2}=\pi^{3}{}_{3},\hspace{1cm}\pi^{1}{}_{1}=-2\pi^{2}{}_{2}=\fracc{2k}{a^2\sigma^3},
\end{equation}
where $k$ is a constant\footnote{It is actually a constant coming from the integration of Einstein equations, see Ref. \cite{bitt_salim} for details.}. The corresponding Riemannian tensor $^{(3)}R_{\alpha\beta\mu\nu}$ of the spatial hypersurface can be written as
\begin{displaymath}
^{(3)}R_{\alpha\beta\mu\nu} = \fracc{\epsilon}{a^2} h_{\alpha\beta\mu\nu} - \pi_{\alpha[\mu}h_{\nu]\beta} + \pi_{\beta[\mu}h_{\nu]\alpha},
\end{displaymath}
where $h_{\alpha\beta\mu\nu} \equiv h_{\alpha\mu}h_{\beta\nu} - h_{\alpha\nu}h_{\beta\mu}$. This geometry is no longer maximally symmetric due to the presence of the last two terms.

Finally, making the coordinate transformation given by $r=\sigma(\chi)$, the line element\ (\ref{fried}) becomes

\begin{equation}
\label{fried_r_pi}
ds^2=dt^2-a^2(t)\left(\fracc{dr^2}{1-\epsilon r^2-\frac{2k}{r}}+r^2d\Omega^2\right).
\end{equation}

The corresponding QM equations of this solution are (see details in Appendix):

\begin{subequations}
\label{qm_gfried}
\begin{eqnarray}
&&\dot\theta+\fracc{\theta^2}{3}=-\fracc{1}{2}(\rho+3p),\label{qm_gfried1}\\[2ex]
&&\dot\rho+(\rho+p)\,\theta=0,\label{qm_gfried2}\\[2ex]
&&E_{\mu\nu}=-\fracc{1}{2}\pi_{\mu\nu},\label{qm_gfried3}\\[2ex]
&&E^{\alpha}{}_{\mu;\alpha}=0,\label{qm_gfried4}\\[2ex]
&&h^{\epsilon}{}_{\mu}h^{\nu}{}_{\lambda}\dot E^{\mu}{}_{\nu} + \frac{2}{3}\,\theta\, E^{\epsilon}{}_{\lambda} =0.\label{qm_gfried5}
\end{eqnarray}
\end{subequations}
Eqs.\ (\ref{qm_gfried1}) and (\ref{qm_gfried2}) correspond to the usual Friedmann equations

\begin{equation}
\label{gr_fried_solved}
H^2+\fracc{\epsilon}{a^2}=\fracc{\rho}{3},\hspace{1cm}\fracc{\ddot a}{a}=-\fracc{1}{6}(3\gamma-2)\rho,
\end{equation}
where $H\equiv\dot a/a$ is the Hubble parameter. Eq.\ (\ref{qm_gfried3}) yields immediately the electric part of the Weyl tensor in terms of the anisotropic pressure. Eq.\ (\ref{qm_gfried4}) represents the compatibility condition of the Einstein equations with the (constant) spatial curvature and Eq.\ (\ref{qm_gfried5}) provides the time evolution of $E_{\mu\nu}$. Note that these equations do not imply that the Weyl tensor is identically zero. Once Eqs.\ (\ref{qm_gfried1}-\ref{qm_gfried2}) are decoupled from Eqs.\ (\ref{qm_gfried3}-\ref{qm_gfried4}) we see that this model can be extended to any equation of state (EOS) of the form $p=(\gamma-1)\rho$, which is also valid for a mixture of non-interacting fluids.

From a straightforward calculation, the electric part of Weyl tensor for the cosmic observer reads

\begin{equation}
\label{el_weyl_r}
[E^i{}_j]=\fracc{k}{a^2r^3}
\left(
\begin{array}{ccc}
-1&0&0\\[.5ex]
0&\frac{1}{2}&0\\[.5ex]
0&0&\frac{1}{2}
\end{array}
\right).
\end{equation}
This equation is very similar to the Newtonian tidal forces multiplied by a time dependent function. We conclude that the Friedmann equations modify the Weyl tensor through the solution for $a(t)$, but the Weyl tensor does not change the Friedmann equations.

The remarkable exact relation\ (\ref{qm_gfried3}), which was not highlighted in the literature before\footnote{In fact, this solution was briefly presented in Lema\^itre's work \cite{lem33} and its mathematical features were more recently displayed by McManus and Coley \cite{coley}, but its full analysis and the issues raised in \cite{bitt_salim} were not envisioned in those works.}, informs us that the dissipative process to which the fluid is subjected is compensated in such a way that the tidal forces of the constituting microscopic parts of the fluid produce a reversal effect. This fact is confirmed in the geodesic deviation of the fluid flow which remains undistorted by these quantities. We now proceed with the set up of the framework for treating the perturbed version of this model.

\section{Construction of the basis}
\label{basis}
Since the seminal Lifshitz paper \cite{lifshitz} and the improvements displayed by Lifshitz and Khalatinikov \cite{lifs_khal}, it has been useful to expand all perturbed quantities in the spherical harmonics basis. Once we are interested only in the linear regime of the perturbations, the Laplace-Beltrami operator defined at the 3-hypersurface orthogonal to $V^{\mu}$ provides a complete set of functions which expand all perturbed quantities lying on this surface. This is also achieved due to the isotropy of the metric\ (\ref{fried_r_pi}), which allows the separation of variables transforming the eigenvalue problem in a set of ordinary differential equations to be solved.

It suffices for our purposes to take into account only the spatial scalar harmonic functions $Q(x^k)$ and its derived vector and tensor quantities
\begin{eqnarray}
&&Q_{i}\doteq Q_{,i},\nonumber\\
&&Q_{ij}\doteq Q_{,i||j}=Q_{,i;j}.\nonumber
\end{eqnarray}
For a while, it is necessary to distinguish covariant derivative in the 4-dimensional space-time by the symbol (;) and the derivative on the spatial hypersurface by (${}_{\|}$).

The functions $Q(x^k)$ obey the following eigenvalue equation in the 3-dimensional background space for each mode
\begin{equation}
 \nabla^2Q_{(m)}=m^2Q_{(m)},
\end{equation}
where $m$ is a constant (the wave number) and
\begin{equation}
\label{lap_bel}
\nabla^2Q\doteq \gamma^{ij}Q_{,i||j}=\gamma^{ij}Q_{,i;j},
\end{equation}
defines the 3-dimensional Laplace-Beltrami operator. The general solution of this equation is given by
$$Q(r,\theta,\phi)=\sum_{p,n}R(r)Y^n_p(\theta,\phi),$$
where $Y^n_p(\theta,\phi)$, with $p=0,1,2,...$ and $n=-p,...,p$, are the spherical harmonics and $R(r)$ satisfies

\begin{equation}
\label{r_eq}
\fracc{d}{dr}\left[r(r-2k-\epsilon r^3)\fracc{dR}{dr}\right] - [m^2r^2+p(p+1)]R=0.
\end{equation}
Note that only the complete integration of the above differential equation can inform the range of values allowed for $m^2$. However, it doesn't have a known analytic solution for arbitrary values of the parameters, particularly, $\epsilon=0$ and $r>2k$ which we are interested in.

We define the traceless operator
\begin{equation}
\hat Q_{ij}=\frac{1}{m^2}Q_{ij}-\frac{1}{3}Q\gamma_{ij},
\end{equation}
and its divergence can be computed yielding
\begin{equation}
\hat Q^{j}{}_{i||j}= 2\left(\frac{1}{3}-\frac{\epsilon}{m^2}\right) Q_i-\frac{\pi_{ij}}{m^2} Q^j.
\end{equation}
In the expression above the Einstein equations were used and $\pi_{ij}$ is a tensor involving only the spatial coordinates.

In particular, all possible projections of the anisotropic pressure\footnote{In the metric under consideration, the anisotropic pressure is the only nonzero tensorial quantity on the background. The electric part of the Weyl tensor, which is also nonzero, is determined by $\pi_{\mu\nu}$.} on the basis components can be rewritten in terms of this basis, if we assume that it is a complete one. Therefore, we write

\begin{equation}
\label{scalar_exp}
\pi_{ij} \hat Q^{ij}_{(m)}=\sum_la_{l(m)}Q_{(l)},
\end{equation}
\begin{equation}
\label{vector_exp}
\pi_{ij} Q^j_{(m)}=\sum_lb_{l(m)}Q_{i(l)},
\end{equation}
and
\begin{equation}
\label{tensor_exp}
\frac{1}{2}\pi_{k(i} \hat Q_{j)}{}^{k}{}_{(m)}=\sum_lc_{l(m)}\hat Q_{ij(l)}+\fracc{\gamma_{ij}}{3}\sum_la_{l(m)}Q_{(l)},
\end{equation}
where the coefficients $a_{l(m)}$, $b_{l(m)}$ and $c_{l(m)}$ are constants for each of the modes $m$ and $l$. Note that the summation symbol should be replaced by an integration symbol depending on the spectrum of the Laplace operator.

For our purposes, it is not important the explicit form of the scalar functions, but instead only the fact that such functions form a complete set with which it is possible to expand all perturbed quantities. Therefore, assuming a small deviation of the metric given in (\ref{fried}) when compared to FLRW, the quantities
$$A_{(m)}\doteq\sum_la_{l(m)}, \quad B_{(m)}\doteq\sum_lb_{l(m)}, \quad C_{(m)}\doteq\sum_lc_{l(m)},$$
should be necessarily bounded, but they are not arbitrarily small. Note that $A$ and $B$ are not independent quantities: from Eqs. (\ref{scalar_exp}) and (\ref{vector_exp}) we have $$A_{(m)}=\frac{1}{m^2}\sum_l b_{l(m)}l^2.$$
Note also that once the free parameter $k$ of the metric\ (\ref{fried_r_pi}) is fixed, and this should be achieved through observations, all these quantities should be completely determined.\\

\section{Gauge-invariant variables and unperturbed equations}
\label{set}
In this section we search for a set of gauge-invariant variables needed to perform the perturbative analysis and their correspondent evolution equations.
According to the evolution equation for the shear tensor (\ref{evol_quant_cine2}), we have
\begin{equation}
X_{\mu\nu}\doteq E_{\mu\nu}+\frac{1}{2}\pi_{\mu\nu},
\end{equation}
which is a good variable as it is null in the background, hence a perturbation on it yields a true physical perturbation. To this variable we add the shear $\sigma_{\mu\nu}$ itself, which is also null in the background. Following \cite{ellis_bruni}, we also consider as good variables the comoving fractional energy density gradient

\begin{equation}
\chi_\alpha\doteq a(t)\frac{h_\alpha{}^\nu\rho_{,\nu}}{\rho},
\end{equation}
and the comoving gradient of the expansion coefficient
\begin{equation}
 Z_\alpha\doteq a(t)h_\alpha{}^\nu\theta_{,\nu}.
\end{equation}

To this set of variables, we can still add other quantities that are null on the background: the acceleration $a_\mu$ and the divergence of the anisotropic pressure $I_\mu\equiv h_\mu{}^\epsilon \pi_\epsilon{}^\nu{}_{;\nu}$.

The unperturbed equations for the above variables follow from the evolution equations (\ref{quase_max4}), (\ref{expl_proj_conserv_mom_eneg1}), (\ref{evol_quant_cine1}) and (\ref{evol_quant_cine2}) and are written as

\begin{equation}
\label{X}
h_\mu{}^\epsilon h_\nu{}^\lambda \dot X_{\epsilon\lambda} =- \theta X_{\mu\nu} - \frac{1}{2}\pi_{\alpha(\mu}\sigma_{\nu)}{}^\alpha + \frac{1}{3}\pi_{\alpha\beta}\sigma^{\alpha\beta}h_{\mu\nu}  -\frac{1}{2}(\rho_t+p_t)\sigma_{\mu\nu}+D_{\mu\nu},
\end{equation}
\begin{equation}
\label{chi}
h_\mu{}^\lambda \dot \chi_\lambda=-\gamma_{ef}Z_\mu + \frac{a}{\rho}h_\mu{}^\lambda(\pi^{\alpha\beta}\sigma_{\alpha\beta})_{,\lambda} + a\,\gamma_{ef}\,\theta\,a_\mu,
\end{equation}
\begin{equation}
\label{theta}
h_\mu{}^\alpha \dot Z_\alpha=-a\,\dot\theta\, a_\mu-\frac{2\theta}{3a} Z_\mu+h_\mu{}^\alpha a^\nu{}_{;\nu;\alpha}-\frac{1}{2}(3\gamma_{ef}-2)\frac{\rho}{a}\chi_\mu,
\end{equation}
\begin{equation}
\label{sigma}
h_{\mu}{}^{\epsilon}h_{\nu}{}^{\lambda}\dot\sigma_{\epsilon\lambda} =- \fracc{1}{3}h_{\mu\nu}a^{\lambda}{}_{;\lambda} - a_{\mu}a_{\nu}+\fracc{1}{2}h_{\mu}{}^{\epsilon}h_{\nu}{}^{\lambda}a_{(\epsilon;\lambda)} - \fracc{2}{3}\theta\sigma_{\mu\nu}-X_{\mu\nu},
\end{equation}
where $D_{\mu\nu}\doteq\frac{2}{3}\theta\pi_{\mu\nu}+h_\mu{}^\epsilon h_\nu{}^\lambda \dot \pi_{\epsilon\lambda}$ and terms that would generate second order perturbations have already been discarded. The quantities $\rho_t$ and $p_t$ represent the total energy density and pressure, respectively, of a non-interacting mixture of simple fluids. They are related through the equation of state $p_t=(\gamma_{ef}-1)\rho_t$ where we have introduced an effective EOS parameter \cite{ellis_bruni} which, in the case of a universe filled with dust and radiation, is given by\footnote{The EOS parameter in this case depend on time, but $\dot\gamma_{ef}\approx 0$ and we can always assume that it has the value of the dominating fluid, cf.\ \cite{ellis_bruni}.}
$$\gamma_{ef}=\frac{\rho_d+4/3\rho_r}{\rho_d+\rho_r}.$$
The frame chosen is such that there's no energy flux, that is, $q^\alpha=0$. To these equations we must add the non-trivial constraint equations (\ref{quase_max1}), (\ref{expl_proj_conserv_mom_eneg2}) and (\ref{eq_vinc_quant_cine1}).

The term $D_{\mu\nu}$ in Eq. (\ref{X}) is determined by the causal thermodynamical relation \cite{israel} restricted by the symmetries of (\ref{fried}). It reads
\begin{equation}
\label{gen_israel_eq}
\tau\dot\pi_{\mu\nu}+\pi_{\mu\nu}=\xi\sigma_{\mu\nu},
\end{equation}
where $\tau$ is the relaxation time and $\xi$ is the viscosity parameter. This equation is valid only in the linear perturbation regime and was derived guided by the principle that the entropy flux is to be strictly local, that is, independent of gradients of the energy-momentum tensor and of the particle flux vector. In our case, in the background we have $$\tau\dot\pi_{\mu\nu}+\pi_{\mu\nu}=0$$ such that relations (\ref{pi}) give the relaxation time
$$\tau=\frac{3}{2\theta}.$$
The relation $\tau\propto 1/\theta$ was already considered in previous works in different contexts \cite{longa, novelloduque}.

\section{Perturbation Theory}
\label{pert}

From the original QM equations we have obtained equations for a set of suitable variables as described in the last section and now we aim to construct the perturbed version of them up to first order scalar perturbations. Similar analyses have been performed in Refs \cite{barrow98,tsagas00} where they have considered the contribution of anisotropic stresses on top of the usual perfect fluid content to the evolution of perturbations of a standard FLRW universe using the covariant approach. In particular, in \cite{tsagas00}, this anisotropic stress is due specifically to a vector magnetic field that should be small in order not to break isotropy. In both cases, terms that couple the anisotropic pressure with shear have been considered as second order as they indeed are in a FLRW background. In our case, however, as seen in section \ref{background}, we restrict ourselves to an anisotropic pressure component non-null at the background caused by random PMF--which has no vector character--and whose effect cannot be perceived at the zeroth order due to a compensation by the electric part of the Weyl tensor. In short, $\pi_{\mu\nu}\neq 0$ at the background, which turns out to be a modified FLRW, and that's the reason why we have to consider terms like $\pi_{\alpha\beta}\sigma^{\alpha\beta}$ as first order ones.

In what follows we present the full set of equations for perturbations at linear order. In particular, in the long wavelength regime, we get a system that is closed in only two variables allowing to perform a simpler phenomenological analysis and to obtain a second order equation for the evolution of such perturbations. Then, a comparison with the standard cosmological scenario in this regime is made.

\subsection{General Case}

We now consider the perturbative analysis associated to the variables previously defined. For instance, the perturbed version of Eq.\ (\ref{X}) is given by
\begin{equation}
\label{deltaX}
h_\mu^\epsilon h_\nu^\lambda \dot{\delta X_{\epsilon\lambda}} + \theta\delta X_{\mu\nu} + \fracc{1}{2}\pi_{\alpha(\mu}\delta\sigma_{\nu)}{}^\alpha - \fracc{1}{3}\pi_{\alpha\beta}\delta\sigma^{\alpha\beta}h_{\mu\nu} = -\fracc{1}{2}\gamma_{ef}\rho_t\delta\sigma_{\mu\nu}+\delta D_{\mu\nu},
\end{equation}
where $\delta D_{\mu\nu}=\xi\theta\delta\sigma_{\mu\nu}$ is given through the perturbed thermodynamical relation (\ref{gen_israel_eq}).

We use the complete basis introduced in Sec.\ \ref{basis} in order to expand the perturbations. For the perturbed equation for the quantity $X_{\epsilon\lambda}$ we set $\delta X_{ij}=X(t)\hat Q_{ij}$ and, for the shear, $\delta \sigma_{ij}=\sigma(t)\hat Q_{ij}$. In order to perform the expansion we need to consider terms like
\begin{eqnarray}
h_{\mu\nu}\pi_{\alpha\beta}\delta\sigma^{\alpha\beta}&=&h_{\mu\nu}\pi_{\alpha\beta}h^{\alpha\gamma}h^{\beta\delta}\delta\sigma_{\gamma\delta}\nonumber\\
&=&\frac{\sigma(t)}{a^4}Ah_{\mu\nu}Q,
\end{eqnarray}
where we have used relation (\ref{scalar_exp}). Remember that $A$ is constant in time but depends on the entire spectrum of wave numbers\footnote{Note that every quantity carries an index associated to its wavenumber, as usual when doing this kind of expansion. Thus we have omitted the subscript $(m)$ in $A$ for consistency of notation, as we have omitted it in the other quantities as well.}. We shall also consider relations (\ref{scalar_exp}) and (\ref{tensor_exp}) to write
\begin{equation}
\fracc{1}{2} \pi_{\alpha(\nu}\delta\sigma_{\mu)}{}^{\alpha} - \fracc{1}{3}\pi_{\alpha\beta}\delta\sigma^{\alpha\beta}h_{\mu\nu} = -\fracc{\sigma(t)}{a^2}C\hat Q_{\mu\nu}.
\end{equation}
which will be used in the expansion of Eq. (\ref{deltaX}).

In an analogous way, for the remaining variables we consider the expansions $\delta \chi_{i}=\tilde{\chi}(t) Q_{i}$, $\delta Z_{i}=Z(t) Q_{i}$, $\delta a_{i}=\psi(t) Q_{i}$ and $\delta I_{i}=I(t) Q_{i}$. The perturbed equations then result
\begin{equation}
\label{xt}
\dot X + \theta X + \left(-\fracc{C}{a^2} + \frac{1}{2}\gamma_{ef}\rho - \xi\theta\right)\sigma=0,
\end{equation}
\begin{equation}
\label{sigmat}
\dot \sigma-m^2\psi+X=0,
\end{equation}

\begin{equation}
\label{zt}
\dot Z + \left(a\,\dot\theta-\fracc{m^2}{a^2}\right)\psi+\frac{2\theta}{3a} Z + \frac{1}{2}(3\gamma_{ef}-1)\rho_t\tilde{\chi} = 0,
\end{equation}

\begin{equation}
\label{chit}
\dot{\tilde{\chi}} + \gamma_{ef}Z - \frac{1}{a^3}\frac{A}{\rho_t}\sigma - a\gamma_{ef}\theta\psi=0.
\end{equation}

The constraint equations yield
\begin{eqnarray}
\gamma_{ef}\psi+\frac{I}{\rho}-(\gamma_{ef}-1)\frac{\tilde{\chi}}{a}=0,\label{constraintPSI}\\
Z -\left(1-\frac{3}{2}\frac{A}{m^2}\right) \fracc{\sigma}{a}=0,\label{constraintZ}\\
\left(\frac{2}{3} - \frac{B}{m^2}\right)\frac{X}{a} -\frac{1}{3}\rho\tilde{\chi}-aI-\frac{B}{a}\psi=0.\label{constraintX}
\end{eqnarray}
From these equations, it is possible to write $\psi$ as a function of $\tilde{\chi}$ and $X$ (for $\gamma_{ef}\neq 0$). Besides, from Eq.\ (\ref{constraintZ}) we see that $Z$ is given only in terms of $\sigma$, which lead us to a closed dynamical system in three variables, from which all others are determined.

The qualitative analysis we are interested in can be done through the characteristic polynomial of the system. For a sake of simplicity, we choose a dust dominate era and write this 3-dimensional closed system in conformal time. Then, it yields

\begin{eqnarray}
p(x)=x^3 + \frac{6(B\eta^4 + 4\eta^2 + 12)}{(B\eta^4 + 12)\eta}\, x^2 &-&\frac{1}{3}\frac{(A - 2C)\eta^6m^2 + 18A\eta^4 - (36C + 432)\eta^2 + 216}{\eta^2(B\eta^4 + 12)}\, x +\nonumber\\&-& \frac{2(A\eta^4m^2 - 12\eta^2m^2 + 18A\eta^2 - 12C\eta^2 + 72)}{(B\eta^4 + 12)\eta}.
\end{eqnarray}

Once the system is non-autonomous we study the time evolution of the eigenvalues, i.e. the roots of $p(x)$, and their sensibility w.r.t. $A$, $B$ and $C$. A simple calculation shows that in the domain of interest of the conformal time all eigenvalues ($x_1$, $x_2$ and $x_3$) are real with $x_1$ always positive and $x_2$ and $x_3$ always negative. The discriminant never changes sign in this region. Only when we approach the singularity $\eta\rightarrow0$, we obtain a degenerate case where $x_1\rightarrow+\infty$, $x_2\rightarrow-\infty$ and $x_3\rightarrow0^-$. Since we cannot determine explicitly $A$, $B$ and $C$, this study was done for a large window in the parameter space (the same we will use afterwards to study the growth of perturbations).

\subsection{Growth of perturbations in the limit of large wavelengths}

In order to describe the structure formation, we can also use the local decomposition in irreducible parts of the projected covariant derivative of $\chi_\mu$ as
\begin{equation}
ah_\mu{}^{\lambda} h_\nu{}^{\epsilon}\chi_{\lambda}{}_{;\epsilon}=\frac{1}{3}h_{\mu\nu}\Delta+\Sigma_{\mu\nu}+W_{\mu\nu},
\end{equation}
where $W_{\mu\nu}$ gives the anti-symmetric part, $\Sigma_{\mu\nu}$ is the symmetric traceless part and, according to \cite{bruni92}, the variable $\Delta$ is the scalar gauge invariant variable that represents the clumping of matter. The equation for $\Delta$ can be derived from Eq.\ (\ref{chi}) and up to first order reads
\begin{equation}
\label{deltadot}
\dot{\Delta}=\frac{a^2}{\rho_t}h^{\alpha\beta}(\pi_{\mu\nu}\sigma^{\mu\nu})_{,\alpha;\beta}-\gamma_{ef}ah^{\alpha\beta}Z_{\alpha;\beta}+a^2\gamma_{ef}\theta h^{\alpha\beta}a_{\alpha;\beta}.
\end{equation}

Once the shear viscosity was widely studied previously, in this paper we focus our analysis only on the role of the anisotropic pressure, reflected by the wave number dependent coefficients $A$, $B$ and $C$. Hence, we set $\xi=0$ from now on.

For large wavelengths, that is, small values of $m$, Eq.\ (\ref{sigmat}) gives us $\dot\sigma=-X$. Deriving this equation once more, changing it to conformal time $d\eta=dt/a(t)$ and using Eq.\ (\ref{xt}) yields
\begin{equation}
\sigma^{\prime\prime}+2\frac{a^\prime}{a}\sigma^\prime+\left(C-\frac{1}{2}\gamma_{ef}a^2\rho_t\right)\sigma=0,
\end{equation}
whose solution for a dust dominated phase ($\gamma_{ef}=1$ and $a\propto \eta^{2}$) is
\begin{equation}
\label{larges}
\sigma(\eta) = \frac{c_1}{\eta^{3/2}} {\rm J}\left(\frac{\sqrt{33}}{2},\sqrt{C}\eta\right) +
\frac{c_2}{\eta^{3/2}} {\rm Y}\left(\frac{\sqrt{33}}{2},\sqrt{C}\eta\right),
\end{equation}
where ${\rm J}$ and ${\rm Y}$ are Bessel functions of first and second kind, respectively\footnote{We assume $C>0$, otherwise we would have modified Bessel functions.}, and $c_1$, $c_2$ and $C$ depend on $m$. For a dust-dominated phase the contribution of the PMF to the energy density is negligible, but the anisotropic pressure component, which goes with $1/a^2$, is still important.

Using Eq.\ (\ref{eq_vinc_quant_cine1}) and the expansion $\delta\Delta=\chi(\eta)Q(x^i)$, we get from Eq.\ (\ref{deltadot})
\begin{equation}
\chi'(\eta) = -\frac{Am^2}{\rho\,a}\,\sigma(\eta) - \frac{3\gamma_{ef}m^2}{2}\,\left( \frac{2}{3}\,a -\frac{B}{a m^2} \right)\sigma(\eta),
\end{equation}
where $A$ and $B$ depend on $m$ and the divergence of the acceleration that is proportional to $m^2$ has been neglected. In the conformal time, we see that $A$, $B$ and $C$ have units of inverse of wavelength squared [$m^2$]. Therefore, using the limit of small values of the argument in (\ref{larges}), $\sqrt{C}\eta\ll1$, we explicitly obtain
\begin{equation}
\label{chisol}
\chi(\eta)=\frac{c_1}{\Gamma\left(\frac{\sqrt{33}}{2}\right)}\left[\frac{3(\sqrt{33}+5)}{8}\,B+\frac{(3-\sqrt{33})m^2\,\eta^4}{12\,\eta_0{}^4} + \frac{(\sqrt{33} - 7)A m^2\,\eta^6}{96\,\eta_0{}^4} \right] \frac{\left(\sqrt{C} \eta \right)^{\frac{\sqrt{33}}{2}}}{(\eta/\eta_0)^{5/2}
\end{equation}
where we have neglected the decaying mode by setting $c_2=0$.

\subsection{Comparison with the Friedmann model}
\label{comparison}

The equivalent of Eq. (\ref{chisol}) in the case of a matter dominated FLRW universe is given by \cite{novello}

\begin{equation}
\chi(\eta)=\frac{c_1}{6}\,\left(\frac{\eta}{\eta_0}\right)^
\end{equation}
We compare the growth in time of the quantity above with the modified version, Eq. (\ref{chisol}), in Fig.\ (\ref{fig1}).
\begin{figure}[!htb]
\centering
\includegraphics[width=10cm,height=9cm]{graph-last.pdf}
\caption{(colors online) Growth of perturbations for different values of the quantities $A$, $B$ and $C$ compared to the dust dominated FLRW case. We have set $c_1=1$ in all cases. Note that the curves related to variations in $A\eta_0^2$ (with $B/m^2$ and $C\eta_0^2$ set to unity) remain very close to each other, whereas variations in $B/m^2$ (with $A\eta_0^2$ and $C\eta_0^2$ set to unity) and variations of $C\eta_0^2$ (with $A\eta_0^2$ and $B/m^2$ set to unity) have a larger range of variation such that the bigger the value of these parameters the faster the growth rate.}
\label{fig1}
\end{figure}
We have plotted different curves $\chi(\eta)$ normalized by $m^2$ for different values of the dimensionless quantities $A\eta_0^2$, $B/m^2$ and $C\eta_0^2$ together with the standard matter-dominated FLRW. Note that even though $A$, $B$ and $C$ are not completely independent and are ultimately related to the constant $k$ present in the metric (\ref{fried_r_pi}), we vary them as if they were to get an intuitive view of how they affect the evolution of $\chi$. We clearly see that variations of one order of magnitude in $A\eta_0^2$, with $B/m^2$ and $C\eta_0^2$ held fixed (set to unity), produce small variations on the solution, while variations of $B/m^2$ and $C\eta_0^2$ are more significant in the sense that they produce larger variations in the comoving fractional energy density gradient when varied in one order of magnitude.

This analysis shows us that it is possible to obtain a larger growth of the inhomogeneities when compared to a dust-dominated FLRW, in the limit of large wavelengths, for a very large range of the parameters. The full analysis of the dependence of the solution on these parameters and consequently on the wavenumber $m$ of course demands the exact solution of Eq.(\ref{r_eq}) and this requires a much deeper analysis that is not in the scope of this work. In spite of that, we see that the Weyl tensor might be efficient for gravitational collapse by allowing a larger growth rate of the perturbations and could {\it in principle} mimic in part the dark matter component in structure formation in this scenario.

\section{Concluding Remarks}

We have performed a perturbative analysis of a quasi-Friedmann model with a non-null Weyl tensor directly related to an anisotropic pressure component due to a primordial magnetic field. We have adopted the covariant approach to perturbations and suitable gauge-invariant variables directly related to observational quantities were used. We have shown that, depending on the values of the parameters involved, it is possible to have a larger growth of the perturbations when compared to the standard FLRW model, which could in principle play the role of dark matter or at least diminish its contribution in structure formation. Clearly, an analysis of the dependence on the wavenumber of the constants involved is needed to confirm it and in particular to treat the issue of scale invariance of the perturbations and the asymptotic behavior for small scales, which shall be treated in a future work. Anyhow, it is a very interesting fact that taking into account a non-null anisotropic pressure component which is hidden at the non-perturbative level could give us a scenario where perturbations are enhanced and that might not fully rely on an unknown dark component.

\acknowledgments The authors EB and GBS acknowledge the financial support provided by the CAPES-ICRANet program through the grants BEX 13956/13-2 and 13955/13-6.

redpajama_set_name: RedPajamaArXiv


text:
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Minnelli, Vincente. Lust for Life, 1956. [Life of painter Vincent Van Gogh]
Ray, Nicholas. 55 Days at Peking, 1963. [China, Boxer Rebellion]
Bertolucci, Bernardo. Novecento (1900), 1976. [Class struggle in twentieth century Italy]
Cameron, James. Titanic, 1997. [Sinking of the RMS Titanic]
Gavron, Sarah. Suffragette, 2015. [British women's suffrage movement]
Eisenstein, Sergei M. Battleship Potemkin, 1925. [Russian Revolution of 1905]
Schaffner, Franklin J. Nicholas and Alexandra, 1971. [Russian Revolution]
Eisenstein, Sergei M. / Aleksandrov, Grigori. October, 1927. [Russian Revolution]
Lean, David. Doctor Zhivago, 1965. [Russian Revolution]
Kazan, Elia. ¡Viva Zapata!, 1952. [Mexican revolutionary Emiliano Zapata]
Lean, David. Lawrence of Arabia, 1962. [Arab tribes' revolt against the Turks]
Weir, Peter. Gallipoli, 1981. [World War I, Battle of Gallipoli]
Renoir, Jean. Grande Illusion, 1937. [World War I]
Milestone, Lewis. All Quiet on the Western Front, 1930. [World War I]
Kubrick, Stanley. Paths of Glory, 1957. [France, World War I]
Mendes, Sam. 1917, 2019. [World War I]
Lean, David. A Passage to India, 1984. [British colonial India, ca. 1920]
Jordan, Neil. Michael Collins, 1996. [Irish independence leader]
Ford, John. The Grapes of Wrath, 1940. [The Great Depression]
Penn, Arthur. Bonnie & Clyde, 1967. [Exploits of Clyde Barrow and Bonnie Parker during the 30s]
Chuan, Lu. City of Life and Death (Nanjing! Nanjing!), 2009. [Nanjing Massacre, committed by Imperial Japanese troops]
Hooper, Tom. The King's Speech, 2010. [A speech therapist helps British King George VI]
Nolan, Christopher. Dunkirk, 2017. [Dunkirk evacuation]
Petersen, Wolfgang. The Boat, 1981. [A german U-boat during World War II]
Fleischer, R. / Fukasaku, F. / Kikushima, R. Tora! Tora! Tora!, 1970. [Surprise attack on the US naval base at Pearl Harbor]
Annaud, Jean-Jacques. Enemy at the Gates, 2001. [Battle of Stalingrad]
Spielberg, Steven. Saving Private Ryan, 1998. [Normandy landings]
Attenborough, Richard. A Bridge Too Far, 1977. [Operation Market Garden]
Noyce, Phillip. The Quiet American, 2002. [Vietnam, 1950s]
Schaffner, Franklin J. Patton, 1970. [The famous general during World War II]
Sturges, John. The Great Escape, 1963. [Escape of allied prisoners from a German camp during World War II]
Spielberg, Steven. Empire of the Sun, 1987. [Shanghai under Japanese occupation during World War II]
Lean, David. The Bridge over the River Kwai, 1957. [British POWs in Burma are employed by the Japanese to build a bridge]
Eastwood, Clint. Letters from Iwo Jima, 2006. [Battle of Iwo Jima]
Gibson, Mel. Hacksaw Ridge, 2016. [Battle of Okinawa]
Hirschbiegel, Oliver. Downfall, 2004. [Hitler's final days in his Berlin bunker]
Spielberg, Steven. Schindler's List, 1993. [Kraków, Holocaust]
Benigni, Roberto. Life is Beautiful, 1997. [Italy, Holocaust]
Polanski, Roman. The Pianist, 2002. [Warsaw, Holocaust]
Kramer, Stanley. Judgment at Nuremberg, 1961. [Alemania]
Mehta, Deepa. Earth, 1998. [Division of British India into India and Pakistan]
Preminger, Otto. Exodus, 1960. [The founding of the state of Israel]
Attenborough, Richard. Gandhi, 1982. [Biopic on the Indian leader]
Bertolucci, Bernardo. The Last Emperor, 1987. [The final Emperor of China]
Yimou, Zhang. To Live!, 1994. [Maoist China]
Kaige, Chen. Farewell My Concubine, 1993. [Pekin, 1925]
Egoyan, Atom. Ararat, 2002. [Armenia, 20th century]
Berlanga, Luis García. Wellcome Mr. Marshall!, 1953. [Failed welcome of Marshall Plan in Spain]
Camus, Mario. The Holy Innocents, 1984. [Campesinos en la España de la posguerra]
Donaldson, Roger. Thirteen Days, 2000. [Cuban Missile Crisis]
Kaufman, Philip. The Right Stuff, 1983. [American space program]
Parker, Alan. Mississippi Burning, 1988. [American Civil Rights]
Stone, Oliver. JFK, 1991. [The Kennedy assassination]
Coppola, Francis Ford. Apocalypse Now, 1979. [Vietnam War]
Stone, Oliver. Platoon, 1986. [Vietnam War]
Spielberg, Bridge of Spies, 2015. [Exchange of spies between the USA and the Soviet Union]
Spielberg, Steven. Munich, 2005. [Arab–Israeli conflict]
Spielberg, Steven. The Post, 2017. [A battle between the press and the US government over a Vietnam cover-up]
Pakula, Alan J. All the Pesident's Men, 1976. [The Watergate scandal]
Greengrass, Paul. Bloody Sunday, 2002. [Massacre in Ireland by British troops]
Sheridan, Jim. In the Name of the Father, 1993. [Some Irish men are wrongfully imprisoned for the bombing of a London pub]
Donnersmarck, Florian Henckel von. The Lives of Others, 2006. [Stasi espionnage in East Germany during 1980s]
Scott, Ridley. Black Hawk Down, 2001. [Somalia, Battle of Mogadishu]
George, Terry. Hotel Rwanda, 2004. [Genocide against the Tutsi]
Eastwood, Clint. Invictus, 2009. [Nelson Mandela and the 1995 Rugby World Cup]
Historical Films by Author


The Bates Center offers a number of opportunities for individuals who wish to support Center activities. Individuals can contribute funds, become a Center member, donate personal papers, and volunteer time. See below for the many ways in which you can become a part of nursing history.
The Bates Center's operating expenses are covered by a combination of gifts, grants and endowment income. Contributions to the Center can be made here .
Membership supports the Center's year-round activities: preservation and processing of records, public reference service, cataloging, and newsletter. By becoming a member, you will receive the Center's newsletter, The Chronicle , as well as information about special events. To apply for membership, please contact nhistory@nursing.upenn.edu or call 215-898-4502.
Individuals interested in donating personal papers of historical interest should contact the Center at nhistory@nursing.upenn.edu or call 215-898-4502. For more information on what we collect and why you should donate your records, please view our guide .
The Center welcomes individuals interested in assisting in processing historical collections. Please contact the Bates Center at nhistory@nursing.upenn.edu or call 215-898-4502 for more information on an interesting and worthwhile volunteer activity.


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When the picture has not been loaded yet then this function will return an empty string.
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Returns the size of the picture, unaffected by scaling.
filename The absolute or relative filename of the picture that should be loaded.