Group discounts aren't just for corporate, student and travel groups. Families, friends, churches, community organizations – any group of 12 or more receives special rates and benefits. Reservations can be made up to a year in advance and your dinner & show ticket includes gratuity! Contact our group sales specialists to discuss your group's specific needs, requests or questions. We look forward to working with you!
Group pricing varies depending on the performance, date and time selected.
Student and senior groups may also be elligible for further discounts.
Group dinner & show tickets always include gratuity on entrées and included beverages!
A dinner & show ticket includes an entrée, bread, side salad (evening performances), coffee, tea, water and milk in addition to your show ticket.
Contact our Group Sales Specialists for specific pricing!
Enhance your experience! Consider adding a package to your group tickets!
-Choice of one basic cocktail (no premium liquors), bottle beers, wine by the glass or 32 oz. refillable soft-drink souvenir Super Sipper.
-Choice of one individual dessert from our menu; desserts for two may be shared by two guests.
-One 32 oz refillable soft drink souvenir Super Sipper.
-Choice of one basic cocktail (no premium liquors), bottle beers, wine by the glass or 32 oz refillable soft-drink souvenir Super Sipper.
-One 32 oz refillable softdrink souvenir Super Sipper.
Interested in appetizer or upgraded entrée options?
We'd love to personalize your event, just ask!
We are open Monday - Friday from 9am to 5pm.
Private dining and viewing area for up to 32 guests!


Creating a paper circuit is a very fun and easy way to learn about circuits while being creative at the same time. In this tutorial, we are going to make a "simple circuit" which is the most basic of all circuits. To begin with, check out this introductory video from Chibitronics that gives a quick overview about working with copper tape.... The switch pocket should be placed underneath the spot where you've put the "press here" button on your card front. To make the switch pocket, cut a 3/4" x 1 3/8" piece of copy paper.
A simple boost converter circuit can be also built using an IC 555 circuit for boosting USB 5V to 24V, or any other desired level. The same design can be used for boosting a 3.7V to 24V from a Li-Ion cell.... Make your circuit even more interactive by adding a switch to control your lights. Follow the video tutorial below to learn how make your own DIY switch! W Follow the video tutorial below to learn how make your own DIY switch!
Make a Simple Circuit but make sure you come back on Monday to find a cool way to make your own switch to turn the simple circuit you made on and off. In the meantime, check out some of the other Hopscotch bloggers like Kendra who is talking about Raising Boys and Angie who is trying some fun New Experiences. Be sure you stick around for the series and beyond. Click on the picture below to how to play jazz music on piano 6/01/2008 · Problem with circuits like this is, that if you make it more sensitive it will also start reacting to other light (environment). Perhaps you could add some posivive feedback, to make it flip over.
BUILD A VIDEO SWITCHER Watch several cameras on one monitor with this simple device With the cost of security cameras going down, adding a surveillance system for your how to make a motion sensor light switch Are you starting out in electronics? Then these simple electronic circuits will make it easy for you to start building electronic circuits. The first time you want to build a circuit, it can be a little bit daunting.
How to get adjustable slew rate in MOSFET switching circuit?
Simple Mains Voltage Stabilizer Circuit: Again, voltage detection becomes the main function of the circuit. The configuration obeys the above discussed parameters and switches ON the "restoration section" when mains voltage crosses a predetermined "high" value which is set by the preset, initially before installation.
The circuit diagram for the simple transistor timer is shown below. Reference Designators The circuit diagram differs from the circuit diagram of tutorial 1 in that the components now have reference designators assigned to them.
The switch pocket should be placed underneath the spot where you've put the "press here" button on your card front. To make the switch pocket, cut a 3/4" x 1 3/8" piece of copy paper.


text:
Writer Recalls Kendrick Lamar Saving Her Toddler From A Kitchen Knife During Interview
Wed, August 31, 2022 at 8:16 AM
Author Jessica Hopper says that Kendrick Lamar once talked her then-toddler into putting down a sharp kitchen knife during an interview prior to the release of good kid, m.A.A.d city. Hopper recalled the story during a pair of tweets posted online, Tuesday.
In response to a post asking for a "true story from your life that sounds made up," Hopper wrote: "I was doing a phone interview with Kendrick Lamar when my then-toddler son appeared holding a very sharp kitchen knife he did not want to let go of and Kendrick talked me through safely disarming him."
Bennett Raglin / Getty Images
After the tweet began going viral, Hopper added: "Well this certainly blew up. If you'd like to read the interview/piece I did on Kendrick, right before Good Kid came out -- it's in my book,The First Collection, which you can find at most indie bookstores and libraries."
In addition to her collection, Hopper's writing has appeared in GQ, Rolling Stone, The New York Times Magazine, The Guardian, Elle, Bookforum, and more outlets over the years. She's also been the editorial director for MTV News and a senior editor at Pitchfork.
In response to the story, many of Lamar's fans began replying with lyrics the rapper could have used in the situation.
"I remember you was conflicted, about putting down that big scary knife," one fan wrote, referencing To Pimp a Butterfly.
Check out Hopper's tweets below.
via: https://www.hotnewhiphop.com/writer-recalls-kendrick-lamar-saving-her-toddler-from-a-kitchen-knife-during-interview-news.157168.html
article, Writer Recalls Kendrick Lamar Saving Her Toddler From A Kitchen Knife During Interview
JustATouchOfJ
April 9, 2011 - Washington Wizards vs. Atl Hawks

redpajama_set_name: RedPajamaCommonCrawl


These organic ingredients are believed to possess several health benefits. Tulsi (a.k.a. holy basil) for it's calming and healing properties, ginger to improve circulation and digestive disorders, and lemon myrtle to promote healing. Together this blend may soothe anxiety, restore peace, and help with motion sickness and nausea.
Ingredients: *tulsi, *ginger root, *lemon myrtle.
Serve Hot- Place 1 rounded teaspoon of loose tea in strainer. Pour 8 oz. boiling water over tea. Steep 3-5 minutes! Sip and enjoy!


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Our commercial painting team at Bold Painters is ready to tackle any commercial project, big or small. With a dedication to the highest quality workmanship, impeccable customer service, and an attention to detail seldom found in the industry, our crews will give your offices the attention they deserve.


Chemical reactions of ammonia in soil. Ammonia (NH3) needs to react with water shortly after application in order to convert into ammonium (NH4+), which is the molecule that can adhere to clay and organic matter in the soil. Ammonia is very soluble in water. After it is placed in the soil, NH3 reacts with water in the soil to form ammonium-N (NH4+), which is retained on the soil cation exchange sites. This process takes a little time – it does not occur immediately upon contact with the soil. The main controlling factors in the conversion of NH3 to ammonium-N are soil temperature, soil moisture, and soil pH. The higher the soil temperature and the wetter the soil, the more rapid the conversion occurs. If the ammonia does not react with water, it will remain as a gas that could escape from the soil. Also, a chemical equilibrium between NH3 and NH4+ occurs and is affected by soil pH. More NH3 will remain unconverted in the soil longer at higher application rates and at higher soil pH levels.
Physical factors that influence sealing and ammonia loss. Dry soils may be cloddy, with large air spaces where the soil has cracked. Getting the soil sealed properly above the injection slot can be a problem in dry soils. This can allow the gas to physically escape into the air before it has a chance to be converted into ammonium. On the other hand wet soils tend to smear, leaving application channels open to the surface and providing a pathway for ammonia loss also. It is very important to make sure at the time of application that the slot created by the shank is sealed shut and that there is adequate soil moisture present for the NH3 to be retained in the soil. If the soil is too dry to retain NH3, or is not sealed well, gaseous NH3 can escape into the atmosphere and be lost for crop use. At today's high N prices, this can quickly become very expensive.


text:
Northern Mordor
o'rodruin ('ruin' is pronounced as in English)
'Mountain of Red Flame'
Amon Amarth, The Fiery Mountain, The Fire-mountain, Mount Doom, Mountain of Fire
Alphabetical: O
Updated 28 December 2003
Orodruin
The Fire-mountain in the northern parts of Mordor, in which Sauron forged the One Ring during the Second Age, and into which the same Ring fell thousands of years later to bring about the Dark Lord's downfall.
When Sauron chose the land of Mordor as his dwelling-place in the Second Age, Orodruin was the reason for his choice. He 'used the fire that welled there from the heart of the earth in his sorceries and his forging' (from Of the Rings of Power and the Third Age); the most famous result of his forging, and in fact the only one we know of for sure, was the One Ring, made in about the year II 1600. So powerful was the sorcery used in the making of the Ring that it could not be unmade, except by casting it back into the same fire that had forged it.
The first opportunity to destroy the Ring came in the last year of the Second Age, at the end of the War of the Last Alliance. Sauron was defeated in that War, and Isildur cut the Ring from his hand. Elrond and Círdan counselled him to destroy the Ring then1 (the battle had taken place on the slopes of Orodruin itself), but Isildur refused, and claimed the Ring for himself. So the doom of the Third Age was made.
Orodruin was far more than a natural volcano - Sauron extended his own power into it, and was able to control its fires. It seems to have lain dormant when Sauron was away from Mordor, and sprung into life when his power grew. After the Downfall of Númenor, for example, the Exiles in Middle-earth first knew that Sauron had also escaped the Downfall when they saw smoke rising from Orodruin, and an Age later at the Council of Elrond (The Lord of the Rings II 2), Boromir says 'Smoke rises once more from Orodruin that we call Mount Doom'.
It isn't clear how Elrond or Círdan could know that throwing the Ring into Orodruin would destroy it - neither of them had had any part in the making of the Rings of Power, and both had refused Sauron's lore when he offered it to them. At this time, though, both Elrond and Círdan were themselves Ring-bearers (of the Elven-rings Vilya and Narya), and perhaps these Rings gave them special insight.
Amon Amarth, Annatar, Ash Mountains, Barad-dûr, Black Country, Chambers of Fire, Cracks of Doom, Dark Lord, Days of Flight, Desolation of the Morannon, Downfall of Barad-dûr, Elendil, Fiery Mountain, Fire of Doom, Fire-mountain, [See the full list...]Fortress of Sauron, Great Rings, Great Signal, Lithlad, Lord of the Black Land, Lord of the Rings, Mordor, Morgul Pass, Morgul-host, Mount Doom, Mountain of Fire, Nine Walkers, Nurn, One Ring, Plateau of Gorgoroth, Quest of Mount Doom, Ring of Power, Ring-bearers, Ring-maker, Sammath Naur, Sauron, Sauron's Road, Second Age, Second Chief, Slag-hills, Tale of the Ring, The Fire, War of the Ring, Window of the Eye
Got a question about Discus or DISC? Why not take a look through our Knowledge Base and see what you can learn?


Grand Rapids birth injury lawyer shares an inspirational story: "Everyone has a place on the team," says a track coach who pushes teen with cerebral palsy to do the impossible – walk.
A boy with cerebral palsy who previously couldn't walk struggled through 30 feet of the high school track, crossing the finish line with a big smile on his face and the sound of loud cheering from his team and fans. This incredible feat was made possible by a track coach who believes that nothing is impossible with hard work.
Sixteen year-old Dillan McCants has had cerebral palsy since birth, when a lack of oxygen to his brain during delivery caused a brain injury called hypoxic ischemic encephalopathy (HIE), leaving him with cerebral palsy and an inability to walk like other children.
When Dillan moved to Phoenixville two years ago and began attending the new high school, he wasn't sure if he'd have any friends and if people would understand his cerebral palsy. Then Dillan met the school's track coach, Dustin Poole, who said to Dillan, "You can do the impossible!". Poole gathered a team of people who began working with Dillan, giving him aggressive physical therapy.
Two years after starting the intense physical therapy, Dillan made his track debut. He was able to walk with the help of a walker, and he became the first person with a disability to receive a varsity letter in track. Poole told reporters that seeing Dillan cross the finish line brought him to tears and it was the greatest coaching moment of his career. At the finish line, Dillan said that having so many people cheer him on was one of the best parts of crossing the line – aside from the fact that he was actually walking. Dillan told reporters that the people at his high school are the best people he's ever met and the school is also one of the best he's attended.
Friends and classmates told reporters that Dillan continuously has a positive and upbeat attitude, despite recent setbacks. The specially equipped van that Dillan's family uses to transport Dillan was damaged in a flood and Dillan's home was majorly damaged when a neighbor's house caught on fire. Despite these huge setbacks, Dillan has never missed a physical therapy session.
No matter what happens, Dillan can hear his coach exclaiming that he can do the impossible. Sometimes the only motivation people need to push themselves to the max is someone to believe in them.
Cerebral palsy (CP) is a group of disorders stemming from brain damage that affects the nervous system and causes children to have problems with muscles, movement, balance and coordination. Cerebral palsy can be severe, causing a child to essentially be paralyzed. Children with severe cerebral palsy may require feeding through a tube that goes directly into their stomach, and they may be unable to control their bowels or bladder. Children with mild to moderate cerebral palsy may have only one or two limbs affected by CP.
Cerebral palsy is a motor disorder. Thus, the brain damage that causes cerebral palsy does not cause intellectual or cognitive problems in children. A child with CP may have difficulty speaking due to poor oral-facial muscle control, but the child may be highly intelligent. Sometimes, however, the event that caused the cerebral palsy may also have caused damage to other areas of the brain – areas that can affect a child's cognitive functions. This is why some children with cerebral palsy also have intellectual disabilities.
The brain injury that causes cerebral palsy does not get worse over time. However, if proper therapy and treatment are not given to a child who has CP, long term muscle imbalance can cause further muscle dysfunction as well as serious problems with bones and joints.
Regular aggressive physical therapy is very important for children who have cerebral palsy, especially since the CP may cause them to be less active than children without the condition. Physical therapy is performed to help muscles develop and to prevent muscle imbalance and contractures. A contracture is a permanent shortening of a muscle, tendon or ligament. Surgical release can be performed to help relieve tightened or shortened muscles.
Another type of surgery that can help children with cerebral palsy is selective dorsal rhizotomy (SDR). SDR is performed on the lower spinal cord to reduce spasticity in the legs. During the surgery, abnormal nerve fibers that cause high muscle tone and tightness are cut. The goal of SDR is to relax the muscles by identifying and cutting only those nerve fibers that contribute to tightness. When SDR is followed by months of aggressive physical therapy, it can improve the child's ability to move and control her muscles. SDR may also reduce the need for future orthopedic surgeries. Severing the abnormal nerve fibers provides long-term improvement in muscle tone because the nerves do not grow back together.
Physical therapy also is performed to help a child get used to using muscles that typically don't get used. In addition, many therapists use techniques that encourage brain re-mapping, which requires the child and therapist to use certain machines and do targeted exercises that help the child's brain develop different pathways with the goal of improving muscle function.
Cerebral palsy often occurs during or near the time of birth. CP can be caused by events that cause brain bleeds, a lack of oxygen in a baby's brain (hypoxic ischemic encephalopathy (HIE)), infection that travels from the mother to the baby at birth, and mismanaged neonatal hypoglycemia and hyperbilirubinemia (jaundice).
Mismanaged conditions that can cause oxygen deprivation and HIE include placental abruption, uterine rupture, umbilical cord prolapse, nuchal cord (cord wrapped around the baby's neck), brain bleeds caused by forceps or vacuum extractors, and failure to recognize fetal distress on the fetal heart rate monitor. When a baby is showing signs of distress, it means she is being deprived of oxygen and must be delivered very quickly. Most of the time, a C-section delivery is the fastest and safest way to deliver a baby who is in distress.
The nationally recognized lawyers at Reiter & Walsh ABC Law Centers have been helping children with cerebral palsy throughout the nation for over two decades. Jesse Reiter, the firm's co-founder and president, has been focusing on birth injury cases his entire 25+ year career, and most of Jesse's cases involve helping children who have cerebral palsy and hypoxic ischemic encephalopathy (HIE). When Jesse and his team of attorneys take a case, they spend a lot of time getting to know the child and family they are helping so they can fully understand the child's needs.
Cerebral palsy and hypoxic ischemic encephalopathy (HIE) are difficult areas of law to pursue due to the complex nature of the disorders and the medical records that support them. The award winning lawyers at ABC Law Centers have decades of experience with cerebral palsy and HIE cases. We handle cases in Michigan, Ohio, Washington, D.C. and throughout the nation and we give personal attention to each child and family we help. We have numerous multi-million dollar verdicts and settlements that attest to our success, and no fees are ever paid to our firm until we win your case. Email or call us at 888-419-2229. Our firm's lawyers are available 24 / 7 to speak with you.
Watch a video of birth injury attorney Jesse Reiter discussing the many treatments, therapies and activities that are available for children who have cerebral palsy.


Donald J. Dietz, RPh, Editor-in-Chief of Inside Patient Care, discusses a new solution to allow each member of a patient's healthcare team to access a patient's health record in a single process called blockchain.
Donald J. Dietz, RPh, Editor-in-Chief of Inside Patient Care, discusses the difference between productivity and efficiency, 3 different fundamentals of a productivity mindset, and the impact they have on retail pharmacies.
Continuing Professional Development: What's in Your Plan?
We ask our student pharmacists to research and present to our team a topic that they believe they need to improve on before taking the pharmacy boards and beginning their career. Often, this is a topic they view as a weak point in their self-assessment; students will frequently research a disease with new treatment guidelines or new drug therapy options that were not covered in their didactic lectures on that therapeutic category.
In this issue of Inside Patient Care, Natalie Kokta, PharmD candidate, describes how community pharmacists can help in preventing antimicrobial resistance.
Recently I became aware of a new practice model to improve patient access to quality and efficient care, with the objective of advancing pharmacy in the broader healthcare setting. The pilot project is titled "Advancing community pharmacy quality: leveraging tech-check-tech (TCT) to expand patient care services in community pharmacies," and is being conducted by the National Association of Chain Drug Stores, in partnership with the Pharmacy Society of Wisconsin.
Diabetes Screenings: A Future Opportunity for Pharmacists?
The pharmacy profession has evolved from an era long ago, when most prescription drugs were compounded, to today, when the vast majority of prescribed medications are tablets, capsules, or prepackaged drugs made by pharmaceutical manufacturers under US Food and Drug Administration approval. To improve efficiency and accuracy, and to control costs, pharmacies have implemented various levels of technology and automation, which free up time for pharmacists to perform additional activities. In many pharmacy environments, this time is used to process more prescriptions, which is often the prudent and most profitable option.
Since 2004, the American Pharmacists Association has designated October as American Pharmacists Month. This awareness month provides opportunities to promote the pharmacy profession, and to acknowledge the involvement of pharmacy personnel in supporting positive health outcomes and improving patient care.
I recently became aware of precision medicine, a new opportunity for healthcare in the United States. President Obama introduced the Precision Medicine Initiative during his 2015 State of the Union Address. Precision medicine is an evidence-based approach that uses innovative tools, biologics, and data science to customize disease prevention, detection, and treatment to improve the effectiveness and quality of patient care.
Incentivized Fees for CPPA Accreditation: One-Off or the Beginning of a Trend?
Recently, I came across an interesting pharmacy reimbursement model introduced by Sunflower Health Plan in Kansas. Sunflower Health Plan is a managed care subsidiary of the Centene Corporation, St. Louis, MO. Sunflower will offer a higher dispensing fee for claims submitted from pharmacies that have achieved accreditation through the Center for Pharmacy Practice Accreditation (CPPA). I was pleased to see that this is truly an increased fee, and not a redistribution of claim withholds, which pharmacies are experiencing with some plans today.


In this episode of Soul of Islam Radio, Ahmad and Ihsan interview Daniel Amin Coleman on his spiritual journey to Islam.
Daniel shares his cultural and spiritual background and his early connection with Buddhism. He also shares how his openness to the inner realities of other traditions propelled him forward along his spiritual journey.
You will learn about how Daniel's first exposure to the spiritual dimension of Islam allowed him to ground his belief and find the essence in the external practices and rituals. He also shares the similarities and differences between Buddhist meditation practices and the practice of Dhikr in Islam.
Daniel shares a number of Divine inspirations and miraculous experiences and how they acted as a call to faith and belief in the One God. He also shares some of the challenges and obstacles he had faced upon his conversion into Islam.
Daniel build's on the importance of social interaction and shares how Islam introduced friendships of love and substance.
Lastly, Daniel shares valuable advice with new converts and people interested in Islam and concludes with a beautiful message to the Muslim community.
Daniel Amin Coleman has a degree in Globalization Studies and Renewable Energy and is a graduate of the University of Spiritual Healing and Sufism. He is a talented guitarist and vocalist and a student of both Sufism and Martial Arts.


What are the options and different ways you can change your Texas registered agent?
There are a couple options. You can change your registered agent in a Certificate of Amendment but it is very expensive. All you really need to do is provide in duplicate along with the filing fee, the completed Form 401, Change of Registered Agent/Office, to the Texas Secretary of State, by mail, fax, in person or at SOSDirect Online for $1. If submitting by fax, accompany the fax with (Form 807) with your credit card information. The registered agent does not sign the form. Texas does not require original signatures.
How much does it cost to change your registered agent in Texas?
There is a $15 filing fee to change your registered agent in Texas. Texas has one universal form for changing registered agent where you select your type of entity at the top of the form. If you are a nonprofit corporation or a cooperative association, the filing fee is $5.
Don't want to pay the change of agent fee? Switch your registered agent to Northwest, and we'll pay the change of agent fee to switch to us! Just sign up for registered agent service. You'll see the pre-populated change of agent form in your online account. Fill it out with your company info, sign it, and email or mail it to us, and we'll get it filed with the state. It's that simple!
How long does it take the state to process and complete the change of registered agent in Texas?
Normal Processing: 3-5 working days. The state will return your file-stamped duplicate copy. Texas offers expedited processing for an additional fee of $25 per document that is accompanied by a cover letter specifically requesting expedited processing and a day time phone number. Your filing will be processed by the close of business the following day.
If you want to view your filed documents on Texas Secretary of State Website, you must log on to SOSDirect Online Searching and Filing. There is a $1 fee every time you log on. Stays logged on all day though and do as many searches and filings as you want. Set up your online Texas account with this link: https://direct.sos.state.tx.us/acct/acct-subscribe.asp.
What form do you file to change your registered agent in Texas?
Form 401, Change of Registered Agent/Office is in your online account immediately, if you sign up for Texas registered agent service with Northwest.
To learn more about registered agents, visit our What is a Registered Agent? page.
Instant Texas forms located directly in your online account to make a filing in Texas.


Although we don't actually write about crab very often, it's very much a part of life here in Washington, D.C. Crabcakes are on menus everywhere, and at least once a year -- especially if we're with friends in Baltimore or with Zach's sister and her family in Annapolis -- we'll partake in a big crab boil, with heaping bushels of fresh steamed crabs spiced with Old Bay.
So last fall, we got a somewhat unusual opportunity that was right up our alley. Zach was asked to freelance a magazine article about Maryland crab shacks for Endless Vacation magazine. The assignment: Find the best crab shacks on the lower part of Maryland's Eastern Shore.
We jumped at the chance! When else might we be able to spend an entire weekend in a crab-eating frenzy?
Our home base for the weekend was Cambridge, Maryland, and we booked a room at the lovely Cambridge House B&B. The innkeepers, Jim and Marianne Benson, were chock-full of crab advice, helping us to narrow down our list. We aimed to hit 10 crab shacks during our visit.
What resulted was 36 hours of a crab-eating frenzy, where we hit nine crab shacks (sadly, one of the 10 was already closed for the season) between Friday night and Sunday afternoon, plus a few B&B breakfasts thrown in the mix, too. Zach's story, featuring seven of the shacks we visited, is now available online. Pick yourself a crab shack and head to Maryland (though we may not recommend tackling the full list in 36 hours).
Below, we've included a rundown of some images from the weekend, and few thoughts about eating crabs.
But first, we'll do something the article doesn't do, which is tell you which was our favorite crab shack. We know, we know, it's not nice to pick favorites. But in this case, we definitely had one. On Sunday, just before we headed back to D.C., we decided to make one final stop in Oxford, Maryland, to visit Schooners. The sun was just about to set. It was still warm, but there was just enough cool in the air that we needed long sleeves -- one of those magical, late-summer moments that brims with the promise of fall.
We got to Schooners and sat down at one of the wooden tables on the deck overlooking the water. A tray piled high with Old-Bay dusted crabs arrived, and we sat there in the late-day sun, happily picking away at them. Our server even introduced us to the waterman who had caught the crabs earlier that day, who happened to be having a drink (or six) at the bar. Was the crab at Schooners actually better than all the other crabs we ate that weekend? Probably not, although it was mighty tasty. But the moment and the experience was a magical mark to the end of summer.
Check out some photos and stories from our crab adventures below -- and we hope you give Zach's article a read, too!
Extra guests have arrived! Our friends Ryan and David stop by (we hadn't initially thought to invite them since they hadn't done dry January). But we're happy to see them! And they brought their own alcohol which is great because God knows we only have about 30 gallons of booze in our house right now.
Speaking of gallons of booze, The Seelbach. At this point in the evening, we've already had sherry, rum, gin, tequila, whiskey and brandy -- clearly we need some champagne.
This is great. Really, a wonderful cocktail. We love it, our guests love it. Everyone loves everything.
But this cocktail party is starting to break down.
Not break down in a "things are winding down and people are getting ready to leave" way. Break down as in "the breakdown of society in a post-apocalyptic hellscape."
This is where things start getting a little blurry.
We were excited about this Diamondback No. 5 because we've had a bottle of Root liquor burning a hole in our liquor cabinet for a long time. We really like its sassafras flavor, but it's a very strong flavor. So you never need very much of it.
This drink, by the way, is probably the priciest one we served at our party. The 375-ml bottle of chartreuse we bought was $30, and we used half of it for drinks for 8 people. Spendy!
Basically this is a twist on an Old Fashioned. It's really good, and the licorice-ness of both the Root and the chartreuse are a great accompaniment to the rye and the apple brandy.
At this point, a couple of our friends had to peel off to go to a birthday party. We were sorry to see them go, but hey, more for the rest of us.
Everybody, including Drew and Ralph, really loves the Redless Snapper. Thanks to the gin and the flavor-infused tomato water, it's bright and clean and bracing in exactly the way a Bloody Mary isn't.
Nearly 160 of you commented for a chance to win dinner with us and with two of your friends. We chose a number at random and matched it to the corresponding comment.
Believe us when we say that we wish we could have dinner with each and every one of you! But 160 might be a bit of a crowd at our dining room table. So in the end, we could only choose one winner.
So who are we going to have over for dinner? It's Margie Wolson! Congratulations, Margie!
Now, as we said, the selection was based on a random number. But coincidentally, you may remember Margie as the Bitten who gave us a basketball-sized squash last fall. She actually dropped it off at our place while we were out, so we didn't get to actually meet Margie -- and now we do!
Let this be a lesson to all of us: If you give away produce, the fates will smile on you.
Thanks to everyone for your great comments, and we look forward to many more great years of blogging with you!


text:
Complications and Contradictions in the Usage of 'Indigenous Religions'
Indigeneity
|indigenous religion
One of the most challenging and enlightening aspects of my fieldwork among the Adi of Arunachal Pradesh, India, in the far eastern Himalayan foothills, has been considering the concept of 'indigenous religions': as a phrase, as a classification, as a rallying point for activism.
By Claire S. Scheid
Claire S. Scheid holds a PhD from the Department of the Study of Religions, National University of Ireland – University College Cork; an MSt in Oriental Studies from the University of Oxford, UK; and a BA in Religious Studies from Rice University, Texas, USA. Her doctoral dissertation examined the Donyipolo movement and the formalisation of indigenous faith among the Adi in the Siang districts of Arunachal Pradesh, India, in the far eastern Himalayan foothills. She has previously done fieldwork with the Lepcha and the Lhopo (Bhutia) in Sikkim, India. She is interested in the processes by which Himalayan ethnic communities reimagine, restructure, and represent their religious beliefs in modernity.
Claire S. Scheid
What do we mean by Indigenous Religion(s)?
We talk a lot about the World Relgions Paradigm at the Religious Studies Project, and this discussion looks more closely at one of the ancillary categories, Indigenous Religion. What exactly does this term refer to? Does it refer to specific religions (plural) or a kind of religion (singular)?
https://media.blubrry.com/the_religious_studies_project/p/www.religiousstudiesproject.com/wp-content/uploads/2017/10/RSP-230-Bjorn-Ola-Tafjord-and-Arkotong-Longkumer.mp3
A Response to David G. Robertson's Interview of Bjørn Ola Tafjord and Arkotong Longkumer
One of the most challenging and enlightening aspects of my fieldwork among the Adi of Arunachal Pradesh, India, in the far eastern Himalayan foothills, has been considering the concept of 'indigenous religions': as a phrase, as a classification, as a rallying point for activism. My research focuses in part on the manner in which Adi community leaders have restructured their 'traditional' faith of Donyipolo ('Sun-moon') to fit the model of dominant worship systems. This has constantly required me to evaluate my word choices in context and to examine the implications of the way that I present my work. For this reason, I am very glad to respond to David G. Robertson's interview of Bjørn Ola Tafjord and Arkotong Longkumer exploring the academic categories and terminological usages of 'indigenous religions'.
It seems to be agreed in this discussion that the use of 'indigenous religions' is multifaceted – and its meaning equivocal. Tafjord brings attention to the broad usage of 'indigenous religions', establishing that the term first represents a 'class' of religions. But this, too, is problematized: as Longkumer emphasizes, the search for one paradigm that includes all manifestations of 'indigenous religions' across cultures will prove futile. I agree; the phrase, in my opinion, draws false parallels that obscure the complicated site-specific religious articulations across the globe that may share very little outside of the classification itself.
As Tafjord points out, an uncritical equation between 'indigenous peoples' and 'indigenous religions' only adds to the problem that the definition of 'indigenous' – and the problem of who can claim 'indigeneity' – is itself unclear. I find Tafjord's concern about conflating 'indigenous peoples' and 'indigenous religions' without explaining context valid; for me, it reinforces that various religions can be practiced within a given indigenous group – not an uncommon occurrence in Northeast India – and further highlights that any specific 'indigenous religion' is not hegemonic but rather may vary significantly even between households. However, I would also note that some Adi, for instance, have mobilized to protect their identity through stressing that they, as an 'indigenous people', follow an 'indigenous religion', relying on popular slogans such as 'loss of religion is loss of culture' and 'loss of culture is loss of identity'.
Longkumer brings up the relevant example of how Hindu nationalist groups 'co-opt' local concepts of 'indigenous religions' in Northeast India in order to claim that Hinduism, itself, is an 'indigenous religion'. I would stress that such categorizations are especially relevant to think about in the context of India, where temporality impacts which groups are considered 'indigenous': regarding modern-day Arunachal Pradesh, one Baptist leader claims that Christianity should be thought of as equally as 'indigenous' as Buddhism and Vaishnavism in the state, maintaining that Christians simply arrived later. We see a similar situation in Sikkim, another Northeast Indian state, in which both the Lepcha and the Lhopo (Bhutia) are 'Scheduled Tribes' and generally considered 'indigenous' to Sikkim – even though the historical Lhopo migration from Tibet is well-known. Claims of 'indigeneity' based on the time that the group arrived – and scholarly acceptance of the 'indigenous' status of such migratory groups – make identifying even the most basic qualifications for 'indigeneity' difficult.
Robertson wonders whether we, as researchers, inherently over-interpret 'religion' in 'indigenous' cultures because we somehow view them as 'primitive'. Longkumer responds that many Westerners believe 'indigenous peoples' to be close to 'nature' and 'spirits', while this is not necessarily the case. He describes their surprise that some Nagas wear Western clothes during Nagaland's famous Hornbill Festival, upending a preconceived notion of 'indigeneity'. It is necessary to address such stereotypes: as Longkumer says, they are a remnant of colonial times. (And, to that end, the problematic academic construction of 'indigenous identity' threatens to mirror Orientalism's false ideation of the East – a point also brought up by Robertson in a previous podcast interview with Tafjord).
However, from my own research among the Adi, I do have the impression that the 'spirit world', in many Adi villages, remains significantly influential, relevant, and omnipresent; the introduction of Western culture does not undermine the prevalence of religion – or the deep ties to nature – within some Adi communities. In our desire to break down the misleading image of nature-centric, deeply religious 'indigenous peoples', we must be cautious not to go too far in the other direction. Encroaching modernity and pervasive belief can exist side-by-side. A man living in Pasighat, the largest Adi town, once described to me that the Adi of the modern day could best be summed up as a teenager, holding a mobile in one hand, a jungle dao (knife) in the other, walking shirtless towards the jungle in designer jeans.
Another topic addressed in the podcast is the idea of 'indigenous religions' as powerful tools to be used by 'indigenous peoples' – for example, as part of 'identity politics' (Robertson); for the purposes of land and water preservation (Longkumer); as a 'foreign relations tool' (Tafjord). International networks of 'indigenous religions' are strengthened by institutions such as the UN, which, in turn, inspire the local movements that promote 'indigeneity' as a method of preservation. Tafjord holds that the emergence of these international indigenous peoples' movements has contributed to the use of the term 'indigenous' as a relational category. I have witnessed the self-aware usage of 'indigenous' as a tool to protect heritage in my work among the Adi: through participating in global conferences of the International Association for Religious Freedom in the 1980s, Adi community leaders concluded that through identifying, structuring, and promoting their 'indigeneity' – particularly their 'indigenous religion' – they would be better equipped to sustain their traditions when faced with the arrival of missionaries and the rapid globalization of Arunachal Pradesh.
According to Tafjord, to be acknowledged as an 'indigenous people' or an 'indigenous religion', one has to 'translate … your traditions, your practices, your narratives into recognizable units'. I have seen this in action among the Adi for years, and I have often referred to the restructurings in the Donyipolo religion as 'translations': the Adi are an example of a community that has self-consciously taken up the mantle of 'indigenous' and deliberately 'translated' their culture, heritage, and faith into a structure recognized as 'religious' by outsiders, thus preserving Donyipolo in an innovative, comprehensible form. Yet in attempting to represent this 'translation', I have often struggled while trying to determine the appropriate words to describe the process. The issue that has become clear to me – and one that is explored in this podcast – is that the phrase 'indigenous religions' is important, yet ambiguous and debatable. It can be employed to clarify and strengthen discussion in the academic environment and serves various roles within different 'indigenous' communities, locally and globally. I agree with Longkumer that these classifications must be 'destabilized'; we must be 'wary of the limitations of these categories'. In my opinion, one way to move forward with this in mind is to actively challenge the meanings, boundaries, and implications of 'indigenous religions' within the communities with whom we work, starting this complicated investigation at a site-specific level.
While a standardized category and definition of the phrase do not appear to be immediately forthcoming, continued examination of these issues during fieldwork communications, across international networks, and within academic discourses will contribute to the nuanced and necessary evaluation of 'indigenous religions' – with its myriad of uses and significant implications for our comprehension of both 'indigeneity' and 'religion' in the modern day.
Yoga in Museums
Yoga, in its modern form, should be of great interest to scholars of religion. While it certainly has roots in Vedic culture, the vast majority of Western practitioners do not see it as "religious", but rather to do with health or "well-being". Yoga's status as religious has been in court, ...
Religion and Cultural Production
"It is a truth generally acknowledged that religions have been the earliest and perhaps the chief progenitors of cultural products in human societies..." Clearly there is no shortage of data for scholars wishing to delve into this broad topic. But what do we actually mean by 'cultural product'? How can we claim that 'religion' is producing these things in any meaningful way?
Religion After Darwin
Charles Darwin's On The Origin of Species was published in 1859, and had an immediate and dramatic effect on religious narratives. Traditional religions were forced to adopt an evolutionary worldview, or to go on the offensive; whereas New Religious Movements like Wicca or New Age adopted an environmental concern as a central part of their belief. And possibly, ...
Substantive Religion and the Functionalist Sacred
Could the difficulties associated with the academic conceptualisation of "religion" be overcome by changing our focus instead to "the sacred"? Jay Demerath tells Chris why we should define religion substantively - that is, in terms of specific attributes like rituals, deities or dogmas - but the sacred in terms of the function it serves in the lives of individuals and cultures.
The World Religions Paradigm
There can't be many listeners who haven't come into contact with the "World Religions" paradigm, either through the podcast or in their own undergraduate studies. Although, C. P. Tiele defined "World Religions" as those which had spread outside of their original cultural context, today the term is taken to mean the "Big Five".
Religious Freedom in America: Theoretical Considerations
Religious freedom is an inherently good thing, right? It's a cherished idea that is easy for state governments to enact, no? In this interview, Finbarr Curtis questions both of these assertions. In The Production of American Religious Freedom, Curtis argues that religious freedom is a fluent and malleable concept that people deploy for various and competing reasons.


text:
Frequently Asked Questions About the COVID Vaccine in Jonesboro
The COVID-19 vaccine is simply the latest in a long line of vaccines.
Although the option to vaccinate against the COVID-19 virus has been available for well over a year now, many people still have questions. To help answer some of the FAQs about the COVID-19 vaccine, we've created this article. Although it is specifically geared toward seniors and those in the high-risk category, this information is backed by the CDC and applies to most adults.
This COVID-19 vaccine FAQ is meant to help address some of our client's most pressing concerns. However, it is not meant as medical advice in any way, shape, or form. You should always consult with your doctor about the best possible medical care for your specific situation.
Thankfully, vaccines are a lot safer these days, and you can get a COVID-19 vaccine almost anywhere.
Why Should I Get Vaccinated?
Why should I get a COVID-19 vaccine? The simple answer is that it works. Data from Wisconsin's Department of Health Services show that, at the peak of the outbreak in 2021, those who received the primary vaccine were around three times less likely to catch COVID-19 than those that remained unvaccinated.
Those that had received the primary vaccine were also around ten times less likely to die from COVID-19 and even less likely to be hospitalized. Those who had received boosters, as well as the initial vaccine, fared even better.
How do Vaccines Work?
Currently, there are three main types of COVID-19 vaccines that are approved or authorized for use in the United States: mRNA, viral vector, and protein subunit. Each type of vaccine prompts our bodies to recognize and help protect us from the virus that causes COVID-19.
None of these vaccines can give you COVID-19.
They do not affect or interact with our DNA.
These vaccines do not enter the nucleus of the cell where our DNA (genetic material) is located, so they cannot change or influence our genes.
To trigger an immune response, many vaccines put a weakened or inactivated germ into our bodies. This is not the case with mRNA vaccines. Instead, mRNA vaccines use mRNA created in a laboratory to teach our cells how to make a protein—or even just a piece of a protein—that triggers an immune response inside our bodies. This immune response, which produces antibodies, is what helps protect us from getting sick from that germ in the future.
Why Do We Need Booster Shots?
The nature of vaccines raises an interesting question, especially regarding the COVID-19 vaccine. If vaccines teach the body how to recognize and combat a virus, why do we need additional shots later on?
This is due to evolution. The theory of evolution states that as creatures reproduce, some mutate. Those with beneficial mutations are more likely to survive and reproduce. This means that the next generation is also more likely to share the same beneficial mutations.
When viruses without the beneficial mutations have died out, and all that is left are viruses with the beneficial mutations, the result is often a new strain. While boosters will help most people fight off these strains, they provide the most benefit for the elderly and the immuno-compromised.
If I've Already Had COVID-19, Do I Still Need to Get Vaccinated?
Yes, you do. You should also get a booster shot if possible. While having COVID-19 does shield you from getting the virus again for a while, the speeds at which viruses mutate means there will eventually be a strain that your body doesn't recognize. As such, it will struggle to fight it off effectively.
A COVID-19 vaccine will help even if it wasn't designed to handle the newest variants. In most cases, the new strain will resemble the old one enough that the primary vaccine will still be fairly effective. Being entirely up to date, however, will still give you the best protection.
Why Should I Get Vaccinated If I'm Going to Get COVID-19 Anyway?
Because it lowers your risk of severe complications and hospitalization. Much like the flu shot lessens the time you are ill regardless of that year's strain, the COVID-19 vaccine helps strengthen your immune system to fight off coronavirus more effectively and quickly than it could otherwise.
This means shorter illness times and less risk of severe complications or hospitalization.
Is the COVID-19 Vaccine Safe?
We should start by saying that all medication has risks. While adverse effects can occur, vaccination is one of the safest and most effective medical practices.
Yes. Although it was developed quickly and there are minor side effects, the COVID-19 vaccine is safe for most individuals. It was run through multiple clinical trials and authorization processes by the FDA and is currently being monitored by health organizations across the nation—and the world.
The odds of being seriously harmed by a vaccine are between one and two in a million. To put that in perspective, here are some things that are more likely to happen: being struck by lightning or being killed by fireworks—yikes.
What's in the COVID-19 Vaccine?
Every brand is a little different, but none of them contain eggs, gelatin, preservatives, or latex. This is to lower the risk of allergic reactions or anaphylactic shock. They are also free of all metals, alloys, electrodes, carbon nanotubes, and semiconductors.
The main ingredient in the vaccine is the mRNA of the coronavirus.
Is There Anyone Who Shouldn't Get Vaccinated?
Some individuals shouldn't be vaccinated, but they make up a very small portion of the population. You should only worry if you're severely allergic to any of the COVID-19 vaccine ingredients.
You shouldn't get vaccinated while you have COVID-19 as this won't help your immune system. If you're unsure whether or not you should receive the COVID-19 vaccine, ask your doctor.Vaccines remain one of the most effective treatments in medicine. Unfortunately, they're also among the most misunderstood. That's why we set out to answer some FAQs about the COVID-19 vaccine.
We can help if you're looking for elderly care in Jonesboro, Arkansas. Please contact us so that you can learn more about what we can do for you.
COVID Vaccine FAQ Jonesboro
Vaccines remain one of the most effective treatments in medicine. Unfortunately, they're also among the most misunderstood. That's why we set out to answer some FAQs about the COVID-19 vaccine.
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Tina Shaire used to be a commercial lawyer and recently opened Zolene, a contemporary restaurant in Ikoyi dedicated to creating great food memories through a touch of western influences on the most loved Nigerian and African dishes. Zolene named after Tina's two daughters has a 40-seater dining room with a cosy lounge space.
It has taken Tina Shaire around 7 years to go from concept to implementation which has left an impression on her: "Whoever said the hustle was sold separately from the dream was closer to the truth than most". It is advisable to have at least funding to support 6-12 months of operating costs in addition to the start-up capital.
We share Tina's sentiment here, there are over 2,000 restaurants in Lagos and the numbers is growing daily. As result, it is even more critical to test new cuisines and menu concepts "to arrive at something eclectic" whilst "creating a cosy ambience all at the same time".
The team also learnt that one must be "open to change that positively impacts" the business direction. Initially the plan was for Zolene not to make deliveries however due to location, the choice was made start food delivery from the first month of opening.
Get smart on operating cost which could hit harder over the longer term. Tina made a few decisions that directly reduced cost base at Zolene: "like taking out table cloths (eliminated the weekly cost of dry cleaning them, which is even the bigger expense) and having food served on reusable mats".
Essential to know what sort of permits and licenses are required in operate: "if you will be using a TV for instance you will need a TV license" or selling liquor, a license is also required. Also ensure the inspectors actually do the work as that will save you headache down the road.
Training the team running the restaurant has to be "an ongoing process, never a one off. If you cannot train, you may do well to create a budget to engage experienced industry experts" As result, Zolene has engaged a culinary school in Lagos to help train staff and provide constructive criticism on menu concept.


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The Pout-Pout Fish and the Can't-Sleep Blues (A Pout-Pout Fish Adventure) (Hardcover)
By Deborah Diesen, Dan Hanna (Illustrator)
Farrar, Straus and Giroux (BYR), 9780374304034, 32pp.
Mr. Fish can't fall asleep in this new jacketed hardcover addition to Deborah Diesen and Dan Hanna's New York Times–bestselling Pout-Pout Fish series.
One night in the ocean, the Pout-Pout Fish can't get to sleep! He's all ready for bed, but he just can't catch a snooze. When he asks his friends for advice, they're all sure they know what he should do—count sheep, use a pillow made of rocks, swim in circles—but nothing works. What to do when good advice isn't good for everyone? Little guppies will love The Pout-Pout Fish and the Can't-Sleep Blues, a bedtime story about learning from experience and doing what's best for you!
Deborah Diesen is the New York Times bestselling author of The Pout-Pout Fish, named by Time Magazine as one of the Ten Best Children's Books of 2008, and The Pout-Pout Fish in the Big-Big Dark. Diesen grew up in Midland, Michigan, and started writing poems at a young age. She has worked as a bookseller and a librarian, and now works for a small nonprofit organization, but her greatest joy comes from writing for children. She lives with her family in Grand Ledge, Michigan.
DAN HANNA has over ten years' experience in the animation industry, and his work has appeared on BBC America and the Cartoon Network. He lives in Santa Barbara, California. He is the illustrator of the Pout-Pout Fish books.


What was Amtrak engineer Brandon Bostian thinking when his speeding train careened off the rails in Philadelphia, killing eight and sending over 200 to the hospital?
Two Democratic senators blasted Republicans for proposing Amtrak budget cuts, saying more investment could have ensured that a critical electronic safety system was in place to prevent the deadly train derailment in Philadelphia.
Blumenthal and Sen. Ed Markey singled out the lack of Positive Train Control at the section of track where the Amtrak #188 derailed. While the electronic safety system has been deployed in sections of the Northeast Corridor, it was not in place at the curve where the accident happened.
A National Transportation Safety Board member agreed, saying positive train control can slow or stop a speeding train.
"Adequate funds are there, no money's been cut from rail safety and the House passed a bill earlier this spring to reauthorize Amtrak, and authorize a lot of these programs.
Secret Service detained a man Thursday afternoon who eyewitnesses tell CNN was trying to fly some sort of remote-controlled aerial device over the White House fence.
The park on the north side of the White House was placed on lockdown while the incident is being investigated. As of Thursday afternoon, the lockdown had been lifted.
President Barack Obama is not currently in the White House and is at Camp David. Additional details of the incident were not immediately available Thursday afternoon.
It's the second drone incident at the White House this year, coming four months after another man — a U.S. intelligence agency employee who had admittedly been drinking alcohol earlier in the night — lost control of a borrowed personal quadcopter drone that he'd been flying around his apartment, intending to send it out his window and then bring it back inside.
Six members of an elite Philadelphia narcotics squad were acquitted Thursday of federal corruption charges.
A jury found Officers Thomas Liciardello, Brian Reynolds, Michael Spicer, Perry Betts, Linwood Norman and John Speiser not guilty of charges they beat and robbed drug suspects during their time as members of the Police Department's Narcotics Field Unit.
Each of the officers had faced one count of racketeering conspiracy. All but Reynolds and Speiser had also been charged with conspiring to violate the civil rights of drug defendants, among other charges.
Outside the federal courthouse Thursday, officers and their supporters exchanged hugs.
Jack McMahon, who represented Reynolds, blasted Commissioner Ramsey, who fired the officers.
City Council President Darrell Clarke took his former colleague, Jim Kenney, on a tour of a North Philadelphia community center and health center Thursday afternoon and then said what everyone was expecting to hear.
Kenney served 23 years on Council before resigning his at-large seat to run for mayor in January.
Speaking with Clarke at 21st Street and Cecil B. Moore Avenue, Kenney said he hopes to "replicate" as mayor the relationship former Mayor Ed Rendell had from 1992 to 1999 with then-Council President John Street.
Clarke's relationship as Council president with Mayor Nutter has been much less cooperative.
Kenney also said he was "gratified" by a new poll that showed him with a commanding lead. That poll was sponsored by The Inquirer, Daily News, Philly.com and NBC10.


ABU DHABI: President His Highness Shaikh Khalifa Bin Zayed Al Nahyan has conferred on Indian Prime Minister Narendra Modi the Zayed Medal, the highest decoration awarded to heads of states, it was announced in the capital yesterday, much to the delight of the Indian community in the UAE.
The award is in appreciation of Modi's role in consolidating the long-standing friendship and joint strategic cooperation between the UAE and India.
Commenting on the announcement, His Highness Shaikh Mohammad Bin Zayed Al Nahyan, Crown Prince of Abu Dhabi and Deputy Supreme Commander of the UAE Armed Forces, said the Indian prime minister had played a pivotal role in enhancing bilateral ties to the level of comprehensive strategic relations.
"By granting our dear friend the Indian Prime Minister the Zayed Medal, we express our appreciation for his role and efforts in developing friendly relations and extending bridges of cooperation between the UAE and the Republic of India in various fields," he said.
Shaikh Mohammad Bin Zayed said the historical relationship that the UAE shares with India is being renewed strategically and strengthened in preparation for the future. He praised the values that characterise Indian society in its diversity, especially tolerance, coexistence and respect.
His Highness expressed pride at the strong friendship and cooperation between the UAE and India, and wished the country and its people continued progress, prosperity, security and stability.
He said UAE and India had witnessed many milestones in the recent past, notably the visit of the Indian prime minister to the UAE in 2015 and the visit of Shaikh Mohammad Bin Zayed Al Nahyan to India in February 2016 and again as chief guest for the Republic Day celebrations in January 2017.
"The honour is also a reflection of Modi's international stature and his close ties with the Islamic world," he said, adding that the Indian prime minister has raised India's standing in the UAE and other parts of the world.
Prominent businessmen from the Indian community said it was a moment of pride for all Indians.


text:
\section{\label{sec:introduction}Introduction}
Ultracold Bose-Bose mixtures are currently produced in many laboratories
offering the unique possibility of studying the interplay between two
Bose-Einstein condensates
(BEC)~\cite{hall,maddaloni,papp,thal,sugawa,carron,pasquiou,ferrier,wacker,bien,bisset,schultze}.
 The high tunability of the atomic interactions,
thanks to the presence of Feshbach resonances, and the combinations
between different elements, different isotopes or different hyperfine
levels enrich dramatically the interest in its physical study. Before the
adventure of BEC gases, the study of Bose-Bose mixtures was purely academic
since there was not such a stable system in Nature. Nevertheless, its
stability was deeply studied in connection with the stable $^3$He-$^4$He
mixture at low $^3$He concentration. In particular, it was proved that the
Bose-Bose mixtures of isotopic Helium are always unstable and phase separate
and that only the right consideration of the Fermi nature of $^3$He atoms could
account for its finite miscibility~\cite{massey,miller,kurten,tapash}.

The very low density of the BEC gases makes feasible a theoretical description
where atomic interactions are modeled by a single parameter, the $s$-wave
scattering length. The miscibility of bulk Bose-Bose mixtures can be easily
derived within mean-field theory~\cite{ho,pu,ohberg} and the predictions of
this approximation
account well for the observed properties in different experiments. However,
quite recently this simple argument has been questioned when the mixtures are
harmonically trapped and a new parameter, based on the shape of the density
profiles, has been suggested~\cite{lee}. The theoretical descriptions rely on
the
Gross-Pitaevskii (GP) equation whose range of applicability has been assumed to
fit in the relevant experimental setups. Recently, it has been proved that if
the interspecies interaction is attractive, instead of repulsive, the mixture
can be stable due to the Lee-Huang-Yang correction which cancels the
mean-field collapse~\cite{petrov}. This partial cancellation between attractive
interspecies and repulsive intraspecies interactions can result in a self-bound
(liquid) system, whose
existence has been checked theoretically by exact quantum Monte Carlo
calculations~\cite{viktor} and recent experiments with mixtures of ultracold
$^{39}$K atoms in different internal states~\cite{cabrera,semeghini}.

In the present paper, we report results of harmonically trapped repulsive
Bose-Bose mixtures in different interaction regimes and with different masses
for the constituents. Our approach is microscopic and relies on the use of
quantum Monte Carlo methods able to solve exactly a given many-body Hamiltonian
for Bose systems (within some statistical noise). The number of particles of
our system is much smaller than the typical values used in GP calculations due
to the complexity of our approach but this allows for an accurate study
of effects
going beyond the mean-field treatment. The numerical simulations have been
carried out
for different combinations of the interaction strengths, covering the mixed and
phase separated regimes. In agreement with previous GP results, the miscibility
rule derived for homogeneous gases fails to describe some of the results.

The rest of the paper is organized as follows. In the next Section we introduce
the theoretical method used for the study. Sec. III contains the density
profiles corresponding to the points of the phase diagram here analyzed, both
in miscible and phase-separated regimes.
In Sec. IV, we study the scaling in terms of the GP interaction strength. Sec.
V discusses the universality of our results by changing the model potential.
Finally, Sec. VI reports the main conclusions of our work.

\section{\label{sec:method}Methods}

We study a mixture of two kind of bosons with masses $m_1$ and $m_2$,
harmonically confined and at zero temperature. The Hamiltonian of the system is
\begin{eqnarray}
H & = &  -\frac{\hbar^2}{2} \sum_{\alpha=1}^{2} \sum_{i=1}^{N_{\alpha}}
\frac{\nabla_i^2}{m_{\alpha}} +
		\frac{1}{2}\sum_{\alpha, \beta=1}^{2} \sum_{i_{\alpha},
j_{\beta=1}}^{N_{\alpha}, N_{\beta}} V^{(\alpha, \beta)}
(r_{i_{\alpha}j_{\beta}}) \nonumber \\
& &		+		\sum_{\alpha=1}^{2} \sum_{i}^{N} V_{\rm
ext}^{(\alpha)} (\mathbf{r}_{i})
\label{hamiltonian} \ .
\end{eqnarray}
The mixture is composed of $N=N_1+N_2$ particles, with $N_1$ and $N_2$ bosons
of type 1 and 2, respectively. The interaction between particles is modeled by
the potentials $V^{(\alpha, \beta)} (r_{i_{\alpha}j_{\beta}})$ and the
confining potential is a standard harmonic term, with frequencies that can be
different for each species,
\begin{equation}
V_{\rm ext}^{(\alpha)} (\mathbf{r})
        =   \frac{1}{2} m_{\alpha} \omega_{\alpha}^2 r^2 \ .
\label{harmonic}
\end{equation}

The many-body problem is solved by means of the diffusion Monte Carlo method
(DMC), a nowadays standard tool for the ab initio study of quantum fluids and
solids. DMC solves stochastically the imaginary-time $N$-body Schr\"odinger
equation in an exact way for bosons within some statistical noise~\cite{dmc}.
In a natural
way, DMC recovers the mean-field results when the system is dilute enough and
can go much beyond since no perturbative approximations are assumed. In brief,
DMC turns the  Schr\"odinger equation into a diffusion process in imaginary
time with a branching term that replicates the energetically
favorable configurations and eliminates the rest. In order to reduce the
variance in the statistical averages it is usual to introduce importance
sampling through a trial wave
function, that drives the random walk away from singularities and focuses the
sampling where one reasonable expects that the ground-state wave function is
large. In the present problem, we have chosen a Jastrow model for the trial
wave function,
\begin{eqnarray}
\Psi(\mathbf{R}) & = &
    \prod_{1=i<j}^{N_1} f^{(1,1)}(r_{ij})
\prod_{1=i<j}^{N_2}f^{(2,2)}(r_{ij}) \prod_{i,j=1}^{N_1,
N_2}f^{(1,2)}(r_{ij}) \nonumber \\
            & & \times \prod_{i=1}^{N_1} h^{(1)}(r_i)
		\prod_{i=1}^{N_2} h^{(2)}(r_i) \ ,
\label{trialw}
\end{eqnarray}
with $\mathbf{R}=\{\mathbf{r}_1,\ldots,\mathbf{r}_N\}$, $f^{(\alpha,\beta)}(r)$
the two-body Jastrow factors accounting for the pair interactions between
$\alpha$ and $\beta$ type of atoms, and $h^{(\alpha)}(r)$ the one-body terms
related to the external harmonic potential.

As one of the objectives of our work is to estimate the validity regime for a
mean-field approach we have also studied the problem by solving the
Gross-Pitaevskii (GP) equations. In this case, one assumes contact interactions
between particles,
\begin{equation}
        V^{(\alpha, \beta)} (r_{i_{\alpha}j_{\beta}})
            =
            g_{\alpha \beta} \, \delta(|\mathbf{r}_{i_{\alpha}} -
\mathbf{r}_{j_{\beta}}|) \ ,
\label{contact}
\end{equation}
with strengths
\begin{equation}
            g_{\alpha, \beta} = \frac{2 \pi \hbar^2 a_{\alpha
\beta}}{\mu_{\alpha\beta}} \ ,
\label{gfactors}
\end{equation}
with $\mu_{\alpha\beta}^{-1}=m_{\alpha}^{-1}+m_{\beta}^{-1}$ the reduced mass and $a_{\alpha
\beta}$ the $s$-wave scattering length of the two-body interaction between
$\alpha$ and $\beta$ particles.

With the Hartree-Fock \textit{ansatz},
\begin{equation}
            \Psi(\mathbf{R})
            =
            \prod_{i=1}^{N_1}
            \phi_{1}(\mathbf{r}_i,t)
            \prod_{j=1}^{N_2}
            \phi_{2}(\mathbf{r}_j,t)
\label{hartree}
\end{equation}
one obtains the coupled GP equations for the mixture~\cite{ho},
\begin{eqnarray}
            i \hbar \frac{\partial \phi_{1} (\mathbf{r},t)}{\partial t}
           & = &
            \left(
            -\frac{\hbar^2}{2 m_{1}} \nabla^2
            +
            V_{\rm ext}^{(1)}(\mathbf{r})
            +
            g_{11} |\phi_{1}(\mathbf{r},t)|^2  \right.  \nonumber \\
         & &    +       g_{12} |\phi_{2}(\mathbf{r},t)|^2
            \bigg)
            \phi_{1} (\mathbf{r},t) \ ,
\label{gp1}
\end{eqnarray}
\begin{eqnarray}
	i \hbar \frac{\partial \phi_{2} (\mathbf{r},t)}{\partial t}
	& = &
	\left(
	-\frac{\hbar^2}{2 m_{2}} \nabla^2
	+
	V_{\rm ext}^{(2)}(\mathbf{r})
	+
	g_{22} |\phi_{2}(\mathbf{r},t)|^2 \right. \nonumber \\
 & &	+
	g_{12} |\phi_{1}(\mathbf{r},t)|^2
	\bigg)
	\phi_{2} (\mathbf{r},t) \ .
\label{gp2}
\end{eqnarray}
We have solved the GP equations (\ref{gp1},\ref{gp2}) by imaginary-time
propagation using a 4th order Runge-Kutta method.

\section{\label{sec:phases}Phase space}

We have explored the phase space of the Bose-Bose mixture using the DMC method
and, in all cases, we have compared DMC with GP results in the
same conditions. We
drive our attention to the density profiles of both species since our main goal
is to determine if the systems are miscible or phase separated. The results
contained in this Section have been obtained by using hard-core potentials
between the different particles,
\begin{equation}
	V^{(\alpha\beta)}(r) =
	\begin{cases}
	\infty  , &  r \leq a_{\alpha \beta}   \\
	0 	  ,&  r > a_{\alpha \beta} \\
\end{cases}
\ ,
\label{hardcore}
\end{equation}
with $a_{\alpha \beta}$ the radius of the hard sphere which
coincides with
its $s$-wave scattering length. The Jastrow factor in the trial wave function
(\ref{trialw}) is chosen as the two-body scattering solution,
$f^{(\alpha,\beta)}(r)=1-a_{\alpha \beta}/r$, and the one-body term corresponds
to the exact single-particle ground-state wave function,
$h^{(\alpha)}(r)=\exp(-r^2/(2a_\alpha^2))$. The length $a_\alpha$ is optimized
variationally but, even for the strongest interaction regime here studied, its
value is at most $~10$\% larger than the one of the non-interacting system,
$l_{\text{ho},\alpha}=\sqrt{\hbar/(m_\alpha \omega_\alpha)}$.
The one-body terms $h^{(\alpha)}(r)$ confine the particles to move within a
finite volume and thus open boundary conditions are used. The influence of
internal parameters of the DMC calculations, such as the number of walkers and the
imaginary-time step, is analyzed and the reported results are converged with
respect to them. The density profiles that we report are derived using the mixed
estimation since we have checked that the correction introduced by using pure
estimators~\cite{pure} is at the same level as the typical statistical noise.

\begin{figure}[]
\centering
\includegraphics[width=0.85\linewidth]{repulsive_phaseSpace.eps}
\caption{Representation of the phase space for the mixture as a function of the
interaction strengths $g_{\alpha \beta}$. The points correspond to the cases
studied, with coordinates given in Table
\ref{table1}. The mean-field theory for
homogeneous system predicts separation (mixing) for all the points above (below)
the mean-field critical line (dashed line). The dotted (green) line stands for
points where $g_{11}=g_{22}$.}
\label{fig1}
\end{figure}

As in Ref.~\cite{lee}, we plot the phase space in terms of the adimensional
variables
$g_{12}/g_{22}$ and $g_{11}/g_{12}$. In Fig. \ref{fig1} we plot it showing the
different regimes, with the line $g_{12}^2=g_{11} g_{22}$ standing for the
critical line separating miscibility and phase separation, using the mean-field
criterion.
In the figure, we plot the points which we have studied; they are selected to
cover the most interesting areas of the phase space. In Table \ref{table1}, we
report the specific coordinates of the interaction strengths.

\begin{table}[]
\centering
\begin{tabular}{c c c c}
	\hline \hline  \rule{0pt}{11pt}
$\text{Label}$ & $g_{12}/g_{22}$ & $g_{11}/g_{12}$ & $\Delta$     \\
                \hline
                $\text{A}$  & $3.0$ & $0.33$ & $-0.89$  \\
                $\text{B}$  & $0.75$ & $0.75$ & 0  \\
                $\text{C}$  & $0.75$ & $1.7$ & $1.27$ \\
                $\text{D}$  & $1.2$ & $1.7$ & $0.42$ \\
                $\text{E}$  & $1.7$ & $1.7$ & 0 \\
                $\text{F}$  & $0.33$ & $3$ & 8 \\
                $\text{G}$  & $3$ & $1.7$ & -0.43 \\
                \hline \hline
		\end{tabular}
\caption{Representative phase space points analyzed in our study.
The values of $\Delta$ are obtained from Eq. (\ref{delta}).}
\label{table1}
\end{table}

As usual in the study of Bose-Bose mixtures we define an adimensional
parameter $\Delta$,
\begin{equation}
	\Delta = \frac{g_{11} g_{22}}{g_{12}^2} - 1 \ ,
\label{delta}
\end{equation}
which classifies the regimes of phase separation ($\Delta < 0$) and miscibility
($\Delta > 0$) according to the mean-field treatment of bulk mixtures. When
$\Delta=0$ we are on the critical line separating both regimes (dashed line in
Fig. \ref{fig1}). In the results reported below, we also calculate the
parameter $\Delta n$ defined as~\cite{lee}
\begin{equation}
	\Delta n = \frac{\rho_1(0)}{\max \rho_1(r)} - \frac{\rho_2(0)}{\max
\rho_2(r)} \ ,
\label{deltan}
\end{equation}
which compares the value of the density profiles $\rho_\alpha(r)$ at the
origin $r=0$ with its maximum value. Then, $\Delta n \simeq 0$ when the peaks
of both density profiles coincide to be at the origin (mixed state) or when
the ratio of the central and maximum density is the same for both species, which
occurs when two species of the same mass separate to two blobs.
For other types of phase separation $|\Delta n| > 0$.

The density profiles reported in this Section have been obtained with a total
number of particles $N=200$ and considering a balanced mixture, i.e.,
$N_1=N_2$. We have repeated some calculations considering
$N_1/N_2=\sqrt{g_{22}/g_{11}}$, which is the optimal balance from the
mean-field theory~\cite{petrov},
and the differences in energy with respect to $N_1=N_2$ are at most 10\%.
Therefore, we
concentrate on the balanced mixture. The role of the confining frequencies
$\omega_\alpha$ is a bit more relevant since we have observed changes in the
results that can reach the 30\%. In general, the energies are lower when the
frequencies obey the rule $m_1 \omega_1^2= m_2 \omega_2^2$ which corresponds to
applying the same harmonic confinement for both species. Therefore, the results
presented below correspond always to this choice.

\subsection{\label{mixed}$\mathbf{\Delta>0}$}

\begin{figure}[]
\centering
\includegraphics[width=0.9\linewidth]{rho_gp_diffFreq_3_arho.eps}
\caption{Point C of the phase space. The points correspond to the DMC results
and the lines to the solution of the GP equations for the same system. For each
case we report the gas parameter of each species calculated at the maximum of
the density profile.}
\label{pointc}
\end{figure}

When $\Delta>0$ the mean-field criterion predicts
mixing between the
two species. We have explored the confined system in three different points of
the phase space. We start with point C, with
$\Delta=1.27$ and the $g_{\alpha \beta}$ values reported in Table \ref{table1}.
In Fig. \ref{pointc}, we show the density profiles of both species. In all
cases, we use as unit length the harmonic oscillator length
$l_{\text{ho},1}$ of species 1. In the nine subfigures of
Fig. \ref{pointc},
going from left to right we increase the parameter  $N a_{11}/
l_{\text{ho},1}$, and from top to bottom we increase the mass of species 2.
The parameter  $N a_{11}/l_{\text{ho},1}$ is chosen because it is the
mean-field scaling variable contained in the GP equation. As we keep the total
number of particles $N$ fixed, increasing that parameter means to increase  the
scattering length of the 11 interaction and thus making $g_{11}$ larger. As
the coordinates in the phase space are fixed at the point C, increasing
$g_{11}$ implies that also the other strengths $g_{12}$ and $g_{22}$
increase. Therefore, moving to the right in the panels of Fig. \ref{pointc}
means an increase of both the interspecies and intraspecies interaction. Moving
down in the panels, for a fixed value $N a_{11}/l_{\text{ho},1}$, means
an
increase of the mass of species 2 and therefore an increase of the scattering
lengths $a_{12}$ and $a_{22}$ because the couplings $g_{12}$ and $g_{22}$ are
kept constant.

The density profiles shown in Fig. \ref{pointc} show in all cases a mixed
state, with $\Delta n \simeq 0$ (\ref{deltan}). In the leftmost column, when
the interaction is very soft, we appreciate that $\rho^{(\alpha)}(r)$ are
basically Gaussians, following the shape of the non-interacting gas. When $m_2$
grows, they are still Gaussians but slightly different in shape because the
frequencies are different. The Gaussian profiles disappear progressively moving
to the right due to the increase of interactions. The comparison between DMC
and GP shows agreement when the interaction is low and they clearly depart when
$N a_{11}/l_{\text{ho}}^{(1)}$ grows. The DMC profiles show the emergence of a
plateau close to $r=0$, in significant contrast with the GP prediction. The
departure of DMC and GP becomes larger when the gas parameter (included in
each panel in Fig. \ref{pointc}, calculated near the maximum of each density
profile), grows.

\begin{figure}[]
\centering
\includegraphics[width=0.9\linewidth]{rho_gp_diffFreq_4_arho.eps}
\caption{Point D of the phase space. The points correspond to the DMC results
and the lines to the solution of the GP equations for the same system.}
\label{pointd}
\end{figure}

\begin{figure}[]
\centering
\includegraphics[width=0.9\linewidth]{rho_gp_diffFreq_6_arho.eps}
\caption{Point F of the phase space. The points correspond to the DMC results
and the lines to the solution of the GP equations for the same system.}
\label{pointf}
\end{figure}

Density profiles for points D ($\Delta= 0.42$) and F ($\Delta=8$) are reported
in Figs. \ref{pointd} and \ref{pointf}, respectively. The results are
qualitatively similar to the ones of point C, showing mixing in both cases.
Point F is deeply located in the mixed part of the phase space (large $\Delta$
value) and the agreement with GP is, in this case, quite satisfactory except
quantitatively  when the mass difference is large and the strength of the
interaction increases. Point $D$,
with a small $\Delta$ value, shows slightly more significant  departures
from GP
predictions that again increase when the difference in mass between both
species increases.

\subsection{\label{critical}$\mathbf{\Delta=0}$}

We have studied two points (B and E, see Table \ref{table1}) of the phase
space which are illustrative of the $\Delta=0$ case. Assuming mean-field theory,
this corresponds to the critical line for mixing in bulk mixtures.

\begin{figure}[]
\centering
\includegraphics[width=0.9\linewidth]{rho_gp_diffFreq_2_arho.eps}
\caption{Point B of the phase space. The points correspond to the DMC results
and the lines to the solution of the GP equations for the same system.}
\label{pointb}
\end{figure}

In point B, we have
$g_{12}/g_{22} = 0.75$ and $g_{11}/g_{12} = 0.75$. With these values,
$g_{22} > g_{12} > g_{11}$, and thus one expects that species 2 goes out of
the trap center because it is more repulsive than species 1. This effect is
emphasized when $m_2>m_1$ because the relation between scattering lengths has
an additional factor $m_2/m_1$. In Fig. \ref{pointb}, we can see the evolution
of the density profiles as a function of the interaction strength and mass
ratio. When the system is only weakly interacting (left column) one appreciates
Gaussian profiles that coincide with GP predictions. The situation changes when
the interaction grows (second and third columns) as we can see that the two
systems start to phase separate, a feature that is measured by the positive
value of the factor $\Delta n$ (\ref{deltan}). If the difference in mass is
enlarged, bottom panels, one can see that the phase separation is even more
clear. In this case, the heaviest component (2) is manifestly going out of the
center and thus it surrounds the core,  mainly occupied by the species 1.
Comparison with GP shows that there is a qualitative agreement with DMC but
quantitatively GP is rather inaccurate, specially when the mass ratio is
$m_2/m_1=4$.

\begin{figure}[]
\centering
\includegraphics[width=0.9\linewidth]{rho_gp_diffFreq_5_arho.eps}
\caption{Point E of the phase space. The points correspond to the DMC results
and the lines to the solution of the GP equations for the same system.}
\label{pointe}
\end{figure}

In point E, we are still in the critical line $\Delta=0$ but now the relation
of interaction strengths is inverted with respect to point B. That is,
$g_{22} < g_{12}<g_{11}$. Therefore, one now expects  species 2  occupying
the center and species 1 moving to the external part of the trap. This is
reflected in the negative values of the parameter $\Delta n$ which are reported
for every panel in Fig. \ref{pointe}. The increase of the factor $m_2/m_1$ goes
in reverse direction and slightly compensates the increase in $a_{22}$.
However, it is shown not to be large enough to change the description.
Comparing with Fig. \ref{pointb}, the phase separation is not complete because
one can see that there is always a finite fraction of species 1 close to the
center.

\subsection{\label{phaseseparated}$\mathbf{\Delta<0}$}

In this subsection, we move to points of the phase space where phase separation
is expected. We have studied two representative points of the phase space,
points A and G (see Table \ref{table1}).

In point A, $g_{12}/g_{22} = 3$ and $g_{11}/g_{12} = 1/3$ producing
$\Delta=-0.89$. The relation of strengths is now
$g_{11}=g_{22} < g_{12}$. By going from left to right in the panels of Fig.
\ref{pointa} one can see that the mixture phase separates when the interaction
between atoms is more important than the one-body confining harmonic
potential. When the masses of both species are equal, one identifies a phase
separation in form of two symmetric separated blobs~\cite{pu,ohberg}, similar
to what one
would observe in
a bulk system. This is also consistent with $\Delta n = 0$. Again, the
mean-field prediction becomes quantitatively worse, as the interaction
strength and the difference in mass between the two components increase.
However, although it is not visible from the radial profiles, in all cases of
point A there is at least partial phase separation in two blobs. In order to
show this, we have calculated the $P(z,\rho)$ distribution, where  the
$z$-direction is defined as a line passing through the two centers of mass,
with the second component being in the positive $z$-direction. $z=0$ is the
geometric center between the two centers of mass. The second variable, $\rho$,
is just the distance of a single particle from this line. Results are
normalized such that $\int 2 \pi \rho d\rho dz P(z, \rho) = N/2$. The results in
the two illustrative cases are presented in Fig. \ref{splot1} and \ref{splot2}.
In the case of equal masses and $N a_{11}/l_{\text{ho},1} = 2$ (Fig.
\ref{splot1}) although both species overlap significantly, the maxima of
their probability distributions are clearly separated. In fact the average
distance of their centers of mass is about $0.4 l_{\text{ho},1}$. Increasing
$N a_{11}/l_{\text{ho},1}$ the overlap between the two species decreases and a
clear two-blob structure becomes visible, with the average distance between the
two centers of mass becoming $3 l_{\text{ho},1}$. The increase of the mass
difference of the two species also favors their separation. The extreme case of
$m_2 = 4m_1$ and  $N a_{11}/l_{\text{ho},1} = 15$ is shown in Fig. \ref{splot2}.
We observe that the two species are clearly separated in two blobs and more
spread in both the $\rho$ and $z$ directions than in Fig. \ref{splot1}, due to
the  larger repulsive interspecies interaction. DMC predicts the more
massive component to be closer to the center of the trap, unlike GP. $|\Delta
n|>0$ is quite large, but remarkably has opposite sign in GP and DMC.

\begin{figure}[]
\centering
\includegraphics[width=0.9\linewidth]{rho_gp_diffFreq_1_arho.eps}
\caption{Point A of the phase space. The points correspond to
the DMC results and the lines to the solution of the GP equations for the same
system.}
\label{pointa}
\end{figure}

\begin{figure}[]
	\centering
	\includegraphics[width=0.6\linewidth,
angle=270]{m2=m1_Na_2.eps}
	\caption{Point A of the phase space for $m_1=m_2$ and $N
a_{11}/l_{\text{ho},1} = 2$. $z$-axis corresponds to the line going through the
centers of mass of the two components, while $\rho$ corresponds to the distance
of a particle from that line. Top and bottom panels stand for the distribution
of species 1 and 2, respectively.}
	\label{splot1}
\end{figure}
\begin{figure}[]
	\centering
	\includegraphics[width=0.6\linewidth,
angle=270]{m2=4m1_Na_15.eps}
	\caption{Same as Fig. \ref{splot1} (point A) for $m_2=4m_1$ and $N
a_{11}/l_{\text{ho},1} = 15$.}
	\label{splot2}
\end{figure}

\begin{figure}[]
\centering
\includegraphics[width=0.9\linewidth]{rho_gp_diffFreq_7_arho.eps}
\caption{Point G of the phase space. The points correspond to
the DMC results
and the lines to the solution of the GP equations for the same system.}
\label{pointg}
\end{figure}

In the last point (G), one expects phase separation because
$\Delta=-0.43$. The
relation of strengths is now $g_{11} >
g_{12} > g_{22}$. We clearly observe a
phase separated system for medium and large interactions and a mixed one when
$Na_{11}/l_{ho,1}=2$. The lighter particle moves progressively out of the
center and finally, when the relation of masses is large, it surrounds
completely the heavier one, which occupies the center of the trap. Contrarily
to point A, here the GP description is in nice agreement with the DMC data even
when the difference in masses is large. To get a better visualization of this
point G, we show in Figs. \ref{splot_g1} and \ref{splot_g2} the function
$P(z,\rho)$ defined above in the same conditions as in Figs. \ref{splot1} and
\ref{splot2}. We can see that Fig. \ref{splot_g1} shows a mixed configuration
whereas Fig. \ref{splot_g2} reports a two ring structure, in agreement with
what is observed in the density profiles of this point (Fig. \ref{pointg}).

\begin{figure}[]
	\centering
	\includegraphics[width=0.6\linewidth,
	angle=270]{G_m2=m1_Na_2.eps}
	\caption{Same as Fig. \ref{splot1} (point G) for $m_2=m_1$ and $N
		a_{11}/l_{\text{ho},1} = 2$.}
	\label{splot_g1}
\end{figure}
\begin{figure}[]
	\centering
	\includegraphics[width=0.6\linewidth,
	angle=270]{G_m2=4m1_Na_15.eps}
	\caption{Same as Fig. \ref{splot1} (point G) for $m_2=4m_1$ and $N
		a_{11}/l_{\text{ho},1} = 15$.}
	\label{splot_g2}
\end{figure}

\section{\label{scaling}Scaling with the interaction parameter ${\bf N
a_{11}/l_{\textbf{ho},1}}$ }

In the previous Section, we have plotted the density profiles considering the
parameter $N a_{11}/l_{ho,1}$ as a scaling parameter to determine the
strength of
the interactions. For a given value of this adimensional parameter we have then
changed the relation of masses between the two species. This parameter has been
taken from the GP equation for a single Bose gas harmonically confined where
it is proved to be the \textit{only}  input parameter of the calculations. In
this section, we check if this is also true in the case of mixtures, both in
regimes where DMC results and GP ones essentially coincide and in others where
we have observed significant discrepancies.

We have chosen two illustrative cases of both situations. In particular,
points A and E of the phase space (see Table \ref{table1}). In both cases we
have changed independently $N$ and $a_{11}$ in such a way to keep the GP
parameter as equal. To this end, we have used a system with $N=100+100$ and a
smaller one, composed by half the number of particles $N=50+50$.

\begin{figure}[]
\centering
\includegraphics[width=0.9\linewidth]
{rho_sameN_diffFreq_1_arho.eps}
\caption{Scaling on the GP parameter in point A of the phase space.
Different points correspond to different number of particles $N$.
}
\label{pointascal}
\end{figure}

In Fig. \ref{pointascal}, we report the results of this analysis for point A.
The results of the density profiles are all normalized to sum up to 200 in order
to make the comparison easier. As we commented in the previous Section, point A
is the one where we have observed the largest departures from the GP results.
The figures shows excellent agreement when the interaction is low and some
discrepancies when the GP parameter grows. However, the effect is not dramatic
and affects only the heaviest species. It is remarkable that even in
situations like the ones of Fig. \ref{pointascal},  where GP strongly
departs from DMC,
one can still observe a very reasonable scaling with the GP interaction
parameter. Moreover, we can see that our results converge for a number of
particles $N \geq 200$ and that these converged results still show
discrepancies with the GP density profiles.

\begin{figure}[]
\centering
\includegraphics[width=0.9\linewidth]
{rho_sameN_diffFreq_5_arho.eps}
\caption{Scaling on the GP parameter in point E of the phase space. Solid and
open points stand for results with $N=200$ and $N=100$, respectively.
}
\label{pointescal}
\end{figure}

Point E was one of the points where the agreement between GP and DMC was
better. In Fig. \ref{pointescal}, we study the the dependence of the density
profile results on the GP parameter as a scaling factor. In this case, the
agreement is practically perfect because the discrepancies are just of the
order of the error bars.

\section{\label{universality} Universality test}
A relevant point in our numerical simulations is the influence of the model
potential on the results. Universality in these terms means that the
interaction can be fully described by a single parameter, the $s$-wave
scattering length, as it corresponds to a very dilute system. In all the
previous results we have used a hard-core model for the interactions between
the atoms (\ref{hardcore}). In this Section, we compare these results with
other ones obtained with a 10-6 potential,
 \begin{equation}
 V^{(\alpha\beta)}(r)=\frac{\hbar^2}{2 \mu_{\alpha\beta}}\, V_0 \left[
\left(\frac{r_0}{r}\right)^{10}-\left(\frac{r_0}{r}\right)^6 \right] \ ,
\label{lenjones}
 \end{equation}
whose $s$-wave scattering length is analytically known~\cite{pade}. We fix the
parameter
$r_0=2 a_{\alpha \beta}$ for all cases and modify the strength $V_0$ to
reproduce the desired scattering length. In Eq. (\ref{lenjones}), the
parameter $\mu_{\alpha\beta}$ is the reduced mass, $\mu_{\alpha\beta}=m_\alpha m_\beta/(m_\alpha+m_\beta)$.

Our analysis has been performed for $m_2=1.5 m_1$, $N=100+100$ particles, and
considering equal harmonic frequencies $\omega_1=\omega_2$. Two interaction
strengths have been used, $Na_{11}/l_{\text{ho}, 1}=8$ and 15. As in the
previous
Section, we have studied points E and A of the phase space, i.e., those
characteristic of agreement and disagreement with GP.

\begin{figure}[]
	\centering
	\includegraphics[width=0.9\linewidth]
	{{rho_100.100_twoPanels_A_arho_vertical}.eps}
	\caption{DMC results for two models are compared to GP results for two values of GP parameter in point A .
	}
	\label{aunivers}
\end{figure}

In Fig. \ref{aunivers}, we show the density profiles of point A, obtained using
the two model potentials normalized in the same way. We can see an overall
agreement between both results with only some differences in the estimation of
the density in the center. Close to $r=0$ the statistical fluctuations are
bigger due to the normalization in a small volume. This feature is always
present but we observe that these fluctuations are larger in the case of the
10-6 potential (\ref{lenjones}).

In Fig. \ref{eunivers}, we analyzed the same for point E in
which we are closer to an effective mean-field description. The comparison also
shows a good agreement between results obtained for both potentials, with some
differences in the inner core of the trap.

We have verified in other points of the phase space the universality of our
results and the conclusion is that this is maintained with respect to the
character of the system (miscible or phase separated) and also the overall
shape of the density profiles. The influence of the model potential is at the
scale of our statistical fluctuations, except close to $r=0$ where small
differences are observed in some cases.

\begin{figure}[]
	\centering
	\includegraphics[width=0.9\linewidth]
	{{rho_100.100_twoPanels_E_arho_vertical}.eps}
	\caption{DMC results for two models are compared to GP results for two values of GP parameter in point E.
	}
	\label{eunivers}
\end{figure}

\section{\label{discuss} Discussion}
Using the diffusion Monte Carlo method, able to provide exact results for
bosonic systems,we have explored the phase space of an harmonically confined
Bose-Bose mixture at zero temperature. Our results are compared in all cases
with a mean-field Gross-Pitaevskii calculation in the same conditions. As
expected, our DMC results agree better with the GP ones when the strength of
interactions is small and worsens progressively when that grows. In spite of
the fact that the prediction for miscibility or phase separation is coincident
in both cases, it is also true that the density profiles can be
rather different. The relevance of quantum fluctuations, which makes the
density profiles to depart from the GP ones, depends on the dimensionality of
the system. It is well known~\cite{astra,edler} that they become much more
significant in the case of one dimension, since the Lee-Huang-Yang term scales
as $n^{1/2}$ instead of the three-dimensional law $n^{3/2}$.

Our results are by construction exact and go beyond mean-field, showing the
limits of this approach. A systematic trend in which GP fails is the dependence
on the mass of the two species. When the asymmetry in the masses grows GP
becomes clearly wrong in some cases. That could be argued to be an effect of
the interaction model used in DMC but our results contradict this point, within
the range of interactions here explored.

The tunability of atomic interactions and the possibility of using atoms with
different mass ratios makes this system specially rich. The phase space shows
regimes of miscibility and, interestingly, two different situations for phase
separation, two blobs or in-out spherical separation, depending in the
relation of masses and interaction strength. It would be very interesting to
produce in the lab smaller systems, with hundreds of atoms, to check the
departure of the physics from the mean-field GP treatment. In this way, one can
start to enter into the realm of fully quantum many-body physics.

\begin{acknowledgments}
This work has been supported in part by the Croatian Science Foundation
under the project number IP-2014-09-2452 and MINECO (Spain) Grants No.
FIS2014-56257-C2-1-P and No. FIS2017-84114-C2-1-P. The computational resources of the Isabella cluster at
Zagreb 	University Computing Center (Srce)  and Croatian National
Grid Infrastructure (CRO NGI) were used.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


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a. It is very easy to grow here.
b. Research: what is bougainvillea? And also: where?
c. Many of the flowers have bright bushy heads, like puppets.
C. The entry way is splotched carpet.
D. Something intended for keys now catches spare change, movie stubs, rubberbands.
a. Keys are still lost.
IV. A man comes in. We do not know if it is the lover or male relative. He knows a lot about paying bills but also her T-shirt is sheer.
V. The lover says something that reveals he is a nice guy most of the time, but that everybody makes mistakes.
VI. The woman thinks something that makes her unforgivable to any reader.
A. Are we the woman or the man? the reader will ask.
VII. Draw attention to the cigarette ash, as it becomes very important here.
A. It is long and it burns with no help.
B. She must be distracted by something, or otherwise lost.
D. The brand is cheap and burns too quickly.
a. It must be a fictional brand so as to avoid her being associated with: cowboys, punks.
E. The lover says nothing about the cigarette ash, nor does he smoke, which indicates they will not last much longer.
VIII. Something happens outside to break the tension, which by now should be like water threatening the drain.
IX. She says the name of a certain flower. He touches something that is not her.