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COVID-19 Leadership Podcast Self-DevelopmentNovember 3, 2020
Ep22: Dr. Jayne Morgan, MD – Clinical Director, Covid Task Force at Piedmont Healthcare
Hills and Valleys is a podcast that uncovers stories from leaders in healthcare, tech, and everything in between. Straight from the heart of Silicon Valley, we give you a look at the good, the bad, and the future, one episode at a time. Brought to you by Potrero Medical.
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About Dr. Jayne Morgan
Jayne Morgan, M.D. is a Cardiologist and the Clinical Director of the Covid Task Force at the Piedmont Healthcare Corporation in Atlanta, GA. Within this role she is developing ongoing community outreach in conjunction with the Division of Diversity and Inclusion between Piedmont and the African American community it serves. Additionally, Dr. Morgan will be analyzing the science and data from Piedmont and nationally, surrounding the disproportionately negative impact of Covid-19 on minority communities. Ultimately, the goal is to identify methods, as well as areas of improved triage, screening, and algorithms for the overall outcomes management of disadvantaged populations positive for Covid19.
Previously, Dr. Morgan was the Director of Innovation at Piedmont Healthcare, Inc. where she set the vision, trajectory, and strategic scaling opportunities, as well as seeking key partnerships and stakeholders to progress these goals. In doing so, the program recognized close to a 50% success rate (national average is less than 10%) following the addition of an external investment of $23,000,000.00 for one project within the Accelerator, and the signing of the first ever licensing contract from an external stakeholder for yet another project.
Dr. Morgan is a native Atlantan and completed her B.S. degree at Spelman College (Atlanta, GA), Medical Degree at Michigan State University (East Lansing, MI), Internal Medicine Residency at George Washington University (Washington, D.C.), and both her Cardiology and Pacemaker Fellowships at Mount Sinai Medical Center (Miami, Fl).
Follow Dr. Morgan on LinkedIn
Khateeb: Hi everyone, I'm Omar the Director of Growth here at Potrero Medical. We have another fantastic interview for Hills and Valleys. This time, I've got someone who's quite hard to get a hold of.
She's got her hands in a lot of different projects and different things in the industry, both in the academic and private sector. Her name is Dr. Jayne Morgan. Dr. Morgan, thank you so much for joining us.
Dr. Morgan: Thank you, Omar. I love being here.
Khateeb: Absolutely. For the listeners out there, Dr. Morgan and I have been connected on LinkedIn for some time and I've just been really inspired by the posts that I've seen. One week she's on the news on CNN talking about vaccine trials, other times she's dealing with innovation and other times she's a physician.
There are so many things that she's involved with and I knew that our audience would love to hear from somebody like her. I guess the first question I have for you is, Who is Dr. Morgan? Where are you from? How did you get into medicine and innovation? Like, what's that story?
Dr. Morgan: Yeah, I'm a native Atlantan. I am a graduate of Spelman college. I went to medical school at Michigan state, and then Internal Medicine residency at George Washington university, and then Cardiology Fellowship at Mount Sinai. So that's a lot. I moved around.
I practiced Cardiology for a while before going into industry, meaning the pharmaceutical industry at Solvay. It was then acquired by Abbott, about four or five years into my tenure. I became part of the acquisition; it was my first experience in being acquired without my input.
All of my projects were killed and that was a blow to my ego. Abbott was not interested in the projects that I was working on, the drugs that was leading the Cardio-renal Division—which is the heart and kidney division of Solvay. They weren't interested in that and they offered me an opportunity to work in their Medical Device Division out in California. I'd never done devices, but that was my only opportunity that was offered. So, I guess it was this or hit the highway. I took it and fell in love with devices.
Abbott bought Solvay at the same time they bought a company called Evalve. Evalve was a company that had a device called the mitral clip, which would be the beginning of the whole structural heart. It would be the beginning of the whole structural heart revolution but, at the time, we didn't know that.
What Abbott did I thought very smartly was it left Evalve entirely intact and brought it into Abbott as a division and they created a new division called the Structural Heart Division. However, the Structural Heart Division was actually the Evalve company, including their location, and their building. Nothing changed and they allowed it to run.
They decided to bring in myself during the acquisition as a Cardiologist to add to this Evalve team, which was really the Structural Heart Division of Abbott. That's really how I began in devices. Even though I was working with Abbott, I was essentially working at a startup. All of the executives were there, they ran as a startup and I loved it. We moved much more quickly than a big pharmaceutical company. Decisions were made much more quickly and things changed much more quickly.
The decision makers from the top to the bottom were all at the table and that was just an environment that I really enjoyed. I thrived. I wasn't aware that that existed and all of that came out of the acquisition.
From there, I was at the American Chemistry Council as Chief Medical Officer, before coming to Piedmont where I've been for the last five years in a multitude of roles. I was hired to lead the cardiovascular research program where I built out the entire structural heart feasibility program since I'm fresh out of Abbott, right?
Khateeb: That's a huge undertaking, especially at a system like Piedmont. What was that like?
Dr. Morgan: Actually, it was less difficult than one might imagine because I had excellent physicians, cardiologists and interventionalists who were already there, very steeped in the aortic valve space. They were utilizing the tuber valves that were on the market. They were very interested but just didn't have that piece of the puzzle where they could begin to do these in trials.
Then I was hired with this big structural heart background and they're already in structural heart, very hungry and interested to move into clinical trials. And so, it was like the pieces of the puzzle coming together. They got that final piece that came in, somebody could who could actually develop this research for them and off we went. We brought in all the mitral trials and tricuspid trials.
It was a big support to our valve center and we were off to the races. However, the success of that was predicated on people who were already there in place. I was the final piece that needed to come into place. They needed that research piece to make it work. And so, when I came, the structure was in place, they just didn't have the capability of someone who was able to build out that research part.
It was easier than you think as far as I didn't have resistance, but then obviously the whole part of you've got to actually build it and get the clinical trials in and get your teams together, that was hard.
Khateeb: Interesting. Well, I've got to say I'm going to respectfully disagree on one part of it. You say that you were a piece of that, but based on your energy and what I see of you online, I think you're probably more of the catalysts that made that whole thing happen. That's just my personal opinion. I appreciate you being so humble.
Dr. Morgan: Well, I will say it takes a team, but I certainly was the final piece that was able to build that and take it over the finish line. However, I couldn't do it if I didn't have doctors who were already interested in these valve placements. It could have been that I would have needed to start it from scratch and actually hire physicians who are specialists in this area. So, my specialist existed when I got to the system.
Khateeb: That's nice. Essentially the foundation was there. I guess as the old saying goes, If you want to go fast, go alone; if you want to go far, you've got to go together.
Dr. Morgan: Right.
Khateeb: There's somethingI want to go back to a little bit. From your time in medical school and residency, through your experience in devices and industry and backend innovation, who were the mentors that you have? How did they influence you? Because you didn't just show up to the Piedmont like, 'This happened on us'.
There was some wisdom and training that you carried with you so that when you arrived, you knew what to do and how to essentially align and power this team. Who are those mentors? What kind of things did they teach you?
Dr. Morgan: Yeah. My experience is probably atypical of most people, but still very typical for black physicians. I would say with sadness that I never had a mentor. There was never someone who reached out to me. The transition in medical school can be very lonely and isolating. My residency program was excellent, but the leadership at my Cardiology Fellowship was very hostile.
That was three years of suffering through. I was one of just a couple of women. There were not black people there either, maybe I was just one of a couple of blacks in. I think it always starts with leadership and the head of the fellowship program was very hostile and unsupportive.
If you're looking for a story of a journey, my journey, I think, is different from the journey of the majority, but typical of the journey of people of black and brown persuasions. And so, I think it can be challenging.
Now, should my journey typify what others do? No! You should certainly seek out mentors and maybe seek out even champions. I would say that at times in my career, I have tried to do that. I never approached people and it just hasn't been welcoming. For the most part, my successes and also my failures are predicated in this innovation space on being able to be agile and not fragile.
Being able to pivot, being able to understand your work even when others don't understand it and being able to stand on your own two feet. I think a lot of entrepreneurs have to be able to stand on their own two feet, right? You're giving pitches and you're trying to convince people who have no vested interest and maybe don't even know much about it or even think it's a value. You've got to really stand on your own and even after multiple rejections, it's your internal fortitude and passion and understanding of what you're doing that keeps you going forward. I would say that in that regard, I tend to have a lot of that fortitude, resilience and attitude to move forward than the average person—maybe even more.
I would say, in many instances, my journey has been hostile. It's been unfair seeing people move ahead that probably shouldn't have moved ahead. That being said, I think having mentorship and champions are incredibly important. These are people who can speak your name in rooms and in situations to which you would otherwise have no access and they can provide that access to you.
And so, if you were able to connect with people, they don't have to be of the same gender or the same race or anything. Just someone who's able to help you move forward. I think in that way, I have reached back and spent lots of time with students and people younger than I am. I really try to bring people forward and help develop their career because I think in my career that that was lacking. I don't do it for that reason. I do it actually, because I do like to teach and I like to mentor. I also like to see people, especially women and minorities, really have an opportunity to reach their potential.
Khateeb: Absolutely. I love that you shared that because my father is a General Surgeon up in Chicago and I heard things very similar to what you just shared. Fortunately, I think in society today we're definitely in a better place.
There's still a lot to be done, but I think at least if I can speak for my generation, something that I think a lot of people can learn a lot is when you don't have someone in your corner supporting you, how do you get that from the most important person, which is yourself? And it sounds like you looked to yourself and you picked yourself and said, I don't care what these people have to say, I don't care about the support that I'm not getting. All I need is myself. What can I do? And essentially you took the responsibility, right?
Dr. Morgan: Yeah, I took the responsibility on. I think it's a matter of surviving, but I would like to see people of color in science and technology not have to survive. We need to be able to transition into thriving. Oftentimes we have to survive. Our careers are often marginalized. We're not a part of the main core of the organization or the academia. We're usually a part of "special projects" or whatever the special thing. We build new entities for them and once it's built, it's handed off to someone else and we're moved out.
This marginalization is very common throughout our entire industry, especially for people of color. I think part of it is that people see us with their brains and not with their eyes.
So, what they see is all of the stereotypes, you know, blacks are dumb, women are docile, and everything else that they see. We're constantly fighting against the stereotypes that people have inherently and they're not able to see what is exactly in front of them, which is the person that they're actually working with. Your brain is so powerful. No matter what, you really have to have significant experiences to overcome whatever has been integrated into you in your formative years and that's very difficult.
Certainly, it's difficult to overcome an entire boardroom of that, but overcoming one or two, may be different. It can sometimes be a lonely journey. However, that being said, I've made a wealth of friends in this journey. Everyone is not like that. I'm talking about the system in general, but within the system are all kinds of people. Certainly, there's a lot of positive activity and, as you've said, I've had a very interesting career. I laughed when you used the word Interesting. You know, there's an old Chinese proverb that's actually Chinese curse and it says, 'May you have an interesting life'.
Khateeb: [Laughs]It's good to know because my boss is Chinese and I'll have to talk to her.
Dr. Morgan: Yes, that's a curse, 'May you have an interesting life'. So, when you introduced my career as interesting, I laughed because within that 'interesting' encompasses the need to have been resilient, to reinvent yourself repeatedly, to be able to stay on your feet and to move forward. All of that is encapsulated in your term 'Interesting'. That's what you see in my career.
Khateeb: I love that because a lot of times we're drawn to those who were like us. My career is definitely interesting because I went from being a biologist to being in med school and then I was in sales and marketing. I think it's part of this thing about understanding that you get to decide who you are. I'm completely different now from who I was a few years ago.
The most important thing is embracing who I was growing up culturally, right? Something that my wife and I talk about is at the end of the day, the human brain is still the same brain we've had for hundreds and thousands of years. It's not designed for modern time. And so, we have to put a lot of conscious effort and energy, even though our brain shortcuts these things where it's like, Oh, this person is coming from a certain area or groups. When it's like this, then we have to say, I need to put more energy and effort into evaluating them as an individual and not use shortcuts, as unconscious as it can be.
That's the thing that I love about this. When I looked at your career in all these places, which half of the places other people would die to have that kind of pedigree, you had to reinvent yourself and say, "This was my identity who I was professionally and culturally at this time. Now, I'm going to take from these pieces that I've seen out in the world that I like and here's what I'm going to move forward with.
Dr. Morgan: Some of these moves are involuntary and you're then forced to take all the pieces of things that you've learned to bring them with you to address this new entity that you've never faced. You need to learn some new things, but you need to apply some old things and you've got to create something new. You need to do it quickly and you need to be very competent and successful in getting it done.
This is what I mean when I say you require the ability to be agile and flexible, because you don't know what's coming. A lot of changes in my career that you see, I didn't choose them or I wasn't pursuing them. I didn't have an aha moment to say, "Now, Dr. James Morgan, what would you like to do with your career? You've been doing this for three years."
No! Change came upon me. Reorganizations is what organizations call it, right? Lots of people suddenly find themselves in a new world and you either sink or swim.
Khateeb: You're absolutely right. A lot of the things that elevated me as a professional didn't happen because I made it happen. It happened because that's what the environment dictated and I said, Okay, it's either I have to change and evolve all these frameworks I had about how the world worked, the world's different. I have to change with it.
If there's one thing that COVID did, it accelerated a lot of trends and showed us how quickly things can change and how you have to change with it, even if it's as simple as saying, Okay now my wife and I are at home 24 hours a day, so we better find more things to do together and enjoy. We never used to workout together, now I've got to find a way to work out in a way that she enjoys and vice versa. It's either we're going to be happier or we're going to stay in the way we are and be miserable.
Just for everybody to know we have a great marriage.
[Both laugh]
Dr. Morgan: Just to throw something else out there, I am a Pilates instructor.
Khateeb: Are you serious?
Dr. Morgan: I have about 17 certifications from two different schools, East coast and West coast, balanced body reformation, every piece of equipment from the chair to the Cadillac, to the tower, you name it. I've done it and I have my own Pilates school where I now teach.
Khateeb: Wow. What's it called?
Dr. Morgan: Pilates with Dr. Jane.
Khateeb: Okay, I'm plugging that into a shout out. This is exactly the thing that I love. A lot of my friends who are coming out of residency and many young physicians who follow me online reached out for advice. I say to them, Listen, you cannot put yourself in this little box and say, 'Oh, I'm a doctor during the day and things like that'.
It's the same person and there's no reason for you to be ashamed. We just interviewed Dr. Andrew Saudis, the Chief of Heart Transplantation and Heartbeat over at KU. He posts a lot about his personal life.
Dr. Morgan: I follow him too.
Khateeb: One thing he says is, I'm sick and tired of having to feel either ashamed or to apologize for who I really am in my personal and professional life and I'm done with it. That's the kind of message that people need to hear. I think many physicians will listen to this podcast and say why is it that a lot of the rules we follow are not actually rules. They're rules that we've somehow put in our head and accepted it like the gospel, but it's not the case at all.
Dr. Morgan: Yeah. For people like me, our existence has been in trying to work around the rules because you get into organizations and you realize the rules really only apply to me. Others are not having to follow these rules, but they're being applied to me.
So, I need to be even more creative.
Each time you're trying to survive within a system that has a lot of inherent bias in it and the constant microaggressions, it's not a matter of growing stronger. You become increasingly more creative each time you're successful. If you're moved or you move to another organization or another job role, all those abilities come with you. Then you're able to create and provide deliverables to an organization at a level that's higher than the other employees, because you've had to rely on many other factors to have the exact same seat. I call it a resilience factor.
Khateeb: Yeah. Of course, it took my generation I'm an older millennial to take things that are ancient wisdom and try to make it more mainstream. There's this concept of how you do stoicism and practice suffering. So, if you didn't grow up developing resilience, you got to find ways to essentially schedule it yourself.
What's interesting is you said something and it's the first time I heard someone articulate it my way. It's that as you have to deal with different things, whether it's microaggressions or different rules and organizations, you pick these things up and you become more creative.
I was speaking to my father about this when he came to the state of Chicago in the seventies, there's a lot of xenophobia towards foreign graduate positions. If you look at hospitals these days, a lot of them by and large are all run by faculties who are foreigners.
I think they realize this and so they've had to become more creative and ask questions like, How do I influence this organization? How do I work with data?
But that's a wonderful way to think about it. When you're going through a very difficult obstacle, the obstacle becomes a way that develops.
Dr. Morgan: I think it's good. One of the things that I often talk about is the interest that I have in improving minority recruitment into clinical trials.
Khateeb: You were on CNN recently discussing that, correct?
Dr. Morgan: I was on CNN talking about it. I've been talking about it for two or three years. Actually, COVID has provided an opportunity to discuss it relevant to the COVID vaccine trials that are being pushed ahead very quickly.
As I took a look at those trials, I began to be able to speak directly and succinctly on why it's important to have black people in these trials. COVID is a great example. The community is being disproportionately impacted in death.
Khateeb: Can you share with the audience how much more is a black community affected by COVID? I want people to hear this.
Dr. Morgan: I don't know the exact numbers but certainly three to four times as much.
Death is certainly much higher. The transmission rate is higher. The long-term sequella seems to be higher too. When I say long-term sequella, meaning long-term effects where you are still feeling unwell even though you've converted to COVID negative. Somehow, you're still not at a hundred percent and something's not right. Those are called long-term sequella.
About 80 or 90 companies are rapidly developing vaccine trials and we're not necessarily a part of these trials. Yet we are the group that is most disproportionately impacted. How can you develop a drug, device or a vaccine and you don't have all kinds of people in them such that the treatment is relevant for everybody in our society?
Even before COVID, that is the point that I would make often when I would talk about minority recruitment into trials, but it's a difficult thing. It's somewhat of a taboo subject within the black community. We're not interested in that. We have a long history of medical atrocities being committed against us in the name of science and research.
It's just cruel and inhumane.
I think there's such a distrust of the healthcare system. In place of trying to understand whether or not you would be a great candidate for trial, it's safer—not better—but it's safer to just say no. Then we don't ever have to worry about what someone is doing because it's not the information that's being provided that we concern ourselves with; it's the information that's not being provided. What didn't they tell us? What didn't I know to ask and they're not telling me and they're going to do harm to me?
What has happened is that we're outside of the system and drugs are developed that are not relevant for us. There are some things that are very specific to different cultures, like enzyme reactions and that type of thing. When we look at the kidneys, for example, you know I did a lot of Cardio-renal work at Solvay.
That's what I'd say when I put together all the Cardio-renal work I did at Solvay, then I understand A1 Adenosine antagonist factors. I understand the Renin-Aldosterone-Angiotensin system, because I was leading those projects when I was at Solvay. So now, when we talk about that, this is another leaf that I can bring in from a previous role to say, All things are not the same. Even the way that our kidneys work sometimes can have little nuances and we need to understand how drugs are eliminated and metabolized. We've certainly had instances of drugs that are FDA approved that then had to subsequently be walked back because black people were being harmed by them, but we were never in the trials.
That's kind of where we are. 80% of all black patients are seen by black physicians, but physicians also are not active in these trials. We are not asked to be principal investigators. The companies don't reach out to us to have us be principal investigators. Usually it's still white men for the most part, the practice of a white male doesn't include black patients. And so, there's that next separation with the black physicians. The number one reason that a person will agree to enroll in a trial is that a trusted physician asked them to enroll. You start to see all these degrees of separation as to why.
And then when we talk about leadership within clinical research, within hospital systems, you don't see people like me, you and others. Therefore, those perspectives are not at the table. Those positions are not advocated and that sensitivity is absent. I've already discussed how oftentimes our roles are marginalized such that we don't have a voice at the table. Again, we have yet a third degree of separation and you can see how there's just a steady, systemic disenfranchisement of the black patient from clinical trials.
However, clinical trials really can serve to close the gap in health equity. This is because it brings you into the system, you have more frequent healthcare visits, you have a direct contact with the nurse or the research coordinator that's working on the trial, you often have your drugs or devices provided for free so if you're uninsured or under-insured, you don't have the capacity to have healthcare. Yet all those things are absent because of multiple layers of a big system.
Khateeb: I think that's a very correct way of putting it. Isolating these things don't seem as bad, but as you start adding just even a couple of these things, the effects and impacts are astounding.
So, how do we start changing that at least with these trials in terms of recruiting more black patients participating in them.
Dr. Morgan: Yeah. I think the first thing that we can do is begin to reach out to the black physicians who also are not involved for all of the same reasons that come up through medical school; you're fairly isolated.
Khateeb: You go to med school for four years and you disappear pretty much.
Dr. Morgan: You just disappear and you're there to take care of patients. The academic centers as well as the corporations, device and pharma companies need to develop these relationships with black physicians who are treating all these black patients.
Secondly, hospitals and study sites must have people in clinical leadership who are competent to develop and lead these programs such that there's visibility and cultural congruence that includes everyone. It should also include diversity of the staff as well who will have that interface with the patient. That's certainly a call to action.
Then when we look at social determinants of health, maybe these study sites need to be set up, not just at major cities, academic and medical centers, but out in rural locations. This should be done such that people don't have to deal with real life issues, such as transportation, taking time off from work, babysitting and all those things that you may not think about, but are real obstacles. If someone has to travel two or three hours to a doctor's appointment or two or three hours home, and they don't have a car, or they've got to take off from work. That's crazy and all that stuff adds up.
Khateeb: What's really disheartening which we saw very early was how COVID had a much higher mortality with the black community. You mentioned Cardio-renal syndrome. From the reports in New York, we're seeing that Acute Kidney Injury is affecting about 37-40% of COVID patients. From a population standpoint, guess who has a lot of issues with the cardiovascular system? It's the black community.
COVID is one thing, but when you add these things, this community is going to be the one who suffers the most post-COVID when "things go back to normal". This is absolutely correct.
Dr. Morgan: That's right. One of the reasons clinical trials is a unique opportunity to begin to close the gap in health equity is getting people into the system.
Khateeb: I never thought of it like that.
Dr. Morgan: Outside the system, because the system is not safe for us. It's not that medical treatment isn't excellent at the medical centers and it's not that you won't treat me. It's that you might mistreat me. I might be neglected. Am I safe? At least if I go to a black physician, I know I have an understanding that this person is not going to do something to hurt me. However, I don't really have an understanding of that when I go to another physician or a healthcare system. All of this intrinsic bias that's invisible really to the keepers of society, shall I say, it's invisible to them. They've created it, but it's obvious in every part of everyday life that the rest of us have to exist in.
That's the part that keeps people away because they recognize that even though their doctor doesn't look like them, it's okay to go to a doctor that doesn't look like them. They also understand that that doctor doesn't understand all that it takes for that person to get there. Everything that it takes for that person to live, raise their children and get clothing.
Therefore, this person can't really treat me. This person can't heal me.
Khateeb: That's a very good point.
Dr. Morgan: Then I see my black physician and now we're back in the circle where the black physician is not connected to the academic center. The black physician is out in the community taking care of patients. And so round and round we go.
Khateeb: I've never heard anybody wrap up that complicated of an issue just in such a short amount of time, but you're absolutely right. What's most helpful is having the awareness of these things, understanding them and discussing them. More importantly, we have tools like social media. How do we use these things to connect to people and start raising the awareness and starting those initiatives? Are there any initiatives like that for the industry side? Are there societies or groups? What's the best place to start to look?
Dr. Morgan: Yeah. That's a big question and we're working on that. I am the co-founder with three others founding a group. I believe we are calling it The Color of Science. It's still very new. Our initiative for the first year is going to be focused exclusively on recruitment of minorities into clinical trials. It'll include educating minorities on clinical trials as well as what is the oversight of the FDA now that wasn't there in the 40s, 50s, 60s and 70s when these experiments with the Tuskegee Airmen were being done. When Henrietta Lacks was coming through the system and we're still benefiting from these HeLa cells.
What's different now? That's the kind of conversation that we're beginning to have with our communities and it's going to be our launch mission for our first year. We've got to start to insist that people that look like me, you, and all other people—whether black or brown—are in key leadership positions in research and are not marginalized and moved out. This should be done such that those voices are at the table, patients can be empowered and there can be an assurance of health equity throughout the system, which is what we're supposed to be about in a healthcare system.
Khateeb: Yeah, you're absolutely right. More often than not, it feels very much like a disease care system. And when it's a disease care system, you're focused on treating, which is one factor.
The big thing is that once the patient leaves the hospital, guess what happens? They're back in the same environment and that's why they end up coming back. During the short amount of time I was in medical school on the border, we had these patients come back and it was kind of blatantly obvious. It's not that these people are stupid or that they don't care or anything. It's just that healing is not an easy thing.
Technically, I guess it can be easy, but it's not simple. It's easy for you to just keep your diabetes low. Don't go home and eat or drink these things. That's easy, but it's not simple because you have to understand from a community as a culture. What are those dynamics and how do they influence things like food, healthcare, all these things?
Dr. Morgan: And what access do you have to them? Do you have access to care?
Khateeb: I agree with youa hundred percent. Kevin Mahoney, who's the CEO of PennMed, talked about this. They launched a free app for behavioral health at the beginning of COVID because they realized that many of their staff and employees don't have access. They have to get an appointment and referrals. So, he said, We need to make this as easy as possible. On the 'plus side' of COVID—actually, I don't even want to say the plus side—it accelerated trends that we needed to happen and it just happened a lot faster, like telemedicine. It's like saying, People are going to be stuck at home and we need to get better access because the world we live in is technically designed for a lot of people who are essentially dead these days. It's an old world. So how do we design it to be better?
Because whether you and I like it or not, this is the reality, so we have to figure out how we can fix these things and innovate around them. Otherwise it's going to perpetuate and get worse, right?
Khateeb: I want to be mindful of your time. We've got two minutes to our stop time.
We said it's going to be a California stop, so we're going to go a little bit passive. I have some quick, rapid fire questions for you. You can take as long or as short as you'd like to answer them.
First question to you. If you had a billboard that went in front of every single hospital and every single major city in the US for a whole year, and everyone's going to read it including healthcare workers, physicians, nurses, and everyone. What would that billboard say and why?
Dr. Morgan: That bill board would say "We are in". It would be the hashtag "We are in". The reason that billboard would say that is because it would be a voice from the African-American community that is saying that we're standing up and we have decided that we are going to be counted in clinical trials now.
We've decided that we're going to move forward and we're going to request this information. We are going to demand that our physicians get involved in these trials, such that they can talk with us about it, and we can hear it from a trusted partner. I would say that billboard would just say, #WeAreIn.
Khateeb: Well, I love that. You should start that hashtag if you haven't already. My next question which might be the last one because I know we have to wrap up, but I do want to make sure that we talk about how people could follow and reach you. I know you're a reader like myself. For everyone who's watching this on video, you can see that I read a lot of books.
What's a book, either a favorite book or a book you've read recently, that you've been gifting most often to people and why?
Dr. Morgan: You know, I rarely gift a book. I'll tell you what, I read a lot. I've been so distraught over The Social Structure and maybe deconstructing the fabric in the last three or four years. I've read White Fragility by Robin DiAngelo, which I thought was very eye-opening really just discussing from a white person the contempt that many white people have for black people, how it starts early and what that means.
I read White Rage by Carol Anderson, which was along the same vein, but going through historical aspects regarding the need for white superiority and that there is a need for the inferiority of blacks for white superiority to exist. I read Grit by Angela Duckworth, and I think it applies to me a lot when you talk about my 'interesting' career.
I believe Grit is a study by a psychiatrist of different people all across the world to know what differentiates people who have that stick-it-out-ness, including in the military. They stay and work at it as opposed to others who fall off and say, Oh, this is too hard I'm going to try something else. It's not that one is better or worse. We need people to try a lot of things and we need some people to stick to things and it's called grit. And so, I've read that book as well.
I've read a lot of books. [Laughs]
Khateeb: Those aregood recommendations. Again, we really appreciate you spending some time with us. I'm just going to tell you right now; I have a feeling that I'm going to be asked to have you back.
[Dr. Morgan laughs]
Khateeb: FYI, that'll happen faster than you know. For those who are listening and watching, what's the best way to find you and follow you on social media?
Dr. Morgan: Well, you know what, I do not have that. However, I'm on LinkedIn. You can find me as Jayne Morgan MD. If you let me know that you were on this podcast, that's great. I am looking to start an Instagram account, so maybe look for it in the next two or three weeks, and it's called Pilates with Dr. Jayne.
Khateeb: Got it. The website you have, is it pilateswithdrjane.com?
Dr. Morgan: There is no website either.
Khateeb: That's more of a reason to do Instagram then.
Dr. Morgan: I think I'm going to just do Instagram. Like everybody else, I sort of just pushed into the virtual world with my Pilates. I've been teaching for 10 years, but started teaching virtually in April. I really was just doing it for about 60 days or so to bridge my clients until we could get back into the studio. Now it looks as if it's going to be a permanent thing. I'll be starting an Instagram page and a webpage, but the IG page will go up first.
Khateeb: When they're ready, you just let me know and I'll update it in the show notes.
Dr. Morgan: Yeah, that'd be great.
Khateeb: Dr. Morgan thank you so much. Please stick around for just a second. Thank you all for listening, it has been another episode of Hills and valleys. Again, we'll leave in the show notes all these links for Dr. Morgan's pages and as always, we'll see you next time. Bye for now.
Previous Ep21: Dr. Andrew J. Sauer, Chief of Heart Failure Therapies Division at The University of Kansas Health System
Next Ep23: Dr. Wael Barsoum, President & Chief Transformation Officer at HOPCo


text:
\section{Introduction}

The observation that quasi-two-dimensional monolayers of granular spherical
particles can be
excited by periodic motion, leading to pattern formation, has been
exploited in the last decades
\cite{Taguchi,Williams,Eu,Grossman,Noije,Clement,Warr,Warr1,Kudrolli,Olafsen}.
A milestone in the field of ordering in granular media
was the observation that some structural properties of a vibrated monolayer of
spheres (in particular, crystallization), were similar to those of the ordinary hard-sphere model, a basic model to understand the structure of matter at the nano- and mesoscopic scales in thermal equilibrium \cite{Mulero}. These phenomena
can be largely understood by applying the standard rules
of equilibrium statistical mechanics \cite{Ojha,Olafsen}.
Many other nonequilibrium phenomena
are observed in periodically agitated granular matter, e.g. the presence of solitons.

Patterns in vibrated monolayer of particles can be found by
suitably choosing the control parameters of the
external drive imposed on the system. In this way, vertically-vibrated
granular rods have recently been shown
to exhibit interesting spatial patterns that resemble liquid-crystalline
phases in two-dimensional systems of anisotropic particles subject to thermal
fluctuations \cite{Narayan,Galanis1,Galanis2,Aranson1,Aranson2,Mueller,us,us1}.
Therefore, the inherently non-equilibrium granular arrangements
of anisotropic grains, when continually excited externally \cite{Melo,Miller},
reach steady-states with particle arrangements
which show typical characteristics of liquid crystals: local and global
nematic ordering \cite{Narayan,Galanis1,Mueller}, competing elastic bulk and
surface energies \cite{Galanis2}, together with typically non-equilibrium
effects \cite{Aranson1,Aranson2,us}. It is tempting to describe the behaviour in these
systems in terms of entropic arguments based on volume exclusion, since forces
between particles are absent except when they collide, and volume-filling
concepts become relevant.
Recently the phase diagram of equilibrium
hard rectangles has been explored by Monte Carlo simulation and seen
to exhibit many similarities, even quantitative, with the steady-state
arrangements of granular rods confined in circular cavities \cite{Mueller}.
We must remind ourselves that the behaviour of hard particles driven
by thermal fluctuations are exclusively controlled by entropy and particle
overlap statistics. This connection between thermal and nonthermal (granular) matter is intriguing.

More recently Gonz\'alez-Pinto et al. \cite{us1,GP}
have analysed defect formation in granular experiments
of metallic rods when their aspect ratio is small. In this regime
\textit{tetratic} arrangements, where particles form a fluid monolayer but with
their long axes pointing along one of two perpendicular, equivalent,
directors, are easily stabilised. As dictated by topological considerations,
extended tetratic phases, when confined to a circular cavity, restore
the four-fold symmetry of the director by creating four point defects with
a total topological charge of +4. This is indeed what is observed in the
granular monolayers, showing that these non-equilibrium systems respond
to geometrical frustration in the same way as their thermal-equilibrium
counterparts. Even more, by assuming that these four defects behave as
point defects of charge $+1$ and that they interact with each other
following elastic theory (i.e. through logarithmic potentials mediated by
the elastic stiffness coefficient of the tetratic phase), the spatial
fluctuations of these defects can be measured and used to extract an
elastic constant, which turns out to be of the same order of magnitude as
typical two-dimensional elastic constants of liquid crystals \cite{GP}.

The picture therefore emerges that, at least in some range of external
parameters, vertically-vibrated monolayers of granular rods
share many properties with corresponding systems governed
by thermal fluctuations. The cause for this apparent connection
is presently unknown: only some partial ideas and basic relations can be
advanced. We are still in the process of collecting as much evidence as
possible on these similarities.

In this article we present yet another
example where granular matter seems to respond to external constraints
in the same way as thermal matter. The system is an annulus, i.e.
a circular cavity with a central circular obstacle
confining the granular particles to a geometry essentially different to that
of a simple
circular cavity. In this case, as discussed below, topology does not
require the formation of point defects. This is indeed observed in our
experiments, but only in part: due to the severe
size restrictions, quantified in terms of the ratio of particle length
and cavity radius, another type of defects, namely (non-point-like) {\it domain walls}
(i.e. extended regions) that separate regions with different liquid-crystalline ordering, are formed.
These extended regions appear due to the severe size restrictions, quantified in terms of the ratio
of particle length and cavity radius, and are similar to domain walls
in materials where domains with different orientation of a
non-scalar order parameter coexist (see e.g. Ref. \cite{Heras} where domain walls separating
uniaxial nematic phases with different orientations were observed in circular cavities
using Monte Carlo simulation).

These structures (which are not required by topology as will be explained below) are created because
elastic, wall effects and intrinsic particle
ordering all compete to somehow satisfy a `maximum entropy principle'.
This is at least the paradigm imposed by equilibrium statistical mechanics,
which again seems to operate, at a presently unknown level, in
vertically-vibrated monolayers of granular rods (the very definition of bulk, wall and elastic
free energies is not clear as these concepts belong to the realm of equilibrium physics).
On top of that, this connection is a potentially interesting result, as it would mean
that granular matter can be used to easily create and control particle
orientations and defects of various kinds by setting up
particular geometric constraints by way of external boundaries, at
accessible --macroscopic--
time and length scales. By contrast, this process
is much more difficult to implement using soft matter based, for example,
on --nanoscopic-- liquid-crystal materials.

Shortly after our work on granular rods confined in annuli was started,
G\^arlea et al. \cite{Mulder} presented results on a similar system,
but using virus particles (i.e. of colloidal size), which are
subject to Brownian (thermal) motion. Computer simulations were also presented
to corroborate the experimental results. Remarkably, the
structures found by G\^arlea et al. are qualitatively similar to those
obtained by us, although the range of parameters is different.
Again this demonstrates the hitherto unknown relation
between two systems, granular and thermal, that are governed by
very different physics at radically different length and time scales.
We will discuss the similarities between our results and those obtained
by G\^arlea et al. in Sec. \ref{Conclusions}.

The article is organised as follows. In the following section
we expand on the theoretical background
needed to frame the discussion into the correct context.
The experiment is then discussed in some detail,
together with the analytical tools used. A section on results
follows where all observations, histograms and distribution functions are
presented. The article ends with a section on discussion and conclusions.

\section{Motivation and theoretical background}

Hard rectangles of sufficiently low aspect ratio $\kappa=L/D$, where
$L$ is the length and $D$ is the width, exhibit an exotic nematic phase
called the tetratic phase.  The orientational distribution function
$h(\varphi)$ of the tetratic phase has four-fold symmetry: it presents
equal-height peaks at angles $\varphi=0$, $\pi/2$, $\pi$ and $3\pi/2$,
where the origin of angles ($x$-axis in the lab frame)
is taken to point along one of the directors. This means that, in an
extended tetratic phase, two equivalent directors can be found at a
relative angle of $90^{\circ}$ with respect to each other. Particles
diffuse, as it corresponds to a nematic fluid, but they orient
along two possible perpendicular directions with higher probability.

The equilibrium phase diagram of hard rectangles has been analysed using
SPT by Schlacken et al. \cite{Schlacken} and more in depth by
Mart\'{\i}nez-Rat\'on et al. \cite{us2}.
The stable phases in the phase
diagram are all spatially uniform, since non-uniform phases were not explored.
They are: isotropic (I), uniaxial nematic (N$_u$) and tetratic nematic
(N$_t$) phases. Tetratic phase stability
occurs for aspect ratios $\kappa$ less than $2.62$. For
larger aspect ratios the stable nematic phase is the uniaxial nematic phase.
The tetratic phase is stable at rather large values of packing fractions,
values which would otherwise correspond to a non-uniform phase, such
as columnar, smectic or crystal. This point may lead one to think that
the tetratic phase should, in a more complete treatment including
spatially nonuniform order, be preempted by one of these phases. However,
further analysis has shown that this is not the case.
Inclusion of higher-order orientational correlations via an
effective third-order virial coefficient \cite{us} leads to an
isotropic-tetratic transition line which is shifted to lower packing fractions.
A consequence of this is that the range of aspect ratios where the tetratic phase
is stable is considerably enlarged up to $3.23$, meaning that three-body
correlations are crucial in the tetratic phase. There are reasons to
believe that inclusion of even higher-order correlations will further
expand the stability of the tetratic phase. In fact, recent Monte Carlo
simulations \cite{Mueller} have shown that the tetratic phase is stable
for $\kappa\alt 7$,
at values of packing fractions which are too low for the crystal and
other nonuniform phases to be thermodynamically stable.

M\"uller et al. \cite{Mueller} have investigated the relation between the
equilibrium system of hard rectangles, analysed by means of Monte Carlo simulation,
and monolayers of granular particles made of cylinders, which project on the horizontal plane approximately
as rectangles. Their experimental setup is similar to ours (to be explained in more detail later):
cylinders were confined into a thin circular cavity which leaves a
small vertical space so that, when vertically agitated, cylinders
move in the horizontal directions via collisions, without overlapping.
Uniaxial nematic and tetratic nematic
order parameters were defined in order to identify different types of order.
Phases were identified as
a function of projected aspect ratio and packing fraction. Overall qualitative
agreement was found between both phase diagrams. In some cases, for example
in the value of
limiting aspect ratio for tetratic stability, the agreement was even
quantitative. This intriguing similarity still awaits for an explanation.

Gonz\'alez-Pinto et al. \cite{us1} have extended the analysis of this system, confirming
some aspects of the work by M\"uller et al. but casting some doubts in the
case of long cylinders. Even though finite-size effects may be at work in this
case, long cylinders do not seem to develop uniaxial ordering but rather a
kind of patched nematic with no global ordering. Nonetheless, the results for
short cylinders were confirmed. Also, the tendency for clustering of groups
of particles was examined and contrasted with results from Monte Carlo
simulations. Clustering is much stronger in the dissipative system \cite{us1},
which is readily understood as particles tend to freeze when they collide, thus
generating an extra ordering tendency. Leaving aside this and other aspects,
the two systems, dissipative and equilibrium, look remarkably similar
in their ordering properties.
\\
\begin{figure*}
\begin{center}
\includegraphics[width=0.90\linewidth,angle=0]{Figure1.png}
\caption{\label{fig2} Values of the $q_2$ (uniaxial), $q_4$ (tetratic) and
$q_s$ (smectic) order parameters on each particle, and
for the four situations investigated in this work. 0: no obstacle;
1: small obstacle; 2: intermediate obstacle; and 4: large obstacle.
In each case the configuration has been chosen more or less at random
during the course of the respective experiments.
Colour code is shown in the vertical bars. In all experiments
particles had $\kappa=4$ and packing fraction was set to $\eta\simeq 0.75$.
	Values for the other parameters were taken as mentioned in Sec. \ref{analysis}.}
\end{center}
\end{figure*}

In additional work, Gonz\'alez-Pinto et al. \cite{GP} have made the observation that,
when the tetratic arrangement of the granular system
prevails, the imposed circular geometry of the cavity forces the monolayer
to create four defects, located close to the inner boundary of the
container and arranged on average at the corners of a square. See Fig. \ref{fig2},
panel 0--$q_4$ (here we use a matrix style to address each image, with
column $=\{0,1,2,4\}$ and row $=\{q_2,q_4,q_s\}$. The meaning of these
labels will be explained in Section \ref{Results}). The figure
shows an instantaneous configuration of the particles, colour-coded
according to the value of the tetratic
order parameter $q_4$ (to be defined later). The packing fraction is $\eta\simeq 0.75$.

The presence of the four defects is revealed by the low value of
the order parameter $q_4$, which is high in the region occupied by the tetratic
phase. Topological arguments can be used to explain this configuration.
The notion is based on the so-called {\it geometrical frustration}:
due to the boundary conditions imposed on a system, which otherwise
develops some specific local order in bulk, the order cannot propagate
to the entire system. In our case, the tetratic order, which imposes
a four-fold orientational order locally (C$_4$ symmetry in the nomenclature of group theory),
cannot satisfy the circular
geometry of the cavity, and the continuity of the tetratic field must be
broken in some regions. The excitation of defects is frequent in
liquid-crystalline materials whose local order-parameter field can be
elastically distorted (with an associated price in elastic free energy),
but the presence of surfaces with some specific geometry may be
incompatible with a distorted order-parameter field because of the high
surface free energy that should be paid to avoid the creation of defects,
even at very low temperature (low energy).

Therefore, we are facing a problem that can be quantified using
the Euler theorem of topology applied to the experimentally-obtained tetratic field \cite{Bowick}.
In the present context the theorem
states that the total topological charge of the system must satisfy the
equation $\sum_i{\cal Q}_i=p\chi$, where $p$ is the symmetry order of the
phase (in the case of the tetratic, $p=4$), while $\chi$ is the
Euler characteristic of the volume.
In the case of a circular cavity consisting of a disc, $\chi = 1$. $Q_i$ is the `topological charge' of
each individual defect present in the volume, a number that reflects the symmetry of the order parameter
around the defect. The Euler theorem gives the total charge of the system, not the number or topological charge
of the defects present. These properties depend on other considerations based on the competition between free
energy contributions of different origin: bulk, wall, elastic and defect core energies. In any case the system
will minimise the free energy by choosing the minimum number of defects that can restore the broken symmetry
induced by the confining boundary.
In a circular cavity the presence of four defects
restores the symmetry broken by the circular geometry of the cavity since the
total charge $+4$ satisfies the constraint imposed by the Euler theorem for a medium with C$_4$ symmetry.

It is remarkable that the steady-state structures reached by a driven system of
dissipative particles follows general laws based on the order-parameter concept,
meant to describe behaviour in systems in thermal equilibrium. With a view to further
exploring the previous findings for the circular cavity,
in this article we describe the results found in
experiments where the granular rods are confined in a cavity with a totally different
topology, namely a circular annulus: a circular cavity with a central hole.
In this case the Euler characteristic is $\chi=0$,
meaning that the total topological charge inside the volume should be zero. In fact, as
discussed later, the integrity of the director field can be maintained, without the presence of
any singularities, by distorting the field around the central hole without ever creating any
conflict with the wall contour. We will see that in this geometry the topological requirements
are not entirely fulfilled by the granular system,
due to reasons that will become clear later.

\section{Experimental setup}

In the experiment
cylinders made of nonmagnetic steel with
length 4 mm and width 1 mm (aspect ratio $\kappa=L/D=4$) are placed inside
a cylindrical cavity of radius $R=7$ cm ($R/L=17.5$). The two planar,
horizontal plates
of the cavity are close enough so that cylinders have a free height of
1.8 mm. Therefore cylinders cannot pass each other and constitute an
effective monolayer. The cavity is mechanically agitated at frequency
$\nu=90$ Hz. The effective acceleration of the system can be measured in
terms of the dimensionless parameter $\Gamma=a_0\nu^2/g$, where
$a_0$ is the amplitude of the vibration, and $g$ is the acceleration of
gravity. In our experiments $\Gamma\simeq 2$--$3$. The upper lid of the
cavity is made of transparent plastic so that a zenithal DSLR
camera aligned along the cavity axis
can record the time evolution of the particles.
The cavity was carefully aligned with the horizontal by using a highly
sensitive bubble level. Vibration of the system
was induced by connecting the container to an electromagnetic
shaker, which allows for the frequency $\nu$ and effective amplitude
$\Gamma$ to be controlled. This is extremely
important as the behaviour of the monolayer depends on these two parameters.
Their values were chosen in order to avoid undesired nonequilibrium effects
such as collective motion or creation of holes.

Particle identification (of position and orientation)
is done using a {\sc Matlab}$^{\textregistered}$ code implemented by the authors. The code locates
the centre of each particle and the angle between the long axis of the
particle and a reference $x$ axis. Distortion due to the curvature effects
is negligible since the camera is at a long distance from the
cavity and works at relatively long focal distance. Uniform illumination of
the cavity is achieved by placing light diffusers surrounding the experiment.
The identification software is very successful as typically only between 1--3\% of
the particles are not correctly identified.

In each experiment the protocol used was the following. First the initial configuration
is prepared by hand: the upper lid of the cavity is removed, and cylinders are placed
on the lower surface, avoiding any overlaps. Then the cavity is covered by the lid and the
packing fraction estimated by taking a picture of the static system and using the identification software.
In case the target density is not achieved particles are removed or added
according to the difference between actual and target packing fractions.
Images are taken typically every 15 s, and experiments are run for several hours. In all cases
the system gets readily ordered after the experiment is started,
but a completely stable (in the steady-state sense) regime is attained only after an hour or more.

\section{Analysis}
\label{analysis}

Previous work on a similar experimental setup \cite{us}
obtained different types of particle arrangements, depending mainly
on the packing density of the system: I, where particles are disordered in both
orientations and positions; N$_t$, where particles show fluid behaviour but are oriented on average
along two equivalent, perpendicular directions; and smectic (S), with particles forming fluid layers.

Each of these configurations can be identified by means of a number of order parameters.
In this case, we define three order parameters. On the one hand, two orientational order parameters:
\begin{eqnarray}
q_n=\left<\cos{n\theta}\right>\hspace{0.4cm}\hbox{with}\hspace{0.4cm}n=2,4,
\end{eqnarray}
which probe two- and four-fold symmetries, respectively uniaxial and tetratic
symmetries.
$\theta$ is the angle between the long axis of a particle and the local alignment
direction $\hat{\bm n}$ (local director). On the other hand, we define the smectic order parameter as
\begin{eqnarray}
q_s=\left<e^{i{\bm q}\cdot{\bm r}}\right>
\end{eqnarray}
(the meaning of the brackets is defined below).
Here ${\bm r}$ is the position of a particle, and ${\bm q}$ a wavevector compatible with the
cylinder length (in fact a little larger to allow for smectic layer fluctuations). Both these
vectors are referred to the frame defined by the local director.
One essential characteristic of our order-parameter-based description is that $q_2, q_4, q_s$ are
not defined as local fields at a point ${\bm r}$, but on each particle. This is similar to the
Eulerian versus Lagrangian views of the flow field of a fluid. The advantage of this approach is
that visualisation of order in separate configurations is much easier. On the other hand, our
`Lagrangian' approach also allows to obtain average values over the whole cavity in the steady state.

For the definition of all three order parameters the local director
$\hat{\bm n}$ on each particle is required.
This is obtained by first defining a circular region $C$ of radius $\xi=4L$ centred at each particle,
and then calculating the $2\times 2$ tensor
\begin{eqnarray}
	Q=\left<2\hat{\bm e}_k\hat{\bm e}_k^T-I\right>=
\frac{1}{M}\sum_{k=1}^M\left(2\hat{\bm e}_k\hat{\bm e}_k^T-I\right),
\end{eqnarray}
which defines the average $\left<\cdots\right>$.
Here $\hat{\bm e}_k$ is the unit column vector along the long axis of
particle $k$, the sum in $k$ extends over all $M$
particles whose centres of mass
are contained in the region $C$, and $I$ is the $2\times 2$ identity matrix. The eigenvector
of $Q$ associated with the largest eigenvalue defines the local director
$\hat{\bm n}$ on the particle.

Now local configurations can be identified as follows:
\begin{itemize}
\item I: $q_2\sim q_4\simeq 0$ and $q_s\simeq 0$
\item N$_u$: $q_2\simeq q_4$ and $q_s\simeq 0$
\item N$_t$: $q_2\ll q_4$ and $q_s\simeq 0$
\item S: $q_2\agt q_4$ and $q_s>0$
\end{itemize}
An essential property of the steady states of this system is that, except at low packing fractions
(a regime which is not explored in detail in the present work), the values of the order
parameters are not the same, not even of the same order, in different regions of the cavity.
Note that, in our experiments for $\kappa=4$, extended uniaxial nematic configurations are not
formed for any value of aspect ratio.

The local order parameters represent a powerful tool to identify the ordering in the cavity
in space and also in time. In practice we analyse all images taken by the acquisition system,
identifying particles and calculating the three order parameters on each particle. Correspondingly,
three sequences of images are produced, which are colour-coded according to the value of the
order parameter. Examples are shown in Fig. \ref{fig2}, with each
row representing a different order--parameter field.
The processed images are piled up to produce videos, which are very helpful
to visualise the ordering dynamics, particle motion and evolution of defected structures in the system.
In addition to these order parameters, we have also defined a number of distribution functions
for the defects inside the cavity, which will be explained in the following section.

\section{Results}
\label{Results}

We have investigated four different systems: no obstacle, `0', small obstacle, `1' (1 cm in diameter), intermediate obstacle, `2' (2 cm in diameter),
and large obstacle, `4' (4 cm in diameter).
These labels are used in Fig. \ref{fig2}.
Several experiments with different packing fraction in each case were considered. However, we
concentrate on comparing cases with approximately the same packing fractions and different
obstacle size. The reason is that the interesting density window is relatively narrow:
(i) for $\eta\alt 0.70$ the tetratic phase is not well developed in the cavity, and therefore
defects are not well-defined entities along the whole
time span of the experiments; and (ii) systems with
$\eta>0.75$ are very difficult to prepare manually due to the high density. Therefore, we focus on
systems with $\eta\simeq 0.75$, for which a well structured tetratic configuration
is developed.

First, a comment on the wall orientation of the particles is in order. Density-functional theory
applied on the equilibrium hard-rectangle model (with the restricted-orientation approximation)
has shown \cite{Yuri} that the preferred orientation of rectangles close to a flat wall is planar,
i.e.  with the long particle axes aligned preferentially parallel to the wall.
This is the most sensible result on theoretical grounds based on packing considerations.
However, as the wall gets curved, planar packing may be less efficient and, for a radius of
curvature larger but of the same order as the particle length, perpendicular alignment
may be more optimal. This change of behaviour has not been proved to occur yet, either
theoretically or by simulation. Given the parameter values used in our experiments,
we seem to be far from this situation.
Notwithstanding this, one cannot discard perpendicular alignment in the
vibrated granular rods, since strong nonequilibrium phenomena such as non-uniform granular
temperature distributions (with granular temperature defined in terms of average horizontal
kinetic energy)
may be more important than simple packing effects, leading to different alignments.
Although in most of the experiments to be presented below
planar alignment obtains, perpendicular orientation has indeed been observed in a few
cases; rationalization of this result and the investigation of its origin
would require more systematic studies (not performed in this work).

\subsection{No obstacle: circular cavity}

This system was studied previously \cite{Mueller,us1,GP}, and is
here reanalysed as a reference case (note that the experiment was slightly redesigned
with respect to that of Refs. \cite{us1,GP}; in particular, the cavity is slightly bigger).
In this section we also define some other quantities that will be used in the
other cases.
Fig. \ref{fig2}, column 0, shows a typical configuration in the steady state. All three order parameters
are shown. The high value of the $q_4$ order parameter in a large fraction
of the area, together with the low value of $q_2$ and $q_s$, point to the
formation of a large domain of tetratic symmetry. In addition, there are four regions
where all three order parameters are depleted, corresponding to regions
where particles are orientationally disordered. These regions are `point'
defects which restore the global symmetry of the tetratic phase. As discussed
previously, this symmetry is broken by the circular cavity, whose symmetry is incompatible
with the four--fold symmetry of the tetratic phase. The defects are located
at the corners of a square, and are `point--like' in the sense that
their associated depleted region is confined to a region (the `core'
of the defect) of finite area. This tetratic configuration with
four defects still forces some distortion of the local tetratic directors
close to the walls between contiguous defects, but the distortion is
assimilated by the system through the accummulation of `elastic free
energy', without producing additional defective regions.

The position of the four defects fluctuates in time, in a manner that will
be described below. However, they always stay close to the cavity wall.
In the frame of equilibrium elastic theory, this would be explained by the existence
of an effective repulsive interaction between the defects. They interact as if they were points particles,
the interaction being mediated by the intervening,
tetratic phase. The interactions can be modelled in terms of logarithmic repulsions, which are explained by elastic theory. The fact that these interactions
are reasonably pairwise and isotropic (i.e. they only depend on distance between pairs
of defects) explains the square configuration for the defects.
Interactions are transmitted through the tetratic medium because
of the stiffness coefficient $K$ of the medium: despite being fluid, the tetratic material
is elastic with respect to local distortion of their (locally perpendicular)
directors. $K$ is the only factor that contributes to the strength of the repulsive interaction. Since it
is expected to increase with density, the medium should
become increasingly stiff as the packing fraction of the tetratic medium
gets larger. Indeed this is clearly seen in the experiments by simple visual inspection
(not shown here). The dynamics of the
defects can in fact be assimilated to that of four point-like interacting Brownian particles
(which fluctuate due to the presence of the faster-moving granular particles).
These Brownian particles interact through the repulsive logarithmic
force which depends on the
stiffness coefficient $K$. Details can be found in Ref. \cite{GP}.

In our experiments, defects were identified and located as follows. First, from the $q_4$ map,
which associates a value of $q_4$ to each granular particle, we select
those particles with an order parameter $q_4<0.4$. This criterion is
sufficient to isolate separate clusters in the system, which will be
potential candidates for the point-like defects. In effect, on most occasions
only four regions are found (otherwise the configuration is discarded), as can be seen in Fig. \ref{fig2}.
The centre of mass of particles that belong to a given isolated cluster is taken
as the defect location.

Typically, in the course of the experiments, the system is prone to
developing a global rotation, which closely corresponds to a rigid rotation.
However, this rotation does not follow a temporal pattern and resembles
a chaotic motion in time, both in amplitude and in the direction of rotation.
In order to eliminate this rotation and extract the inherent fluctuations
of the defects, we define an instantaneous reference frame where the
average azimuthal position of the defects is constant. Motion of the
defects with respect to this frame should then contain the inherent fluctuations of the
defects. In the remainder of this article it should be understood that
all results are defined in this average reference frame.

In Ref. \cite{GP} it proved useful to characterise the motion of the defects
in terms of distribution functions. We also adopt this approach here and define two functions:
\begin{itemize}
\item $f_1(r)$. This is the {\it radial function}, which gives
the spatial distribution of the defects with respect to their distance $r$
from the centre of the cavity.
\item $f_2(s)$. This is the {\it inter-defect function}, which gives
the distribution with respect to the relative distance between two
defects $s$.
\end{itemize}
Both functions are averaged over time. $f_1(r)$ is further averaged
over the four defects, while $f_2(s)$ is averaged over distinct pairs of
defects. $r$ and $s$ are conveniently scaled by the cavity radius $R$. Since
defects are mostly located close to the cavity wall, one expects that
$f_1(r)$ presents a maximum at a radial distance $r/R\alt 1$, while the
square-like arrangement of the four defects gives rise to
two peaks in $f_2(s)$, associated with the distance between first
neighbours (along the sides of an imaginary square) and second neighbours
(along the square diagonal), with the two distances having a ratio $\sqrt{2}$.
Analysis of these two functions allows for a proper evaluation of the
excursions of the defects inside the cavity and the fluctuations of their
spatial arrangement which, in general and as mentioned before, we expect
it to have a square geometry on average. Since $f_1(r)$ is more informative
than $f_2(s)$ in the case of the annuli, we only report results on the radial
function.

\begin{figure}
\begin{center}
\includegraphics[width=0.9\linewidth,angle=0]{Figure2.pdf}
\caption{\label{distort} Schematic of the director field of
a tetratic configuration inside an annulus. The local orientation of
the directors $\hat{\bm n}$ and $\hat{\bm m}$ is indicated at four
particular locations. The system is invariant under the local symmetry
operations $\hat{\bm n}\to -\hat{\bm n}$ and
$\hat{\bm m}\to -\hat{\bm m}$. Continuous lines represent director
field lines.}
\end{center}
\end{figure}

\subsection{Annuli}

Having discussed the reference system, where no central obstacle is introduced
in the cavity, we now turn to the annular cavities.
The topology of the annulus is different from that
of the disc, and in fact is fully compatible with that of the tetratic
phase. Therefore, we should not expect the presence of defects in the cavity
but simply a tangentially distorted tetratic phase, with the two locally perpendicular
directors $\hat{\bm n}$ and $\hat{\bm m}$
showing splay ($\hat{\bm n}$,
the one pointing in the radial direction) and bend ($\hat{\bm m}$,
the one along the azimuthal direction) deformations, respectively.
Note that the system is invariant under the symmetry
operations $\hat{\bm n}\to -\hat{\bm n}$ and
$\hat{\bm m}\to -\hat{\bm m}$.
See Fig. \ref{distort} for a schematic representation of a distorted
tetratic directors inside an annulus; distortion avoids the excitation of
defects because the condition of parallel orientation at the boundary
is perfectly fulfilled without compromising the global symmetry of the system.

Topological arguments were successful in explaining the global properties
of the cavity in the case where no obstacle is present.
However, even though topological arguments preclude the existence of defects
in the annular cavity, things are more complicated. A central problem is
the finite size of the system. Topology assumes the existence of a continuous
field (the director field), except at point-like regions where the field
is not defined, and states the conditions under which singularities
should occur and the number and characteristics of these singularities.
Another assumption is the {\it strong boundary condition} at the walls,
i.e. the fact that the director field has to be oriented as dictated by
the wall, with no relaxing or free-energy penalty condition.
This assumption may not be valid in real situations.

To understand this point more clearly, let us introduce the typical lengths of
our system: $L$, the particle length; $R$, the radius
of the cavity; and $R_{\rm obs}$, the radius of the central obstacle.
The continuous field assumption rests on the conditions $R\gg L$ and
$R_{\rm obs}\gg L$. While the first condition is probably fulfilled in our experiments,
which have $R/L=17.5$ (and the success of topological arguments in the no-obstacle
case strongly supports this), in the case of the small obstacle we have $R_{\rm obs}=0.5$ cm
and consequently $R_{\rm obs}/L=1.25$.
The perimeter of the central
obstacle is covered by only $\sim 2\pi R_{\rm obs}/L\sim 8$ particles
forming an octagon.
Certainly, the continuum approximation breaks down, and topological
arguments may not be valid in this case.
For the other obstacles we have $R_{\rm obs}/L=2.5$ and $5$, still too small for the continuum approximation to be valid.

The results for the granular system confined in annuli, in comparison
with the reference case with no obstacle,
can be inferred very clearly from the order-parameter maps, Fig. \ref{fig2}.
In this figure typical particle configurations with
the value of the order parameters superimposed are shown.
The column labelled 1 corresponds to the
small obstacle. At first sight, from the $q_4$ map, we may think that the
four defects, already analysed in the obstacle-free cavity,
are still present. Indeed, from the $q_4$ maps for the other cases with
increasing obstacle size, we can draw the same conclusion: spatially
limited regions with a depleted tetratic order parameter are clearly
excited. The arguments taken from topology are apparently not valid
which, at the end of the day, is not a far-reaching conclusion
as the conditions for the continuum approximation are not fulfilled
by any of the experiments using an annular cavity.

There are, however, important differences between the circular and annular
cavities. If we forget about topology which, as discussed above, may not be valid
to explain the results, we may regard the obstacle
as a perturbation to the tetratic field weakening
the long-range interaction between defects, especially
second-neighbour defects (those
located along the diagonal of the square defined by the four defects).
As a consequence, we might expect to see larger
fluctuations in the defect positions:
excursions of the defects away from
the wall and into the bulk of the cavity will be longer, while the
integrity of the defects as point-like particles will remain intact.
However, this effect is not very clear
when comparing the $q_4$ maps as we move from experiment 1 to
experiment 4.

\begin{figure}
\begin{center}
\includegraphics[width=0.90\linewidth,angle=0]{Figure3.png}
\caption{\label{fig4} Radial distribution of defect positions for
(a) no obstacle, (b) obstacles of diameter $d=1$, (c) $d=2$ and
(d) $d=4$. Shaded areas indicate regions that cannot be explored by the
defects (central obstacle at left and region outside cavity at right).}
\end{center}
\end{figure}

The key idea
comes from a combined interpretation of all three order-parameter
fields. The $q_2$ maps show a clear-cut qualitative
difference between the obstacle-free
case and the rest. In the first case, the order parameter is low, except
for localised, very dynamic regions, which correspond to the
excitation of local uniaxial order, associated with smectic order.
These local structures are short-lived and decay quite rapidly.
However, in the annular experiments, the $q_2$ maps exhibit
very apparent and persistent structures with a high value of $q_2$.
On the one hand, there are large regions
where the $q_2$ order parameter is depleted. The remarkable
thing is that both regions (with high and low values of $q_2$)
are \textit{spatially complementary}:
The order parameters are indicating the presence of a
cross-shaped structure consisting of `bridges', oriented at relative
angles of $90^{\circ}$, which connect the wall of the container with
the wall of the central obstacle.
One of these bridges can be seen in column 4 of Fig. \ref{fig2}.
In between these bridges, regions
with a high value of the $q_2$ order parameter are created. By
looking at the $q_4$ and $q_s$ maps in each case, we can reach the
conclusion that these four regions correspond to stable smectic
domains. These structures are very robust and persistent in time,
the more so as the size of the central obstacle becomes larger.

The comparison between the different order-parameter maps not
only provides a hint about the structure of the regions in between
the cross-shaped bridges, but also the structure inside the bridges.
This structure is complex. Close to the cavity walls both $q_2$ and $q_4$
are depleted, which indicates that particles are orientationally
disordered (isotropic region); this is reminiscent of the no-obstacle
situation. But as we move away from this wall towards the central
obstacle and along the radial direction, we see that the $q_2$
order parameter remains depleted. The conclusion is that these
bridges are actually \textit{domain walls} that separate the
smectic regions and have a complex structure: isotropic close to the
cavity wall and tetratic close to the obstacle wall. In some cases
bridges can be seen in the $q_4$ map as well.
We can think of this structure as {\it point-like defects embedded in a
tetratic domain wall}.
Note that the smectic regions also
behave as domain walls for these tetratic regions, and as a
consequence particles can easily accommodate
in a tetratic configuration close to the obstacle, despite its
large curvature (only a small length of the obstacle wall is
covered by particles with tetratic ordering).

Let us discuss the structure of the point defects within the domain walls by
looking at quantities that go beyond the order-parameter maps. The results that
follow will not only corroborate the evidence collected from these maps, but
will also help quantify the structure. We start with the
radial functions $f_1(r)$, the histogram of which is shown in Fig. \ref{fig4}.
In this and all the other histograms shown in the following,
error bars were not included since the number of defects
is small and, as a consequence, statistics is rather poor.
Panel (a) of \ref{fig4} shows the reference case, with no obstacle.
We can see that the distribution is quite broad,
spanning approximately half the available radial distance. As indicated
in \cite{GP} (which corresponds to a different experiment on a slightly
smaller cavity) the radial distribution seems to be bimodal, with two
typical distances: one at $r/R=0.85$ and another at $0.65$. As advanced
in \cite{GP}, this bimodality might be caused by the layered structure
formed by the rods close to the wall, which pushes the defects away from
the wall at a distance that depends on the orientation of the rods and
the number of layers. The opposing effect coming from defect repulsion
competes with the wall repulsion and may give rise to a bistable
position. Although the surface structure at the wall has not been
investigated carefully, it is observed that it is quite dynamic.
In panel (b) we plot the results for the situation with the small obstacle.
In this case the bimodality disappears and the distribution is broader,
exhibiting a long tail towards the cavity centre which indicates the
tendency of the point defects to explore larger radial distances within
the tetratic domain walls. The effect is more pronounced as the obstacle becomes bigger.
\\
\begin{figure}
\begin{center}
\includegraphics[width=0.70\linewidth,angle=90]{Figure4.pdf}
\caption{\label{fig5} Histogram of the number of defects, $n_c$ inside the
cavity (for clusters larger than five rods)
for all the cases explored.
Note that the horizontal axis has been displaced in each case. Labels
on the top indicate the diameter of the obstacle in cm.}
\end{center}
\end{figure}
\\
Another interesting quantity is the histogram of the number
of defects in the cavity, Fig. \ref{fig5}.
Only defects formed by clusters of more than five particles have been
included in the calculation to avoid clusters that simply represent
local fluctuations and are not related to fully developed defects that
participate in the global interactions inside the cavity.
Clearly, in the no-obstacle case, in most configurations one finds four
defects, and only a few times are more or less than four defects
excited inside the cavity. However, when the small obstacle is present,
it is more likely to find more than four defects, which means that
defect interactions have been weakened and the restrictions imposed by
topology are relaxed.
The figure also indicates that the number of defected regions becomes larger
as the obstacle size increases.

\begin{figure}
\begin{center}
\includegraphics[width=1.20\linewidth,angle=90]{Figure5.pdf}
\caption{\label{fig6} Distribution of number of rods $n_r$ in clusters containing more than five rods.
From top to bottom: no obstacle, and obstacles of small, intermediate and
large size. Labels indicate the diameter of the obstacle in cm.}
\end{center}
\end{figure}

We have also calculated the distribution of the size of the defects
(number of rods belonging to the defect cluster). Fig. \ref{fig6}
shows the distribution of clusters with a size larger than five rods.
The peaks of the distribution in the circular and annular cavities
occur at sizes that increase slightly, but the distribution gets broader
as the obstacle becomes larger, indicating that the defects
are slightly larger on average when the obstacle perturbs the tetratic
field. Also of importance is the shape of the defects. When there is
no obstacle, defects are not completely circular because they are
close to the wall and therefore in an anisotropic environment. The presence
of a central obstacle amplifies this effect, as we presently show.
In Fig. \ref{fig7} the distribution in $a$ and $b$, the two principal
lengths of all clusters larger than five rods, are
shown. Both lengths are normalised with the radius of the cavity $R$.
These lengths have been obtained by diagonalising the moment of
inertia tensor calculated from all rods that belong to a given cluster
(assigning a unit mass to the rods), and then taking the square root.
We can see that, as the size of the central obstacle increases,
the two lengths get more different, meaning that the defects become
more elongated. From the corresponding eigenvectors it is inferred that
the direction along which the long size of the clusters points changes
from azimuthal (no obstacle) to radial (towards the cavity centre, in the
case of the 2 and 4 obstacles; these results are not shown).
One obvious explanation is that point defects are now confined into thin
domain walls, becoming elongated along the radial direction.

In the case of the large obstacle the distribution associated to
the long axis gets broader and in fact the probability that the defect
spans the whole radial distance (from the obstacle to the wall, meaning that
the whole domain wall becomes disordered) increases
dramatically. By contrast, the short axis remains more localised.
This means that very frequently the defects
connect the inner and the outer boundaries of the cavity
by a bridge. Inspection of the videos (not shown) confirms this scenario which,
as already mentioned, becomes more evident as the size of the central obstacle
becomes larger.

\begin{figure}
\begin{center}
\includegraphics[width=0.95\linewidth,angle=90]{Figure6.pdf}
\caption{\label{fig7} Distribution of principal lengths of the defects $a$
and $b$. From top to bottom: no obstacle, and obstacles of small, intermediate
and large size. Red: long axis; green: short axis.
Labels indicate the diameter of the obstacle in cm.}
\end{center}
\end{figure}

Fig. \ref{fig8} shows the distribution of the
ratio between the two principal lengths, $\epsilon=b/a$.
As the obstacle gets larger, the distribution
in $\epsilon$ becomes broader, with the mean value of $\epsilon$
increasing from $\sim 0.30$ to $\sim 0.45$.

\begin{figure}
\begin{center}
\includegraphics[width=0.95\linewidth,angle=90]{Figure7.pdf}
\caption{\label{fig8} Distribution of the ratio $\epsilon=b/a$
of small-to-large defect length.
Labels indicate the diameter of the obstacle in cm.}
\end{center}
\end{figure}

Finally, Fig. \ref{fig9} shows a schematic diagram showing the structure of the domain walls
in the annulus. S regions are separated by domain walls consisting of N$_t$ and
I, defective regions. This structure can be deduced from the order-parameter
maps of Fig. \ref{fig2}. The point-like defects are reminiscent of the structure in an obstacle-free cavity.
It seems that point-like defects are easily formed due to the high tendency of the system to develop
orientational order, either uniaxial (smectic) or tetratic. In turn, tetratic regions are developed
in the radial segment of the point-like defects to avoid distortion of the smectic layers.
Note that the regions close to the obstacle wall in each smectic domains usually tend to be tetratic,
especially in the case of the smaller obstacles since curvature is too large to support
bent smectic layers (see Fig. \ref{fig2}).

Despite the presence of the obstacle, which forces
the particles to dramatically rearrange into a complex structure,
the dynamics can still be interpreted in terms of point defects
(isotropic regions) that interact at distance. Clearly the obstacle
will tend to weaken the long-range interaction, but the now smectic
(instead of tetratic) regions between nearest-neighbour defects
will certainly reinforce the repulsive interaction. The reason is that
in this case the interaction is mostly mediated by smectic layers, in the
direction perpendicular to the layers. Since smectic phases have
a small compresibility and, consequently, a large stiffness coefficient
associated to the layer periodicity, the amplitude of the logarithmic
interaction will probably be very large. Defects still stay close to
the cavity wall because of the overall strong inter-defect repulsion.

\section{Discussion and conclusions}
\label{Conclusions}

We have performed vibration experiments
on monolayers of cylindrical rods confined into annular cavities, in the hope
to see radical changes in the steady-state patterns with respect to similar
experiments with circular cavities. These changes are suggested by the
application of topological arguments which imply that four point-like
defects should be created in circular cavities, while no defects are expected
in the annuli since the phase symmetry should not be compromised in this case,
i.e. no geometrical frustration should exist. Our results for the annular
cavities do not conform to topological requirements. However, this is not surprising given
the reduced size of the cavity, and in particular of the central obstacle,
compared with the length of the cylinders: the continuum approximation based
on a smoothly distorted tetratic field is not valid. If the size of the obstacle
is of the order of a few particle lengths, arguments based on topology
make no sense and other considerations are needed to explain the phenomenology.
As soon as the tetratic field is disrupted by the presence of a central
obstacle, regardless of its size,
the system is divided up into regions arranged in the azimuthal direction
as successive patterns. These patterns consist of: (i) regions with smectic order and
(ii) regions with tetratic order containing point-like defects where the order is
absent. The latter regions are reminiscent of the point-like defects observed in
the systems with no central obstacle. These structures tend to migrate slightly towards the central
obstacle and their shape becomes more elongated, due to their more anisotropic environment, with
respect to the obstacle-free case.

\begin{figure}
\begin{center}
\includegraphics[width=0.80\linewidth,angle=0]{Figure8.png}
\caption{\label{fig9} Schematic diagram showing the structure of domain walls (shaded) in
the circular annulus. Smectic (S) regions are separated by domain walls consisting of tetratic (T) regions
and isotropic (I), defective regions. Dashed lines separate regions close to the inner wall
where the type of order, either smectic or tetratic, depends on the obstacle size.}
\end{center}
\end{figure}

In the annular experiments point-like defects close to the outer wall are readily created,
which indicates that these structures are very stable. This is because
interdefect interactions are probably quite strong, despite the presence of the obstacle.
But the high curvature of the central obstacle makes it impossible for the tetratic field
to accommodate in the central area as a distorted field. Instead, the field breaks up
into azimuthally distinct regions which connect radially with the point defects. These
structures can be viewed as domain walls separating the smectic regions. Smectic layers
are arranged with layers along the radial directions. Despite the fact
that, rigorously speaking, smectic layers cannot get distorted in a bending deformation
because of the high energy price entailed in bending the layers (which would cause a
nonuniform layer spacing along the radial direction), smectic regions of limited size can
be stabilised in the annulus. The number of these regions is invariably equal to four in our
experiments.
This number may result from a balance between available space, curvature of the inner wall,
and layer stiffness (akin to the layer compressibility in an equilibrium smectic material).
Larger systems with reduced and more similar curvatures in both walls might lead to
different number of smectic regions along the azimuthal direction. However at some point,
as the curvature gets small enough and particle length becomes negligible with respect to
inverse curvature, we expect the situation predicted by topology to be restored, namely
the presence of a uniform smectic or tetratic state without any defects or domain walls.

At present, for lack of a proper theory for vibrated granular particles,
we can only especulate on the physics behind the phenomena described.
As discussed in the introduction, computer simulations based on
equilibrium Monte Carlo methods have been useful in the past to discuss the phenomenology
of vibrated monolayers. For the present annular systems direct simulations of an
equivalent system do not exist. Therefore, it would be interesting to analyse this
system using equilibrium simulation techniques, which would help elucidate the nonequilibrium
origin or otherwise of the structures observed in the present work. Interestingly,
G{\^a}rlea et al. \cite{Mulder} have observed similar structures in systems of virus
particles confined into circular cavities and in annular cavities. Their system is
different in that (i) virus particles have a high length to width ratio, meaning that
their stable liquid-crystalline phase is a uniaxial nematic phase, and (ii) the ratio
of inner and outer wall radii is larger. In this case domains of nematic order with
different orientation separated
by domain walls are observed. Accompanying simulations that try to mimic the experimental
system were also presented. In this case structures with increasing numbers of domains are
observed as the size of the central obstacle is increased and the two wall curvatures
become more similar.

Even though the system explored by G{\^a}rlea et al. \cite{Mulder}
is in a different range of length
parameters, and the nature of the orientational ordering is simpler, the main result
is qualitatively similar: the presence of ordered domains induced by reduced space and
geometrical frustration of the parameter order.
In our case, however, the structure of the domain walls seems to be far more complex.
In particular, the existence of point-like defects with an orientationally disordered
structure inside the domain walls
cannot be explained. It would seem that the breaking up of the system into
domain walls with alternating smectic and tetratic regions is sufficient to absorb
the high elastic energy imposed by the boundary of the central obstacle on
the director field.
Clearly in this system
the alternation of spatially ordered and disordered phases is necessary to
accommodate the interfaces associated to domain walls. But the structure of the tetratic domain
walls remains unexplained: there is no reason a priori to break the tetratic field inside
a given domain wall, close to the outer boundary, in the form of a point-like defect,
since the curvature of this boundary is low and there should be no symmetry conflicts.
This fine structure of the tetratic domain walls may be a genuinely nonequilibrium
effect of vibrated monolayers, with point-like defects less prone to distabilise
by the imposed annular symmetry than in equilibrium  systems, or it may be simply
the result of the different symmetry of the order parameter and the richer `bulk' phase
diagram with more phases, one of them spatially nonuniform, competing in the same
region. As already discussed, future simulations of equivalent equilibrium systems may
give hints in this respect.

\acknowledgements

Financial support under grant FIS2017-86007-C3-1-P
from Ministerio de Econom\'{\i}a, Industria y Competitividad (MINECO) of Spain,
and PGC2018-096606-B-100 from Agencia Estatal de Investigaci\'on-Ministerio de Ciencia e Innovaci\'on of Spain,
is acknowledged. We also gratefully acknowledge technical assistance by F. Borondo.

redpajama_set_name: RedPajamaArXiv


text:
Three sentenced to jail for skipping Philly jury duty
Tom MacDonald
Philadelphia court officials are cracking down on those who ignore summons to serve as jurors. Three scofflaws were sentenced Wednesday to a day in jail and fines for skipping jury duty.
People have been ducking jury duty for years in Philadelphia, but now three scofflaws have spent time behind bars as officials rolled out the first phase of a crackdown.
Too many people were regarding a jury duty summons as a mere suggestion, said Rich McSorley, deputy court administrator.
"Last year, we sent out a total of 596,477 questionnaires, and 219,000 of those didn't even respond to us," he said. "Out of those who did respond to us, only 13.8 percent showed up."
So McSorley sent out officers to escort some of the worst offenders to court Wednesday.
"Our warrant unit went out that morning and arrested three people and brought them in," he said. "Those people were taken in front of the judge and had a contempt hearing. Two of them pleaded guilty, and they were sentenced to a day in jail and given a $300 fine."
"One person wanted to fight the case" he continued. "She was found guilty, sentenced to a day in jail and given a $400 fine."
The crackdown is not over, McSorley warned, suggesting that if you have an outstanding summons you should resolve it before you are hauled into court.
Bidens pack carrots, apples into boxes during Philabundance stop
Before heading to the warehouse floor where conveyor belts carried cardboard boxes full of donated food, Biden said the child tax credit needed to be renewed.
6abc
Showers, Wind Advisory follow winter storm in Philly region
As the storm departs on Monday, there will be some leftover rain and snow showers, along with high winds.
PennDOT announces vehicle restrictions due to winter storm
The snow will transition into freezing rain and sleet before changing into a steady rain.
About Tom MacDonald
@TMacDonaldWHYY tmacdonald@whyy.org

redpajama_set_name: RedPajamaCommonCrawl