All right, you ready to do this, co-host? Oh, I'm ready, co-host. Let's light it up this Monday morning. All right, then. Welcome to the Educator Rising Voices podcast, where we amplify the voices of young professionals in higher education. I'm Wes Johnson, and I'm joined by the amazing. Sarah Buska. All right, and today first, Sarah, how are you doing? I am doing so well today, Wes, and the topic of today's conversation, I feel, is so apropos because we're coming off of a holiday weekend. Things get it. So I'm feeling great. I've been away from work for four days. So life is good. It's great to see you this Monday morning. How about you? How are you doing? So the feeling's mutual, great to see you. Still got a case of the Mondays, no matter how long I've been away. I still, it still feels like a Monday, but feeling good also after the break, looking forward to the next break, where I got it set up to be a little bit longer Thanksgiving, because I'm very much in need of the recharge this year. It's been a busy year. It's been a very busy year. Well, no. I feel like my brain is still somewhere in July. I don't know what happened. I don't know how it's December this month or this week. It's just, it's crazy. I don't know. I feel like ever since pandemic times, each year since 2020, I feel like it's just been better, just even more so than we've, you know, had historically. And I always find myself at this time of year feeling like, how did all of that happen in such a short amount of time, even though it's the same calendar time? Ain't that the truth? Yeah. I start my weeks by looking at my list, my to-do list, which is a bit of like my wish list more than my actual to-do list on whether I get it done or not. But I was looking at it and just how many things I had marked as December. I'm like, okay, but I got to December. It's like, oh yeah, okay. December next week, all right. Yeah. I feel that. I feel that. All this work on our plate and talks a break, I guess it makes this a very timely topic for us, which is why recharge is important and how to reconnect and reintegrate after the holidays. I can definitely preach on why recharge is important. So maybe we'll start there. I'm actually very interested in the reintegrating part because I feel like that's just a bunch of walking in the dark until I get back into my pace. So I'm very interested in that plug. Let's start with why recharge is important. I'll tell you now for me personally, kind of what you were speaking on since COVID, but it feels like IT's been speeding up for forever and whatever they were doing with 30 years ago, we're at a much faster pace now because we've automated the thing that they were dealing with, right? And to be able to, like we're always problem solving because that's what we're fixed to do, at least in the IT, the technology space. We're fixed to problem solve. So we're always jumping from one thing to the next to the next. And I just can't keep up if I don't completely separate from the process. I think to recharge one, of course, it helps me have time for my family, have time for myself, but also gives me a moment to remember why the heck I'm even coming into this, eight to five to begin with. When you get caught up in the work, at least for me, I lose sight of that. I'm just going from problem to problem, forgetting sometimes forget the bigger picture of why I even come in today, why we're here, why these jobs exist. So it's nice to just step away and be able to look at it for a sec, not touch it. Just look at it for a sec. Just look in the distance. Yeah, just gotta look out and say, you know what I mean? So what about you? Those are, I mean, I love what you're saying, Wes, and it's so true. I think what I was hearing a lot from your comments are on perspective, right? And just being able to recognize that ourselves and in work and in our work bubble are not the only places where we exist. And we need to take a step back and see yourselves outside of that space, but also see ourselves in other spaces as well and make sure we're setting time for that. And I think a lot about, you know, when I was an undergrad, this was a wool, wool over a decade ago, but I remember some advice I got my freshman year from my Russian professor. It was more like a mentor and a friend to me who I still talk to this day, but I remember I was studying for my first Russian exam. It was so hard. I had never taken Russian before. I had no idea what I was getting myself into. I just thought it was cool and wanted to sign up for it. So there I am. It was awesome, but it was hard. It was very hard. And I remember my first exam, I was studying and I was thinking, okay, I'm gonna pull an all matter. I'm just gonna stay up and just pack all of this into my brain and keep going until I just can memorize basically every page, every verb conjugation, every vocabulary, you know, all of that. And I was telling my professor the strategy and he was just looking at me and smiling and nodding. And I have to give him credit to this day. He let me go on and on about how I was going to memorize everything when he could have just cut me off.  And he's like, I can tell you, you will not pass. And he's like, just go to sleep. Just go to sleep. Just get a good night's rest. Just relax.  And I had never pulled an all matter. Never in my college career, even though I was a grad student, well over a decade later, we'll never do it. I always prioritize sleep. And that kind of just woke me up. But I think it's something that we all implicitly know and are aware of. But sometimes we just don't make the time for it and we don't really prioritize it. And it's not so simple to get some sleep, but it's something that I think is a skill to learn. Just like recharging is a skill to learn. Just like happiness is a skill to learn. Yeah, and I think about that often. Even when I'm convinced I'm in grad school to stay up and finish my work.  Yeah, what a great professor. And I'd say there's also a lesson in that in like the, it sounds like the professor was kind of setting up an environment to say, hey, look, that whole all nighter thing is not gonna work.  But I'm telling you, I don't think that's gonna work.  If you've been doing what you've been supposed to been doing this whole class, I think you'll be good to go. It's kind of what I'm teasing out in there. And that's very similar in our roles, right? Like I hope that I set an example with my staff and my teams to take advantage of time taking off. And I know that some of that can be as much cultural as it is like individualized. But to your point, it's also learned. Like you have to get, some of us have to get comfortable with even saying like, hey, I'm gonna be, for lack of a better term, selfish this week. I'm not gonna, I'm not checking. I'm not gonna be very easy to contact. No, I'm not gonna be problem solving this week, at least not here. I got some other things that I wanna prioritize for the next week. And it's not here this week, I'm taking my time. And that could be quite the space to be in sometimes, especially when you have a large amount of people depending on whether it's direct report lines or a project you're leading or just a process that you know you're the most knowledgeable about. Yeah, yeah, it's so true. And what I'm hearing you say in another thing, I think is a really essential skill for all of us to learn, especially during the time of holidays when we want to disconnect and then later reconnect is how we state boundaries and how we hold them. And I think those are two very different things and require different skill sets, right? It's one thing to say to our teams, say to our staff, say to our leaders, I'm not available during this time. I have been taking vacation, right? Or I'm celebrating my anniversary, what have you? For whatever reason, if you're saying I'm not available, that's one thing. But if you're contacted when you're not available in response, well, you're not holding your boundary and you're just teaching that person that you are available. You know, and that is something I think is a true skill too, because I think a lot of us, myself included, sometimes struggle with that guilt, right?  You know, being folks in IT, we love to do that, right? It's almost like this like adrenaline-pinching experience to just solve a problem and fix something. But if we've said that, hey, I'm out of office, or even I'm just taking a personal day, thick of day, what have you, then take it. You're not at that point being held accountable and the only person who's holding you accountable to that is you, to show up when you've said you're not going to be available. Yeah, absolutely, you know, there was a lesson I learned from a previous leader, his name's Mike Lucas, when we were at the University of Georgia and I was working the help desk at the time. And I was one of those folks, we just got the help desk kind of running smoothly at the time and we didn't, you know, we didn't want that to stop. And so I had none of us, me or my team had taken much time off over a good one, two year period, just trying to get everything going. And Mike Lucas, who was our CTO at the time, he came to me and he actually, if I was like, hey man, holiday's coming up, you know, I think just want to encourage you and your staff, take advantage of the time, whatever, and I was just like, yeah, yeah, yeah, whatever, you know, I got some stuff I need to get done. So I might just take advantage of the quiet time, like we all like to say. And he stopped and he looked at me, he said, look Wes, I get it, cause you know, things are going good and you and your team should be proud of that. This university's been here a very long time, Wes, both before you, it'll be here after you. And there's been a lot of stuff that's broken along the way, yet the university's still here. Just remember that, as you think about it, you should be in for that extra few days to get that little bit more work done. You know, the university will be here regardless, I think you're good.  Right, right, and I can't- It's yeah, it will still be here when you get back, I promise. And if it's gone, it's not because of what you knew, I promise you, it's not. It's not, you can't forget you're there. That's such a good point.  I actually, I want to touch on something, because you mentioned the help desk and I started my technology career working in a help desk. So I have a very special spot in my heart and respect for folks who work in a help desk, just because I think we all know who've been in it, at least, how much of a grueling role it can be, just being front lines, working with folks directly who are calling because something's wrong, right? They're upset and typically those folks who are dealing with, you know, hundreds of calls a day of just really upset people. I'm saying new things, right? And, you know, and that's an essential service, right? It's something that even if there's a holiday, even if there is a break, those services don't stop just because there's a holiday or a break. It's a freight train moving, you know, hundreds of miles an hour and it needs to run to support the university. And so I just want to kind of call this out because I want to tease this apart a little bit on the show because those folks in those positions, sometimes they can't take off, right? Sometimes they don't have the luxury of taking two weeks off, three weeks off. Sometimes they need to work to support their families, right? Sometimes they just are willing to make that sacrifice to make sure that they have more money coming in if they're not in a salary position. And, you know, when we're thinking about recharge and how you kind of disconnect, if you really can't maybe physically leave work or physically take that time off, how do you do that, right? How do you find that respite or that recharge when you still have to come and show up? Do you have any recommendations? Yeah, that's always one of the challenges in the, at least in the frontline areas likely and some others, but I know frontline feels that a lot. One is, you know, the typical times a year to take off on the only times is the thing I used to do at my staff, like, sure, we might have to cover during the Thanksgiving or the New Year's and we rotate on who can, we keep track of who's here this year, but some people, like you said, they'd rather work and get the time.  I mean, sometimes, you know, it gets to some of your own individual values, I think you do, like for some people, you know, you pick a certain field, a certain job and in my personal opinion, there are certain sacrifices that come with anything you choose to do and say, if you choose to go into IT and your past start, sorry, is at the help desk, then I think it's best to have an understanding of, okay, here's the sacrifices that come with that. If this help desk is 24 seven through holidays, then that means that the typical times I expect to be off, I may not be able to get off, but what can I do to adjust if I still value this time for myself and then work around that, but then I still keep in mind that if it crosses the line, then maybe there's another field or another place, not every help desk is 24 seven. I've worked this song where we did get the holidays off. So, you know, there's a lot that goes into that and I don't want to hog the whole episode. Some of it's individualized, some of it is just, you know, take advantage of other times that are slow and I'd say the leaders, like particularly those who are in management are those that run, you know, you understand the business, I hope, you know, you advocate and push for your staff to take advantage of the times that you know they can take advantage of, even if it means they can't take a month off, like maybe some of their faculty partners or some of their other individuals who have that advantage in their role, they are, take it when you can. What about you? What are your thoughts on that? I first, I just want to say, I think those are great comments and I really love how you're framing it from, you know, an individual lens and there's things that are under your control and your agency and that you are responsible for. And then there's of course, you know, the situation and the role and the company, the organization, what have you. You know, there's responsibility there as well, it's shared, it's not on one entirely or the other entirely, it's shared and I think it's all of our responsibilities as workers, as leaders, as managers to know how to advocate for ourselves, for our roles, for our university, for our team and how to negotiate and compromise, right? I mean, I think there's so many of us and maybe we learned, at least I learned this a lot during the pandemic is think up and flow, you know? Even if you started the year off by saying, we will do X, Y and Z, while a global pandemic comes up and well, you kind of have to throw that out of the window. So how are you going to adapt and reframe and recognize that, hey, maybe we need to take a step back a little bit and give everyone some time off? But we also are expecting folks, if they're working in front lines, like you said, help Jess, maybe there's something that they need to be working on too and taking some agency and accountability for. Like you said, if they had a realization that that's not their role, that's okay, right? I think so many of us maybe have felt that or are feeling that now and I think it's okay to say, hey, this isn't for me or this isn't working out or I don't feel like I'm getting recharged in the way that I should, because I think if we really are in a role that we like, we may not like all the tasks that we do, but we should be getting recharged or at least fueled in getting some wins in ourselves from the work that we're doing, if we're really enjoying it, if it's aligning with our skills and our personality and our career goals and all those types of things. So I think it's multifaceted, right? But I do think that individual component is huge.   Those little things, I used to do that when I worked in the help desk all the time, I would take 15 of the breaks when I could and just go for a walk outside. And it was so helpful, just kind of profiting everything, getting exposed to nature, getting that perspective. And I think that's a really, I think helpful tool to remember that we all have to be intentional in practicing that. And it doesn't mean you have to go and like, spend a lot of money and join some fancy gym and all that kind of stuff. It is within grass, if you're willing to to make the time for it and to at least bring folks along who you care and love about to help hold you accountable too. Yeah, absolutely, definitely a double one down on the walks, we used to, I used to do that also. I still do it today, but not as much with this new kind of COVID work environment, I guess post COVID work environment. You do wear wops at home. Oh, ain't that the truth? Yeah, so I walk, start the coffee, you forget about the coffee at the thing. Usually my walk. But yeah, I used to walk a whole lot on campus, particularly around this time of year. It's a beautiful time if you're out east and some other areas too, but I know back home, east and south, it's a very beautiful time of year to go walk your campuses. Also gave me perspective where mommy is this big place that we support and help solve problems, solve for. So I definitely just want to double up on the walks. I used to tell my staff all the time, hey, every 10 minutes on the hour, get away from the desk. I don't care if you just walk to the back of the building or take a walk outside, stop looking at that screen for 10 minutes every hour, please. That's all right, let's please save our eyeball. Yeah. Let's see, so going up next, I think we had a couple more pieces of feedback. So have something to put on your mind when you're away other than work. I think you kind of spoke on that, but are there hobbies that you do outside of work? I have a couple actors here, but what about you, Sarah, are there things that you do when you do get that down time for you? Yes, I do, I can't wait to hear your hobbies. I think I know some already. Actually, I think two of our hobbies might align. So I'm curious to see what it plays out. But one hobby I love, and I've been doing this since I was in second grade, it's been a long time, I play violin. And I've been just playing for so long in orchestra by myself with friends, just to kind of the whole Shimura's board, if you will. And right before the pandemic, I was playing when I was working at the University of Wisconsin, playing in the University of Wisconsin Chamber Orchestra. And I was loving it. I was fully committed. I was spending way too many hours a week with it, which was good and bad for different reasons. But when the pandemic hit, that's when everything shut down. So I couldn't play with the orchestra anymore. And it was something where I was thinking, okay, well, what's keeping me playing this, is that the orchestra is because I really, really like it, because at this point, I'm busy with the career, all these other things. And I still kept playing. And I did many little orchestra concerts and playing sessions like on Instagram and all that kind of stuff for months, just playing by myself. And I still, I still am playing, even though I'm in grad school now, I don't have as much time, but I still play just not for the orchestra. And that's one thing I think that's always been very important to me and just an escape and just a way that I can kind of focus my mind in a different way is through music. And I know that's for you too. Oh yeah, yeah. Want to do a mash-up? Yeah, we should, yeah. We should. We could add you to the intro, Sarah. Yeah. Although I think our intro for this show is really awesome, thanks to you. For folks in the audience who may not know, Wes created our intro music. So that's why it sounds so cool. Thank you for that, yeah. Speaking of, I do do music. That is a big one. I rap and produce. And so I was actually writing some songs a little bit this weekend, just for the fun of it. I think the trap that I've sometimes fallen in is because music was my first love. And go back 10, 15 years, I was gonna be a rap star, none of this high teen stuff. Who was gonna work at nine to five?  That's what I was gonna do, or at least a big time producer. Life didn't necessarily work out that way, but it kind of put me at this line of, is music a hobby or is it my other job? And I haven't quite landed on the answers to that question, and I go back and forth on what that is. So really the lesson in the tale is, it's helpful to know what that hobby truly is, because it can easily turn into work too, which is happening to me. But it doesn't have the same recharge effect once you go rap for it. But the music definitely, I like getting lost in it. I do, sometimes during my lunch breaks, I'll make a couple beats as fast as I can, and then throw it up on my Instagram or something. So definitely music, but also enjoy just hikes. So I go on a lot of hikes, so being in the Bay Area, I'm getting to explore a bunch of new hikes that I've never seen before, and it's very beautiful out here in this state. So I've been exploring a good bit on that, and it's just real cool to, when you get to one of the hikes you're trying to go to, to realize that you're just kind of out there, probably don't have say a reception. Yeah. Unreachable, oh no. Yeah, right, right. It's a beautiful thing. So me and the family do that a good bit too. Yeah, that's really good. I have to say, so even though I'm at Stanford, and you're technically our enemy in Berkeley, I have to say, I love Berkeley's campus, the Botanical Gardens there, I've gotten lost there, just wandering around, spending time there. The views are just incredible. That Redwood Grove is just whimsical and magical, and I feel like I'm literally spirited away when I go there, and it's amazing. So that's another hobby of mine too. We have the same hobbies, music and like getting outside. Yeah, yeah. Who knew? I don't know. The co-host. All right. I like the vibes here. See, who got us folks? Get outside and play some music, your recharge. There you go. I have a buddy that, I can't remember his name, I can't think of his name right now, but he also does production. And one of the things he does, he currently lives, I think like out in Tokyo or something like that. And he'll go on hikes and then do a video of him producing or doing some beat at like the point of the hype. So there's been a couple where he's like sitting on a mountain edge in the youth lane or something. Blending the tear together, I like that. Yeah, yeah, yeah. I'm not quite that blended yet. I don't really care all the year. Actually, this is quick 30 seconds story during the pandemic. I think we all might remember this, 2020, like March, April timeframe, people were all, you know, quarantining or in their homes kind of stuck, right? And there were so many people going out on balconies and playing their instruments. And I was living in downtown Madison at the time. And I did that. I went out on my balcony, played my violin. I played Hallelujah. You know, it's kind of like a Melancholy song, but I think we were all feeling that at the time. And it was just, it was so interesting because there was kind of this like cacophony of people who kind of poked their heads out and then also started playing whatever their instrument was or stinging along or something. It was just in this really small and accurate era, probably only a handful of people actually heard, but it was just kind of fun. It was just a liberating thing to like just go outside and play your instrument. So I don't know, maybe that's our homework. Maybe that's our new level of recharging less. Yeah, so I caution y'all, maybe there was a little bit of COVID effect. I can also see a scenario where you go out there playing your instrument downtown and they're just like, hey, stop, I'm working. I feel like now I feel like I'm gonna get yelled at and people are gonna be like, I'm good, you know, but then I don't know, people were like, okay, this is incredible. So we talked a good bit about things we can do, hobbies that we've done outside, making like blocking time to take time, but what about like once you've got that time, right? So you're in your hobby, what have we done to your point earlier about making sure folks know that, hey, I'm not actually available for your daily operation and stuff, I'm away, I've took it some time for myself. What's some stuff that you've done to make yourself unavailable? One thing I've learned is if I know that there's something where I'm the single point of failure, if you will, or the only person who knows something, before I leave, I make sure I write down whatever it is that someone might need to know and I work with my boss and or members of my team directly and say, hey, if this comes up when I'm out, here's what you need to know. Here's the history, here's the situation, here's some of the background, this is kind of what's been happening and background information that you need to know, names of people, what the project is, things like that, maybe some history if there is anything to share. Here's my, right now, my current assessment of the situation, what I think is happening, what might come up and here's my recommendation, if something does come up, what to do? And almost like somewhat of a decision tree, like if it does come up and it's not urgent and you can wait until they come back, do nothing, just let me handle it, make sure you make me aware, right? But if it is something where you've tried all these steps that I've outlined and you've gone through everything and it's still not looking good, then you can contact me or then you can contact my boss's boss or something like that. It's a little framework I call an SBAR because I highlight a situation background, assessment and recommendation and it's literally only supposed to be one page or less, right? I mean, it could be one sentence for each, but it really helps someone readily orient themselves to what's going on and to be able to take some type of action. And sometimes an action is just telling whomever is reaching out, sorry, we'll get to this next week, right? That's not an action, but it's at least acknowledging someone and saying, hey, we can't get to this today, here's one you can expect to hear back by, if not, here's what to do. And I found that that, and not even only for unplugging and leaving work, but that communication tool for any type of communication is so helpful. So that would be a recommendation, I think to this podcast and our listeners, it's to try that out, try highlighting a situation background assessment and recommendation the next time, some problem or challenge comes into your lab as a way to communicate to your boss or your leaders for what to do. But another thing that I like to do is to make sure that I let the people I'm working with know before I leave, especially if I'm anticipating something coming up, hey, I'll be out here so you can talk to. So just proactively telling them that and then telling them when I'll be back and telling them that I will be away and giving them an email or contact for someone else and letting them know, hey, if this is a true emergency, here's who you contact. And that helps a lot too, because most folks understand most folks are reasonable, right?  Do not contact me, that's what I've done. And you know, it's fair and people get that, right? People are reasonable, no one's going to do that. And I would be thankful. You didn't take your laptop to the wedding? What do you mean? Oh, no. No, I didn't and I took my email off my phone, everything and to be fair, my team was amazing. I had just had a new teammate start. He had been in their role for maybe like a week or two and was already reaching out, trying to like get all these things off my plate and help me out. And you know, it was just this wonderful camaraderie and making sure that I didn't pick up any new projects when I knew I would be out for a month, which I was out for a solid month. So, you know, it's things like that too. It's being strategic. Like you said earlier, like your individual agency I think is really important and I think that shows like leaderful skills when you're thinking ahead and say, you know, for me, I left in March and if my boss or someone came to me and said, hey, we need to do this project, I may or may not volunteer for that. I'll try to negotiate, you know, what my level of commitment looks like and what I start and what the expectations are knowing that I will be gone for a month. And I think that helps a lot too. But I'll stop there because I'm curious what you think. Yeah, no, those are great at, within Berkeley IT, we actually have a process very similar in regards to when you were mentioning like naming who to contact for this. They have a process that all of us, as part of the executive leadership team have to do, we have to go into this document, put the dates and then name who our backup is. And then if there is an emergency, like is there any way to contact you? There's been a couple of times like, nope, I'm hiking in the mountains. You won't be able to contact me at all during this period of time. So there's been stuff like that that we do and I do similar within my teams. We all share our calendar, et cetera, et cetera. But speaking of, so something I've noticed, I'll be curious after I share if you've seen the same is as I've moved up into work, what constitutes as an emergency becomes more and more great. Like it's really not always clear when you're starting to be like a leader of directors and their managers and their staff. Like it becomes a little more blurry on what that emergency is. It's very unlikely to be just some specific, like this X stopped working, West, what do I do? It's usually like X stopped working and has broken these other downstream systems, West, how do we want to communicate while I'm out in Malibu or something? I don't know. I don't know. I don't know, figure it out. Bye. It gets a little challenging. At least in my personal experience, the more I've moved up that balance because it does feel like there's a expectation as you move up where you're a little bit more available in some of these scenarios versus where when someone's more individual, contributor focus, it's more, at least in my experience, more tied to like the specific service or system. And so the scope of the problems tend to be a little bit more narrow. So I have found some struggles in my, I've only been in this role for a couple of years now, some struggles in knowing when to jump in. So a lot of it comes back now to my own view on things as an individual with a sense of the team, right? You got to keep the team in mind too. But I have found that the biggest thing for me as far as keeping myself as free as possible when I do take time is that's really set that time long before the time comes to actually take time off. Like the way back to what we were discussing earlier, the way that I've supported other folks taking their time off, they'll hear me and me. I've all individually joined meetings because they thought the meeting was super important. But it was the day, the first day they decided to take off for the week. And I kicked them out the meeting, not to be rude, but to just... You're holding boundaries. Yeah, yeah, I'm off to do that with you. And part of it is to make sure they understand like, hey, look, I appreciate you being here, but you don't have to be here. We scheduled the meeting on a time when you were out. So we made a decision that we could still have this meeting without you or we'll cancel it. So part of it is that. And then the other part of it is, so when I don't show up to meetings, when I'm out for a week, it shouldn't be a surprise to you because I don't support anybody doing that. Yeah, yeah, exactly. Yeah, great point. You kicking someone out of a meeting. Yeah, it's been a, it's been surprisingly more than I thought I'd have to do in my career. I thought most folks were more like automatically, like, yeah, whatever's on the calendar, I'm not coming, but there's been a few times where I've had individuals that show up for, you know, in their defense, they were trying to support, they, you know, they were the ones that were most knowledgeable about something. So they just wanted to make sure it was successful. But no, I kicked them out and just say, look, if we weren't successful at this meeting, we'll schedule another one or, you know, shame on us for not canceling it. We'll do it. Right, right. It's all a learning experience. And when you're bringing this up, I have a few thoughts that what came to my mind initially was Fria Parker's book, The Art of Gathering. And I know she was the keynote speaker at the Edge of Cause annual conference last year in Denver. And I just thought it was amazing that she was there because what I read her book a few years ago, and it really helped inform a lot of my wedding planning, actually. And there was a passage that she has in that book where she talks about your responsibility for your guests, for people in your meeting, you know, is to make sure that they're protected, right? And they're having a good time that they're set up for success, all of those things. And if you just open the floodgates and let everyone and everything end, well, you're not doing your job, you know, stewarding that meeting in a leader or someone hosting a wedding, right? If you're just letting the floodgates open and just letting everything happen and hoping that it'll be okay, right? Hope is not a plan. And what I learned from Fria Parker in her book is it's actually your responsibility to be able to make those decisions and to be able to stand up for what you want and to recognize your role in that, right? And if you think that adding one person to a meeting may or may not help or bringing one person to your wedding might spoil it for the rest of the folks. Well, if you have 300 people going to your wedding and one person you're worried about, well, why would you bring that one person who could potentially spoil the time of 300 people? You know, but it's a hard thing to do. It's a hard thing to stand your ground and to say no. But sometimes saying no is the kindest thing we can do. Not only for ourselves, but for those 300 guests, for those folks in your meeting, but also for the person themselves, right? Because if they're on vacation and coming into a meeting, well, chances are they probably don't have good reception, right? Probably don't have what they need in front of them to be effective, right? They have all these other things in their head. It's like no one's set up for success at that point. And the only thing that that's going to do is have that person coming to the meeting without the right things that they need, maybe fail. You know, as a leader, it's our responsibility to make sure that they're set up for success. And if we feel like we can have this meeting without you, then we can have this meeting without you.  And it's not that we don't think you don't care. It's just that we need to move this forward. And, you know, it's a hard thing to think about because I grew up in the Midwest. I'm Midwest, like modest, nice, to a tee. And it's something that when I was raised, it was everyone to have to be included, be nice to everybody, invite everybody and everybody's welcome, right? And I think I had to realize that there's a distinction between that mentality being welcoming and hospitable and also being respectful and caring. And they aren't necessarily mutually exclusive, but you are being respectful and caring and welcoming if you do close the door on certain people and certain things in specific occasions or places.  If you didn't have a good time, the likelihood of being successful in any of the situations is probably low. So, yeah, so I think about that a lot and I think it's a really good thing to do that. And back to your comment actually about what an emergency is. I love this, I love this one because when I was working at the University of Wisconsin, my previous role was to lead a team who was responsible for critical infrastructure services. So, fixed life and health safety services, one of them was the door access system for campus. So, that included all doors on the university's campus and the hospital. So, this is in the thousands. And one of the challenges with that system is, if it goes down, well, people could be trapped, right? People could be stuck in places even though the doors should fail open, right? For safety reasons, sometimes things happen, right? And there is always a lot of kind of fear, I think with that team I was with of the worst possible outcome happening, which is a good, I mean, it's a good thing. I think we should be aware of the likelihood of that. We should be aware of what we're up against and what challenges may come. But the likelihood of those happening, especially how great the team was, were really low. And if something did happen, it would have probably been out of the team's responsibility, right? It would have been some extreme things. We had thought of everything. We had redundant systems, separate networks. I mean, you name it, the DR plan for all of these services was just phenomenal, right? And that's the credit to the team, right? We had thought everything through. There was backups upon backups. We had a lot of funding supporting all of it. It was solid. But still, it's easy and our brains are just kind of designed to go into this, kind of doom and gloom place, right? The worst outcome possible. And when you're working with a team of 16, 20 people who focus on that all day and their primary role is to keep critical infrastructure running, well, it's very easy and, you know, it makes sense that they're thinking about those things because they're getting paid to think about them. But the challenge is like, how do we put that in perspective and context, right? And I think what worked well for us in that space is because we would literally talk about scenarios where, oh, is there blood on the floor, right?  Like, we would literally talk about that. And I know it sounds kind of like crazy because we're an IT and what does blood have to do with IT? But, you know, in that scenario, that was a potential outcome, right? And so I think from my lens, anything that doesn't have blood on the floor is not an emergency. Right. Wow. And I know that's an emergency, but I use that as a perspective all the time because there's so many things where, you know, it's like, yes, the system went down. Somebody can't get to the portal or access something, but it's typically not an emergency unless it touches like payroll or finance or like life health safety things, like everything else can wait. It really can. Yes, will there be an impact? Of course. But there is no blood on the floor from this impact. And that's how I frame it and just work backwards from there. Because my first thought always, and I think it probably will be this way for a long time, is someone hurt? If someone isn't physically hurt, it can wait. Typically in my mind, you can wait, unless like I said finance or things like that, people need to get paid, all that kind of stuff. But if someone isn't hurt, if there's no blood on the floor, I'm like, we're good, we can figure this out. You know, it's a completely different headspace. And I think folks who've worked in emergency services or anything like that might understand kind of the headspace that I'm coming from when I share that. It's not from a place of insensitivity. It's just from a place of perspective, really. Yeah, that's helpful. It's actually, I actually use my health safety colleagues as my example of non-emergencies with my non-health safety colleagues. I actually use that metaphor a part of it. Just like, well, y'all, we don't work at a hospital. So is it really an emergency? It's interesting that you actually have direct experience in that field. And so I've always wondered, what is it that you all say to make it a non-emergency? No, I know. Yeah, it's pretty much like, is there blood on the floor? No, okay, it's fine. Like, we'll figure it out. And honestly, but I also want to say, just because something isn't an emergency doesn't mean it's not, like, important or necessary work or anything like that that has nothing to do with it. And I think that's a distinction that sometimes can be blurred or confused.  You're not willing to drop everything and come and fix this. And, you know, in the grand game of things, the museum completely out, and you're outside of your department, you're outside of even the university, and you're looking at just a bigger, broader picture of the world. Like the world will continue moving and circling if we don't get to this in four hours. You know what I mean? Yeah. And I know that that's kind of an extremely, and I know I can't generalize everything, but I think that helps at least keep me calm in those scenarios because there's been many scenarios in my career and experience where shit really did hit the fan. Where it truly was an emergency. And I was up, you know, at 2 a.m. trying to figure something out, calling my deputies just at the time at 2 in the morning for something, you know. And it really was. And, you know, sometimes it's like hard to make that call in the moment, but the only thing I felt like really was my role was to remain calm and make sure everyone else felt like they had what they needed and could get it done. And maybe that's a... Maybe that's a 2 a.m. call. Yeah, I know, right? And maybe that's a future episode.  What did we do? We have one new story. We have one new story. So then I guess now we get towards the end of this, I want to ask one question, right?  We've talked about some of the fun things that we do. So we have, you know, this is going to be episode after the holiday. So let's tell folks in review, right? Your holiday season, your December is now over when January. What did you do if you don't mind sharing? What's one fun thing you did during the holidays if things go according to the syrup of master plan? Well, actually my husband and I are going to Mexico. We're going to Puerto Vallarta for Christmas. And the one thing I will be doing is laying on a beach somewhere with a pina colada and not being disturbed. I don't want to look at anyone, I want to talk to anybody. I just want to listen to music, drink my cocktail, and be by the water, and relax. That's like... Bring the viola. You want to bring it out? Actually, not in this trip. Not in this trip. But that's, you know, everything goes to plan.  And it'll be my winter break from grad school. And I won't have classes. So I will have finished 10 classes by then. I know, right? So I'm like, I'm ready just to, you know, I don't know if you've ever seen Severance, that show on Apple TV. Yeah. When I first saw that show, it was before I started grad school and how they just like separated, you know, work from non-work, just literally in like a blink of an eye, just moving out of the space. I really didn't understand that until I started grad school. Now I feel like I can do that better. And I think that's the skill too. Yeah, almost feels like the show was written by a grad student. And now I'm wondering, what's going on with you? Some days are easier than others, but sometimes I'm like, I'm just shutting this and I just can't think about anything more. Like I feel like my brain is so stuffed that there's just literally nothing else to do, but to like focus on something else or just not even think about it. And it's really hard to describe if it's a new feeling for me for sure because I've always kind of struggled with shutting that off. But I'm going to be shutting off on a beach in Mexico in a few weeks here. But what about you? That sounds very, very nice. So I will be going to a beach, but my hope is here in Oakland at the Oakland Zoo, they do a thing every year called Glofari where they light up the whole zoo in holiday lights and festive stuff. I have not seen it yet. So my hope is that we sign up for one of these nights. It's extremely hard to sign up for, but they slow down the website and put you in queues during the holiday season because they get so much activity early on in the season and then folks book it all the way out. So fingers crossed, we didn't make it last year. Fingers crossed we make it in the list this year and get to go, yeah. My fingers are crossed. It's like you're trying to get Taylor Swift tickets for the arrows to wear. Yeah, yeah, yeah. Yeah, maybe odds be over in your favor. Yeah, yeah, yeah. They're thinking it'd be this hard to go to the zoo, but here we are. I know, really, I hope that works out for you all. That sounds like it'll be fun. Yeah. Well, with that, thank you everyone. Happy holidays to you and yours, Sarah. Happy holidays to our viewers. Thank you to the whole Rising Voices podcast team for all of our work. This will be episode number, what, four? So we're four deep. We're keeping them down. We hope you all are entertained. I'm Wes Johnson and... And I'm Sarah Buska. Thank you all for listening.


I believe that God made me for a purpose, for China, but He also made me fast, and when I run, I feel His pleasure. Aside from the opening soundtrack, this is the moment that I remember most from Chariots of Fire, because this is the moment I have discovered to be true in my own life as an aspiring runner. I feel the ground beneath my feet, the breath in my lungs, the pleasure and pain of my body. I feel the connection with other runners I pass, with the trail that countless others have run before me, and countless others will run after me. When I run, I feel creativity, energy, insight, inspiration, invisible lines of connection between me and every atom in the cosmos. When I run, I feel God's pleasure.


Okay, very good morning. It is Tuesday the 9th of November. Hope you're doing well in the brief I'm going to talk about crypto where Bitcoin has surpassed 68,000 for the first time. Ether record high is the market cap of the crypto world now topping $3 trillion in the equity space alphabet as well joins the two trillion club the S&P 500 closes higher again yesterday for the 8th consecutive session and that marks the longest winning streak since 2017 we're also going to talk about why Goldman Sachs is buying distressed Chinese property debt And what they're thinking a rationale is there and then we'll also have a look at the charts in general There's some other news as well to talk about where potentially a secondary candidate to drone power for the Fed share Leo brainard has also surfaced last night as well But as per usual quick look before we get into those stories in a bit more detail at the charts this morning And it's a relatively quiet open FX markets probably reflecting that the most Both currency pairs top left euro dollar and cable relatively unchanged equity index futures Pretty much in a period of consolidation at the moment the calendar today Generally is quite light. There's not really much in a way of any major economic data You've got the German ZDW survey later at 10 a.m. This morning US PPI at 130 all different trees in the API at 9 30 But there's quite a few speakers which we'll look at coming out this afternoon Otherwise gold on the daily chart just looking fairly interesting here from a broader context from where we've been trading I mean this is looking at gold over the year to date Perspective and you can see that FM FMC markup that I've got that was that Infamous June meeting where they make that quite distinct Hawkes shift where they were talking about the increase in rate rises sooner And that was what really weighed on gold in that move But we're coming back up to the top end of the trading range that has really held prices since this Well after that move since July in the summer You can see through the period of late July and through August crossing into September That's been a key area of upside resistance and we're within Site of that at the moment trading it around those levels so something to just be aware of Otherwise then let's get straight into the news and let's talk about I'm gonna kick things off with crypto Actually, it's some pretty interesting stuff that's been happening and as I said Bitcoin has passed sixty eight thousand for the first time ether tots at four thousand eight hundred This is a look at the the general price movement You can see here Bitcoin just seeing further extensions of the breakthrough The highs that we're seeing at the end of Q1 and just a few weeks ago and from a market Capitalization point of view for the crypto space now it has momentarily crossed the three trillion dollar mark And quite phenomenal really to see you know from a timings perspective This was really that low that we saw at beginning of 2020 here was the onset of the global pandemic And it was really going through into what has been this year really year to date We broke out from a from general crypto activity Influencing then the overall market size through that peak of what we had through 2017 18 And that was through that 700 billion marker and that was really right at the beginning of the year We had some of the breakouts in in Bitcoin at the time and you can say see here Most recently we had that Retest up and around the same similar size to market that we saw in August So what we had in April of this year since then we've really seen the next leg of the move higher At the moment there are a couple of things just to talk about here Bitcoin assigned a lot of people being drawn Into the crypto space or the crypto economy for so-called decentralized Financial services as well as non fungible tokens or NFTs Which allow for digital collectibles like online art for example that's seen a massive explosion specifically this year Blockchain networks like Ethereum Solana continue to upgrade to deliver such functionality and and the nascent metaverse Which of course has been brought back to the forefront It's always been around but really accelerated through Facebook's almost Necessity to shift and accelerate its move in that direction for lots of different Reasons specific for that company, but that's again highlighted just the Dependency that an immersive online environment could create in virtual reality for further adoption of crypto currencies particular Things like ether for example Meanwhile concerns around ether's block chains scalability and high transaction fees To move parts of the markets attention to so-called Ethereum alternatives and what we've actually been seeing is tokens like Solana polka dot Terra avalanche Have all been seeing some really good games Data from blockchain data firm Keiko shows that Ethereum is actually losing Market share to other popular layer one block chains Since the beginning of the year layer one block chain is essentially a set of solutions that improves the base protocol in itself To make the overall system a lot more what more scalable And ether's trading volume on Binance the largest crypto Exchange in the world has actually been decreasing and is now around 42% from 76% in the beginning of the year Where's the lost volume shifting to those other? Layer one tokens for example, so yes, I'm really interesting things happening at the moment That's causing this kind of bullish sentiment at the moment for the crypto space not much more individual news story that's Quite funny as much as it is. I'm sure it's going to be the next kind of Ridiculous gains that we'll see from a crypto currency, but this is AMC They had their earnings last night, but away from the earnings They they're kind of share price chops around an aftermarket trade But the world's largest theater chain is exploring the creation of its own Cryptocurrency So really trying to just take advantage of the obviously retail interest that that stock has generated for some time now as part of the original kind of stocks in in play The company is also talking to Hollywood studios about creating crime commemorative non-fungible tokens So NFTs related to major films essentially So they're definitely looking to take advantage of that search and interest that that's seeing at the moment And who's to say that that doesn't take off massively particularly in NFTs related to major films Can imagine a lot of interest for people to pick up little segments of a very notorious Screen screen plays and moments from those films. So it'd be interesting to see how that plays out Just wrapping up kind of crypto into some single stock news another kind of one that came out last night was was Robin Hood their shares dropped About four percent actually finished down about three point four percent Robin Hood said personal information of millions of customers circa seven million Was compromised in a data breach last week and that the culprit demanded a payment from the firm So their shares were under pressure last night, but moving off crypto and back to the world of macro and I guess I just want to have a quick chat about the overall equity space really and let's have a look at the actual Heatmap and how things closed yesterday and as you can see Relative gains seen particularly selling conductors pretty decent based on materials financials, but overall I mean Tesla came off in the end closed down about close to five percent Remember it did gap down and hit lows down around seven and a half percent following that Elon Musk poll about selling shares But their stock price generally recovered I mean five percent is a flash in the pan compared to the 37 odd percent that they rallied in two weeks So one could argue it's a very masterful stroke from from Musk of course to Forward-guide the market towards the potential of him Offloading some shares and and we talked about that in length yesterday But one of the other stocks here was alphabet finished up just marginally point one percent But that does mean that they've breached now two trillion on a market cap valuation Fueled by rebounding spending and digital ads and we also ongoing growth in its cloud business alphabet We've said before is kind of being the real outperformer of the mega cap tech stocks It's up about 70% on the year alone and Of 49 analysts tracked by Bloomberg who cover the stock I read last night that all but one Recommend buying alphabet shares and that's even at this current state of play and the average 12 months price target for the stock is 3321 which suggests and around a 11% return from its current current share price The other thing to mention here. I don't have a preset kind of article to flash To you right now actually I might do if I go to and this is a good time to shout out the Amplify me Twitter account which I do share I'd say good 10 to 12 articles a day of kind of must-read articles relevant to what's moving markets across the macro space single stocks crypto and so on But there was one last night that I would have shared I would imagine If I just scroll back down, this is it and this is Goldman Sachs And what what the deal was here is that obviously there's still a lot of concerns about the Chinese property market at the moment But Goldman Sachs asset management came out with an interesting comment yesterday and they said they're buying Chinese real estate debt Which perhaps sounds incredibly risky But the firm says they're adding a quote modest amount of risk through high yield bonds issued by Chinese property developers and Denominated in US dollars China ever grand group Obviously has moved closer to potential default and that has created fears over the last several months about that might reverberate across the entire sector if not beyond into the domestic economy and beyond in China But from GS's point of view, they state that the market is over Estimating that contagion risk And they said an interview on late on Friday and thus therefore is creating opportunities at the moment because They see distress priced in as a significant is significantly out of alignment and hence the rationale behind why they're snapping up Some of that Chinese property debt at a good value. Some might say if you hold that view The other article of interest is this I talked about I think it was last week and it was reported in the Wall Street Journal that It was Jerome power who is having these meetings with various different politicians in on Capitol Hill and meeting with Biden and the administration now it's the time of the only real other candidate in the running Which is the Fed governor Leo Brainard who was interviewed for the top job at the US central bank when she visited the White House as well Last week. It's just emerged according to Bloomberg according to people familiar with the discussions power's current term for context comes to Exploration in February Biden said back at the beginning of the month that he'll make a decision fairly quickly most people the majority of analysts expect power to Get the job and one would suggest that either power or Brainard really would support this idea of having more of a Mindset of a measured perhaps then perceived more dovish stance of monetary policy Which is probably useful for Biden and his administration generally that that slow pace of normalization is a supportive Crutch if you like to the market More broadly speaking and and obviously management of the economy the stock market These sorts of things will have some impact towards the optics on his ability and his success of his administration Brainard and power have obviously worked together on multiple issues. She's a governor. He's the Fed chair at the moment They are viewed as holding fairly similar views The probably slight disparity is the fact that perhaps Brainard's a little bit more Little bit more serious a bit more onerous on on bank and regulation side And perhaps holds a slightly more historically dovish view Than power albeit not too dissimilar from her background point of view. She's a PhD Harvard University Seen as highly competent very experienced macroeconomists. So yeah, a credible candidate But I don't think it for me it really changes the The narrative too far away from Powell at this point But even if she did get in I'd say that's probably the smoothest transition to an alternate candidate As you're probably gonna get if we get to that point. So just as an update We did have some comments as well just pivoting off this from the Bank of England governor the un the unreliable boyfriend Of which promises the world and never comes through When it comes to crunch time Following that kind of really badly managed and poorly communicated press conference most of proceed from Bailey where you know a lack of really Acceptance of the fact that that Market pricing through none other than really his inability to clearly forward guide in an appropriate fashion He's been speaking again He said that much of the rise in inflation that has to do with the reopening after lockdown And they will have to act with rates if they see evidence of higher inflation expectations feeding into into wages so Playing into this kind of more transitory idea again So that's more in fitting and keeping with what we heard from the likes of the ECB The the Fed and so on but certainly is quite away from where we were just a few weeks ago when the market was obviously very aggressively Pricing in rate hikes with the lack of pushback that we were getting from the governor So he's got to earn his credibility back at the moment His comments then really brushed aside not really having any impact this morning Okay, so quick look to finish off. I've already talked about the data of the day So the other thing was just speakers from an ECB perspective You got ECB's not speaking 1150 Christina guard does speak but only on banking supervision a bit later on at 1 p.m And ECB Schnabel at 4 from the Fed side of things non-voting member Bullard speaks at 1250 Fed chair Powell does speak today, but just on diversity So wouldn't be expecting anything explicit on the economy or policy But he will be on at 2 p.m. London time and then Fed voting member Mary Daley speaks at 435 And that is it. So I'm gonna let you guys get on with the session. Have a good day ahead Any questions at all feel free to let me know. Otherwise, I'll see you same time tomorrow. Thanks very much


So, welcome to this lecture on multiphase flows. We saw some introductory concepts about stability analysis in the last class. Jason spoke about a 2 dimensional system and it took an example and he just worked out how you go about calculating the stability of a system. And especially if there is a parameter working you know in the system, then that parameter could be something which you can control as an experimentalist and what you want to do is you want to find out how the stability of a system changes as you vary that parameter. So, that parameter could be flow rate, it could be temperature, it could be concentration okay. So, like was mentioned in the last class, what we really have to do as far as finding stability of a system, I mean it is decided by the response to perturbations, response to disturbances right. This is defined on the basis of the response to disturbances, if you give a disturbance and if the system deviates from the steady state you say it is unstable, if it comes back to the steady state you say it is stable okay. So, if the system comes back to the steady state, the state is stable else it is unstable. So, I just wanted to emphasize again that when I am talking about stability, I am talking about stability of a state okay. Now this is what you understand in English and what we want to do is we want to develop a mathematical framework and what you got is some idea about this mathematical framework with the in the context of a system of 2 variables which are dependent only on time but not on space. So, just to keep the mathematics simple, so the example that was illustrated in the last class was that of 2 ordinary differential equations. So, you need the time dependency because whenever you are talking about stability, you are talking about response with respect to time. So, you always are talking about an unstable or an unsteady state system okay and therefore you need the time dependency to keep the math simple we made it well stirred and then you neglected the spatial variations. So, the basic idea, so whenever you want to find out the stability of system, what are the steps you need? The steps to find stability is first write the governing equations. This could be continuity equation of momentum, conservation of mass whatever it is which are going to describe the system okay. Then once you have the governing equations what is the next thing you have to do? The next thing you have to do is find the steady state okay and this will be dependent upon the problem you are considering the first step. The second thing is find the steady state okay because it is the stability of the steady state which you are interested in. So, you need to find the steady state whose stability you are talking about and then what do we do? We spoke about disturbances being given. So, what we want to do is we want to give disturbances to the steady state okay and what we do is we impose small and I say small I mean infinite symbol disturbances and here is where the order of epsilon comes in. So, these are basically of order epsilon very small disturbances and that is the connection which I want you to make with the perturbation series thing that you have seen earlier when you are trying to actually do things at order epsilon you will be neglecting higher order terms okay. So, what we want to do is we want to impose small disturbances and what this basically allows me to do is this order epsilon disturbance linearization of the governing equations. So, the original equations will typically be non-linear okay and since you are talking only about small disturbances what you will be doing is linearization that is something which you also saw you have a begin with a non-linear system and you linearize it because you are giving only small disturbances that is what you are doing you do is you do a Taylor series expansion and you need only the first order term you do not go beyond the first order term you do not take higher order terms because higher order terms will be non-linear and then we look at the growth rate of the disturbances. Now, the growth rate the disturbances growth rate growth or decay rate is given is exponential in time whether it is of the form e power lambda t and if lambda and since lambda will be some eigenvalue of some linear operator which you will see lambda it will turn out to be something like an eigenvalue if the real part of lambda is negative then it is going to decay and you have a stable system if the real part of lambda is positive it is going to grow okay. So, basically what this means is the lambdas will be say eigenvalues of a linear operator if the real part of lambda is negative the steady state is stable and if the real part of lambda is positive it is unstable there is just one subtle thing which I want to mention here that when you are doing this calculation if it turns out that the real part of lambda is positive that means even when you give a small disturbance it is unstable. So, when you give any disturbance a large disturbance it will be unstable. So, if the real part of lambda is greater than 0 you can definitely conclude that the system is unstable okay for all disturbances but if the real part of lambda is less than 0 you only know that it is stable for small disturbances but suppose you give a big disturbance it could be unstable okay. So you have to be kind of careful here. So, this is whatever I am doing here is in context of small disturbances okay. So, real part of lambda being greater than 0 is sufficient to guarantee the instability while real part of lambda is less than 0 is necessary to have stability. Let us just say that you can have the condition can be a necessary condition or a sufficient condition for something to happen. So, I am just trying to tell you the real part of lambda is greater than 0 is sufficient if it is satisfied your guarantee it is unstable that is enough you do not have to do anything else in life. If this is less than 0 you only know that the necessary condition has been satisfied it is not assuring you and you are unstable because of this thing of small disturbances you know. So, whatever stability we are going to be doing is actually going to be based on this linearized analysis. So, whatever we are going to be doing in this course is going to be based on this linearized analysis what this means is these are what are called local stability conditions okay that is only restricted to small disturbances okay. So, the stability analysis we will see in this class is based on linearization and hence local in nature as opposed to what is the other one global okay. So, whatever stability we are talking about is the local stability condition or a linearized stability condition okay. So, the analysis is called linearized stability analysis. So, it turns out these eigenvalues which are going to basically decide stability they are going to be dependent upon your operating conditions your flow rate or your temperature or your this thing concentration and as you vary the parameter these eigenvalues can actually change from having a negative real part to a positive real part the growth rate I want to use a more general term the growth rate which basically tells you how disturbances at a particular point change with time okay. They can change from decay to growth and that is the thing that we are interested in we are trying to find out this critical value when that is going to be a change in the behavior of the system okay. So, that is basically this is the mathematical framework. So, we spoke something in English now we are trying to put things in mathematical framework. So, I have given any problem you can actually work and proceed and address the question of finding the stability okay because that is the advantage of doing mathematics you can apply to any system. So, it helps you generalize things okay. So, what we will do today is work on a particular problem which is basically going to take you to a partial differential equation but it is not a flow problem okay and then we will do a flow problem later on. Because normally when you do a flow problem in a stability there is more than one equation. So, we are just going to slowly add up the complexity. So, I am going to talk about stability in a reaction diffusion system okay. So, since I belong to the chemical engineering department I need to have a chemical engineering example and one of the reasons why I am choosing this example is because I only have to deal with one variable either a concentration or temperature. So, in this case there is a concentration. So, we can see there are catalyst particles which sustain chemical reactions and most of you know that catalysts exist because you have done this in our course in chemistry what it does is it basically provides an alternative path for the reaction to take place and makes the reaction go faster okay. So, but the thing is the catalyst is usually deposited on a surface and it provides the site for the reaction to take place okay. Now, in order for you to maximize the surface area available for the reaction to occur what is normally done is that these catalysts are usually very porous okay. So, basically what I am saying is the catalysts are porous in nature and this is to maximize the surface area available for reaction okay. So, we will keep life simple and rather than talk about a spherical particle we will just say that the particle is a rectangular slab okay. So, imagine just for the sake of working with Cartesian geometry you can work with spherical coordinates. We assume one dimensional problem because I just want to illustrate some ideas dimensional problem. You see my one dimensional system which means take a rectangular slab of thickness l in the x direction extending to infinity in the y and z directions okay. So, I am just extending to infinity in the other direction. So, what this helps me do is keep my life simple that is I am just going to worry about variations in the x direction and since I am talking about a stability problem I want to worry about the time dependency as well okay. So, now I am just going to draw this lab here. Imagine so this is porous okay all kinds of pores all over the place some random network of pores will be there and this is a porous solid. So, the transport of gas assuming this is the gas reaction which takes place on the solid surface transport of gas inside the solid is going to be only by diffusion okay. There is not going to be any great velocity inside this pore. So, what I am trying to talk to you say here is that only flux we are going to transport the species inside this slab is the diffusive process okay. We are also going to keep life simple and say that there is no exothermicity and so we are talking about the temperature being constant okay. So, point is isothermal reaction okay. If we have a negligible heat of reaction diffusion is the only mechanism for transport of mass. Now you can write down the governing equations in many different ways but we will just do a shortcut in the sense you know how a species balance looks okay. You have the convective term, you have the diffusive term, you have the accumulation term and you have the generation term. So, we will just simplify things here. We just say that there is no convection it is only accumulation term. The species balance written as the partial derivative u equals okay. So, this is in some sense this is Reynolds transport theorem for you but I am doing a species balance here. I am doing it for a small infinitesimal control volume. What does this term represent? This term represents the what is this? The accumulation term okay. This is the flux okay because of only diffusion convection I am saying is not present. When we did the Navier-Stokes equation you had the convective term on the left hand side. You only had the viscous transport here. So, this is your diffusion flux. So, basically if you had your overall species balance which you must have done in earlier courses if you write it down and you drop off terms which do not exist then you will get this equation. That is the idea. I am dropping off all the velocity terms that goes off. I have diffusion only in the x direction and the y and z direction have taken it to infinity. So, I do not worry about it and this here I am just saying is my reaction kinetics. So, this kind of reaction kinetics would actually arise when you have an autocatalytic reaction okay. So, this is you are used to things like first order reaction, second order reaction. If it had been a first order reaction you would have had just u or something like that but since it is an autocatalytic reaction it is u times 1-u. So, u is basically representing something like a concentration okay. So, here u is concentration of a species. Clearly this is going to be a subject to some boundary conditions. The boundary conditions are taken as u equals 0 at x equals 0 and l. So, the thickness of the slab is l okay. The thickness of the slab is l and both the ends I am just saying u is 0. So, that is my governing equation. So, what I did is I just did my first step which is write out the governing equation for the system. So, I have a catalytic reaction which is isothermal taking place in the slab. I do not have any temperature. So, isothermal no energy balance. I only need to worry about how the concentration is changing okay. And I need to forget about velocity because there is no convection inside the porous catalyst okay. It is very negligible. So, now the next thing is we need to find a steady state right. So, for the steady state what do you do? Steady state means you need to put us as implies d by dt of us is 0 which means okay subject to. So, since I am looking at a steady state the time derivative goes off and my steady state has to satisfy this equation. So, one of the reasons why we actually chose this problem. So, the one steady state which immediately pops out is one which can be spatially uniform. If supposing you do not have any variation in the x direction okay. Supposing you do not have any variation x direction then this second derivative is going to be 0. So, that is a spatially uniform state or homogeneous state where the concentration everywhere inside my pallet is equal. So, what kind of a spatially homogeneous solution can this system have? Clearly if this is 0 then USS could be 0 or it could be 1 okay. So, if we look for a spatially homogeneous solution okay then d square USS by dx square equals 0 which implies USS times 1-USS equals 0 or USS equals 0 or 1. But then your solution should also satisfy the boundary conditions okay. So, this guy USS equal to 0 satisfies the boundary conditions whereas USS equal to 1 does not satisfy the boundary conditions. So, USS equal to 1 is not a solution. The only thing that is possible is USS equal to 0 is the only solution possible you understand. So, USS equal to 0 is the only spatially homogeneous solution okay. So, my question now is when would this the concentration inside my catalyst be spatially uniform okay. I mean this is a possible solution. So, now what are the different processes which are actually taking place inside your system? One is you have the diffusive process and one is you have the reaction process okay. So, if the diffusion is very very fast diffusion remember works to make things spatially uniform. So, basically if the diffusion is very very fast your concentration is going to become uniform whereas if the diffusion is slow you are going to have you can see a concentration gradient. But this is just English diffusion being fast and diffusion being small. What you want to do is so in relation to the rate of reaction I expect that there is if the diffusion is larger than a critical value I expect that U equal to 0 is going to be USS equal to 0 is going to be something which I can observe. Because if even if there was a disturbance diffusion is going to make it even whereas if there is a disturbance and if diffusion is very slow there will be a non uniform solution okay. So, there will be a variation of concentration inside the catalyst pellet. So, that is the question which you are trying to answer we are trying to find out whether that is some kind of what is the critical value quantitatively can I quantify this just like you were able to quantify terms of the Reynolds number 2100 okay. Can I quantify the value of this diffusion coefficient in some kind of a dimensionless group which will tell me when is this stable when is this unstable. So, that is the question okay and the reason why I talked about diffusion is because say at the end of the day whatever mathematics tells us has to be in line with whatever our physics tells us it is not that they are two completely different things as engineers we had to put mathematics and physics together okay. So, now so what I have given you is a possible solution which is spatially homogeneous which USS is equal to 0 it satisfies the differential equation satisfies the boundary condition okay and I am telling you that look this is a spatially homogeneous solution I expect the solution to be stable when diffusion is very fast as compared to reaction okay. But these are the critical threshold value which decides what is fast and what is slow and that is what mathematics will tell us okay and that is what we are going to find out by doing the linear stability analysis. So, now what we are going to do is we are going to assume okay. So, let me write this down. So, if D is large I am going to put this in you know invert commas because I want to compare that with something else which has the same units of meter square per second okay. D is large then disturbances in the concentration get smeared out we can expect spatially uniform solution to be stable okay. But D is large means what D is larger so what is the critical threshold of D above which we have stability that is the question okay and of course one should not talk in terms of D because the diffusion coefficient will depend upon your slab and all that it is good to work in dimensionless coordinates okay. It is preferable to work with dimensionless groups for having greater validity that is what I want otherwise we will say diffusion that is specific to a particular system rather than in a dimensionless group then it becomes more general okay. So, let us go to the next step. So, this is the first step write out the governing equation I wrote the I did not derive it but I mean it is okay. I think we just wrote out the steady state now we have to do the linearization right. So, I just want to mention that this corresponds to x equal to 0 here and x equals L here where that was my thickness of my slab. So, what we are going to do is look at imposing small disturbances and what do these disturbances measure they measure the deviation from the steady state okay. The disturbances basically tells you how far the system is away from the steady state. Your steady state is USS equals 0. So, now I am going to this is my disturbance variable I am just putting the tilde on top to signify as a disturbance and this tells me how far is u from the steady state. u is the actual concentration and USS is the steady state concentration in this case of course USS stands out to be 0 but you could have a problem where USS is non-zero okay. So, I mean just to keep things general I am writing it like this. So, I have u tilde written as u- USS and what I am going to ask you to remember is that this is of order epsilon this is very small okay. So, if it is of order epsilon I can I may want to specify that is of order epsilon by writing it as to explicitly show this I can write this as epsilon times u tilde equals u- USS but now u tilde will be of order 1 because epsilon u tilde is of order epsilon okay. So, this is to explicitly show that this is of order epsilon. I just want to put things in perspective with what you already done in perturbation analysis. So, now it is like saying I am seeking us USS plus epsilon u1 sorry u tilde okay.  The absence of disturbances it is equal to USS now epsilon tells you the magnitude of the disturbance that epsilon told you something about the parameter value okay. So, we write it like this and now I just have to substitute this in my differential equation okay. I need to substitute this particular form in my differential equation and since I am considering only small deviations I am going to linearize the term the only term which is nonlinear is my reaction term which has the quadratic dependency u multiplied by 1-u okay. So, let me just go back and write this equation here equals this is my equation x square maybe I should just write it here itself okay.  What I want to do is group all the terms together of order epsilon to the power 0 and of order epsilon order epsilon to the power 0 will be my base state my steady state solution order epsilon to the power 1 will be my linearized solution because I am going to basically take only the linear terms okay order epsilon to the power 0 gives the steady state and should give the steady state order epsilon to the power 1 should give the linearized equations okay. So, let us just do that. So, I have d at order epsilon to the power 0 d by dt of USS equals d d square USS by dx square plus a times USS times 1- USS that is what I get because this multiplied by this will give me epsilon term this multiplied by this gives me the 0th order term okay this not x to the okay and this is multiplied by this will give me order epsilon. So, this is my steady state solution about which I am doing the linearization okay because steady state that goes out to 0 and the solution that we are looking at is USS equal to 0 which satisfies the boundary conditions. What about the order epsilon to the power 1 term?  When I have this multiplying this I have one term and this multiplying this I have the other term the other term is order epsilon squared. So, I neglect it clearly now what I am going to do is use the information which I already have about USS just like you did your perturbation series analysis you have to use this information about the steady state being 0 and I put steady state equal to 0 and then I am fine is that okay minus yeah minus what is this?  This should be negative yeah you are right that is negative yeah now put USS equal to 0 okay and your linearized equation is d by dt of u tilde equals d times d square u tilde by dx square plus a u tilde that is your equation at order epsilon to the power 1 and what are the boundary conditions? The boundary conditions are going to be u is going to satisfy 0 0 you steady state satisfies 0 0 so u tilde also has to satisfy 0 0 at the boundary okay and u tilde equals 0 at x equals 0 comma l okay. So, this comes from the boundary condition you have to put this perturbation again in the boundary condition and get this what I want to emphasize here is whenever that is a linear equation for you because that is what we have done we have essentially done a linearization you have done this linearization using Jacobian which is what was discussed last time you can you will get the same result okay you should do that and verify for yourself. So, at order epsilon to the power 1 the equation is linear and what do I get a u tilde and u tilde equals 0 at x equals 0 comma l the other not only is it linear it is also homogeneous and I think if you do a linearization whenever you are working out a problem after doing the linearization and after looking at things at order epsilon to the power 1 if you find that your equation is not linear then something is wrong what you do god is wrong you find that there is a non-homogeneity that means something is wrong. The point I am trying to make here is that the linearized equation should always admit 0 as a solution okay. So, this linearized equation must admit 0 as a solution always. So, that is a simple check you can make now just because it admits 0 the solution does not mean you have it right but if it does not admit it is wrong okay. So, I think that is the only thing you can do. So, what I am trying to tell you is that this is a linear and homogeneous and now you know once I started off with a non-linear problem and I got a steady state I have done a linearization and now that is a linear equation I am kind of comfortably I mean my comfort zone because I know how to solve this equation using some of the things that you people have learned in your class like separation of variables okay. So, now I have a linear equation subject to homogeneous my boundary conditions also have to be homogeneous everything has to be homogeneous only then I can have this. So, this is something like an eigenvalue problem if you remember x equals lambda x x equal to 0 is always a solution. There are some values of lambda for which we have non-zero solution that is the kind of thing we are looking at here. So, 0 as a solution must always be satisfied this no matter what the parameters are and what we are trying to find out is because it is linear since it is linear we can solve this analytically. So, for example of course a linear equation is a partial differential equation. So, this is one level of complexity more than what you did yesterday. Yesterday you do not have this x square term you only have the time derivative term after linearization but you have 2 equations. Today I have only one equation but it is partial differential. When we start doing fluid flow problems it is going to be partial differential and more than one variable okay and by the way this is also very relevant to multi phase flow because I am talking about a gas in a solid. So, there are 2 phases right there is a solid and there is a gas. So, if you do not ask me how is this relevant to fluid flow it is definitely there is a fluid flowing and there is a solid particle okay. So, this is very relevant to fluid I was beginning to justify to myself that this is indeed relevant for this course and it is okay.  We will solve right now using separation of variables. So, this u is a function of x and t and what I am going to do is I am going to write seek u is a function of x and t as x of x multiply t of t okay the product of 2 functions one which depends only on x and the other which depends only on time. What we will do is we will what you normally do is you substitute this in that partial differential equation get the x dependency get the time dependency and then you will be in a position to understand by looking at the growth rate the exponential term which I spoke about earlier whether the thing is stable or unstable right. So, that is what we will do substitute this in the actually this will be u tilde in the u tilde equation what do you get x of x multiplied by t dash equals d multiplied by x double dash of x times t plus a times x of x times t of t okay. What we do now is we divide throughout by x multiplied by t okay divide by x t and what do you get t dash by t equals d times x double prime plus a x divided by x okay we just divide by x t and that is what we get. And so the classical argument that this left hand side is a function only of time the right hand side is a function only of x. So, the only way these guys can be equal is this is equal to a constant and what this basically tells me is I can solve for this ordinary differential equation which is first order in time I can solve for this ordinary differential equation which is second order in space and then hope to proceed to get my solution. So, we will do this tomorrow and we will wrap up this problem okay.