Hello everyone, my name is Swangileswanda, a female age 43, coming all the way from Zimbabwe. I've had a problem of a chronic ulcer for 33 years and I've been in and out of hospital. I had tried everything around Zimbabwe. I even went to South Africa to see vascular surgeons and they told me they can't do anything on my left leg. But I thank God to the people of Zimbabwe because they accounted me the opportunity to come to India. I came here and was admitted on the 18th, 19th. I had my procedure after undergoing all the necessary tests to prepare the team, led by my best friend, always like a father to me, because he has given me some extra years to live. After the procedure, my wound was very big. I couldn't wear shoes. I was always putting on slippers for the rest of my life, whether it's the right season or it's cold. I was always putting on slippers. Right after the procedure was done, there was the bulging, there was the laser, there was the blocking of the veins that were no longer functioning. And after all that, I did my dressing twice a week. I was putting on the lifestyle and the foliar bandage. It all worked because now my wound is closed. The color and skin of my leg has changed. It's now almost the same because it is now very black, but now it's light. And even the size of my leg, it is now almost normal. And I'm able to work and walk without any support. I'm now even feeling the flow of blood. It has really improved. I can even feel it from inside that I have some bit of relief because I have poor circulation of blood. And it was really stressing me, but I'm very happy that just for after a month, I'm fit and strong tomorrow. I'll be going back home and my family and my people from Zimbabwe are waiting for me. And I have the request that the doctor can come and share notes and have a camp in Zimbabwe and share with the doctors in Zimbabwe just to impart the knowledge and the technical know-how of how people or doctors should deal with the veins. I think it could have an impact in my country and change a lot of lives because there are a lot of people now suffering from veins and I'm very happy and excited. Thank you. Hi, so I'm Dr. Tapesh Sahu, Heading Department of Vascular Endovascular Sciences at Manipal Hospitals in Delhi and Gurgaon. So this is a very wonderful patient, Mrs. Sivangali Sivandarshi, 43-year-old female who came all the way from Zimbabwe with a non-healing wound since 33 years. That was daunting because she was not able to walk. She had a constantly oozing, weeping wound in her left ankle. The crux of the whole case is that a proper diagnosis needs to be made. It's not a pure varicose vein that we're treating. She had a deep venous partial stenosis with superficial reflux. So the whole procedure was planned. Thankfully, she had trust in us and we, percutinously without any cuts or sutures, performed an intravascular ultrasound which is done at very few centers across India, did a ballooning of her deep veins and also superficial venous system which was having reflux was identified on a Doppler and treated without any cuts. She was afraid at that time that what will happen and so much of operation, longest operation that will happen but next day she was able to walk properly and today in a month's time we have a healed wound, a healed venous ulcer on her left leg. She's going back to her country happily, all thanks to her faith and God Almighty which helped us. Thanks Manipur Hospital for all the support and all the services that we get here so that we can treat patients like this who are suffering for a long time. Thank you so much.


We will use the thermite reaction as an example of a very exothermic reaction. The thermite mixture consists of iron-3 oxide and aluminum powder. A small piece of magnesium ribbon is used as an igniter. The reaction is extremely exothermic, is an oxidation reduction reaction between the aluminum and the iron plus 3 ion. The iron plus 3 ion is reduced by the aluminum to iron metal. The reaction is so exothermic that the iron is melted and drips through the bottom of the flower pot. The melting point of iron is about 1500 degrees Celsius.


Our fourth inductee is Holly Bentz. Holly was a two-time team MVP for the women's tennis team in 1994-95 and 1997-98, despite never having played tennis before her arrival on campus. She had 18 singles and 11 doubles victories over her career. Holly Bentz Sajak, the first thing that comes to mind is a great teammate. Also a person that even if she hadn't experienced it before, she was willing to try anything. And keep in mind it was 1994 and it was our very first year of the NCAAs. And we were looking to field teams and we had 54 athletes the year before. I think that year we had 92 and so we had many athletes that we needed to fill out the minimum sports sponsorship roster. So I was looking for people to play and actually I put out a flyer saying if you didn't matter whether you had experience or not I could teach you. So Holly came to the team and first of all she was an amazing athlete. To give you an idea of the athlete that she was, she had never played tennis before prior to coming other than recreationally. And immediately in the first year she was our number one singles player and number one doubles player and she's held the number one or two singles position for the next four years. I know there's a lot of cliches about great teammate, great leader and so on. But she really was an epitome of a great teammate. She made practice fun for the coaches as well as teammates. They got together off campus and her happy go lucky slash of course attitude really made it fun to be around. Both as an administrator, coach and also her teammates. That is infectious and that is what really helped launch our tennis programs. What was also unique is at the end of her sophomore year Holly had an opportunity to transfer and I talked to her about other opportunities on campus and actually talked her into running cross country. And soon quickly became a very avid runner as well as a great tennis player. And matter of fact that experience in running at Villa Julie at that time propelled her into racing and so on post graduation. She was a really special athlete and in all my years I've been involved in 27 years of college coaching. She is one of the most unique athletes with an ability level to learn quickly, adapt quickly and she did it with such positive attitude which is a reflection of what the Dick Watts Athletic Hall of Fame is. From the class of 1998 it is my honor to welcome Holly Bence into the Dick Watts Athletics Hall of Fame. Thank you so much for that introduction.  I'm so honored to be recognized by Stevenson as a pioneering athlete who helped to build the foundation for this really incredible program. This past January my nephew came out from Atlanta to do a transfer student tour of the campus and that was the first time I'd seen the facilities in over 20 years and I was so impressed at where the school has grown to and just the level of athletics and everything but still maintaining the personal relationships with the students. It's a really incredible balance. So I'm also proud to be a member of the first NCAA Division III tennis team where I actually learned to play tennis from coach Adams. He recruited me and it was a really, really great experience. So it's been 20 years since I've been back to campus and I don't remember all of the game points or the big matches or big points or anything like that but what I do remember is just a lot of fun. We had such a special time together and so much fun. A lot of cold, freezing cold March 7 a.m. practices where I had to drive an hour each way with no classes that day and we just had so much fun and coach Adams spent so much time with me just between classes just going down to the courts and practicing and everything. So I've just been really blessed with this amazing journey full of inspiring people. I want to especially thank my parents for sending me to Villa Julie and making this opportunity possible. I was the first person in my family to ever college and graduate so that was really great they made that happen. I also want to thank my sister who you saw the picture of. We got to play doubles together and she spent a lot of time off the court as well playing tennis with me so that was really neat to have that together. And my husband is here. We actually met in computer class and I talked him into joining the men's tennis team and we got to have a really great time playing tennis together. Unfortunately he didn't get the great experience of having coach Adams as his coach but nonetheless he had fun. And lastly I want to thank one of my life mentors coach Adams who is such a special person to me. He recruited me and taught me how to play tennis. He encouraged me and instilled so much confidence in me just as a person and as an athlete and I've continued that journey the rest of my life so I've continued to stay an athlete doing all sorts of different things and I just feel like there's nothing I can't do now and I can just pick up any sport and play so it's really nice to feel that whatever I do I can be good at. So I just want to tell you one quick story. So coach Adams started it but what I want to say is we was after a game in the spring of my sophomore year and I told him I was going to transfer to Salisbury State. I said my best friends there they have sororities or fraternities and fun things that college kids want to do and I want to go to Salisbury and I had already played them in tennis so I knew I could probably get on the team somehow. So I was thinking I was really sure I was going to do this and he was like you know what just give it one more semester just see how it goes. So I was like okay alright fine I'll do that. So I took his advice and it totally changed 100% the trajectory of my life. That semester I actually ended up meeting my future husband in computer class and he's the love of my life and I wouldn't change a thing about it so I just thank you. So as I sat down and thought about what I was going to write tonight I reflected on all the experiences that Stevenson offered and I thought about all the amazing faculty and staff who are here and the personal relationships that I developed with so many people and it just created this wonderful experience that I really don't think that I could have experienced at any other university. So I want to just thank everybody and I know Chip Rouss is here and she was really fantastic. So I just want to say thank you for inducting me and for including me in this group. I'm so proud to be a pioneer and being included in this and I'm so thankful I was able to give something back to this really special institution. Thank you.


okay you guys so it's about 11 p.m. here I've let it set up for a couple hours it's still a little bit foldable so after I unmold it I'm gonna put it back in position so it's peeling off fairly easy some areas got a little thin and I can definitely see the texture of the little dots and it looks like the back of it's not that shiny so we'll have to do a spray on it to lighten it up any kind of like spray gloss should be just fine or you could like brush some resin on so this mat is gonna be reusable and I'm gonna have to clean up a couple of these edges where it overflowed but you can see that see-through and it'll look great just sitting up as a piece of decoration you know what we should do as a flag that would be cool make it an American flag can I see your light it's a little too bright for that but super sparkly we'll do another video and post it in the group and tomorrow it should be better set so we'll show it on our live feed tomorrow but I hope you guys try this out it's a very neat thing to do the resin but I definitely am gonna have to let it set up for a few more days so that it doesn't lose its shape you want to make sure that you leave it in whatever form you want it till it's full set so that's gonna be a few days because as you can see I can bend it still a little bit so we're just gonna let this set and we will see you guys tomorrow at 2 p.m. central standard United States time till then bye bye give stripper music


Hello everyone, I'm Mary Kuch, Education Manager at Moodle HQ and today we're going to be learning about how to transfer your Moodle data easily and safely. And as a Moodle admin myself, I well understand the challenges of Moodle admins if you want to connect your Moodle site to external sources such as marketing platforms or a CRM for enrolments or even an online store. And today we're going to be looking at a plugin, a free open source plugin in the Moodle plugins directory that enables you to do just that. And to tell us about it, we're going to be hearing from Miriam For who is the CEO of Midalware and Alexi Troitsky who is a developer also at Midalware. So after the presentation, do feel free to ask your questions in the chat and I will really lay them to Miriam and Alexi. So what I'm going to do now is I'm going to stop sharing my screen and I'm going to look forward to listening to Miriam, I believe first of all. Hello everyone, it's Miriam from France and I'm more than happy to do this presentation with my co-worker Alexi here. Thank you for joining us. So I'm Miriam and I am a co-CEO, I'm not alone, I'm co-CEO at Midalware. I'm also a mango addict, but this has nothing to do with our presentation. We agree on that. So guys, I would like to show you how you can then connect your data safely and your Moodle data safely using Midalware. So as you use a marketing platform, this will be our first user case. So you use a marketing platform to send emails to your speech therapist students, let's say. And as you can see here on the Moodle side, this is, you know how it works for most of you. So you have users, enrollment and course. And on the on the merchant side, you have member and list. So as you can see on the Moodle side, you have all your student information, the courses and the enrollment. To be able to send emails to a particular list, you need to create a list for each course. And with all the users of your course and send them an email, you can obviously do as many lists as you have courses actually. You can also do groups of students. Let's say you can do a group of students who are from 2020. These are the students affected by the pandemic. And you'd like to know how they're doing, where they are at in the course, or if they would like to join another course. Okay, so you can ask them all these informations. So by connecting your marketing platform to Moodle, you basically making your life much easier, because you can make your life easier, because you'll be using an automation system to send emails to your students. And according to their needs, this is also a great way to take care of your relationships with those students. I hope I made myself clear. But if not, we'll have, as Mary said, a question session where you can ask us anything at the end of the presentation. So a second case scenario. And on this case, we have, we want to connect Moodle to a CRM. Let's say you would like your CRM to manage all the enrollments of your students, your student statistics, course, module, completion, and everything concerning your students progression to be sent back to CRM to follow, to track your students activities, which can be any CRM, you're using Salesforce, CRM, Sugar, CRM. We are open to any CRM actually. So let's say we have Stephen Jackson, he's a student and he's enrolled in a pharmacy degree. And student Jackson, you have everything you need on the student, the user enrollment, we've seen that earlier. And on the, at the bottom, you also have activities, course, badges, and on the CRM side, as you can see, you have a few, a few modules. So we've added, so we have Stephen Jackson, and he is, you want to know where he is at with his science course, or if he gets a badge after completing the chemistry course. So by using Moodleware, the CRM here on the left side, we'll handle all the contacts, all the contacts. And this contacts, you want them to be users in Moodleware. So your courses in Moodleware are then considered products in the CRM. And in your CRM, which will be a hotspot of Salesforce as we choose to, these two for this presentation. And Moodleware can help you to connect your CRM. And each time you link a contact to a product, it creates an enrollment, as you can see here. The user will then be enrolled in the Moodle course. And every activity in Moodleware will be sent back into the CRM. This is made possible through the web service technology. And you can have more information on this particular technology we are using at the end of the presentation. Again, please don't be shy to ask. So this means basically that if you have an academic admin or any student relationship manager, who these are the people who are actually in touch with the students on a daily basis, they don't actually need an access to Moodleware to track on the student activities. Every piece of information they need will be automatically synchronized into the CRM. Our third user case, in our third user case, you want to connect your Moodle to an online store. Let's say you are a training organization and you have a range of courses available on your website, available to buy on the website. So let's see, you have this new customer, Jen Smith. She is Jen Smith and Jen Smith wants to take an engineer course with you. So this customer will be a user in Moodle and all the products in your online store are sent as courses in Moodle. This way, every time a customer buys a product, as you say, as we said, she's an engineer student, every time a student buys a product, he's enrolled automatically in the right course. This student will then receive an email from Moodle, giving him all the credentials he needs to connect to Moodle and attend the courses. So this means that you can sell your courses online and your client will have access to the courses that they bought from you without you having to do anything. This is the joy of automation, actually. So now I will hand it over to my colleague, Alexi, and he will show you what Moodle looks like from the inside. Okay, thank you very much, Miriam. So if everybody can now look at my screen, we're going to look at your typical situation. You have a customer in PrestoShop, and we're going to use Mr. Henry Cavill here, and Mr. Henry Cavill wants to learn French. Luckily, in our catalogue of PrestoShop, we have a French course right here, and so we're going to see exactly how it's going to go. All of that process is going to be inserted into Moodleware. So we start by looking at Mr. Henry Cavill. We see that he has an idea of eight, and all of that information is going to be set. We go into Moodle, and so far we can see that Mr. Cavill is not in Moodle. We go into Moodleware. This is an actual web app, so it's not in the cloud. You actually need to go and log in inside of it. When you go into Moodleware, you have a set of rules, and these are the rules that are going to interest us. The rules are the bridge, the process that connects your source solution here, PrestoShop, and your target solution here, Moodle. Now, you see, we're going to manually activate these rules today for the purpose of the presentation, but keep in mind that, as Miriam said, every single thing is automated. The rules are going to be activated at the regularity of your desire, and they're all going to send all the information automatically. So if you wanted to activate the rules, we would have little switches like that, and then the process would start immediately. Now, we're going to manually go into one of the rules. We're going to start by sending Henry Cavill into Moodle. So we have the rule here, and that's for the user. It gets the users from PrestoShop and send them into Moodle. How it works is that it uses drag and drop fields, and you can take the fields from the list on the left. You drag and drop them into the target fields in the squares on the right, and you also see, if you look at the username, you have little formulas that allow us to customize and filter the information in any way we want. For instance, here, what's going to happen is that since for the username in Moodle, it needs to be in lowercase, we have a little formula here that is going to automatically take the first name and the last name of the PrestoShop user and put them in the right format for Moodle. Now that this is good, we're going to simply run the rule, and once we started, we can follow the progress of the rule, and here, for instance, we can see that the document was properly sent to Moodle. We can go into its detail, and we have three parts. We have the source. This is how the source was interpreted by Metalware. This is how it comes from PrestoShop. Then in the middle, you have the target. This is how the information will look like on Moodle, and then the history on the right. This is if you want to update the information and not create new information. If you want to compare, let's say Henry Cavill wants to change his name to John. On the right, it will be written Henry, and in the middle, it will be the new name John. Now that this is good, we can look at Moodle, and when we refresh the page, we see that we have one more user, and we see that Henry Cavill is here in Moodle. That was the first part. Now we actually need to get the French class because it's not in Moodle either. So if you look at our products, we have the French course here, and if we look at the rule for the courses, we're going to do exactly the same thing. You see that we have also some peels here with the full name of the course, the short name, the summary, and the category. We run the rule, and then we go to the Moodle section of the courses. Again, we see that the document was properly sent, and when we update, we can see that there is now the French course in Moodle. Now, all we need to do is refresh our, is an order the course on the side of Henry. He needs to buy the course in order to be able to enroll in Moodle. We select Henry, and then we select the French class, the product, and we select Moodle. Now that we have our order here, all we have to do is to run the rule that connects the orders. It's good. Finally, we run the rule that handles all of the remaining information. It takes the resulting info from the other rules, and then it sends it as an enrollment to Moodle. Once all of that is done, we can see here that we have, if we look at the target ID here, 45 is the idea, respectively of the user, the course, and the rule. Now, if we go to see our French class, and if we go to see the enroll the users, we can see that we have Henry to be able to. So we did exactly what we wanted. We had a customer in PrestoShop with a product, and it transformed into a user who was enrolled into a course on Moodle. Thank you for your attention. Thank you, Alexie. Thank you. Next, we'll see then, as Alexie showed you, you can don't, sorry, that's very French, you can actually connect your apps with using my order. Not only two apps, you can connect a few apps together. Let's say you have your Moodle, you have an online store, like PrestoShop, CRM, or you might even use two CRMs, and my order can enable multi-connectivity. We are open to lots of apps, and we are willing to do some custom made also connectivities for you as well. So these are a few apps that are actually connected to MyDorel, but we have many more to come, and we can do more according to your needs. So who we are at MyDorel? MyDorel is a free open source software, just like Moodle. Our aim is to facilitate data synchronization and integration between systems. We actually started with working for charity, and as this charity grew bigger, we grew with them. So why is a My in MyDorel? Some people don't really know how to pronounce it. We are also confused, but we'll get there. Because it's yours, you can actually make MyDorel your own by customizing it to your very needs. So as I already said, MyDorel is free and open source. So if you want to have a look at MyDorel and see how it works for you, you can download MyDorel. It works the exact same way as Moodle. We also have an amazing community on GitHub. You can go and ask your questions from people and people who are actually using MyDorel already. We'll be more than happy to answer. We're also there. The team is also there. You have to install the plugin. This is very important, because even if MyDorel is a proper app with his own database, it won't work if you don't connect it using a plugin so that MyDorel and Moodle can communicate with each other. So this is what we wanted to show you on the Moodle so working place. I'm in the database. Yeah, plugin directory. Yes. So that's where you can actually download MyDorel. So guys, this is your time to shine. If you have any questions, maybe you've already asked them on the chat. We're happy to answer. And Stefan, the CEO, is the one who will be answering the question. Hello again. Thank you so much, Miriam, Alexi and Stefan for your very clear presentation. That's very interesting. We have one question already, and I'm inviting people now to type any other questions in the chat. So I'm going to read out this question from Jordi. Are all configurations of the processes to migrate from the origin to the target setup? Are they only on the web, on the MyDorel instance? Or are there some kinds of files or web services to call to set them up? And he says, I imagine some kind of control version of the configuration, like via Git, and then some kind of process to update the whole set of rules and processes. If you didn't follow me, then perhaps you'd like to reread the question in the chat as well. I'm not sure to understand. I think what the person is saying is they're asking if we always have to manually configure every single rule and every single field. And Stefan, to answer that, I think you can just explain that we have templates. You can generate a template of configuration for the rule. And then when you create the rule, you can select the template. For a few apps, we have a model template that you can use. So for example, what Alexi shown is a template. There were four rules. He didn't create it manually one by one. He just select PrestaShop and model and generate the template. We work on creating more and more templates. But if you don't have the template, you can create the rule one by one. And we can help you on the forum or we can assist you directly with support. I hope we have answered. So to clarify then that the plugin, anyone can have the plugin and the plugin is free and open source. But you, as a company, Midalware, you offer the support for this. And yes, apparently that was a very good answer. So thank you to both of you. Actually, I have a question. I think you mentioned it briefly in your presentation. So what if I know of a particular site that you don't currently connect with? Could I propose that you do that for me, for my Midal site? Yeah, if you want to connect another application, we don't already connect. We provide service to develop new connectors. We talk about CRM Dynamics, for example, from Microsoft. There is several ways to do it. We can develop it for you. So we work for you. If you have a developer team, you can just contribute to the open source project. We like this. So we can guide you to show you how to create a connector. There is a tutorial on our documentation. And then we, sorry, Marie? Oh, I said yes, yes. Okay.  So we can develop it or you can develop it. Great. Thank you. That's a beauty of open source, I think. Now, Dean has a question. Can this be used as well for HRIS systems? HRIS, you know, we can connect every application that can be accessible from the external core. If Midal can call your application, we can connect it. We just need an API to be able to talk with your application. If there is an API, we can connect it. So yeah, so she's saying for the purposes of single sign-on, of course, yes. Okay. In this case, we need to connect to the application of sign-on. We can synchronize the database of the user and password, but this is very specific. So you don't use Midalware to connect to Moodle without creating a password. We can synchronize the users. It's not a module to have a single sign-on, but we can synchronize the user from your other system to the user of Moodle, and then your people will be able to connect to Moodle. But there is a password to set, and this is very specific. So we need to talk about it. This is specific. I'm not sure I understand. I answer the question properly, but... Well, we don't think we have any more questions. Please do type them if you want to. Otherwise, we will move on. But I must say that was a very useful presentation that will explain why you might need Midalware and how you can get it, and then how also you can not only get extra support, but how you can suggest things to connect to yourself. For instance, Jordy says, for the purposes of a login to Midalware, can some kind of SSO application like some, I don't know how you say it, SAML, SAML protocol be configured so that only authorized users can log into the Midalware instance. So here is another question for you. Yeah, we could add this to Midalware, but you know Midalware is a pack of this system. So even if in the company there is 100 employees or 1000, usually we have just two or three people that connect to Midalware, just to configure the things and the rules and manage the error. So if we can do it, but usually only a few people access to Midalware because it's a real pack of this system. At least LDAP is supported. He asks LDAP. We can add it, but it's not yet developed this to log into Midalware. But we're happy to do it, to do it with you. Good to know. Good to know. Okay, are there any more questions? No, a big thanks. So nothing, you're going to get a lot of thanks. As we draw to a close, I will just like to point out a few things about Midal Academy also, which is that if you've enjoyed this webinar, then please help us to grow Midal Academy by contributing to its development, by suggesting other topic ideas. Many of our webinars come about because people suggested the topic. We have a course called Get Involved on Midal Academy. You can see the light bulb on the front page. Click there to join the course and make suggestions. And of course, if like Stefan and Miriam and Alexi, you think you have something that you'd like to present with us, then do make a suggestion and you can present your webinar and even help create courses. You can get a badge for that. Also, and this is a subject very close to my heart, our courses are mainly in English, but we do have special plug-in allowing them to be translated. And we would love it if you can help translate our courses into other languages to help make Midal Academy more inclusive. That's very, very important. And finally, please help spread the word. So if you complete courses and earn a badge, put your badge out on social media. Tell others about Midal Academy, particularly when we share the link to this Midal webinar, perhaps you would share it as well. And if you're an educator, a story reminder that we have the high-quality PhD of Midal Educators, which is the Midal Educator Certification Programme. I'm going to say thank you to Stefan and Miriam and Alexi. Is there anything? Thank you, Mary. Anyone would like to add? Thank you very much, everyone. And if you have any questions, we can ask here on the forum as well. Yes, that's great. Thank you very much for that. Okay, so thank you, everyone. And goodbye. Bye. Bye.


So, the components of labor regulation really are these rules about hiring workers, about firing workers, how much you have to pay to fire workers, so that all of those things, the more rigid are the labor regulations, that's likely to make it harder for the firms to adjust to shocks that come along in the economy, but on the other hand, it kind of protects workers against shocks that they might feel, and it seems to me what we'd like to have is a good set of policies that will balance these two. In developed countries, you have most of the people that are working in the labor market are working in so-called formal sector, where the rules and regulations really apply, whereas in developing countries, you have so much of the economy that's in the informal sector. In developing countries, we'd like to see more of the economy be part of the formal sector, where you can take advantage of capital formation, you can take advantage of human capital formation, and that's going to lead you more towards a developed country. What we've tried to do, and we're doing it in still ongoing work, is to try to quantify as much as we can the key aspects of labor regulations, and that means looking at, in the first place, rules about hiring, about how hard it is to hire, can you hire workers on a short-term contract, and likewise on firing, how easy it is to fire workers, different types, what procedures do you have to go through, do you need approval of some ministry, what are the costs of firing workers, that if you do lay them off, what do you've got to pay them? Each of them needs to be kind of quantified, because labor laws are very long, there's lots of chapters and things like that, so we're trying to come up with a nice system of quantification of these four dimensions of the labor laws, and then aggregating them into a single dimension. A key takeaway is to have policy, labor market regulation policy, that's designed in such a way as to be somewhat differentiated, perhaps between different industries, between different types of countries. We've tried to get, you might say, a toolbox that we have quantifications of what the rules are, so that we can track their effects over time as carefully as possible, and recognizing that some of the effects of any type of regulation are going to be beneficial for some dimensions, but not beneficial in other directions, and therefore we want to find what's the best mix. What we want to do is to then take these measures that we have of everything, tie it together to performance, and then we could have a policy set of policies that would seem to fit individual country situations, so as to get the best out of everything, of growth, of low unemployment, of being able to take advantages of trade, to bring people into the formal sector so they pay taxes, and people can get the advantages of capital formation.


And yes, ladies and gentlemen, it is now time to listen into a man who honestly needs no introduction. He's recognized as one of the most influential persons in the media and entertainment industry and continues to lead Madison as the largest independent media agency in the country. With more than 30 years at the forefront of media and advertising industry, Mr. Sambal Sara, chairman of Madison World, has an ocean of knowledge and insights that very few in this industry have. May I now invite Sam to share with us the key highlights for the Pitch Madison Advertising Report 2021. A very warm welcome to you, Mr. Bal Sara. Good afternoon, friends. I stand before you once again this time within a short gap of just five months since we had presented to you an interim report in August last year. Thank you very much indeed for participating in this webinar and for keeping your date with us year after year. Last year was the year when COVID virus brought about a catastrophic disruption in our personal, social and business lives and caused havoc in the economy. So, it's no surprise that Indian addicts could not remain insulated from the environment around us. In our estimate, addicts dropped in 2020 by as much as 20% and digital was the only medium that bucked the trend and grew last year by 10%. However, if you look at only traditional media, it has dropped by a dramatic 29%. So, almost one-third of traditional addicts got shaved off last year. If you look at figures for H1 and H2, they are even more dramatic both in terms of drop in H1 and in terms of the recovery in H2. The drop being as much as 39% in H1 and almost a full recovery in H2 with a minor 1% growth over H2. Quarter-wise, the data is even more startling with three-quarters declining and only the last quarter registering a substantial increase of 16% over quarter 419. Predictably, quarter 2, when a strict lockdown was imposed, saw a decline of as much as 65%. That is why in 2020, the quarter-wise contribution looks very different from earlier years. Quarter 4 last year contributed as much as 37% and quarter 2 only 12%. In absolute terms, addicts has degrown from 67,603 crore in 2019 to 54,151 crore, a drop of a whopping 13,452 crore, the highest drop ever in one year in Indian addicts' history. With this drop, addicts in 2020 has receded back to almost its 2017 number and if you look at only traditional addicts, we went back five years to the 2015 number, thus resulting in a 20% degrowth in addicts. It is a bit disappointing to see that Indian addicts is not as robust as the global addicts and is more susceptible to vagaries of economic changes because work tells us that globally, addicts de-grow only by 9% whereas in India, as I told you, we de-grow by 20%. US addicts will be surprised to know de-grow only by 4% and Chinese addicts by just 5%. Though UK addicts de-grow by a substantial 14%, our de-growth of 20% makes India the most impacted advertising market in the world. Coming back to India, each medium behaved very different. Digital came out unscathed and as I said earlier was the only medium to grow by 10%. All other mediums were negatively affected though TV was the least affected with a de-growth of just 11%. Print de-grew by 41%. But percentages here don't tell the real story.  OH and radio also suffered substantially but since these are smaller mediums the actual numbers of de-growth are not very high. Cinema understandably because of lockdown of cinema halls virtually got knocked out of addicts with a 83% drop and ended up with a share of just 0.34%. In terms of share of each medium, the big news is that digital has overtaken print as the second largest medium with a share of 31% and print has lost as much as 8 percentage points having dropped in share from 30% to 22% and slipped down to third rank. TV not only continues to be the largest medium but it further improved its share by 4 percentage points from 37% to almost 42%. Share of digital continued its onward march eating into traditional media as this chart shows with traditional media losing its share by as much as 8 percentage points from 77% to 69%. Mind you traditional addicts in India one would have to recognize is quite resilient because even at a 69% share it is probably the only major country in the world with such a high share. Globally traditional media is 41% of total addicts. Coming to different categories e-commerce and education are the only two categories that buck the trend and showed positive growth in groupie terms. FMCG though it degroup by 13% jumped up in share from 33% to 38% and became an even more dominant category in our addicts. Many advertisers deserted TV, print and radio in quarter 2 but by quarter 4 almost all advertisers have returned to the advertising fold. I will come to a new list of top 50 advertisers and what changes one saw in this tumultuous year in a minute. But before that I want to say that looking at the total number of advertisers in India one will have to recognize that in a country of 1.2 billion with a GDP of almost 3 trillion US dollars then this number is abysmally small. A large number and medium India businesses it would appear are yet to discover the power and business building potential of let us see who were the top advertisers in 2020. Our list is diverse with FMCG, telecom, auto e-commerce, mobile gaming and consumer durables. But FMCG dominates the list with as many as 19 in top 50 and as many as 6 in top 10. Rekit made a big push last year and rose up in rank from rank 11 to rank 2 this year. Contribution of top 50 advertisers went up marginally to 35%. Top 10 advertisers contribution went up to 18%. TV and digital are getting stronger by the day in Indian ad-ex and therefore it is no surprise that our top advertisers spend 86% of their ATL budgets on these two mediums. Top advertisers spend 86% of their budgets on TV and digital establishing firmly that these are two dominant mediums of ad-ex and the relative size also confirm this. Last year this number was 78%. 10 new advertisers entered an elite list prominent amongst them are PhonePay, PepsiCo, Facebook and Hotstar. Many advertisers like Rekit, Hero, Colgate, Nestle and GSK have moved up many ranks. Whereas Dream11, Samsung, Google, ATL and Oppo have dropped many ranks. The million dollar question to now ask is what growth can we expect? In 2021, the COVID strain in India is receding. Commercial activities have returned with a vengeance. GST collection, January 2021 has been at an all-time high of 1.20 lakh crores. The economic survey projects that the Indian economy will grow in 21-22 by 11% in terms of real growth and 15.4% in terms of nominal growth and our finance budget is more pro-growth than any previous budget. Vaccination has started and chances of a second wave which has engulfed UK and parts of Europe are low. What's more, Indian ad-ex in quarter 4-20 has grown by 61% over quarter 3 and by 16% over quarter 4 of 2019. All this gives us the confidence to predict a growth rate of a substantial 26% which will take ad-ex to 68,325 crore. The last time that Indian ad-ex had grown by 26% or even higher was in the year 2010 when it grew by 28% following a degrowth in 2009 by 9%. If we grow by 26%, India will become the fastest growing ad-ex market in the world followed only distantly by UK with a growth rate of 14.7% and Australia 13.2%. Whilst in the past digital has always grown at a higher pace than traditional media, this year we predict that the growth rates of the two will be similar given that traditional media has degrown by as much as 27% and digital on the other hand has grown by 10% because many traditional media users who stopped advertising have come back only in quarter 4 and we expect them to continue to advertise in 2021. Now even if we grow by 26% in 2021, we feel ad-ex will still settle at the same number we achieved in 2019 thus highlighting that the corona virus has knocked out two years from ad-ex's life. Besides the fact that ad-ex de-grew substantially in 2020, there are a number of enabling events likely to take place this year which we believe will help us to realize our 26% growth forecast. More categories and new advertisers are likely to get active after a hiatus and advertisers in OTT, edutect, mobile gaming and digital payment categories are expected to spend heavily besides many new launches are expected in the auto sector. Again, we expect a wide variation in growth rates across different mediums with digital expected to grow by 25%, TV by 17% and print by as much as 35%. It could perhaps be more meaningful to view growth in 2021 against 2019 which shows up that digital should grow up by 37% followed by TV at 4%. Of course, we do not expect cinema, radio and print to return to the 2019 numbers. TV we believe will drop in share marginally but OH and print will grow their shares from last year. Digital cinema, radio and outdoor more or less will maintain moving to individual media. Let us see television in a little more detail. Now, for television, the year 2020 saw it all with the mood swinging from despair to confidence. Slowdown in the first quarter, pre-COVID collapsed in the second quarter due to COVID, no original programming on GEC, repeat of old Durudarshan classics which busted the charts in terms of viewership, all-time high viewership in news genre, IPL in quarter four and an astounding performance in quarter four in terms of ADEX. Whilst television ADEX did suffer on account of COVID, the drop in ADEX could be considered minor at just 11% compared to other traditional media's degrowth to reach close to 22,500 crore almost at par with the year 2018. The ego boosting fact for the television industry is that TV has grown its share of ADEX to a high of 42% from 37% in 2019. TV ADEX moved like a yo-yo during the year. The year started poorly with quarter one registering an unusual 13% degrowth over quarter one 19 which rose to a 61% degrowth in quarter two thanks to COVID. Quarter three saw a quick recovery to almost the same level as 2019 but quarter four saw an astounding increase of 56% thanks to IPL and festival period. Whilst TV medium returned almost to normalcy as early as August 2020, January 21 volumes suggest that TV is booming. This gives us confidence to predict a 17% increase in 2021 which will take TV ADEX to 26,350 crore. While 17 is a good number, if you compare our 21 number with 2019, it's merely 4% higher. Two categories that stand out in TV ADEX are e-commerce and education. E-commerce almost doubled in size growing 95% with its share going up from 5% to 11% and education tripled in size taking its share from 1% to 4%. White hat junior Vedantu and Baiju's helped their education category grow. Whilst FMCG de-grew by 9%, it increased its share from 49% to 51%. Taking a closer look at genre wise contribution by FCT, it appears that degrowth in regional channels has been the least implying that national brands prioritize campaigns in their strong markets and regional brands came back to ADEX faster than national brands. Hindi GEC channels, the largest contributor to TV ADEX also suffered but not as much as Hindi GEC second line with de-grew by as much as 24%. Though we estimate IPL to have contributed as much as 2700 crores or 30% to TV ADEX in quarter 4, share of sports genre shows a degrowth of 26% given that live sports resume play only from September 20 onwards. A major casualty of COVID has been English channels who suffered a 40% decline in FCT. Now let's see print. COVID damage to print has indeed been massive and print ADEX lost as much as 8120 crore or 41% due to COVID and lost its number 2 rank in ADEX with its share having dropped from 30% to 22%. Understandably the ravage done in quarter 2 when newspapers could not be distributed was massive at a minus 79%. But the good news is that in quarter 4, print ADEX is recovering to the pre-COVID level of quarter 1 though it is still lower compared to quarter 4 of last year by 15%. We are bullish on print making a sharp recovery this year and adding another 4000 crore which would mean a growth of as high as 35%. We believe a media barons will use every trick in the book fight tooth and nail to at least partially regain their share of ADEX. Coming to categories, all categories we see have got affected in print including e-commerce with degrowth by as much as 57%. Also education, auto and FMCG were affected though to a lesser degree. In terms of share, education has increased its share of ADEX from 10% to 15%, FMCG from 14% to 17% and auto from 13% to 16%. And these three categories account for almost half of our print ADEX. Newspapers circulation in metros was affected a little more and recovery seems to have taken longer because of the share of Hindi newspapers has moved up from 35% to 38% and English from 25 come down marginally to 24%. Canada and Malayalam newspapers showed lowest degrowth whereas Tamil, Telugu and Marathi newspapers degroup the most. Now let's look at the superstar of all media, digital. As I mentioned earlier, digital is the only medium that grew in 2020 by a decent 10%. With this growth digital ADEX has reached a value of 17000 crores and a share of 31% of ADEX. It's also significant that digital has grown in three quarters last year and degroup only in quarter two by 35% when there was a strict lockdown. This drop of 35% is to be seen in comparison to print's drop of 79% and TV's drop of 69% for the same quarter. We expect digital to grow by a further 25% this year to touch 21000 crores. Over two years 2020 and 2021 digital will add 5773 crores compared to TV which will add only 1059 crores. 95% of all digital spends are on mobile. Looking at digital ADEX by various verticals it is noted that share of search has come down by 5 percentage points and now stands at 18%. This is not because search has degrown in numbers but other verticals have degrown much faster. Not only video has the largest share in digital but in fact it has increased its share from 30 to 32% during the year. Both social and display too have marginally improved their share at the expense of search. Programmatic has taken firm route in India and our estimate is that almost 40% of all digital spends are through programmatic. Let's see what's happening in outdoor or OOH. Our estimate is that in 2020 outdoor ADEX lost as much as 2203 crores or 63% taking it to a new low of just 1292 crores. Outdoor has lost as much as 3 percentage points in terms of share dropping from a 5 share to a 2 share. At 1292 crores it has gone back 12 years because that is the number we achieved way back in 2007. Quarter 2 and quarter 3 have been virtually washouts for the outdoor medium but the medium has recovered somewhat in quarter 4 though it is roughly only half of last year's quarter 4. We expect OOH to double its size this year to almost 2500 crores but even with this substantial addition it will be 30% lower than the number for 2019 but it will gain share of ADEX from 2.4% last year to 3.6% this year. Whilst every category in OOH de-grew real estate and media de-grew the least. Real estate is also the largest category followed by FMCG. Let's review radio. Radio ADEX was the third worst affected medium which de-grew by almost 44% and came down in value from 2260 crores to just 1270 crores. This sharp drop has taken radio back to the year 2014 when it was 1300 crores. With this drop radio has lost 1% market share and now has a share of just 2%. Looking at quarter wise figures whilst quarter 2 and quarter 3 were disastrous for radio. Quarter 4 the festival quarter has shown good recovery registering over 4 times the number it achieved in quarter 3 but even with this dramatic increase radio ADEX is still 17% lower than quarter 4 of last year. We expect radio to achieve a growth rate of 38% in 2021. This will take radio ADEX to 1750 crores still falling short by 23% of 2019 levels. Radio share of ADEX is expected to go up marginally from 2 to 3%. Looking at radio ADEX by category whilst all categories showed de-growth the de-growth is least in BFSI at minus 13% and this category has grown its share to 12% to share the credit of being the top most category along with FMCG which improved its share from 9% to 12%. Auto another important category for radio de-grew by 31% but improved its share from 7% to 9%. 5 categories now contribute to 51% of total radio ADEX in 2020. Lastly let's take a look at what happened in cinema. Cinema suffered the most in terms of percentage drop and in our estimate suffered a 83% drop capsizing its low base of just a little over 1000 crore to under 200 crore a number it had achieved way back in 2007. This is understandable since cinema halls remained locked from the third week of March to November last year. Whatever cinema achieved last year was all achieved in quarter one with a balance three quarters being a virtual no show. Cinema will definitely positively jump up in 21 but since most of the steady growth we believe will settle in only from age 2 we expect cinema ADEX this year to be less than half of 2019 at 475 crore. Since I come to the end of our report as usual we would like to end with some advice for all my advertiser friends. Advice number one is that advertisers would be well advised to use attribution modeling to discover uniquely what works and what does not for their brand. To continue to select channels or any medium on CPRP or CPT alone is a mistake in today's noisy and technology backed environment. The old belief that a GRP is a GRP is a GRP is no longer true. A second piece of advice is that advertisers should bring pressure on respective research bodies to restart media research. Currently in print both IRS and ABC are on hold and in TV ratings news channel ratings are not being released. Media owners we believe are under the mistaken notion that by putting media research on hold advertising would quickly return to 2019 level. Such data in fact will provide confidence to advertisers that life is returning to normal. Final piece of advice is that whilst digital and TV are two reigning monarchs of ADEX advertisers would do well to look at using print, outdoor, radio or cinema in a strategic way at least in some markets for some brands for multi brand companies. These are by themselves strong and proven media and advertisers could take advantage of the softening of rates compared to 2019 rates that are likely to prevail in these media in this year. Thank you ladies and gentlemen for patiently listening to me. Ladies and gentlemen it is now time to unveil the much anticipated Pitch Madison Advertising Report 2021. So I hope all of you are ready to join us. Here we go everyone without further ado we present to you the Pitch Madison Advertising Report 2021. Well there you have it ladies and gentlemen that is the cover of the Pitch Madison Advertising Report 2021. Don't forget to keep your conversations going on Twitter using the hashtag PMAR2021. We would love to hear from all of you the report will be made available shortly.


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We were looking at perturbations on a thin film coating a rod of radius r naught without proving it I had told you that one can show that if you put perturbations of wavelength lambda or wave number k then the dispersion relation is given by the expression that I have written here. Now just to check for consistency it is useful to take the limit r 0 going to 0. So, you can see that when r 0 goes to 0 r 0 is the radius of the rod. So, I am shrinking the rod you can think of this process as one which holds this entire distance constant and shrinks the radius of the rod. So, the space that is occupied by the rod gets now occupied by the fluid. Now as the rod thickness shrinks to 0 in that limit this should reduce to a fluid thread or a fluid cylinder whose radius is r 1 and so we should the dispersion relation should reduce to the case that we have already derived earlier. This is just a check on the consistency of this dispersion relation. Now this can be shown easily that when r naught goes to 0 then this part is finite and this term is finite. This goes to 0 and this goes to 0 and so we are left with just the first term here and here. Note that the first term on in both numerator and denominator has a k 1 and k 1 the argument if I set it to 0 k 1 diverges. However, there is a k 1 in the numerator and a k 1 in the denominator.  So, I am canceling out this k 1 and this k 1 both of them will diverge k 1 diverges at the origin. So, as I said r naught to 0 for a fixed small k the argument will go to 0 and both the numerator and the denominator will diverge but both of them will diverge in exactly the same way because they are the same functions. So, it can be cancelled out and so it remains what remains is I 1 of k r 1 divided by I naught of k r 1 and you can check that this is exactly the same dispersion relation that we have obtained earlier. Now, we have replaced r 0 in the previous relation with r 1 now and that is because as the keeping this length fixed if I shrink the radius of the rod then the space that was earlier occupied by the rod now gets occupied by the fluid and the limit when the rod shrinks to 0 or just a line then it just becomes a fluid cylinder and so I should recover the same dispersion relation that we had got earlier except that now we are writing r 1 because the radius of the fluid cylinder is now r 1. So, it is this, it is this number. So, this is consistent with what we have done so far and kind of generalizes what we have done for a fluid cylinder. So, now let us analyze this dispersion relation you can once again go to MATLAB or Mathematica and plot this quantity and you will find that this quantity is always positive for all k this quantity is always positive for all k this can be shown. So, once again this dispersion relation can have omega square can become negative but the only place which can become negative is once again our old familiar term k square r 1 square minus 1.  Now of course, for k r 1 greater than 1 you get waves or oscillations. So, there is no growth let us analyze this a little bit more. So, we will do exactly what we had done earlier I am going to substitute omega is equal to i omega i where omega i is now real that will introduce a minus omega i square on the left hand side like before and I am going to reverse this part in red. So, that it is positive now because I am looking at this limit of looking at this range of k r 1 less than 1. So, if k r 1 is less than 1 then k square r 1 square minus 1 is negative and so I am going to reverse it and bring out an overall negative sign like before the negative sign on the left and the negative sign on the right will cancel each other and I can plot omega i square as a function of the right hand side. So, once again I will do the same thing I will define a omega i star square which is a non-dimensional omega i square which is basically just omega i square divided by t by rho r 1 cube. Note that I am working on the full dispersion relation and so this is equal to it is just k r 1 into I have reversed this now. So, I will write it as 1 minus k square r 1 square into this part it is a long one. So, I am not going to write it again and so now this is purely positive because I have reversed the part which is actually negative. So, I have reversed the part and now I am going to plot the left hand side as a function of right hand side. So, if I do that or rather if I plot it as a function of omega i square as a function of k r 1 then you will see once again the same thing. So, while doing this you will have to choose a value of r naught. So, you will have to choose a value of the radius of the rod and then plot it as a function of k r 1. If you do that once again you will get a very similar curve and the curve will look like this. Once again this will hit the x axis at 1, 1.0 and that is because beyond k r 1 when it is greater than 1 omega i square is negative or in other words we are going to the regime where there would be oscillations and not instability. So, this is the place where we are getting growth k r 1 is less than 1. Does the growth rate get affected by the presence of the rod? That depends on what is the location of this maxima. Earlier we had seen that the location of the maxima was 0.697. In this case this maxima is approximately at 0.706 or approximately 1 by square root 2. So, it gets slightly shifted. So, now this is the fastest growing mode and so if this film breaks up into droplets or rather cylindrical droplets which will coat the rod then this will give us the wavelength of those or the size of those droplets. This wavelength will be the fastest growing mode. As you can see like before the criteria for whether it will grow or not grow is independent of surface tension. It is purely a geometric criteria which is given by this quantity k r 1 less than 1. So, any wave number which is less than any wave number which satisfies k r 1 less than 1 will exhibit instability and will cause exponential growth. Among all such wave numbers the wave number which grows the fastest satisfies k r 1 is equal to 1 by square root 2. This is slightly different from what we had done earlier for a liquid cylinder. Now this is a solid cylinder coated with a liquid film still prone to the relay plateau instability and the criteria remains the same. Let us now move over to yet another problem where we see the same instability and you will find that yet in this problem also the criteria for the instability remains exactly the same. It is a very analogous criteria that we have now seen 2 times. So, let us the third problem is that of a cylindrical bubble or a cylindrical column of air you know in water let us say. Such columns of air often get trapped when waves break in the ocean and it leads to air entrapment trapping a cylindrical column of air inside just below the surface of water. Now we will simplify that problem and we will ask the question that suppose I have a cylinder of some radius r naught and there is gas inside it. So, let us say there is air inside it and outside there is some liquid let us say it is water. Now due to the density difference between air and water we are going to ignore the dynamics of the medium inside we will model this column as being infinitely long. So, it goes from minus infinity. So, the coordinate system is again like before this is z and this is r and so the interface between air and water we are going to impose perturbations on it and we are going to solve. But now we are going to solve for the fluid outside not for the fluid inside. So, this is a filament with air inside it we are going to impose axisymmetric perturbations on it and we are going to ask are those perturbations stable to the oscillate or do they grow in time. We will find that some of these perturbations are still unstable to the relay plateau instability. So, this is here the base state once again is quiescent. So, both air and water is quiescent. We are going to ignore air the density of air is much less than that of water. So, as a first approximation we are going to ignore air. We have ignored air in all the examples that we have done until now except that in all the examples the gas was present either above or outside now the gas is present inside. So, this is like a air bubble. So, we are not solving for the air inside the bubble we are going to solve for water outside the bubble that is still modeled by Laplace equation. So, when we have perturbations the perturbation velocity potential in the water is going to be still modeled by the Laplace equation. Let us do that. So, in the base state the pressure once again is. So, if I say that the pressure here air pressure here is 0. In the earlier example when we had done it for a liquid cylinder we had modeled the air pressure outside to be 0 and so the pressure inside was more and so that was t by r naught. Now we are saying the pressure inside is 0 the pressure inside because of the weight is curved is always more than the pressure outside. So, if I have said the pressure inside to be 0 then the pressure outside has to be less than the pressure inside. So, that is minus t by r naught. So, this is the pressure in the water outside it is a uniform pressure we are ignoring the presence of gravity and we are going to solve for perturbations on the surface. We have already done this geometry. So, I am just going to skip a few steps because they are identical to what we have done for a cylindrical column of liquid. So, like before using variable separation in cylindrical coordinates axisymmetric we will find that the velocity potential the perturbation velocity potential is once again given by and now for the radial dependence we are going to have k naught and i naught. So, for the radial part of the velocity potential like earlier we will have two choices k naught and i naught and it will be a linear combination of the two. Now our domain we are not solving for air inside. So, our domain extends from r is equal to r naught plus some eta that we will put on the surface to infinity. So, our domain goes from r naught plus eta to infinity. So, small r does not go to 0. Recall that k naught diverges at small r, i naught diverges at large r. So, we our domain actually goes to infinity. So, I cannot include i naught in my calculation because i naught will diverge as the radius becomes larger and larger and we are solving for. So, we are solving for the water and the water is unbounded it is radially unbounded. So, I will write this. So, phi is the velocity potential in water. So, we are solving only for water we are not solving for air we are assuming the air to be quiescent and the pressure in the air to be always 0. So, then we are going to get a k0 of kr here. I hope you understand why. Earlier it was i0 of kr because the domain included small r equal to 0. Now it is k0 of kr because the domain includes small r is equal to infinity or small r going to infinity and so i0 diverges as small r becomes larger and larger. So, we have to set the coefficient of i0 to 0 now and only k0 will survive. Similarly, eta would be e cos kz plus f sin kz into e to the power i omega t. Like before eta is only a function of z and t by definition eta does not depend on r and these are my normal mode approximations. And so like earlier we will write the Bernoulli equation the total pressure plus the total velocity potential in this case the total velocity potential is just the perturbation velocity potential because this quiescent fluid in the base state. And this is equal to the Bernoulli constant the Bernoulli constant is once again found by applying the same equation in the base state. And in the base state it is just p b by rho p b by rho in the base state is just it is just p b by and like before so the pressure jump condition now becomes p at r is equal to r0 plus eta is equal to minus t grad dot m. Earlier our n was pointing from the fluid where we were solving into the fluid where we were not solving. Now also our n continues to point but now we are not solving for air but we are solving for water. So the n is still radially outward and that brings in this minus sign. So this is at r is equal to r0 plus eta. So now so n points from so n is a unit vector pointing from gas to liquid. You can check that this minus sign is necessary because this equation is also true in the base state and without this minus sign you will not so if you apply this equation in the base state and if you calculate the curvature in the base state that is just a constant and you will find that it recovers this equation only if you take that minus sign. So the minus sign is necessary. So now we will once again like before we are going to work out what is divergence of n. So this is we have already done this before. So divergence of n at r is equal to r0 plus eta is just going to be. So I am just going to write down expressions that we have already written. So we have done this before so I am just going to straight away give you the expressions and you can check it for yourself. This is exactly the same procedure that we have followed. You have to define a function capital F whose value is constant on the surface and then you have to take the gradient of that the components of that so the denominator is not there in the linear approximation. So n approximately is just gradient of capital F and then you have to calculate the various components of grad F in cylindrical coordinates and then take the divergence of that quantity. Once you take the divergence then you will get this omega t plus k square. Please refer to the previous video where we have already done this and of course there is a complex conjugate which I am suppressing. And then the expression we have just written that the total pressure at r0 plus eta is equal to minus t and then I can write my left hand side as pb and pb in the base state there is no eta. So it is just at r is equal to r0 plus the perturbation pressure at r0 plus eta is whatever we have calculated from this. So I am just substituting. So there is a minus sign overall. So minus t by r0 plus t by r0 square into e cos kz plus f sin and then minus k square tk square into e cos kz plus f sin kz e i omega t and then I have to write it plus cc also but I am not writing that. And we know that pb in the base state is just minus t by r0. In the base state there is a uniform pressure in the water outside. That pressure is just minus t by r0. There has to be a pressure difference between inside and outside. If we say that the pressure inside in the air is 0 in the base state then the pressure outside has to be lower and that is minus t by r0. It is only the difference which matters. So then this quantity and this quantity get cancelled out using this and so like before we just recover an expression for perturbation pressure. So p at r is equal to r0 plus eta is just the same thing. So t so it is e cos kz plus f sin kz into e to the power i omega t t into 1 by r0 square minus k square. Very similar expressions. There will be a overall difference of minus sign because now in the pressure boundary condition there is a minus sign compared to what was there earlier. So that is the only difference. So once again you can go back and substitute it into the linearized Bernoulli equation. So the linearized Bernoulli equation is just once again like we have to find that the perturbation pressure has to be applied at r is equal to r0 and not r is equal to r0 plus eta because that will bring in a nonlinear term is equal to minus rho. Similarly del phi by del t the perturbation the time derivative of the perturbation velocity potential also has to be evaluated at r equal to r0. If you substitute whatever we have found in the last slide we will recover the equation rho i omega I am straight away writing the equation. So compared to the last example where we had done this for a liquid cylinder the only difference is there is a minus sign and instead of i0 there we have k0 here. i0 was the modified Bessel function here this is the modified Bessel function the second kind. So instead of i0 here we have k0 a plus t into 1 by r0 square minus k square into e and this whole thing gets multiplied by cos kz plus rho i omega k0 k r0 B plus t 1 by r0 square minus k square into f this gets multiplied by sin kz the whole thing is multiplied by e to the power i omega t plus cc is equal to 0. This will be my equation 1 coming from Bernoulli equation linearized Bernoulli equation. Second so Bernoulli equation the second thing will come from kinematic boundary condition and so we will have del eta by del t is equal to del phi by del r at r equal to r0. This will involve derivatives of k0 with respect to its argument. So this will lead to I am straight away writing the final answer this will give you i omega e plus k into the modified Bessel function plus i omega f plus k this whole thing multiplied by e to the power i omega t plus a complex conjugate is equal to 0 and this is equation 2. Like before we have to set the coefficients of cos and sin to 0, four equations in four unknowns a, b, e and f the determinant will determine the dispersion relation. I will write down the dispersion relation it just requires a little bit of algebra you can do it yourself and verify that this is correct. So the final dispersion relation looks like omega square is equal to t by r0 cube into k r0 k square r0 square minus 1 into k1 of kr0 divided by k0 small k r0. You might be wondering where did all the minus the extra minus sign that we got why did not that made a difference to the dispersion relation. You can see that this k1 earlier we had a i1 in the numerator and i0 in the denominator and we had seen that the derivative of i0 with respect to its argument is i1. Here there will be an extra minus sign overall but the derivative of k0 with respect to its argument will be minus k1. So that minus and the overall minus will cancel and lead to exactly the same dispersion relation except that now we will have k1 and k0 here. So this is the only difference the rest of it remains the same. You can see that this also has the same structure as before that this is something so this is the part which has the dimensions of frequency squared. So this is the dimensional part and the rest of it is non-dimensional. So I can once again write it as maybe some capital H some function of small k r0 and capital H of small k r0 is defined as it is a non-dimensional function 0 by k0 of k r0. Once again you can show this part is always positive. So if this dispersion relation has to admit instability that instability has to again come from this part. Once again we find the exactly is the same criteria that all wave numbers which satisfy k r0 less than 1 are unstable. We have now seen three examples one of a liquid filament one of a thin film coating a cylindrical rod and one of an air bubble. In all of them the criteria for instability is the same the growth rates will be different. In this case the growth rate if you plot the growth rate so you can non-dimensionalize omega square. So you can substitute omega is equal to i times omega i like before omega i is real. This will give you a minus sign and then you can reverse. So you can write it as omega i square is equal to t by rho r0 cube into k r0 and reverse this 1 minus k square r0 square into k1 of k r0 and k0 of k r0 and this whole thing will be positive in the range k r0 less than 1. So you can plot it as a function of k r0 and it will look something like this. Once again it will hit the x axis at 1 and the maximum growth rate will be about 0.4838. So k r0 or rather the mode which grows the fastest so k max into r0 is equal to 0.4838. So you can see that whether we have a denser fluid inside or whether we have a denser fluid outside whether we have a solid inside it makes no difference to the criteria of instability. It makes a difference only to the growth rates of the fastest growing mode. So we will find that we will try to understand the origin of this behavior that what is so special about k r0 less than 1 and why does this cause instability in each and every case that we have seen so far. In all the cases k r0 greater than 1 gives you stability at least it is linearly stable and so you expect small amplitude oscillations governed by the dispersion relation. The dispersion relation is actually different in all the three cases. So the frequencies are not the same. However the criteria the boundary between stability and instability remains the same in all the three cases. We will examine the reason for this in the next lecture.