The senator representing Anambra South Senatorial District, Ifa Yuba, has vowed to stop the Monday seated home order in his constituency with immediate effect. He seated this at the Ifa Yuba International Stadium, Neiwi, when he addressed the state's vigilante and community security watch operatives from the four quarters of Neiwi. Yuba urged the people of his constituency to start opening their businesses on Monday, stating that adequate security measures and equipment have been put in place to ensure watertight security of lives and properties. The Indigenous people of Biafra, IPUB initiated the Monday's seated home in 2021 to protest the rendition and detention of IPUB leader Namdi Kano. We have observed every Monday as seated at home, but we are privileged in the spirit of observing every Monday as seated at home. We have also found out that we are losing our economic base, and most people are losing jobs and business opportunities. As the representative of the group we call Anambra South, Neiwi will not be able to pick up the call of Anambra South. We give the fees to say we will not continue to have seated at home on Mondays. For this Monday, every business venture Neiwi will be open for business. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


Hello and welcome to Around the World in 8 Minutes, a show by People's Dispatch. In this show, we bring you stories from the frontlines of struggle against capitalist exploitation. In today's episode, we'll begin by looking at the ongoing strike by the teachers and support staff of Chicago for an equitable education system. We then move to Argentina where medical professionals went on a strike demanding the payment of salaries and we conclude with the struggle by workers in Spain regarding the protection of their jobs. Over the past year, we have seen a wave of strikes and protests by teachers and support staff across the United States. In state after state, teachers have risen in anger, frustrated over poor pay and dismal facilities at schools. In 2012, a massive strike was held in Chicago over many of these issues. This strike is believed to have inaugurated a new era of organizing by teachers. Last week, the teachers and support staff of Chicago went on strike again demanding an overhaul of the education system. The strike has now entered its second week. On October 23rd, between 20,000 and 30,000 teachers marched to the city hall while Mayor Lori Lightfoot was presenting her maiden budget, where she made the usual austerity filled speech. For union representatives, this demonstrated an unwillingness to listen to their demands and they have indicated that they will intensify the strike. The strike is being organized by the Chicago Teachers Union, the CTU, along with the Chicago chapter of the Service Employees International Union, SEIU or Local 73. Over 25,000 teachers and close to 8,000 support staff are taking part. The strike has led to the shutting down of classes in more than 600 schools that cater to nearly 350,000 students. The teachers have called for the infusion of nearly US$1 billion into the education system. In recent negotiations, the Chicago Public Schools which is the administering authority has made some concessions. These include a 16% wage hike for teachers, bringing down co-pays in medical insurances and a moratorium on privately run schools or charter schools. The city also offered a 5-year plan to invest $500 million which was deemed insufficient. However, the city has made little commitments on important demands. These include a wage hike for support staff and their formalization, bringing down cloud sizes, increasing the number of full-time support staff like nurses and counsellors, and expanding resources in schools such as libraries and health centres. Mayor Lightfoot has argued that the CPS does not have the money to deliver on these demands. In her speech, she focused on bridging the fiscal gap, making it clear that no investments would be possible soon. Union representatives pointed out that Lightfoot's comments came even as the CPS had a record TIF surplus. The TIF is the tax increment financing which allows school districts to raise funds. However, instead of using the $163 million surplus on the school, the mayor plans to use it to bridge the city's deficit. After the city administration refused to engage with the teachers and support staff properly, CTU and Local 73 released a statement which promised that negotiators will not waste their time trying to talk to a brick wall. Instead, they will head back to the picket lines and build the kind of solidarity that has already led to progress towards a fair contract. The statement involved. We now move to Argentina where hundreds of young healthcare professionals in the public sector hospitals began a 48-hour strike on October 23rd. These first-year residents are demanding an immediate payment to salaries which they have not received since June. Their other demands include a compliance of the laws and regulations governing the residents and an increase in salaries as their current pay is below the poverty line pay due to rampant inflation and devaluation of the national currency. They also want negotiations to discuss salary hikes and the application of work risk insurance to all the residents. This is the third strike by residents of national hospitals this month. The first strike took place on October 2nd and hundreds of doctors marched to the Ministry of Health. At the ministry, they were received by government authorities who assured them they would pay all the amount, the whole amount, in two parts by October 10th. The authorities also guaranteed that they would provide access to the ART by October 11th, pay the rest of the dues in the month of November and establish a negotiation table to discuss salary hikes. The deadlines came and went but no promises were fulfilled. The residents carried out another strike on October 16th. When they marched this time, the government delegation which met them refused to take any responsibility for what was happening and refused to sign any written commitment and just blame the state bureaucracy. It was then that the young doctors decided to call for another strike this time for 48 hours. The workers from the Civil and Trade Union Association of Professionals and the technicians of Garahan Hospital also joined the strike. In addition, hundreds of doctors and other healthcare workers associated with the Trade Union Association of Healthcare Professionals of Buenos Aires Province went on a 24-hour strike on the same day. Due to the strike, over 80 public hospitals and health centers in Buenos Aires Province remained closed or provided only emergency services. The unions also denounced the lack of investment in the sector by the right-wing government of Buenos Aires led by Maria Eugenia Vidal and its unwillingness to resolve the crisis. In the last four years of its governance, the government of Mauricio Macri has implemented neoliberal economic measures which have reduced investment in a number of public sector health services. Healthcare workers have noted that the budgetary cuts have had a direct impact on the health of the population and have seen an increase in cases of tuberculosis and syphilis in the country. The presidential elections in Argentina are scheduled for October 27th.  In our last story, on October 23rd, the industrial workers and energy sector workers in Galicia in Spain protested in front of the Spanish authorities at Acoruna, demanding an energy pact for industries and a protection of jobs for workers. This is in the backdrop of the government policy of energy transition in the country. This energy transition policy pursued by the Spanish government will close down coal mines in the country in order to address environmental concerns. The workers in the coal mines and related industries like thermal power plants are concerned about the future of their jobs. There are also a number of jobs in heavy industries that depend on the energy sector. On Wednesday, workers in unions from a number of plants rallied at Acoruna. The call for the demonstration was given by the workers commission, CCOO. CCOO Secretary General of the Industry for Galicia, Victor Ledo, demanded that the regional and central governments establish a state pact for energy and the industry along with short-term plants for the thermal plants which are going to be closed. Ledo said that the situation of the industry in Galicia was serious both because of labour reform as well as a high price of energy and the lack of a thought out industrial policy. He expressed the concern that the region would become an industrial desert and sought concrete commitments instead of vague promises. The regional government in Galicia has also appealed to the Spanish government to address the concerns on energy, industries and jobs. The transition to a climate neutral economy will have a massive impact on all sectors and their workforce and hence trade unions in Spain have demanded a new social contract to engage workers in this transition and push it forward instead of holding it back. That's all we have in this episode of Around the World in 8 Minutes. To read more about these stories, visit our website peoplesdispatch.org and follow us on Facebook, Twitter and Instagram. Thanks for watching.


Hey, stampers! Welcome to another week of Watch It Weekly Wednesday. I'm Aubrey, part of the Stampin' Jill Creative team. Today I'm excited to share with you a new stamp set that's in the mini catalog. It's here on page 57. Medley Mix is what it's called, and it coordinates with the Inked and Tiled Punch Pack from the Annual Catalog. Super fun! So I love when a stamp set coordinates with something from the Annual Catalog because it just doubles the bang for your buck. So I want to show you some fun ideas that you can make using this stamp set. One of my favorite stamps in here is this kind of geometric pattern. It looks kind of like a background pattern. And the cool thing about it is that it's like a puzzle piece. When you stamp it all together, it just fits right inside of each other and makes it really easy to stamp, like a big nice background piece. So I wanted to show you that.  And I'm just going to make a little background here.  It makes it really easy to line up. And because it's photopolymer, you can see right through it and line it up pretty easily. Just like that. And then just finish that off. And just like that you have a fun background for your card. Just with stamps and ink. Okay, I want to show you a few card ideas I've come up with using this technique. Here's this one with that Moody Mauve background and you can see using the punch there. Here's another one using Misty Moonlight and that cute circle piece there. It also coordinates with the circle punch that's available right now on our online exclusives. And a few other ideas using the punches and the stamps in here. You can use the other fun patterns and make a really fun background there. And one more. So fun. If you've already purchased the Inked and Tiled Bundle with these punches from the annual catalog, you'll want to grab the Medley Mix stamp set from the new mini catalog to coordinate. I've had a lot of fun playing with it and I hope you will too. If you have any questions, make sure to let us know in the comments below. If you like these products, make sure to click the links below. Thanks so much. We'll see you next week for another Watch It Weekly Wednesday. I feel like a news reporter for some reason. Thanks so much.


Alrighty new version here with sound let's watch this in full of course. I have super powers I have super strength. I can fly I have laser vision all the good stuff is just you know I got to keep it on the down low All right, I'm turning on the sound on my end just tad That's all pretty cool. I like the changes that you made how tiny things here and there, but other than that You mentioned an email first pass Kind of a rough Idea of what she's going to do. I think that's pretty cool. I think those that's all the right idea Just watching this. I know I know it gets into this, but then you still got kind of a 20 pose. It's almost like I'll just put that like she has her hand on the thigh here closer And maybe that just you know, maybe goes up a bit might not have enough times And we just maybe split the difference here with a bit of a Just like a gesture like a finger Point or something I mean, it's not a point But just something a bit different from this side I could be a more triangular simple pose with a bit more complex finger pose getting into this Just so it's not the Kind of same pose kind of twins. I Think that's cute. I think we could Potentially can push that a bit more off to one side And that way it will also get away from that idea, but with arms here So if you have potentially this hand here right and in this hand here It might force her into a bit more of a lean maybe I'm not sure but and then that way you have Just the overall feel of head and arms giving you that kind of line towards the girl if that makes sense Where we can kind of push that line of action a little bit That's super cute. I mean I like all of that. That's all cute Same thing here Again, I'm harping on things, but then you get into it's getting a bit similar I know there's an offset there visually getting very close here to a mirror And I know it's kind of anticipating into this, but even that if they could be maybe Maybe there that has a framework to offset and giving us a bit of a Lower arm High arm and I know at the end it's kind of almost the same But just I'm trying to get away from believe a mirrored aspect was then you got That feeling just a bit mirrored there And even if you get up on something like this, maybe she could just have straight a leg so that when you go into this That's the big contrast. So otherwise we're getting kind into the same leg poses as well just with the weight shift And same thing with that where we kind of go out even though it's silhouette wise offset for sure I wonder if there's anything you can do differently I can fly with this this is more like a tada or something, but what could be a cute little thing for a kid I can fly This is like don't do that, but like, you know arms down Iron Man style With the head like a head wiggle or something and imagine she gets on her tippy toes again legs together and and she will go up up up Knows up a bit something and I feel like that could be something a bit more interesting with that moment I like that. This made me laugh. This was really good. And then here not sure that you need That I'm all it mainly be acting because this is all cute, but then watch out again. We're getting into similarities there Yes, it breaks it up here But what I like is this that you she's telling her something It was okay. Well, I got to figure something else. I got a light to her I had to say this and if we could kind of go from that to that where her arms again might be down where Hey again in an offset thing where maybe When you go down, it's kind of like the way you have it here. I like this a lot where one is is Hidden so you maybe go from here Straight to that arm hidden and this could be the tapping the sides or she could have kind of a finger wiggle Like she's getting nervous and it's kind of the body Kind of telling that idea you like to face lies, but the body can't So yeah, she has a bit of a nervous thing with the fingers kind of figuring out What should I say and then that leads into this? That's really cute. I like how you Down low and how you go then down with the head into that. I think that's really cute I would just look at eyeliner gets a bit tricky there So it's kind of working on that a bit And you're asking about steps To spline and blocking it always kind of tricky. I think what I would do is people kind of lost I would look at transitions and kind of the beats if you look at okay. What is she doing from here to here? But with this clip she has very clear beats where she goes always into a separate move That are there's always something new and I think you can really then What I call this is chunk it up into different sections and work on that and by working on that I mean you look at like all the pose that we talked about look at eyeliner and all the details But then I would look at just kind of the breakdowns like how do you want? Care to go from there to there like what is the body part that leads? Where can you start finessing things a bit more? You will have to kind of work on contact there a little bit Turn transitions as that arm goes up and suddenly stops. It's kind of making sure all that stuff gets a bit more It's love there in terms of just the breakdowns and in-betweens. So you have a bit more control of that But it's already really promising. It'll be like the timing Like the way it snaps into this. It's all really promising. So to me just kind of changes here in terms of posing Other than that and I will elaborate a bit more in the email if you want Just let me know and that's that. Thank you. All right There's an email you can sign up you can start whenever you want you can submit whatever you want You get 16 submissions either way a like and subscribe would be awesome. All right. Thank you


Welcome to the 27th lecture in the course Engineering Electromagnetics. For the last few lectures we have been considering the parallel plane guide as the last topic in the series we consider the attenuation constant of the various types of waves that we have considered on the parallel plane guide. For this purpose we make the following considerations. You would recall that in general the propagation constant gamma bar for the parallel plane guide was written to have the following expression. We wrote gamma bar equal to m pi by a whole squared minus omega squared mu epsilon whole square root and we said that for the frequency range such that omega is less than a certain frequency called the cutoff frequency. Gamma bar is completely real we may call it alpha bar and for the frequencies greater than this cutoff frequency gamma bar is completely imaginary and we call it let us say j beta bar. And we said that this frequency range does not correspond to propagating waves and the fields would just attenuate exponentially with the attenuation constant alpha bar. On the other hand in this frequency range the fields would propagate without any attenuation in the idealized situation that there is no lost presence. We consider the conductors constituting the parallel plane guide to be perfect conductors and the material filling the parallel plane guide also to be a perfect dilute. And therefore, in that idealization this situation is quite fine. However, when we consider practical materials, practical materials which constitute the parallel planes or practical media which would fill the parallel plane guide they are going to have some loss. And therefore, in the frequency range where in the ideal case we said that there is no attenuation there is going to be a small amount of attenuation present depending on the quality of the material that we utilize for fabricating the wave guide. This small amount of attenuation is very different in quantity and nature from the large attenuation constant that exists in the frequency range below the cutoff frequency. This distinction we must keep in mind and therefore, we say that in practice actually gamma bar would be equal to a small attenuation constant plus j beta bar even in the frequency range in which normally we said that wave propagation takes place. Now, how do we estimate this small attenuation constant that is present in the frequency range in which waves propagate on the parallel plane guide? We discuss a general method for obtaining this. The method for calculating the attenuation constant and so that there is no doubt left we may write here for the frequency range where omega is greater than omega c. And for this purpose for obtaining a general method for estimating this small attenuation constant we once again make use of the transmission line equations.  But in general for a practical transmission line there will be some attenuation constant alpha and a phase shift constant beta. Similarly, we are going to have the associated current which may be expressed as i naught e to the power minus alpha z e to the power minus j beta z. And now let us calculate the power that is associated with this wave and we calculate the average transmitted power. And let us use the symbol for power transmitted as W t and we call this average power which is going to be given by half real of v i star using the notion of complex power. Therefore, it turns out to be half real of v naught i naught star e to the power minus twice alpha z. And immediately we see that the transmitted power at different values of z as the wave propagates is decreasing by virtue of the attenuation which is continuously taking place. So, let us consider the change in the transmitted power per unit length or the rate of change of transmitted power as a function of z. And we can estimate this by taking the derivative of the power transmitted with respect to z. So, we write del W t average by del z which is going to be minus 2 alpha times half real of v naught i naught star e to the power minus 2 alpha z or in brief it is going to be minus 2 alpha and W t average itself. Now normally this derivative is interpreted as the rate of increase of let us say W t. Since we have a negative sign appearing we may interpret this as a rate of decrease by associating a negative sign in front of this, which is also quite realistic because of attenuation the total power transmitted is reducing. So, negative rate of change of W t average is going to be positive. Rate of change of rate of decrease of transmitted power is equal to twice alpha times the total power transmitted. What is this rate of decrease of power transmitted? Why is this power transmitted decreasing? It is decreasing because there is power loss. And therefore, this we make call W L average. And that gives us very simple expression for estimating alpha the attenuation constant for the propagating wave that is alpha is equal to W L average divided by twice W t average or in words it is the total power loss total power loss per unit length. This is the W L average per unit length that we have to keep in mind total power loss per unit length divided by twice the total power transmitted. Now somebody may raise an objection that we are not using the qualifying word average in these two terms the numerator and the denominator. Now actually that is not necessary as long as both are calculated on the same basis. It could be the peak powers or it could be the average powers as long as we are using the same kind of calculation for both it does not really matter. And that gives us a very straight forward expression for estimating the attenuation constant alpha. Now therefore, what is our strategy for calculating this attenuation constant alpha? We use what is called an engineering approximation. The steps in this engineering approximation can be listed as follows. We list down so that we can utilize this later on also the method which is known as the engineering approximation for estimating the attenuation constant. What are the steps in this engineering approximation? We first say that estimate the fields in the given structure ignoring losses like we have done for the parallel plane wave kind. Calculate the fields satisfying the boundary conditions imposed by the structure at hand and in the first step we ignore losses. If there is a conducting material which is being used we assume it to be perfect. If there is a dielectric material appearing in the structure we assume it to be perfect again. Now we make the important assumption that even in the presence of losses even in the presence of small amount of losses the basic field structure is not going to change. As long as the losses are small this is a reasonable engineering approximation. So, the second step amounts to assuming that the fields unchanged even in the presence of small amount of losses. Now this is somewhat restrictive it means that if the losses are large then we have to solve the problem taking the losses into account from the beginning. But that is rarely the case mostly the waveguides that we are going to make will have small amount of loss then only they will be of practical utility. Then we calculate the power transmitted and as we just clarified it may be peak or it may be efferent it is not going to really matter as long as the other term is also calculated on the same basis. So, we calculate the power transmitted along the length of the waveguide. For example, if you have assumed the wave propagation in the z direction in the parallel plane guide. So, what is the power transmitted in the z direction that is what we calculate here. Then we estimate the power loss estimate the power loss in whatever material is lossy it may be the conductor or it may be the dielectric or it may be both estimate the power loss in the lossy conductor and the dielectric. And then of course, we have got an expression for alpha saying that alpha is the total power loss per unit length divided by the total power transmitted as we just wrote down. This is the method which is known as the engineering approximation and it works quite well as long as the losses are small. Having obtained an estimate of the attenuation constant alpha this way if one is more interested in arriving at accurate expressions for the fields for the lossy waveguide one can use this in the fields and then undergo another iteration for calculating the attenuation constant. And hence that will be a refined estimate of the attenuation constant and the field expressions can be defined further. However, in practice the second iteration is rarely necessary because we use waveguides which have a low loss low attenuation constant. Now, this method can be demonstrated for the various types of waves that the parallel plane waveguide supports but before that let us see how we may estimate the power loss in the conductor. Usually the dielectric material that is utilized has a smaller relatively much smaller contribution to the total power loss as compared to the conductor loss. Let us see how this can be estimated in practice. You would recall that the waveguide that we are dealing with is the parallel plane waveguide and now we are interested in let us say estimating the power that is lost in the conducting planes per unit length in the direction of propagation. How are we going to be able to do that? We consider the component of power that flows normally into these planes. That is the power which is taken away from the power flow in the z direction and that is the power loss. The power loss has to be considered in both the conducting planes naturally. And for this purpose we assume again not a very restrictive assumption that the thing thickness of the conducting planes is sufficiently large. What would be sufficiently large? A thickness which is several skin depths will be considered a thickness which is sufficiently large and therefore the effect is that we can consider the power that is lost in the conducting medium propagating as a plane wave uniform plane wave in the conducting planes. That is the advantage of these simplifying assumptions and therefore for the power loss in the conducting planes or we may write this simply as conductor loss. We use the expression that P n average. The normal component of the pointing vector flowing normally into the conducting surface. That is what would be associated with the power loss in the conductor. And what would be what would this be equal to? It will be half real of E tan cross H tan star. Now as far as the tendential component of the magnetic field all these are both of these are at the surface at the conducting surface where we want to estimate this normal component of the pointing vector that should be quite obvious. As far as the tendential component of the magnetic field is concerned we have got expressions for the magnetic field for various types of mode supported within this parallel plane guide and we can pick the component which is tendential. Calculate its value at these conducting planes and use that here. What about the tendential component of the electric field? We impose the condition that for these perfect conductors the tendential component of the electric field must be 0. But it is also clear that for the practical case when the conductors do not have infinite conductivity there will be some small value of the tendential electric field which is going to be present. How is this to be estimated? So then we recall the relationship between the fields for a uniform plane wave propagating into an infinite medium composed of the material of the conducting planes. And then these two are going to be related through the surface impedance so that we can write E tan by H tan is equal to the surface impedance of the material the conducting material at hand which also is equal to the intrinsic impedance of this conducting material as we have seen. And it is equal to R s into 1 plus j where R s is omega mu m by 2 sigma m where the subscript m goes to show that these are the quantities for the conducting materials or for metal. Using this therefore we can obtain p n average as half R s magnitude H tan square because that is what H tan multiplied by H tan complex conjugate is going to be and these are going to be mutually perpendicular to the direction of propagation of power into the conducting planes. And therefore the cross product will be simply a multiplication it can be seen easily that this is simply the I squared R kind of loss in the conducting medium the units of this are going to be watts per meter square. The tangential component of the magnetic field is associated with a linear current density on the surface of the conducting material and the relation the vector relation is as follows J s linear current density is equal to n cap cross H tan where n cap is the unit outward normal at the surface at which we want to estimate the linear current density. Magnitude wise it is simply J s equal to H tan and therefore we see that the normal component of the pointing vector is equal to half R s magnitude J s square this is the power loss this is the ohmic loss per unit area of the conducting material. Since you already have the magnetic field it is easiest to apply it in the form half R s magnitude H tan square right. Now this thing can be applied to calculating the attenuation constant alpha for the various types of waves that we have become familiar with on the parallel plane guide. We do this calculation first for the TEM wave attenuation constant for TEM wave. Recalling the steps in the engineering approximation method of estimating the attenuation constant the first step was calculate the fields ignoring losses. This part we have already done and the fields obtained were as follows we have the y component of the magnetic field in terms of an amplitude constant C 4 times e to the power minus J beta z and the other field component present in this case was E x equal to eta times C 4 e to the power minus J beta z where eta is square root of mu upon epsilon the permeability and the permittivity of the medium filling the parallel plane wave guide and beta in this case also had a very simple expression beta was simply omega times square root of mu epsilon. Since this is in the idealization that no losses are present the loss mechanisms the conductivity of the conductor or that of the dielectric is not appearing in these expressions that is quite fine. The next step is to calculate the power loss and as I said while in general the power loss could occur because of the lossy dielectric material as well as the lossy conducting material the dielectric loss is relatively much less and therefore we calculate the conductor loss and the magnetic field that is now present H of y one can visualize this as follows H of y in the y direction it is uniform throughout the space between the conducting planes and if we consider the unit normal to these conducting planes it is going to be in this direction this will be n cap for the top plane and this will be n cap for the bottom plane and H of y is of course in the y direction. So n cap cross H y is going to be in which direction it is going to be in equal and opposite directions and it will be a direction which is like this in the upper plane which we may call J s and a direction like this for the lower conducting plane and if you obtain J s that will be the current per unit width along the y direction that is how it is called linear current density. And if you calculate the loss based on this that will be the power loss per unit area for a unit width along the y direction and for a unit length along the z direction. So with this clarification we can now proceed with the calculation of the power loss we saw that pn average is equal to half rs magnitude h tan square and it is going to have a value which is half rs c4 square assuming that c4 is real. This is the power loss per unit area of each of the conducting planes and therefore the total power loss W L and since this is calculated on the basis of the power loss in the conductor sometimes a subscript is also added here either just a c or conductor. What will be the total power loss in the conductor? It will be twice of this since there are two conducting planes alright times let us say b times half rs c4 square where b is the width of the structure along the y direction. So per unit per for a width b of the structure and for a unit length of the structure this is the total power loss. For calculating the power transmitted also we will use the same width of the structure because otherwise the structure is of infinite width. So to get around that problem we say that let us assume that the structure is of width b which is simply b times rs times c4 square. Similarly we can calculate the pointing vector which will be involved in the total power transmitted. We can calculate p t average as half real of e x cross h y star and we can put vector signs here and say that we consider the z component of this which is the only component appearing in this case which is going to be equal to half eta c4 square which is the power transmitted per unit area and therefore this is in watts per meter square. Now what is it that we require for the attenuation constant what we require is the total power transmitted which can be obtained by integrating this pointing vector over the cross section of the waveguide that is wt average is equal to p t average da integrated over the cross section of the waveguide. For the simple case of the TEM wave since the pointing vector or the z component of the pointing vector is uniform everywhere within the waveguide the integration is trivial. We just consider what is the cross sectional area now how much is the cross sectional area the spacing is a along the x direction and along the y direction we once again use the width b to be consistent and therefore this is simply half ab eta c4 square. So, that now we have everything for calculating the attenuation constant and alpha comes out to be w l by twice wt and as you can see it is in a straight forward manner r s by eta times a. We can substitute the expressions for eta and r s but before we do that a simple comparison is quite instructive one can compare this with the attenuation constant that we obtained for low loss transmission lines if we considered only the resistive term and in that case alpha was half r by z naught and the correspondence between the two expressions is quite clear there we had z naught as the characteristic impedance of the transmission line here eta is the characteristic impedance or the wave impedance for the TEM wave in the parallel plane guide. We can substitute for these expressions r s and eta and we obtain this as 1 by a square root of epsilon by mu and then omega mu m by 2 sigma m once again whole square. So, following our method we have obtained the expression for the attenuation constant. We started with ignoring losses calculated fields and then we assume that the field expressions do not really change even if a small amount of loss is present and then we calculated the power loss and the total power transmitted. If the dielectric were also lossy that dielectric loss can also be estimated in a straight forward manner using the method described in the context of the transmission line. And therefore, it is the total loss that will appear here instead of just the conductor loss and this is the kind of expression that we are going to have. The expression can be plotted as a function of frequency one can see that it is going to vary with frequency as the square root of frequency. This kind of variation in the attenuation constant because of the surface resistance of the skin resistance was pointed out in the case of the transmission lines also. The plot for the attenuation constant as a function of frequency is shown here. The frequency axis is here the abscissa and this is the attenuation constant and for the TEM wave for which we have just calculated the attenuation constant the variation in the attenuation constant as a function of frequency or omega is like this. Since there is no cut off frequency for this wave it starts from 0 frequency onwards and it starts rising as the square root of frequency. If there are no questions then we proceed to calculate these attenuation constant for the TE waves as well. The method of calculation is going to remain the same attenuation constant for let us say TE M0 modes. The starting point would be the field expressions obtained ignoring losses and in the frequency range in which wave propagation takes place these field components are written as follows. E y is C1 sin of M pi by A x e to the power minus j beta bar z and H x is minus beta bar by omega mu C1 sin of M pi by A x e to the power minus j beta bar z. And we also have the z component of the magnetic field in this case H z equal to j M pi by omega mu A C1 cosine of M pi by A x e to the power minus j beta bar z. And as you would recall here beta bar is omega squared mu epsilon minus M pi by A whole squared whole square. And we assume that even in the presence of a small amount of loss this is the kind of fields that are going to propagate. And for power loss we write p n average which is going to be half r s magnitude h tan square. We have two components of the magnetic field here right, but it is quite easy to make out which of these is the tendential field component. This is the parallel plane waveguide and it is the z component of the magnetic field which is going to be tendential to the conducting planes. And that is what is going to be involved in this calculation. And while in general H z is a function of x it has to be evaluated at x equal to 0 or at x equal to a for this purpose. And therefore, it is simply half r s and then M pi C1 by omega mu A whole square. So, that the power loss in the conductor W L average taking into account both conductors both conducting planes is going to be and if you assume that the width is B along the y direction it is going to be B times r s M pi C1 by omega mu A whole square. Next we undertake the calculation of the power transmitted. And for that purpose we first have to estimate the pointing vector in the z direction and calculate its average value. And it is going to be half real of E y cross H x star. And of course, it will have only the z component and one can see that it is going to be the negative sign is going to be nullified it will be beta bar C1 squared by twice mu into omega. And then sign squared M pi x y now in this case because of the variation of the fields along the x direction the pointing vector giving the power flow in the z direction is not uniform at all values of x. It is varying in this manner and therefore an integration is going to be required however the integration is going to be quite straight forward. The total power total transmitted power is going to be p t average integrated over the cross section. And when we integrate this part from 0 to a we are simply going to get a value a by 2 alright. And then of course we are going to consider that the width along the y direction is b. So, keeping these two things in mind we are going to get the average power transmitted as follows it will be beta bar C1 squared by 4 omega mu times a b. So, that the attenuation constant turns out to have the following expression alpha is twice M squared pi squared by omega mu a cube and then r s by beta bar. One can write the expressions for r s and beta bar and obtain the expression for the attenuation constant as twice M squared pi squared and then omega mu M by twice sigma M by omega mu a cube into beta bar which is omega squared mu epsilon minus M pi by a whole square root. Of course it is a function of frequency and the variation that it has as a function of frequency is shown here. The interesting thing is that the attenuation constant now is decreasing with frequency. This is the variation of the attenuation constant for the T e modes. And of course below the cutoff frequency there is no wave propagation and therefore there is no attenuation associated with the wave propagation. The expression for the attenuation constant for the T m M 0 modes can also be obtained in a similar manner and for the sake of completeness it is mentioned here alpha T m M 0 modes and the expression turns out to be twice omega epsilon r s by a beta bar. One can expand this further by writing down the full expressions for the surface resistance and the phase shift constant. This has a different type of variation with frequency and it is plotted here. The attenuation constant as a function of frequency for the T m modes is the one shown in blue. And the interesting thing about this is that it undergoes a minimum. At the cutoff frequency this also rises very sharply and then it starts varying in a manner very similar to that of the T m waves. And at root 3 times f c which can be seen by considering its derivative with respect to omega and considering where it is 0. It can be seen that at this value of the frequency the attenuation constant undergoes a minimum. Now all these observations can be very important when we want to utilize the parallel plane guide in practice. This is where we will stop this lecture. In the lecture today we have considered the attenuation constant for the various types of waves that are supported on the parallel plane guide. We first introduced a general method for estimating the attenuation constant using an engineering approximation and then we obtained the expressions for the T e m and T e waves on the parallel plane guide. We also considered the frequency variation of the attenuation constant. Thank you.


Hello, everyone. Thank you, Martha. Thank you, Aliyah, for organizing today and last night. Taylor Hobson is an almost PhD candidate in history of art at Brynmore College. His dissertation, which is tentatively entitled Expanded Theatres, Reconfigured Screens, Projection in the Installations of Douglas Gordon, Jim Campbell, and Janet Cardiff is in progress. He received a master's degree in art history from the University of Georgia and has worked at the press office of the National Gallery of Art in Washington, D.C. Hi, thank you, Hommay, and thanks for everybody at the Barnes and everyone participating. This has been a really great day, and it's great to meet everybody. John Ford's 1956 film, The Searchers, holds a unique position as a critical and popular standard bearer of a contentious Hollywood genre. The Western is often cited as an example of studio era Hollywood's irresponsible historical and social revisionism. Here, the American frontier is reimagined as a binary of savagery against civilization, a caricature which excuses travesties committed against Native Americans. Yet The Searchers has avoided much of this criticism, in part due to its characters psychological complexity. Although the film features the genre's token settings and figures including its most famous leading man, John Wayne, the conflicts in which these settlers find themselves suggest a chronic lack of power. The film begins with a home invasion and the murder of almost all the characters initially introduced. Afterward, Ethan Edwards, played by Wayne, goes looking for his abducted niece Debbie, who remains a captive as a presence always just beyond the visible horizon. This search thus faces the aggressive antagonist of the Comanche Raiders, but also of the American wilderness itself.  A constant sense of alienation and disorientation during the search renders the very achievement of its goals questionable. In such divestment of authority, from its heroes, invites the viewer of the film to interrogate the genre at large. And yet the focus away from fast-paced action might puzzle some audiences. Scottish artist Douglas Gordon recalls his childhood and asking his father how a film could be about nothing. Quote, he tried to explain to me that the film was not at all about nothing. It was about searching and waiting and waiting and searching and hoping when all hope is gone and how this was a very important thing in life. End quote. And this is all to say that the searchers takes its time. If not slowly paced, the film foregrounds its narrative duration in a way that makes viewers reflective. Is this a typical Western? Does it subvert or perpetuate the genre's common social criticisms? The searchers quietly deflects these questions back onto its spectator. Five year drive-by originally conceived by Douglas Gordon in 1995 but only shown in part relies on common home video technology to slow down a copy of Ford's movie. Extending its typical two hour runtime to five years. The time spent searching within the fiction of the film. The proposal suggests an outdoor screening in the American West which is later specified as Monument Valley, Utah. The favorite shooting location of John Ford and one used for much of the searchers. Gordon would thus surround the film with the landscape of its original setting where daylight would inevitably threaten visibility. This spatial condition effectively aligns the screening of the movie with its screened images, further connecting the viewer's experience to that of the film's narrative. In fact, I argue that five year drive-by transfers the searchers' anguish and hope outward and onto the installation's formal elements. Gordon's prolonged screening dissolves the searchers' narrative continuity within an excess of time. The film's opening shot establishes a point of view with Martha, the matriarch of the doomed Texas family. However, this domestic alignment is only the first in the sequence of shots. Martha's gaze pushes outward with the camera, but is cauterized by a reverse shot of Ethan as her implied object. At 16 minutes per frame, this visual dialogue between Martha's gaze and Ethan's approach is lost to the viewer. Gordon's deceleration likewise dissolves actors' dialogue, interactions, or any natural gesture. In lieu of associations between consecutive film frames, Gordon establishes a visual connection between the image within the screen and the landscape without. The open desert, here doubled, plays a role in pacing in the film's narrative. The trails followed in the searchers are swallowed up in the vast and dangerous southwestern landscape, obscuring concrete directionality. The film, too, features a cyclical structure. Its closing shot, for instance, finds Wayne's character leaving the home to which he returned in the first scene, and its framing recalls the opening to suggest a bookended tale of Ethan returning to the nomadic life from which he came. This unfolding of time has a filmmaking analog in editing. For the most part, the searchers avoid quick splicing and frenetic sequences. Instead, the cut as an ellipsis emerges as its characteristic maneuver, one which compresses time. Each gap that separates linear frames in a film reel is an opportunity for a cut away, but also for a connection. The searchers plays with this duality during several consecutive sequences that feature Wayne and his companions, tracking Debbie's captors. Ford's compositions are just different enough through this sequence to suggest a steady passing of time, but for hours, for days, we're not really sure. Suddenly, another cut finds the men among falling snow, and we are caught off guard. Nature tips us off to a more expansive and seasonal timeframe. The next scene, which is back among dry dust, confirms with dialogue that the first shot occurred one year ago. Where Ford used editing to disguise the tedium of a five-year period, Gordon reverses the process, exposing the spectator to that temporal vastness. But what does a restaging of the searchers' diagetic time actually preserve of its narrative effect? Ford's meandering setting remain, to be sure, but the plot of the searchers is far more direct. Ethan simply looks for Debbie. Emotion arises not from twists and surprises, but rather from the stoic persistence in the face of unbearable vastness of time and space. As the days pass, the chance of finding Debbie alive lessens, and so it is the duration of the search that heightens conflict within the film. Centered around its single, unwavering task, the action of the searchers is more accurately in action. Ethan rides, tracks, talks, looks, with only the occasional fight against a swarm of Comanche. And Ford undercuts the excitement of even these scenes, avoiding the frenzy of, say, a close-up of charging hooves for wider composition. Action does not take up space, it is encroached upon by towering mesas. Even the searching becomes more aligned with waiting. Constant traveling also resembles wandering. And yet the searchers is not boring. Rather, its narrative is driven by an acknowledged lack, a search for someone against the odds, odds which become increasingly antagonistic with every passing day. Like the overbearing rocks, the enormity of Ethan's goal sacrifices immediate action for a bigger picture. Gordon recalls his own frustration with the incongruity between diegetic time and the film's duration. Quote, how can one film, which lasts only two hours, possibly convey the fear, the desperation, the heartache, the real searching and waiting and hoping that my father had tried to explain to me? The film's stasis here underscores the mobility that's taken for granted in a traditional projection. Emphasizing narrative pace bites very absence. No longer immersed in the projected world, the once passive viewer film becomes what Laura Mulvey, borrowing from Raymond Ballour, calls a pensive spectator. Without the distraction of 24 frames per second, attention gives way to contemplation of one's own responses to these diffused images and of the time they bracket off in associations with or misremembrings of the original film. Mulvey's pensive viewing makes room within the viewer to consider the nature of cinema. Physically, however, Gordon's screening reroutes attention outward. Without constant stimulation, attention escapes to the world surrounding the image. Gordon further expands this increasingly public space to the natural world. His outdoor environment is anathema to theater experience in general, and yet it is intensely aligned with the searchers in particular. Gordon incorporates the landscape with a site specificity that relinquishes his projection to the desert. Less controlled than gallery-based installations, five-year drive-by recalls the monumental earthworks of Robert Smithson. Most famously, Smithson's 1970s spiral jetty inhabits a similar southwestern setting. Smithson also uses tools of appropriation and manipulation. He mines the earth for his natural materials, which he then rearranges and offers back to the land. The spiral also suffers deterioration from weather and erosion, not to mention its decades-long submersion within the Great Salt Lake. Gordon exposes the searchers to similar environmental challenges. He spotlights his geology with light, another material with overtly entropic properties, one that does not require eons of aging to expose its vulnerabilities. By pairing unsustainable porous light with the aggressively fluctuating western landscape, Gordon invites the destruction of his work. I would argue further that this outdoor placement becomes less significant in terms of geographical location, as much as that location susceptibility to the natural signifiers of time, the rise and fall of the sun on the earth. It is not space which causes the fluctuating visibility of the film, but rather time mediated through space. Gordon foregrounds the natural materials of cinema, bypassing the constructed shelter of the theater. His spectator faces the elements the earth made bare and essential, and viewing is robbed of the safe distance that buffers the theater from its screened past. As the immensity of the film is also made immediate, Gordon's description of Ethan's search resonates five long years. Five years of waning hope, but also an ebbing drive of life. I argue that by dismantling the theater, Gordon activates the drama of the search, defined by its five-year duration, and the anguish and determination it circumscribes. The duration as a hiatus, a waiting, a hoping, a suffering persists, both in the excruciatingly slow projection and in the desolate landscape on either side of the frame. Outside of the searchers, there is now only Monument Valley, whose geography conveys time more than solid matter. The sparse environment is defined by absence. A binary of rock and air testifies to evaporated waters in the footprints of negative space. The valley itself thus embodies the passing of time on an epic scale, biblical as the searchers has been described sometimes. The searchers still images conjure memories not only of the American frontier, but also of Hollywood in the 1950s, which presented spectacles for its audience on its own outdoor monument, the drive-in theater. Five-year drive-by still addresses us. It is long but not interminable. Its pace is still perceptible to a human viewer, even a distracted one who can only extrapolate the larger film. And so how is the searchers seen by Gordon's spectator? The image on screen would often double the surrounding landscape, but even in optimal drive-in conditions, the projection of a warm technicolor earth might appear artificial, oversaturated against its present-day incarnation. A close-up of Wayne fits in here, as Ethan is implicitly surrounded by the same canyons, though now his stoic heroicism tips over into an impotent stillness. Even a triumphant widescreen interior shot is shrouded by the surrounding valley. Despite domestic spaces within the searchers, shelters are never sanctuaries, only temporary refuges from the wilderness. Gordon aligns the domestic interior of 1868 with the movie house that projected its fantastic reimagining in 1956. Time pushes the viewer away from narrative and toward monument valley, where survival infringes upon enjoyment. If ruined in this desert, the spectator paradoxically never leaves the frame of the movie. Rather, the five-year interval immerses the viewer into the time and the space of the searchers. That search and the projection persists despite natural obstacles. Gordon's concept reduces a film to a billboard, a format that drew audiences to its first screenings. However, I would argue that this viewer is more than pensive. Mulvey's spectator is empowered by home viewing technology to pause film, rewind it. Gordon's audience is without control. Pauses simply become instead the new prescribed mode of viewing. Rather, five-year drive-by produces a stranded spectator. Driven out and abandoned, this viewer turns from the uninviting screen to an even less hospitable desert landscape. Thetidium remains a constant companion near towns like Tombstone and Deadwood, names like warnings, hence Gordon's suggestion that we simply drive by. With so little here to orient the mind, one is exposed, endangered, and lost. Yet it is this capacity of time to overwhelm the individual which drives the searchers. Ethan faces his odds head-on in the cyclone narrative of the film with a vow to find Debbie as the turnin' of the earth. And so, despite the alienation, even because of it, the film's desperation, fortitude, and faith become a lived experience. Lost in the desert, Gordon's nomadic cinephile resembles Ethan, who finds his stable home only to witness its invasion, who comes and goes with the wild Western landscape. But time also uncovers hidden artifacts. Five-Year Drive-By allows for the emergence of a marginalized character like the abducted Debbie. Natalie Wood appears only in relatively few frames in the film, but with Gordon's abstraction of the film, her presence as the search's objective grows immeasurably. Shadowed by her image within the Comanche camp, the stranded spectator also becomes a captive one. By relocating the site of projection, Gordon translates without words the psychological tensions of the film's premise to his spectator, who is lost in an open land that also threatens to enter its visitor. No longer captive, captivated, but rather held captive by the expanded film, the stranded spectator lives towards Western, one defined not by a showdown as much as a search. And the searchers renders even that act a passive one of waiting, of hoping, and holding out against time. Accordingly, Gordon constructs a screening that offers the film back to its origin, a vastness of nature that encroaches upon the individual, regardless of identity. Thank you.