The photo you see here is of Joseph Louis Gelussac and in early 1800s Gelussac was experimenting with how different volumes of gases combine and based on his calculations another chemist arrived at a relationship involving gases. So this relationship which is called Gelussac's law or the pressure law can be stated as pressure is directly proportional to the temperature but this relationship between the pressure and the temperature of the gas assumes two conditions. One that the volume occupied by the gas is fixed and two that the amount of gas is also fixed. So let me just write down both of these conditions here. To understand this better we can consider this setup where we have this box and in this box we have a few molecules of the gas and because our box is a rigid box and the gas is within this box the volume is now fixed and also because we are not adding more gas or removing the gas from this box the amount of gas in this case is fixed. So now both of these conditions are met and we know that these gas molecules will be randomly moving around and while they are randomly moving about like this they could be colliding with any of these phases of the box. So now to better understand this relationship let's take another box and this box is an identical box with the same amount of gas in this box as well and in this box also the gas molecules will be moving in random directions. So now that we have two identical boxes and for both of them both of these conditions are met. What if we heat this box when we are heating this lower phase of the box what happens is because of the heat the kinetic energy of these molecules increases which means that their velocities also increase and they start moving faster in the box and we know that when the kinetic energy increases the momentum will also increase and we define force as the rate of change of momentum. So effectively what's happening is when we heat this phase as the molecules collide with this phase and their kinetic energy increases they collide with each of these phases faster and because of this increased momentum the force applied on each of these phases increases and we know that the pressure is defined as force upon area. So since the force increases the pressure also increases. So what happened here was by increasing the temperature we see how the pressure also increases but this was a very qualitative description of what's happening. Let's see how we can express this mathematically and what new information we can get from there. So I have written down our earlier relationship between pressure and temperature like this that is P is proportional to T where the P is pressure and T is temperature. I can get rid of the proportionality sign and write it in the form of an equation as P is equal to some M times T where M is a constant and here you can see that M is a dimensional constant. So going back to our molecules in a box if we know the temperature at which this box is kept and if we know the pressure at that point we can get the value of this M and it will be in some pressure per temperature units. So now if we just rearrange this we can write this as P divided by T is constant and what this rearrangement does is that it simplifies some calculation for us. So again if we go back to this box let's say we started at some temperature T1 and at that time the pressure was P1 and we then increase the temperature to T2 because of which the pressure then became P2. We know that the ratio P by T is constant. So we can write this as P1 by T1 is equal to P2 by T2 because we know that the ratios of pressure and temperature will be constant. If we know any three of these quantities we can easily find the fourth one. Now again if we look at this equation we can see that this resembles the equation of a straight line. If you think of the equation of a straight line written as y is equal to ax plus b and let's say if this intercept is 0. So we can write the equation of the line as something like y is equal to ax and this equation here resembles this form. So if we were to graphically represent this relationship if we have pressure on the y-axis and temperature on the x-axis we can show this relationship as a straight line but there is one very important point to note here. This temperature that we are talking about here is in the form of Kelvin and not in the form of degree Celsius and not just here whenever we write this relationship in this form or in the form of a ratio everywhere the temperatures that we take are in Kelvin and so if the temperatures which are known if they're given in degree Celsius what we do is we add 273 to it and we can get the temperatures in Kelvin which we can use in these equations. So now let's go through one example problem and see how these calculations are done. Now let's look at this problem which is asking us to calculate the pressure change when a constant volume of gas at a pressure of 180 is heated from 20 degree Celsius to 30 degree Celsius. So if you want you can pause the video here and give this a try. Okay so let's write down what is known from the information given to us. So first we can see that we've been told the gas has a constant volume and so if it is in a box like we saw before the amount of gas is also fixed. So in that case we can apply Galer-Sachs law and we can write P1 by T1 will be equal to P2 by T2 where we know that our initial pressure is 180 and initial temperature is 20 degree Celsius. We know that the final temperature is 30 degree Celsius. So if we rearrange this we can write P2 as T2 divided by T1 into P1 and as we saw before the temperatures that we use here should be in Kelvin and not in degree Celsius. So if we directly substitute 30 and 20 here instead of T2 and T1 we'll get the wrong answer. So to use this relation we will first convert these temperatures into Kelvin. So we will add 273 to both of these. So now the initial temperature becomes 293 Kelvin and the final temperature becomes 303 Kelvin and so we can substitute these two temperatures and the initial pressure in this equation to calculate P2 which is 303 divided by 293 into 1.08 m and if you solve this we get P2 to be 1.03 8 m and then to calculate the pressure change what we're going to do is the pressure change will be equal to P2 minus P1 which is this 1.03 minus the initial pressure which is 180 m and we get the pressure change to be 0.03 8 m.


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U.S. deeply engaged on Azerbaijan-Armenia peace talks. The United States continues to believe that a durable peace between Armenia and Azerbaijan is possible, the State Department said Turin Agency reports. It's something that the Department will continue to work towards. Principal Deputy Spokesperson Vedant Patel told a daily briefing in response to Turin's questions about the current state of the peace process, following Special Advisor Louis Bono's talks in the region this week. Obviously, Coordinator Bono, the Secretary of State and others continue to be deeply engaged on this, Patel added. In the meantime, he refrained from previewing any upcoming plans or conversations. Earlier, James O'Brien, Assistant Secretary of State in charge of Eurasia, also expressed Washington's intention to continue supporting the peace process. There are more to work through and to the extent we can be helpful as they do, we're happy to support. Separately, the State Department also announced Secretary Blinken's upcoming travel to Davos next week, saying that he will meet with leaders to discuss issues of global concern, including Washington's commitment to transatlantic security and the rules-based international order. It wasn't immediately clear whether Blinken will meet with Azerbaijani or Armenian leaders at Davos.


Let us start our today's lecture of this NPTEL video course on Geotechnical Earthquake Engineering. On this course, we are now going through our module 5, which is wave propagation. Let us quickly recap what we have learnt in our previous lecture. In the previous lecture, we have seen for one-dimensional wave propagation in an infinite rod. For the case of longitudinal wave, what is the particle velocity? How we can estimate the particle velocity from the displacement function and using the strain displacement relationship as well as the stress versus strain relationship? We arrived at this relationship and the v p is nothing but the primary wave velocity or p wave velocity or longitudinal wave velocity which is expressed as root over m by rho. So, this is the relationship as we have seen earlier as I was mentioning v p is nothing but root over m by rho, m is nothing but the strain modulus rho is the density of the material and this is the relationship between the particle velocity with respect to stresses and this parameter the multiplication of density with respect to the velocity of the wave of this p wave that function rho v p is known as specific impedance. So, that is the specific impedance of the material. Then in the previous lecture, we have derived what will be the governing equation of motion for a torsional wave when it travels through an infinite rod in one dimension. So, this is the derivation we have seen the difference of torque at both the ends of this infinitesimal element of the rod with the different magnitude of rotational displacement theta at this end and at this end. Then after considering the equilibrium we had derived at this relationship of torque versus rotation in this form where J is the polar moment of inertia after that we had applied the relationship between torque and rotational displacement through the shear modulus and polar moment of inertia in this form. And on further simplification what we had arrived finally is this one where this parameter again we have defined as square of shear wave velocity. So, shear wave velocity is nothing but root over G by rho where G is the shear modulus of the material and rho is the density of the material. And hence the governing equation of motion in terms of the acceleration this is the rotational acceleration and this is the second order differential of the rotational displacement with respect to the x axis system or space coordinate system related through the shear wave velocity of the media for this torsional wave. So, general form of governing equation of motion for any wave traveling in this one dimension can be represented by this equation. So, for longitudinal wave it will be v p for torsional wave it will be v s and corresponding displacement right for longitudinal wave it is u for torsional wave it is theta that is the rotational component of the displacement. And we have seen for this type of governing equation of motion we have the general form of solution expressed in this format. Now, this general form of solution again we can get a particular solution depending on the loading conditions. So, these functions depends on what type of load is applied to the system. So, we have also seen for harmonic loading this is the response what we have obtained where we have defined this parameter k as a wave number which is nothing but ratio of the circular frequency to the velocity of wave in that media. We had also defined another parameter which is known as wavelength lambda which is related to the wave number in this format. And we have seen the similarity between the relationship of this wavelength lambda with respect to wave number k. And in the time coordinate system we have seen the relationship between time period with respect to the natural circular frequency. After that what we have seen in the previous lecture we can see the slide here. We have considered various boundary conditions like this where center line where displacement will be 0. Then at the fixed end where the displacement has to be 0. Also a boundary effect where both says stress and displacement has to be 0. Then at the free end where stress has to be 0. Then we have seen the boundary effect that is material boundary when there is a layered body. How this incident wave then transmitted wave and reflected wave they are related to each other through this example that is for one dimensional case. When wave is travelling in this one dimension in a layered body like this we have seen this is material one this is material two. We have defined the x coordinate system in such a way that this is the positive x direction and this boundary itself is the x equals to 0. And incident wave comes from material one. Some of that goes in the material two as transmitted wave and some of the wave comes back in the same media as reflected wave. Then we have seen how this stresses of incident transmitted and reflected wave can be represented in a harmonic fashion. Also how the displacement functions can be represented through this form. Then applying the known stress strain relationship through this modulus that is when we are talking about longitudinal wave we have to take constrained modulus like this. So, we have obtained what are the relationship between amplitudes of the stresses and displacement. So, this is the relationship of amplitude only stress amplitude with respect to the displacement amplitude. Also we had seen in the previous lecture that at the interface of two material this boundary condition has to be satisfied that is the displacement compatibility and equilibrium of stress. So, these two conditions has to be maintained. Hence this incident wave displacement at x equals to 0 plus the reflected wave displacement at x equals to 0 should be equals to the transmitted wave displacement at x equals to 0. So, that is from the displacement compatibility whereas from equilibrium of stress condition we will get stress due to that incident wave at x equals to 0 plus stress due to the reflected wave at x equals to 0 should be equals to the stress due to the transmitted wave at x equals to 0. Now, let us continue this in today's lecture further. So, what we can write from the previous known relationship that if we equate the amplitudes the displacement amplitude of incident wave plus displacement amplitude of reflected wave should be equals to the displacement amplitude of transmitted wave in the similar form. So, this is from the displacement compatibility relationship and from the equilibrium of stress relationship we get the amplitude of incident wave plus amplitude of reflected wave should be equals to the amplitude of this transmitted wave. Now, at the interface using the known relationship of this one what we can write further by putting the values of this a i and a r with a t we will get this relationship. So, on further rearrangement if we do the further rearrangement of this relationship of displacement amplitude to the reflected and incident wave with respect to the transmitted wave what we will get suppose this reflected wave amplitude we are interested to know because in most of the cases what will be known the incident wave properties will be known from a media we will know what is the stress and displacement of incident wave we have to now find out what are the stresses and displacement in the reflected and transmitted wave that is what we are more concerned about in practice. So, this is the correlation if you put this simple relationship in this equation then on further simplification you will get like this and knowing this a i and a r to determine as so a t also you can determine with respect to a i in this form because a r we have represented in this format. So, hence you can represent your transmitted wave amplitude also in terms of this incident wave amplitude displacement amplitude. Now, let us look at this parameter very carefully this rho times v that is density times the velocity what is that we have already mentioned that is nothing, but in the previous lecture we discussed it is specific impedance this is nothing, but specific impedance of material 2 and this is the specific impedance of material 1. So, that ratio which is called as impedance ratio. So, what is impedance ratio? So, the definition of impedance ratio is nothing, but it is the ratio of specific impedance of two materials and when we are taking that ratio always in the numerator there will be the material which is in the transmitted zone that is the incident wave where from it is the material is the wave is coming that will be in the denominator. So, that is why you can see this rho 1 v 1 for material 1 is in the denominator that is the incident wave region that is the specific impedance of the material where the incident wave is coming from and rho 2 v 2 is the specific impedance of material 2 where the transmitted wave goes in. So, that is the definition of impedance ratio this is the very important parameter because this defines through the material parameter of two materials this gives us the idea how much displacement amplitude of transmitted wave and how much stress amplitude of transmitted wave will occur for a particular incident wave. Why this is important as we I am mentioning because suppose when earthquake occurs at a large depth. So, basically from base rock level or bed rock level that wave will start travelling where that earthquake focus is existing through this form of seismic waves. Now, when this wave travels and finally, it comes close to the ground surface we should know that after travelling through various layers of material that is from rock to stiff soil to soft soil typically what will be the changes in the displacement amplitude and stress amplitude of the stresses because that is most important we need to find out. So, there this use of impedance ratio is very important which we will be easily able to obtain from knowing the density and that particular velocity of the wave suppose we if we are talking about shear wave velocity we have to take shear wave velocity of two material. If we are talking about the primary wave velocity we have to take corresponding primary wave velocity in the two medium like that. So, we have to find out the impedance ratio of the two material, but remember the impedance ratio for primary wave or shear wave etcetera will remain same for between two material between two given material why it will not vary between primary and secondary because if we have remembered the relationship between primary wave and secondary wave that is three is through a constant relationship between the ratio. So, it is a ratio of two similar parameters. So, that is why it gives us the similar value of impedance ratio whether it is a p wave or s wave. So, now what we can see from this slide the displacement amplitude of the reflected and transmitted waves they can be represented through this impedance ratio in this simplest format. So, these two equations are very very important we should be able to find out what is the displacement amplitude of the reflected wave with respect to the incident wave amplitude displacement amplitude over this impedance ratio and what is the displacement amplitude of the transmitted wave related to this displacement amplitude of the incident wave through this impedance ratio that is why impedance ratio is so important. And how to estimate this incident wave displacement amplitude if you know the loading condition or the stresses which are getting developed for your incident wave. So, this is the stress amplitude this is how the displacement is related to the stress amplitude in this format that we have already seen the derivation in the previous lecture. Also for the reflected wave displacement amplitude is related to the reflected wave stress amplitude in this form and the transmitted wave displacement amplitude is related to the transmitted wave stress amplitude in this form through their modulus. Now, stresses they can be expressed in the similar fashion like through this impedance ratio like this that is the reflected wave stress can be obtained using this relationship for a given stress amplitude of incident wave also the transmitted wave stress amplitude can be obtained from the incident wave stress amplitude through this impedance ratio. So, what does it mean if suppose we know the stress amplitude of the incident wave of any particular earthquake and if we know the material property of two different layers of media we can easily estimate all other parameters can you see. So, only parameter we should know is this sigma i. So, if sigma i is known you can compute from sigma i a i once you know a i you will get a r a t once you know sigma i you will get sigma r sigma t clear. So, let us look at this table this table is taken from Kramer's book table 5.1 what are the influences of this impedance ratio value that alpha z value on this displacement and stress amplitude of the reflected and transmitted waves. If you see the impedance ratio equals to 0 what does it mean impedance ratio equals to 0 let us go back to the definition impedance ratio 0 means this is 0 am I right. So, in that case incident wave displacement amplitude and reflected wave displacement amplitude they remain same transmitted wave displacement amplitude is double of this that you can easily get by putting alpha z equals to 0 in this equation and incident wave alpha i will be reflected wave minus alpha i and transmitted wave stress amplitude will be 0. What is this situation can you guess it is nothing but it is nothing but a free boundary where the stress at the boundary condition has to be 0 that is what it shows suppose if we are talking about shear wave velocity when this becomes 0 when we comes close to the ground surface because it cannot travel in your air media am I right. So, in that case you will get this rho 2 V 2 equals to 0. So, that is nothing but when you come to a boundary and end of a material there you will get displacement amplitude gets doubled but stress amplitude there will be 0 that is what if you remember in our previous lecture we have discussed this we have mentioned that that boundary effect of free end what happens at the free end stress becomes 0 but displacement is doubled can you see this. So, that is what now we have seen through this mathematical expression also which is valid. Now, let us check another case impedance ratio equals to 1 what does it mean impedance ratio equals to 1 that means this material and this material are same that is there is no in fact any material boundary the wave is traveling through the same material. So, what is expected same incident wave only will continue. So, let us look at the displacement amplitude of incident wave A i reflected is 0 which is quite obvious nothing should gets reflected entire thing should continue as a transmitted. So, that is the same wave will continue. So, A i will continue and let us look at the stress conditions incident wave stress amplitude is sigma i there is nothing called reflected and entire thing gets transmitted that is the same wave continues. So, sigma i clear. So, these are the cross check whether these derivations of equations are correct or not through this common known conditions and what is the impedance ratio of infinity what does it mean when it will become infinity. That means if this one becomes 0 suppose there is a wave safety wave which travels in the air also goes to another media. So, we have incident wave displacement amplitude reflected wave displacement amplitude is negative of that that is in opposite direction negative sign indicates it goes in the opposite direction always remember all the negative sign indicates the opposite direction transmitted nothing gets transmitted whereas, for stress amplitude what happens the incident wave and reflected wave stress amplitudes are same for transmitted wave stress amplitude it gets doubled. Now, what are the common practical form of impedance ratio for our geotechnical earthquake engineering if we go back to this definition of impedance ratio we will see typically when we come from layered soil. So, let us say here say we are coming from stiff soil rock soft soil this is the typical profile. Now from rock your waves are coming incident wave. So, some of that will get transmitted some of that will get reflected am I right. Now, depending on the values of this rho and v of this material and this material rho of rock v of rock and rho of soil v of soil which one will have more density of course, the rock compared to soil. Now, which one will have more velocity of wave of course, again rock compared to soil. So, the which material will have more specific impedance of course, rock will have more specific impedance than the soil. So, when we are talking about this alpha z between these two layers we are considering alpha z between these two layers which is rho of soil v of soil by rho of rock v of rock because generally this waves are coming from here. So, this is our material 1 here and this is material 2. So, that is what what we have seen in this slide the definition of impedance ratio is specific impedance of material 2 divided by specific impedance of material 1. Now, which parameter is more this parameter is much higher than this. So, now rho s v s is much lower than rho r v r that is the typical case for our geotechnical earthquake engineering which practically we will get at site. So, at site if we get this situation obviously our alpha z should be all practical cases will be less than 1. So, that is the practical range of alpha z it should be between 0 to 1 equality of 0 also we have seen equality of 1 also we have seen. So, most practical site condition in terms of our geotechnical earthquake engineering is alpha z should be between 0 to 1. So, if alpha z is at 0 to 1 let us see what happens let us look at this table once again. So, alpha z value is between 0 to 1. So, this are the common ranges as it is given 0.25 0.5 it can be different values based on your known soil parameters or rock parameters that can be any value between 0 to 1 what happens in this cases let us say alpha z is 0.5 for that 0.5 what happens when displacement amplitude incident wave is a i reflected is a i by 3 just putting that alpha z equals to 0.5 you will get this you will get this also right similarly you will get this and this that is what we are doing here. So, alpha z of 0.5 will give us reflected wave displacement amplitude much lower than what is the displacement wave amplitude for the incident wave. But let us look at the transmitted wave it is 4 a i by 3 what does it mean that means the displacement amplitude of transmitted wave increased from that what was there for the incident wave let us look at the stresses stress incident wave is this one reflected wave is this minus that is opposite direction and transmitted wave stresses two-third of the incident wave. So, stresses is not increasing it reducing for most of our practical geotechnical earthquake engineering problem. But where the big difficulty arises difficulty arises with respect to this displacement that is the reason an earthquake wave which is not imperceptible or not that much damaging at large depth in rocks media when it reaches through various soft soil there will be manifold increase of this displacement amplitude of that wave that creates more displacement when it reaches or goes through a stiffer to a softer media that is the reason as I have already mentioned in the introductory lecture Mexico City earthquake of 1985 is an example of this phenomenon of soil amplification that amplification mostly occurs in the case of when you have a very soft soil. So, from bedrock to if the wave travels through various soil layers and finally, it goes through a soft soil media you will see displacement amplitude of the transmitted wave in the soft media gets magnified gets increased much more than what that incident wave was clear. So, we have to be very careful about the values. So, which we can easily estimate in the beginning itself knowing the material property of various layers. So, that is why knowing the material property is very important to estimate the impedance ratio which automatically will give us the what will be the displacement amplitude of any transmitted wave. Now, let us come to the three dimensional wave propagation so for three dimensional wave propagation let us first take a note of the stress notations. So, this is a three dimensional element. So, far we have discussed about only one dimensional wave propagation. Now, we are considering wave is travelling in all the three directions. So, this is x coordinate system y coordinate system and z coordinate system we have the normal stresses in x direction sigma x x in y direction sigma y y in z direction sigma z z and the shear stresses like sigma x y this indicates as we know the first parameter indicates the plane the second one indicates in which direction it works. So, sigma x means it is acting on x plane in y direction this is sigma x z in x plane again, but in z direction these two are the shear stresses. Again on this phase we can have sigma y x sigma z y so these are this is actually sigma y z it should be that is on y plane in z direction now considering the stress notations of equivalence that is shear stresses of sigma x y should be equals to sigma y x y because to maintain the equilibrium of the body otherwise if they are different there will be a formation of a couple. So, to maintain the equilibrium the other phase shear stress has to be the same and in opposite direction like sigma x y in the opposite direction should act over here and this sigma y x should be equals to sigma x y to maintain the equilibrium of the cube or of the soil element in three dimension. Similarly, sigma x z should be equals to sigma z x and sigma y z should be equals to sigma z y. So, that is why this shear stresses over here sigma z y in y direction sigma z x in x direction this is sigma actually z y it will be y z because in z direction. So, direction will come last, but as we know sigma y z equals to z y that is why it is written as sigma z y similarly this is sigma y x in the x direction which is equals to the sigma x y. So, knowing this stress condition let us start deriving that is for three dimensional wave propagation what will be for three dimensional wave propagation what will be the basic equation of motion that we are planning to find out. So, now let us take the stresses on the face let us say this is our x axis this is our y axis and this is our x axis. And this is our z axis let us take only in one direction first then it will be easy to understand in the similar other directions as well. So, now in the x direction we have at this face. So, this is basically the origin as you can see. So, on this face let us say the normal stress is sigma x x and what are the dimensions of various sides of this small infinitesimal element. Let us say in x direction it is d x in y direction let us say it is d y and in z direction let us say it is d z. So, this to this is d x this to this is d y and this to this is d z. These are the dimensions of the material and let us say the density of the material is known as rho corresponding displacements also let us define in x direction let us say displacement is denoted as u in y direction let us say displacement is denoted as v and in z direction displacement is denoted as w u v w. These are the corresponding displacement in the direction of x in the direction of y in the direction of z fine. Now, if stress when wave is travelling through this infinitesimal element what is happening? This is the stress normal stress at one face the other face on this side the stress will be sigma x x plus there will be change of the dimension of sigma x x over del x into this distance d x that is the increment in the change or stress condition on the other side of the element. Why it happens? Because wave travels through this media. So, there is an inertia acting on the system that inertia will create the stress difference between two faces like we have seen in the one dimensional wave propagation equation also the similar thing we are observing over here.  So, now we are considering the shear stresses the shear stress in this direction is this is sigma x y and in this direction we have sigma x z. Now, as I said let us first concentrate only direction of wave in the x direction of wave in the x direction only. So, we will be interested to know all the stresses acting in x direction. Now, this is not in x direction this is not in x direction. So, we need not to consider these at this moment because we are only considering the x direction stresses. So, what are the x direction stresses we will see here x direction stresses will be on this space there will be this direction this is sigma it is in which plane it is in z plane in x direction. So, it will be z x if we can write the same notation as we have mentioned x z also we can write am I right. So, it is basically sigma z in x direction so z x as we know sigma z x equals to sigma x z that is why we could write this as sigma x z remember that what will be the change over a travel of this distance of d y there will be on this face in this direction opposite direction this should be sigma x z plus del sigma x z changing over the distance of d y. Del of into it is changing over the length of y it should be y it has change through this distance of y. So, what it should be sigma x z plus del sigma x z that is varying with respect to the distance of y. So, this should be not del z this will be del y over the distance of d y because see here it is sigma x z when it goes to on when it goes to on this face it moves by a distance of d y. So, it is change will be over the length of this d y so del y times d y am I right. Now, what will be the another one in x direction in x direction if I want to find out one more stress what that should be on this plane on this plane I have taken then x y another x y should come from I have sigma x y over here.  So, this back face will have this direction the back face back side in the x direction. So, what it should be that is on which plane that is x y plane am I right. So, that is sigma I can write x y it is essentially sigma y x because sigma y x equals to sigma x y that is the reason why I could write it as sigma x y it is on the back side. So, when it travels through a distance of d z on this front side on this front side this face it will be this one what it should be it should be sigma x y which is changing del sigma x y over the distance of it travels in the d z directions over del z times d z am I right. Now, if I consider the equilibrium of this forces that is on the outer face or after the travel in the x y z directions the increase in the stresses whether it is normal stress or shear stress in x direction. So, all x direction forces now if we consider what we will see let us write it down further we can write down that sigma x x plus del sigma x x del x into d x this is working on which plane this force is acting or this stress is acting on the plane with cross sectional area of how much this is d z this is d y multiplied by d y d z that is the force that is the force that is the force positive force in this direction opposite force in the other direction is sigma x x times same d y d z. So, minus sigma x x d y d z clear to that is the resultant force in positive x direction due to the normal stress difference am I right. Next I have to write another one which is sigma x y plus del sigma x y plus del sigma x del sigma x y del z into d z this shear stress let us look at here this stress is acting on which plane the cross sectional area is d x times d y am I right look at this plane front plane this shear stress is acting on this front plane. So, if I multiply that shear stress with respect to this area cross sectional area d x times this vertical d y we will get the net force in the x direction. So, d x d y in the other direction what is the force which is acting this dotted one in black color on the other side of the face on this side on that side. So, that will be minus sigma x y times d x d y fine what else we have another force let us look at here. We have in this we have taken actually the direction will be different in the positive direction it is increasing. So, it should be the incremental portion in should be always in positive direction and this should be in this negative direction. So, that is the direction cosines also we can check why it should be in this direction because this and this should be in this formant and this the other side should be in this. So, that they are in equivalence. So, with this direction what we can write now this is my positive direction in x this is the shear stress incremental part that is acting on which plane what is the cross sectional area over here that is d x times d z. So, sigma x z plus del sigma x z del y times d y times d x d z minus what is this one acting is this one in the other direction sigma x z. So, sigma x z times d x d z now this net force which we are getting this should be equals to it should be equals to the inertia in x direction. What should be the inertia mass times acceleration now what is acceleration in x direction that is if you differentiate displacement twice with respect to time displacement in x direction is u we have already mentioned. So, del 2 u del t square is the acceleration and what is the mass mass is density into the volume what is the volume of that element d x d y and d z. So, inertia has two balance that difference in stresses at two phases of the element in x direction. So, this is the derivation for in x direction only. So, what we can write this gets cancelled this gets cancelled this gets cancelled. So, on simplification of this equation we can further write that del sigma x x del y times d z times d z times del x into d x d y d z plus del sigma x y del z into d x d y d z plus del sigma x z d del sigma x y del z into d x d y d z plus del sigma x z d del y into d x d y d z that is equals to rho d x d y d z times del 2 u by del t square. So, this term I can cancel from both the sides because this is the volume of the element which is non-zero has to be non-zero. Therefore, what we can write del sigma x x del x plus del sigma x x del x plus del sigma x z del y plus del sigma x y del z equals to rho del square u by del t square. So, this is our basic governing equation of motion for three-dimension wave propagating in x direction. So, this is in x direction only. Similarly, if I want to find out what will be the equation in y and z direction in the similar format if we want to derive the form of the equation will be let me write it down for a y and z directions. So, in y direction it should be sigma del sigma y y del y because this is the normal stress component plus del sigma x y del x plus del sigma y z. So, del z del z should be equals to rho times del square v by del t square and we will get here in z direction in the similar form del sigma z z del z that is the normal stress plus del sigma z z del z that is the normal stress plus del sigma x z del x plus del sigma y z del y equals to rho del square w by del t square. So, these are three-dimension governing equation of motion which we will get after solving this three-dimensional wave equation in the solid which is shown over here. You can see in this slide three-dimensional elastic solid which we have derived now. So, this is the final derived equation as I have mentioned just now. So, now using the strain notations the strain notations what we can use the normal strain in x direction in y direction in z direction those are nothing but epsilon x x is del u del x epsilon y y is del v del y epsilon z z is del w by del z these are normal strain. What are the shear strain? These are the shear strain epsilon x y. So, del v del x plus del u del y epsilon y z del w del y plus del v del z epsilon z x del u del z plus del w del x and what are the torsional strain? Torsional strain in x y and z directions can be represented by these equations. So, now using the stress strain relationship how we can use the stress strain relationship for this three-dimensional wave equation. This normal stress in x direction sigma x x can be represented through strain through some modulus. So, c 1 1 epsilon x x plus some modulus c 1 2 epsilon y y plus c 1 3 epsilon z z plus c 1 4 epsilon x y this modulus is related to the shear because it is relating to the shear strain these are relating to the normal strain. So, basically what you can see other two shear strain all these modulus coefficients that is stress versus strain can be easily written in the form of a matrix that is what it shows right. So, what is that form of the matrix in the simplest form if we want to rewrite it. The stress strain relationship is something like this sigma x x sigma y y sigma z z sigma x y sigma y z sigma z x these are the six shear strain. These three normal stresses and three shear stresses they are related through some modulus which is nothing but a modulus matrix through the strain. What are those strain epsilon x x epsilon y y epsilon z z epsilon x y epsilon y z epsilon z x. So, these strains are first three normal strain and these three are shear strain they are related through this matrix what we were showing over here c 1 1 c 1 2 c 1 3 c 1 4 c 1 5 c 1 6 c 2 1 c 2 2 c 2 3 c 2 4 c 2 5 c 2 6 c 2 3 c 2 4 c 2 3 c 2 3 c 2 4 c 2 4 c 2 5 c 2 6 so on this one will be c 6 1 this one will be c 6 2. Similarly, it goes over here up to c 6 6 like that. So, this matrix is nothing but modulus matrix. So, this stress strain relationship can be expressed through this modulus matrix. So, with this we have come to the end of today's lecture we will continue further in the next lecture.


Thank you very much, Mari, for that very kind introduction. It's really a pleasure to be home. And of course, it's an honour to speak at the Institute for International and European Affairs for the second time. And I want to thank Ben Tonner and Mari Kross from the Security and Defence Group for inviting me to speak to you today about the future of EU defence policy. Now, originally when we had discussed this idea with Ben and Mari, we thought it might be interesting to talk about what progress has been made since 2013, what will come out of the summit that was held last week. If I do that, it will be a very short speech because no progress has been made and defence wasn't even discussed at last week's summit because of course there were many other crises to deal with whether it's Greece or migration or Russia and so on. So I won't focus so much on that but I will try and focus on something that was decided at the summit. The EU leaders, the heads of government, gave a mandate to the high representative for foreign policy, Federica Mogherini, to draw up what they call a global strategy on EU foreign and security policy and to write this strategy in time for a summit in June 2016. So she has a year to do this process. And it's sort of but not only updating the European Security Strategy of 2003, it will be broader. It's not just about security, it's broader foreign policy. But of course there will be a CSDP component at least in the debate. I'm not sure the strategy will actually say much about CSDP specifically, but it will certainly impact the debate on the future of EU defence policy and indeed the future of EU defence policy is crucial for the future of EU foreign policy because as we know EU defence policy is not a defence policy. It's actually part of EU foreign policy. The EU is not a military alliance. It doesn't do the business of territorial defence the way NATO does, for example. So I'll start off just with a few remarks about our changing security environment. Now I think it's fairly obvious to say that the strategic environment we're facing is rapidly becoming much more challenging and in particular in the EU's broad neighbourhood which frankly is in a mess. And the turbulence that is ongoing there I think will continue across this broad neighbourhood for a very long time. To take one example, Russia is going to be a major security challenge for the EU for many years to come. Not just because of its aggression in Ukraine or its enclaves in Moldova or Georgia but also because of its own internal weaknesses. Russia has serious demographic decline and an over-reliance on energy exports for economic growth. And we've seen the negative impact the oil price has had on Russia's economy along with the sanctions of course. And in a way I would argue that Russian aggression is actually masking its fragility which means that Russia is going to really remain a very serious security challenge for a long time to come. Looking south there is increasing disorder across the Middle East. In fact disorder I would argue is the new normal in the Middle East. Consider Libya, consider Syria, Iraq, Yemen and so on. But on top of these ongoing conflicts the structural factors that created the Arab Spring by that I mean demographic growth in contrast to Russia, resource shortages, economic stagnation, these are going to intensify in the years ahead and they are going to contribute to more instability in the future on top of the ongoing conflicts. Consider for example the average, the about 50% of the population of Iraq is under 19 half the population. That is a serious socioeconomic challenge for instance. And in general if you look at the broad neighbourhoods including the Sahel, West Africa, even stretching not just Eastern Europe, the Caucasus over to Central Asia most or I think the majority of the world's fragile states or failing states or even failed states are within that broad space. Europe's broad neighbourhood is the ozone hole currently of global security. This space, so we will be very busy for many years to come. Now of course Europe's neighbourhood is not just Europe's neighbourhood, it's Russia's neighbourhood, it's Turkey's neighbourhood, it's Japan's neighbourhood, it's India's neighbourhood and it's increasingly China's neighbourhood. But we will likely have to deal and respond autonomously as Europeans to more crises in the future because the United States is much more ambiguous and much more selective about what it's willing to do or not to across our neighbourhood with the exception of the Gulf but in the rest of the neighbourhood the United States is much more selective but in the rest of the neighbourhoods we cannot expect the United States to solve our security problems or solve all our security problems in the future. We will have to do it ourselves increasingly and you see this already if you look at the 30 or so CSDP, EU defence operations, EU peace operations really that we've carried out all bar two of those 30 or so were carried out in that broad neighbourhood. The two exceptions are Afghanistan and Malaysia in Indonesia but all the others were carried out in that broad space in the neighbourhood which I think tells us something. This is not to say of course that we don't have global security interests maritime security in East Asia and I know this is of interest to Mark Millet for example is a serious security issue for Europeans as well but precisely because we cannot do very much about it partly because we're so busy and precisely because the US is increasingly focusing on China and China is the biggest question facing the international system today and this is why the US is becoming much more selective about its activity in our neighbourhood that means that we will have to do more ourselves to cope with security challenges in that broad space. Now I do want to emphasise that Europeans won't and don't always act through the European Union they act through the United Nations they act through NATO or they act nationally I think the French operations for example in Mali or the Central African Republic are very good examples of that and of course sometimes the EU works with the United Nations in Chad or Mali or works with NATO in Kosovo Afghanistan and so on so it's not a simple either or either and of course this is not just about using military force the EU tries to mix many different instruments but the majority of CSDP the vast majority of CSDP operations have been civilian and so the EU only uses military force when it really really feels it's necessary but it is bearing in mind that any serious foreign policy needs a military component consider Irish farm policy Irish farm policy basically does three things we do diplomacy treaties at the EU level or international treaty we do development of course and we have an outstanding record on development and we do peacekeeping the defence component if you like and our defence forces have an outstanding record in international peacekeeping likewise if the EU wants a serious foreign policy the EU needs a serious military option and of course if you have a military option you should be as prepared as you possibly can for many different types of contingencies that you have and CSDP is an important option for European governments because the UN may not always be quick enough to act NATO may not always be available if the United States is not interested and of course France may not always be able to act alone right so CSDP is an important option however if we look at the record of the 30 or so EU operation since 2003 30 is an impressive figure so there's been a lot of quantity but I would argue there's not been a huge amount of quality there are some exceptions Chad is a very good example which our defence forces led the counter piracy operation of Somalia is another excellent example but frankly some of the operations have been very small and very ineffective and pretty much a waste of money so I would like to see more quality the EU for instance has not done what the UN has done in Lebanon or in Congo the EU should be trying to do more of those types of more serious robust and substantial operations now of course CSDP EU defence policy when it was conceived in 1999 it was launched at the Cologne summit in June 1999 it was conceived as a crisis management policy essentially that means doing everything but territorial defence that's fine these days though the EU seems to do everything but crisis management and this is the focus at the moment is very much on capacity building, training, equipping and I really wonder if that is sustainable if you're serious about having an effective contribution to international security particularly given the range of the security challenges that I try to outline in the EU's neighbourhood it's dangerous to assume that EU defence policy will only do capacity building for the next decade and beyond partly because as we know when you're doing for example military training operation a peacekeeping operation can quickly look like war fighting we saw what our defence forces went through with undef on the Golan Heights we've seen it in Afghanistan Europeans have had that experience as well secondly the EU sent from Mali to back up the French military intervention there but what if France had needed more robust help would we just stand there looking at them even though they are actually making an intervention that is for the benefit of our security or thirdly and this is maybe a bit more controversial if there was another Libya style crisis like the 2011 crisis and the United States said we will not intervene and don't forget there was a debate in Washington at the time the Pentagon did not want to intervene in Libya actually and would have been happy to leave it to Britain and France and other Europeans but if the next time the US said we're not going to do it, this is your problem and I don't think the US would be particularly keen to intervene in Libya today what would we do what would the Europeans do I leave that as an open question perhaps for the debate so in other words I'm trying to describe really that the strategic demand for a more effective EU defence policy is growing but I would argue that there is a very strange dichotomy in EU defence policy because the strategic demand on the one hand is growing but the political interest in national capitals on the other hand is actually weakening, it's actually lessening and we should ask ourselves why is that the case given all these security challenges which are intensifying this should be the moment that the EU really shows what it's made of CSTP has existed what 15, 16 years now 16 years and it doesn't have a huge amount to show surely this is the time that the EU can really show what it's made of but it's not showing that yet and there are a few reasons for this it seems to me one is very understandably Europeans are weary and wary of military interventions some Europeans invaded and it failed some Europeans invaded and didn't occupy Libya and it failed and some Europeans neither invaded nor occupied Syria and it has failed so military interventions do not have a good reputation and I think it's quite understandable there are counter examples I would argue I would argue that the interventions in the western Balkans and the effort since on peacekeeping on development on state building has been actually quite successful but it's precisely because of that effort since that it showed that the military intervention was worth doing so we shouldn't just assume that military interventions are always a bad idea so that is one factor and of course if you look for example at the European contributions to international peacekeeping or international deployments they've actually have since 2008 I think there were around 80,000 soldiers deployed on various operations NATO UNEU national in 2008 it's less than 40,000 now today so that tells you something the interest the willingness to carry out international operations has lessened to a huge degree I think a second reason why there's less political interest in CSTP is the Ukraine crisis because that has placed a huge emphasis on territorial defense rather than external operations which means fewer resources will be available for external operations if countries are focusing more on territorial defense particularly at a time where defense resources have fallen in a nutshell the Ukraine crisis has been a shot in the arm for NATO but it may prove to be a shot in the leg for CSTP if there are fewer resources available for expeditionary operations because this is what CSTP does external operations are the oxygen of EU defense policy now linked to that there are two emerging divisions in European defense one is functional this territorial versus expeditionary debate and the other is geographic those who are focused more on the east and those who are focused more on the south and you see this for instance the recent polish national security strategy is very focused on Eastern Europe hardly says anything about the Middle East or the southern part of the neighborhood and the new Italian white book is very focused on the Mediterranean and maintaining or developing military primacy in the Mediterranean as they put it so it's a very clear example of this divide now there is some overlap it's not a smooth division between the two groups and there are some countries like France and the UK who try and focus on both and try and be able to do both defense territorial defense and expeditionary but these divisions are emerging and a final reason why there is a lack of political interest in EU defense policy at this time is that there are big divisions big differences between the big three the big three meaning France Germany and the UK and essentially the UK is not very keen on acting through the EU for its foreign policy Germany is not very keen on using military force externally and France is stuck in the middle which is why France has had to mainly act nationally now the German debate is changing to some degree and you know Foreign Minister Steinmeier Defense Minister von der Leyen President Gauke have all made speeches saying Germany needs to wake up and assume more leadership and contribute more to international security and assume more responsibility and like Ireland Germany is going through its own defense white book process at the moment and I had the pleasure of speaking at one of their preparatory seminars for the Vice Book in Brussels recently and the Minister von der Leyen was there all day and very unusually for a politician she actually listened all day and said nothing and that was very refreshing I'm not used to politicians listening to me so that was really quite interesting but what struck me in that debate was that Germany is clearly very comfortable acting through NATO particularly on territorial defense it's comfortable with trying to beef up NATO's efforts because of the Ukraine crisis but it's very uncomfortable with external deployments and doing anything beyond training and equipping capacity building Germany is one of the biggest contributors for example to the EU training mission in Mali but doing anything beyond that makes Germany very nervous and the reality is that EU defense policy is likely to do more than the German political market can bear so if Germany does not change its attitude on the external use of force even though there is a very interesting debate developing in Germany until Germany really starts to be willing to do more I'm skeptical that CSTP will do much more than training and equipping if Germany only wants to do training and equipping the other factor of course is Brexit now I doubt that David Cameron will want to appear or sound to pro EU defense policy over the next 18 months, 2 years of the referendum debate headlines of British Armed Forces subsumed by Euro Army are probably the last thing he would like to see so we can't expect too many positive noises publicly at least from London but I think more seriously though if the UK left the EU that would do tremendous damage to the military credibility of EU defense policy because the UK and France are the Deutschmarks of EU defense policy they are the two that set the standard and if you lose half of that that greatly damages the credibility aside from the fact that we all lose if the UK leaves the EU would be greatly damaging for the EU as a whole but it would certainly greatly damage EU defense policy and this lack of political interest and a lack of a coherent vision or coherent ambition explains why there has been so little progress on developing military capabilities or better armed forces on opening up defence markets on defence industrial consolidation on pooling and sharing defence money there's been very little progress just to give one small fact in 1999 when EU defense policy was launched the EU member states who were then 15 could deploy and sustain around 7.5% of their armed forces in 2015 the EU 28 can deploy and sustain around 7.5% of their armed forces so there clearly hasn't been much progress in that area because of this lack of political interest which is pretty poor now of course this strategy debate may help at least revitalise the discussions on EU defence policy and maybe the next summit or another summit will actually discuss defence policy in detail because of course this strategy there will be a discussion on EU values but there will also be a discussion on EU interests international interests and of course on security challenges and how are we going to tackle these security challenges not only through CSDP or not only with the military instrument but CSDP is part of it at least among think tankers which cancel nothing I suppose because you have various sectoral strategies being discussed in Brussels at the moment on trade, on the neighbourhood alongside this foreign policy strategy discussion it would be helpful maybe after the strategy to have a CSDP specific discussion with a CSDP specific document not a white book necessarily but some sort of guidelines might be helpful so if the strategy led to that that would actually be quite useful but I wouldn't bet on that happening so what does this kind of strange dichotomy this strategic demand versus political interest dichotomy, what does this mean for Ireland I think there's a few things as we know EU defence policy has been controversial in the past in some referenda on EU treaties but successive Irish governments have been very supportive of EU defence policy in terms of their party or coalition make up why because the whole point of CSDP is to support the United Nations is to support the implementation of international law and is to ensure and encourage that Europeans contribute to international peacekeeping and contribute more therefore to international security added to that the EU is supposed to help tackle security challenges that affect our security because when European security is threatened so it's very much in our interest that the EU can tackle and cope with the variety of challenges we face this is why long air knock etna was sent to the Mediterranean for the search and rescue operation which is not technically a CSDP operation but is to help save lives and to help manage the migration crisis in the Mediterranean because our security is intricably linked with Italian security with German security, with Baltic security and I think we need to understand this in the Irish debate now of course the EU approach to international security very much matches the Irish approach because it's very similar to the UN approach you mix different instruments you use diplomacy, you use the military when necessary you use development, law enforcement and so on and it's also true that the politics of EU defence policy have suited Ireland in many ways because of various differences down the years these differences have ensured that the EU has neither become part of NATO nor become a military alliance which is suited Ireland perfectly and of course our defence forces have benefited enormously working with EU partners not just on capability development but concept development, doctrine development training particularly for example through the Nordic battle group that's of benefit for our defence forces but the main dilemma it seems to me if CSDP is ineffective and if this is an example of Europeans doing less in international security particularly on international peacekeeping that is not in Ireland's interest that is not in Ireland's interest so to conclude if the combination of middle eastern disorder Russian aggression the US pivot to Asia and falling defence budgets doesn't encourage Europeans to cooperate more closely on military matters I really wonder what will how bad do things have to get how serious does the crisis have to become for us to knock our heads together and cooperate more closely and more effectively given the range of challenges we're facing it's getting to the stage now where either we get serious about EU defence policy and we meaning all EU member states not just Ireland or we give up because as long as this strange dichotomy of going strategic demand on the one side and lessening weakening political interest on the other as long as that strange dichotomy of EU defence policy continues well if it continues we will soon see the strange death of EU defence policy thank you very much for your time and attention


In recent years, cultural heritage and cultural expressions have increasingly become the direct target of systematic and deliberate attacks in numerous conflicts around the world. According to Chief G.D. Jude, a Bocchile chairman in Agbor Local Government Area, culture is a means of providing security to those who inherit them. A Bocchile said this at the Kerr Music Entertainment Award in Agbor, Delta State. Chief noted that cultural extinction is prevailing due to borrowed foreign culture, which is also modeling individual values. 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.


Hi, welcome. I'm Jodi Evans and one of the co-founders of Code Pink, and we're here to David Swanson, the director of World Beyond War, an amazing journalist, organizer, activist. I mean, really, he's one of the rock stars of the Peace Movement, and he's been our partner at Code Pink since we started almost 16 years ago, if you could believe it. So David's always awesome at being able to debunk what's happening around war, and I love reading his work because he gets to the core and he gets to the root and he kind of tugs at them and explodes the lies open and gives us tools that we can use as activists. So I was kind of shocked when I read his piece a few weeks ago that said, Russia is our friend. There we go, David, courageous and provocative as usual, poking the place where we're all shocked. Like, why is everybody so upset about Russia, and why did, you know, people, progressives, get upset when diplomacy was happening, when leaders of countries that have the most nuclear weapons decided to talk to each other. So very grateful to David for, you know, his article, and I wanted to talk to you, David, about Russia is our friend.  Well, thank you, Jodi, for everything you've been doing for years and for having me on and for liking this article, because I thought it was one of, it was an important article compared to some others I've written, and I was glad that some people agreed. You know, I'm here in Charlottesville, where last spring and last summer, there were Nazis came to town and, you know, to defend Confederate statues, and they were shouting things like Russia is our friend, by which they seemed to mean that they had bought the accusation that Russia helped elect Trump, and they approved, and or they saw Russia as part of their white supremacist fantasy. And I actually, you know, wanted to take that phrase and use it in a different way and say, Russia is a friend of the United States in a particular way that is unacknowledged, by which I meant that not just in recent years and not just for the Cold War, but from 1917 up to today, the United States has treated Russia horribly, viciously, unfairly, and Russia has put up with it and tried to be friends and asked to join NATO and asked to join Europe and asked to ban cyber war together and asked to ban weapons in space together and tried to disarm and reduce nuclear weapons. More often that came from the Russian side and the US said, no, Russia on 9-11 gave the United States this giant monument of a giant teardrop in sorrow for the victims of 9-11, and the United States downplayed it, hid it in New Jersey, and most searches for it on the internet find people who think it's a false story and never happened. And so what I did in the article was to give a chronology of things that the United States did to Russia between 1917 and today that nobody other than a friend would put up with. So it's not to make a case that Russia is paradise or Russia is a good world citizen or Russian, the Russian government is good to its people or anything of a sort. I mean, I began the article by pointing out that the Russian military had tried to hire me to distribute their propaganda and I told them to go to hell, you know, but it's to talk specifically about the relationship between the US government and the Russian government. Never mind what either of those governments does to its people. And I think it's a history of US cruelty to Russia. Well, could you be specific about some of those instances that you think aren't well known? Yeah, well, I think maybe the least well known in the United States, though it's known in, you know, to a much greater degree in Russia, is that right from the start of the Russian Revolution in 1917, the United States was funding one side was trying to blockade Russia. And by 1918 had led a dozen other nations in a military invasion of Russia to try to take sides in a Russian civil war, not just through Facebook, but through armed troops to try to turn back a revolution. And to this day, US journalists, officials, presidents will say our two countries have never been at war, and the Russians will spit out their coffee and say, what? You know, their tea, their vodka. What are you talking about? You know, because this was from day one, this turn many historians view turned the revolution itself in undesirable ways. And it was put under this threat. And then it was seen as an enemy by the United States that this socialist enemy, the threat to oligarchy, you know, from that day forward, troops were there until 1920 and gave up and pulled out. But through the 1930s, through the rise of Nazism in Germany, socialism, Russian communism was seen as the enemy. Senator Taft said better for the Nazis to win than the commies. Senator Truman, future president, said if the Russians are winning, let's help the Germans. And if the Germans are winning, let's help the Russians that way more die. And so through the course of World War Two, the real enemy was the ally, Russia, so that the United States, you know, got into the war. And then for two and a half years, had Russia begging and pleading for an invasion from the West, and the United States wouldn't do it, wanted the Russians to do most of the killing and dying, which they did. Weren't there a lot of American corporations also, you know, speaking of the oligarchy that we still have, weren't there a lot of American corporations helping the Nazis because of Russia? Indeed, right up to the war and right through the war and afterwards, major U.S. corporations, IBM, Ford, Standard Oil, I mean, were supplying absolutely necessary supplies, vehicles, fuel, metals to to the Nazis, without which they never could have done what they did. And the U.S. military and the U.S. government not only didn't hold these corporations responsible for treason and for violation of the Trading with the Enemies Act, but avoided bombing their their buildings in Germany and paid them damages when they did. And you know, so this is not how things would have gone against the Russian enemy. There's also two things you mentioned during that period of time. One really major, but, you know, destruction of human life that the U.S. did as threats to Russia that, you know, are just, you know, they're they're they're the hell that we hold at the heart of the U.S. and and you saying your article that those were both provoked in a way to show Russia who was strong. I think I know what you mean. And one would be Dresden, which people, you know, people need to realize that World War two turned war into something that kills mostly innocent civilians rather than what it had been up to World War two. And yet people still wonder at the extremity of the escalation in this conduct when the United States absolutely destroyed the city and the population of Dresden. And it becomes a little clearer why this happened when you find out that it was originally planned. It actually happened some days later, but it was originally planned for the first day of of the meeting in Yalta in Crimea between Churchill and Roosevelt and Stalin. This was to be a message to Stalin that we can do this to you after the war. And the second thing I think you're asking about is is the use of nuclear weapons in Japan, which of course, I mean, there's there's no dispute if you look at the statements, public and private and the diaries of US officials at the time, the concern was to get the war against Japan ended before the Soviets came and got involved so that the United States would be the sole occupier of Japan after the war, as well as to demonstrate what they called nuclear diplomacy soon thereafter demonstrate the power of these nuclear weapons to the the future enemy, the the Soviets. Yeah, and you know, even Einstein and his diary said that the Germans had the capacity to use the nuclear bomb, but they didn't because of what they understood it would do. So it also reflects on who we are in the United States is what level of violence we we allowed, which is just horrific. While we're blaming Russia for so many things. I'll have to go read that comment from Einstein. I had not understood the Germans to have developed the nuclear weapon. They of course, may have D prioritized pursuing it. But I, I think D prioritized it because they knew what would happen. Yeah. Yeah, well, there certainly were scientists within Germany, including those working on it, who had those concerns as there were scientists in the United States, but not enough of them. They had those concerns and went right ahead with with regret in their hearts, which never saves any lives. So yeah, but I think the Nazis, it's it's important when the Nazis won't go farther, because this is the epitome of evil in US culture for for good reasons. And yet this war, World War two that after the fact is justified as saving the Jews from the Nazis, which at the time had nothing to do with it, killed 10 times the number of people in the war, as we're killed in the camps. And so, you know, but but the focus of this article was really to say, look at who was really the enemy in the minds of US officials through the course of the war. And right after when they started hiring hundreds of top Nazis into the US military and putting Nazis in power and reinstalling almost fascist governments in Italy and France and making sure West Germany wouldn't pay reparations payments to the Soviets and so on. I mean, on the day that the Nazis surrendered, Churchill proposed using Nazi troops together with Allied troops for a new war on the Soviet Union. And this was something that had been in the works that that US generals and British generals had been planning for they've been maneuvering partial German surrenders keeping the troops armed and ready. It didn't happen. But the Cold War happened and the Cold War was created by the US government. Well, so let's talk about the well, let's move to maybe Afghanistan. And maybe talk a little bit about what most people don't know about US provoking Russia a geopolitical war and using Afghanistan. Well, as being of Brzezinski brags slash confesses that the United States was involved in maneuvering the Soviet Union into Afghanistan to give it its own Vietnam, understanding the damage that the Vietnam War on Vietnam had done not just to Vietnam, but to the United States. And so the United States was arming, you know, the predecessors of of Al Qaeda, the Musa edin in Afghanistan before the Soviet Union was a reason for it. The intention was to pull the Soviet Union to provoke the Soviet Union into a war and then arm the other side. And so this was done. It's not a very friendly neighborly thing to do to the Russians, or to the Afghans, only to the weapons makers, only to the pursuers of global dominance. And then you have the United States maneuver Boris Yeltsin into power in Russia and brag about it.  And then as the Cold War ended, the United States promised Mikhail Gorbachev NATO will not expand toward Russia. Well, it quickly begins expanding to Russia and over the past decades has expanded right up to Russia's borders and missiles have been put in and troops have been put in and threats have been made. So that Russia, you know, is surrounded by US weapons, then the US goes into Afghanistan with its own war in part motivated by the desire to put weapons in there, aimed at Russia. So, you know, you have the modern period, follow decades of consistent hostility toward Russia, regardless of whether it's communist or non communist has the Warsaw Pact or has abolished it, consistent hostility toward Russia. The Iran deal Russia wanted it, it's gone. The coup in Ukraine, orchestrated by Obama's government is assisted anyway by Obama's government and then now being armed again, literally Nazis being armed by the United States. While Trump is blaming Russia for controlling Germany, Russia being the one victor of World War Two that isn't still occupying Germany. Trump is blaming them for that. Russia is being blamed for shooting down airplanes for killing a guy in prison for using chemical weapons in in England. You know, you can't swear Russia is innocent of every charge. But it's innocent of most of them and you can't and there isn't any proof including of hacking and election. I mean, this week we got proof of collusion and election hacking from a guy named Michael Cohen, but Russia was nowhere to be seen in that story. So, you know, now it remains to be seen if anybody cares about it. So, why do you think the Cold War has been over for a very long time?  Is that seem right? Yeah, I mean, when people thought that when the Cold War ended, US militarism would end because the Kami threat had gone away.  It was it was cute. It was it was easy to sympathize with. I would like that sort of thing to be true, but it was ridiculous. I mean, the Kami threat was largely manufactured. The Domino theory had no evidence behind it, you know, never happened. And the fear of the Kami's in little third world countries was, I mean, it's often non-existent or, you know, absolutely minimal. And so it was a reason to pursue. It was it was propaganda for US militarism, which is not to say that the that the Soviet government was a good one. It's just to say that the Soviet government was not actually trying to take over Nicaragua and invade Texas. You know, this didn't exist. And so when that went away, you needed you needed new propaganda. And you got the global war on terrorism, which is handy because terrorism can never go away. But that didn't didn't pan out as a way to sell as many weapons as as Russia or China, which, you know, again, are being promoted anew as the justification. And you have Pentagon officials openly telling journalists, this is this is about making money. This is about keeping NATO going. I mean, it's almost shameless. But this is this is where it comes from. Well, I encourage everyone to read your piece. Russia is our friend. And just your tongue in cheek of like, nobody would allow this behavior except for a friend. Really, I think opens minds up to what's going on here. But, you know, you have the world beyond war and we it could paint we're working on a new campaign together to go after the money.  And so you want to talk about what you're what will be on war is doing in the divest campaign? Well, we we are trying to ramp this up as you all at Code Pink are doing a wonderful job as well. And, you know, one focus we've put is is on public dollars. And so we're researching where local and state governments and pension funds in the United States are invested in major weapons companies. So the people who've done good things like teachers have their retirement depended on there being more wars so that, you know, the money in their retirement funds doesn't go away. And this is this is obscene. And and so we're figuring out where to target public officials to get the money out of the weaponry. But that's also a lie, by the way. So you don't get a better return on investment from weapons. And there's been studies done and they're on the divest website, our code pink slash divest that show that studies have been done and it doesn't bring you more money.  So we can't we can't allow that argument. And also, we know that the weapons are get to be produced because they get congress to vote for them. And the way they do that is get a piece of it developed in any congressional district and promise jobs. And for that amount of money, those jobs could fund another four teachers for the community instead. Yeah, no, I completely agree. My point was that if you're invested in the stocks of a weapons company, then your stocks go up or down with that weapons company. But if the U.S. government chose to invest in people or in green energy or in education or in infrastructure, it would actually benefit most of us who aren't CEOs of weapons companies far more that you know that the studies that I think you're referring to that you've done at the University of Massachusetts Amherst find that you get more jobs and better paying jobs and better economic impact from putting that money in other places or even never taxing it from working people in the first place. So military spending, taxing and military spending is literally a drain on the economy, which makes sense when you're making destructive stuff that has to be destroyed to make more of it. And when it's so unaccountable that you have analyses finding that the Pentagon over the past few decades has misplaced 21 trillion dollars, and you get laws passed that say it has to be audited and but they don't actually audit it. You know there's no way that this makes economic sense. But imagine what it sounds like to somebody around the world when they hear a U.S. Congress member say, well actually this is a jobs program, this pursuit of weapons with which to bomb you. I saw Jack Matlock, the last U.S. ambassador to the Soviet Union just in recent years on a stage with Vladimir Putin say, Vladimir, those missiles were putting in your neighboring countries have nothing to do with you. It's just a jobs program for back in the States. Now Putin was rightly outraged. I would have loved for Putin to have in his hands one of these studies from Massachusetts Amherst to say, you know you actually would get more jobs if you weren't you know pursuing this sociopathic sort of jobs program. But I mean how disgusting, never mind false, that people justify militarism as a way to make jobs. Disgusting, right. And also if you just even look at the fear of communism which is taking social production and instead of private accumulation, social accumulation that benefits all is what we were afraid of.  It's an interesting you know look at it that this is the fear and this is we've killed tens of thousands tens of millions of people because they were communists. Yeah. You know what they were trying to do is move the money to the people. It's an interesting also conundrum in that. It's a horrible, horrible legacy of the gun in 1917 right at this time. I mean I think Woodrow Wilson's done more damage to the world than Thomas Jefferson. I you know Charlottesville you know has a lot of apologies to make to the world but it really is a nice town and the Nazis aren't from here. You know it's something we've got to break away from this this idea that that because a country is going to try however imperfectly to help people rather than an oligarchy it has to be an enemy and not just an enemy but a place where you go and impose an oligarchy and corrupt corporate cronyism back in the 1990s and brag about it openly despite the horrible damage that that did you know if there was a way to make people regret the collapse of the Soviet Union that was it. It's just like the neocon plan for Iraq that very quickly had people regretting the loss of Saddam Hussein. I mean you're imposing something worse than the horrors you're using to justify militarism. Nothing can justify militarism. Thank you. And where's the lie? So thank you David Swanson for being with us. Just one more thing like how do people engage with World Beyond War? Go to worldbeyondwar.org. Click where it says sign the declaration of peace. We were just discussing earlier Jodi people have have signed in I think 173 countries and we'd like to get those last couple dozen remaining countries so spread the word around the world and sign the declaration of peace at worldbeyondwar.org. And you can join us in our divest campaign at codepink.org backslash divest. Onward to peace.