Russia Waging New Hybrid War Against Georgia President Zorabishvili Despite failure or because of it, Russia has launched a new hybrid war against Georgia using all forms of weapons, stated the President of Georgia, Salome Zorabishvili. According to her, Russia continues to wage a hybrid war against Georgia using all its tools. Speaking about the challenges facing Georgia in 2023, the President of Georgia recalled the war in Ukraine. Russia could not break Ukraine. Indeed, it failed to undermine the unity and solidarity of Europe and even strengthened it. Despite failure or because of it, Russia has started a new hybrid war against Georgia for which it uses all forms of weapons. Zorabishvili said, she also emphasized that Russia's plan to turn the Ochamchera port into a military base aims to shift the confrontation to the Black Sea into their territorial waters, thereby creating a threat to the strategic perspective of the Black Sea. Zorabishvili spoke about the declaration of mobilization in the occupied territories as well as the steps taken toward annexation, mentioning the capture of the Ochamchera port, the state residence in Bitsyvinty and the Babushera airport in Tsukumi. According to her, constant intimidation, persecution, kidnapping and killing of residents continue along the occupation line. The official authorities of Georgia consider Abkhazia and South Ossetia as territories occupied by Russia. Earlier, the head of the occupation administration of Abkhazia, Aslan Bzania, claimed to have reached an agreement with Russia to establish a base on the region's territory where the Black Sea fleet will be stationed. However, the parliament of Georgia decided not to consider a resolution condemning the plans of the Russians to build a base for the Black Sea fleet in occupied Abkhazia.


Okay, we have a session about electron phonon interaction. So just a brief introduction. With Yambo, we have several basic topics like GW, because of Peter, but in addition, there are several models of the code that allowed out in the years of produce different models of teaching models. So there is electron phonon or linear optics and also magnetic properties. So this year we decided to concentrate on electron phonon. And electron phonon is actually a theory that as GW is based on a series of pre-calculations.  And the very basics, there is density function perturbation theory. And this is what Elena Kanucha will talk about today. So please, Elena, the stage is yours. So thanks, Andrea. Good morning, everybody. I have the pleasure to open the this morning section on the electron phonon coupling. And at the end of the day, you will live with, let's say, with the take home message in the sense that you will realize that the electron phonon, in order to calculate the electron phonon coupling, what you need, you need basically two main ingredients that are the phonon modes and the electron phonon matrix element. The electron phonon matrix elements are, let's say it's the matrix elements in the sense that they give you the probability that an electron in the state i scatters through a phonon in a state j. Both terms, phonon modes and electron phonon matrix element can be calculated in the framework of density function perturbation theory that I'm going to talk about with this lecture. So let's start from what is a response function. Imagine that you have a system and you want like a material or molecule, let's say, and you are interested in calculating certain property that can be expressed as the variation of a variable with respect to the strength. What are variables, what are strengths? The variable is, let's say it's a quantity which depends on the atomic coordinates of your system and it may depends also on an external perturbation that you may let act on your system. And the strength is the strength of this external perturbation. So then calculating the variation of this variable with respect to the strength gives you a certain property that you want to study. For example, by calculating the variation the double system with respect to the electric field you get the polarizability as a response function. Or if you calculate the variation of the stress or the pressure with respect to the you get the elastic constant. And if you calculate the variation of the force acting on an atom high with respect to the displacement J, you get the interatomic force constant like here. Or moreover, if you calculate the variation of the dipole system with respect to the displacement, atomic displacement, you get the born effective charges. The first two response functions act at microscopic level. So you can have some microscopic response functions. And the third and the fourth that I wrote in these slides are microscopic response functions. So depending on the system that you are studying and the physical properties that you want to address you can define a different response function. So the fundamental theoretical ingredient of the response theory is the Elman-Pheumam theorem, which has been formulated in 30s by independently by Elman and Pheumam. This theorem states the following. Let's start from a time-dependent Schrodinger equation that you can see here. This time-dependent Schrodinger equation so depends on an Hamiltonian, depends on Hamiltonian, which depends on a parameter lambda. And as a consequence, the wave function and the eigenvalues depends on lambda too. This parameter lambda can be for example, the strength of the external perturbation that I was mentioning before. Or in the case of the Bernoulli-Penamina-Miltonian, lambda is the set, the collection of the atomic position. So lambda can be also a set of parameters. Anyway, this lambda parameter, this lambda is just a parameter does not corresponds to an internal dynamical variable. And in the sense that the theoretician can set lambda at his or her will. And an experimentalist can tune it in the laboratory. The Elman-Pheumam theorem allows to answer to a specific question, which is the following. Imagine that you want to know how the eigenvalue e-lander, the variation of the, you want to calculate the variation of this eigenvalue e-lander with respect to the parameter lambda. So what you do is to differentiate the expectation value of c-lander, h-lander, c-lander. And by applying the chain rule, first you derive the bra, then you derive the operator. And then in the end, so the bra, the operator and the ket. But by the fact that the wave function is normalized to one, the derivative with respect to lambda is equal to zero. So you end up just with this term. We end up just with this term, meaning that the variation of the eigenvalue e with respect to the parameter lambda is calculated just by differentiating the operator h with respect to lambda. So you don't need to calculate the variation of the wave function with respect to lambda. And this is a powerful and non-trivial results because not only, I mean, the amount depends on lambda but in principle, so the wave function. So the first take home message from this lecture is that you know that, for example, you know the calculate force system, your system, you don't need to calculate the derivative of the wave functions. So let's see how this theorem applies in the context of DFT. So we are building, we want to answer to this question and we go step by step. First of all, the Elman-Fiemann theory also, when you can set your formulate, the problems in terms of the variational principle. And variational principles is written here. You have an energy e lambda, which is the minimum overall, the possible wave function of this expectation value. And so now let's imagine that we have a function generic function g lambda, which is the minimum of a function g, which depends on internal variable e x and the parameter lambda. And g lambda is the minimum of this function. So here x plays the role of psi. And the question is, which is this derivative, the g prime lambda? How can we express dg over d lambda? So this is our question. Well, since capital G depends on x and lambda, calculating the minimum means that you want, you have to, with respect to x, you calculate the derivative of g with respect to x and you calculate this derivative at the specific point that this is the minimum, that this is equal to zero. Basically means that for each parameter lambda, you have a different function, capital G, and for each one you have a minimum. So the function, the g lambda here is equal to the capital G function, calculated at the minimum, and for a given parameter lambda. And if we differentiate this function, we calculate then g prime lambda, this is equal to the derivative of g with respect to x, calculated at the minimum, plus the derivative of g with respect to lambda. But because of the fact that the derivative of g with respect to x at this particular point is equal to zero, we don't have to calculate, we don't need to calculate this term. So g prime lambda do not depend on this term, but just on the derivative of the capital G function with respect to lambda, where g has been calculated at the minimum. Okay, so these are the main ingredients that we need in order to see how these theorems can be applied to the DFT. So we go on, we go on, and we observe that we do another step forward, and we consider that we have a physical perturbation, A. A is a physical perturbation, operator A. And B is an observer that we want to measure. So A is the physical perturbation, so it's added to them, to them perturbed Hamiltonian, and alpha plays the role of lambda, the lambda that we saw before. The question again is, which is the variation of the unobservable that we want to measure with respect to the strength of this external perturbation? So the derivative of expectation value of B with respect to alpha. So we use a trick here. We say that B is the external perturbation of an Hamiltonian. And because of Elma Feynman's theorem, we can say that the derivative of the energy beta with respect to beta is equal to the expectation value of the derivative of the operator H beta with respect to beta, which then, because of that, is equal to the expectation value of beta, or B. And if we add the two, but if you have an Hamiltonian with the two external perturbation the same time alpha A plus beta B, the derivative, the second derivative of the energy alpha beta with respect to the two perturbation is equal to the derivative of B with respect to alpha, which is the response function that we wanted to, that we were interested in. So let's generalize a little bit. And we consider an Hamiltonian, which is given by an Ampertabes Hamiltonian plus a linear combination of perturbation where lambda i are the strength of the perturbation B i. And the energy, we can think of the energy of the system in terms of Taylor's function. So we have this term here, which is Ampertabes Hamiltonian energy. And then we have the first and the second order term. The first, let's leave a name to these terms. The first one is the derivative of the energy with respect to lambda i, calculated lambda is equal to zero is the forces acting on the system, which are used to get the structure optimization and molecular dynamics. And the molecular dynamics. Then the second order, we have the second derivative of the energy with respect to lambda i and lambda g calculated at lambda equal to zero, that are, as we saw in the previous slides, this is the second derivatives corresponded to static response functions, elastic constants or the electric, electric tensor. These are the response functions that I gave you as an example at the very beginning. And by the second derivative of the energy, this second order term, let's say, is also related to vibrational modes in the robotic approximation, teratomic force constants, and burn effective charges. So here you have the very same equation that we had in the previous slide. And so the forces, what is the forces is equal to minus, the expectation value of the perturbation v i, since I'm calculating the forces, the f i, let's say, the derivative of the energy with respect to the perturbation i. This is equal to the minus expectation value of the perturbation v i, calculated on the per-target wave function. And if the v i is a local perturbation, this can be written in this term, the integral v i, r, and zero, which is the charge-density distribution on per-target charge-density distribution. You see that, which is the power of the Elman Feynman team that in order to get, for example, the forces active on the system, you don't need to calculate the derivative of the wave functions. And going to the second order, the second order, the second derivative of e with respect to lambda i and lambda j, this is equal to two times the sum over n, overall the possible states, and the product of these two matrix elements divided by e zero minus e n. And in green, you can recognize the first order perturbation theory wave function. And so that allows to write that can be, so rearranged in this way. So the second order derivative of e is equal to two times the expectation value of the perturbation v i between c zero and c prime g, which is the first order perturbation theory of wave function with respect to the perturbation j, which is equal to the integral of v i r and the first order derivative of the density with respect to the perturbation j. In the same way, we can write, it's perfectly equivalent, equivalent writing that this h i j, these terms are equal to two times c prime i v i c zero, and the integral v i r and prime i r d r. So this is the integral. So then let's see how definitely, so now we see how to apply all we have seen before in the framework of condensate functional theory. So we take a potential v which depends on lambda, which as before, the parameters like for example, the strengths of this term perturbation expressed in terms of an unperturbed potential, plus the combination of external perturbation. So in DFT, what we know is that the energy or our system is the minimum of all the possible densities of the function, which is given by universal functional f plus the integral of this v lambda times the charge density distribution with the constraint that the integral of the density is equal to n to the number of electrons. So this is what we know from DFT. What we know from the Elman-Fiemann theorem is that the derivative of the energy with respect to the external perturbation lambda i is equal then to the derivative of this function here in parentheses that plays the role of the capital G that we have before, sorry. So the derivative of that function in parentheses with respect to the perturbation lambda i calculated at the minimum of this function. So we have the integral of n lambda r pi r dr. Okay, and then for the second order, sorry, the second order derivative of the energy with respect to lambda i lambda j is the integral of the derivative of lambda with respect to the perturbation j v i r dr. So what we do in density function perturbation theory is not to calculate in this system the second derivative in this way by doing the derivative but calculating this integral. And in order to do that, we see that we need to express the variation of the density with respect to the perturbation j. So let's say we have to calculate the response of the density. So the density in density functional theory is expressed in terms of the Kohn-Eschamm orbitals which are, so then it's the sum of the occupied states of phi v r square modulus. And the derivative of the density with respect to the perturbation is then given by this expression. So here we have the first order derivative of the Kohn-Eschamm orbital. But this is the first order derivative in first order perturbation theory, just from quantum mechanics is given by this expression is the sum of all the possible state different from the state that you want to perturb of this expression. Actually, the sum would split in two terms, in two sums. The first is the sum over all the states v different from v prime different from v from that one I want to correct plus the sum over the empty states. Okay, but when we put this expression for phi prime v in the expression for the n prime so the variation of the density, we observe that by summing over v this sum is equal to zero, so that this sum does not contribute. In the end, phi prime v is just the sum over c over the empty states of this part of this expression. But we, okay, and then we have to put this expression for phi prime here and calculate the density, the n prime r. The problem is that as you see, we express phi prime v as a sum over the empty states which can be, that actually is, but in principle you can have a lot of empty states so this is not the way that we are going to follow. But what we observe is that this phi prime v, we can actually demonstrate that this phi prime v is the solution of this inhomogeneous shedding equation, which is, so here on the left, we have h0, the perturbed Hamiltonian, the eigenvalue, minus the eigenvalue times the phi prime v equal to minus pc, which is the projector on the empty states, v prime, which is the perturbation, phi v is the connexia orbital, but we observe, so the way we calculate phi prime is not this, the first line, but the second one. And we also observe also that the projector, pc is equal to one minus p, the projector of the occupied states. So in the end, you can replace p, there's a projector p over the empty states by one minus the projector of occupied states. So in the end, you don't need to calculate any empty states. And this equation is solved iteratively with the same algorithms that are used to solve the connexia equation. So we established the parallelism between DFT and the density functional perturbation theory. On the left, you have DFT, you can establish these binuclear correspondence between the density and the external perturbation with zero, here. Then by solving the connexia equation, we get the orbital, then we calculate the density and the potential, and so on. And this scheme is solved iteratively. In the very same way, on the right, we have this correspondence between v prime and prime r. And so you solve more or less the same scheme in the sense that here you see v prime and prime and v prime. Okay, so now let's see how we can use density functional perturbation theory in order to simulate the atomic vibrations. On the left, we have the crystal with the atom in the equilibrium position. And on the right, this place, for example, the atom in the position r, of the quantity u r, or the atom in the position r prime of the quantity u r prime. And we want to, we ask ourselves which is the response of the system to this kind of perturbation. So we have, we have our potential is equal to them per target one, which corresponds to the left side of the slide, plus the linear combination of the external perturbation given by the displacement of the atoms. And the energy would be the zero, plus here we don't have the first order, the derivative, because of the term is equal to zero, since the, we started from, we supposed to start from the atoms in the equilibrium position, the forces acting on the atoms are zero. Since the forces are the derivative of the energy with respect to the position of the atom. And then we end up with the second order term for the energy. But what we know from, from before that that is the second derivative of the energy is equal to the derivative of the forces with respect to new to the displacement of the atom. These are, these are, this is one of the response function that I showed you before. These are the interatomic force constants. The interatomic force constant which are the forces acting on atom r with respect to the, the atom displaced in position r prime. And these interatomic force constants are principle very big matrices of the size of these matrices 3n by 3n, n is the number of atoms and 3 are the Le Cartesian coordinates. And the, the, the, the, the, the, the, the, and so these are the, and the value of these matrices are the omega square. So the, the, the final modes, the final frequencies squared. And I insist on the fact that we don't have to calculate the second derivative of the energy in this way, but by using them on Feynman theory, we calculate the density function of perturbation to use the perturbation. As I showed in the previous slide. So these are the, the diagonalization of these, these matrices gives you the final modes, omega square. If the calculation has been properly in principle, these final frequencies are positive. But if sometimes they can, they can be negative because of some numerical problem or in the case, you are in presence of a real dynamical instability of the system and in this case, you can address, you can, that may deserve to be studied. So now, so then when you calculate phonons in principle, you, you have to use a supercells, supercells because in order to accommodate, let's say the perturbation, which may have a wavelength, an arbitrarily large wavelength. So, but so the supercells, big supercells means a size of very, very big size of these inter atomic force constant matrices. So means that the calculation can be heavy. But in principle, the phonon, since the phonon ones can be classified by their wave number. So the symmetry helps us and so they each perturbation is as given a wave number as I show here, you have a perturbation v prime, which has a certain wavelength, which is given by 2 pi over q. And by using this factor, you have that in the right and the right hand side, the question of the that I showed you before, this is the right hand side. Here we have the perturbation and the function, for example, and you see that the right hand side, the total wave number of the right hand side is k plus q. And the left hand side must have the same wave number k plus q. In the end, it's possible to demonstrate, but I don't do that. The perturbation as a given q vector leads to the variation of the density which depends on just on that q vector and the self consistent potential also depends on that q vector, meaning that for each q vector you that each q vector is independent from the other, and the calculation can be done separately. And in the case of polar materials, things become a little bit complicated, more complicated because of the fact that these displacement generate microscopic electric field. So let me write the energy as a function of the displacement and the electric field in this way. And then if we calculate f, the forces acting on the system like the derivative of the energy with respect to the displacement and the electric induction like the derivative of the energy with respect to the electric field by just differentiating this expression we get the f and the special for f and the special for d in terms of the displacement in terms of the electric field. This the carl of the electric field in C++ is given by q vector between q and e, and if we have the displacement perpendicular to the q vector, this means that e must be equal to 0. This is true for the transverse phonons meaning that if e equals to 0, the force acting on the atom is just this expression so the frequency is equal to omega 0. The frequency of the transverse phonon is equal to omega 0. But if we have longitudinal phonon longitudinal phonon means that the electric induction is equal to 0 and this is the case of the longitudinal phonon meaning that this implies that the frequency has an extra term which is given by the and the electric constant so that's why in order to treat polar materials in when you calculate phonons in polar materials, you have to to calculate these two quantities by for example, this is true for GW you have to for quantum espresso, sorry you have to switch on this plug epsilon equal to 2 and that allows you to take into account the calculated electric constant and the benefit in order to properly calculate this extra term which is added to the to the frequency. This means that here you have the splitting between LO and TO and the frequency of the longitudinal phonon is larger than the frequency of the transverse phonon. This is not true for the two-dimensional materials as Tiboso showed in 2017 because in this case the longitudinal phonons acquire a finite derivative here as you see so there is not this splitting at the gamma, the splitting is not true anymore so these two phonons are degenerated gamma and this is true due to the fact that if you have two-dimensional materials it's a question of dimensionality going from 3D case to 2D case and actually if you have a two-dimensional material you increase the number of layers and calculate phonons you see that the breakdown of the splitting is removed by increasing the number of layers meaning that the 3D case is recovered so in order to treat properly the two-dimensional case I copied here the description of quantum espresso PW input you have to be careful to switch on this flag assume isolated and put it equal to 2D which allows you to treat properly the two-dimensional case with this you finished so I want to thank you for your attention and part of these slides have been inspired from the Stefano Baroni lectures from a previous quantum espresso school and see and that's it, that's all for me okay, so we are now open to questions and comments everything please Tom unmute yourself and make your questions yes thank you very much for that I mean I've never been brave enough to look at this perturbation theory derivation every time I see this projection operator it scares me but thank you it's very clear and well laid out okay early on you make the point that to express the coefficients of the Taylor expansion of the energy in terms of the density you have to assume that each of these coefficients whatever they are if it's first or the second order etc they have to be local with respect to the position so you can move the bra through it and then take the density on the left right here yes here yeah and the slides before yes we've been hearing a lot this school write about how in the electron case the screening is non-local and this is very important so is this just because in phonons you can assume that generally speaking things behave like structuralist dialectics and you can always move the screening through or I mean if there are vacancies and there is more structure and so forth you can't do anymore no okay let's see let's say that when you move from here to there you can say imagine that you don't have the dance the wave function you just know the density in this case you know that I mean if you don't have access to the wave function just to the density you need that your standard perturbation is local but since with the density function perturbation theory scheme we have access to the first order derivative of the wave function actually we can treat also non-local perturbations displacements phonon displacements are you can treat the non-local perturbation house sorry I didn't follow that last bit in the sense that when you solve the density function perturbation theory equations the scheme of the three equations that I showed here you have here you actually you have access to the wave function to the first order derivative of this wave function by solving this equation so you you can have whatever right so you can calculate it in this cone sham formalism you don't need to actually write it in this way right okay that makes sense and if I could I've never understood the longitudinal transverse phonon thing because you say okay e is zero it's transverse d is zero it's longitudinal but in my head a system is either e is zero or d is zero so how do you have two phonons at the same time it depends on the what the way I see it depends on the the orientation of the displacement with respect to the to the q vector like here here you see the q vector is on the plane the displacement is in one case is perpendicular to the to the q and the other case parallel I see so it's like you have to consider q and then also this this little capital q whatever you want to I see that makes sense okay thank you so much you're welcome so there is a question by Mukesh Singh if you can unmute yourself hello hello thank you for this thank you for this nice talk so my question is that why do we give so much importance to Helman-Ferman theorem so we know the variational principle and it seems that both are same can you comment on that the importance of Helman-Ferman theorem yes importance of Helman so why do we give so much importance to Helman-Ferman theorem the variational principle right so what is the difference between them the Helman-Ferman theorem allows you to to to calculate the instead of calculate the derivative of the energy with respect to lambda i to the perturbation lambda i allows you to imagine it to apply the Helman-Ferman theorem to the density to functional theorem so we are in this context and we want to calculate the variation of E with respect to lambda i because it's related to the forces and because of Helman-Ferman theorem you don't have to make this derivative but this integral since you have access to the to the density no wait wait I think my question is since we are getting the same let me understand you probably you are saying that there is a variational principle the one you apply to ask to focus on whatever other problem and then as a why are you stressing so much that you just don't use the normal variational principle is it correct yes yes yes so you are applying variation principle to an Hamiltonian problem it's different so you are not calculating the minimum of a trajectory of someone on a skate running on a hill this is a variational problem in terms of a mission object Hamiltonian and a ground state and Helman-Ferman is exactly based on the property that the state you are calculating the average is the ground state of the operator is a specific variational principle and actually makes your life enormously easier did I answer your question yes yes yes yes thank you thank you so if I can so why do we call the perturbation external perturbation as a strength here sorry can you repeat that why do we call external perturbation strength strength yes so let's say we want to displace a better when we do the full on calculation we do some kind of displacement right so in that case displacement is in my head displacement is perturbation so do we call the strength that displacement as a strength the strength yes the displacement the amount of the displacement is the strength actually so whenever I whenever I see strength I start some kind of differences in our potential so I'm not able to relate that but this is calculated at zero strength at zero displacement I think that he has a problem in connecting the displacement to the strength of the perturbation I think Elena partially answered maybe the last piece is that is a Taylor expansion so you have delta R multiplied by a derivative so it's a whole thing that does the perturbation so more you stretch stronger is the perturbation so it's not a potential it's a stretched potential it's written there so okay okay the UR means okay thank you very much I understand okay so we don't have any other question and we thank Elena again thank you


That's kryptonite, Superman. Little souvenir from the old hometown. I spared no expense to make you feel right at home So I was just having this amazing conversation with a really good youtuber friend of mine And I was like, you know what? I'm not gonna be selfish. I'm gonna make a video about this and help the entire world What is up everybody? This is Chris from the Rewired Soul where we talk about the problem But focus on the solution and if you're new to my channel, my channel is all about mental health So all of my videos are designed to help you with your mental and emotional well-being So if you're into that kind of stuff, make sure you subscribe and ring that notification bell So yeah, we'll start this video with a little bit of story time Let me introduce you to a friend of mine, a very dear friend of mine This is Kayla from the channel Panko Bunny. All right, I will provide links to her channel down below Go check her channel out and subscribe. She makes a ton of amazing adorable delicious treats She also does other kind of recipes and you'll see through the conversation that we had Like she will be making some more cool content But anyways Kayla is on a train right now and me and her were chatting and she was congratulating me on my recent success Thank you Kayla and Kayla's been around like since the beginning like since I first started my youtube channel And I have like less than like 500 subscribers Kayla and I have been talking She's given me advice and tips because she's been in YouTube for a while. She has like over 60,000 subscribers She's gigantic over on Instagram and she's helped me a lot a lot on the way And we were just having conversation because she was congratulating me on the success I'm like girl like one of my missions in life is to get Kayla to a hundred thousand subscribers So I try to chat with her and toss around ideas and brainstorm and we're gonna get you there girl We're gonna get you that silver play button. Anyways, um, she was talking about it And I was just giving her ideas like I'm always trying to figure out, you know, obviously like what what can I do? How can I take this topic everybody's talking about and use it to bring in a new audience and find things that people can relate to Right, so Kayla with her niche in food. I'm like, how can how can she do this? So I started tossing around ideas with her and she she's told me that she's worried about being a sellout Right and that's why I was like girl girl. I'm like, you know what our kryptonite is Do you know what our kryptonite is ego and fear those things are kryptonite, right? So we're talking about this and I'm gonna touch on this again later because she has a she has a healthy fear She's afraid her version of selling out.  My ego is something that kept me angry My ego is something that held me back from being truly happy and what's ego? What is this ego thing? There's a great book that I'm trying to find the time to read But until I get to that book and make a review of it, like check out this short clip from alpha and omega the ego creation Wants and seeks the approval from the outside. It wants to be fed by likes.  Well that whatever you just produced or that that's beautiful. That's great Yeah, I think that you're really Worthy now the thing is that what if it's taken away from me? Bingo right there. So our ego it's fed by these things this this social status, right?  Think about how you think that you have to have a certain car or certain clothes or a certain job or a certain amount of money Or a certain house all these different things the way you got a look on Instagram or Facebook or Twitter all these things That are based on your ego how you want the world to perceive you because you care so much about what people think, right? So when I was talking to Kayla like part of this this whole sellout thing like we're worried about what people are gonna think about us, right? Like the only reason the only reason my channel is starting to have an incline is because I got rid of that I got rid of the ego aspect. I got rid of the fears, right? And you've been seeing me trudge through it and like I hope you guys see underlying messages with my videos of who I am And what I'm doing like you will see that I give less than zero About some of the comments out there, right? Like I have people who have commented in my YouTube comments and they said oh Chris I've been with you since the beginning before you started making you videos about YouTubers by the way if you want some more details on that watch my last patreon Q&A, but like yeah My ego might have held me back and like welcome back to tough love Chris like here's the thing Here's the thing like me being cool is not gonna get me anywhere me like caring like oh, yeah I don't care. I don't care like in my treatment center. Do you know how many times I gave tough love to the people in my addiction? Treatment center. There are so many people young people young men young women even older men and older women They spend their entire treatment episode trying to look cool And then they go back out and relapse some of them even pass away, right? So your need to feel cool to look cool to other people like where's that gonna get you? I did that for a long time. I was like, oh, I gotta be cool. I gotta look cool I gotta put under this persona this facade and all I did was keep me sick all I did was keep me sick like I Think I think unless like I'm just in a bubble I think we're out of the hipster phase, but wasn't that the problem with hipsters like oh, yeah, like I'm just so cool I'm so cool that I don't do trendy things Right, like what what are you talking about like I used to be that guy Like I'm the kind of guy where I could tell you stories about how like I interviewed fallout boy before they got big Like we in her fault interviewed fallout boy when their tickets were only ten dollars, right? And then they quote unquote sold out screw it good for them I love those guys sell out all you want. You know what I mean Because like selling out is something that we got to think of and by the way quick plug speaking of selling out You want this cool shirt? You want to be my 20 head over to the rewiring soul merch store get yourself one Anyways back to selling out like what's selling out and what are the pros and cons by the way? Have any of you ever heard that song by real big fish sell out great song? I loved it I used to be a little Scott kid anyways What is selling out like selling out is kind of what I think Kayla's fear is backing brands that she doesn't believe in you know what I mean and and putting putting on this fake show This is something that's been going on in the beauty community Like saying they love this product or like this product like we sell out when we promote things for money This is one way to sell out. We promote things for money and we don't really believe in them We don't really back them. We make up lies like oh, I love this product forever and all of that right and like That's the thing like I've gotten flack about better help. That's a great example My ego gives zero once again, you know why because I check in with my moral compass I am not latched on to better help because of my affiliate links I am not Lashed on to them because of that I am lashed on to them because I truly believe within the depths of my soul that they are a good good company You know why because my girlfriend has benefited from their services Udo from positively Udo has benefited from their service a lot of people from my channel have benefited from my services But but if I cared about what the other people thought I wouldn't promote a service I can possibly help people because I'm so worried about what you're thinking and that affects my ego My ego is this monster inside of me that can change who I am and make me do things that destroy my mental health So now let's talk about the second piece of kryptonite that destroys our mental health Fear our fears right so now that we've identified the ego Okay, this thing that is fed by social status and what people think of us now We can start looking at these as fears right fear of not being liked right fear of being judged Fear of not being accepted for youtubers fear of losing subscribers fear of bad comments Think about these things think about all of these fears and I'm somebody with a generalized anxiety disorder So something I've had to do to manage my anxiety and this crazy thing up here is to walk through fears and really identify these fears It's saying are these rational or irrational fears right things that affect my ego are not things that I need to be afraid of You know I need to be afraid of like things that can cause Health problems to myself to my son to Tristan to my loved ones to the planet, right? But if Joe Schmoe 576 in my comment section doesn't like what I'm doing Peace out Joe. You know what I mean like we need to start separating our fears and saying is this something I should be afraid of like I have so many youtuber friends so many youtuber friends who like tell me all these things They're afraid of doing for losing subscribers or what their subscribers are going to think and all this and again This goes back to your moral compass It goes right back to your moral compass if you are staying true, right? If you are doing things with the proper motives and the proper intentions, yes, you're gonna lose people along the way Sorry, you think I haven't lost people along the way of course I have but look at how many more people I'm helping as well You see what I mean? So like and this is some more tough love like I have no pity for you I have no sympathy for you if you're letting your fear of numbers your fear of likes your fear of comments If you're letting those things run your life, I don't feel sorry for you Right because what happens is that people stay stuck in the problem and they don't move to the solution It's really easy for youtubers or even us as people to say oh Society's keeping us down or oh the algorithms keeping us down like don't get me wrong Society and the algorithm of YouTube definitely have their problems, but what good does it do when we focus on those problems? Why don't we start moving towards the solution? So that's what I'm saying I don't feel sorry for anybody anybody who is letting the fears of Subscribers or likes Determine their success in life. You see what I mean because that's something I wouldn't want you to feel bad for me That's all me. You know what I mean? It's not on them. It's on me So how do you keep your fears and your egos in check something I mentioned all the time? I'm gonna mention it again mindfulness mindfulness mindfulness mindfulness whenever thoughts come in my head, right? I'm able to sit down and notice all mindfulness is is noticing it's slowing down As you know, I have a lot of energy I slow down and I'm like where is this thought coming from? Where is this fear coming from is this from my ego, right? Is this a rational or irrational fear because a lot of us what happens is we let our minds get the best of us and just run Away, and they turn these small things into gigantic things because we don't catch them soon enough All right, but the more we practice mindfulness the more we can catch these things So now I can catch this thing and say okay. Is this my ego? What are my motives? What are my intentions? Am I really selling out? Am I doing something with the wrong motives with the wrong intentions? Am I supporting something bad? Just so I can make a dollar off of it. Oh, wait. No I'm actually trying to help people. I'm trying to spread my message a little bit more. I'm trying to entertain people, right? I'm trying to support my child. I'm trying to do these things. Does that make sense? So whatever it is mindfulness will help you slow down and start acknowledging the ego and the fear, okay? So anyways, that's what I got. Again, go check out Kayla. We need to get Kayla aka Panko Bunny to 100,000 subscribers. It is one of my goals in life, all right? And she is going to be doing a lot of cool new content. We've tossed around some ideas This is also a great way for you to help me keep her accountable, okay? So go subscribe to her channel so we can watch and we can see if she tries to put some new things in motion All right, but let me know let me know down in the comments below How do you feel that your ego right and your fears affect your mental health? Okay, what are your fears of social status and what people are going to think of you? How much is that controlling your life? But you know how we do also tell me about the solution down in the comments below All right, but that's all I got for you with this video If you liked this video, please give it a thumbs up if you're new make sure to subscribe and ring that notification Bell and a huge huge huge thank you to everybody supporting the channel over on patreon You're all amazing and again if you would like to sell out with me Go pick up yourself some rewired soul merch by clicking or tapping on that icon right there All right. Thanks so much for watching get your ego in check and I'll see you next time


efficient computation of sparse matrix functions for large-scale electronic structure calculation as implemented in the chess library. Okay, thank you very much for giving me the possibility to present our work. So I will talk about the chess library that we developed during the past months and years at the museum collaboration with various people also from abroad, in particular from France and from Japan. So the outline of the talk, first I will talk a little bit about the motivation and the applicability of chess in electronic structure codes. Then I will briefly talk about the theory behind chess, a few words about sparsity and truncation, and then several performance figures, so accuracy, scaling, parallel scaling, and finally also comparison with other methods. As you all know, linear algebra is a very important topic in electronic structure codes, sooner or later all codes will have to deal with this. And you can do it in standard way, for instance with lap-hacks, scale-up-hacks, standard libraries, but they can become a bottleneck because in the worst case they scale cubically, and so your codes will hit the wall. And it's even worse if you have sparse matrices because in this way if you have sparse matrices and use these standard tools, then you just multiply a lot of zeros and you will waste a lot of compute time. And sparse matrices are actually quite abundant. You will find them if you have a specific basis set that incorporates localization or also if you have intrinsic localization properties of your matrices. And to deal with this we created a standalone library for sparse linear algebra, in particular tailored for electronic structure codes. We called it chess, which stands for Jebyshev sparse solvers. I will show you later how it works just to start. I can already tell you that chess works very well if your matrices exhibit a very small spectral width. So it's really tailored for this purpose. Another question is do we encounter such situations in electronic structure codes? And of course it depends on the basis that you use that you need it's possible. I show you here a few systems, all of them are very large and very sparse. They are calculated with the localized basis as implemented in the big DFT code, which is a code that was first coupled with chess. And I show you here for the overlap matrix, the condition number and you see the basis is really very nice and leads to an addition number that are only of the order of two. And also if you look at the spectral width of the Hamiltonians, these are electron volts. You can see that we are of the order of 32, 40, maybe 50 electron volts. And if you are in such a setup, chess performance extremely well as I will show you later. So the basic idea of chess is not new. Well, it was developed, the basic idea about 20 years ago. So the idea is to develop our matrix function in terms of Chebyshev polynomials like this. Well, this is the matrix that you want to develop. You have to scale and shift it since these polynomials are already defined from minus 1 to plus 1. And the expansion coefficients, it looks complicated but it's not. This is the standard textbook formula. The most important point and also the heaviest is the calculation of the Chebyshev polynomial matrices down here. But they have a very nice recursion relation. So you have just to iteratively apply a matrix to another matrix or actually a matrix to a vector. Because it turns out if you look at this formula that each column of your matrix is independent. So this is an algorithm that you can parallelize very well because you just put several columns to one processor and then each processor does its work independently. As I told you, chess at the moment is tailored for electronic structure code. So we implemented the functions that you need to perform density functional theory. In particular, this is the calculation of the density matrix. The function that you want to expand is just a Fermi function. You can also calculate the energy density matrix, which is very similar. Or matrix powers. This is the most general that we have. So with the power here, the A can be anything, also non-inject value. So you can also calculate square roots, inverse square roots, etc. But it's very easy to generalize this. So we could also include more functions. The only thing that we have to change to implement here is the calculation of these coefficients, which is very easy to do. As I told you, chess works with sparse matrices, and if you have sparse matrices you have to choose a sparsity pattern. And we decided to work with a fixed sparsity map pattern that is used to define. So a user in the beginning has to define what is your sparsity pattern and then chess does the calculation within this pattern. So we have in chess three patterns. So first of all is the pattern of the original matrix M that's usually defined by your setup, by your base function. Then we have to sparse this pattern for the matrix function which is usually a bit larger so that the function has a space to expand. And then there's a third auxiliary pattern for the multiplication. That's the technical detail. And here I show you how it looks like in a typical setup. So we have here a sparse matrix. You can see in gray this is the entries that are set to zero. And here on the right hand side, this is the inverse of this matrix. You can calculate it with any constraint just with a dense calculation. And you can see the matrix spreads out a little bit but still there's a lot of white space meaning at that tier there are a lot of zeros. So it's justified to do this calculation here also within a sparse pattern. And indeed that is what we did here. So this is the calculation with chess where in gray we again define our enlarged sparsity pattern. And as you can see we really capture very well the entries that are non-zero. And this is the difference between this and this one on a different scale. You can see the typical error is of the order of 10 to the minus 10. So really really small. Now let's talk a bit about the accuracy. And as you can imagine there are two factors that affect the accuracy. So first it's the error that you introduce by the sparsity pattern. And secondly it's the error that you introduce by the Chebyshev feed. So it's not really clear what is actually the correct solution. The most straightforward way would be to define the correct solution as the one that you obtain if you do a calculation with for instance LAPAC without any constraints and sparsity constraints and then you just junk it. But then the problem is that this solution usually does not fulfill this identity. So if you calculate the matrix function and then apply the inverse you should again get back the original function. But with this approach it is not true. So we think that the better way is to define the correct solution as the one that you directly calculate with in the sparsity pattern. And then you ask for the fulfillment of this identity here. This is how we define our correct solution. Because in this way we can get rid of the bias that you introduce by the sparsity pattern. One more slide about sparsity. So as I told you we work with a fixed sparsity pattern but an alternative would be to use a dynamic approach so that during the calculation you set to zero all elements that are below a given threshold. The advantage of this is that it's very flexible and you can control the error that you have. But on the other hand the sparsity of your matrix can decrease a lot and then your calculation cost can explode. And this is a test that we did with the purification method which has such a dynamic sparsity control. And you can see the start here with a sparsity of more than 98%. But then we have a very strong fill in and at iteration 10, 11 we already have a sparsity of only 93%. So you can imagine that the cost here is much, much higher than here. And this is very hard to know beforehand. That's why we think it's better to work with a strict, with a predefined sparsity pattern and in this way we already know in the beginning what will be the cost of your calculation. So now about the accuracy. I show you here two benchmarks. First for the inverse and here are two errors. As I said before this is the error down here which is related to the Chebyshev fit. And you can see that it's negligible of the order of 10 to the minus 11. So the Chebyshev fit is really, really accurate. And up here you see the error that is introduced due to the sparsity pattern. It's a bit larger but still of the order of 10 to the minus 7 which in practice doesn't matter at all. Looking at the density matrix here I calculate the energy the trace of the curl. Here's the matrix times the Hamiltonian matrix and we can see that the relative error is of the order of 0.01% which in practice also is very, very small and negligible. Now thanks to the fact that we can exploit sparsity our chess library scales linearly with respect to the number of non-zero elements. This is shown in this plot here. So I show you the runtime to invert the matrix. So I have various matrices from 6,000 times 6,000 up to 36,000 square. But as you can see the runtime does not depend on the total matrix size but only on the number of non-zero elements. So whether you have a small matrix or a big matrix the only important thing number that actually matters is the number of non-zero elements and it shows that the library exploits sparsity really well. I've already told you that it's very sensitive to the spectrary and this is shown here. This is the runtime and the polynomial degree that we need to invert the matrix for various condition numbers. So on the left hand side we see we saw the condition number of about 2 which leads to a polynomial degree of 50 and the runtime of a few seconds. But then if you increase the condition number and we go here on the right hand side where we have a few thousand you can see that it explodes. So with the polynomial degree that we need to well approximate the function is already of the order of 2, 3,000 and the runtime already of 10 minutes. You can see if we are able to work in this regime it's really really an efficient algorithm. If we work here then we should better use another approach. This is also here visible for the calculation of the density matrix. Again we can see that for the large of the spectral it's more expensive. It's a calculation so we can see here for a spectrary of 150 electron volts we need more than 2,000 polynomials whereas if you have a spectrary of 50 we can bring it down to the order of a few hundreds. For the density matrix another important point is the gap, the homo-lumo gap. If you imagine if you have a small, well a gap less system then the Fermi function is more or less a solution which is very hard to approximate with the polynomial and also the cost becomes very high. So the bottom line of this library is very good for systems with a gap, large band gap and with a small spectral width. Finally before comparing with other methods one word about parallelization. As I've told you the algorithm of chess well it's really can be parallelized in a very efficient way and we also need a lot of effort in this direction to reach a really a good scaling. This is again the calculation of the inverse you can see here the number of cores and this is speed up and you can see even the matrices are not very big but even for more than 2,000 cores we are very, very close to the perfect scaling and on the right hand side these are the run times you can see if we use many cores we can invert the matrices of the order of 30,000 square within only a few seconds which is not so bad. We also went further we wanted to really know what's extreme scaling so we went up to 16,000 cores and of course here now it becomes a bit flat but still if the matrix that we looked at the 96,000 squared is not really huge so using 16,000 cores to invert this matrix and still getting the speed up is not bad and you've noticed that this speed up is relative with respect to the first point which we already used in 1,500 cores so overall we get here a speed up of the order of 5,6,7,000 which is quite good. Now to conclude we compare chess to two other methods so first of all we compare it to selected inversion which is another method that can calculate the inverse and exploit sparsity and then we also compared it with two dense standard approaches namely scale up back and lay back. We have here five different matrices so from 6,000 squared to 30,000 squared and we did this benchmark for various condition numbers here from 2 to about 150. So first let's look at the dense solutions these are the yellow and the blue lines here so first of all they are constant so there is no dependence on the spectral width and as you will expect their cost explodes because they are scaling well up uniquely. If you look at selected inversion also selected inversion shows no dependence on spectral width and you can gain a lot compared to these dense approaches but you can see here the purple curve is chess library and if you are working with small spectral width it is the fastest method. Compared with selected inversion the crossover with respect to condition number is at about 150. So if you have a matrix with the condition number below this value well you can use chess to save some time otherwise I think it's better to go to selected inversion. Finally we also compared the calculation of density matrix here so first of all we don't compare it with lay back because it's obviously worse. But we compared with pexi that's a library that was developed here by Lin Lin and that can also use exploit as varsity and we compared two different setups. Let's first look at the MPI only version we did this because pexi is very efficient with MPI parallelization so these are the blue and the yellow curve here for these small matrices pexi here is the fastest in this setup. Later on there's a switch so chess becomes more efficient because chess really scales linearly whereas pexi in this case because it's a three dimensional system has a quadratic scale. On the other hand if you use a hybrid scheme so MPI and open MP parallelization we can see that in all cases chess is the most efficient method but this is not the problem of pexi because the bad algorithm just because pexi is not very well parallelized with open MP that's why we gain here but you can see here that really with chess you can calculate the density matrix density kernel within a few seconds even for very big systems. Last slide now presented to chess with the library to calculate the density matrix algebra but it's not the only one there are also libraries. I've talked about pexi but there is also and sometimes it might be cumbersome for a code developer to interface with all of these codes. Imagine every time that someone changes you have to change again your interface etc. And therefore some people in the US started this LC project and their idea is to unify all of these libraries. This means that in the electronic structure code you only have to interface with LC and then internally LC interfaces with all of these various drivers. So in this way for a code developer for maintenance it's much easier to keep up to date with all the developments that are going on down here. At the moment chess is not yet in LC but we are working with them and we're hoping that in the future chess will also be included in LC so if your code already interfaces LC you will get chess for free without any work. Let me conclude so I present you chess which is a flexible tool for the calculation of matrix function tailored specifically for density functional theory but it can also be extended to other functionalities for the purposes. It can explore the sparsities of the matrices in this way reach a linear scaling with respect to the system size. It works very well for small spectral width of the matrices so it was specifically tailored for this purpose and last but not least it exhibits a very good parallel scaling. We have a hybrid scheme which works with both MPI and OpenMP. That's all. Thank you very much for your attention.


He had literally had $500 in his account, and I think he's approaching the million dollar mark right now, guys.  You know, that's all it takes. All it takes is one trade at a time and adds up with time. He did not do this overnight. This is years. I met him. You know, he's one of the first members of MIC and it's been like four years. So it's like four years. It took him four years to be overnight success, right? That's what we guys always say, right? It's two hours and four or five years to become overnight success. So.


Okay, so I'm going to present a project that's on unraveling the impact of biofuel production. So unraveling biofuel impacts on ecosystem services human well-being and poverty alleviation in sub-Saharan Africa. I'm listed there as a presenter, but otherwise this is a project that involves several institutions and several people here, these Francis and Patricia, who are involved in the project. So what's the main motivation behind this project? These are the kind of images you tend to see when you talk of biofuel. So it's about competition between land and food, for instance, which sort of people are taking different sides, almost two sides to it. So they are those who see it as very bad dates, leading to land unavailability, while without looking that there could possibly be a middle ground. And so with this research, the aim is to try and identify what is the true human well-being and poverty alleviation effects of biofuel expansion in Africa. So for instance, by using land available to produce biofuel, people would lose land and ecosystem services derived from that land. And with less land for agricultural production, there can be food insecurity and poverty. But then when you look from the other side as well in getting in biofuel production could provide the much needed income and employment creation. And this income could actually contribute to food security if during, at a time of non-havest period, so people with income coming from biofuels would be more food secure, for instance, than those who are not. But then these are just assumptions. There's been a very limited attempt to empirically test them. So the main questions for the study are that how can biofuel production ideas become an agent of poverty alleviation in least developed countries? And then it's testing three main hypotheses that those who are engaged in biofuel projects have higher income. There's higher income opportunities from this than engaging in other agricultural activities. And that small, best biofuel project would offer higher income and benefits than light-scale plantations that target the export market. And then the extra income from this small-scale feedstock production, where feedstock we are mainly looking at sugarcane and geotrophic, can actually increase the resilience of households to livelihood shocks. So at this stage we are at the point of developing methodologies for the field work, which will be done looking at case studies in Malawi, in Swaziland, and in Mozambique, where you have light-scale plantations that target fuel for transport sector. And in Mozambique you have small-scale ones that one of that produces fuel actually targeted at households for cooking as a cooking fuel. So the whole approach, the study adopts an ecosystem services approach. So we are in trying to look at the impact of biofuel. You look at the impacts on the whole ecosystem services. So provisioning services, regulating services, cultural, as well as supporting services. And with the different partners there are different methods for this. So for instance, there will be life-cycle analysis to look at the energy, impacts on energy. On provisioning services will be focused on surveys. There will be assessment of impact of biofuel production on water quality, which is going to do modelling and measurements. Then there's greenhouse gas emissions that's going to utilize life-cycle analysis approach. But for SEI, our component is mainly on human well-being and poverty reduction. So I'm going next to discuss some of the methods we are still thinking through and developing for trying to quantify this impact. So our main exposure variable, we are going to look at the biofuel production. So how does it impact on poverty? On this we look at various scales of production. So small scale production versus large scale. Jatropha versus sugarcane. Ownership type links to market, which market is targeted. And we are also going to look at use. So does biofuel that's used for transport have more poverty alleviation impact than if it's targeted at cooking or at lighting, for instance. And then our outcome, then we are looking at poverty alleviation, which is very complex. And so we are spending a lot of time trying to define what are the indicators of poverty and how we measure them. So income opportunities is obvious, but then there's also income uses. So for instance, the income coming from biofuel. So what is it used for? Because that could determine how it impacts on poverty. So we are looking at some variables derived from the multidimensional poverty index. Where you look at health, education and living standard dimension. But we may also consider progress out of poverty index and other indicators relevant to biofuels and to the study settings. So the approach we will adopt, we are looking at two possible approaches, some sort of cross-sectional studies. So in the villages we will go and sample households that have been engaged in biofuel production and those who have not. And then try to compare their income status and their poverty status between the two groups. Then we are also with a longitudinal approach as well. So we compare the same household to itself. What was its situation before it engaged in biofuel production and what is its situation afterwards. So based on participants recall or some secondary data as well. So using the two methods. But a big concern is of course confounders. For instance you may find households engaged in biofuel production probably have higher income. But they could have had this before even they started engaging in biofuel. So it's their socioeconomic status that determined that they engaged in this production. And without accounting for these factors we could lead to have a very wrong conclusion. So we will document all these factors as well. And in the analysis we will try to adjust for them. So poverty we will use two dimensions. And then using descriptive statistics and regression modeling then we can account for some of these factors. Thank you.


Hey guys, welcome to tutor terrific today. I'm going to be doing a problem-solving video in physics This is a video about force problems on inclines this is a commonly difficult problem for those of you who studying Newtonian dynamics and This one's going to involve friction to to make it extra saucy and complicated so The problem at hand requires you and this video really requires you to have a good facility in kinematics which involves these equations over here, which we'll be using today and in some basic Newtonian dynamics such as the sum of the forces equals mass times acceleration and Kinetic friction is an equation Coefficient of kinetic friction and the normal force multiplied together So you need to have a basic facility in these things to really understand or make use of this But if you do, this is the problem for you. So today we have a bar of soap that is accelerating down an incline that is 8.0 degrees and the length of the incline is 8 meters and It also gives you the problem the coefficient of kinetic friction very small 0.05 Zero between the soap and the ramp So there's some friction there. We can't ignore all friction But we are asked how long will it take the soap bar to traverse this entire ramp eight meters long? given that information so this is quite a lengthy problem, but The first step is always to draw a picture which we already have thankfully everything is already labeled for us that we know and After that if you already have the picture or you've drawn your picture based on the verbiage of the problem Your next step is to draw a free-body diagram a free-body diagram For the soap bar now that is a map which shows all the forces that are acting on The object not forces that the object imparts on other things But the force is imparted on the soap bar itself So I'm gonna draw the soap bar right here Let's talk about the forces acting on the soap Well, the soap has mass we weren't given mass which might scare some of you But we don't need it, but it does have mass and so it has a force of gravity Because it has weight That'll point straight down Okay, there's the force of gravity on the soap The soap is resting on a surface And if that's true then there's a normal force which is perpendicular to the surface itself So that would be at this eight-degree angle Like this. That's the normal force Okay In addition to these two forces We were told that there's a coefficient of kinetic friction Which means there's friction in the kinetic sense and that always opposes motion So if the direction of velocity as this soap bar accelerates is down the hill parallel to the ramp The force of friction will be pointing parallel to the ramp, but anti-parallel to that velocity so backwards So like this at a right angle to the normal force like so Alright, so this Designates a somewhat of a problem for us when we're analyzing this situation Because we have two forces at an angle. It is much easier to reduce the number of forces at an angle if you can And that is done by rotating the axes. Currently the axes are like this vertical straight up and horizontal It's straight left and right. Well, that means we have two forces at an angle. If we were to rotate the axes such that the y-axis pointed directly parallel to the normal force and the x-axis pointed Horizontal to that 90 degrees to that we have just one Vector at an angle that would be gravity. So what we're going to do is we're going to redraw this picture Where the axes themselves are rotated So it says the normal force points directly upwards Okay, so I'm drawing it like this and you'll see why in a second the friction force will point this way Okay, directly horizontal now and gravity will point at an 8th degree east of south direction Like this there's the force of gravity, okay After you've rotated your axes to the desired location You need to now resolve any vector at an angle still into components only gravity is at an angle And so I'm gonna go ahead and Resolve gravity into components and its components will be these dashed lines Okay, so show their components of an existing vector the horizontal component We will call f gx and the vertical component. We will call f g y the angle Which is right here using geometry is actually congruent to this eight degree angle here. So this is 8.0 Degrees, I'm not going to show that right now. If you do enough of these problems You'll realize that that is going to be the angle Between gravity vector and vertical is the same after you rotate the axes as the vertical of the incline originally now Something to keep in mind that I didn't already mention is the value of the acceleration due to gravity lowercase g That is 9.8 meters per second squared we are going to be using that in Our I'll put an extra zero on there. We're going to be using that in this problem Okay, now Why did we do this? Well, remember we need to find time. Okay, we're gonna have to since this is a force problem on inclines Get to time by using Newton's second law The force sum equals mass times acceleration We can actually split this up into two equations one for the y direction and one for the x direction and Everything is in components except for the mass So I could set up an equation for the sum of forces in the y direction I'm going to leave some space here, and I could set up a sum of forces in the x direction So what you literally do for each of these equations is you add up the vectors in those particular directions whether Up or down for y or right or left for x. So let's do it for a sum of forces y I usually set this one up first because it's a little simpler than the other one. There's less going on in this case That would be true So let's look at f y we need to determine a positive Direction before we can continue with this analysis, and I always choose when we are going down an incline I choose downward as Positive okay, but you could also set upwards as positive if you like it doesn't matter So if downward is positive that means f g y the vertical component of gravity which points straight down is a positive vector That I'm going to add to f n now normal force if positive is downward will be negative So I'm going to actually subtract its value This will equal ma, but here's the thing is there acceleration in the y direction Well, that would only be true remember. We're rotating our axes. So this is the y direction now It would only be true if the soap Is levitating off the ramp which it's not or if it's falling through the ramp which it's not So that means ma is m times zero or zero Okay, let's continue our analysis. I'm going to need an expression for the normal force in this problem So I'm going to separate the normal force right now F g y excuse me Not x f g y will equal f n when I add it to the other side Okay, now let's look at f g y itself If you look closely you notice that f g y is trigonometrically related to f g If you make this a right angle here, you realize that that's the same as f g x We've got a little right triangle Okay, f g y is the adjacent side to the angle and F g would be the hypotenuse. So you might notice a cosine relationship between them That's because f g y is equal to f g times the cosine of eight degrees. That is very true So we can write f g cosine 8.0 degrees Equals f n Now I want you to remember something from physics in addition to this the force of gravity Is always usually replaced with mass times g a 9.8 meters per second squared you can always replace f g with mg as we say so back here I'm going to replace f g with the expression m G so now I have mg cosine 8.0 degrees equals the normal force. I will be using this very soon Now let's move on to the sum of forces in the x direction okay This expression has two forces as well f g x and f k, but we'll do a little more Substitution than we did in the f y sum equation So we need to choose a positive direction. I'm going to choose the direction the soap is traveling which is to the right as positive Okay, and remember it's a little bit downward, but we've rotated our axis from here to here So now this is to the right in our rotated axis diagram So f g x is positive and f k then would be negative because it points in the wrong direction quote-unquote So the sum of the forces would be f g x plus negative f k Now is there acceleration in the x direction you betcha This f g x is a little bit bigger than the friction because this soaps Accelerates down the hill in order to get to the other end at a certain time The ray we also know that it accelerates is because it is set from rest at the top of the hill and allowed to slide under its own quote-unquote power So that means there's an acceleration So the sum of these forces equals mass times acceleration because acceleration is not zero Realized though that this is a horizontal acceleration.  I'm not even given that But what's the goal? We have to remember the goal. The goal is to get time. Okay? Now as you may have guessed and you'd be right none of these force equations have time in them none of them So we have to have a go-between So we can get back to the kinematic equations up here known as the big three which have time in them And it looks like according to those equations. We need a The acceleration and we can get that Through these force equations the acceleration is like the liaison or the go-between Between the force equations and the kinematics equations. So we have to find this a x. There's no Vertical acceleration. So all we need is a x So that's why we're going to do some substitution now F g x. Let's look at that f g x is here also here in our Triangle analysis this geometric analysis notice how it's opposite the eight degree angle And so we know that sine is opposite over hypotenuse. So f g x will equal f g sine 8.0 degrees That's the force of gravity in the x direction Next we have the force of friction luckily, I have this nice expression for the force of friction in terms of some things that I Could know I'm definitely no mu k 0.05 And I have an expression for the normal force Hopefully I can use that. Well, I'm going to substitute those in So the force of friction is excuse me. We're going to subtract force of friction, which is mu k Times f n. I'm going to use this expression right here for f n M g cosine 8.0 degrees That equals m a x Okay, almost done with the substitutions. Now remember what I said about f g Even if there's this sign next to it, you can still replace the f g with mass times gravity m g So I'm going to write that m g sign 8.0 degrees minus mu k M g cosine 8.0 degrees equals m a x. Oh my goodness Looks like I made this worse rather than better, but that's not true. Remember how I told you we didn't have mass Well, we don't need it. That's because if you look at all of these terms There's a mass in each and every one. So that means it cancels So you can divide out the m's from every term now all that's left is things that we know So what I'm going to do is I'm going to move things up a little bit I'm going to continue the problem So now the next step is to write that same expression without the m's in it. So we have g sign of 8.0 degrees Minus mu k g cosine 8.0 degrees And that equals The acceleration we're after Okay, now remember that g equals 9.8 Minus per second squared and that we learned earlier in physics and we also know mu k Mu k the coefficient of kinetic friction. That's 0.05 So we're going to plug this all in and get our expression for a of x Your calculator you want to make sure that you are first in the proper mode, which should be degree mode Because we're working with degrees. That's how you do it on the ti 83 or 84 calculators check out one of my calculator tutorial videos for more information then We're gonna start plugging this in so this is the first term in 9.8 times the sign of 8.0 degrees close those parentheses. That's one term that we're going to subtract from that A larger product of things first the coefficient of kinetic friction 0.05 times 9.8 times the cosine of 8.0 degrees close those parentheses and That should equal our acceleration. Let's see Aha 0.87 much less acceleration than due to gravity because that's a very Very flat angle very low angle and so that is our acceleration now Let's keep a lot of the digits because we don't want to round too many times and we're not had we're not at our final answer yet So I'm going to write the following down for a x Write down about four or five actually six significant figures point eight seven eight six six five meters per second squared So now I'm going to make room and we're gonna move on and figure out which kinematic equations We will need to use to figure out how long it takes to get down the ramp So I've made some room now and I've written down our Solved for acceleration partially rounded point eight seven eight six six five meters per second squared now I need to figure out what set or single Kinematics equation. I'm gonna have to use to get to time from here. That's my goal remember is to get to time Now realize also that this is the only acceleration. It's in one dimension. These are one dimensional kinematic equations So I don't really need the x near the a any more In order to figure out which one of these and I only have to use one of these kinematic equations I need I need to write down what else I know and I know a few things. I actually know the initial position The initial velocity Okay, that's really helpful the initial position since I know the entire length I'm traveling can be set to zero zero meters. That's really helpful In addition, I know that I'm starting the soap from the top at rest and that means the initial velocity is zero as well This is going to help me a ton Determine which equation is best to use to figure out the total time Now if you look at the first one that has time in it It's really nice, but the problem is I don't know the final velocity that the soap has at the end of the ramp If I did I'd be able to use that very nicely The third equation here does not have time in it However, I could use it to solve for V and then plug V into here and then get time However, that's two equations when I only really need one the middle one. That's right I can use the middle equation which looks scary, especially when it comes to T. However, it's not so bad Let me show you I'm gonna write that here again Let's talk about some things. I told you that the x naught is zero. So that means this first term is Zero we don't have to worry about it. I also told you that The initial velocity is zero So that means this term is also zero So now we don't have to worry about this being a nasty quadratic equation. It's very simple We just have x equals one half a T squared awesome Well now I just have to solve for T Now if with you using your algebra skills, we could see that this one half I'm gonna multiply both sides by two Then I got a divide by a and then I just have this expression equals T squared Which would require us to square root both sides. So that means T equals the square root of 2x over a Okay, so now I have to do is plug in the final x value, which is eight meters and the a which we derived Earlier, so we have two times 8.0 meters And that's all divided by 0.8 7 8 6 6 5 meters per second squared I always want to check and make sure that my units work out and Meters cancel and the second squared are on the bottom of the bottom. So they'd come to the top square root them. I get seconds perfect now when I Calculate this time in my calculator. I get 4.26 and lots more It's quite a long decimal actually But let's check out the significant figures that I'm allowed to have if you come back up to the top You can see all of my initial measurements have two significant figures since there's plenty of adding and multiplying Dividing we're gonna have to go by the accounting rule Which is just you can only have as many sig figs no matter where they are as your least accurate measurement And so two sig figs is what I'm limited to because of all my measurements being two sig figs So I have to round this guy and he's gonna round upwards. He's gonna round up to 4.3 seconds Perfect, this is our time Now that's an 8 meter ramp. So 4.3 seconds seems kind of reasonable for a rather moderate acceleration Awesome guys. Thanks for watching appreciate your views and your comments and your likes. So keep it up This is Falconator signing out


Hey guys, welcome to AXIV Vlogs! This is your first time here and you would like to know more about life in Dubai. Don't forget to hit the subscribe button and the notification icon so you will not miss anything. And in this video I want to talk about the new Dubai program for those who work remotely and how you can get a visa. As we all know, the global pandemic changed our lifestyle. A lot of people still work from home for their companies. Dubai has launched a new program for those who work remotely overseas to live in Dubai. So it means you can move to Dubai with your family, live here on an annual basis. Dubai is a great place to live. It's safe, you have amazing lifestyle and the weather is great during winter. If you join this program you can open a bank account, you can get a local phone number, you can connect internet and even you can enroll your kids in school. In addition, remote workers will need to pay taxes, income taxes in Dubai. There are plenty of co-working spaces across Dubai and you can get daily, weekly, monthly, yearly packages. So it's very flexible. If you're looking for a long-term membership, I can recommend you in five. In five it's like a hub for entrepreneurs and professionals in media and tech sectors. So they have amazing facilities, they have meeting rooms, co-working spaces, production studio and the price is I think the best on the market I've seen so far. It's only 1000 dirhams per year. So how can you get this remote work visa? This visa costs 287 dollars. You need to have a health insurance with UAE coverage, passport with minimum six months validity, proof of employment from current employer with a one-year contract validity, a minimum of 5000 dollars per month salary, last month's pay sleep and three months bank statements. If you have your own company, you need to provide proof of ownership of company for one year or more with an average monthly income of 5000 dollars per month and three months bank statements. So this was the information about the new remote work visa. If you work remotely and you would like to live in Dubai, this is an opportunity for you and of course you need to meet the requirements. Thank you for watching. If you have any questions, please leave them in the comments below and please if you find my videos useful, don't forget to support me with your likes and I will see you in the next video. Bye-bye.


Hello, hello, hello. Hello, hello, hello.  Hello.  It's me, Corbin. Hello. You can follow us on Instagram, Twitter for more juicy content. Thank you so much on Patreon, follow us on official Twitter account, subscribe if you haven't hit the like button and helps the algorithm! We should do a full informational commercial that says, you know put like a just a computer in a cage it says The algorithm suffering Look, it's innocent innocent beautiful algorithm. Would you please would you please like the video kind of the algorithm? Just like just by liking a video you can help thousands and thousands of algorithms idea. That's a funny idea Today we got more our content because they keep releasing it Yeah, you can't stop won't stop variety released this six hours ago So it was post post post Oscars, but it was a rom-tron getting ready for the Oscars Okay, cool. You know how they do these things. I love how much yeah, and this is actually you had the thing I mean vanity fair. Yeah, this is vanity fair vanity fair And so they do they've done these a lot with different celebrities getting. Oh, I think they've done it with the pica Priyanka Indians that I can think of. Yep, but this year they did it with rom-tron, which is awesome Him getting ready for the Oscar-winning RRR film and not to not to song Which is fantastic, and so I thought it'd be fun to react to this and see how he got ready He was really well-dressed. Oh, yeah, I would have loved to see NTRs, too I know that because I loved his outfit me too Here we go Is that his wife? Hey vanity fair crew, how are you guys? Thanks for coming and being part of this journey and let's see. Let's get ready Nice Airbnb Usually my wife and I set up this small temple this ritual It just is connected to our energies. I'm India and it's very important for all of us to begin this day thanking showing gratitude to everything and every person who has helped us be here and Not too much, but it's just a few moments and and we get that sweet that is beautiful Definitely anxiety is kicking in actually not seeing my outfit until now until this morning and wow It's it's a beautiful work. He's done and I don't think I'll leave the suspended job to the people Like I said, we've done it all now. I think the people are taking the suspended look So let's get ready now and I'll see you guys in a bit He's had like the his military outfit from the film. Yeah, they definitely they both for a piece of cloth and we chose this in contrast to romsters all black outfit because it will be an amazing Well, and it's representative of their characters. Yeah Then to shine on the red carpet, but they're also like simplistic pieces. They were beautiful. Yeah more when it comes to fantastic Yeah, and everybody did that the designers all did that last night less is more I was sad run beer was a family business That's a nice Who's been doing my work for more than two years? She came up with a very very well known designer Shantanu Nikhil, he's one of my favorite designers in India, but they put in a lot of Appreciate them. That's shark So yeah, it's come out great and I'm feeling like I'm wearing India It's detailed with everything and yeah, thanks to Shantanu. You love Indians have for India It's just like because India's pride is also on our shoulder and it is a little heavy Literally, thank you. Thank you.  Yeah, you have beautiful. Look at the lining. Yeah I'm most with the barred symbol and that's Nikhil thank you. I Love that they did this celebrity makeup artist. I'll tell you I'll tell you his story He was in software working in my family company Then he quit to become a makeup artist after that I thought that he was such a rockstar and I've kept him for over 10 years now That's awesome follow your dreams What pasnamam is wearing it's a beautiful jewelry it also symbolizes the lithium flower in life-sized by Beena Gowenka. She's amazing Mumbai based avant-garde jewelry designer Gorgeous. Oh gorgeous looks great Her sorry is basically made out of silk scraps and by Thalingana artisans back in India So it means a lot for them to be wearing that and representing their state and their city on the red carpet Nikita has styled him so well with gorgeous. Looks amazing. So complimentary. It's a very special woman for all of us This is where we depart we need all your luck all India's luck. Oh, I love it. I couldn't tell it's kind of purple. Yeah Much prettier on the outdoors and you see that purple hue to the coat Fantastic, but they were in Look like they weren't Brentwood. Yeah Yeah, it did They probably it actually it kind of looked like they may have been staying at I forgot the name of the hotel Wouldn't surprise me it looked like the driveway. I don't think it was a hotel. I think it was a I think it was a house It could have been a suite at a I thought I thought it was just like an Airbnb It may have been yeah, and it may have been they may have preferred to do that But yeah, that was I love it because when I think a lot of people do this one They especially when they come from different cultures and to Hollywood. Yes, especially for the Oscars So they can represent their culture But it doesn't happen for India a lot. No, but the fact that they've through the entire process to every award show I've seen them in these awesome. I don't know. I don't know. I just call them like fancy kirtas because that's the only thing I can think of right But I'm sure it has a much more Name but yeah, India has such a rich history in culture film Clothes like they like in the fact that they were representing not only their film, but their culture Yeah, the fact that they've all said they're carrying the pride with India around with them Which they are they are and that's it's because India is they they love their films. They love their stars They love their culture. They love India So much and so it means so much to them But I love the fact that they were able to display their culture because they looked now It looks so amazing and there's every person at the Oscars There's there's details like that not necessarily cultural representations But I do love that Vanity Fair did this piece on them and we got to see the specificity of what was going into both of their Outfits that that they were wearing gorgeous. It was as good as it gets. That's they couldn't have asked for anything more beautiful. Yeah, that was That was really great. I really enjoyed that. I wish I would have done one with a rom-toron as well I know love to have NTR. I know I know yeah junior NTR. I would have loved to have seen the whole Who's responsible for the Loved his but I I loved junior NTRs even more just maybe the tiger the flare of that on the shoulder cool Yeah, it was very cool something. I wish I could wear. Yeah. Do we know who dressed to pika? She probably got dressed herself No, I don't know she might have one they might be releasing junior NTRs and then to pika's in the next yeah Who knows because I did what you don't get to see it depending on what red carpet coverage you get You don't get to see everybody who comes to the awards show So there's a lot of people you don't get to see and hear them say because they're always asked who are you wearing? Yeah, I was sad Ranveer wasn't there. I thought he would like since the pika's presenting Sure, he would be her guest. He may have been but he may have been working Yeah, he may have been working that's the only cuz I would have like loved to have seen what my goodness of course On on the red carpet. It's just gonna keep happening more. I feel like yeah We're gonna have more Indian presenters gonna have more Indian films represented Hopefully Because we know the quality is there. Yeah, and well and more and more Indian superstars are Being representative by the big three here Big four now basically Primarily Gersh and creative artists CAA and Gersh are the ones that have particularly CAA Dupika's was I think the pika's actually with I think she and Aliya is with CAA. She's with CAA I think the pika and Rithika with Gersh Gersh both are huge there But massive Rajmouli's with creative artists on your odds with creative artists Anyway, that's that's a wonderful thing because that means that's that's America wanting and appreciating in ways they never have before hopefully getting roles that are actual meaty not, you know Priyanka and Baywatch. Yeah, I never saw it, but I'm assuming it wasn't like a great role No, no granted Prankha did accept the role And so it is on and got paid. Well, but do you know a little trivia? I just heard her say that Citadel and she said I might get in trouble for saying this But I'm gonna say it anyway Citadel is the first time she's gotten equal pay with her costar nice In America, I'm guessing obviously any film She's that's why she said she said I've done 70 films and Three TV series now and this is the first time I have equal pay with a costar Well, I mean you could argue she should be paid more than what's his face? Internationally well, I don't know I don't know Priyanka's nobody knows his name. They call him Robb Stark Well, that's a good way to know your name. I mean, why do you think he's why do you think he was considered for the role? But everybody knows who roll we can go to anybody, but everybody knows who Priyanka Chopra, of course Even out of not just not including acting. No, of course, you know who Priyanka Chopra is Nick Jonas's wife Anyways, that was that was great. I hope we get more of these. Yeah, so let us know what you thought about the video down below


In conjunction with National Police Officers Memorial Week, the Pikeville Police Department hosted an officer appreciation ceremony Friday at the East Kentucky Expo Center. The ceremony first started three years ago when area law enforcement officers joined together to pray around a flagpole. But now the ceremony has grown into something bigger. They have events other places but there's a lot of names on this memorial. There's a lot of officers that gave their lives in the line of duty for our Eastern Kentucky community. Other area law enforcement officers say ceremonies like this are very meaningful to them and are happy to share it with their families. Each and every time that your loved one is an officer you know puts their uniform on and leaves home to go to work you know you never know anything can happen. One state trooper was on duty when another trooper was killed in a car crash. He says that is what this ceremony is all about. It makes you feel good and it's really not about us it's about remembering the family and helping keep their sacrifice remembered and so they're not forgotten. After the ceremony inside the Expo Center, law enforcement, family and community members joined together at the fallen officer's monument outside the courthouse for a moment of silence. Family members place special roses beside the monument to remember those they have lost. Reporting in Pikeville for EKB News, I'm Shelby Steele.