I'll try to be more kinetic. Gary, what is it? It's trying to understand microscopic properties on the basis of a microscopic picture, in particular, the general round of mountains. So, last week, I think most of what we're going to say, we saw that in classical statistical mechanics, there is an equal partition principle. It says there's a contribution to internal energy associated with each of the accessible means that it's a variable, and the energy depends quadratically on that variable. Accessible means that the temperature is high enough so that this degree of freedom is excited. And so we've talked about the example of a diatomic molecule, which in addition to its center of mass movement, in three dimensions, depends on the three components of momentum. Maybe I should say px, py, pz squared for each one of molecules in the gas. In addition, there is a vibrational degree of freedom, vibrating along the axis, and rotational degrees of freedom along two axes, the diagram's getting a little indecipherable, but think of it as a little stick, which has a non-zero moment of inertia for rotating about two different axes. And so if everything is accessible, the internal energy per particle would be three-halves tau, or in other words, kt, associated with the center of mass motion, three quadratic variables for each molecule, px squared, py squared, and pz squared. And then plus another tau, because there are two rotational kinetic degrees of freedom, the kinetic energy of rotation of about two different axes, or if you like the angular momentum, l1 squared, l2 squared, about two different axes, another two quadratic degrees of freedom. And then there's another tau associated with vibration, because now we have a p squared and an x squared, which is a restoring force for the vibrational degree of freedom. So p squared is required for concentration along the axes. So if everything is accessible, we have half tau for the energy per particle in the case of a diatomic molecule. So why does px squared, py squared, and pz squared be three-halves? Are the other ones only at one? Well, everybody gets one-half tau, and so it's a rather good one. One-half tau per degree of freedom. Right. So this is three degrees of freedom, and this is two, and this is two. And so what does that mean to be accessible? When the temperature is sufficiently low as to be comparable to the level spacing for the quantum acceptations, either rotational or vibrational, then quantum effects become important. So if pt, that is tau, is small compared to h bar squared over twice the moment of inertia, or h bar squared over i, then patience frees up when the temperature is small compared to h bar or negative, which has a score, and vibration frees up. For typical molecules, vibration frees up at a high temperature. In classical, just on the edge, we can also talk about the distribution of velocities for particles and effects. As we discussed many times, if we count orbitals, we have to consider three dimensions integrating over position and momentum. And there's a power of, we can point this concept, h2i h bar associated with each dimension of this normalization factor. So if I integrate the position in the case of a free particle over the whole box, there's a factor of volume. So I can write that as volume, and then I can assume that we have a rotationally invariant distribution of momentum integrated over the orientation of the momentum. And so I would integrate the area of a shell momentum space dp divided by the normalization factor. Now, the people in the 19th century who were trying to understand statistical mechanics didn't know about h bar, but they did have the idea that when we count states, we should count a volume in the xp space. So they could write down a formula like this. They just didn't know how to normalize it. For a lot of purposes, the normalization doesn't matter. If we're considering non-relativistic particles with momentum equal to mass times velocity, we can say there's some constant and who knows what it is or cares, a factor of volume, and then the number of states per interval of velocity or speed, right, v here is the magnitude of velocity, is weighted by v squared. That's coming from this p squared in the density of orbitals. So when we normalize it, the constant c drops out. I want to know what the probability of distribution is. Chosen so that when I integrate p of e to v over all speeds, I get 1. So the denominator is the integral. And then the Boltzmann factor, here I'm counting the number of orbitals, but then Boltzmann and Maxwell also knew that the probability of an orbital being I didn't use that word would be suppressed by a Boltzmann factor. So it's also a factor which goes like into the kinetic energy divided by tau, and I should put that in the numerator. And so this integral, if we change to dimensionless variables, so I can write this as the integral 0 to infinity dx x squared e to the minus x where I'm choosing x squared equals 1 half and v squared over tau. So I'm doing this out. I'm multiplied by m over 2 tau twice here and once here, then I have to put in and compensate a factor of m over 2 tau to the minus 3 halves. And this is just the number which is everybody knows is squared out of 4. And so when we divide by that factor it is the square root of 4 over 5 e to the minus 1 half of the square root of 5. It's called the Maxwell Distribution of Velocities. It means that if we have ideal gas and then I randomly pick a particle in the gas and measure its speed and do that many times and find out if I find many particles, I will find undistributed according to the Maxwell Distribution. Did you miss a v squared? Did you miss a v squared? I can't hear you. Did you miss a v squared? I sure did. Thank you. He asked me if I missed a v squared. Each time a particle comes out through the hole, then the distribution will be biased because faster particles come out through the time. And hence my factor of v. Why is the correct weight v? Why is the correct weight v after the particles coming out through the hole? Because there's some the number of particles coming out is going to go like a density of particles times the factor of velocity. Okay? So it's going to be proportional to v times density. So think of this probability distribution as describing if you think of the density as being a density of particles in a certain speed window in an integrated dv. But the rate at which they're coming out in beginning time will be enhanced by a factor of speed. Okay? So look at some little time interval. Take all the particles that came out measure their speed. Okay, so at least we have the right dimensions. You can do something with that. Yeah, but I mean the rate faster particles are more likely to come out in a given time interval. But that makes faster particles. Oh, I see why they're proportional to p. Well, I'm just saying that there's a flux. A flux is proportional to number per unit volume times speed. This is flux, meaning number of particles per area in time. So we have some hole fixed area. Right? And in each time interval the if I compare particles with two different speeds, right, with the same density, the particles which have higher speed will be coming out at a rate per unit time which is enhanced by a factor of speed. Then if I look at all the particles that came out and I measure all their speeds, I'll have a distribution which is enhanced by an extra factor of speed. How should I say p will be 2 times? If I do kind of hole out and let particles leak out for a while, both in distribution which starts out quadraticly as function v, the particles that will escape will be biased towards the higher end of the distribution. So when the particles escape then the mean value of the speed is going to be shifted down. Of course, if we just were to say we can take away the high speed particles, that's no longer a Boltzmann distribution because it's no longer an equilibrium. But if we wait a while the particles, let's say, open the hole for a while and let some of the high speed particles escape, then I close the hole. After a while, because of collisions among the particles, they'll redistribute the energy and come back to equilibrium. But after they re-equilibrate or re-thermalize, the distribution will be shifted to the left. So the particles will be cooler than before. They'll still have match Boltzmann distribution, but shifted to a smaller mean velocity hence a smaller temperature. So that's an example of cooling by letting particles where the particles that escape are biased towards high speed is the way the upper end of the cooling will be something to talk about in the context of reaching the ultra-cooled temperatures for dilute atomic gases. Well, the story which I think you've seen before, but it's fun to briefly revisit it is how we understand pressure from the point of view of an adversary and an idealist. So we have gas in a box and look at one of the balls of the box. One of the walls of the box and why is it that we have balls? We do have balls. We have the dimensions of the molecules with one of the walls and there will if we have events at the end particles, let's say this is the z direction and I'm looking at the wall which is normal to the z direction and half the particles will be moving up and half will be moving down so if I'm interested in the rate at which particles are bumping into the wall I only consider the upward blocks which means I'll consider half of the density of the particles and multiply that by the speed in z direction to get the flux of upward of flux. I'm a particle bounce into the wall and bounces off elastically it will give an impulse to the wall which is twice its z component momentum, so that impulse since it has upward momentum MVZ in the z direction before the collision downward momentum MVZ after the collision the changing momentum is 2 MVZ and so the pressure which is the average force for the unit area and as the impulse comes the rate at which collisions are occurring in the number of places. The force is the impulse absorbed by the wall of per unit time so this is the pressure and so I can write the pressure as an average over the distribution of speeds in the gas of the density because that goes into the flux times the mean value MVZ squared because I have a 2 MVZ in the impulse and a 1 half N MVZ in the upward flux so in other words it's number of particles per unit value put in the vector 2 and this is the kinetic energy coming from motion in the z direction people partition tells me that classically this is a quadratic degree of freedom this is the kinetic energy due to that convenient degree of freedom so that's 1 half N now this is N tau over P that's the ideal gas law as interpreted from a might just an awkward point of view in the theory arising from molecular collisions what we like to do is understand the departures from ideal behavior which we haven't talked about very much in this course coming from the fact that the molecules actually do collide with one another and the gas is not an ideal so we're going to take a very naive point of view but which will be good for understanding and qualitatively and for order of magnitude calculations which is to think of each one of the molecules has a billiard ball which can collide elastically with a billiard ball and with some finite size which is going to be important or maybe stupidly I call the radius of the billiard ball P which sounds a lot like this I am but D for distance let D be the radius of one of the billiard balls and now let's consider one of these billiard balls moving along sweeping out a cylinder over time and in a while there will be another billiard ball not necessarily with its velocity oriented to collide head on but such that there's a collision and when the collisions occur what I really should do is average over the impact parameters of the collision but we'll consider a collision to just be something that randomizes the direction speeding another curve in the approximation and so think of this cylinder being swept out by the moving billiard ball but every once in a while the billiard ball forgets what its previous direction of motion is and heads off in a new direction so it moves for a while and then there's collision then it moves off in a new direction and then there's another collision and then a new direction again in its own and how often do collisions occur? so determined by two things one is the size of the particles and the other is the typical separation between particles or the density of particles and we can think about it this way if the molecule moves a distance out this cylinder that is sweeping south has a volume which is its cross-sectional area which is just of high D squared times the distance out that it travels is the particle going to bump into other particles when it moves a distance out the volume per particle is one over the concentration by definition so the number of collisions is going to be the typical number of particles contained in the volume occupied by this cylinder so we'll say the number of collisions is the swept volume of the cylinder divided by the volume per particle so that will be divided by volume per particle means multiplying by 10 just high D squared L and we'll call the mean free path the typical distance that the particle travels before a collision occurs when the number of collisions is 1 that means the particle has a distance L given by the mean free path M and P mean free path concentration times high D squared let's say a few other terms it's a concentration of an ideal gas at standard temperature and pressure 22.4 moles per liter that was quick ideal gas let's say at 0 degrees Celsius and 1 atmosphere concentration translating what you just said is something like 227 times 10 to the 19 particles per cubic centimeter and so what we find for the mean free path is 1 centimeter so it's larger than the size of the molecules in the vector of maybe a few hundred or so and it's larger than the mean distance between molecules in fact vectors like pi and stuff goes like the typical separation between molecules 2 because that's just another expression for the volume per particle or volume density and then divided by D squared is what we call a cross-sectional area of a molecule so if we compare mean free path to typical distance between molecules that goes like the separation size of molecules squared the separation is large compared to the size of the molecule and then the mean free path is larger still so when we speak about in physical systems the behavior the system over distance scales are large compared to the mean free path so on that scale if we were following the motion of a particular molecule it would get scattered many times having its motion randomized typically in some characteristic distance scale and its trajectory would look just like that so we call this the diffusive regime or the behavior of a molecule which is scattered many times and walks around in random directions it's called diffusion and it's important because it arises in many different physical contexts which in a few we can consider the diffusion of energy in let's say a gas where the temperature is not uniform so in some regions of the system the molecules are higher temperature in other regions lower temperature is what happens while the energy diffuses the higher energy particles gathering many times eventually the energy that they carry gets spread out until the system internalizes so diffusion of energy that's what we call thermal conduct it tells us how quickly high temperature moves towards a low chance of curing the system when we consider a diffusion of electrical charge that's electrical conduct tells us how quickly electric charge will flow from a region of high electric potential to low electric potential with the electrons being scattered many times diffusion of momentum in a fluid governs what we call hydrogen resistance to the low all of these things are diffusive processes for all of them it's important that we're talking about a scale which is largely compared to the mean free path when microscopically particles are scattered many times the context of the diffusion arises is mixing there's an example of mixing I let water and I put a little drop of ink and the ink is starting to spread out so it looks less blue than before and the region which is colored is bigger and then it comes back a few minutes later and it's spread out even more why is that happening is because the ink consists of many molecules they're being repeatedly scattered by water molecules and that's causing the distribution of the molecules to gradually spread giving rise to mixing after a long time the ink would be formally distributed in the chamber of report so many experiments with ink drops over the years watching how fast they spread reproduce something called fix law as anyone did so something that's empirically observed to be true and what it says is if I consider the flux in case of any flux of ink molecules once in that rate if I put down a surface somewhere in the water at which the ink molecules per unit area and time are flowing across that surface that's equal to well it's proportional to the gradient of the density the minus sign and the constant which I'm called capital D so in the case of ink I started out with the high concentration of ink right in the center near the edge of the droplet there's a big gradient in the intensity and that makes the impulse spread out and this is how it spreads out and D is called the diffusion constant or something that's called the diffusivity by writing this law of diffusion was to make use of the continuity equation the ink molecules are conserved there's some fixed number of ink molecules floating around in the water so if I consider some little cell or a volume in the water or this and then there are two things I can equate one is the total of flux of ink through the walls integrated over the boundary of the cell so that's the total flux out in the number of ink molecules per unit time that's equal to obtained by integrating the flux over the boundary of the cell and I can use the divergence there to write that as an integral over the volume of the flux and another expression for the rate at which the ink molecules are leaving the cell is while I consider the quantity of ink molecules in the volume integrated over the volume that's the total number of ink molecules in the cell and this is the rate at which that is increasing so I can write that as the integral of a minus of the density per unit time so since I can equate these two there's a continuity equation satisfied by ink molecules in the key density of ink molecules is equal to minus the divergence of the flux but according to the fit the flux can be written as minus d times the gradient of the density which becomes d times the gradient squared of density so our conclusion is that the density of ink molecules obeys partial differential equation I consider n as the function of time and position is satisfied as d dt n equals d gradient squared which is called the diffusion equation what we'd like to do is understand that equation from a microscopic point of view how it arises from molecular collisions who was the first to explain the diffusion equation from a microscopic point of view? Yes in 1907 what year? 1905 and what I decided to realize is that we can understand diffusion by thinking of molecules making random walks like this picture that each one of the ink molecules actually is walking around and turning in a random direction each ink molecule has no preference between going one way or another one it kind of moves in an isotropic way but if we have a gradient where there are more ink molecules lower on the left than there are on the right then if I look at some particular cut of the system into two parts we'll have more ink molecules flowing from left to right than from right to left if I'm worrying molecules over on the left side of the cut and that will cause the distribution to smooth out from the gradient to go down and that's what the diffusion equation describes so the smoothie is not due to interactions? it's not it's due to collisions but microscopically each ink molecule has no doesn't care whether it goes left or right it's as likely to go left as well but there are more on the left and therefore there are more going from left to right than right to left across the cut so if I have some initial distribution of ink molecules let's say it looks like a Gaussian what's going to happen it's going to spread out and that's what the diffusion equation describes so I want to have a simple model in which we can see that how that flow from high density to low density results from decisions that are made by individual molecules at the single molecule level it's a very big and low simplified model but it also takes a point very nicely and I'll stick with one dimension to start with since that's the easiest thing to discuss mathematically so I've got a one dimensional gas but it's not an ideal gas the particles are colliding a particular particle let's start with what it does and let's imagine although the system might really be continuous making it discreet for purposes of analysis so I'm going to consider a particle which lives on a lattice lives on a set of discrete points and there will be some time step which I'll call epsilon and a lattice spacing I'll call delta a delta is the spatial distance between these lattice sites and the time step epsilon well every time epsilon the particle is going to decide to either hop from its current position to the side on the left or the side on the right so it always hops it always hops by one lattice spacing but it's indifferent about whether it hops to the left or to the right in each time set there's no point to decide what to do whose two neighboring sites it goes to the left imagine there's some probability distribution to begin with describing where the particle is at a particular time in each set that probability distribution will change in a little while and then we'd like to consider over many time steps how the probability distribution changes and we'll see that if we imagine taking the formal limit of some time step goes to zero we get the distribution equation let's see how that works well in fact you kind of you kind of recognize the model it's from the first lecture but it changes in a way to protect the innocent suppose we start I'm going to consider the physician in other words to be s times delta delta is the lattice spacing and the time is equal to I'll call it n I guess may regret that not the same thing as the density but that's what I have in mind where n is an integer plus one that means we go from a time set to a time set and when s goes to s plus one that means the particle moves to the side on the right when s goes to s minus one it moves to the side on the left so after n times sets suppose we start at time zero or an angle zero with at the origin and I mean that's true with probability one we can learn to look like after many steps well what's s going to be it's the number of steps that we make to the right minus the number we make to the left that's where we wind up each time we either go left or right and the total number of steps to the right we've made is n right minus n left it can be either positive or negative having a moment of one look to the right of the origin or the left of the origin the total times is the total number of the discrete time is the total number of steps some of them I went to the right some of them I went to the left so this is just like tossing a coin at times and asking what's the excess of heads over chips the calculation we've done when we consider um in the process of many time steps we know we have a Gaussian distribution for s after n flips or in time steps we're using the Stirling approximation if we can adjust the function in this large and um so I think of that as a probability density on the line you just give it a random walk I'm just doing a random walk it's unbiased so I go probably one half to the left or to the right so I could also describe this as a probability density because now it's a probability density and if I want to know the probability that the particle is found in some interval which has length delta times an integer I multiply this probability distribution by the length of the set and then I can put this in terms of um since the time is an epsilon and the position is s delta I can write this as the square root of 2 pi delta squared that's just putting this delta inside the square root and then write n as time over epsilon so delta squared over epsilon times time and then in the exponential I have e to the minus epsilon over 2 delta squared x squared over t again just writing s as x over delta and n as t over x so I'd like to convince you that we can get this same formula in a different way by writing down a microscopic equation that describes the evolution of the probability distribution and the insolvent equation which will be the diffusion equation by starting out with a difference equation using this discrete model and then take a limit in which the time step becomes small and the light spacing comes out and looks like this it's a difference equation for the probability distribution which depends on the integer value of times and on both time steps and the integer value position the number of lattice spacings to the right when s is positive to the left when s is negative and the observation we make is this that if we want to know what the probability is how can you be at site s at time n well if you're at site s at time n where were you at time n minus 1 in each step you either move to the left or to the right if you're at site s at time n then at time n minus 1 you have to either be at s plus 1 and to have taken a step to the left or at site s minus 1 and taken a step to the right those two things are equally probable so in other words the probability that you wind up at site s with at time n the probability that you jump to the right times the probability that you were at site s minus 1 at time n minus 1 plus 1 half the probability that you were at s plus 1 at n minus 1 because if you were at s plus 1 at time n minus 1 then the probability 1 half you jumped to the left and you wound up here and if you were at s minus 1 you wouldn't believe that equation so I'd like to write an equation for how the probability of being of being at s changed between time set n minus 1 and time set n so I'll subtract that away from both sides the amount by which the probability of being at site s increased between time set n minus 1 and time set n is 1 half the probability of being at 4 s minus 1 n minus 1 but then I subtract this away and I'm figuring out 1 half so I'll put in a 2 minus 2 probability of being at s n minus 1 plus at s plus 1 and you can prevent me from saying the same thing as 1 half the probability of being at s plus 1 at time n minus 1 minus the probability of being at s at time n minus 1 minus the probability of being at s at time n minus 1 minus the probability of being at s minus 1 yeah even the probability of x t why do you divide by delta? why did I divide by delta here? that's because this is the probability density by that I mean that the probability of being between x and x plus dx probably of x dx but changing the integer by delta times that amount so I had to divide by delta so now I want to take a so to speak continual limit in other words I want to imagine that the probability distribution changes very smoothly when I change the lattice spacing so the characteristic scale which the probability distribution is changing is not the lattice spacing and the probability distribution is changing just a little bit in each time step because I've chosen the time step to be very short if p of x t is smooth on the scale I'll say delta x and delta t of order epsilon then we can approximate difference equation by differential equation think of this difference as being the elapsed time and one time step which is epsilon times the derivative of the probability distribution at side s or at some particular position x with respect to time so the left hand side becomes the partial derivative of probability distribution with respect to time times the time step epsilon and I guess quickly speaking I can say it's evaluated at position s on the lattice and a time in between time epsilon and time epsilon n minus one which this derivative is defined as the midpoint of the derivative and what I have on the right hand side I can think of as the lattice spacing delta times the partial derivative of probability distribution with respect to x as this difference between probability at time s plus one and probability at side s plus one probability at side s think of that as the difference delta times the spatial derivative of probability at the midpoint so that's delta times partial derivative of p with respect to x evaluated at position s plus one half time n minus one but then I have minus delta with respect to x evaluated now at s minus one that's in the second term I'm subtracting the probability at side s minus probability of side s minus one so this is the first derivative of the probability distribution I'm taking the difference between two positions which are one that is facing apart so we can think of this as another factor of delta times the second derivative of the function with the right position and now evaluated at the midpoint of this interval which is s and time n minus one my order corrections have to do with the fact that here I have time n minus one half and here I have time n minus one which I'll be able to ignore when I take the limit of epsilon to zero we have the probability distribution in this smooth limit satisfies the differential equation derivative of probability density with respect to time equals delta squared over epsilon if I divide both of them by epsilon times one half I'll put a two in the denominator the second derivative would be with respect to position so that looks just like a diffusion equation if I identify delta squared with two epsilon as the diffusivity of the diffusion constant well the one half came from here and here but I had it here but I missed it there it's the one half because of the one half of the expression on the boreal but I don't want to drive the cameraman crazy and walk over there again so I can just pack up the big one and so d is equal to delta squared over two epsilon so let's talk about the density instead of the probability it's just they just differ by constant factor so the density obeys the same differential equation as the probability distribution mainly the diffusion equation and actually we can consider the case now in the continual language that we considered here where we started out with the origin we can ask what is the solution to the diffusion equation if the probability density times zero is just a delta function well I said that I'm supposed to so the integral p of x so if there's any justice it's really to be interpreted as a differential equation governing a probability distribution it will be non-negative as probabilities should be normalized at all times well if we look at the expression just by thinking about the unbiased point for the probability density as a function of position and time written in terms of what we've now identified as the diffusivity delta squared over two epsilon time t solution with this boundary condition when we start out with the origin we're going over to square root of four pi e t e to the minus x squared over four e t and you can chat just by differentiating with respect x twice and differentiating with respect t once that expression obeys the diffusion question is the unique solution obeying our boundary condition that the probability distribution is a delta function at time zero and it is normalized correctly at all times non-negative so we can chat in the integral and so our delta function should be spread out distribution at time zero and then at a later time here's a broader Gaussian and at a still broader Gaussian the variance of this probability distribution tell us in front of this mean square value of x is given by the variance of this Gaussian and that's just d t where t is the diffusion factor which we now know in terms of our lattice model we can write delta squared over epsilon on time t so the width of the distribution throws out the square root of t the square root the square value of x squared is equal to the square root of t dt in terms of our naive microscopic model we can think about it this way think of each time step as the time the particle travels a mean free path and then get position re-randomized so after it moves distance delta it forgets what direction it was moving and moves off in a random direction either left or right the probability you have so you can think of delta as being like a mean free path how fast are the particles moving well they hop either to the left or the right a distance delta in epsilon so the speed is delta over epsilon so at least in our naive model we can think of the diffusion constant from the point of view of a microscopic theory of our molecular gas as a factor of one half which we shouldn't take two series depending on the free model of our chosen but what it is of broader interest is we can think of it as a mean free path time to speed a mean free path is how far you travel before you forget what your initial direction of motion is to be as how fast you travel the product of the tube is essentially the diffusion constant which tells you how quickly the probability of distribution spreads so the formal limit that we took to get a diffusion equation is the limit in which I call it the delta goes to zero limit delta goes to zero and epsilon goes to zero but what we hold fixed which is delta squared over 2 epsilon we're saying delta goes to zero that means we're observing the behavior of this fluid on a characteristic distance scale which is larger compared to the mean free path and over time scales which are long compared to the typical collision time epsilon now something that's kind of weird about this is that when we take this formal limit if the speed delta over epsilon is behaving like the diffusion constant which we're holding fixed divided by delta so the speed is actually going to infinity another way of saying it may be a better way of saying it is that if we look at x as a function of t in our lattice model x is hopping back and forth we start out at the origin maybe we go up, down, up, up, down up, up, down down, up, down and so on, kind of at random and now we want to consider the behavior of that curve when we take the time interval between jumps going to zero and what happens as delta epsilon go to zero is that x of t is continuous with no derivative no first derivative another way of saying that is if you think of this x as a function of t is being governed by some trajectory some function of time x is the square root of x where it's increasing like the square root of t so that's smooth as t goes to zero but its first derivative is blowing up if you look with a microscope at an instant particle with better and better resolution it's always wiggling you can't take a limit in which the resolution gets arbitrarily fine and becomes smooth now of course that's kind of an artifact of the fact that we've taken this limit of delta to 0 in practice there really is some cutoff in the collision time so if you finally look with good enough spatial resolution and time resolution so that you can see individual collisions then you see the particle has a trajectory and it's differentiable except for the discontinuous change in the direction of the velocity at each collision of course we can also generalize more dimensions and in fact in three dimensions it's really the same thing you can think about a three dimensional lattice that we've already mentioned so each position on the lattice has six neighbors now in fact if it's d dimensions that's because there are d dimensions d lines along which you can move for each of them you can either move up or back possibilities along each axis so if we do the same analysis that we've already done it's exactly the same thing except now we'll say in each time step probability each of two d possible directions or two d in other words it's a uniform distribution there are two d possible ways to be done they're all equally probable before we had two ways and probability was one half so in three dimensions there are six possible ways to move up or down left or right or over back so we will again get a diffusion equation the probability distribution will obey the differential equation if we take the same formal continual limit delta and epsilon going to zero as before the time derivative of the probability is diffusion equation times gradient squared p because I'll have different first derivatives like this for each one of the three directions x, y and c and where the diffusion constant now will be delta squared over in d dimensions two d times epsilon instead of two epsilon in the denominator that's just coming from the probability of being one over two d instead of one half for each of the directions so in particular in three dimensions so if you want to think of that as expressed in terms of a mean free path or in terms of a mean free path and its speed in constant is one sixth delta delta over epsilon for one sixth a mean free path is speed actually in the book they write down a similar formula but with the one third instead of a one sixth but don't worry about it it's both using kind of crude models and actually a different the important thing is that diffusion counts unlike we found in the one dimensional model scales like a mean free path times the speed of the molecules and that determines how quickly probability is spread out probably the easiest way to think about it is if you have three dimensional diffusion the particle is independently doing a random walk in the x, y and z directions each one of which we can think of as described by flipping an unbiased coin many times so the distribution that we get after a long time if we start out at the origin it's just going to be the product of the one dimensional distribution that we found earlier in the deltilation for the x, y and z directions so in other words if equal to zero we have a delta function normalized to the one that would support at the origin then at time t the probability distribution will be 1 over 4 pi e to the 3 halves e to the minus x squared over 4 dp that's just the product of the probability distribution I wrote down earlier for the x direction, the y direction and the z direction so I get x squared plus y squared plus c squared here or in other words the total distance of the travel squared and again you can check this by to this form of the diffusion equation and in three dimensions this is a solution and as anyone to mention the distance that our particle travels in time t goes like the square root of t when t is small so we can think of the path that we regard the diffusion equation as describing the probability distribution for a diffusing particle as one that is continuous but not differentiable at any point the particle keeps changing its mind about the y direction so Einstein did another great thing in this 1905 paper which was his third best paper from here and that was he derived the so-called Einstein relation relation between the diffusion constant and something called the mobility involving temperature the mobility a statement about what an article is diffusing through a medium and we apply a force to it at what point it reaches terminal velocity so in other words if we apply a force the terminal velocity in the presence of that force is proportional to that and the constant of proportionality is called the mobility so this is terminal speed terminal velocity a lot of force to pull an object through the fluid and this is the mobility it's kind of a remarkable equation because the statement about mobility this definition of mobility mobility characterizes dissipation it's the resistance the friction that the particle encounters when it flows through the fluid the diffusion constant though has to do with fluctuations the way the distribution spreads out and we'll see next time why the two are related


Everybody forced to your rip in 2021 top scrum platinum anniversary baseball light 8 box number 14 This is a random team style break and you can always find the results of late sports cards calm Thanks, everyone for joining the good luck Here we go. Yeah, I played games because they're fun most of the time I guess it fizzled yeah, I didn't play a lot lately because once you get to this point online Everybody's got like stacked teams Refractor Cardinals Yachty Molina Haven't last year. I played like I played super hard for like three months. I'm like, yeah, I'm not like elite So I don't care like Blue mini diamond Dodgers Cody Belanger to 199 Blackaway mini diamond a Israeli fingers. No mustache Raleigh fingers. Let's see a super factor So I'm pulled out of this refractor Orioles Anthony Santander. Yeah, one of my buddies would be like, oh go check in the bathroom Oh my god, like my mini diamond Tigers rookie Terry scoobal. It's just a lot less fun I'll say when you have to look up the answer Ock away Philly Scott Kingery refractor Dodgers Justin Turner Is it worse to cheat at something that's really high stakes or is it worse to cheat at something that has like no stakes?  You'll be the judge Angels black-white mini diamond, right silly glaciers. I know it's worse to cheat in the world series guys It's worse to be the Chicago Black Sox Cleveland extractor Jose Ramirez Refractor match tick of the gromp black-white mini diamond white Sox Michael Kopeck a lot of trivia now that I see that I hear about is um It's kind of been named that tune because it's a lot harder to do you can't really cheat at it You actually have to like know the song refractor rookie Yankees, Davey Garcia It's pretty obvious when you're trying to Get your phone to recognize a song to tell you what it is Yeah, we're obvious Plot in a mini diamond rookie blue Jay Santiago Espinale. That's to 70 black and white mini diamond Giants Brandon Crawford I agree with you Bradley. It's still fun to play. It's just There's early on you can tell the people that have like bought their team essentially Yeah, I like that's not fun like in the first month of the game. They have like all the expensive players You're like, okay.  We could just like a fantasy draft Refractor Brewers Warren spawn I have not a legal. What's that?  It's so hard extra factor Wilson Katera's cubs Dodgers black Yeah, I've had that thing where you swing to get by the ball you're like, wow Fractor rookie Astros Blake Taylor Lou we got to hang out at the show man the national Refractor Braves Fred McGriff got my battle royale. It just gets like I Don't know blue mini diamond Pedro to 199 your red Sox. I just don't play a ton of it I still like to unlock cards and like play with those cards and like level up the guys that I have try to get Super fractors and stuff black white mini diamond d-backs Randy Johnson Mets refractor David Wright It's normally the young guys single-player Black by mini diamond Mets Dom Smith Aqua wave Royals George Brett showdown We're like you have to like different levels and you unlock like more as you go and you Cardinals Refractor Carlos Martinez. I like to showdowns. I wish they had more of them. Yeah Like every so often the showdown the showdown is a fun mode. Some of them are pretty challenging some of them are pretty easy Tony Gwyn black white mini diamond Padres Extractor Jesus Aguilar Marlins The grip Hall of Famer. I don't know it's not about my griff. I can't say I Feel about that deep backs refractor Nick Ahmed. Hey, there we go and auto Mets Pink refractor to 15 Marcus Strowman. We were just talking about that. There you go Mets James W Very rare auto hit in the light It's a 15 on the pink refractor Heck yeah, man. Good stuff black white mini diamond Rockies John Gray. I still think that's the first one I pulled out of light. I said one of every 300 some odd packs I feel like we have been very unlucky in that case then because I risked quite a few times Light we've done a lot of both hobby and lights. Yeah, I don't know This is only eight bucks number 13. I guess that's Yeah, so the so that that's why the autos are rare in this because they're pink refractor They're probably exclusive to this and they're low-numbered J Ram refractor Cleveland. Yeah, good stuff. And that's an awesome hit I like stro. Let's hope the Red Sox you go get them last off season Not doing so well with the cubs though Black white mini diamond Cleveland James Karen check But since he's a guy that's not like velocity relying I still think you'll have good seasons going forward Refractor Phil Rizzuto Yankees or Rarudo I knew was Brad the way the door opens That's like when when I when the door used to open really hard.   What should me and illegal do in a? AC We're not at the show Do not leave the area Braves refractor Phil Negro. Yeah, we know that so what else is there to do? casino gamble and go to like very nearby restaurants and bars That's really good seafood on the ocean black my mini diamonds Kirby Yates for the jays Extractor Dodgers David Price That'll probably happen Are you gonna go to any of the trade night? The trade nights are gonna be we're all like a lot of fun is that you're gonna drink and hanging out All kinds of people be meeting up black and white mini diamond Braves, Andre Jones Yeah, well pretty much most LSE crew be hanging out together most of time I'm going where Cortesco so that if I get in trouble she could bail me out Fractor Mets Domsmith. I'm there.  I'm not gonna drive period not safe Fractor Cardinals Tommy Edmond, but like right outside that talk about was a couple crossroads streets that are just Really just stay away green and yellow to 99 a is Martin McGuire. It's a sweet color match He looks like the the bully kid in a Christmas story right there We had a guy at that talk about And he sprayed my buddy's mustangs Royals black of my mini diamond Salvador Perez They're like hey, hey Mark, can you look directly into the sun so we can take your photo and that's exactly what happened Dodgers refractor Trevor Bauer Ball I'm sure I don't know what trade nights were going to I just know that we're going to them So I couldn't tell you where when Cortez and Lane know I'm just gonna I'm just gonna go where I'm supposed to go, you know black and white mini diamond white socks Louise Robert Yeah, big Mac look right into the sun so we can take your photo Aqua wave j cave twins. I gotta get some cards together. That's coming up soon, man I gotta get a choose which cards I'm bringing refractor Mads Edwin Diaz Like why many diamond Dodger Steve Garvey Extractor Cub Sammy Sosa refractor Yankees a decky Matsui. Yeah, that's how I'm gonna go though Lane go with y'all I'm gonna stick around I'm not saying it like I like I feel obligated to go. I just I kind of want to You know like my mini diamond that's Josh Bell like I don't I'll say as long as Lane Lane stays of these things until the break It on Rarudo. Yep That's right Billy Madison Very educational movie for me. That's how I know who Phil Razzuto is Reddit Sonic to 100 hip hip or hey for the Yankees Cubs refractor David Bodie. That sounds very good Jonathan I've seen Boris on burgers before but that sounds fantastic There's a local like Hub or tavern or whatever in Orlando called the whiskey and They pretty much just do burgers for food Cubs refractor or sorry Reds refractor a you henny Osora's They used to have a Borsen burger not anymore They got like a they got a burger with like a fried green tomato on it What's from a lot and all that record refractor Mets or Marlon's Hazy Sanchez? Borson is like that It's like that cheese spread like garlic like cheese spread You can find it like any supermarket. It's a brand. It's a brand Kind of it's more of it like a cheese dip or spread essentially refractor blue jays Lord as Gertie L. Jr. It's a brand of stuff like that pretty good. They do like garlic one. They have like a shallot one It's like a garlic cheese butter basically So good though Twins Ken's my eight of refractor now we got I'm gonna I don't even know what my meal plans are Just get food whenever whenever wherever 20 bolognese refractor Cubs Ron Santo a platter of fries with a carousel dipping sauces Game changer Ricky refractor tigers Brian Garcia. I said Brad was just saying Bradley Extractor Dodgers Don Sutton black, white, mini, diamond, Yankee, Sissy, Sebastian. I love seafood man So I will have to make it a point to get some Tuesday night is probably the only night we're really gonna have like time to go get like a meal together Thank refractor Phillies Ryan Howard, which I'm totally cool with these coasters are all right Get some decent ones from like Maine and stuff. I prefer Oysters from like the Northwest like BC and that area all that black and white mini diamond the front meal Ray has Cleveland. Oh I've had some Nova Scotia stuff that I'd like to oysters Aqua wave Yankees Clark Schmidt Cubs refractor David Bodee Good oysters from the South to but yeah, I agree Northwest is the best is the best way to go raw oysters I would anybody cooked oysters. It's weird Black wine mini diamond giant chef Samarjo. That's just weird to me. I don't know I Have cooked oysters once and I was like They're all right. I guess Unless they're like smoked or something. I really grilled I guess one of my cousins did this really cool wedding on Like an intercoastal river in South Carolina at this old old oyster company Got twins refractor Bob Lemon or no Cleveland Cleveland. Sorry Cleveland Bob Lemon refractor It's a current twins or reds logo, but they were like shucking and oysters like right there for like as they're like the cocktail hour They're putting it right over like a wood grill or you could just take them off Probably eat like a dozen myself black and white mini diamond tigers Wilson Ramos. That was pretty dope Okay, now the only time I'd have fried oysters is like a po boy. That's pretty much it Extractor Hunter Dozier Royals. Yeah, I'd much rather have them fried. I think than anything, but still how many fried seafood It's gonna be like shrimp.  There was a good New Orleans style like Kitchen near the old shop that I order from every now and then. Oh my god. It was so good Brandon belt black, white mini diamond Giants. Do I ordered a po boy? I ordered a crawfish po boy Before I went live one day. The thing was like a 12-foot crawfish po boy. It was massive I was full for like 24 hours regretted nothing. No, of course refractor Giants will be maize Yeah, I wouldn't see there's like places I would order oysters the places I wouldn't Red Insomac Alex Cobb angels to 100 Yeah, like I don't know if there's not like a raw bar That I would like trust. I don't know if I'd order oysters black and white mini diamond rookie marlins louis india's Cubs refractor martin grace When I live downtown or like in the fort and park area Got black and white mini diamond Yankees Ron Gidry This is before all the pandemic and all that but there was a Cajun style place near me That's pretty pretty good stuff, but they would bring in their They would bring in their seafood twice a week and I would go on like those days They would bring it open like pork canaveral the aqua wave angels Dylan Bundy Yeah, and I that's not go get like oyster stuff. They sometimes they would do like Half off a dozen on certain days of like a week like a happy hour. I'm like, oh, I'm there no matter what Chipper Jones braves refractor Happy hour beers and oysters spend like 40 bucks get like two dozen oysters and a couple beers. I'm like, that's You know doesn't oyster for everybody Some beers and that's a bargain black white mini diamond Orioles Jim Palmer At least for not being on the coast What's oh crab Extractor oats restaurant. No, I don't think so. I don't know. Extractor Beltray for the Rangers black and white mini diamond Julio Franco for Cleveland Cleveland refractor Caesar Hernandez Number to parallel recap here Dodgers Bellinger blue mini diamond to 199 Pedro to 199 red sox red atomic or the 100 alex cob angels Jorge Posada Yankees Platinum mini diamond rookie espionel for the blue jays to 75 Yellow green the 99 mark McGuire for the a's and pink auto to 15 Mets Marcus Strowman very rare light auto there congrats Mets We've got top strong black coming up. Thanks everybody


now that i'd really follow and unfortunately we haven't much to follow at the moment we're beating there a couple of weeks ago i'm mulla horn and the famous mulla horn would be my club and my team and uh i played back the years with a man i don't know if you have a heard the every hair the gunner brady i played with one of them in my time the the famous gunner brady mulla horn but no mulla horn would be me club but like i'd go i'd be up i'd be up with me neb you he lives between down there conva between conva and cashless sin and he's a great man for the football and he knows i like to get to the games and and him i'm up and donagall with him he he'd set him to the game on and say i'm there at the weekend would up and it was a a good game of football it was and and and ballet buffet a good game that's a that's a good that's that's a good side that uh you know so i'll be just a good team and uh there i would i seen that and next weekend i hope to be if i'm alive with the help of god or sorry not next weekend the weekend after i'll be at the cabin final of brestley park good man and i go i go i go wherever i am i i be down at home most of the time but it would be time to come up to me nebby and donagall here for stuff for a couple weeks and and that's just why you do get around but i do know i do know for sure uh greg that the foot the charges the charges is only is only a fiver and that's for fact quick word and a quick word on gunner brady he's all island uh winner in 47 48 52 uh did you ever reach the heady heights of intercan team maxi no i played i played minor which happened i played minor but i never i never played senior no i never i was i i tell you the truth and you know what i started doing them he hung theirs too was funny oh i got too fond of the even back then in my time to say that's happening now with the youngsters a lot but i got too fond of the good life for a few old points at the weekend and uh and maybe uh those barn dancers and uh chess and after women and everything like that you're like like george besty george best was asked what he did with all his money i think he said he spent it on women drink and partying and the rest he wasted i think that's oh jessie was a good player too well come here now till i tell you and and because i can't believe him after the going on the radio and i was on radio station before but if you look at you never know the hell it could go on the lately a show yet after all this why not no but no we've given you your grounding you wouldn't be the first one got the start here on hide and radio and ended up on arty and ended up on arty maxi come here listen go on thank you for that thank you for that and sure i'd be listening i'd be listening now to your program just as a matter of interest stay there for a second maxi stay there because we want to try and save you a few quid here right schnade brine is a volunteer with the gea in donigolan joins us now hi schnade good to chat to you hi greg how are you yeah i'm brilliant schnade do you listen to maxi there uh he's a calvin man he's he's he's proud yeah he's having a go with i'm a proud man i'm woman i mean him i can get on but we're given a go okay but anyway schnade you heard what maxi had to say he goes to the games i did yeah look at as i say i'm a volunteer with the association and it absolutely breaks my heart when i hear somebody that would stay away from the game because of the price now i have absolutely no jurisdiction over pricing in any game obviously as correctly said by whoever gave you um you know the statement it is decided by county committee and every club in the county have two volunteers that attend and that is agreed by by every club but i would hate as a as a human being that lives and breathes for our association i would hate to see anybody stay away because of the price in every game now i personally will leave tickets for maxi and his son at the gate for the final i'd love to see him attend it just one thing i have to say to him while gone or ready with a great player who's no need to use here we go let's not maxi maxi go on it you're not going to let her out with that are you no no i'll be right now there are different times all right but i know it's funny don't you know that's that woman there now i hear monah and woman and you know what it is and i have good friends too and monah and and there's a player that i have great time for and monah and i'll be just he's still playing too he was as good as ever was in monah and uh paul finley he's a great footballer i i love what i love what i know what from myself yeah yeah and i remember cari woman and he's balibé yeah yeah yeah and he played well he was playing i was listening to her course on the radio they're in the finally in there and he played well at that too yesterday our great player but uh definitely i tell you i can't remember your first name in there what's chenade chenade chenade that's that's that's that's very very kind of you and thanks very much for that now okay it's not so much for that it's not so much for that i know i know it's an ongoing thing 100 percent yes and i do agree yeah highlighted with something to highlight it will all even though as i said earlier they're too great as a cavern man which is the same value that will fight for you know like i don't like to i don't like to waste but but like it's more it's more to bring it into the public to me and that and maxi do you know what it might make a difference and uh it's a gesture from chenade so we have a monah and woman given a cavern man two tickets the donagall final sure what where where else would you get it well that's just that's just fantastic you wouldn't get in any other organization i agree the geisha is a wonderful wonderful organization sure sure none of it i don't know what we do we couldn't survive without it like you know because it's it's just it's in every little corner and and look in ireland of the clubs and there doesn't small clubs or big clubs that keep the life and so on one of the areas but where would i get them now well we'll sort that out maxi we'll sort that out we'll sort that out out fair don't worry we'll make sure we've a ticket for you and your nephew uh so we'll sort that out fair maxi to make sure it's simple for you and you'll know exactly where the our schnades are gonna gonna work with us on that schnade listen thanks so much you might you might mess you may send me a message here to know i'd be i'd go to that that's isn't that next song that is and anybody yes yes don't you worry i'll get in touch and i think your nephew most actually live quite close to me anyway so don't worry maxi we'll sort out the logistics no problem but i hope you enjoy it thanks thanks very much and you'll get to see a good quality final maxi after all the ones you've watched down in cavern which is good god bless you maxi lovely chatting to you god bless thank you bye bye and schnade fair play to you for making the ball i know you've no impact on it but it's a it's a lovely gesture uh it's not actually about the money i think it's about the fairness i know absolutely and i agree with him but i hate to see any human being but clearly he said himself is in the 70s he's been following our association his whole life he should be able to attend games and and that's it and i do hope it's something that we lock out and when the conversation comes up again they're not being able to put cash at give cash at the ground for whatever reason we change that i have a pile of messages here from people who want to be able to pay for cash and actually aren't going to games because they don't want to put their cards in and we do so many warnings on scams and what have you here i think particularly for a generation yeah just the option to be able to hold hand over that cash it would be great if we could see that return but anyway schnade that's above you and i i'll pay grades but anyway i think we agree schnade thanks very much well done to you no problem i take care thank you that's schnade brine uh they're very hard-working uh volunteer with the gea here in canty donnie gall the nine till noon show with letter kenny credit union do you need to switch your current account or loan we are now offering my cu current account and debit mastercard bringing full banking features and competitive rate switcher loans oh amy my little one i ask myself a million questions every day when will you give me your first smile how much sleep do you need how can i help you and your big brother to get along at the hsc's my child dot ie and in the free my child books you'll find the answers you need from doctors midwives public health nurses dietitians and lots of other experts my child dot ie expert advice for every step of pregnancy baby and toddler health from the hsc it's back the furniture show and i is now on at cfc interiors camp c dairy cfc fs with massive discounts from leading brands in 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expert advice on the convenience of breastfeeding at mychild dot ie from the hsc okay now on monday focus for this monday is on the family farm transfers and to help us understand this a little bit better we're joined on the program i buy kevin connelly financial management specialist with chagas he's joining us ahead of a meeting which is taken place tomorrow we'll talk more about that in a moment good morning to you kevin thanks for taking the call today thanks very much gregg happy to be here is this a uh is this a tough subject for farm families or is it a complicated one that maybe people try and put off or avoid or are people open to this and just are really hungry for information it's all of the above great really it's uh yeah it is it can be quite a tough and complex subject for for farm families to deal with there's quite a lot of emotion associated with the family farm business there's obviously um you know people have built up the business and family members have worked hard on the business uh over a period of years um and then you have the asset value associated with as well you know so it's uh and you quite rightly refer to it as a business there but it's not like you have necessarily a ceo a manager uh someone in charge of hr and finance do you know a lot of the time you could have multiple children and there uh it could be hard to gauge their input their you know their role or what have you it would be a tough conversation to have I think for most families as to how things might be transferred or divvied up or whatever the situation might be yeah a very tough conversation and to be honest we agree that that's usually where the major stumbling block is is is actually getting that conversation going within within the family um and it's it's it's an important step that that farm families have to have to do in order to ensure that the that the conventional transfer goes off successfully but it's actually getting family members around the table and getting them to air their views as to what a successful transfer would look like you know usually the way we would assess it is a successful transfer would be you have the older generation are happy the succeeding generation in other words the next generation of farmers that are taken over the business are happy although family members are happy as well that are not directly involved in the farm um and everybody on both sides uh are all clear as regards the tax and the legal implications associated with with what's going going to happen so you know once those things are the bottom line is is it's going to happen um at some point or other uh best to get out in front of it then and get it sorted and done and dusted because as I say eventually you know someone will pass and their assets will have to be moved on exactly exactly and you know I suppose in relation to the moving on of assets them and a very important step after the conversation step is to put some kind of a safety net in place just in case all these best laid plans that it regards the transfer and the timing of it doesn't doesn't kind of happen the way we we want it and you know when death in the family supersedes all that so putting a will in place is is is a is an absolute necessity to just to cover off that eventuality that in the case of uh where the transfer doesn't happen in the normal way that you have a backup plan right okay to help people there is a family farm clinic taking place in the raddison blue hotel uh on tuesday october 4th that is tomorrow it starts at 10 a.m and it's one of a series of uh meetings taking place around the country organized by uh chagas talk to me about the type of I mean I think we're touching on probably a lot of what will be touched on uh at the meeting but in much greater detail tomorrow so talk to me the format of uh the format of these talks yeah the format Greg it's not a kind of typical chagas meeting as such uh in that uh we it's held in in the raddison blue as you say uh and the first 10 15 minutes will be kind of traditional uh given some information and a few slides just setting the tone or given out some basic information on on on the topic of succession but then it it's very much moves on to a one-to-one clinic format where individuals farm families and you know the focus is on farm family attendees so we're looking for and we've run these clinics successfully over a good number of years you see you know older generation younger generation as I said the succeeding generation of farmers plus other family members that might be directly uh involved in the farm in future years all attending these meetings and they get a chance to come as a family and sit in front of experts in the various different areas including the tax area financial um or sorry legal and what if you took in the fair deal scheme does that complicated at all of course it does uh but we have we have experts there in relation to the fair deal scheme from the citizens information uh service who will be able to give advice on on the principles associated with fair deal as well as the whole issue of um state pensions and so on which quite a complex area which which also kind of comes into this area yeah and and and we've a long way to go because I mean even in some cases I read a quote by um senator uh Boyan that in some cases couples don't discuss uh the the making of a will that one party would make a will without discussing uh it with their partner uh you know I mean that's the sort of the basic start and point I think and we're not doing that and there's an awful lot of head burying I think and sure look at the consulted out themselves or I'm going to be around for forever anyway and or don't even want to face the the reality of our mortality by making a will do you know but at the end of the day as I said five minutes ago this all has to be gone through at some point might as well do it in the least acrimonious way and the best organized way as is possible absolutely I mean we would be advocating in chagas you know the development of a succession plan to do it in a planned way and to cover off all those different areas and different angles around the tax and the legals and and you know put a will in place but make sure that you're doing it in a planned way and and you know have a timeline in mind uh one of the biggest issues that we find is is people just get stuck in a rut that all it can seem just too complex the conversations are too difficult to have and the easiest decision is just sit around I sit on the hands and do nothing and hope it all works out and sometimes it does but in a lot of cases you know it can cause problems so it's better to do it in a planned way. People who've held land for generations want to make sure it stays in the family name for example and maybe want to avoid the maybe an awkward conversation with the daughter or something who's to say. Exactly okay so do we have an idea as to what proportion of of uh uh successions are done in a planned way uh and ahead of time Kevin like is it the norm that people plan this and and have it organized or is it the norm that they don't? It's becoming more the norm Greg that that that it is done in a planned way I suppose a lot of the focus uh recently in in state tax legislation has been around promoting young farmers or the encouragement of young farmers to get involved earlier so you know there's quite good tax reliefs there around earlier transfer to encourage people to transfer before the age of 35 uh to to a young farmer before the age of 35 but in saying that I mean if we look at the statistics uh the the census of agriculture that was done in 2020 you know there's still a significant portion of farm holders that are over the age of 65 I think it's a third just short of 33% of of holders of farm holdings are are over the age of 65 and and those that are holding holding farms that are under the age of 35 are only around the 7% mark so it's it's it's it's we still have a way to go on this you know. Yeah and it is very complicated and maybe people don't even want to to get into this space but I think a good first step is to go to a talk like this where people understand what the situation is where someone can give you some advice maybe help you see the wood for the trees you don't have to commit to anything you don't even have to start a process but knowledge is power and we can hide for things I'm the worst for that myself get out in front of it and attend tomorrow. Now you talked about a one-on-one element to it is do you have to book a slot or is there going to be a lot of people there that might be able to accommodate all the attendees or how's that side of things working Kevin? Yeah we would be encouraging people to book in it's not you don't book a slot as such and we have we have four accountants and four solicitor firms there including and then we will also have a good number of Chagas staff our own staff advisors on the ground there in in Donegal would be would be very much clued into some of the aspects around this because they'd be dealing with farm families you know all the time and they've seen both successful and unsuccessful kind of transfers happen so they're in a good position to give their opinion on that. We have people there from the succession mediation side of things to help families get that conversation going and then as I said we have people there from citizens information so there are enough possibilities there for a one-to-one and it will run from around half ten tomorrow morning and finish up around one or two o'clock but during that period as I said the clinic format will run for at least two and a quarter hours so there'll definitely be a chance for every farm family to sit in front of an expert and put their question to it and it's very much the focus is very much on getting answers to these individual farm family questions rather than just throwing out general guidelines it's people getting answers to their own situation. Yeah it's a tough one isn't it because who starts the conversation because if a young person a younger person say though the person who's likely to succeed their father or mother or both you know if you if you try start the conversation you know even if these are close relationships if someone came to me and sort of says what are you going to do about this that and the other you know you can sort of you could find yourself maybe getting very defensive in question someone's motivation so I suppose even in terms of who starts the conversation and how it started even that part of it's tough Kevin. It is it is and as I said at the outset you know it can be the the the stumbling block that kind of stops people from doing anything and I mean our own staffer have come across those situations in the past where they've had to you know maybe initiate or help that conversation get going but there are professionals in this area professional mediators that have been quite successful in dealing with farm families where there are where there are difficulties just even in getting everybody around the table and getting their views heard and they can they have a process that they can go through with the farm family to get that conversation going so and there will be people there if you from the succession mediation say the things that are clinic tomorrow. Right okay so the clinic the family farm clinic is in the Radisson Blue Hotel tomorrow starts at 10 a.m. you mentioned people registering in advance where do they do that Kevin? If they go on our website chagas.ie there's a link there to the events tomorrow in the transfer and the farm events and they just go in there and book and book their book their place it's not a slot as such to no numbers to no numbers as well to no numbers exactly that's preferable but can people walk up if they don't say have access to the internet or they can they can of course walk up and but we'd prefer people to get an idea of numbers and all that type so that makes a great deal of sense people will understand that Kevin thanks for your time this morning. No problem at all. Okay take care of yourself that was Kevin Connelly financial management specialist with chagas. The Ninetal Noon Show is brought to you by letter Kenny Credit Union digital loans now available apply online or via our app today and get your loan transferred directly to your current account. At on post we believe in giving you more power over how you bank that's why AIB and Bank of Ireland customers can now lodge and withdraw money at any of our 900 post offices across Ireland six days a week that's right your bank is in your post office for personal and business banking alike meaning you can bank wherever you live or work visit your local post office or onpost.com slash everyday banking onposts your money for your world. Allied Irish Banks PLC and Bank of Ireland are regulated by the central bank of Ireland. Collins Funfair is back in letter Kenny for 10 days only come along and enjoy the high flying sky glider the spinning energy and the super sizzler twist plus much more Ireland's largest touring Funfair Collins Funfair in letter Kenny from the seventh until the 16th of October a Port Road letter Kenny just opposite the pennies roundabout at Volkswagen commercial vehicles the wait is over production is back now your plans can really begin whether that's scaling your business or smartening your service offering with HP finance from 3.9% purchase contributions of up to 3000 euro and service plans from 12 euro 99 per month don't wait secure your next caddy cargo transporter 6.1 or crafter at your local Volkswagen commercial vehicles dealer or visit Volkswagen vans.ie be ready to really deliver offers for business customers only finance provided by way of higher purchase agreement from Volkswagen financial services Ireland and subject to lending criteria. Call into Connelly's Volkswagen letter Kenny today or visit connelly's.ie to book a test drive. All right you're very welcome back to the program and we are going to say good morning now to Oshin Kelly who is presenting the DL debate this evening and it's another busy one Oshin good morning to you thanks for popping in. Yeah Greg good to see it. Good to have you with us. Right okay, Terman won by free kicks to take the Donegal seating your ladies title not necessarily maybe the way you want to win one but sure listen the W's the W isn't it? The W's the W and congratulations to Terman the senior champions again commiserations to Glen Funn. I'm not a fan in Gillick football either starting the match with penalties or starting the match with free kicks like at the end of the day if you looked at extra time Terman had to come back from three down to force to force the free kicks. There was nothing between the two sides throughout the game that sort of purple patches each Glen Funn won three up and then Terman then came back. I'm not a fan of a way to decide a Gillick football match be it for the men or the ladies. There was room for a replay Greg they're not straight back out into Ulster next weekend if you look at the men's final which is coming up on Sunday extra time will be played if required at the end of extra time a replay will take place and I think they could have done that with the ladies. Probably. Some will say it's unfair but at the end of the day that's the rules everybody played by the rules they went to the free kicks. Exactly. First time ever a senior decider was a senior final was decided on free kick so congratulations to Terman but joy and heartbreak all at the same time. That's the way it is on finals day and it's going to be the same for the men on Sunday. Well listen you started off with something like we could have got 20 minutes out of your bugger you could have come in at half 11 so we're going to have to rattle through the rest of it because that's going to be an interesting conversation I'm sure and you've got a great panel. Regular pundits Brendan Cullcoyne Jungle Day are in Neil McGee what a bit nice bit of time into joining the panel after his big news. Yeah stepping away from under county football 17 years is a long time. Playing at a top level 195 games for Dunnegaw. He's been a fantastic servant of Dunnegaw probably the toughest hardest most talented fullbacks that the county has ever had and he's a sound fella he's a great lad. Very very excellent football you know like somebody gets three all-stars Greg you know that you're one of the best. If they get three all-stars. If Neil McGee thought that he could give another five years he would. That's the type. So it's good to have him on the panel tonight we're going to get his thoughts in the big county to say they're coming up at the weekend and we'll also be talking to him about his brilliant career as well where he was one of the rocks and one of the the main cogs in the whole Dunnegaw machine that's in Ulster and all our success Greg. Well listen there's a lot of stuff you read a lot of games we covered a lot of games at the weekend you're going to have to go through all that because we don't have the time but just to remind us the deal debate it's broadcast live after the seven news tonight Neil McGee's joining Brendan Cullcoyne and John Gilday will also have a better reaction from the ladies and not forget it about Dunlop congratulations them intermediate champions as well we'll be recapping on what's been a busy weekend and looking forward to another busy one Greg. Yeah and if you want to watch the show as well by the way and all guests will be in studio you'll be able to do so by going on to our website you'll hit the watch now tap it about seven o'clock or on YouTube or Facebook and you can see all the guests in studio as well so no reason not to watch the deal debate and then it's podcast of course after. Oshin thanks for your time I really appreciate it okay take care of yourself. Oshin, Kelly there thank you so much to all of you who listened to the show, texted in, got involved in any which way you did we really appreciate it we're back with you.


and you can jump into the live broadcast chat channel. I'm also keeping an eye over on our YouTube chat. Hello, Dave Odessa. Thanks for stopping by. Hey, Randall Bone. Hello, and welcome, and vroom vroom. Let's see what have we got going on here. I want to send you to this URL right here, if you want to check out this week's product pick before we even talk about it. And that QR code will take you there as well. Hold on a second. I'm adjusting my mic, but I heard that was a little low. That's better. Let me know if that peaks out too much. So yeah, if you head right there, you will see this product pick and this show is taking place right inside of the product page itself. So you're safe watching from right within there. And product picks during this show and only during this show are on a huge, huge discount. This week's is 50% off and you don't need a coupon code or anything like that. Just go and grab it, maximum of 10 per customer. Sometimes we sell out before the show is over, so if it's something you're thinking of getting, encourage you to grab it. If not, maybe you'll just hang out for the ride in the demo. But before I go any further, let's have Lady Aida jump back just a little bit in time and tell us about this week's product pick. Please take it away, Lady Aida, from the past in your video form. Okay, so we've got the BNL055, it's actually one of our popular breakouts. This is a sensor that has a nine-duff accelerometer, gyroscope, magnetometer in it. And it will also give you quaternion and Euler values output. And why is that handy? Well, you can use a microcontroller that's fairly high-powered like Cortex-M0 or M4 to perform calculations on the fly using a nine-degree of freedom data to get orientation. However, it's kind of a pain. You have to calibrate the sensor and you have to keep it calibrated. You have to run the algorithm constantly. You have to tune the algorithm. It's kind of like not a fun experience. I mean, you can do it and it's definitely less expensive. But if you have a simpler microcontroller, like an 8-bit AVR, or something where you don't want to spend your cycles because you don't want to have your microcontroller constantly on, spending cycles doing calculation, the Vienna 055 is great for that. It basically just spits out calibration, quaternion, Euler data for you. And we've had a breakout for a while, but now we have it in an adorable new STEMI QT format. And so here, I show you can just plug in one of our cables. It's a PowerLED. And so this is really nice because you have four mounting holes. You can attach it to whatever you want to measure and then connect power ground, clock, and data to any microcontroller. And here you can see the XYZ orientation data. If you stay still, it doesn't really move. And then as you twist and move around, it tells you, this is the Euler angles. You can also get quaternion. And at the bottom, it has the statistics or the status of the auto calibration. So as long as you see M3, it means that the magnetometer is calibrated. So these are really nice. They're all in one. This uses a Bosch sensor. And then I think Hilcrest bonded a Cortex M0. Basically, at SAMD20 is inside of here, which is kind of cool. You could directly run circuit 5 on this chip. And it does the calculations and then spits them out over I squared C. So people really like these. I will say there's one downside they have. I squared C clock stretching. So on Raspberry Pi, you have to do a couple of things to get them going. But they're very easy to use. And there's a library code support for spotting a microcontroller. And the chip we're using on this feather is one of the slower ones we have. It's at Mega 32 U4. So it's an 8-bit microcontroller. We're not without a ton of RAM. It's driving the OLED while it's reading this data. It doesn't have to do the quaternion calculations on its own, thanks to this built-in orientation data calculator. So that's the B&L 055, now an adorable STEMI QT format for easy plug-and-play with any Python or microcontroller Arduino project. Yes, indeed it is. Look at it right there.  Right there, that's my product pick of the week this week. B&O 0559 DOF, Absolute Orientation IMU Breakout. This, this is the one. This is the one you want. If your project involves trying to figure out where you're pointing something or maybe where you're pointing yourself, the fact that it does the sensor fusion, which is to say it takes the magnetometer, accelerometer, gyro, takes all of that and does the calculations, does the math, to figure out where the heck is this thing pointed in 3D space. That's the good stuff. That's the hard stuff to do.  So like Lady has said, your code is simpler. Your microcontroller doesn't have to think so much about this stuff. It can just say, all right, hey, sensor, hey, B&O 055, where am I pointed? And then do stuff with it. So let's take a look at the product page for this. So here you go. This is the product ID 4646. And during this show, right now, it is half off $14.98, a great price for a really tremendous sensor. This is one I featured before. And over the life of this product, it has gone through a change from a traditional breakout board to a STEMA QT slash quick type of breakout board. So you can see we have those little plugs on the ends there. It makes it easy to integrate into your project without any soldering, without any breadboards or proto boards. If you're using a board that has a STEMA QT connector on it, you can just plug them into each other. And like we said, that can be a pretty simple board. I'll show you in a moment a little product, not a product. I'll show you in a moment a project I put together that uses a QT Pi RP2040 as the microcontroller and then offloads all of the tricky, where my pointing calculations to this breakout board right here.  We have the datasheet for the chip. We have fabrication files. We have a couple of learn guides, the original that shows that bunny demo, that little WebGL bunny demo, which is a really nice way to get started. And then this project, the PowerWash simulator nozzle controller. This is the one I wanted to show you. I've got it set up over here. And I'll plug that in just so you can see it in action. But here you can see in the code section, there is some info about getting set up with it, getting it set up for your offsets based on where you are on the planet. That'll matter for your magnetometer offsets because it acts like a compass. And then other offsets based on which way your project is in sort of its neutral position. The key thing to this is there is a link to this Adafruit playground that C Grover did. C Grover put together the code for doing very straightforward calibration and offsets for this sensor. So you can get calibrated to start with. And then you can do offsets for your project as needed to give it a relative offset. Other things I wanted to mention. So there was actually a question in the chat about this. The output of the sort of fused sensor data, getting all of these different things together and saying, if my gyro is doing this and my accelerometer is doing that and the magnetometer is doing that, which way am I pointed? And we actually can get two different versions of that. One is Euler calculations, which you can think of as three-dimensional. And then quaternions, which is more like a point on a globe, sort of a vector from inside of a globe pointing to any point on the surface. It's usually four numbers, at least when I dealt with these in 3D animation. And they can be trickier to deal with, but they do not suffer some of the problems that Euler rotation does, including gimbal locks. There was a question about gimbal locks. Sometimes when you align two of the three axes, you kind of get stuck and you can't get any info about rotation because there's an order to the rotation. The 0 and the 360 can kind of become the same number as well. And you can get sudden flipping. So gimbal lock and flipping are some issues you will face with Euler rotation. And so that's why quaternion is available. For the project I'm doing, I can get away, which is nice with the simpler Euler calculations. And so let's take a look at this. So here is, I've got, let me go to a full screen here so you can see the camera a little better. So I've got behind me, this is a PC game called PowerWash Simulator. It's like any first person shooter game. We're pointing some sort of a gun. We want to be able to aim that thing. So we want to know where in 3D space am I oriented? We can even also use things like roll if we want. But for this one, we just want to know which way am I pointed at this screen here. And so this little BNO-055 is mounted inside of here, along with the QDPI and a couple other goodies. So what I'll do is plug this in. And when it recognizes it, it's going to use the direction I'm pointing as its sort of relative starting point. So you can see, even though I'm not pointing at my monitor back there, I was able to get the orientation to work. And there's a little bit of lag in the video here. But this is fun. This is go clean up a really disgustingly dirty house. And I'm also using a little Wiimote there to move around. But you can see I can point this thing up. I can point this thing down. I can go left. I can go right. That is all based on, let me set that down so it doesn't flip out, that is all based on those Euler values that are being spit out for my absolute orientation. Where am I pointed? And then some relative offsets based on the fact that I wasn't actually pointing at the screen. I was pointing away from the screen. But that's all taken care of in code. So let's see, what else have we got? Code wise, we'll look at just a little bit here. This is a big project with a lot of code doing a whole bunch of different things. But some of the key stuff you'll see here, we set this up by just importing this driver. This is in Circuit Python. We can also use this in Arduino. So you can see here I'm bringing the BNO055 library. And then I am setting it up to use I square C. Here I'm creating an object called Sensor. Sensor equals A different BNO055, 055 over I square C. And then we can also set modes based on what info we want to get off of it. So I'm using end-off, which is the 9-off multiple, all the sensor fusion. Give me all the info you can version of it. But you could use it just simply as a magnetometer, simply as a gyro or an accelerometer, if you want to. There's a few different modes there. And then there's some math being done here. This is stuff that C Grover worked on. Thank you so much to calculate reference points based on your relative and absolute. And here you can see we're also setting up these magnetometer, gyro, and accelerometer values. So we can see those or use them on their own if we want. And then the main loop of the program here, we're just simply saying SensorEuler equals Sensor.Euler. So that's how you ask for it. You can just say, hey, give me that position I'm pointed to and roll in space. And it'll just spit back those values as a tuple for you. And I'm breaking those up into three separate variables to make them easier to use in code, which is heading, roll, and pitch. And so you can see there are some nice examples in both the main guide and in this setup part of this guide as well as this playground on doing like what you saw in Lady Aida's demo, which is just saying, hey, tell me, where am I pointed on the compass? Or what are those three values that I'm getting back? This project is, I think, really nice because it combines all that stuff into what I really want when I use something like this, which is, where am I pointed? That's actually much harder to get than you think. In fact, the main other way that this works well is, if you remember, on the Wii controller, pointing at a pair of infrared lights. There's a little camera. It's pointing at a pair of infrared lights. And it was doing some math to figure out if we're moving closer or further, then those two lights will change their distance between them. And if we are seeing them do this kind of stuff, we're tilting left and right if we're aiming at one or aiming at other. So that works really well, but it does require that secondary setup of an emitter source, the two IR LEDs, whereas something like this is really fantastic for having just a single solution that can give you the orientation of your object in space. Let's see if there's any questions. Mike says, I'm guessing Euler anglers come from the Craternians and there wouldn't be a gimbal lock issue. Todd was saying the data sheet indicates that it's doing real Quaternians, which is good. Just faking it. Yeah, so that's a great point. If it's starting from the real proper Quaternian and then giving you the Euler values, then it's not as likely or maybe it won't experience gimbal lock, which is great. Yeah, OK. I think that is it. So let me know if you have any other questions in the chats. If you want to go pick some of these up, head right here to that product ID you see, 4646. They are still in stock. Yes, they are. They are in stock and they are only $14.98 right now. During the show, you don't need a coupon code. Just throw them in your cart and you'll get them at that price. And here, by the way, since I set it up, I wanted to show you here some nice close-up images there of the board. So you can see you can solder header pins to it and put it into a breadboard or put it onto a Promo Proto if you want, depending on the type of project you're doing. Or you can simply plug into those Stemma QT ports that are on the sides. Is that it? I think that does it. So thank you, everyone, for making jokes about sandwiches. Mike Jones, Euler was eating a gyro. I want to know which way it was pointing one time. Gyro? Gyro? Her brain says mechanically, I don't think MEMS gyroscopes are susceptible to gimbal lock as our gimbals don't really rotate. That's a good point. It's not a mechanical thing. It is separate sensors. So I'm thinking old fashioned. So yeah, I think we're safe from gimbal lock. That'll be good. OK, that's going to do it then. So if you want to get one of these or up to 10 of these, that's the limit at this price. Head on over to product ID 4646, throw them in your cart, get them before the show is over or within a few minutes grace period, and you can get started on some of your orientation types of projects. Let's see. I think I hit all the notes. Yeah, that's going to do it. All right. Thank you, everyone, so much for stopping by that. Right there. I wanted to get it right side up, which makes sense. That right there is my product pick of the week this week. It is the B&O 0559 DOF, Absolute Orientation IMU Breakout Board. Phew. Thanks, everyone. I will see you next time. Bye-bye.


Prigozin challenges Putin and Russian authorities. The owner of the Russian Wagner group, Yevgeny Prigozin, who has previously sharply criticized the Russian Ministry of Defense, has now challenged the head of the Kremlin, Vladimir Putin, according to UK Defence Intelligence. UK Defence Intelligence recalled that on the 10th of June, the Russian Ministry of Defense stated that all volunteers formations, such as the Wagner group, should sign contracts directly with the Russian Ministry of Defense. Speaking on television on the 13th of June, Putin directly supported this move. The UK Ministry of Defense noted that Prigozin has sharply criticised the leadership of the Russian Ministry of Defense, but relied on Putin's authority. However, despite Putin's comments, Prigozin said on the 14th of June that none of Wagner's fighters is ready to go down the path of shame again. That's why they will not sign the contracts. Prigozin's rhetoric is evolving into defiance of broader sections of the Russian establishment. On the 1st of July 2023, the headline for the volunteers to sign contracts is likely to be a key waypoint in the feud, the report said. In a rare direct show of defiance towards the Russian leader, Prigozin said none of Wagner's fighters is ready to go down the path of shame again. That's why they will not sign the contracts.