 about this topic, so I will present it instead of him. And there are basic problems that exist in detonation initiation. So still, after many years, many decades of research, there is many models, ideas of what happened on microscopic level, or mesoscopic 2, which leads to initiation or ignition of the high explosive, condensed explosive. So in this talk, we will focus on the porous explosive and we'll try to make as a final step to do mesoscopic simulation. But as a first step, we want to just do some preliminary thermistic simulation to find the equation of state, reaction rates, and all chemistry on an atomic level, molecular level. So the major idea behind the ignition, which may describe the ignition in the all kind of practical high explosive material, or energetic material, which are not ideal crystal, which always have some imperfection in form of the grains, voids, and so on. So that the ignition happens through the initiated or started from the formation of the so-called hot spot. So hot spot usually associated with some small pore, or small void between grains, this size of maybe micrometer, or even 100 nanometers. And this pore may lead to formation of the high temperature spot after compression and collapse of this pore. This idea has a long history and still because the complexity of direct simulation, mesoscopic simulation of such samples, there is many uncertainty about what the mechanism behind of this heating. Of course, the collapse is a just general thing, but some void can produce additional heating and transfer to detonation way. But some pores may be very small pores. It may just simply collapse and do not cause any effect. So here I show that our first hydrodynamic simulation, not a thymistic simulation, but this hydrodynamic simulation using smooth particle hydrodynamics code was performed on the basis of a thymistic simulation. So all chemistry here, all reaction rate equation of state was obtained from the first step of the simulation and molecular dynamic simulation of some model energetic material we call AB. You may think it suggests N O atoms. I will tell you about it later. So the term hotspot actually means a class of the objects which may lead to the initiation or ignition of detonation. It suggests simply if you go to a restaurant and ask, I want to fish. Maybe no one understood you well. So because a fish itself has a very different sort of fish. And we have to think in the same way for meaning of hotspot. If you talk hotspot, we definitely ask first in what condition this hotspot was formed. And the evolution, the life of this hotspot, will it survive or will it die soon, will depend on the environment condition or the type or class of this hotspot. So the simplest I'll discuss it about classification later. And itself classification, as I said, is important. And yeah, there are some examples. So poor collapse will lead to formation of one type of the hotspot. But laser heating will provide another type of hotspot. So in laser heating, we have some high temperature, maybe in hotspot produced by poor collapse, low temperature, but high pressure. Quite different condition. And the life of this hotspot will be quite different. And the critical condition it will die or expand infinitely will also depend on such class or type of hotspot. So you see, I'll say a few words about this simulation. The porous material just consists of the spherical pore here. They are not shown here. It's just a shadow of wall three-dimensional sample. So pore size will be realistic about 50 microns and some length 10 millimeters. Of course, such dimension sizes are not achievable in molecular dynamics, a timeistic approach. But here, as I said already, all chemistry taken from the molecular dynamics simulation. You see that the wave, initial wave, propagates without actually heating here. The temperature remains cold. However, after colors, a few, several pores you may see here. So the reaction initiated somewhere here, far from the piston, by the way. And detonation just in the forward direction is initiated here. And backward detonation wave also initiated from this area. Well, the ensemble of hotspot was quite strong to produce this transition to detonation regime. So the outline of talk. So first, classification of hotspot. I already said that it's really required to understand the various ignition scenario. So actually, classification still, we don't have a good classification in literature. The idea of classification, of course, kind of in air. But usually, experimentally, we do some kind of conclusion. We cook this kind of hotspot in such condition. Maybe we cook another hotspot in another condition. But theoretical classification still is like that. So then I will show some MD simulation of two classes, I think the most important classes of hotspot is produced by fast laser heating. And then there's a kind of hot hotspot. And then another hotspot produced by the collapse of the pore. So produced by external pressure or short compression. And finally, just conclusion and further work. So to transition to from atomistic level to hydrodynamic level of simulation. OK, the simplest and I think very natural classification of hotspot can be based on the characteristic times of the major process driving or guiding this process of formation of hotspot. First is the reaction time. It's quite of general kind of the definition. I will tell you about definition of characteristic time later. Of course, it's not simple quantity because it must include major chemical reactions initiated in the explosion. But we may derive it or even obtain an experimental condition. So heating time, of course, it's clear that the hotspot produced by laser or electric spark may be controlled by the heating. Slow heating or fast heating will give us different results. And acoustic time or sound wave time. Typically, it is associated with the radius of hotspot and the sound speed in the material clearly. So it determines how fast the reaction wave unload with hotspot or how fast compression or shock wave propagate inside. Anyway, so the combination of these three characteristic time may give us about six class or six type of hotspot. But however, I will just focus on two type of hotspot, that the heating time much lower, much less than the acoustic time. Of course, if heating time much longer than acoustic time, then actually we cannot really produce a good hotspot because unloading wave will release a pressure and maybe just some class of hotspot will never survive. OK, anyway, so time of heating much less. Reaction time and acoustic. This is one of sorts, one of kind of hotspot. So it produce fast heating, decomposition, and hydrodynamic flow. So and here just one example, sorry, is one kind of hotspot. Is the reaction time much less than acoustic time? Then much less. So the reaction, it's probably opposite. Reaction time, if reaction time is here, should replace growth here and extension here, is acoustic time much shorter than reaction time? Then much shorter. OK, then it will lead to extinction. So we have a hotspot produced by a laser heating, but due to unloading, fast unloading temperature, reaction have no time to produce a temperature. So it should be replaced to grow here and extension here. And the opposite case is the reaction is very short. So unloading wave cannot reach the center of the hotspot. Then reaction will complete, release a lot of energy, and hotspots survive and start to expand. OK. So here, as I said, two major types of the hotspot. So the fast heating, fast heating in this area, so the boundary contact between reagent material, so initial material here and hotspot here. So fast heating results in the high pressure there and high temperature here. So density remains the constant, just isohoric heating because of too fast. So another hotspot here. So slow heating in mechanical equilibrium. So we have a, but because mechanical will be low density here, and the pressure is just constant. But we have a high temperature, very high temperature. So heating in mechanical equilibrium. Yeah. OK. So let's first try to simulate, I will show the simulation of the cylindrical hotspot produced by fast heating. It means heating is much shorter than the acoustic time, unloading time of the hotspot. And yeah, first I will discuss about what potential, what the forces acting between atoms. About two decades ago, the very simple classical interatomic potential for the reactive material, which includes valency, chemical bonds between atoms was developed by Brenner and Covofer. So this year. So this potential is quite actually simple and consists of two parts. For chemical bond, we have a very deep wheel, very energetic 2EV, presented by Morse potential, short range potential. And for large distance between molecules actually, we have one there was force, using a linear just potential. Actually quite simple. There is another important thing is a bond order. I show next slide. But I would like to say that this potential, AB called some kind of AB potential, or reactive, reactive, empiric bond order potential, plays exactly the same role as a Lener-Jones potential, which probably everyone knows very well. So Lener-Jones potential is good for just theoretical study of equation of state, operations, many things just to understand anatomic level what happened inside the material. But Lener-Jones potential has no way to select, this atom will connect to this atom, like make a bond. And the bond should saturate at valency, at given valency. And in order to include the valency in classical MT, we, Brenner-Slistkofer introduced bond order. So if one atom close to another atom, then this assume valency one. Valency is saturated, and all third, fourth atoms cannot contact and make chemical bond with a central atom. It's clear. So it's not simply, it's not a simple actually function, but it's a very effective from a computational point of view potential. It's just about two, three times has a low speed, calculation speed, than the Lener-Jones potential. OK. Here, OK. Wonder-Wall's term for a system energy of anatomism. Wonder-Wall's force is a long range of forces, repulsive forces, and the attractive force, which depends on bond order. If a bond order just one, then attractive force is large. It means we may make atom make chemical bond. If it's just zero, it suggests eliminate attractive force and only repulsive is active. OK. About the characteristic time of chemical reaction, you know that the real energetic material explosive a lot, I mean thousands, or maybe 100,000 reactions. Of course, there are very some virtual reaction, but it's not no way to include in a realistic simulation program, include all of them. And the problem even deeper, we may write many equations, so thousands equation, kinetic equation. However, we also, in order to close the system, we need also to provide equation of state of each species. So it's an equation of state of some radicals and other radicals. And now another intermediate some active molecules. So it's really not no any way to do this. And typically, people that just combine all of reaction as a initial, a reagent material products and reaction, intermediate reaction, like radicals. Here, it's simply very visible. A star, B star. So this interaction between B and A and B may result in formation molecule and production of the radical atoms. Radicals are important. They are very important in the initiation of the chain of reaction, production of the release of energy. Sorry for interrupting, but your talk is only 25 minutes. You've nearly taken 20 already. All right, thank you. I will think so. OK, so then the reaction in the hot spot will all combine it to the isochoric thermal decomposition time. In the isochoric heating condition, the time is measured when the product of the product are formed, as on this time will depend on the density, initial density, and initial temperature. So doing this way, we may extract the canonical equation to use in the hydrodynamic code. OK, so fast heating of cylinder. So initially it was heated here. Pressure jump, temperature jump here, and then expand star. What we may say just in brief that acoustic time of hot spot is quite about 10 picosecond. It's much smaller than heating time. It means the hot spot produced by a laser heating will expand long time. And the reaction may have time to test complete and release energy. And just from such simple thing, we may just derive that the critical radius of this hot will be order, not equal here, but order, that the sound speed on reaction time. It means that if the radius will be low, then this critical radius. Then unloading wave will come to the center faster than the reaction will happen. And then unloading wave kill the reaction, drop the temperature, and the reaction will stop. OK, here the profile of the radial profile of velocity and density in unloading wave, reflection of convergent wave coming to the center. So at time 8 picosecond, wave reaches center, refaction wave. Conversion, refaction wave. It starts to reflect from the center. Refaction wave starts to reflect from the center, produce another new reflected refaction wave. Reflected refaction wave will lead to formation of inflow. You see the negative here, velocity. Produce that densification of central part. It may result in decrease of density here. And density, as I showed you before, high density provide a good chance for development of reaction, ignition of this point. So next. So critical radius here. In such condition, we found that critical radius of the hot spot is about 23 nanometers. So these small radius, 21, died. Hot spot dies here. Then it's expand, and this product is a product. Cycle is a product, and dashed line is a density. So because densification at this point happened at the center, you see the density jump. Due to reflection of refaction wave from the center, densification may, you see, change slope of this production of the final state of molecules. And then it starts to accelerate. So finally, we found that such condition may really happen in such hot spot. So let's keep it. And few words about hot spot after collapse. So shock compression of the material, shock compression, that low compression amplitude, will never produce any reaction. It's too small for this material. However, we have a pore. The collapse may result in the increase of pressure at the center, you see. And it depends on radius. Here, a radius was 16 nanometers, 12, 14, 16. So the critical radius is at the 14 nanometers. So if a pressure will exceed some critical limit, I guess about 10 GPA, somewhere here, 11 GPA. So the initiation pressure and temperature inside the center will be large enough to produce a reaction. Here's some just repeating that we need maybe 1% of radicals at the center produced by the collapse in order to give a chance of collapse to form a living hot spot. OK. And then in conclusion. So what we did, maybe we did some preliminary classification of the hot spot based on the characteristic time of the major process, guiding of evolution of hot spot. And the critical condition for hot spot generated by fast heating is acceleration of the exothermic reaction due to a reflection of the refaction wave coming to the center. Let's reflect, make additional densification in the center, which results, which triggers chemical reaction. And then hot spots survive and start to grow. And the collapse in power leads to high pressure. If the pressure is enough to produce a high concentration of radical atoms, then it supports, I mean, the hot spot start to grow. And the reaction accelerated just is the center of the pore. And at the future, and I already show some preliminary in the beginning of my talk, SPH simulation. So we want to make a mesoscopic simulation. It could be many pores and use a atomistic-based reaction rates, equation of state, in order to make a combined and consistent simulation on the atomistic level and the hydrodynamic level. Thank you very much.