 Ок, коллега, господин Шерман, мы говорим о компрессивности с двухфейсом ликвито-вейпером, миксерами металлов с высокими температурами. Вы меня слышали? Нет? Ок. Да, у меня есть. Эта работа mainly devoted to the problem of equation of state of materials at high energy densities. Equation of state is fundamental characteristic of matter and it is needed for numerical simulations of different processes like turbulent mixing and beyond. Here you can see an example of such process. It is high velocity impact of metallic plate on another metallic plate. In this diagram you can see a change of state of both materials on phase diagrams of these two metals, titanium and aluminum. Initial point is A and at the moment of collision of these plates state of materials jumps to this point on shock-hugonium curve B. And then in the release wave material will be expanded at constant entropy and reach region of liquid-vapor mixture here. Another example is interaction of intense laser pulse, ultra-short laser pulse, 100 femtoseconds with metal. Here gold is an example. States of material near the irradiated surface changed at first either vertically and outer layer of metal almost operated totally and shock wave propagates inside the target. So if we have a multi-phase equation of state, analyze this process. Here you can see a general view of phase diagram of aluminum with pressure in bar and compression ratio. Solid lines correspond to shock compression experiment with samples of different initial porosity. Porosity is normal density of this material divided by density of initial density of sample. These markers correspond to experimental data and dotted lines correspond to isentropic release experiments. In such experiments material experience expansion after shock compression expansion and reach region of two-phase liquid-vapor region. And also here you can see these crosses. These crosses correspond to experiments with electrical explosion of wires and foils. Here you can see a surface that is determined by equation of state and all such processes takes place on this surface. This is main meaning of equation of state. This is fundamental characteristics of material. Also you can see blue lines corresponding to shock wave experiments with solid and porous samples. Green lines are release isentropes. Red lines are phase boundaries melting and evaporation. To describe this surface we should use white range equation of state. Such white range models have old history. Here we will use equation of state that is some modification after Bushman and others using harmonic approximation of white range of temperatures and Thomas Fermi model at zero temperature and high densities up to one million more than normal density of metal. Here you can see general form of this equation of state. It is based on Gilm-Golff's free energy as function of specific volume and temperature. It consists of three terms. First corresponds to zero temperature and it depends only on volume. Second is thermal contribution of atoms, ions, nuclei. And last term corresponds to thermal contribution of electrons. All three terms may have different forms for different phase states. Here you can see formulas for equation of state at zero temperature for solid phase. Also thermal atomic contribution for solid phase. It is a harmonic approximation with taking into account acoustical and optical modes of lattice vibrations. Also zero Kelvin equation of state for liquid phase. It is based on solid equation of state. And second term allows for correct value of liquid phase at melting point. You can see formulas for atomic contribution for liquid phase. Electronic part is taken from Bushman model. Further I will show you results of calculations in comparison with some experimental data. Here you can see tungsten at zero temperature. It is a very wide range of compression ratios up to 10,000. Squares correspond to Thomas Fermi model with corrections. Black line is from this model. And other green and red curves correspond to another model. Here you can see calculated principle Hugoniot curves for titanium and tin. Shock velocity versus particle velocity. Markers correspond to experimental data. And here you can see calculated adiabat with kinks that those correspond to phase transformations. Polymorphic and here melting also. На анализинг шоквейф эксперимент, мы использовали генералозы консервации массы, моменты и энергии. Эти три элементы имеют 5 параметров. И два параметра, обычно это шок и патрик. Из эксперимента используя эти три элементы, у нас есть калория. Это relation of internal energy, pressure, and volume. And vice versa, if we have equation of state, we can calculate shock adiabat using these equations. Here you can see phase diagram of metal, of tin metal. Temperature versus pressure. Dash dot lines correspond to phase boundaries for polymorphic transformation and for melting. And solid line is principle hugonium of this material. Markers, open markers are temperature measured static conditions in diamond anvil cells experiments. And solid circle and square correspond to shock wave experiments. How we can calculate phase boundaries? So we used two equations for Gibbs energy and for pressure of two phases at given temperature. We can calculate, we can find specific volumes of these two phases. And also here calculated shock agonium and release isentrop are compared with experimental data for tin. For solid samples and for porous samples. You can see good agreement. And using such isentropic release technique, we can investigate region of two phase liquid vapor mixture. Here for aluminum, this region is shown as in a plane density versus temperature. And also this region is shown on this diagram. Here you can see also wide range of negative pressures. It corresponds to tensile stresses. And so we can calculate shock adiabats for liquid vapor mixture. Here you can see example for tungsten metal. These curves correspond to different initial volumes here and initial atmospheric pressure. On these curves we find region where sound instability happens. This phenomena was investigated, was discovered by Dyakov. And further works by Kantarovich, Faulis and Kuznetsov. Here you can see criteria for corrugation and stability. And inside this region, sound instability can appear. If this condition takes place. Also this region was investigated in this papers. And here, final picture, this phase diagram of two phase mixture. Of tungsten shows boundaries of this sound instability region inside two phase region. These boundaries correspond to different initial pressure of this liquid vapor mixture. And finally this line is critical isentrop. So this region mainly takes place under critical entropies. And these are my conclusions. Thank you for your attention. These triangles correspond to results of calculations by Sinko and Smirnov. They used full potential linear muffin tin approximation. Thank you.