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In our recent works, we proposed a theory of turbulence creation via the mean field effect of an intermolecular potential, which in part relies on the empirically observed "equilibrated" behavior of the pressure variable in a low Mach, high Reynolds number flow -- that is, while the density and temperature may exhibit considerable variations, the pressure is (nearly) constant. At the same time, conventional kinetic theory does not offer satisfactory explanation for such a behavior of the pressure variable, instead leading to an isentropic flow in the form of the usual compressible Euler or Navier-Stokes equations. In the current work, we introduce a novel correction term into the pair correlation function in the closure of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the deterministic, Vlasov-type collision integral. This term adjusts the density of incident and recedent pairs of particles to the macroscopic compression or expansion rate of the gas. Remarkably, the novel term does not affect the mass and momentum transport equations, and manifests solely in the pressure transport equation. Moreover, its effect on the pressure dynamics matches the observed behavior -- that is, it tends to attenuate the acoustic waves and smooth out the pressure solution. We also find that the novel correction term fails to produce such an effect in a stochastic, Boltzmann-type collision integral. This suggests that simplifying potential interactions via instantaneous collisions may lead to the loss of observable macroscopic effects in solutions of the fluid mechanics equations., Comment: 34 pages

In recent works, we proposed a hypothesis, according to which turbulence in gases is created by the mean field effect of an intermolecular potential. We discovered that, in a numerically simulated inertial flow, turbulent solutions indeed spontaneously emerge from a laminar initial condition, as observed in nature and experiments. To study the origin of turbulent dynamics, in the current work we examine the equations of a two-dimensional inertial flow, linearized around a large scale constant vorticity state. Remarkably, even in this simplified setting, we find that turbulent dynamics emerge as linearly unstable fluctuations of the velocity divergence. In particular, for the linearized dynamics at a high Reynolds number, we find that, at short time scales, the coupling of the mean field potential with the large scale background vorticity creates linearly unstable, rapidly oscillating fluctuations of the divergence of velocity at inertial scales. In the asymptotic time limit, we find a persistent eigenvector, also aligned largely with the divergence of velocity, which allows these fluctuations to propagate in the form of traveling waves in the Fourier domain. Remarkably, these traveling waves decay at a constant, scale-independent exponential rate, which is rather unusual, because all explicitly dissipative terms in the equations are viscous. Furthermore, it appears that the famous Kolmogorov scaling of the kinetic energy is produced by this persistent velocity divergence, due to a cubic relation between the physical time variable, and a pseudo-time variable, in which the dynamics become asymptotically autonomous. These effects vanish when the mean field potential is removed., Comment: 24 pages

In our recent works we proposed a theory of turbulence in inertial gas flow via the mean field effect of an intermolecular potential. We found that, in inertial flow, turbulence indeed spontaneously develops from a laminar initial condition, just as observed in nature and experiments. However, we also found that density and temperature in our inertial flow model behave unrealistically. The goal of the current work is to demonstrate technical possibility of modeling compressible, turbulent flow at low Mach number where both density and temperature behave in a more realistic fashion. Here we focus on a new treatment of the pressure variable, which constitutes a compromise between compressible, incompressible and inertial flow. Similarly to incompressible flow, the proposed equation for the pressure variable is artificial, rather than derived directly from kinetic formulation. However, unlike that for incompressible flow, our pressure equation only damps the divergence of velocity, instead of setting it directly to zero. We find that turbulence develops in our weakly compressible model much like it does in the inertial flow model, but density and temperature behave more realistically., Comment: 20 pages, 8 figures

Turbulence in fluids is an ubiquitous phenomenon, characterized by spontaneous transition of a smooth, laminar flow to rapidly changing, chaotic dynamics. In 1883, Reynolds experimentally demonstrated that, in an initially laminar flow of water, turbulent motions emerge without any measurable external disturbance. To this day, turbulence remains a major unresolved phenomenon in fluid mechanics; in particular, there is a lack of a mathematical model where turbulent dynamics emerge naturally from a laminar flow. Recently, we proposed a new theory of turbulence in gases, according to which turbulent motions are created in an inertial gas flow by the mean field effect of the intermolecular potential. In the current work, we investigate the effect of viscosity in our turbulence model, by numerically simulating the air flow at normal conditions in a straight pipe for different values of the Reynolds number. We find that the transition between the laminar and turbulent flows in our model occurs without any deliberate perturbations as the Reynolds number increases from 2000 to 4000. As the simulated flow becomes turbulent, the decay rate of the time averaged Fourier spectrum of the kinetic energy in our model approaches Kolmogorov's inverse five-thirds law. Both results are consistent with experiments and observations., Comment: 11 pages, 3 figures

We develop a tractable interaction model for a polyatomic gas, whose kinetic equation combines a Vlasov-type mean field forcing due to an intermolecular potential, and a Boltzmann-type collision integral due to rotational interactions. We construct a velocity moment hierarchy for the new kinetic equation, and find that, under the high Reynolds number condition, the pressure equation becomes decoupled from the angular momentum and stress. For the heat flux, we propose a novel closure by prescribing the specific heat capacity of the gas flow. Setting the specific heat capacity to that of a constant-pressure process leads to the system of equations for a balanced flow, where the momentum transport equation contains the mean field forcing, which is an averaged effect of the intermolecular potential. Remarkably, the balanced flow equations do not contain any information about internal thermodynamic properties of the gas, and are thereby applicable to a broad range of different gases. We conduct numerical simulations for an air-like gas at normal conditions in the inertial flow regime, where the pressure is constant throughout the domain. We find that the presence of the intermolecular potential produces a distinctly turbulent flow, whose time-averaged Fourier spectra of the kinetic energy and temperature exhibit Kolmogorov's power decay., Comment: 36 pages, 6 figures (added some references and changes in text)

In recent works we developed a model of balanced gas flow where the momentum equation possesses an additional mean field forcing term, which originates from the hard sphere interaction potential between the gas particles. We demonstrated that, in our model, a turbulent gas flow with a Kolmogorov kinetic energy spectrum develops from an otherwise laminar initial jet. In the current work, we investigate the possibility of a similar turbulent flow developing in a large scale two-dimensional setting, where a strong external acceleration compresses the gas into a relatively thin slab along the third dimension. The main motivation behind the current work is the following. According to observations, horizontal turbulent motions in the Earth atmosphere manifest in a wide range of spatial scales, from hundreds of meters to thousands of kilometers. Yet, the air density rapidly decays with altitude, roughly by an order of magnitude each 15-20 kilometers. This naturally raises the question as to whether or not there exists a dynamical mechanism which can produce large scale turbulence within a purely two-dimensional gas flow. To our surprise, we discover that our model indeed produces turbulent flows and the corresponding Kolmogorov energy spectra in such a two-dimensional setting., Comment: 25 pages, 9 figures

In recent works, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential, and examined the proposed mechanics of turbulence formation in a simple model of two particles for a variety of different potentials. In this work, we use the same hypothesis to develop new fluid mechanics equations which model turbulent gas flow on a macroscopic scale. The main difference between our approach and the conventional formalism is that we avoid replacing the potential interaction between particles with the Boltzmann collision integral. Due to this difference, the velocity moment closure, which we implement for the shear stress and heat flux, relies upon the high Reynolds number condition, rather than the Newton law of viscosity and the Fourier law of heat conduction. The resulting system of equations of fluid mechanics differs considerably from the standard Euler and Navier-Stokes equations. A numerical simulation of our system shows that a laminar Bernoulli jet of an argon-like hard sphere gas in a straight pipe rapidly becomes a turbulent flow. The time-averaged Fourier spectra of the kinetic energy of this flow exhibit Kolmogorov's negative five-thirds power decay rate., Comment: 18 pages, 3 figures

This paper contains suggestions for experiments with usage of the Spin Physics Detector (SPD) at the first stage of the SPD NICA Programme developing at JINR. Double polarized pp-, dd- and pd- collisions at c.m.s. NN energies of 3.4-10 GeV, which will be accessible at the initial stage of experiments, allow one to study spin dependence of the NN interaction, search for multiquark states at double strangeness, charm and beauty thresholds, study the short-range structure of the deuteron. Double polarized pd scattering offer a possibility to test the Standard Model through the search for T-invariance violation., Comment: 140 pages, 44 figures, prepared for Physics of Elementary Particles and Atomic Nuclei

In a recent work, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential - for example, the interatomic potential at short ranges, and the electrostatic potential at long ranges. Here, we examine the proposed mechanics of turbulence formation in a simple model of two particles, which interact solely via a potential. Following the kinetic theory approach, we derive a hierarchy of the velocity moment transport equations, and then truncate it via a novel closure based on the high Reynolds number condition. While standard closures of the velocity moment hierarchy of the Boltzmann equation lead to the compressible Euler and Navier-Stokes systems of equations, our closure leads to a transport equation for the velocity alone, which is driven by the potential forcing. Starting from a large scale laminar shear flow, we numerically simulate the solutions of our velocity transport equation for the electrostatic, gravity, Thomas-Fermi and Lennard-Jones potentials, as well as the Vlasov-type large scale mean field potential. In all studied scenarios, the time-averaged Fourier spectra of the kinetic energy clearly exhibit Kolmogorov's "five-thirds" power decay rate., Comment: 35 pages

For a large system of identical particles interacting by means of a potential, we find that a strong large scale flow velocity can induce motions in the inertial range via the potential coupling. This forcing lies in special bundles in the Fourier space, which are formed by pairs of particles. These bundles are not present in the Boltzmann, Euler and Navier-Stokes equations, because they are destroyed by the Bogoliubov-Born-Green-Kirkwood-Yvon formalism. However, measurements of the flow can detect certain bulk effects shared across these bundles, such as the power scaling of the kinetic energy. We estimate the scaling effects produced by two types of potentials: the Thomas-Fermi interatomic potential (as well as its variations, such as the Ziegler-Biersack-Littmark potential), and the electrostatic potential. In the near-viscous inertial range, our estimates yield the inverse five-thirds power decay of the kinetic energy for both the Thomas-Fermi and electrostatic potentials. The electrostatic potential is also predicted to produce the inverse cubic power scaling of the kinetic energy at large inertial scales. Standard laboratory experiments confirm the scaling estimates for both the Thomas-Fermi and electrostatic potentials at near-viscous scales. Surprisingly, the observed kinetic energy spectrum in the Earth atmosphere at large scales behaves as if induced by the electrostatic potential. Given that the Earth atmosphere is not electrostatically neutral, we cautiously suggest a hypothesis that the atmospheric kinetic energy spectra in the inertial range are indeed driven by the large scale flow via the electrostatic potential coupling., Comment: 28 pages, 1 figure (minor revision is done)

The design and parameters of the polarized-beam facility at U-70 proton synchrotron of NRC Kurchatov Institute - IHEP are presented. The new beamline 24A will provide the polarized proton and antiproton beams for carrying out the rich physics program of the SPASCHARM experiment for comprehensive studies of spin phenomena in a wide spectrum of hadronic reactions in the energy range of 10-45 GeV., Comment: 13 pages, 10 figures

A key feature of the classical Fluctuation Dissipation theorem is its ability to approximate the average response of a dynamical system to a sufficiently small external perturbation from an appropriate time correlation function of the unperturbed dynamics of this system. In the present work, we examine the situation where the state of a nonlinear dynamical system is perturbed by a finitely large, instantaneous external perturbation (jump) -- for example, the Earth climate perturbed by an extinction level event. Such jump can be either deterministic or stochastic, and in the case of a stochastic jump its randomness can be spatial, or temporal, or both. We show that, even for large instantaneous jumps, the average response of the system can be expressed in the form of a suitable time correlation function of the corresponding unperturbed dynamics. For stochastic jumps, we consider two situations: one where a single spatially random jump of a system state occurs at a predetermined time, and another where jumps occur randomly in time with small space-time dependent statistical intensity. For all studied configurations, we compute the corresponding average response formulas in the form of suitable time correlation functions of the unperturbed dynamics. Some efficiently computable approximations are derived for practical modeling scenarios., Comment: 34 pages (added Section 6, which discusses the accuracy of the leading order response)