Thermodynamic and Kinetic Description of the Main Effects Related to the Memory Effect during Carbon Dioxide Hydrates Formation in a Confined Environment

This article consists of an experimental description about how the memory effect intervenes on hydrates formation. In particular, carbon dioxide hydrates were formed in a lab–scale apparatus and in presence of demineralized water and a pure quartz porous medium. The same gas-water mixture was used. Half of experiments was carried out in order to ensure that the system retained memory of previous processes, while in the other half, such effect was completely avoided. Experiments were characterized thermodynamically and kinetically. The local conditions, required for hydrates formation, were compared with those of equilibrium. Moreover, the time needed for the process completion and the rate constant trend over time, were defined. The study of these parameters, together with the observation that hydrates formation was quantitatively similar in both types of experiments, allowed to conclude that the memory effect mainly acted as kinetic promoter for carbon dioxide hydrates formation.

Medium-induced fragmentation and equilibration of highly energetic partons

We investigate the energy loss and equilibration of highly energetic particles/jets inside a QCD medium. Based on an effective kinetic description of QCD, including 2 ↔ 2 elastic processes, radiative 1 ↔ 2 processes, as well as the back-reaction of jet constituents onto the thermal medium, we describe the in-medium evolution of jets from the energy scale of the jet ∼ E all the way to the medium scale ∼ T. While elastic processes and back-reaction are important to describe the equilibration of soft fragments of the jet, we find that the energy loss is dominated by an inverse turbulent cascade due to successive radiative branchings, which has interesting implications for the energy spectra and chemistry of jet fragments.

Formation of Kinetics Coherent Structures in Weakly Collisional Media

The formation of nonlinear, nonstationary structures in weakly collisional media with collective interactions are investigated analytically within the framework of the kinetic description. This issue is considered in one-dimensional geometry using collision integral in the Bhatnagar-Gross-Krook form and some model forms of the interparticle interaction potentials that ensure the finiteness of the energy and momentum of the systems under consideration. As such potentials, we select the Yukawa potential, the δ-potential, which describes coherent structures in a plasma. For such potentials we obtained a dispersion relation which makes it possible to estimate the size and type of the forming structures.

Thin current sheets of sub-ion scales observed in planetary magnetotails

<p>Current sheets (CSs) play a crucial role in the storage and conversion of magnetic energy in planetary magnetotails. Spacecraft observations in the terrestrial magnetotail reported that the CS thinning and intensification can result in formation of multiscale current structure in which a very thin and intense current layer at the center of the CS is embedded into a thicker sheet. To describe such CSs fully kinetic description taking into account all peculiarities of non-adiabatic particle dynamics is required. Kinetic description brings kinetic scales to the CS models. Ion scales are controlled by thermal ion Larmor radius, while scales of sub-ion embedded CS are controlled by the topology of magnetic field lines until the electron motion is magnetized by a small component of the magnetic field existing in a very center of the CS. MMS observations in the Earth magnetotail as well as MAVEN observations in the Martian magnetotail with high time resolution revealed the formation of similar multiscale structure of the cross-tail CS in spite of very different local plasma characteristics. We revealed that the typical half‐thickness of the embedded Super Thin Current Sheet (STCSs) observed at the center of the CS in the magnetotails of both planets is much less than the gyroradius of thermal protons. The formation of STCS does not depend on ion composition, density and temperature,  but it is controlled by the small value of the normal component of the magnetic field at the neutral plane. Our analysis showed that there is a good agreement between the spatial scaling of multiscale CSs observed in both magnetotails and the scaling predicted by the quasi-adiabatic model of thin anisotropic CS taking into account the coupling between ion and electron currents. Thus, in spite of the significant differences in the CS formation, ion composition, and plasma characteristics in the Earth’s and Martian magnetotails, similar kinetic features are observed in the CS structures in the magnetotails of both planets. This phenomenon can be explained by the universal principles of nature. The CS once has been formed, then it should be self-consistently supported by the internal coupling of the total current carried by particles in the CS and its magnetic configuration, and as soon as the system achieved the quasi-equilibrium state, it “forgets” the mechanisms of its formation, and its following existence is ruled by the general principles of plasma kinetic described by Vlasov–Maxwell equations.</p><p>This work is supported by the Russian Science Foundation grant № 20-42-04418</p>

Kinetic description of site ensembles on catalytic surfaces

We demonstrate that the Langmuir–Hinshelwood formalism is an incomplete kinetic description and, in particular, that the Hinshelwood assumption (i.e., that adsorbates are randomly distributed on the surface) is inappropriate even in catalytic reactions as simple as A + A → A2. The Hinshelwood assumption results in miscounting of site pairs (e.g., A*–A*) and, consequently, in erroneous rates, reaction orders, and identification of rate-determining steps. The clustering and isolation of surface species unnoticed by the Langmuir–Hinshelwood model is rigorously accounted for by derivation of higher-order rate terms containing statistical factors specific to each site ensemble. Ensemble-specific statistical rate terms arise irrespective of and couple with lateral adsorbate interactions, are distinct for each elementary step including surface diffusion events (e.g., A* + * → * + A*), and provide physical insight obscured by the nonanalytical nature of the kinetic Monte Carlo (kMC) method—with which the higher-order formalism quantitatively agrees. The limitations of the Langmuir–Hinshelwood model are attributed to the incorrect assertion that the rate of an elementary step is the same with respect to each site ensemble. In actuality, each elementary step—including adsorbate diffusion—traverses through each ensemble with unique rate, reversibility, and kinetic-relevance to the overall reaction rate. Explicit kinetic description of ensemble-specific paths is key to the improvements of the higher-order formalism; enables quantification of ensemble-specific rate, reversibility, and degree of rate control of surface diffusion; and reveals that a single elementary step can, counter intuitively, be both equilibrated and rate determining.

On the derivation of the wave kinetic equation for NLS

A fundamental question in wave turbulence theory is to understand how the wave kinetic equation describes the long-time dynamics of its associated nonlinear dispersive equation. Formal derivations in the physics literature, dating back to the work of Peierls in 1928, suggest that such a kinetic description should hold (for well-prepared random data) at a large kinetic time scale $T_{\mathrm {kin}} \gg 1$ and in a limiting regime where the size L of the domain goes to infinity and the strength $\alpha $ of the nonlinearity goes to $0$ (weak nonlinearity). For the cubic nonlinear Schrödinger equation, $T_{\mathrm {kin}}=O\left (\alpha ^{-2}\right )$ and $\alpha $ is related to the conserved mass $\lambda $ of the solution via $\alpha =\lambda ^2 L^{-d}$ . In this paper, we study the rigorous justification of this monumental statement and show that the answer seems to depend on the particular scaling law in which the $(\alpha , L)$ limit is taken, in a spirit similar to how the Boltzmann–Grad scaling law is imposed in the derivation of Boltzmann’s equation. In particular, there appear to be two favourable scaling laws: when $\alpha $ approaches $0$ like $L^{-\varepsilon +}$ or like $L^{-1-\frac {\varepsilon }{2}+}$ (for arbitrary small $\varepsilon $ ), we exhibit the wave kinetic equation up to time scales $O(T_{\mathrm {kin}}L^{-\varepsilon })$ , by showing that the relevant Feynman-diagram expansions converge absolutely (as a sum over paired trees). For the other scaling laws, we justify the onset of the kinetic description at time scales $T_*\ll T_{\mathrm {kin}}$ and identify specific interactions that become very large for times beyond $T_*$ . In particular, the relevant tree expansion diverges absolutely there. In light of those interactions, extending the kinetic description beyond $T_*$ toward $T_{\mathrm {kin}}$ for such scaling laws seems to require new methods and ideas.

Boltzmann-type equations for multi-agent systems with label switching

<p style='text-indent:20px;'>In this paper, we propose a Boltzmann-type kinetic description of mass-varying interacting multi-agent systems. Our agents are characterised by a microscopic state, which changes due to their mutual interactions, and by a label, which identifies a group to which they belong. Besides interacting within and across the groups, the agents may change label according to a state-dependent Markov-type jump process. We derive general kinetic equations for the joint interaction/label switch processes in each group. For prototypical birth/death dynamics, we characterise the transient and equilibrium kinetic distributions of the groups via a Fokker-Planck asymptotic analysis. Then we introduce and analyse a simple model for the contagion of infectious diseases, which takes advantage of the joint interaction/label switch processes to describe quarantine measures.</p>