arXiv subjects

Nikolay Brilliantov

Publications and source records attributed to Nikolay Brilliantov.

5 recordsLinked to original sources

arXiv2024

Hydrodynamic equations for space-inhomogeneous aggregating fluids with first-principle kinetic coefficients

We derive from the first principles new hydrodynamic equations -- Smoluchowski-Euler equations for aggregation kinetics in space-inhomogeneous fluids with fluxes. Starting from Boltzmann equations, we obtain microscopic expressions for aggregation rates for clusters of different sizes and observe that they significantly differ from currently used phenomenological rates. Moreover, we show that for a complete description of aggregating systems, novel kinetic coefficients are needed. They share properties of transport and reaction-rate coefficients; for them we report microscopic expressions. For two representative examples -- aggregation of particles at sedimentation and aggregation after an explosion we numerically solve Smoluchowski-Euler equations and perform Direct Simulation Monte Carlo (DSMC). We find that while the new theory agrees well with DSMC results, a noticeable difference is observed for the phenomenological theory. This manifests the unreliability of the currently used phenomenological theory and the need to apply new, first-principle equations.

cond-mat.stat-mech↗

arXiv2023

Knowledge-Informed Neuro-Integrators for Aggregation Kinetics

We report a novel approach for the efficient computation of solutions of a broad class of large-scale systems of non-linear ordinary differential equations, describing aggregation kinetics. The method is based on a new take on the dimensionality reduction for this class of equations which can be naturally implemented by a cascade of small feed-forward artificial neural networks. We show that this cascade, of otherwise static models, is capable of predicting solutions of the original large-scale system over large intervals of time, using the information about the solution computed over much smaller intervals. The computational cost of the method depends very mildly on the temporal horizon, which is a major improvement over the current state-of-the-art methods, whose complexity increases super-linearly with the system's size and proportionally to the simulation time. In cases when prior information about the values of solutions over a relatively small interval of time is already available, the method's computational complexity does not depend explicitly on the system's size. The successful application of the new method is illustrated for spatially-homogeneous systems, with a source of monomers, for a number of the most representative reaction rates kernels.

math.NA↗

arXiv2022

Exact solutions of temperature-dependent Smoluchowski equations

We report a number of exact solutions for temperature-dependent Smoluchowski equations. These equations quantify the ballistic agglomeration, where the evolution of densities of agglomerates of different size is entangled with the evolution of the mean kinetic energy (partial temperatures) of such clusters. The obtained exact solutions may be used as a benchmark to assess the accuracy and computational efficiency of the numerical approaches, developed to solve the temperature-dependent Smoluchowski equations. Moreover, they may also illustrate the possible evolution regimes in these systems. The exact solutions have been obtained for a series of model rate coefficients, and we demonstrate that there may be an infinite number of such model coefficient which allow exact analysis. We compare our exact solutions with the numerical solutions for various evolution regimes; an excellent agreement between numerical and exact results proves the accuracy of the exploited numerical method.

cond-mat.stat-mech↗

arXiv2019

Temperature distribution in driven granular mixtures does not depend on mechanism of energy dissipation

We study analytically and numerically the distribution of granular temperatures in granular mixtures for different dissipation mechanisms of inelastic inter-particle collisions. Both driven and force-free systems are analyzed. We demonstrate that the simplified model of a constant restitution coefficient fails to predict even qualitatively a granular temperature distribution in a homogeneous cooling state. At the same time we reveal for driven systems a stunning result -- the distribution of temperatures in granular mixtures is universal. That is, it does not depend on a particular dissipation mechanism of inter-particles collisions, provided the size distributions of particles is steep enough. The results of the analytic theory are compared with simulation results obtained by the direct simulation Monte Carlo (DSMC). The agreement between the theory and simulations is perfect. The reported results may have important consequences for fundamental science as well as for numerous application, e.g. for the experimental modelling in a lab of natural processes.

cond-mat.soft↗

arXiv2014

Universality of temperature distribution in granular gas mixtures with a steep particle size distribution

Distribution of granular temperatures in granular gas mixtures is investigated analytically and numerically. We analyze space uniform systems in a homogeneous cooling state (HCS) and under a uniform heating with a mass-dependent heating rate $Γ_k\sim m_k^γ$. We demonstrate that for steep size distributions of particles the granular temperatures obey a universal power-law distribution, $T_k \sim m_k^α$, where the exponent $α$ does not depend on a particular form of the size distribution, the number of species and inelasticity of the grains. Moreover, $α$ is a universal constant for a HCS and depends piecewise linearly on $γ$ for heated gases. The predictions of our scaling theory agree well with the numerical results.

cond-mat.stat-mech↗