Nikolai V. Brilliantov

We introduce a physics-informed method for finding numerical solutions of large systems of equations governing aggregation kinetics. The method enables accurate reconstruction of density distributions for both large and small clusters, with notable improvements for small cluster sizes, as compared to previous numerical approaches. The efficiency and accuracy are improved by restricting the physics-informed loss to a small interval, enabling long time horizons with minimal extra computational cost. The superiority of the method has been demonstrated for basic aggregation kernels – constant, additive, multiplicative and generalised Brownian kernel, showing that one simple neural architecture can be used for four distinct kernels. In addition to numerical examples, we provide rigorous mathematical justification for the approach and derive relevant analytical error bounds. Combined high efficiency and low error margins of the method indicate strong potential for long-term prediction and integration into broader computational systems.

Selectors are non-linear elements used in memristor circuits. We explore a Ti/TiO2/Ti selector as part of a one-selector–one-resistor memristor for high-density crossbar arrays. The Ti/TiO2/Ti stack is fabricated using magnetron sputtering and e-gun thermal evaporation. Selectors fabricated via magnetron sputtering consistently exhibit non-linear behavior, with a non-linearity coefficient reaching 6.2 at a low operating voltage (0.5 V), stable performance at high current, and a fabrication compatible with the standard silicon technology. The observed non-linearity can be explained by the combination of electron trapping/detrapping with an excitation energy of ∼0.3 eV. In contrast, selectors fabricated using e-gun thermal evaporation have history-dependent voltage-controlled negative differential resistance. Later, their behavior evolves into a non-linear rectifying I–V curve. This phenomenon can be attributed to the evolution of the oxygen vacancies in TiO2.

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 atomistic simulations by 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. Published by the American Physical Society 2024

We analyze the pattern formation in systems of active particles with chiral forces in the context of pedestrian dynamics. To describe the interparticle interactions, we use the standard social force model and supplement it with a new type of force that reflects chirality. We perform numerical simulations of two pedestrian flows moving in opposite directions along a corridor. We observe two dynamic phase transitions that occur for varying number densities of particles and strengths of the chirality force: one from disordered motion to multi-lane motion and another from multi-lane to two-lane motion. We develop a qualitative theory that describes the demarcation lines for these phase transitions in the phase diagram chirality-density. The results of our analysis agree fairly well with the simulation data. A comparison with previously reported experimental data has been provided. Our findings may find applications in urban and transportation-planning problems.