arXiv subjects

Nikolai Brilliantov

Publications and source records attributed to Nikolai Brilliantov.

15 recordsLinked to original sources

arXiv2026

Investigation of filamentation in a-Si/Ag/Cu memristors with atomic force microscope

Cation-based Ag/Cu filaments formed in an insulating $α$-Si matrix are widely used as memristors in crossbar arrays for efficient in-memory computing. However, the stochastic nature of filament formation and rupture gives rise to device-to-device and cycle-to-cycle variation. Despite successful implementation of large-scale memristor arrays, systematic studies of filament parameters and their spatial distribution in the memristors are scarce. In this work, we use conductive atomic force microscopy (c-AFM) to probe the spatial distribution of conductive filaments in $α$-Si memristors. The charge transport is dominated by a limited number of discrete filaments rather than by uniform conduction across the device area. The systematic analysis of the experiment gives the mean surface density of the conductive filaments $\sim$3200 per $μ\text{m}^2$. Both volatile and non-volatile filaments can be found within one memristor. The experimental data and the nature of volatile and non-volatile filaments may be explained within the model of multiple trap assisted tunnelling. The model yields reasonable estimates for physical properties for both types of filaments.

cond-mat.mtrl-sci↗

arXiv2024

Physics-informed neural networks for aggregation kinetics

We introduce a novel physics-informed approach for accurately modeling aggregation kinetics which provides a comprehensive solution in a single run by outputting all model parameters simultaneously, a clear advancement over traditional single-output networks that require multiple executions. This method effectively captures the density distributions of both large and small clusters, showcasing a notable improvement in predicting small particles, which have historically posed challenges in computational models. This approach yields significant advancements in computational efficiency and accuracy for solving the Smoluchowski equations by minimizing the interval over which the physics-informed loss function operates, allowing for efficient computation over extended time-frames with minimal increase in computational cost. Due to the the independence of predefined shapes for bias or weight outputs, it removes the dependency on prior assumptions about output structures. Furthermore, our physics-informed framework exhibits high compatibility with the generalized Brownian kernel, maintaining robust accuracy for this previously unaddressed kernel type. The framework's notable novelty also lies in addressing four different kernels with one neural network architecture. Therefore with high computational efficiency, combined with low error margins it indicates significant potential for long-term predictions and integration into broader computational systems.

math.DS↗

arXiv2021

Collision fragmentation of aggregates. The role of the interaction potential between comprising particles

We investigate disruptive collisions of aggregates comprised of particles with different interaction potentials. We study Lennard-Jones (L-J), Tersoff, modified L-J potential and the one associated with Johnson-Kendall-Roberts (JKR) model. These refer to short, middle and long-ranged inter-particle potentials and describe both inter-atomic interactions and interactions of macroscopic adhesive bodies. We perform comprehensive molecular dynamics simulations and observe for all four potentials power-law dependencies for the size distribution of collision fragments and for their size-velocity correlation. We introduce a new fragmentation characteristic -- the shattering degree $S$, quantifying the fraction of monomers in debris and reveal its universal behavior. Namely, we demonstrate that for all potentials, $1-S$ is described by a universal function of the impact velocity. Using the above results, we perform the impact classification and construct the respective collision phase diagram. Finally, we present a qualitative theory that explains the observed scaling behavior.

cond-mat.mes-hall↗

arXiv2016

Regimes of strong electrostatic collapse of a highly charged polyelectrolyte in a poor solvent

We perform extensive molecular dynamics simulations of a highly charged flexible polyelectrolyte (PE) chain in a poor solvent for the case when the chain is in a collapsed state and the electrostatic interactions, characterized by the reduced Bjerrum length $\ell_B$, are strong. We detect the existence of several sub-regimes, $R_g \sim \ell_B^{-γ}$, in the dependence of the gyration radius of the chain $R_g$ on $\ell_B$. In contrast to a good solvent, the exponent $γ$ for a poor solvent crucially depends on the size and valency of counterions. To explain the different sub-regimes we generalize the existing counterion fluctuation theory by a more complete account of the volume interactions in the free energy of the chain. These include interactions between the chain monomers, between monomers and counterions and the counterions themselves. We also demonstrate that the presence of the condensed counterions can modify the effective attraction among the chain monomers and impact the sign of the second virial coefficient.

cond-mat.soft↗

arXiv2015

Size distribution of particles in Saturn's rings from aggregation and fragmentation

Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative inter-particle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, $\sim r^{-q}$ with $q \approx 3$, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent $q$ to be constrained to the interval $2.75 \le q \le 3.5$. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff-radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of micro-structures seen in Saturn's rings.

astro-ph.EP↗

arXiv2015

Smoluchowski aggregation-fragmentation equations: Fast numerical algorithm for steady-state solution

We propose an efficient and fast numerical algorithm of finding a \emph{stationary} solution of large systems of aggregation-fragmentation equations of Smoluchowski type for concentrations of reacting particles. This method is applicable when the stationary concentrations steeply decreases with increasing aggregate size, which is fulfilled for the most important cases. We show that under rather mild restrictions, imposed on the kernel of the Smoluchowski equation, the following numerical procedure may be used: First, a complete solution for a relatively small number of equations (a "seed system") is generated and then the result is exploited in a fast iterative scheme. In this way the new algorithm allows to obtain a steady-state solution for rather large systems of equations, by orders of magnitude faster than the standard schemes.

physics.comp-ph↗

arXiv2013

Velocity distribution function and effective constant restitution coefficient for granular gas of viscoelastic particles

We perform large-scale event-driven Molecular dynamics (MD) simulations for granular gases of particles interacting with the impact-velocity dependent restitution coefficient. We use the simplest first-principle collision model of viscoelastic spheres. Both cases of force-free and uniformly heated gases are studied. We formulate a simplified model of an effective constant restitution coefficient, which depends on a current granular temperature and compute the effective constant restitution coefficient, using the kinetic theory. We develop a theory of the velocity distribution function for driven gases of viscoelastic particles and analyze evolution of granular temperature and of the Sonine coefficients, which characterize the form of the velocity distribution function. We observe that for not large dissipation the simulation results are in an excellent agreement with the theory for both, homogeneous cooling state and uniformly heated gases. At the same time a noticeable discrepancy between the theory and MD results for the Sonine coefficients is detected for large dissipation. We analyze the accuracy of the simplified model, based on the effective restitution coefficient and conclude that this model can accurately describe granular temperature. It provides also an acceptable accuracy for the velocity distribution function for small dissipation, but fails when dissipation is large.

cond-mat.stat-mech↗

arXiv2012

Intermediate regimes in granular Brownian motion: Superdiffusion and subdiffusion

Brownian motion in a granular gas in a homogeneous cooling state is studied theoretically and by means of molecular dynamics. We use the simplest first-principle model for the impact-velocity dependent restitution coefficient, as it follows for the model of viscoelastic spheres. We reveal that for a wide range of initial conditions the ratio of granular temperatures of Brownian and bath particles demonstrates complicated non-monotonous behavior, which results in transition between different regimes of Brownian dynamics: It starts from the ballistic motion, switches later to superballistic one and turns at still later times into subdiffusion; eventually normal diffusion is achieved. Our theory agrees very well with the MD results, although extreme computational costs prevented to detect the final diffusion regime. Qualitatively, the reported intermediate diffusion regimes are generic for granular gases with any realistic dependence of the restitution coefficient on the impact velocity.

cond-mat.stat-mech↗

arXiv2012

Self-diffusion in granular gases: An impact of particles' roughness

An impact of particles' roughness on the self-diffusion coefficient in granular gases is investigated. For a simplified collision model where the normal and tangential restitution coefficients are assumed to be constant we develop an analytical theory for the diffusion coefficient, which takes into account non-Maxwellain form of the velocity-angular velocity distribution function. We perform molecular dynamics simulations for a gas in a homogeneous cooling state and study the dependence of the self-diffusion coefficient on restitution coefficients. Our theoretical results are in a good agreement with the simulation data.

cond-mat.stat-mech↗

arXiv2006

Impact of high-energy tails on granular gas properties

The velocity distribution function of granular gases in the homogeneous cooling state as well as some heated granular gases decays for large velocities as $f\propto\exp(- {\rm const.} v)$. That is, its high-energy tail is overpopulated as compared with the Maxwell distribution. At the present time, there is no theory to describe the influence of the tail on the kinetic characteristics of granular gases. We develop an approach to quantify the overpopulated tail and analyze its impact on granular gas properties, in particular on the cooling coefficient. We observe and explain anomalously slow relaxation of the velocity distribution function to its steady state.

cond-mat.stat-mech↗

arXiv2005

Rolling friction and bistability of rolling motion

The rolling motion of a rigid cylinder on an inclined flat viscous surface is investigated and the nonlinear resistance force against rolling, $F_R(v)$, is derived. For small velocities $F_R(v)$ increases with velocity due to increasing deformation rate of the surface material. For larger velocity it decreases with velocity due to decreasing contact area between the rolling cylinder and the deformed surface. The cylinder is, moreover, subjected to a viscous drag force and stochastic fluctuations due to a surrounding medium (air). For this system, in a wide range of parameters we observe bistability of the rolling motion. Depending on the material parameters, increasing the noise level may lead to increasing or decreasing average velocity.

cond-mat.mtrl-sci↗

arXiv2004

Transient structures in a Granular Gas

A force-free granular gas is considered with impact-velocity dependent coefficient of restitution as it follows from the model of viscoelastic particles. We analyze structure formation in this system by means of three independent methods: Molecular Dynamics, numerical solution of the hydrodynamic equations and linear stability analysis of these equations. All these approaches indicate that structure formation occurs in force-free granular gases only as a transient process.

cond-mat.stat-mech↗

arXiv2003

Hydrodynamics and transport coefficients for Granular Gases

The hydrodynamics of granular gases of viscoelastic particles, whose collision is described by an impact-velocity dependent coefficient of restitution, is developed using a modified Chapman-Enskog approach. We derive the hydrodynamic equations and the according transport coefficients with the assumption that the shape of the velocity distribution function follows adiabatically the decaying temperature. We show numerically that this approximation is justified up to intermediate dissipation. The transport coefficients and the coefficient of cooling are expressed in terms of the elastic and dissipative parameters of the particle material and by the gas parameters. The dependence of these coefficients on temperature differs qualitatively from that obtained with the simplifying assumption of a constant coefficient of restitution which was used in previous studies. The approach formulated for gases of viscoelastic particles may be applied also for other impact-velocity dependencies of the restitution coefficient.

cond-mat.stat-mech↗

arXiv1998

Effective Magnetic Hamiltonian and Ginzburg Criterion for Fluids

We develop further the approach of Hubbard and Schofield (Phys.Lett., A40 (1972) 245), which maps the fluid Hamiltonian onto a magnetic one. We show that all coefficients of the resulting effective Landau-Ginzburg-Wilson (LGW) Hamiltonian may be expressed in terms of the compressibility of a reference fluid containing only repulsive interactions, and its density derivatives; we calculate the first few coefficients in the case of the hard-core reference fluid. From this LGW-Hamiltonian we deduce approximate mean-field relations between critical parameters and test them on data for Lennard-Jones, square-well and hard-core-Yukawa fluids. We estimate the Ginzburg criterion for these fluids.

cond-mat.stat-mech↗

arXiv1996

Nonstationary Transport by Internal White Noise and "Localization" in Ratchets

We revealed a right-left asymmetry of the inter-well mean first passage times for the Brownian particles in a ratchet potential under internal white noise. We showed analytically and numerically that this asymmetry gives rise to the following phenomena: (i) nonstationary transport; (ii) localization or ultraslow (Sinai) diffusion for ratchets with a disorder in the asymmetry parameter of the potential; (iii) equilibrium "drift of labels" in circular ratchets.

cond-mat↗