arXiv subjects

N. V. Brilliantov

Publications and source records attributed to N. V. Brilliantov.

At least 19 recordsLinked to original sources

arXiv2024

Lane formation in an active particle model with chirality for pedestrian traffic

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.

cond-mat.stat-mech↗

arXiv2023

Application of machine learning technique for a fast forecast of aggregation kinetics in space-inhomogeneous systems

Modeling of aggregation processes in space-inhomogeneous systems is extremely numerically challenging since complicated aggregation equations -- Smoluchowski equations are to be solved at each space point along with the computation of particle propagation. Low rank approximation for the aggregation kernels can significantly speed up the solution of Smoluchowski equations, while particle propagation could be done in parallel. Yet the simulations with many aggregate sizes remain quite resource-demanding. Here, we explore the way to reduce the amount of direct computations with the use of modern machine learning (ML) techniques. Namely, we propose to replace the actual numerical solution of the Smoluchowki equations with the respective density transformations learned with the application of the conditional normalising flow. We demonstrate that the ML predictions for the space distribution of aggregates and their size distribution requires drastically less computation time and agrees fairly well with the results of direct numerical simulations. Such an opportunity of a quick forecast of space-dependent particle size distribution could be important in practice, especially for the online prediction and visualisation of pollution processes, providing a tool with a reasonable tradeoff between the prediction accuracy and the computational time.

physics.comp-ph↗

arXiv2023

Steady oscillations in aggregation-fragmentation processes

We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are observed for the class of aggregation kernels $K_{i,j} = i^νj^μ + j^νi^μ$ homogeneous in masses $i$ and $j$ of merging clusters and fragmentation kernels, $F_{ij}=λK_{ij}$, with parameter $λ$ quantifying the intensity of the disruptive impacts. We assume a complete decomposition (shattering) of colliding partners into monomers. We show that an assumption of a steady-state distribution of cluster sizes, compatible with governing equations, yields a power law with an exponential cutoff. This prediction agrees with simulations results when $ θ\equiv ν-μ<1$. For $ θ=ν-μ>1$, however, the densities exhibit an oscillatory behavior. While these oscillations decay for not very small $λ$, they become steady if $θ$ is close to two and $λ$ is very small. Simulation results lead to a conjecture that for $ θ<1$ the system has a stable fixed point, corresponding to the steady-state density distribution, while for any $θ>1 $ there exists a critical value $λ_c(θ)$, such that for $λ< λ_c(θ)$, the system has an attracting limit cycle. This is rather striking for a closed system of Smoluchowski-like equations, lacking any sinks and sources of mass.

cond-mat.stat-mech↗

arXiv2021

Anomalous aggregation regimes of temperature-dependent Smoluchowski equations

Temperature-dependent Smoluchowski equations describe the ballistic agglomeration. In contrast to the standard Smoluchowski equations for the evolution of cluster densities with constant rate coefficients, the temperature-dependent equations describe both -- the evolution of the densities as well as cluster temperatures, which determine the aggregation rates. To solve these equations, we develop a novel Monte Carlo technique based on the low-rank approximation for the aggregation kernel. Using this highly effective approach, we perform a comprehensive study of the phase diagram of the system and reveal a few surprising regimes, including permanent temperature growth and "density separation", with a large gap in the size distribution for middle-size clusters. We perform classification of the aggregation kernels for the temperature-dependent equations and conjecture the lack of gelation. The results of our scaling analysis agree well with the simulation data.

cond-mat.stat-mech↗

arXiv2021

Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics

We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We test the performance and accuracy of the extended methods and compare their performance with efficient deterministic finite-difference method applied to the same model. We validate the stochastic methods on the test problems and apply them to verify the existence of oscillating regimes in the aggregation-fragmentation kinetics recently detected in deterministic simulations. We confirm the emergence of steady oscillations of densities in such systems and prove the stability of the oscillations with respect to fluctuations and noise.

math.NA↗

arXiv2020

The role of energy in ballistic agglomeration

We study a ballistic agglomeration process in the reaction-controlled limit. Cluster densities obey an infinite set of Smoluchowski rate equations, with rates dependent on the average particle energy. The latter is the same for all cluster species in the reaction-controlled limit and obeys an equation depending on densities. We express the average energy through the total cluster density that allows us to reduce the governing equations to the standard Smoluchowski equations. We derive basic asymptotic behaviors and verify them numerically. We also apply our formalism to the agglomeration of dark matter.

cond-mat.stat-mech↗

arXiv2017

Phase Transitions in Systems with Aggregation and Shattering

We consider a system of clusters made of elementary building blocks, monomers, and evolving via collisions between diffusing monomers and immobile composite clusters. In our model, the cluster-monomer collision can lead to the attachment of the monomer to the cluster (addition process) or to the total break-up of the cluster (shattering process). A phase transition, separating qualitatively different behaviors, occurs when the probability of shattering events exceeds a certain threshold. The novel feature of the phase transition is the dramatic dependence on the initial conditions.

cond-mat.stat-mech↗

arXiv2017

Oscillations in aggregation-shattering processes

We observe never-ending oscillations in systems undergoing aggregation and collision-controlled shattering. Specifically, we investigate aggregation-shattering processes with aggregation kernels K_{i,j} = (i/j)^a+(j/i)^a and shattering kernels F_{i,j}=λK_{i,j}, where i and j are cluster sizes and parameter λquantifies the strength of shattering. When 0<a<1/2, there are no oscillations and the system monotonically approaches to a steady state for all values of λ; in this region we obtain an analytical solution for the stationary cluster size distribution. Numerical solutions of the rate equations show that oscillations emerge in the 1/2<a<1 range. When the shattering rate is sufficiently large oscillations decay and eventually disappear, while for λ<λ_c(a) oscillations apparently persist forever. Thus never-ending oscillations can arise in closed aggregation-shattering processes without sinks and sources of particles.

cond-mat.stat-mech↗

arXiv2016

Generation of mechanical force by grafted polyelectrolytes in an electric field. Application to polyelectrolyte-based nano-devices

We analyze theoretically and by means of molecular dynamics (MD) simulations the generation of mechanical force by a polyelectrolyte (PE) chain grafted to a plane. The PE is exposed to an external electric field that favors its adsorption on the plane. The free end of the chain is linked to a deformable target body. Varying the field one can alter the length of the non-adsorbed part of the chain. This entails variation of the deformation of the target body and hence variation of the arising in the body force. Our theoretical predictions for the generated force are in a very good agreement with the MD data. Using the developed theory for the generated force we study the effectiveness of possible PE-based nano-vices, comprised of two clenching planes connected by PEs and exposed to an external electric field. We exploit Cundall-Struck solid friction model to describe the friction between a particle and the clenching planes. We compute the self-diffusion coefficient of a clenched particle and show that it drastically decreases even in weak applied fields. This demonstrates the efficacy of the PE-based nano-vices, which may be a a possible alternative to the existing nano-tube nano-tweezers and optical tweezers.

cond-mat.soft↗

arXiv2016

Generation of mechanical force by grafted polyelectrolytes in an electric field

We study theoretically and by means of molecular dynamics (MD) simulations the generation of mechanical force by grafted polyelectrolytes in an external electric field, which favors its adsorption on the grafting plane. The force arises in deformable bodies linked to the free end of the chain. Varying the field, one controls the length of the non-adsorbed part of the chain and hence the deformation of the target body, i.e., the arising force too. We consider target bodies with a linear force-deformation relation and with a Hertzian one. While the first relation models a coiled Gaussian chain, the second one describes the force response of a squeezed colloidal particle. The theoretical dependencies of generated force and compression of the target body on applied field agree very well with the results of MD simulations. The analyzed phenomenon may play an important role in a future nano-machinery, e.g. it may be used to design nano-vices to fix nano-sized objects.

cond-mat.soft↗

arXiv2013

Non-Fickian Diffusion and the Accumulation of Methane Bubbles in Deep-Water Sediments

In the absence of fractures, methane bubbles in deep-water sediments can be immovably trapped within a porous matrix by surface tension. The dominant mechanism of transfer of gas mass therefore becomes the diffusion of gas molecules through porewater. The accurate description of this process requires non-Fickian diffusion to be accounted for, including both thermodiffusion and gravitational action. We evaluate the diffusive flux of aqueous methane considering non-Fickian diffusion and predict the existence of extensive bubble mass accumulation zones within deep-water sediments. The limitation on the hydrate deposit capacity is revealed; too weak deposits cannot reach the base of the hydrate stability zone and form any bubbly horizon.

cond-mat.stat-mech↗

arXiv2011

A Statistical Model of Aggregates Fragmentation

A statistical model of fragmentation of aggregates is proposed, based on the stochastic propagation of cracks through the body. The propagation rules are formulated on a lattice and mimic two important features of the process -- a crack moves against the stress gradient and its energy depletes as it grows. We perform numerical simulations of the model for two-dimensional lattice and reveal that the mass distribution for small and intermediate-size fragments obeys a power-law, F(m)\propto m^(-3/2), in agreement with experimental observations. We develop an analytical theory which explains the detected power-law and demonstrate that the overall fragment mass distribution in our model agrees qualitatively with that, observed in experiments.

cond-mat.stat-mech↗

arXiv2009

Granular gas of viscoelastic particles in a homogeneous cooling state

Kinetic properties of a granular gas of viscoelastic particles in a homogeneous cooling state are studied analytically and numerically. We employ the most recent expression for the velocity-dependent restitution coefficient for colliding viscoelastic particles, which allows to describe systems with large inelasticity. In contrast to previous studies, the third coefficient a3 of the Sonine polynomials expansion of the velocity distribution function is taken into account. We observe a complicated evolution of this coefficient. Moreover, we find that a3 is always of the same order of magnitude as the leading second Sonine coefficient a2; this contradicts the existing hypothesis that the subsequent Sonine coefficients a2, a3 ..., are of an ascending order of a small parameter, characterizing particles inelasticity. We analyze evolution of the high-energy tail of the velocity distribution function. In particular, we study the time dependence of the tail amplitude and of the threshold velocity, which demarcates the main part of the velocity distribution and the high-energy part. We also study evolution of the self-diffusion coefficient D and explore the impact of the third Sonine coefficient on the self-diffusion. Our analytical predictions for the third Sonine coefficient, threshold velocity and the self-diffusion coefficient are in a good agreement with the numerical finding.

cond-mat.stat-mech↗

arXiv2008

Correlation of spin and velocity in granular gases

In a granular gas of rough particles the spin of a grain is correlated with its linear velocity. We develop an analytical theory to account for these correlations and compare its predictions to numerical simulations, using Direct Simulation Monte Carlo as well as Molecular Dynamics. The system is shown to relax from an arbitrary initial state to a quasi-stationary state, which is characterized by time-independent, finite correlations of spin and linear velocity. The latter are analysed systematically for a wide range of system parameters, including the coefficients of tangential and normal restitution as well as the moment of inertia of the particles. For most parameter values the axis of rotation and the direction of linear momentum are perpendicular like in a sliced tennis ball, while parallel orientation, like in a rifled bullet, occurs only for a small range of parameters. The limit of smooth spheres is singular: any arbitrarily small roughness unavoidably causes significant translation-rotation correlations, whereas for perfectly smooth spheres the rotational degrees of freedom are completely decoupled from the dynamic evolution of the gas.

cond-mat.stat-mech↗

arXiv2002

Surface tension of liquids near the critical point

A simple analytical microscopic expression for the surface tension of liquids $γ$ is obtained which is in a good agreement with available data of numerical experiments. We apply the integral transformation that maps the fluid Hamiltonian onto the field-theoretical Hamiltonian and show that the order parameter of the effective Hamiltonian corresponds to the one-body potential in the fluid. Revealing the physical meaning of the order parameter allows calculation of $γ$.

cond-mat.soft↗

arXiv1998

Polydisperse Adsorption: Pattern Formation Kinetics, Fractal Properties, and Transition to Order

We investigate the process of random sequential adsorption of polydisperse particles whose size distribution exhibits a power-law dependence in the small size limit, $P(R)\sim R^{α-1}$. We reveal a relation between pattern formation kinetics and structural properties of arising patterns. We propose a mean-field theory which provides a fair description for sufficiently small $α$. When $α\to \infty$, highly ordered structures locally identical to the Apollonian packing are formed. We introduce a quantitative criterion of the regularity of the pattern formation process. When $α\gg 1$, a sharp transition from irregular to regular pattern formation regime is found to occur near the jamming coverage of standard random sequential adsorption with monodisperse size distribution.

cond-mat.stat-mech↗

arXiv1998

Accurate first-principle equation of state for the One-Component Plasma

Accurate "first-principle" expressions for the excess free energy $F_{ex}$ and internal energy $U_{ex}$ of the classical one-component plasma (OCP) are obtained. We use the Hubbard-Schofield transformation that maps the OCP Hamiltonian onto the Ising-like Hamiltonian, with coefficients expressed in terms of equilibrium correlation functions of a reference system. We use the ideal gas as a reference system for which all the correlation functions are known. Explicit calculations are performed with the high-order terms in the Ising-like Hamiltonian omitted. For small values of the plasma parameter $Γ$ the Debye-Huckel result for $F_{ex}$ and $U_{ex}$ is recovered. For large $Γ$ these depend linearly on $Γ$ in accordance with the Monte Carlo findings for the OCP. The MC data for the internal energy are reproduced fairly well by the obtained analytical expression.

cond-mat.stat-mech↗

arXiv1998

Chain Collapse and Counterion Condensation in Dilute Polyelectrolyte Solutions

A new quantitative theory for polyelectrolytes in salt free dilute solutions is developed. Depending on the electrostatic interaction strength, polyelectrolytes in solutions can undergo strong stretching (with polyelectrolyte dimension R_g\sim l_B^{1/3}N, where l_B is the Bjerrum length and N is the number of the chain segments) or strong compression (with R_g\sim l_B^{-1/2}N^{1/3}). A strong polymer collapse occurs as a first-order phase transition due to accompanying counterion condensation.

cond-mat.soft↗