arXiv subjects

S. A. Matveev

Publications and source records attributed to S. A. Matveev.

5 recordsLinked to original sources

arXiv2026

Generating functions for aggregation and fragmentation: review

In this work, we review and revisit the generating function techniques that provide exact analytical solutions for aggregation and fragmentation equations across several physical regimes including spontaneous and collisonal shattering. For discrete coagulation-fragmentation equations with size-independent rates under monodisperse initial conditions, we show the derivation of sevaral explicit closed-form solutions. We also briefly report the exact solutions for continuous, three-particle, $D$-particle collisions and two-component generalizations. Source-driven aggregation yields steady distributions featuring a universal $s^{-3/2}$ power-law decay and a cutoff mass scaling $s_{*} \sim t^{2}$.

math.DS↗

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

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↗

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↗

arXiv1998

Internal Time Peculiarities as a Cause of Bifurcations Arising in Classical Trajectory Problem and Quantum Chaos Creation in Three-Body System

A new formulation of the theory of quantum mechanical multichannel scattering for three-body collinear systems is proposed. It is shown, that in this simple case the principle of quantum determinism in the general case breaks down and we have a micro-irreversible quantum mechanics. The first principle calculations of the quantum chaos (wave chaos) were pursued on the example of an elementary chemical reaction Li+(FH)->(LiFH)*->(LiF)+H.

quant-ph↗