Related papers: Long-time behaviour of rouleau formation models
Gelation in the Smoluchowski coagulation equation is commonly interpreted as a finite-time singularity marked by mass loss or moment divergence. We instead characterize gelation as a loss of dynamical stability of the Smoluchowski flow,…
We consider the long time behavior of solutions to a nonlocal reaction diffusion equation that arises in the study of directed polymers. The model is characterized by convolution with a kernel $R$ and an $L^2$ inner product. In one spatial…
We study the rheological response at low temperature of a sheared model disordered material as a function of the bond rigidity. We find that the flow curves follow a Herschel-Bulkley law, whatever is the bond rigidity, with an exponent…
This article investigates the properties of the solutions of the dispersionless two-component Burgers (B2) equation, derived as a model for blood-flow in arteries with elastic walls. The phenomenon of wave breaking is investigated as well…
We study the behaviour as $t\to\infty$ of solutions $(c_j(t))$ to the Redner--Ben-Avraham--Kahng coagulation system with positive and compactly supported initial data, rigorously proving and slightly extending results originally established…
We investigate irreversible aggregation processes driven by a source of small mass clusters. In the spatially homogeneous situation, a well-mixed system is consists of clusters of various masses whose concentrations evolve according to an…
We show that solutions to Smoluchowski's equation with a constant coagulation kernel and an initial datum with some regularity and exponentially decaying tail converge exponentially fast to a self-similar profile. This convergence holds in…
We introduce an extended Smoluchowski equation describing coagulation processes for which clusters of mass s grow between collisions with $ds/dt=As^\beta$. A physical example, dropwise condensation is provided, and its collision kernel K is…
Two typical morphology of two-dimensional aggregates are considered: compact crystalline clusters and string-like non-compact conformations. Simulated trajectories of both types of aggregates are analysed with fine spatial resolution. While…
This article is devoted to a generalized version of Smoluchowski's coagulation equation. This model describes the time evolution of a system of aggregating particles under the effect of external input and output particles. We show that for…
In this paper we study the fundamental solution of the equation obtained by the linearisation of the Smoluchowski coagulation equation with the multiplicative kernel $(x y)^{\lambda/2}$ with $\lambda\in (1, 2)$ around the steady state…
Mixing describes the process by which solutes evolve from an initial heterogeneous state to uniformity under the stirring action of a fluid flow. Fluid stretching forms thin scalar lamellae which coalesce due to molecular diffusion. Owing…
We study a spatial Markovian particle system with pairwise coagulation, a spatial version of the Marcus--Lushnikov process: according to a coagulation kernel $K$, particle pairs merge into a single particle, and their masses are united. We…
The paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete, and the binary aggregation alone governs the time evolution of the systems. By considering the growth…
In this paper, we establish smoothness of moments of the solutions of discrete coagulation-diffusion systems. As key assumptions, we suppose that the coagulation coefficients grow at most sub-linearly and that the diffusion coefficients…
We take into account a coagulation model that simulates a distinct kind of dynamics. In this model, two particles collide to produce a single particle, but the resulting particle decreases in size, allowing each particle to be fully…
In this paper, we investigate the use of so called "duality lemmas" to study the system of discrete coagulation-fragmentation equations with diffusion. When the fragmentation is strong enough with respect to the coagulation, we show that we…
Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic…
This manuscript studies the numerical solution of the time-fractional Burgers-Huxley equation in a reproducing kernel Hilbert space. The analytical solution of the equation is obtained in terms of a convergent series with easily computable…
By means of molecular dynamics, we study a model system for colloidal suspensions where the interaction is based on a competition between attraction and repulsion. At low temperatures the relaxation time $\tau$ first increases as a power…