Related papers: The Smoluchowski Ensemble: Statistical Mechanics o…
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…
Smoluchowski's equation is a macroscopic description of a many particle system with coagulation and shattering interactions. We give a microscopic model of the system from which we derive this equation rigorously. Provided the existence of…
We present a detailed study of the statistics of a system of diffusing aggregating particles with a steady monomer source. We emphasise the case of low spatial dimensions where strong diffusive fluctuations invalidate the mean-field…
The paper compares the statistical description of physical-metallurgical processes and ceramic-polycrystalline evolutions, termed the normal grain growth (NGG), as adopted to soft- and chemically-reactive grains, with a Smoluchowski's…
This study shows that the generalized Boltzmann distribution is the only distribution mathematically consistent with thermodynamics when the system is described by an ensemble of a certain mathematical form. This mathematical form is very…
We consider the scaling solutions of Smoluchowski's equation of irreversible aggregation, for a non gelling collision kernel. The scaling mass distribution f(s) diverges as s^{-tau} when s->0. tau is non trivial and could, until now, only…
We study a coupled thermo-diffusion system that accounts for the dynamics of hot colloids in periodically heterogeneous media. Our model describes the joint evolution of temperature and colloidal concentrations in a saturated porous…
A notion of measure solution is formulated for a coagulation-diffusion equation, which is the natural counterpart of Smoluchowski's coagulation equation in a spatially inhomogeneous setting. Some general properties of such solutions are…
We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels $K(x,y)=2$, $x+y$…
In this article a stochastic particle system approximation to the parametric sensitivity in the Smoluchowski coagulation equation is introduced. The parametric sensitivity is the derivative of the solution to the equation with respect to…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
We consider Smoluchowski's coagulation equation with a kernel of the form $K = 2 + \epsilon W$, where $W$ is a bounded kernel of homogeneity zero. For small $\epsilon$, we prove that solutions approach a universal, unique self-similar…
We revisit the scaling theory of the Smoluchowski equation with special emphasis on the dimensional analysis to derive the scaling ansatz and to give an insightful foundation to it. It has long been argued that the homogeneity exponent…
The Smoluchowski coagulation equation (SCE) is a population balance model that describes the time evolution of cluster size distributions resulting from particle aggregation. Although it is formally a mass-conserving system, solutions may…
We consider two simple models for the formation of polymers where at the initial time, each monomer has a certain number of potential links (called arms in the text) that are consumed when aggregations occur. Loosely speaking, this imposes…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
We consider the classical Smoluchowski coagulation equation with a general frequency kernel. We show that there exists a natural deterministic solution expansion in the non-associative algebra generated by the convolution product of the…
The use of the isoconfigurational ensemble to explore structure-dynamic correlations in supercooled liquids is examined. The statistical error of the dynamic propensity and its spatial distribution are determined. The authors present the…
We study the solutions of the Smoluchowski coagulation equation with a regularisation term which removes clusters from the system when their mass exceeds a specified cut-off size, M. We focus primarily on collision kernels which would…
We study a generic model of self-assembling chains which can branch and form networks with branching points (junctions) of arbitrary functionality. The physical realizations include physical gels, wormlike micells, dipolar fluids and…