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The idealized general model of aggregate growth is considered on the basis of the simple additive rules that correspond to one-step aggregation process. The two idealized cases were analytically investigated and simulated by Monte Carlo…
We introduce a comprehensive numerical framework to generically infer the emergent macroscopic properties of uniaxial nematic and cholesteric phases from that of their microscopic constituent mesogens. This approach, based on the full…
Micro-organisms aggregate through chemotaxis against a concentration gradient of signals secreted by themselves. We have numerically studied a model consisting of elements with intracellular dynamics, random walks with a state-dependent…
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…
This work outlines an exact combinatorial approach to finite coagulating systems through recursive equations and use of generating function method. In the classic approach the mean-field Smoluchowski coagulation is used. However, the…
Colloidal particles can self-assemble into various ordered structures in fluid flows that have potential applications in biomedicine, materials synthesis and encryption. These dynamic processes are also of fundamental interest for probing…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
The capability to simulate a two-way coupled interaction between a rarefied gas and an arbitrary-shaped colloidal particle is important for many practical applications, such as aerospace engineering, lung drug deliver and semiconductor…
A system of stochastic differential equations describing diffusive phenomena, which has arbitrary friction depending on both state and distribution is investigated. The Smoluchowski-Kramers approximation is seen to describe dynamics in the…
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…
Porosity evolution of dust aggregates is crucial in understanding dust evolution in protoplanetary disks. In this study, we present useful tools to study the coagulation and porosity evolution of dust aggregates. First, we present a new…
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…
Using a novel approximation scheme within the convective diffusion (two body Smoluchowski) equation framework, we unveil the shear-driven aggregation mechanism at the origin of structure-formation in sheared colloidal systems. The theory,…
The Coupled-Cluster theory is one of the most successful high precision methods used to solve the stationary Schr\"odinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in…
Researchers have employed variations of the Smoluchowski coagulation equation to model a wide variety of both organic and inorganic phenomena and with relatively few known analytical solutions, numerical solutions play an important role in…
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 address the problem of likelihood based inference for correlated diffusion processes using Markov chain Monte Carlo (MCMC) techniques. Such a task presents two interesting problems. First, the construction of the MCMC scheme should…
We investigate with Monte Carlo computer simulations the capillary phase behaviour of model colloid-polymer mixtures confined between a flat wall and a corrugated wall. The corrugation is modelled via a sine wave as a function of one of the…
Diffusion behavior of Brownian particles in confined spaces was studied for the displacements notably shorter than the confinement size. The confinements, resembling structure of porous solids, were modeled using a spatially-varying…
The strong friction regime at low temperatures is analyzed systematically starting from the formally exact path integral expression for the reduced dynamics. This quantum Smoluchowski regime allows for a type of semiclassical treatment in…