Related papers: Ostwald Ripening on Nanoscale
We study the expected redshift evolution of galaxy cluster abundance between 0 < z < 3 in different cosmologies, including the effects of the cosmic equation of state parameter w=p/rho. Using the halo mass function obtained in recent large…
The near-threshold clustering phenomenon is well understood by the low-energy universality, for shallow bound states below the threshold. Nevertheless, the characteristics of resonances slightly above the threshold still lack thorough…
We show that the thermodynamic limit of a bistable phosphorylation-dephosphorylation cycle has a selection rule for the "more stable" macroscopic steady state. The analysis is akin to the Maxwell construction. Based on the chemical master…
We have performed a new and homogeneous analysis of all the Li data available in the literature for main sequence stars (spectral-types from late F to K) in open clusters. In the present paper we focus on a detailed investigation of MS Li…
For a model with many-to-one connectivity it is widely expected that mean-field theory captures the exact many-particle $N\to\infty$ limit, and that higher-order cumulant expansions of the Heisenberg equations converge to this same limit…
An interesting problem in statistical physics is the condensation of classical particles in droplets or clusters when the pair-interaction is given by a stable Lennard-Jones-type potential. We study two aspects of this problem. We start by…
It remains a prime question of how to describe the optical properties of large molecular clusters accurately. Quantum chemical methods capture essential electronic details but are infeasible for entire clusters, while optical simulations…
We consider the problem of clustering (or reconstruction) in the stochastic block model, in the regime where the average degree is constant. For the case of two clusters with equal sizes, recent results by Mossel, Neeman and Sly, and by…
This papers addresses the connection between two classical models of phase transition phenomena describing different stages of the growth of clusters. The Becker-D\"oring model (BD) describes discrete-sized clusters through an infinite set…
We consider systems of exponentials with frequencies belonging to simple quasicrystals in $\mathbb{R}^d$. We ask if there exist domains $S$ in $\mathbb{R}^d$ which admit such a system as a Riesz basis for the space $L^2(S)$. We prove that…
We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each…
In this paper, we introduce a renormalisation procedure for the density associated with the system of nonlinear Schr\"odinger equations (NLSS) on a circle. We show that this renormalised density satisfies better orthonormal Strichartz…
Motivated by applications to deep learning which often fail standard Lipschitz smoothness requirements, we examine the problem of sampling from distributions that are not log-concave and are only weakly dissipative, with log-gradients…
Understanding how multi-component liquid mixtures undergo phase separation is central to elucidating biophysical organization in the cell. Here, combining analytical and numerical results, we characterise the dynamics of mixtures with…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…
A self-consistent theory for the classical description of the interaction of light and matter at the nano-scale is presented, which takes into account spatial dispersion. Up to now, the Maxwell equations in nanostructured materials with…
We consider the Keller--Rubinow model for Liesegang rings in one spatial dimension in the fast reaction limit as introduced by Hilhorst, van der Hout, Mimura, and Ohnishi in 2007. Numerical evidence suggests that solutions to this model…
We investigate Lifshits-tail behaviour of the integrated density of states for a wide class of Schr\"odinger operators with positive random potentials. The setting includes alloy-type and Poissonian random potentials. The considered…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
We have only rules of thumb with which to predict how a material will crystallize, chief among which is Ostwald's rule of stages. It states that the first phase to appear upon transformation of a parent phase is the one closest to it in…