Related papers: Scaling Theory for Migration-Driven Aggregate Grow…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
We explore analytically and numerically agglomeration driven by advection and localized source. The system is inhomogeneous in one dimension, viz. along the direction of advection. We analyze a simplified model with mass-independent…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
A model is proposed and studied describing an infinite population of point migrants arriving in and departing from $X\subseteq \mathbf{R}^d$, $d\geq 1$. Both these acts occur at random with state-dependent rates. That is, depending on their…
We investigate aggregation driven by mass injection. In this stochastic process, mass is added with constant rate r and clusters merge at a constant total rate 1, so that both the total number of clusters and the total mass steadily grow…
Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…
We consider a size-structured aggregation and growth model of phytoplankton community proposed by Ackleh and Fitzpatrick [2]. The model accounts for basic biological phenomena in phytoplankton community such as growth, gravitational…
We consider a simple model of firm/city/etc. growth based on a multi-item criterion: whenever entity B fares better that entity A on a subset of $M$ items out of $K$, the agent originally in A moves to B. We solve the model analytically in…
Motile organisms can form stable agglomerates such as cities or colonies. In the outbreak of a highly contagious disease, the control of large-scale epidemic spread depends on factors like the number and size of agglomerates, travel rate…
The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase…
We introduce the notions of scaling transition and distributional long-range dependence for stationary random fields $Y$ on $\mathbb {Z}^2$ whose normalized partial sums on rectangles with sides growing at rates $O(n)$ and $O(n^{\gamma})$…
We propose a model for aggregation where particles are continuously growing by heterogeneous condensation in one dimension and solve it exactly. We show that the particle size spectra exhibit transition to dynamic scaling $c(x,t)\sim…
We consider nonparametric regression under covariate shift, where we observe samples from both the target distribution and a related but distinct source distribution. We introduce a novel object, the transfer function, and show that…
A connection is made between the random turns model of vicious walkers and random permutations indexed by their increasing subsequences. Consequently the scaled distribution of the maximum displacements in a particular asymmeteric version…
Periodicity in population dynamics is a fundamental issue. In addition to current species-specific analyses, allometry facilitates understanding of limit cycles amongst different species. So far, body-size regressions have been derived for…
We investigate aggregation and fragmentation dynamics of tracers and inertial aggregates in random flows leading to steady state size distributions. Our objective is to elucidate the impact of changes in aggregation rates, due to…
We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size $s$ follow $D(s) \sim s^\gamma$ and $v(s)…
The Markov evolution of states of a continuum migration model is studied. The model describes an infinite system of entities placed in $\mathds{R}^d$ in which the constituents appear (immigrate) with rate $b(x)$ and disappear, also due to…
Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…
Irreversible aggregation is revisited in view of recent work on renormalization of complex networks. Its scaling laws and phase transitions are related to percolation transitions seen in the latter. We illustrate our points by giving the…