相关论文: Diffusion-limited-aggregation on a directed small …
We establish the zero-diffusion limit for both continuous and discrete aggregation models over convex and bounded domains. Compared with a similar zero-diffusion limit derived in [44], our approach is different and relies on a coupling…
We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…
Supplementing a lattice with long-range connections effectively models small-world networks characterized by a high local and global interconnectedness observed in systems ranging from society to the brain. If the links have a wiring cost…
The capacity of a fractal wireless network with direct social interactions is studied in this paper. Specifically, we mathematically formulate the self-similarity of a fractal wireless network by a power-law degree distribution $ P(k) $,…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
In this study, the concept of small worlds is investigated in the context of large-scale wireless ad hoc and sensor networks. Wireless networks are spatial graphs that are usually much more clustered than random networks and have much…
Diffusion limited aggregation (DLA) is a well studied phenomenon in which diffusing particles cumulatively aggregate on a starting fixed seed point, forming a pattern which is fractal in structure. Here we report an interesting DLA process…
The process by which one may take a discrete model of a biophysical process and construct a continuous model based on it is of mathematical interest as well as being of practical use. In this paper, we first study the singular limit of a…
Channel modelling is essential to designing modern wireless communication systems. The increasing complexity of channel modelling and the cost of collecting high-quality wireless channel data have become major challenges. In this paper, we…
A generalized form of the Hastings and Levitov (HL) algorithm for simulation of diffusion-limited aggregation (DLA) restricted in a sector geometry is studied. It is found that this generalization with uniform measure produces "wedge-like"…
An exactly solvable model for the rewiring dynamics of weighted, directed networks is introduced. Simulations indicate that the model exhibits two types of condensation: (i) a phase in which, for each node, a finite fraction of its total…
Complex networks are a successful framework to describe collective behaviour in many applications, but a notable gap remains in the current literature, that of proving asymptotic convergence in networks of piecewise-smooth systems. Indeed,…
Diffusion-limited aggregation has a natural generalization to the "$\eta$-models", in which $\eta$ random walkers must arrive at a point on the cluster surface in order for growth to occur. It has recently been proposed that in spatial…
We present a conditional diffusion model for electromagnetic inverse design that generates structured media geometries directly from target differential scattering cross-section profiles, bypassing expensive iterative optimization. Our 1D…
In this brief report, we present a disordered version of recursive networks. Depending on the structural parameters $u$ and $v$, the networks are either fractals with a finite fractal dimension $d_{f}$ or transfinite fractals (transfractal)…
Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time…
We study with numerical simulation the possible limit behaviors of synchronous discrete-time deterministic recurrent neural networks composed of N binary neurons as a function of a network's level of dilution and asymmetry. The network…
In analogy to recent results on non-universal roughening in surface growth [Lam and Sander, Phys. Rev. Lett. {\bf 69}, 3338 (1992)], we propose a variant of diffusion-limited aggregation ($DLA$) in which the radii of the particles are…
We examine diffusion-limited aggregation generated by a random walk on Z with long jumps. We derive upper and lower bounds on the growth rate of the aggregate as a function of the number moments a single step of the walk has. Under various…
The multilayer network framework has served to describe and uncover a number of novel and unforeseen physical behaviors and regimes in interacting complex systems. However, the majority of existing studies are built on undirected multilayer…