Related papers: A Unified Computational Framework for Two Dimensio…
Highly accurate estimates of the urban fractal dimension $D_f$ are obtained by implementing the Detrended Moving Average algorithm (DMA) on WorldView2 satellite high-resolution multi-spectral images covering the largest European cities.…
In close analogy to diffusion limited aggregation (DLA) and inspired by a work of Roux, a random walker algorithm is constructed to solve the problem of crack growth in an elastic medium. In contrast to conventional lattice approaches, the…
Rigidity transitions induced by the formation of system-spanning disordered rigid clusters, like the jamming transition, can be well-described in most physically relevant dimensions by mean-field theories. A dynamical mean-field theory…
One-dimensional detrended fluctuation analysis (1D DFA) and multifractal detrended fluctuation analysis (1D MF-DFA) are widely used in the scaling analysis of fractal and multifractal time series because of being accurate and easy to…
We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
Diffusion Limited Aggregation and its generalization, Dielectric Breakdown model play an important role in physics, approximating a range of natural phenomena. Yet little is known about them, with the famous Kesten's estimate on the DLAs…
The document layout analysis (DLA) aims to split the document image into different interest regions and understand the role of each region, which has wide application such as optical character recognition (OCR) systems and document…
Large-scale multi-objective optimization poses challenges to existing evolutionary algorithms in maintaining the performances of convergence and diversity because of high dimensional decision variables. Inspired by the motion of particles…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
Diffusion Probabilistic Field (DPF) models the distribution of continuous functions defined over metric spaces. While DPF shows great potential for unifying data generation of various modalities including images, videos, and 3D geometry, it…
Using off-lattice noise reduction it is possible to estimate the asymptotic properties of diffusion-limited aggregation clusters grown in three dimensions with greater accuracy than would otherwise be possible. The fractal dimension of…
The ability to separate and analyze chemical species with high resolution, sensitivity, and throughput is central to the development of microfluidics systems. Deterministic lateral displacement (DLD) is a continuous separation method based…
Computer simulations and scaling theory are used to investigate the damping of oscillations during epitaxial growth on high-symmetry surfaces. The crossover from smooth to rough growth takes place after the deposition of (D/F)^\delta…
We explicitly build a generalized local-density approximation (GLDA) correlation functional based on one-dimensional (1D) uniform electron gases (UEGs). The fundamental parameters of the GLDA \textemdash a generalization of the widely-known…
We study the multifractal analysis (MFA) of electronic wavefunctions at the localisation-delocalisation transition in the 3D Anderson model for very large system sizes up to $240^3$. The singularity spectrum $f(\alpha)$ is numerically…
This paper investigates the predictive performance of model averaging in high-dimensional linear regression where the number of regressors is comparable to the sample size. We demonstrate that the double descent trajectory manifests within…
Kinetic Monte-Carlo (KMC) simulations are a well-established numerical tool to investigate the time-dependent surface morphology in molecular beam epitaxy (MBE) experiments. In parallel, simplified approaches such as limited mobility (LM)…
Disentangled representation learning (DRL) aims to break down observed data into core intrinsic factors for a profound understanding of the data. In real-world scenarios, manually defining and labeling these factors are non-trivial, making…
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…