Related papers: The branching structure of diffusion-limited aggre…
Recent advances in diffusion models have significantly improved the synthesis of materials, textures, and 3D shapes. By conditioning these models via text or images, users can guide the generation, reducing the time required to create…
We consider a cluster growth model on Z^d, called internal diffusion limited aggregation (internal DLA). In this model, random walks start at the origin, one at a time, and stop moving when reaching a site not occupied by previous walks. It…
We give a Large Deviation Principle (LDP) with explicit rate function for the distribution of vertex degrees in plane trees, a combinatorial model of RNA secondary structures. We calculate the typical degree distributions based on nearest…
We analytically investigate a 1d branching-coalescing model with reflecting boundaries in a canonical ensemble where the total number of particles on the chain is conserved. Exact analytical calculations show that the model has two…
The structure of the QCD gluonic cascade in configuration space is investigated. The explicit form of the inclusive single particle density in configuration space transverse coordinates is derived in the double logarithmic approximation…
In wall-bounded parallel flows, sustained turbulence can occur even while laminar flow is still stable. Channel flow is one of such flows and displays spatio-temporal fluctuating patterns of localized turbulence along its way from/to…
Two-dimensional structures grown with Witten and Sander algorithm are investigated. We analyze clusters grown off-lattice and clusters grown with antenna method with $N_{fp}=3,4,5,6,7$ and 8 allowed growth directions. With the help of…
Internal diffusion-limited aggregation (IDLA) is a stochastic growth model on a graph $G$ which describes the formation of a random set of vertices growing from the origin (some fixed vertex) of $G$. Particles start at the origin and…
We consider a general model of branch competition that automatically leads to a critical branching configuration. This model is inspired by the $4-\eta$ expansion of the dielectric breakdown model (DBM), but the mechanism of arriving at the…
We examine a bulk-edge correspondence of branching MERA networks at finite temperatures in terms of algebraic and differential topology. By using homeomorphic mapping, we derive that the networks are nonorientable manifolds such as a…
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 apply a probabilistic clustering method, Latent Dirichlet Allocation (LDA), to characterize the largescale dynamics of Rayleigh-B\'enard convection. The method, introduced in Frihat et al. 2021, is applied to a collection of snapshots in…
An early (and influential) scaling relation in the multifractal theory of Diffusion Limited Aggregation(DLA) is the Turkevich-Scher conjecture that relates the exponent \alpha_{min} that characterizes the ``hottest'' region of the harmonic…
Thermomechanical processing such as annealing is one of the main methods to tailor the mechanical properties of materials, however, much is unknown about the reorganization of dislocation structures deep inside macroscopic crystals that…
We develop an obstruction theory for Hirsch extensions of cbba's with twisted coefficients. This leads to a variety of applications, including a structural theorem for minimal cbba's, a construction of relative minimal models with twisted…
The Materials Project crystal structure database has been searched for materials possessing layered motifs in their crystal structures using a topology-scaling algorithm. The algorithm identifies and measures the sizes of bonded atomic…
In the diffusion-collision model, the unfolding rates are given by the likelihood of secondary structural cluster dissociation. In this work, we introduce an unfolding rate calculation for proteins whose secondary structural elements are…
We introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford's alpha model to multifurcating trees and includes the trees obtained by uniform sampling from…
We explore the macroscopic consequences of lattice anisotropy for Diffusion Limited Aggregation (DLA) in three dimensions. Simple cubic and BCC lattice growths are shown to approach universal asymptotic states in a coherent fashion, and the…
Accurate quantification of the extent of lung pathological patterns (fibrosis, ground-glass opacity, emphysema, consolidation) is prerequisite for diagnosis and follow-up of interstitial lung diseases. However, segmentation is challenging…