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Ruled surfaces play an important role in various types of design, architecture, manufacturing, art, and sculpture. They can be created in a variety of ways, which is a topic that has been the subject of much discussion in mathematics and…
The evolution of the interface propagation in a slowly rotating half-filled horizontal cylinder is studied using MRI. Initially, the cylinder contains two axially segregated bands of small and large particles with a sharp interface. The…
We study a model for the movement of surfaces, namely the conserved, restricted solid-on-solid model. The surface configurations are restricted such that the difference between the heights at adjacent sites is no more than one. In addition…
In this study, we develop a complex network approach on a rough fracture, where evolution of elementary aperture during translational shear is characterized. In this manner, based on some hidden metric spaces (similarity measurements)…
We study recursive-cube-of-rings (RCR), a class of scalable graphs that can potentially provide rich inter-connection network topology for the emerging distributed and parallel computing infrastructure. Through rigorous proof and validating…
A quantitative model of the mobility of functionalized particles at the interface is pivotal to understanding important systems in biology and nanotechnology. In this work, we investigate the emerging dynamics of particles anchored through…
For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thomas mixed elements in two-dimension and for the…
We study fluctuations of interfaces in the Kardar-Parisi-Zhang (KPZ) universality class with curved initial conditions. By simulations of a cluster growth model and experiments of liquid-crystal turbulence, we determine the universal…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
In this work, we investigate an off-lattice version of the diffusion-reaction model, $A + A \leftrightarrow A$. We consider extensive numerical simulation of the radial system obtained from a single seed. Observed fluctuations in such an…
We consider a discrete-time model for random interface growth which admits exact formulas and converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the…
The complicated dynamics of the contact line of a moving droplet on a solid substrate often hamper the efficient modeling of microfluidic systems. In particular, the selection of the effective boundary conditions, specifying the contact…
The irreversible growth of a binary mixture under far-from-equilibrium conditions is studied in three-dimensional confined geometries of size $L_x \times L_y \times L_z$, where $L_z \gg L_x = L_y$ is the growing direction. A competing…
We present a generative diffusion model specifically tailored to the discovery of surface structures. The generative model takes into account substrate registry and periodicity by including masked atoms and $z$-directional confinement.…
Networks are widely used to model the interaction between individual dynamical systems. In many instances, the total number of units as well as the interaction coupling are not fixed in time, but rather constantly evolve. In terms of…
The short time behavior of the 1+1 dimensional KPZ growth equation with a flat initial condition is obtained from the exact expressions of the moments of the partition function of a directed polymer with one endpoint free and the other…
We discuss the steady state dynamics of interfaces with periodic boundary conditions arising from body-centered solid-on-solid growth models in $1+1$ dimensions involving random aggregation of extended particles (dimers,…
We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…
Robust and efficient design of networks on a realistic geographical space is one of the important issues for the realization of dependable communication systems. In this paper, based on a percolation theory and a geometric graph property,…
Stochastic interface dynamics serve as mathematical models for diverse time-dependent physical phenomena: the evolution of boundaries between thermodynamic phases, crystal growth, random deposition... Interesting limits arise at large…