Related papers: Continuum models for surface growth
This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…
As a departure from existing continuum approaches for describing the stability and evolution of surfaces of crystalline materials, this article provides a description of surface evolution based on the physics of the main feature imposed by…
Complex spatiotemporal dynamics of physicochemical processes are often modeled at a microscopic level (through e.g. atomistic, agent-based or lattice models) based on first principles. Some of these processes can also be successfully…
Persistence probabilities of the interface height in (1+1)- and (2+1)-dimensional atomistic, solid-on-solid, stochastic models of surface growth are studied using kinetic Monte Carlo simulations, with emphasis on models that belong to the…
Complexes and cohomology, traditionally central to topology, have emerged as fundamental tools across applied mathematics and the sciences. This survey explores their roles in diverse areas, from partial differential equations and continuum…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
Discrete fine-scale models, in the form of either particle or lattice models, have been formulated successfully to simulate the behavior of quasi-brittle materials whose mechanical behavior is inherently connected to fracture processes…
Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and…
Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…
We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples…
We study model spaces, in the sense of Hairer, for stochastic partial differential equations involving the fractional Laplacian. We prove that the fractional Laplacian is a singular kernel suitable to apply the theory of regularity…
Aiming to investigate the upper critical dimension, $d_u$, of the KPZ class, in [EPL 103 (2013) 10005] some growth models were numerically analyzed using Cayley trees (CTs) as substrates, as a way to access their behavior in the…
We present a general purpose method for solving partial differential equations on a closed surface, based on a technique for discretizing the surface introduced by Wenjun Ying and Wei-Cheng Wang [J. Comput. Phys. 252 (2013), pp. 606-624]…
We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly. The same method, applied to PDEs with constant dissipative structure,…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…
Recently, various evolutionary partial differential equations (PDEs) with a mixed derivative have been emerged and drawn much attention. Nonetheless, their PDE-theoretical and numerical studies are still in their early stage. In this paper,…
We propose a novel framework to solve PDEs on moving manifolds, where the evolving surface is represented by a moving point cloud. This has the advantage of avoiding the need to discretize the bulk volume around the surface, while also…
The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which…
We consider incorporation of particle detachment in Smoluchowski model of colloidal growth. Two approaches are considered, utilizing phenomenological rate equation and exact large-time results. Our main conclusion is that the value of the…
We present a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of pattern-forming physics. The motivation comes from developmental…