Related papers: Fronts under arrest II: analytical foundations
An analytical model based on variational principles for a thin-walled stiffened plate subjected to axial compression is presented. A system of nonlinear differential and integral equations is derived and solved using numerical continuation.…
This thesis is about the study of complex systems through simple models. Our work evidences the relevance of this kind of modeling in science, which provides us with a better understanding of nature at minimum cost. The fundamentals tools…
This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…
We simulate a two dimensional model of self-propelled particles confined by a deformable boundary. The particles tend to accumulate near the boundary and the shape of the boundary deforms upon the collisions. We find that there are two…
Urbanization is a phenomenon of concern for planning and public health: projections are difficult because of policy changes and natural events, and indicators are multiple. There are previous studies of development that used fractals, but…
A classification of dynamical systems in terms of their variational properties is reviewed. Within this classification, front propagation is discussed in a non-gradient relaxational potential flow. The model is motivated by transient…
The emergent dynamics in phase-separated mixtures of isometric active and passive Brownian particles is studied numerically in two dimensions. A novel steady-state of well-defined traveling fronts is observed, where the interface between…
A behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of boundary set guarantees preservation of the networks types for minimal spanning trees, minimal…
We perform an analytical investigation of the cell interface dynamics in the framework of a minimal phase field model of cell motility suggested in [1], which consists of two coupled evolution equations for the order parameter and a…
We develop a description of diffusion limited growth in solid-solid transformations, which are strongly influenced by elastic effects. Density differences and structural transformations provoke stresses at interfaces, which affect the phase…
Mechanistic interpretability has transformed the analysis of transformer circuits by decomposing model behavior into competing algorithms, identifying phase transitions during training, and deriving closed-form predictions for when and why…
One of the basic frameworks in science views behavioral products as a process within a dynamic system. The mechanism might be seen as a representation of many instances of centralized control in real time. Many real systems, however,…
We consider atomistic systems consisting of interacting particles arranged in atomic lattices whose quasi-static evolution is driven by time-dependent boundary conditions. The interaction of the particles is modeled by classical interaction…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
The dynamics and internal structure of doping fronts in organic semiconductors are investigated theoretically using an extended drift-diffusion model for ions, electrons and holes. The model also involves the injection barriers for…
We present a generic mechanism by which reproducing microorganisms, with a diffusivity that depends on the local population density, can form stable patterns. It is known that a decrease of swimming speed with density can promote separation…
Modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. When the speed is the curvature this leads to one of the classical degenerate…
It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach…
Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…