Related papers: Hexagonal eutectic solidification patterns operati…
We study the dynamics of an entangled, isotropic solution of polar filaments coupled by molecular motors which generate relative motion of the filaments in two and three dimensions. We investigate the stability of the homogeneous state for…
A mesoscopic continuum model is employed to analyse the transport mechanisms and structure formation during the redistribution stage of deposition experiments where organic molecules are deposited on a solid substrate with periodic…
The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…
The existing theoretical analyses of solidification dynamics lack the insights of historical relevance and transport processes in the whole system. Through the phase-field model, this paper investigates the evolution in the whole domain…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
We propose a quantitative direct method to prove the local stability of a stationary solution for a rough differential equation and its regular discretization scheme. Using Doss-Sussmann technique and stopping time analysis, we provide…
Particle suspensions, present in many natural and industrial settings, typically contain aggregates or other microstructures that can complicate macroscopic flow behaviors and damage processing equipment. Recent work found that applying…
In this work we introduce a topological method for the search of fixed points and periodic points for continuous maps defined on generalized rectangles in finite dimensional Euclidean spaces. We name our technique "Stretching Along the…
Using x-ray photon correlation spectroscopy, we studied the layer fluctuations in the lamellar phase of an ionic lyotropic system. We measured the relaxation rate of in-plane (undulation) fluctuations as a function of the wave vector.…
When a droplet is brought in contact with an undercooled surface, it wets the substrate and solidifies at the same time. The interplay between the phase transition effects and the contact-line motion, leading to its arrest, remains poorly…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
The possible role of growing static order in the dynamical slowing down towards the glass transition has recently attracted considerable attention. On the basis of random first-order transition (RFOT) theory, a new method to measure the…
We study flow driven through a finite-length planar rigid channel by a fixed upstream flux, where a segment of one wall is replaced by a pre-stressed elastic beam subject to uniform external pressure. The steady and unsteady systems are…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
The shear-banding instability in quasi-statically driven bulk metallic glasses emerges from collective dynamics, mediated by shear transformation zones and associated non-local elastic interactions. It is also phenomenologically known that…
We establish an exponential stabilization result for linear port-Hamiltonian systems of first order with quite general, not necessarily continuous, energy densities. In fact, we have only to require the energy density of the system to be of…
In this paper, we consider certain partially hyperbolic diffeomorphisms with center of arbitrary dimension and obtain continuity properties of the topological entropy under $C^1$ perturbations. The systems considered have subexponential…
A two-dimensional lattice model for the formation and evolution of shear bands in granular media is proposed. Each lattice site is assigned a random variable which reflects the local density. At every time step, the strain is localized…
Quantitative phase field models have been extensively used to study the solidification behavior of alloys under different conditions. However, a longstanding challenge of phase field models is the directional bias caused by the…
We model the phase oscillations of electrons in race-track microtrons by means of an area preserving map with a fixed point at the origin, which represents the synchronous trajectory of a reference particle in the beam. We study the…