相关论文: The Dynamics of Curved Fronts: Beyond Geometry

Solutions of the perturbed Painlev\'e-2 equation are typical for describing a dynamic bifurcation of soft loss of stability. The bifurcation boundary separates solutions of different types before bifurcation and before loss of stability.…

Spiral waves are ubiquitous signatures of non equilibrium dynamics, appearing across chemical, biological, and active systems. Yet, in many living systems these waves unfold on curved and folded surfaces whose geometry has rarely been…

We introduce circular evolutes and involutes of framed curves in the Euclidean space. Circular evolutes of framed curves stem from the curvature circles of Bishop directions and singular value sets of normal surfaces of Bishop directions.…

In this article, we first investigate the kinematics of specific geodesic flows on two dimensional media with constant curvature, by explicitly solving the evolution (Raychaudhuri) equations for the expansion, shear and rotation along the…

Spiral waves in excitable media possess both wave-like and particle-like properties. When resonantly forced (forced at the spiral rotation frequency) spiral cores travel along straight trajectories, but may reflect from medium boundaries.…

Accretion of mineralized thin wall-like structures via localized growth along their edges is observed in a range of physical and biological systems ranging from molluscan and brachiopod shells to carbonate-silica composite precipitates. To…

We study traveling fronts in a system of one dimensional reaction-diffusion-advection equations motivated by problems in reactive flows. In the limit as a parameter tends to infinity, we construct the approximate front profile and determine…

We derive regularized contour dynamics equations for the motion of infinite sharp fronts in the two-dimensional incompressible Euler, surface quasi-geostrophic (SQG), and generalized surface quasi-geostrophic (gSQG) equations. We derive a…

Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…

The differential equations satisfied by the wavefunction coefficients of conformally coupled scalars in a power-law cosmology can be recast into an iterative differential system of basis functions. These functions can be encoded within…

We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…

We construct entire solutions of bistable reaction-diffusion equations by mixing finite planar fronts, which form a finite-dimensional manifold. These entire solutions are generalized traveling fronts, that is, transition fronts. We also…

We present dynamic equations for two dimensional closed surfaces and analytically solve it for some simplified cases. We derive final equations for surface normal motions by two different ways. The solution of the equations of motions in…

Vertical thermal convection is a non-equilibrium system in which both buoyancy and shear forces play a role in driving the convective flow. Beyond the onset of convection, the driven dissipative system exhibits chaotic dynamics and…

We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of…

Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…

We prove generalizations of the isoperimetric inequality for both spherical and hyperbolic wave fronts (i.e. piecewise smooth curves which may have cusps). We then discuss "bicycle curves" using the generalized isoperimetric inequalities.…

We put disks on a sphere between two parallels of this sphere. The disks have the curvature of the sphere and interact via a simplified Hertz law. We analyze the behavior of the total kinetic energy of the whole assembly of disks with…

We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear flow. The far-field modal and amplitude equations for the ring waves are presented in dimensional form. We re-derive them from the…

This paper presents causal block-diagram models to represent the equations of motion of multi-body systems in a very compact and simple closed form. Both the forward dynamics (from the forces and torques imposed at the various…