Kinematic equations for the motion of slowly propagating, weakly curved fronts in bistable media are derived. The equations generalize earlier derivations where algebraic relations between the normal front velocity and its curvature are assumed. Such relations do not capture the dynamics near nonequilibrium Ising-Bloch (NIB) bifurcations, where transitions between counterpropagating Bloch front...

We report the developments of hydrodynamic instabilities in several wellbalanced finite volume schemes that are observed during the computation of the temporal evolution of an out-balance flow which is essentially a kinematic wave. The numerical simulations are based on the one-dimensional shallow-water equations for a uniformly sloping bed with hydraulic resistance. Subsequently, we highlight ...

We present a new set of kinematic equations for front motion in bistable media. The equations extend earlier kinematic approaches by coupling the front curvature with the order parameter associated with a parity breaking front bifurcation. In addition to naturally describing the core region of rotating spiral waves the equations can be be used to study the nucleation of spiral-wave pairs along ...

The Radcliffe Wave (RW) is a recently discovered sinusoidal vertical feature of dense gas in the proximity Sun. In disk plane, it aligned with Local Arm. However, origin its undulation still unknown. This study constrains kinematics RW, using young stars and open clusters as tracers, explores possibility this oscillation being part more extended mode. We median velocity trends along RW extend f...

In this paper a space-averaged Navier–Stokes approach was deployed to simulate the wave propagation over coastal structures. The developed model is based on the smoothed particle hydrodynamic (SPH) method which is a pure Lagrangian approach and can handle large deformations of the free surface with high accuracy. In this study, the large eddy simulation (LES) turbulent model was coupled with th...

This paper presents improved solution methods for kinematic wave traffic problems with concave flow-density relations. As explained in part I of this work, the solution of a kinematic wave problem is a set of continuum least-cost paths in space-time. The least cost to reach a point is the vehicle number. The idea here consists in overlaying a dense but discrete network with appropriate costs in...