We investigate the stability of self-similar solutions for a gravitationally collapsing isothermal sphere in Newtonian gravity by means of a normal mode analysis. It is found that the Hunter series of solutions are highly unstable, while neither the Larson-Penston solution nor the homogeneous collapse one have an analytic unstable mode. Since the homogeneous collapse solution is known to suffer...

We present the results from a numerical study of critical gravitational collapse of axisymmetric distributions of massless scalar field energy. We find threshold behavior that can be described by the spherically symmetric critical solution with axisymmetric perturbations. However, we see indications of a growing, nonspherical mode about the spherically symmetric critical solution. The effect of...

We consider the propagation of a crack in a brittle material along a prescribed crack path and define a quasi-static evolution by means of stationary points of the free energy. We show that this evolution satisfies Griffith’s criterion in a suitable form which takes into account both stable and unstable propagation, as well as an energy balance formula which accounts for dissipation in the unst...

We develop a semianalytic formulation suitable for solving the Navier-Stokes equations governing the induced steady, axially symmetric motion of an incompressible viscous fluid confined in a wide gap between two differentially rotating concentric spheres. The method is valid for arbitrarily high Reynolds number and aids in the presentation of multiple steady-state flow patterns and their bifurc...

Under certain conditions the problem of morphogenesis in development and the problem of morphology in block copolymers may be reduced to one geometric problem. In two dimensions two new types of solutions are found. The first type of solution is a disconnected set of many components, each of which is close to a ring. The sizes and locations of the rings are precisely determined from the paramet...

this paper addresses the validity of two hypotheses concerning changes of vowel quality in persian. the theory of centralization claims that there is a strong correlation between vowel duration and vowel quality. as vowel duration is shortened in unstressed contexts, the size of the vowel inventory reduces toward the center, leading to considerable overlap between different categories and a red...

We study the dynamics of head-on collisions of traveling pulses for a three-component reaction diffusion system. A variety of outputs with large deformation such as annihilation, repulsion, and fusion are observed after collision, however it remains open for a long time that what kind of mathematical structure controls the input-output relation at collision point. A series of works [18, 19, 20,...

systems in which reaction terms are coupled to diffusion and advection transports arise in awide range of chemical engineering applications, physics, biology and environmental. in these cases, thecomponents of the unknown can denote concentrations or population sizes which represent quantities andthey need to remain positive. classical finite difference schemes may produce numerical drawbacks s...

By using Lyapunov's second method [13], some new results are established, which insure that the zero solution of non-linear vector differential equations of the form is unstable.

Meteorological numerical weather prediction (NWP) models solve a system of partial differential equations in time and space. Semi-lagrangian advection schemes allow for long time steps. These longer time steps can result in instabilities occurring in the model physics. A system of differential equations in which some solution components decay more rapidly than others is stiff. In this case it i...