# Cusp formation and threshold effects in break-up collisions

## Related Articles

- Squeeze Flow of Multiply-Connected Fluid Domains in a Hele-Shaw Cell. Crowdy, D.; Kang, H. // Journal of Nonlinear Science;2001, Vol. 11 Issue 4, p279
Summary. The theory of algebraic curves and quadrature domains is used to construct exact solutions to the problem of the squeeze flow of multiply-connected fluid domains in a Hele-Shaw cell. The solutions are exact in that they can be written down in terms of a finite set of time-evolving...

- Singularities of the one- and two-point mass gravitational lens. Witt, Hans J.; Petters, Arlie O. // Journal of Mathematical Physics;Sep93, Vol. 34 Issue 9, p4093
A detailed study of when a change in the number of caustics and cusps occurs for one- and two-point mass gravitational lens lying on a single plane with continuously distributed matter and an external shear are presented herein. The equations for the positions of the cusps generated by such lens...

- Signs of the cusps in binary lenses. Bozza, V. // Journal of Mathematical Physics;Sep2000, Vol. 41 Issue 9
The cusps of the caustics of any gravitational lens model can be classified into positive and negative ones. This distinction lies on the parity of the images involved in the creation/destruction of pairs occurring when a source crosses a caustic in a cusp. In this paper, we generalize the...

- The resonance spectrum of the cusp map in the space of analytic functions. Antoniou, I.; Shkarin, S. A.; Yarevsky, E. // Journal of Mathematical Physics;Jul2002, Vol. 43 Issue 7, p3746
We prove that the Frobenius-Perron operator U of the cusp map F:[-1,1] â†’[-1,1], F(x) = 1 -2 âˆšÏ‡ (which is an approximation of the PoincarÃ© section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for...

- Applications of singularity theory to gravitational lensing. I. Multiple lens planes. Levine, H. I.; Petters, A. O.; Wambsganss, J. // Journal of Mathematical Physics;Oct93, Vol. 34 Issue 10, p4781
The basic local and global features of stable multiple plane gravitational lens systems are investigated using tools from singularity theory. All stable multiple plane time-delay and lensing maps are classified, and the following global facts are proven under the weaker assumption of local...

- Cuspidal coverings for pairs of congruence subgroups. Gilbert, George T.; Richey, Matthew P. // Journal of Mathematical Physics;Jan1995, Vol. 36 Issue 1, p426
Develops a formula for the number of cusps in certain congruence subgroups equivalent to a given cusp in certain larger subgroups. Necessary and sufficient conditions for the number to be independent of the particular cusp; Applications to statistical mechanics.

- Formation of curvature singularity along vortex line in an axisymmetric, swirling vortex sheet. Sakajo, Takashi // Physics of Fluids;Aug2002, Vol. 14 Issue 8, p2886
We consider an axisymmetric, swirling vortex sheet in an inviscid and incompressible flow. Caflisch et al. pointed out that the vortex sheet acquired a singularity in finite time, but the property of the singularity was not revealed. In the present paper we show convincing numerical evidences of...

- A CLASSICAL CHARACTERIZATION OF NEWFORMS WITH EQUIVALENT EIGENFORMS IN ${S_{k + 1/2}}(4N, \chi)$. SHARON M. FRECHETTE // Journal of the London Mathematical Society;Dec2003, Vol. 68 Issue 3, p563
The paper continues the investigation of the Hecke structure of spaces of half-integral weight cusp forms ${S_{k + 1/2}}(4N, \chi)$, where $k$ and $N$ are positive integers with $N$ odd, and $\chi$ is an even quadratic Dirichlet character modulo $4N$. In the Hecke decomposition of these spaces,...

- The length of intersection lines and the number of cusps in assemblies of interpenetrating spheres. Thompson, Aidan P.; Glandt, Eduardo D. // Journal of Chemical Physics;8/1/1992, Vol. 97 Issue 3, p1932
A previously derived expression for the specific surface area of a dispersion of mutually penetrable spheres or pores is generalized for the calculation of the length of sphereâ€“sphere intersections (lines common to two pores) and the number of cusps (points common to three pores). The...