arXiv subjects
Publications and source records attributed to Zbislaw Tabor.
Building on previous work on the critical behavior in gravitational collapse of the self-gravitating SU(2) $σ$-field and using high precision numerical methods we uncover a fine structure hidden in a narrow window of parameter space. We argue that this numerical finding has a natural explanation within a dynamical system framework of critical collapse.
In this paper we report on numerical studies of formation of singularities for the semilinear wave equations with a focusing power nonlinearity $u_{tt} - Δu = u^{p}$ in three space dimensions. We show that for generic large initial data that lead to singularities, the spatial pattern of blowup can be described in terms of linearized perturbations about the fundamental self-similar (homogeneous in space) solution. We consider also non-generic initial data which are fine-tuned to the threshold for blowup and identify critical solutions that separate blowup from dispersal for some values of the exponent $p$.
In this paper we report on numerical studies of the Cauchy problem for equivariant wave maps from 2+1 dimensional Minkowski spacetime into the two-sphere. Our results provide strong evidence for the conjecture that large energy initial data develop singularities in finite time and that singularity formation has the universal form of adiabatic shrinking of the degree-one harmonic map from $\mathbb{R}^2$ into $S^2$.
We continue our study of the gravitational collapse of spherically symmetric skyrmions. For certain families of initial data, we find the discretely self-similar Type II critical transition characterized by the mass scaling exponent $γ\approx 0.20$ and the echoing period $Δ\approx 0.74$. We argue that the coincidence of these critical exponents with those found previously in the Einstein-Yang-Mills model is not accidental but, in fact, the two models belong to the same universality class.