Related papers: Critical Phenomena in Non-spherically Symmetric Sc…
We study the singularity created in the supercritical collapse of a spherical massless scalar field. We first model the geometry and the scalar field to be homogeneous, and find a generic solution (in terms of a formal series expansion)…
Failure of amorphous solids is fundamental to various phenomena, including landslides and earthquakes. Recent experiments indicate that highly plastic regions form elongated structures that are especially apparent near the maximal shear…
We study the effects of curved background geometries on the critical behavior of scalar field theory. In particular we concentrate on two maximally symmetric spaces: $d$-dimensional spheres and hyperboloids. In the first part of the paper,…
We perform fully nonlinear numerical simulations to study aspherical deformations of the critical self-similar solution in the gravitational collapse of ultra-relativistic fluids. Adopting a perturbative calculation, Gundlach predicted that…
We study the dynamics of the critical collapse of a spherically symmetric scalar field. Approximate analytic expressions for the metric functions and matter field in the large-radius region are obtained. In the central region, owing to the…
Homothetic scalar field collapse is considered in this article. By making a suitable choice of variables the equations are reduced to an autonomous system. Then using a combination of numerical and analytic techniques it is shown that there…
The second-order phase transitions in the Ising model and liquid-gas systems share a universality class and critical exponents, despite the absence of $Z_2$ symmetry in the liquid-gas Hamiltonian. This discrepancy highlights a central…
Similarity solutions are found for the adiabatic collapse of density perturbations $\delta M/M \propto r^{-s}$ $(s>0)$ in a flat universe containing collisional gas only. The solutions are obtained for planar, cylindrical, and spherical…
We study the gravitational collapse of an inhomogeneous scalar field with quantum gravity corrections associated with singularity avoidance. Numerical simulations indicate that there is critical behaviour at the onset of black hole…
Under increasing compression, an unbuckled shell is in a metastable state which becomes increasingly precarious as the buckling load is approached. So to induce premature buckling a lateral disturbance will have to overcome a decreasing…
We consider solutions to the nonlinear sigma model (wave maps) with target space S^3 and base space 3+1 Minkowski space, and we find critical behavior separating singular solutions from nonsingular solutions. For families of solutions with…
We analyze the Rayleigh equation for the collapse of an empty bubble and provide an explanation for some recent analytical approximations to the model. We derive the form of the singularity at the second boundary point and discuss the…
Experiments studying renormalization group flows in the quantum Hall system provide significant evidence for the existence of an emergent holomorphic modular symmetry $\Gamma_0(2)$. We briefly review this evidence and show that, for the…
In the quest of the critical solution for scalar field collapse in 2+1 gravity with a negative cosmological constant, we present a one parameter family of solutions with continuous self similar (CSS) behaviour near the central singularity.…
We derive a theoretical model of mass and angular momentum scaling in type-II critical collapse with rotation. We focus on the case where the critical solution has precisely one, spherically symmetric, unstable mode. We demonstrate…
We consider mean-field vector spin glasses with possibly non-convex interactions. Up to a small perturbation of the parameters defining the model, the asymptotic behavior of the Gibbs measure is described in terms of a critical point of an…
We study critical behavior in gravitational collapse of a general spherically symmetric Yang-Mills field coupled to the Einstein equations. Unlike the magnetic ansatz used in previous numerical work, the general Yang-Mills connection has…
We describe results of a numerical calculation of circularly symmetric scalar field collapse in three spacetime dimensions with negative cosmological constant. The procedure uses a double null formulation of the Einstein-scalar equations.…
A simple analytic model is presented which exhibits a critical behavior in black hole formation, namely, collapse of a thin shell coupled with outgoing null fluid. It is seen that the critical behavior is caused by the gravitational…
We investigate, at a laboratory scale, the collapse of cylindrical shells of radius $R$ and thickness $t$ induced by a granular discharge. We measure the critical filling height for which the structure fails upon discharge. We observe that…