We present results from a study of the fine structure of oscillon dynamics in the 3+1 spherically symmetric Klein-Gordon model with a symmetric double-well potential. We show that in addition to the previously understood longevity of oscillons, there exists a resonant (and critical) behavior which exhibits a time-scaling law. The mode structure of the critical solutions is examined, and we also show that the upper-bound to oscillon formation (in r0 space) is either non-existent or higher than previously believed. Our results are generated using a novel technique for implementing nonreflecting boundary conditions in the finite difference solution of wave equations. The method uses a coordinate transformation which blue-shifts and "freezes" outgoing radiation. The frozen radiation is then annihilated via dissipation explicitly added to the finite-difference scheme, with very little reflection into the interior of the computational domain.

Results are presented from numerical simulations of the flat-space nonlinear Klein-Gordon equation with an asymmetric double-well potential in spherical symmetry. Exit criteria are defined for the simulations that are used to help understand the boundaries of the basins of attraction for Gaussian "bubble" initial data. The first exit criteria, based on the immediate collapse or expansion of bubble radius, is used to observe the departure of the scalar field from a static intermediate attractor solution. The boundary separating these two behaviors in parameter space is smooth and demonstrates a time-scaling law with an exponent that depends on the asymmetry of the potential. The second exit criteria differentiates between the creation of an expanding true-vacuum bubble and dispersion of the field leaving the false vacuum; the boundary separating these basins of attraction is shown to demonstrate fractal behavior. The basins are defined by the number of bounces that the field undergoes before inducing a phase transition. A third, hybrid exit criteria is used to determine the location of the boundary to arbitrary precision and to characterize the threshold behavior. The possible effects this behavior might have on cosmological phase transitions are briefly discussed.

Results are presented from numerical simulations of the Einstein-Maxwell-Higgs equations with a broken U(1) symmetry. Coherent nontopological soliton solutions are shown to exist that separate an Anti-de Sitter (AdS) true vacuum interior from a Reissner-Nordstrom (RN) false vacuum exterior. The stability of these bubble solutions is tested by perturbing the charge of the coherent solution and evolving the time-dependent equations of motion. In the weak gravitational limit, the short-term stability depends on the sign of (ω/Q) ∂ωQ, similar to Q-balls. The long-term end state of the perturbed solutions demonstrates a rich structure and is visualized using "phase diagrams." Regions of both stability and instability are shown to exist for κg 0.015, while solutions with κg 0.015 were observed to be entirely unstable. Threshold solutions are shown to demonstrate time-scaling laws, and the space separating true and false vacuum end states is shown to be fractal in nature, similar to oscillons. Coherent states with superextremal charge-to-mass ratios are shown to exist and observed to collapse or expand, depending on the sign of the charge perturbation. Expanding superextremal bubbles induce a phase transition to the true AdS vacuum, while collapsing superextremal bubbles can form nonsingular strongly gravitating solutions with superextremal RN exteriors.

Results are presented from numerical simulations of the flat-space nonlinear Maxwell-Klein-Gordon equations demonstrating deep inelastic scattering of m ¼ 1 vortices for a range of Ginzburg-Landau (or Abelian-Higgs) parameters (κ), impact parameters (b), and initial velocities (v 0). The threshold (v à 0) of right-angle scattering is explored for head-on (b ¼ 0) collisions by varying v 0. Solutions obey time-scaling laws, T ∝ α lnðv 0 − v à 0 Þ, with κ-dependent scaling exponents, α, and have v à 0 that appear not to have the previously reported upper bound. The arbitrarily long-lived static intermediate attractor at criticality (v 0 ¼ v à 0) is observed to be the κ-specific m ¼ 2 vortex solution. Scattering angles are observed for off-axis (b ≠ 0) collisions for a wide range of b, v 0 , and κ. It is shown that for arbitrarily small impact parameters (b → 0), the unstable κ-dependent m ¼ 2 "critical" vortex is an intermediate attractor and decays with a κ-independent scattering angle of 135°, as opposed to either of the well-known values of 180°or 90°for b ¼ 0.

Cost functions that are constructed by coherently summing (model-to-data) correlations over hydrophone pairs and frequency have been used successfully for source localization [E. K. Westwood, J. Acoust. Soc. Am. 91, 2777–2789 (1992)] as well as source localization and environmental inversion [Neilsen, J. Acoust. Soc. Am. (to be published)]. Although the coherent sum is usually taken over the same frequency for both data and model, it is shown that summing over other regions of the fdata⊗fmodel space is also useful and may facilitate more efficient source localization. It is shown that lines of constant fdata/fmodel correspond to different source bearings. Although looking along lines of constant fdata/fmodel can be used as a crude form of spatial filtering, a new non-plane-wave spatial filter is also constructed that helps localize sources in the presence of multiple interferers. The spatial filter employed uses the environmental model to construct its set of basis functions and is therefore theoretically capable of spatially filtering in full 3-D as opposed to just bearing, as is done in adaptive beamforming.