Chaotic Explosions

We investigate chaotic dynamical systems for which the intensity of trajectories might grow unlimited in time. We show that (i) the intensity grows exponentially in time and is distributed spatially according to a fractal measure with an information dimension smaller than that of the phase space,(ii) such exploding cases can be described by an operator formalism similar to the one applied to chaotic systems with absorption (decaying intensities), but (iii) the invariant quantities characterizing explosion and absorption are typically not directly related to each other, e.g., the decay rate and fractal dimensions of absorbing maps typically differ from the ones computed in the corresponding inverse (exploding) maps. We illustrate our general results through numerical simulation in the cardioid billiard mimicking a lasing optical cavity, and through analytical calculations in the baker map.Comment: 7 pages, 5 figure

The characterization and evaluation of accidental explosions

Accidental explosions are discussed from a number of viewpoints. First, all accidental explosions, intentional explosions and natural explosions are characterized by type. Second, the nature of the blast wave produced by an ideal (point source or HE) explosion is discussed to form a basis for describing how other explosion processes yield deviations from ideal blast wave behavior. The current status blast damage mechanism evaluation is also discussed. Third, the current status of our understanding of each different category of accidental explosions is discussed in some detail

Mass distribution of orbiting man-made space debris

Three ways of producing space debris were considered, and data were analyzed to determine mass distributions for man-made space debris. Hypervelocity (3.0 to 4.5 km/sec) projectile impact with a spacecraft wall, high intensity explosions and low intensity explosions were studied. For hypervelocity projectile impact of a spacecraft wall, the number of fragments fits a power law. The number of fragments for both high intensity and low intensity explosions fits an exponential law. However, the number of fragments produced by low intensity explosions is much lower than the number of fragments produced by high intensity explosions. Fragment masses down to 10 to the -7 power gram were produced from hypervelocity impact, but the smallest fragment mass resulting from an explosion appeared to be about 10 mg. Velocities of fragments resulting from hypervelocity impact were about 10 m/sec, and those from low intensity explosions were about 100 m/sec. Velocities of fragments from high intensity explosions were about 3 km/sec

The generalized recurrent set, explosions and Lyapunov functions

We consider explosions in the generalized recurrent set for homeomorphisms on a compact metric space. We provide multiple examples to show that such explosions can occur, in contrast to the case for the chain recurrent set. We give sufficient conditions to avoid explosions and discuss their necessity. Moreover, we explain the relations between explosions and cycles for the generalized recurrent set. In particular, for a compact topological manifold with dimension greater or equal $2$, we characterize explosion phenomena in terms of existence of cycles. We apply our results to give sufficient conditions for stability, under $\mathscr{C}^0$ perturbations, of the property of admitting a continuous Lyapunov function which is not a first integral

Neutrino-driven Explosions

The question why and how core-collapse supernovae (SNe) explode is one of the central and most long-standing riddles of stellar astrophysics. A solution is crucial for deciphering the SN phenomenon, for predicting observable signals such as light curves and spectra, nucleosynthesis, neutrinos, and gravitational waves, for defining the role of SNe in the evolution of galaxies, and for explaining the birth conditions and properties of neutron stars (NSs) and stellar-mass black holes. Since the formation of such compact remnants releases over hundred times more energy in neutrinos than the SN in the explosion, neutrinos can be the decisive agents for powering the SN outburst. According to the standard paradigm of the neutrino-driven mechanism, the energy transfer by the intense neutrino flux to the medium behind the stagnating core-bounce shock, assisted by violent hydrodynamic mass motions (sometimes subsumed by the term "turbulence"), revives the outward shock motion and thus initiates the SN blast. Because of the weak coupling of neutrinos in the region of this energy deposition, detailed, multidimensional hydrodynamic models including neutrino transport and a wide variety of physics are needed to assess the viability of the mechanism. Owing to advanced numerical codes and increasing supercomputer power, considerable progress has been achieved in our understanding of the physical processes that have to act in concert for the success of neutrino-driven explosions. First studies begin to reveal observational implications and avenues to test the theoretical picture by data from individual SNe and SN remnants but also from population-integrated observables. While models will be further refined, a real breakthrough is expected through the next Galactic core-collapse SN, when neutrinos and gravitational waves can be used to probe the conditions deep inside the dying star. (abridged)Comment: Author version of chapter for 'Handbook of Supernovae,' edited by A. Alsabti and P. Murdin, Springer. 54 pages, 13 figure