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We investigate the stability of self-similar solutions for a gravitationally collapsing isothermal sphere in Newtonian gravity by means of a normal mode analysis. It is found that the Hunter series of solutions are highly unstable, while neither the Larson-Penston solution nor the homogeneous collapse one have an analytic unstable mode. Since the… (More)
Presence of inhomogeneous layered structures of ionic liquid (IL) molecules at IL/HOPG and IL/mica interfaces was directly detected and imaged by using frequency-modulation atomic force microscopy. High stability of the layered structures may disturb their interface applications to catalysis and electrochemistry.
This paper proposes a general video game playing AI that combines a pathfmding algorithm with Knowledge-based Fast-Evolutionary Monte-Carlo tree search (KB Fast-Evo MCTS). This AI is able to acquire knowledge of the game through simulation, select suitable targets on the map using the acquired knowledge, and head to the target in an efficient manner. In… (More)
Lemaitre–Tolman–Bondi models as specific spherically symmetric solutions of general relativity simplify in their reduced form some of the mathematical ingredients of black hole or cosmological applications. The conditions imposed in addition to spherical symmetry turn out to take a simple form at the kinematical level of loop quantum gravity, which allows a… (More)
The asynchronous evolution has an advantage when evolving solutions with excessively different evaluation time since the asynchronous evolution evolves each solution independently without waiting for other evaluations, unlike the synchronous evolution requires evaluations of all solutions at the same time. As a novel asynchronous evolution approach, this… (More)
General relativity as well as Newtonian gravity admits self-similar solutions due to its scale-invariance. This is a review on these self-similar solutions and their relevance to gravitational collapse. In particular, our attention is mainly paid on the crucial role of self-similar solutions in the critical behavior and attraction in gravitational collapse.