Salt creeping is a ubiquitous phenomenon in which crystals precipitate far from an evaporating salt solution boundary, which constitutes a major problem in outdoor electronics, civil engineering, artworks, and agriculture. We report a novel experimental approach that allows to quantitatively describe the creeping mechanism and demonstrate its universality with respect to different salts. We show that there exists a critical contact angle below which salt creeping occurs, provided also the nucleation of multiple crystals is favored. The precipitation of new crystals happens ahead of the contact line by the meniscus that progressively advances over the crystals forming also nanometric precursor films. This enlarges the evaporative area, causing an exponential increase in the crystal mass in time. The self-amplifying process then results in a spectacular three-dimensional crystal network at macroscopic distances from the solution reservoir. These findings also allow us to control the creeping by using crystallization modifiers.

We numerically investigate free and self-interacting ultralight scalar fields around black holes in General Relativity. We focus on complex scalar fields Φ whose self-interactions are described by the quartic potential V ∝ λ |Φ|4, and ignore the black hole spin in order to disentangle the effects of self interactions on the boson cloud. Using the spectral solver Kadath, we compute quasi-equilibrium configurations of the dominant eigenstates, including their backreaction on the spacetime metric. For scenarios with -10-2 ≲ λ ≲ 10-2 we find the mass of the self-interacting scalar cloud to be up to ∼ 70% larger than that of a free scalar cloud, though the additional backreaction effect on the spacetime metric is only up to ∼ 1% due to the low-density nature of the bosonic configurations. In this region of parameter space we observe approximate quadratic scalings between the mass of the cloud with λ, the scalar field amplitude, and the couplings between these two parameters. For systems with λ beyond this range, the eigenfrequencies differ sufficiently from the known free-test-field values used as inputs in our numerical setup to make the results, though convergent, physically unreliable. This bounds the range of λ in which the free scalar field solution remains a good approximation to self-interacting scalar field configurations. Our work is among the first nonperturbative explorations of self-interacting bosonic clouds around black holes, yielding detailed new insights into such systems in the nonlinear regime, while also overcoming technical challenges and quantifying limitations. Additionally, our results provide useful inputs for fully dynamical numerical relativity simulations and for future explorations of spinning black holes and real scalar fields.

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A key problem in network theory is how to reconfigure a graph in order to optimize a quantifiable objective. Given the ubiquity of networked systems, such work has broad practical applications in a variety of situations, ranging from drug and material design to telecommunications. The large decision space of possible reconfigurations, however, makes this problem computationally intensive. In this paper, we cast the problem of network rewiring for optimizing a specified structural property as a Markov Decision Process (MDP), in which a decision-maker is given a budget of modifications that are performed sequentially. We then propose a general approach based on the Deep Q-Network (DQN) algorithm and graph neural networks (GNNs) that can efficiently learn strategies for rewiring networks. We then discuss a cybersecurity case study, i.e., an application to the computer network reconfiguration problem for intrusion protection. In a typical scenario, an attacker might have a (partial) map of the system they plan to penetrate; if the network is effectively "scrambled", they would not be able to navigate it since their prior knowledge would become obsolete. This can be viewed as an entropy maximization problem, in which the goal is to increase the surprise of the network. Indeed, entropy acts as a proxy measurement of the difficulty of navigating the network topology. We demonstrate the general ability of the proposed method to obtain better entropy gains than random rewiring on synthetic and real-world graphs while being computationally inexpensive, as well as being able to generalize to larger graphs than those seen during training. Simulations of attack scenarios confirm the effectiveness of the learned rewiring strategies.Preprint. Under review.