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This paper proposes a new test for a change point in the mean of high-dimensional data based on the spatial sign and self-normalization. The test is easy to implement with no tuning parameters, robust to heavy-tailedness and theoretically justified with both fixed-and sequential asymptotics under both null and alternatives, where n is the sample size. We demonstrate that the fixed-n asymptotics provide a better approximation to the finite sample distribution and thus should be preferred in both testing and testing-based estimation. To estimate the number and locations when multiple change-points are present, we propose to combine the p-value under the fixed-n asymptotics with the seeded binary segmentation (SBS) algorithm. Through numerical experiments, we show that the spatial sign based procedures are robust with respect to the heavy-tailedness and strong coordinate-wise dependence, whereas their non-robust counterparts proposed in Wang et al. (2022) [28] appear to under-perform. A real data example is also provided to illustrate the robustness and broad applicability of the proposed test and its corresponding estimation algorithm. 

Abstract Channel cutoff is the process by which an active lightning channel cools down, goes dark, and loses its ability to effectively conduct electricity. Current cutoff precedes several lightning phenomena, notably dart leaders and return strokes, but the process by which a hot, highly‐conducting leader channel can undergo current cutoff is poorly understood. In this work, we present self‐consistent simulations of positive leader propagation, which include coupled treatment of electrodynamics and plasma physics. The unstable positive leader spontaneously undergoes channel cutoff and creates the conditions for the emission of dart leaders, that is, it accumulates a packet of negative charge at the intersection between cutoff and conducting channel segments. A residual conductivity in the cutoff section facilitates the conversion of the electric field enhancement into a traveling wave, which retraces and reionizes the channel. This is critical for allowing the frail positive leader to keep propagating. 

Surface waves are excited at the boundary of a mechanically vibrated cylindrical container and are referred to as edge waves. Resonant waves are considered, which are formed by a travelling wave formed at the edge and constructively interfering with its centre reflection. These waves exhibit an axisymmetric spatial structure defined by the mode number $$n$$ . Viscoelastic effects are investigated using two materials with tunable properties; (i) glycerol/water mixtures (viscosity) and (ii) agarose gels (elasticity). Long-exposure white-light imaging is used to quantify the magnitude of the wave slope from which frequency-response diagrams are obtained via frequency sweeps. Resonance peaks and bandwidths are identified. These results show that for a given $$n$$ , the resonance frequency decreases with viscosity and increases with elasticity. The amplitude of the resonance peaks are much lower for gels and decrease further with mode number, indicating that much larger driving amplitudes are needed to overcome the elasticity and excite edge waves. The natural frequencies for a viscoelastic fluid in a cylindrical container with a pinned contact-line are computed from a theoretical model that depends upon the dimensionless Ohnesorge number $${Oh}$$ , elastocapillary number $${Ec}$$ and Bond number $${Bo}$$ . All show good agreement with experimental observations. The eigenvalue problem is equivalent to the classic damped-driven oscillator model on linear operators with viscosity appearing as a damping force and elasticity and surface tension as restorative forces, consistent with our physical interpretation of these viscoelastic effects. 

Surface waves are excited by mechanical vibration of a cylindrical container having an air/water interface pinned at the rim, and the dynamics of pattern formation is analysed from both an experimental and theoretical perspective. The wave conforms to the geometry of the container and its spatial structure is described by the mode number pair ( $$n,\ell$$ ) that is identified by long exposure time white light imaging. A laser light system is used to detect the surface wave frequency, which exhibits either a (i) harmonic response for low driving amplitude edge waves or (ii) sub-harmonic response for driving amplitude above the Faraday wave threshold. The first 50 resonant modes are discovered. Control of the meniscus geometry is used to great effect. Specifically, when flat, edge waves are suppressed and only Faraday waves are observed. For a concave meniscus, edge waves are observed and, at higher amplitudes, Faraday waves appear as well, leading to complicated mode mixing. Theoretical predictions for the natural frequency of surface oscillations for an inviscid liquid in a cylindrical container with a pinned contact line are made using the Rayleigh–Ritz procedure and are in excellent agreement with experimental results.