We derive a Doi-Peliti field theory for free active Ornstein-Uhlenbeck particles, or, equivalently, free inertial Brownian particles, and present a way to diagonalize the quadratic part of the action and calculate the propagator. Unlike previous coarse-grained approaches this formulation correctly tracks particle identity and yet can easily be expanded to include potentials and arbitrary reactions.The zeroth law is one of the oldest conjectures in turbulence that is still unproven. Here, we consider weak solutions of one-dimensional compressible magnetohydrodynamics and demonstrate that the lack of smoothness of the fields introduces a dissipative term, named inertial dissipation, into the expression of energy conservation that is neither viscous nor resistive in nature. We propose exact solutions assuming that the kinematic viscosity and the magnetic diffusivity are equal, and we demonstrate that the associated inertial dissipation is positive and equal on average to the mean viscous dissipation rate in the limit of small viscosity, proving the conjecture of the zeroth law of turbulence and the existence of an anomalous dissipation. As an illustration, we evaluate the shock heating produced by discontinuities detected by Voyager in the solar wind around 5 AU. We deduce a heating rate of ∼10^-18Jm^-3s^-1, which is significantly higher than the value obtained from the turbulent fluctuations. This suggests that collisionless shocks can be a dominant source of heating in the outer solar wind.Understanding of the behavior of an individual droplet suspended in a liquid and subjected to a stress is important for studying and designing more complex systems, such as emulsions. Here, we present an experimental study of the behavior of a particle-covered droplet and its particle shell under compressive stress. The stress was induced by an application of a DC electric field. this website We studied how the particle coverage (φ), particle size (d), and the strength of an electric field (E) influence the magnitude of the droplet deformation (D). The experimental results indicate that adding electrically insulating particles to a droplet interface drastically changes the droplet deformation by increasing its magnitude. We also found that the magnitude of the deformation is not retraceable during the electric field sweeping, i.e., the strain-stress curves form a hysteresis loop due to the energy dissipation. The field-induced droplet deformation was accompanied by structural and morphological changes in the particle shell. We found that shells made of smaller particles were more prone to jamming and formation of arrested shells after removal of an electric stress.The derivative nonlinear Schrödinger (DNLS) equation is the canonical model for the dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the DNLS equation. We show that the space-time localization of a rogue wave is only possible if the periodic standing wave is modulationally unstable. If the periodic standing wave is modulationally stable, the rogue wave solutions degenerate into algebraic solitons propagating along the background and interacting with the periodic standing waves. Maximal amplitudes of rogue waves are found analytically and confirmed numerically.This is a continuation of previous works [S. Takata and T. Noguchi, J. Stat. Phys. 172, 880 (2018)JSTPBS0022-471510.1007/s10955-018-2068-z; S. Takata, T. Matsumoto, A. Hirahara, and M. Hattori, Phys. Rev. E 98, 052123 (2018)2470-004510.1103/PhysRevE.98.052123]. The simple model proposed in the previous works is extended to be free from the isothermal assumption. The new model conserves the total mass, momentum, and energy in the periodic domain. A monotone functional is found, assuring the H theorem for the new model. Different approaches are taken to tell apart the stable, the metastable, and the unstable uniform equilibrium state. Numerical simulations are also conducted for spatially one-dimensional cases to demonstrate various features occurring in the time evolution process. A prediction method for the profile at the stationary state is discussed as well.We study some dynamical properties of a charged particle that moves in a nonhomogeneous electric field and collides against an oscillating platform. Depending on the values of parameters, the system presents (i) predominantly regular dynamics or (ii) structures of chaotic behavior in phase space conditioned to the initial conditions. The localization of the fixed points and their stability are carefully discussed. Average properties of the chaotic sea are investigated under a scaling approach. We show that the system belongs to the same universality class as the Fermi-Ulam model.We report on the prewavy (PW) instability in ac field-driven electrohydrodynamics that is induced in a nematic liquid crystal (NLC) sandwiched between parallel electrodes. The instability is characterized by a twist mode of the NLC director along the vertical orientation to the electrodes (i.e., the z axis), generating a periodic pattern having a large wavelength (λ_PW) in the xy plane. The PW periodic to the preferred director n_0 of the NLC should be distinguished from well-known electroconvection (EC) such as normal rolls (NRs) and abnormal rolls (ARs) with similar wave vectors. A reentrant PW (PW2) was discovered by employing well-adjusted optical conditions and a dynamic image-process method. The wavelength λ_PW2 of the PW2 accompanying turbulent EC was measured as functions of the applied ac voltage and frequency, which was distinguished from λ_PW1 of the primary PW (PW1) separated from the NR. Moreover, the appearance, disappearance, and reappearance of the PW were investigated for five frequency regions classified in the ac field-driven EC; it was found that the high frequency and high voltage causes competition between the rising mode (θ, tilting angle to the xy plane) and twist mode (ϕ, in-plane angle to the x axis) of the director through electrohydrodynamic coupling between the director field and flows. We discuss how the PW2 can arise by considering another twist mode known as AR instability.