Erosion waves: transverse instabilities and fingering

Two laboratory scale experiments of dry and under-water avalanches of non-cohesive granular materials are investigated. We trigger solitary waves and study the conditions under which the front is transversally stable. We show the existence of a linear instability followed by a coarsening dynamics and finally the onset of a fingering pattern. Due to the different operating conditions, both experiments strongly differ by the spatial and time scales involved. Nevertheless, the quantitative agreement between the stability diagram, the wavelengths selected and the avalanche morphology reveals a common scenario for an erosion/deposition process.Comment: 4 pages, 6 figures, submitted to PR

Stabilization of unstable steady states by variable delay feedback control

We report on a dramatic improvement of the performance of the classical time-delayed autosynchronization method (TDAS) to control unstable steady states, by applying a time-varying delay in the TDAS control scheme in a form of a deterministic or stochastic delay-modulation in a fixed interval around a nominal value $T_0$. The successfulness of this variable delay feedback control (VDFC) is illustrated by a numerical control simulation of the Lorenz and R\"{o}ssler systems using three different types of time-delay modulations: a sawtooth wave, a sine wave, and a uniform random distribution. We perform a comparative analysis between the VDFC method and the standard TDAS method for a sawtooth-wave modulation by analytically determining the domains of control for the generic case of an unstable fixed point of focus type.Comment: 7 pages, 4 figures, RevTe

Squeezing superfluid from a stone: Coupling superfluidity and elasticity in a supersolid

In this work we start from the assumption that normal solid to supersolid (NS-SS) phase transition is continuous, and develop a phenomenological Landau theory of the transition in which superfluidity is coupled to the elasticity of the crystalline $^4$He lattice. We find that the elasticity does not affect the universal properties of the superfluid transition, so that in an unstressed crystal the well-known $\lambda$-anomaly in the heat capacity of the superfluid transition should also appear at the NS-SS transition. We also find that the onset of supersolidity leads to anomalies in the elastic constants near the transition; conversely, inhomogeneous strains in the lattice can induce local variations of the superfluid transition temperature, leading to a broadened transition.Comment: 4 page

Out-of-equilibrium states as statistical equilibria of an effective dynamics

We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Non equilibrium structures are shown to correspond to statistical equilibria of an effective dynamics, which is derived using averaging techniques. This simple behavior might be a prototype of others observed in more complicated systems with long-range interactions, like two-dimensional incompressible fluids or self-gravitating systems.Comment: 4 figure

Quantum Brownian motion under rapid periodic forcing

We study the steady state behaviour of a confined quantum Brownian particle subjected to a space-dependent, rapidly oscillating time-periodic force. To leading order in the period of driving, the result of the oscillating force is an effective static potential which has a quantum dissipative contribution, $V_{QD}$, which adds on to the classical result. This is shown using a coherent state representation of bath oscillators. $V_{QD}$ is evaluated exactly in the case of an Ohmic dissipation bath. It is strongest for intermediate values of the damping, where it can have pronounced effects.Comment: 11 Pages and 3 figures, Content change

Multi-threshold second-order phase transition

We present a theory of the multi-threshold second-order phase transition, and experimentally demonstrate the multi-threshold second-order phase transition phenomenon. With carefully selected parameters, in an external cavity diode laser system, we observe second-order phase transition with multiple (three or four) thresholds in the measured power-current-temperature three dimensional phase diagram. Such controlled death and revival of second-order phase transition sheds new insight into the nature of ubiquitous second-order phase transition. Our theory and experiment show that the single threshold second-order phase transition is only a special case of the more general multi-threshold second-order phase transition, which is an even richer phenomenon.Comment: 5 pages, 3 figure