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A thin solid (e.g., paper), burning against an oxidizing wind, develops a fingering instability with two decoupled length scales. The spacing between fingers is determined by the Peclet number (ratio between advection and diffusion). The finger width is determined by the degree two dimensionality. Dense fingers develop by recurrent tip splitting. The effect is observed when vertical mass transport (due to gravity) is suppressed. The experimental results quantitatively verify a model based on diffusion limited transport.
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The shape instability of magnetic domain walls under current is investigated in a ferromagnetic (Ga,Mn)(As,P) film with perpendicular anisotropy. Domain wall motion is driven by the spin transfer torque mechanism. A current density gradient is found either to stabilize domains with walls perpendicular to current lines or to produce finger-like patterns, depending on the domain wall motion direction. The instability mechanism is shown to result from the non-adiabatic contribution of the spin transfer torque mechanism.
The growth dynamics of an air finger injected in a visco-elastic gel (a PVA/borax aqueous solution) is studied in a linear Hele-Shaw cell. Besides the standard Saffmann-Taylor instability, we observe - with increasing finger velocities - the existence of two new regimes: (a) a stick-slip regime for which the finger tip velocity oscillates between 2 different values, producing local pinching of the finger at regular intervals, (b) a ``tadpole regime where a fracture-type propagation is observed. A scaling argument is proposed to interpret the dependence of the stick-slip frequency with the measured rheological properties of the gel.
While analytical solutions of critical (phase) transitions in physical systems are abundant for simple nonlinear systems, such analysis remains intractable for real-life dynamical systems. A key example of such a physical system is thermoacoustic instability in combustion, where prediction or early detection of an onset of instability is a hard technical challenge, which needs to be addressed to build safer and more energy-efficient gas turbine engines powering aerospace and energy industries. The instabilities arising in combustion chambers of engines are mathematically too complex to model. To address this issue in a data-driven manner instead, we propose a novel deep learning architecture called 3D convolutional selective autoencoder (3D-CSAE) to detect the evolution of self-excited oscillations using spatiotemporal data, i.e., hi-speed videos taken from a swirl-stabilized combustor (laboratory surrogate of gas turbine engine combustor). 3D-CSAE consists of filters to learn, in a hierarchical fashion, the complex visual and dynamic features related to combustion instability. We train the 3D-CSAE on frames of videos obtained from a limited set of operating conditions. We select the 3D-CSAE hyper-parameters that are effective for characterizing hierarchical and multiscale instability structure evolution by utilizing the dynamic information available in the video. The proposed model clearly shows performance improvement in detecting the precursors of instability. The machine learning-driven results are verified with physics-based off-line measures. Advanced active control mechanisms can directly leverage the proposed online detection capability of 3D-CSAE to mitigate the adverse effects of combustion instabilities on the engine operating under various stringent requirements and conditions.
Neural networks (NN) are implemented as sub-grid flame models in a large-eddy simulation of a single-injector liquid-propellant rocket engine. The NN training process presents an extraordinary challenge. The multi-dimensional combustion instability problem involves multi-scale lengths and characteristic times in an unsteady flow problem with nonlinear acoustics, addressing both transient and dynamic-equilibrium behaviors, superimposed on a turbulent reacting flow with very narrow, moving flame regions. Accurate interpolation between the points of the training data becomes vital. The NNs proposed here are trained based on data processed from a few CFD simulations of a single-injector liquid-propellant rocket engine with different dynamical configurations to reproduce the information stored in a flamelet table. The training set is also enriched by data from the physical characteristics and considerations of the combustion model. Flame temperature is used as an extra input for other flame variables to improve the NN-based model accuracy and physical consistency. The trained NNs are first tested offline on the flamelet table. These physics-aware NN-based closure models are successfully implemented into CFD simulations and verified by being tested on various dynamical configurations. The results from those tests compare favorably with counterpart table-based CFD simulations.
Recent observations of a large number of DA and DB white dwarfs show evidence of debris disks, which are the remnants of old planetary systems. The infrared excess detected with emph{Spitzer} and the lines of heavy elements observed in their atmospheres with high-resolution spectroscopy converge on the idea that planetary material accretes onto these stars. Accretion rates have been derived by several authors with the assumption of a steady state between accretion and gravitational settling. The results are unrealistically different for DA and DB white dwarfs. When heavy matter is accreted onto stars, it induces an inverse $mu$-gradient that leads to fingering (thermohaline) convection. The aim of this letter is to study the impact of this specific process on the derived accretion rates in white dwarfs and on the difference between DA and DB. We solve the diffusion equation for the accreted heavy elements with a time-dependent method. The models we use have been obtained both with the IRAP code, which computes static models, and the La Plata code, which computes evolutionary sequences. Computations with pure gravitational settling are compared with computations that include fingering convection. The most important result is that fingering convection has very important effects on DAs but is inefficient in DBs. When only gravitational settling is taken into account, the time-dependent computations lead to a steady state, as postulated by previous authors. When fingering convection is added, this steady state occurs much later. The surprising difference found in the past for the accretion rates derived for DA and DB white dwarfs disappears. The derived accretion rates for DAs are increased when fingering convection is taken into account, whereas those for DBs are not modified. More precise and developed results will be given in a forthcoming paper.
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