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Early warning for epilepsy patients is crucial for their safety and well being, in particular, to prevent or minimize the severity of seizures. Through the patients’ electroencephalography (EEG) data, we propose a meta learning framework to improve the prediction of early ictal signals. The proposed bilevel optimization framework can help automatically label noisy data at the early ictal stage, as well as optimize the training accuracy of the backbone model. To validate our approach, we conduct a series of experiments to predict seizure onset in various long-term windows, with long short-term memory (LSTM) and ResNet implemented as the baseline models. Our study demonstrates that not only is the ictal prediction accuracy obtained by meta learning significantly improved, but also the resulting model captures some intrinsic patterns of the noisy data that a single backbone model could not learn. As a result, the predicted probability generated by the meta network serves as a highly effective early warning indicator.
We first derive Alber’s equation for the Wigner distribution function using the fourth-order nonlinear Schrödinger equation, and on the basis of this equation we next analyse the stability of the narrowband approximation of the Joint North Sea Wave Project spectrum. Therefore, one interesting result of this study concerns the effect of modulational instability obtained from the fourth-order nonlinear Schrödinger equation. The analysis is restricted to one horizontal direction, parallel to the direction of wave motion, to take advantage of potential flow theory. We find that shear currents considerably modify the instability behaviours of weakly nonlinear waves. The key point of this study is that the present fourth-order analysis shows considerable deviations in the modulational instability properties from the third-order analysis and reduces the growth rate of instability. Moreover, we present here a connection between the random and deterministic properties of a random wavetrain for vanishing spectrum bandwidth.
This succinct introduction to the fundamental physical principles of turbulence provides a modern perspective through statistical theory, experiments, and high-fidelity numerical simulations. It describes classical concepts of turbulence and offers new computational perspectives on their interpretation based on numerical simulation databases, introducing students to phenomena at a wide range of scales. Unique, practical, multi-part physics-based exercises use realistic data of canonical turbulent flows developed by the Stanford Center for Turbulence Research to equip students with hands-on experience with practical and predictive analysis tools. Over 20 case studies spanning real-world settings such as wind farms and airplanes, color illustrations, and color-coded pedagogy support student learning. Accompanied by downloadable datasets, and solutions for instructors, this is the ideal introduction for students in aerospace, civil, environmental, and mechanical engineering and the physical sciences studying a graduate-level one-semester course on turbulence, advanced fluid mechanics, and turbulence simulation.
The hydroelastic interaction between water waves and multiple submerged porous elastic plates of arbitrary lengths in deep water is examined using the Galerkin approximation technique. We observe the influence of flexible porous plates of arbitrary lengths by analysing the reflection coefficient, dissipated energy and wave forces acting on the plates. Results are presented for various values of angle of incidence, separation lengths of plates, porosity levels, submergence depth and flexural rigidity. The convergence and accuracy of the method are verified by comparing the results with existing literature. The significant impact of flexural rigidity in the presence of porosity on wave reflection, dissipated energy and wave forces is demonstrated. Moreover, a notable reduction in wave load is observed with an increase in the number of plates.
It is critical to evaluate whether the flow has transitioned into turbulence because most of the impact of large-scale mixing occurs when the flow becomes fully developed turbulence. Hydrodynamic instability flows are even more complex because of their time-dependent nature; therefore, both spatial and temporal criteria will be introduced in great detail to demonstrate the necessary and sufficient conditions for the flow to transition to turbulence. These criteria will be extremely helpful for designing experiments and numeric simulations with the goal to study large-scale turbulence mixing. One spatial criterion is that the Reynolds number must achieve a critical minimum value of 160,000. In addition, the temporal criteria suggest that flows need to be given approximately four eddy-turnover-times. This chapter will expand on these issues.
We focus on three integrated measures of the mixing: the mixed-width, mixedness, and mixed mass. I will also examine the dependence of these mixing parameters on density disparities, Mach numbers, and other flow properties. It is shown that the mixed mass is nondecreasing. The asymmetry of the bubble and spike is also discussed.
There is significant simulation and experimental evidence suggesting that hydrodynamic instability induced flows may be dependent on how the initial conditions are set up. The initial surface perturbations, density disparity, and the strength of the shockwaves could all be factors that lead to a completely different flow field in later stages.
The nonlinear stage starts when the amplitude of the unstable flow feature becomes significant. This chapter first studies the nonlinear growth of the interface amplitude and its associated terminal velocity with potential flow models, both for RM and RT. Next, one describes several models intended to predict the evolution of the bubble and spike heights, and the corresponding velocities, for the nonlinear stage. The success and limitations of each model are assessed with comparison to experiments and numerical simulations. The sensitivities to viscosity, density ratio and Mach number are discussed.
I will describe how certain external factors, such as rotation and time-dependent acceleration/deceleration, could suppress the evolution of the hydrodynamic instabilities.
By necessity, experimental studies have been the key to advancement in fluid dynamics for centuries. However, with the rapid increase of computational capabilities, numerical approaches have become an acceptable surrogate for experiments. Calculations must resolve the Navier–Stokes equations or approximate methods constructed from them. I will discuss the pros and cons of various types of approaches used, including direct numerical simulations, subgrid models, and implicit grid-discretization-based large-eddy simulation.
This chapter contains a discussion of the coupling of a magnetic field, through the framework of magnetohydrodynamics (MHD), to the hydrodynamic body forces. This leads to an additional body force, namely the Lorentz force on electrical currents in the fluid. Due to their conductivity, this effect is especially important for ionized plasmas. The intuitive result is that the magnetic field lines follow the flow, and they have an effective tension that can stabilize the RTI. As with the RTI, the RMI can be suppressed by a magnetic field.
The challenge confronting researchers is significant in many ways. One can start by noting that multiple instabilities might exist simultaneously and interact with each other. As an example, oblique shocks generate all three instabilities: RT, RM, and KH. In this chapter, several combined instabilities are discussed: RTI and RMI, RTI and/or RMI with KHI.
In this chapter, we will focus on the statistical spectral dynamics which are paramount to understanding the development of the integrated mixing quantities described in Chapter 5. Reynolds flow averaging and the turbulent kinetic energy are introduced. In addition, I will discuss how the energy of the flows is transferred from large scale to small scale modes, as well as the impact of the shockwave and gravity on the isotropy of the flows. The flow spectra allow several important length scales to be defined. Numeric simulations and experimental data will be offered to provide insights on the mixing processes.
This chapter will provide a detailed presentation of the basic structure of the supernova and its core collapse process to illustrate the roles that RMI, RTI, and KHI play in the different stages of these processes. During the explosions, the shockwave passing through the onion-like supernova core will generate both RMI and RTI. The RTI is the key physical process creating the filament structures observed in the Crab Nebula. MHD RT instabilities will be presented to show how they can further improve the comparison between simulations and observations. Several additional applications where hydrodynamic instability plays an important role will also be examined. Geophysics and solar physics also present effective lenses to view the importance of hydrodynamic instabilities. In the case of solar physics, I will describe how RTI’s impact can be viewed through various phenomena, such as the plumes that rise from low density bubbles as well as eruptions that occur as material returns to the solar surface. Once again, MHD RT instabilities are relevant.
After the RM instability grows from a first shock, it can be hit by a second shock. These reshock scenarios have been found in the key applications of inertial confinement fusion implosions or supernova explosions. In this chapter, I will introduce the efforts to model the growth of the mixing layer induced by the first shock and subsequent reshock and describe how the turbulence kinetic energy and anisotropy might be affected by the reshock events. Data from shock tube experiments and numeric simulations will also be introduced to provide insight into the reshock RM induced flows.