Prediction of the drag reduction effect of pulsating pipe flow based on machine learning

Prediction of drag reduction effect caused by pulsating pipe flows is examined using machine learning. First, a large set of flow field data is obtained experimentally by measuring turbulent pipe flows with various pulsation patterns. Consequently, more than 7000 waveforms are applied, obtaining a maximum drag reduction rate and maximum energy saving rate of 38.6% and 31.4%, respectively. The results indicate that the pulsating flow effect can be characterized by the pulsation period and pressure gradient during acceleration and deceleration. Subsequently, two machine learning models are tested to predict the drag reduction rate. The results confirm that the machine learning model developed for predicting the time variation of the flow velocity and differential pressure with respect to the pump voltage can accurately predict the nonlinearity of pressure gradients. Therefore, using this model, the drag reduction effect can be estimated with high accuracy.     

Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Parametric modeling of steady-state gradient coil vibration: Resonance dynamics under variations in cylinder geometry

Gradient coil (GC) vibration is the root cause of many problems in MRI adversely affecting scanner performance, image quality, and acoustic noise levels. A critical issue is that GC vibration will be significantly increased close to any GC mechanical resonances. It is well known that altering the dimensions of a GC fundamentally affects the mechanical resonances excited by the GC windings. The precise nature of the effects (i.e., how the resonances are affected) is however not well understood. The purpose of the present paper is to study how the mechanical resonances excited by closed whole-body Z-gradient coils are affected by variations in cylinder geometry. A mathematical Z-gradient coil vibration model recently developed and validated by the authors is used to theoretically study the resonance dynamics under variation(s) in cylinder: (i) length, (ii) mean radius, and (iii) radial thickness. The forced-vibration response to Lorentz-force excitation is in each case analyzed in terms of the frequency response of the GC cylinder's displacement. In cases (i) and (ii), the qualitative dynamics are simple: reducing the cylinder length and/or mean radius causes all mechanical resonances to shift to higher frequencies. In case (iii), the qualitative dynamics are much more complicated with different resonances shifting in different directions and additional dependencies on the cylinder length. The more detailed dynamics are intricate owing to the fact that resonances shift at comparatively different rates and this leads to several novel and theoretically interesting predicted effects. Knowledge of these effects advance our understanding of the basic mechanics of GC vibration and offer practically useful insights into how such vibration may be passively reduced.     

Dynamics of laser-induced cavitation bubble during expansion over sharp-edge geometry submerged in liquid – an inside view by diffuse illumination

Laser ablation in liquids is growing in popularity for various applications including nanoparticle production, breakdown spectroscopy, and surface functionalization. When laser pulse ablates the solid target submerged in liquid, a cavitation bubble develops. In case of “finite” geometries of ablated solids, liquid dynamical phenomena can occur inside the bubble when the bubble overflows the surface edge. To observe this dynamics, we use diffuse illumination of a flashlamp in combination with a high-speed videography by exposure times down to 250 ns. The developed theoretical modelling and its comparison with the experimental observations clearly prove that this approach widens the observable area inside the bubble. We thereby use it to study the dynamics of laser-induced cavitation bubble during its expansion over a sharp-edge (“cliff-like” 90°) geometry submerged in water, ethanol, and polyethylene glycol 300. The samples are 17 mm wide stainless steel plates with thickness in the range of 0.025–2 mm. Bubbles are induced on the samples by 1064-nm laser pulses with pulse durations of 7–60 ns and pulse energies of 10–55 mJ. We observe formation of a fixed-type secondary cavity behind the edge where low-pressure area develops due to bubble-driven flow of the liquid. This occurs when the velocity of liquid overflow exceeds ~20 m s⁻¹. A re-entrant liquid injection with up to ~40 m s⁻¹ velocity may occur inside the bubble when the bubble overflows the edge of the sample. Formation and characteristics of the jet evidently depend on the relation between the breakdown-edge offset and the bubble energy, as well as the properties of the surrounding liquid. Higher viscosity of the liquid prevents the generation of the jet.     

Transfer learning in deep neural network based under-sampled MR image reconstruction

In Magnetic Resonance Imaging (MRI), the success of deep learning-based under-sampled MR image reconstruction depends on: (i) size of the training dataset, (ii) generalization capabilities of the trained neural network. Whenever there is a mismatch between the training and testing data, there is a need to retrain the neural network from scratch with thousands of MR images obtained using the same protocol. This may not be possible in MRI as it is costly and time consuming to acquire data. In this research, a transfer learning approach i.e. end-to-end fine tuning is proposed for U-Net to address the data scarcity and generalization problems of deep learning-based MR image reconstruction. First the generalization capabilities of a pre-trained U-Net (initially trained on the human brain images of 1.5 T scanner) are assessed for: (a) MR images acquired from MRI scanners of different magnetic field strengths, (b) MR images of different anatomies and (c) MR images under-sampled by different acceleration factors. Later, end-to-end fine tuning of the pre-trained U-Net is proposed for the reconstruction of the above-mentioned MR images (i.e. (a), (b) and (c)). The results show successful reconstructions obtained from the proposed method as reflected by the Structural SIMilarity index, Root Mean Square Error, Peak Signal-to-Noise Ratio and central line profile of the reconstructed images.     

Stabilization to a positive equilibrium for some reaction–diffusion systems

The aim of this paper is to study the asymptotic behavior of solutions for some reaction–diffusion systems in biology. First, we establish a Liouville type theorem for entire solutions of these reaction–diffusion systems. Based on this theorem, we derive the stabilization of the solutions of the reaction–diffusion system to the unique positive constant state, under the condition that this positive constant state is globally stable in the corresponding kinetic systems. Two specific examples about spreading phenomena from ecology and epidemiology are given to illustrate the application of this theory.     

Behavior and process of background signal formation of hydrogen,carbon, nitrogen,and oxygen in silicon wafers during depth profiling using dual-beam TOF-SIMS

The behavior and mechanism of background signals during depth profiling of atmospheric elements using dual-beam time-of-flight secondary ion mass spectrometry (TOF-SIMS) have been experimentally investigated for silicon wafers. The background signals of atmospheric elements were found to be inversely proportional to the sputtering rate. Most of the background signals are largely attributable to the accumulation of components through adsorption and ion bombardment in the pre-equilibrium state. On the other hand, the contribution of real-time adsorption during the instant after the last sputtering in the equilibrium state is negligible under the present experimental conditions. H₂O is dominant in the background formation process of hydrogen and oxygen, which is supported by the higher adsorption coefficients. The background levels of carbon and nitrogen are lower than those of hydrogen and oxygen. Furthermore, the background signal of carbon with respect to the sputtering rate shows a different trend than the other elements. This could be attributed to accumulation in the pre-equilibrium state. These results indicate that the background levels can be lowered close to those of dynamic-SIMS by using an extremely high sputtering rate in dual-beam TOF-SIMS.