scholarly journals A neural network closure for the Euler-Poisson system based on kinetic simulations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Léo Bois ◽  
Emmanuel Franck ◽  
Laurent Navoret ◽  
Vincent Vigon
Keyword(s):  
Neural Network ◽  
Spatial Density ◽  
Data Generation ◽  
Poisson System ◽  
Mean Velocity ◽  
One Dimensional ◽  
Poisson Equations ◽  
Wide Range ◽  
The One ◽  
Uniform Accuracy

<p style='text-indent:20px;'>This work deals with the modeling of plasmas, which are ionized gases. Thanks to machine learning, we construct a closure for the one-dimensional Euler-Poisson system valid for a wide range of collisional regimes. This closure, based on a fully convolutional neural network called V-net, takes as input the whole spatial density, mean velocity and temperature and predicts as output the whole heat flux. It is learned from data coming from kinetic simulations of the Vlasov-Poisson equations. Data generation and preprocessings are designed to ensure an almost uniform accuracy over the chosen range of Knudsen numbers (which parametrize collisional regimes). Finally, several numerical tests are carried out to assess validity and flexibility of the whole pipeline.</p>

scholarly journals Application of Deep Learning in Fault Diagnosis of Rotating Machinery

Processes ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 919
Author(s):  
Wanlu Jiang ◽  
Chenyang Wang ◽  
Jiayun Zou ◽  
Shuqing Zhang
Keyword(s):  
Neural Network ◽  
Feature Extraction ◽  
Fault Diagnosis ◽  
Rotating Machinery ◽  
Generative Adversarial Networks ◽  
Extraction Ability ◽  
One Dimensional ◽  
Adversarial Networks ◽  
Diagnosis Model ◽  
The One

The field of mechanical fault diagnosis has entered the era of “big data”. However, existing diagnostic algorithms, relying on artificial feature extraction and expert knowledge are of poor extraction ability and lack self-adaptability in the mass data. In the fault diagnosis of rotating machinery, due to the accidental occurrence of equipment faults, the proportion of fault samples is small, the samples are imbalanced, and available data are scarce, which leads to the low accuracy rate of the intelligent diagnosis model trained to identify the equipment state. To solve the above problems, an end-to-end diagnosis model is first proposed, which is an intelligent fault diagnosis method based on one-dimensional convolutional neural network (1D-CNN). That is to say, the original vibration signal is directly input into the model for identification. After that, through combining the convolutional neural network with the generative adversarial networks, a data expansion method based on the one-dimensional deep convolutional generative adversarial networks (1D-DCGAN) is constructed to generate small sample size fault samples and construct the balanced data set. Meanwhile, in order to solve the problem that the network is difficult to optimize, gradient penalty and Wasserstein distance are introduced. Through the test of bearing database and hydraulic pump, it shows that the one-dimensional convolution operation has strong feature extraction ability for vibration signals. The proposed method is very accurate for fault diagnosis of the two kinds of equipment, and high-quality expansion of the original data can be achieved.

Global Solutions to the One-Dimensional Compressible Navier--Stokes--Poisson Equations with Large Data

2013 ◽  
Vol 45 (2) ◽  
pp. 547-571 ◽  
Author(s):  
Zhong Tan ◽  
Tong Yang ◽  
Huijiang Zhao ◽  
Qingyang Zou
Keyword(s):  
Global Solutions ◽  
Large Data ◽  
Navier Stokes ◽  
One Dimensional ◽  
Poisson Equations ◽  
The One

scholarly journals Plane thermonuclear detonation waves initiated by proton beams and quasi-one-dimensional model of fast ignition

2014 ◽  
Vol 33 (1) ◽  
pp. 65-80 ◽  
Author(s):  
Alexander A. Charakhch'yan ◽  
Konstantin V. Khishchenko
Keyword(s):  
Detonation Wave ◽  
Fusion Reaction ◽  
Plasma Heating ◽  
Symmetry Plane ◽  
Detonation Waves ◽  
Proton Beams ◽  
One Dimensional ◽  
Wide Range ◽  
The One ◽  
Α Particles

AbstractThe one-dimensional problem on bilatiral irradiation by proton beams of the plane layer of condensed DT mixture with length 2H and density ρ0 ≤ 100ρs, where ρs is the fuel solid-state density at atmospheric pressure and temperature of 4 K, is considered. The proton kinetic energy is 1 MeV, the beam intensity is 1019 W/cm2 and duration is 50 ps. A mathematical model is based on the one-fluid two-temperature hydrodynamics with a wide-range equation of state of the fuel, electron and ion heat conduction, DT fusion reaction kinetics, self-radiation of plasma and plasma heating by α-particles. If the ignition occurs, a plane detonation wave, which is adjacent to the front of the rarefaction wave, appears. Upon reflection of this detonation wave from the symmetry plane, the flow with the linear velocity profile along the spatial variable x and with a weak dependence of the thermodynamic functions of x occurs. An appropriate solution of the equations of hydrodynamics is found analytically up to an arbitrary constant, which can be chosen so that the analytical solution describes with good accuracy the numerical one. The gain with respect to the energy of neutrons G ≈ 200 at Hρ0 ≈ 1 g/cm2, and G > 2000 at Hρ0 ≈ 5 g/cm2. To evaluate the ignition energy Eig of cylindrical targets, the quasi-1D model, limiting trajectories of α-particles by a cylinder of a given radius, is suggested. The model reproduces the known theoretical dependence Eig ~ ρ0−2 and gives Eig = 160 kJ for ρ0 = 100ρs ≈ 22 g/cm3.

scholarly journals THE ONE-DIMENSIONAL WAVE SPECTRA AT LIMITED FETCH

1972 ◽  
Vol 1 (13) ◽  
pp. 13
Author(s):  
Hisashi Mitsuyasu
Keyword(s):  
Similarity Theory ◽  
Wind Waves ◽  
Laboratory Data ◽  
Peak Frequency ◽  
Wave Spectra ◽  
One Dimensional ◽  
Wide Range ◽  
Laboratory Tank ◽  
The One ◽  
Dimensional Wave

The data for the spectra of wind-generated waves measured in a laboratory tank and in a bay are analyzed using the similarity theory of Kitaigorodski, and the one-dimensional spectra of fetch-limited wind waves are determined from the data. The combined field and laboratory data cover such a wide range of dimensionless fetch F (= gF/u2 ) as F : 102 ~ 10 . The fetch relations for the growthes of spectral peak frequency u)m and of total energy E of the spectrum are derived from the proposed spectra, which are consistent with those derived directly from the measured spectra.

scholarly journals Rare temperature histories and cirrus ice number density in a parcel and a one-dimensional model

2014 ◽  
Vol 14 (23) ◽  
pp. 13013-13022 ◽  
Author(s):  
D. M. Murphy
Keyword(s):  
Temperature Dependence ◽  
Low Temperatures ◽  
Ice Crystals ◽  
Strong Increase ◽  
Number Density ◽  
Dimensional Model ◽  
One Dimensional ◽  
Slow Growth Rate ◽  
Wide Range ◽  
The One

Abstract. A parcel and a one-dimensional model are used to investigate the temperature dependence of ice crystal number density. The number of ice crystals initially formed in a cold cirrus cloud is very sensitive to the nucleation mechanism and the detailed history of cooling rates during nucleation. A possible small spread in the homogeneous freezing threshold due to varying particle composition is identified as a sensitive nucleation parameter. In a parcel model, the slow growth rate of ice crystals at low temperatures inherently leads to a strong increase in ice number density at low temperatures. This temperature dependence is not observed. The model temperature dependence occurs for a wide range of assumptions and for either homogeneous or, less strongly, heterogeneous freezing. However, the parcel model also shows that random temperature fluctuations result in an extremely wide range of ice number densities. A one-dimensional model is used to show that the rare temperature trajectories resulting in the lowest number densities are disproportionately important. Low number density ice crystals sediment and influence a large volume of air. When such fall streaks are included, the ice number becomes less sensitive to the details of nucleation than it is in a parcel model. The one-dimensional simulations have a more realistic temperature dependence than the parcel mode. The one-dimensional model also produces layers with vertical dimensions of meters even if the temperature forcing has a much broader vertical wavelength. Unlike warm clouds, cirrus clouds are frequently surrounded by supersaturated air. Sedimentation through supersaturated air increases the importance of any process that produces small numbers of ice crystals. This paper emphasizes the relatively rare temperature trajectories that produce the fewest crystals. Other processes are heterogeneous nucleation, sedimentation from the very bottom of clouds, annealing of disordered to hexagonal ice, and entrainment.

Numerical model of plasma double layers using the Vlasov equation

1980 ◽  
Vol 23 (3) ◽  
pp. 433-452 ◽  
Author(s):  
Lloyd E. Johnson
Keyword(s):  
Magnetic Field ◽  
Double Layer ◽  
Axial Magnetic Field ◽  
Double Layers ◽  
Plasma Region ◽  
Langmuir Waves ◽  
One Dimensional ◽  
Poisson Equations ◽  
The One ◽  
Do So

The one-dimensional plasma double layer is modelled by numerically integrating the time-dependent Vlasov and Poisson equations. A constant magnetic field at an arbitrary angle with respect to the layer is included. The model shows that such a plasma region can generate as well as reflect Langmuir waves and shows how RF emission may arise. An axial magnetic field does not inhibit the formation of a double layer, although a non-axial field may do so.

Asymptotics toward a nonlinear wave for an outflow problem of a model of viscous ions motion

2017 ◽  
Vol 27 (11) ◽  
pp. 2111-2145 ◽  
Author(s):  
Yeping Li ◽  
Peicheng Zhu
Keyword(s):  
Nonlinear Wave ◽  
The Self ◽  
Navier Stokes ◽  
Asymptotically Stable ◽  
Spatial Decay ◽  
Main Ingredient ◽  
One Dimensional ◽  
Poisson Equations ◽  
Self Consistent ◽  
The One

We shall investigate the asymptotic stability, toward a nonlinear wave, of the solution to an outflow problem for the one-dimensional compressible Navier–Stokes–Poisson equations. First, we construct this nonlinear wave which, under suitable assumptions, is the superposition of a stationary solution and a rarefaction wave. Then it is shown that the nonlinear wave is asymptotically stable in the case that the initial data are a suitably small perturbation of the nonlinear wave. The main ingredient of the proof is the [Formula: see text]-energy method that takes into account both the effect of the self-consistent electrostatic potential and the spatial decay of the stationary part of the nonlinear wave.

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