Experiment and m.h.d. theory of stability and relaxation in toroidal discharges

1981 ◽  
Vol 300 (1456) ◽  
pp. 525-533 ◽  
Keyword(s):  
Field Line ◽  
Time Scales ◽  
Solar Flares ◽  
Magnetic Energy ◽  
Self Control ◽  
Control Mechanisms ◽  
High Current ◽  
Linear And Nonlinear ◽  
Ideal Magnetohydrodynamic ◽  
Good Agreement

The experimental behaviour of plasma instabilities in high-current discharges is found to be in good agreement with the predictions of linear and nonlinear magnetohydrodynamic theory. Observations show that on time-scales comparable with the Alfven transit time there are rapidly growing ideal magnetohydrodynamic perturbations whereas experiments on longer time-scales show the growth and saturation of resistive instabilities which involve changes in field line topology. The plasmas are observed to exhibit self-control mechanisms which are related to the relaxation of configurations to states of lower magnetic energy. Rapid magnetic field line reconnection phenomena, as in solar flares, are observed.

scholarly journals Seasonal Estimates and Uncertainties of Snow Accumulation from CloudSat Precipitation Retrievals

Atmosphere ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 363
Author(s):  
George Duffy ◽  
Fraser King ◽  
Ralf Bennartz ◽  
Christopher G. Fletcher
Keyword(s):  
Time Scales ◽  
Snow Water Equivalent ◽  
Spatial Scales ◽  
Snow Accumulation ◽  
High Latitudes ◽  
Percentage Points ◽  
Snow Water ◽  
Time Periods ◽  
Predicted Values ◽  
Good Agreement

CloudSat is often the only measurement of snowfall rate available at high latitudes, making it a valuable tool for understanding snow climatology. The capability of CloudSat to provide information on seasonal and subseasonal time scales, however, has yet to be explored. In this study, we use subsampled reanalysis estimates to predict the uncertainties of CloudSat snow water equivalent (SWE) accumulation measurements at various space and time resolutions. An idealized/simulated subsampling model predicts that CloudSat may provide seasonal SWE estimates with median percent errors below 50% at spatial scales as small as 2° × 2°. By converting these predictions to percent differences, we can evaluate CloudSat snowfall accumulations against a blend of gridded SWE measurements during frozen time periods. Our predictions are in good agreement with results. The 25th, 50th, and 75th percentiles of the percent differences between the two measurements all match predicted values within eight percentage points. We interpret these results to suggest that CloudSat snowfall estimates are in sufficient agreement with other, thoroughly vetted, gridded SWE products. This implies that CloudSat may provide useful estimates of snow accumulation over remote regions within seasonal time scales.

OPTIMAL VELOCITY MODEL WITH RELATIVE VELOCITY

2006 ◽  
Vol 17 (01) ◽  
pp. 65-73 ◽  
Author(s):  
SHIRO SAWADA
Keyword(s):  
Nonlinear Analysis ◽  
Relative Velocity ◽  
Velocity Model ◽  
Fundamental Diagram ◽  
Optimal Velocity ◽  
Traffic Jam ◽  
Optimal Velocity Model ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Good Agreement

The optimal velocity model which depends not only on the headway but also on the relative velocity is analyzed in detail. We investigate the effect of considering the relative velocity based on the linear and nonlinear analysis of the model. The linear stability analysis shows that the improvement in the stability of the traffic flow is obtained by taking into account the relative velocity. From the nonlinear analysis, the relative velocity dependence of the propagating kink solution for traffic jam is obtained. The relation between the headway and the velocity and the fundamental diagram are examined by numerical simulation. We find that the results by the linear and nonlinear analysis of the model are in good agreement with the numerical results.

Turbulent dispersion in a non-homogeneous field

1999 ◽  
Vol 392 ◽  
pp. 45-71 ◽  
Author(s):  
ILIAS ILIOPOULOS ◽  
THOMAS J. HANRATTY
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Stochastic Model ◽  
Point Source ◽  
Time Scales ◽  
Langevin Equation ◽  
Turbulent Dispersion ◽  
Homogeneous Field ◽  
Fully Developed Flow ◽  
Good Agreement

Dispersion of fluid particles in non-homogeneous turbulence was studied for fully developed flow in a channel. A point source at a distance of 40 wall units from the wall is considered. Data obtained by carrying out experiments in a direct numerical simulation (DNS) are used to test a stochastic model which utilized a modified Langevin equation. All of the parameters, with the exception of the time scales, are obtained from Eulerian statistics. Good agreement is obtained by making simple assumptions about the spatial variation of the time scales.

scholarly journals Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-28
Author(s):  
Jiang Zhu ◽  
Dongmei Liu
Keyword(s):  
Time Scales ◽  
Initial Value Problems ◽  
Second Order ◽  
Dynamic Equations ◽  
Maximum Principles ◽  
Uniqueness Theorems ◽  
Initial Value ◽  
Approximation Theorems ◽  
Construction Techniques ◽  
Linear And Nonlinear

Some delta-nabla type maximum principles for second-order dynamic equations on time scales are proved. By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.

scholarly journals The development of magnetic field line wander by plasma turbulence

2017 ◽  
Vol 83 (4) ◽  
Author(s):  
Gregory G. Howes ◽  
Sofiane Bourouaine
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Large Scale ◽  
Magnetic Energy ◽  
Plasma Turbulence ◽  
Alfven Wave ◽  
Astrophysical Plasmas ◽  
Field Lines ◽  
The Magnetic Field

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices and the fundamental processes of turbulence, magnetic reconnection and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfvén wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

scholarly journals A Novel Approach to Measure the Hydraulic Capacitance of a Microfluidic Membrane Pump

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Chun-Hui Wu ◽  
Chia-Wei Chen ◽  
Long-Sheng Kuo ◽  
Ping-Hei Chen
Keyword(s):  
Linear Correlation ◽  
Experimental Results ◽  
Membrane Thickness ◽  
Membrane Pump ◽  
Novel Approach ◽  
Hydraulic Capacitance ◽  
Linear And Nonlinear ◽  
Center Deflection ◽  
Membrane Deflection ◽  
Good Agreement

A novel approach was proposed to measure the hydraulic capacitance of a microfluidic membrane pump. Membrane deflection equations were modified from various studies to propose six theoretical equations to estimate the hydraulic capacitance of a microfluidic membrane pump. Thus, measuring the center deflection of the membrane allows the corresponding pressure and hydraulic capacitance of the pump to be determined. This study also investigated how membrane thickness affected the Young’s modulus of a polydimethylsiloxane (PDMS) membrane. Based on the experimental results, a linear correlation was proposed to estimate the hydraulic capacitance. The measured hydraulic capacitance data and the proposed equations in the linear and nonlinear regions qualitatively exhibited good agreement.

scholarly journals Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Adel Al-Rabtah ◽  
Shaher Momani ◽  
Mohamed A. Ramadan
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Analytical Solutions ◽  
Spline Functions ◽  
Exact Analytical Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Good Agreement

Suitable spline functions of polynomial form are derived and used to solve linear and nonlinear fractional differential equations. The proposed method is applicable for0<α≤1andα≥1, whereαdenotes the order of the fractional derivative in the Caputo sense. The results obtained are in good agreement with the exact analytical solutions and the numerical results presented elsewhere. Results also show that the technique introduced here is robust and easy to apply.

Pulsed high-current discharge in water: adiabatic model of expanding plasma channel and acoustic wave

2021 ◽  
Author(s):  
Andrey V. Kozyrev ◽  
Andrey A. Zherlitsyn ◽  
Natalia S. Semeniuk
Keyword(s):  
Acoustic Wave ◽  
Pulsed Power ◽  
High Current ◽  
Number Density ◽  
Pulsed Discharge ◽  
Current Channel ◽  
High Current Discharge ◽  
Isothermal Plasma ◽  
A Current ◽  
Good Agreement

Abstract This paper presents the results of a theoretical and experimental study of the use of a pulsed discharge in water to obtain a strong acoustic wave in a liquid medium. A discharge with a current amplitude of 10 kA, a duration of 400 ns, and an amplitude pulsed power of 280 MW in water at atmospheric pressure created an expanding acoustic wave with an amplitude of more than 100 MPa. To describe the formation of the discharge channel, an isothermal plasma model has been developed, which made it possible to calculate both the expansion dynamics of a high-current channel and the strong acoustic wave generated by it. Our calculations show that the number density of plasma in the channel reaches 10^20 cm^(–3), while the degree of water vapour ionization is about 10%, and the channel wall extends with a velocity of 500 m/s. The calculations for the acoustic wave are in good agreement with measurements

Plasma Diagnostics of Microflares observed by STIX and AIA

2021 ◽  
Author(s):  
Jonas Saqri ◽  
Astrid Veronig ◽  
Ewan Dickson ◽  
Säm Krucker ◽  
Andrea Francesco Battaglia ◽  
...  
Keyword(s):  
Solar Flares ◽  
Magnetic Energy ◽  
Emission Measure ◽  
Transport Processes ◽  
X Rays ◽  
Solar Dynamics Observatory ◽  
Energy Bands ◽  
Accurate Analysis ◽  
Great Opportunity ◽  
Wide Range

&lt;p&gt;Solar flares are generally thought to be the impulsive release of magnetic energy giving rise to a wide range of solar phenomena that influence the heliosphere and in some cases even conditions of earth. Part of this liberated energy is used for particle acceleration and to heat up the solar plasma. The Spectrometer/Telescope for Imaging X-rays (STIX) instrument onboard the Solar Orbiter mission launched on February 10th 2020 promises advances in the study of solar flares of various sizes. It is capable of measuring X-ray spectra from 4 to 150 keV with 1 keV resolution binned into 32 energy bins before downlinking. With this energy range and sensitivity, STIX is capable of sampling thermal plasma with temperatures of&amp;#8819;10 MK, and to diagnose the nonthermal bremsstrahlung emission of flare-accelerated electrons. During the spacecraft commissioning phase in the first half of the year 2020, STIX observed 68 microflares. Of this set, 26 events could clearly be identified in at least two energy channels, all of which originated in an active region that was also visible from earth. These events provided a great opportunity to combine the STIX observations with the multi-band EUV imagery from the Atmospheric Imaging Assembly (AIA) instrument on board the earth orbiting Solar Dynamics Observatory (SDO). For the microflares that could be identified in two STIX science energy bands, it was possible to derive the temperature and emission measure (EM) of the flaring plasma assuming an isothermal source. For larger events where more detailed spectra could be derived, a more accurate analysis was performed by fitting the spectra assuming various thermal and nonthermal sources. These results are compared to the diagnostics derived from AIA images. To this aim, the Differential EmissionMeasure (DEM) was reconstructed from AIA observations to infer plasma temperatures and EM in the flaring regions. Combined with the the relative timing between the emission seen by STIX and AIA, this allows us to get deeper insight into the flare energy release and transport processes.&lt;/p&gt;

The Life Course of Baby Boomers

Hurt ◽  
2017 ◽  
Author(s):  
Miriam Boeri
Keyword(s):  
Drug Use ◽  
Life Course ◽  
Social Control ◽  
Informal Social Control ◽  
Self Control ◽  
Life Course Theory ◽  
Control Mechanisms ◽  
Problematic Drug ◽  
Social Controls ◽  
The Life Course

Life course theory focuses attention on the impact of history, timing, and important transitions in life trajectories. In this chapter, the life course analysis of boomer drug users reveals that drug trajectories were not developmental. Instead, they were discontinuous, interrupted phases dependent on social context and situations that changed over time. The chapter provides a closer inspection of the turning points into and out of drug use phases to better understand the causes of problematic drug use and what resources are needed to control it. In contrast to law enforcement and treatment professionals, who view problematic drug use as a lack of self-control, research finds that informal social control mechanisms are more important for maintaining or regaining control over drug use. Life course theory predicts that missing critical transitions in life, such as graduating from high school, leads to fewer informal social controls. The stories in this chapter reveal the negative impact of juvenile incarceration, which did not help anyone become drug free, but instead plunged youths into a criminal culture and broke their social bonds to mainstream social networks and access to informal social control mechanisms.

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