Interaction of electrostatic waves in collisionless plasmast

1971 ◽  
Vol 5 (1) ◽  
pp. 51-63 ◽  
Author(s):  
G. J. Lewak
Keyword(s):  
Energy Conservation ◽  
Fourth Order ◽  
Time Reversal ◽  
Phase Plane ◽  
Collisionless Plasma ◽  
Particle Interaction ◽  
Coupling Constants ◽  
Electrostatic Waves ◽  
Hybrid Frequency ◽  
The Difference

The interaction of three electrostatic waves in a collisionless plasma is treated to fourth order neglecting the wave—particle interaction (damping). Using the principles of energy conservation, and invariance under time reversal, conditions on the coupling constants are derived, enabling the solution to be expressed as a function of only two coupling constants. Phase plane diagrams of the solutions are sketched showing that the only singular points are stable equili bria. It is suggested how the theory may be applied to the explanation of the ‘floating spike’ resonance observable when one-half the hybrid frequency is the difference between the plasma and gyro frequencies (Hagg & Muldrew 1968).

Relation between Magnetic, Spectroscopic and Structural Properties of Binuclear Copper(II) Complexes of Pentadentate Schiff-base Ligand, Semi-empirical and ab-initio Calculations

2003 ◽  
Vol 58 (5-6) ◽  
pp. 363-372 ◽  
Author(s):  
Y. Elerman ◽  
H. Kara ◽  
A. Elmali
Keyword(s):  
Ab Initio ◽  
Coupling Constants ◽  
Antiferromagnetic Coupling ◽  
X Ray Diffraction ◽  
Hartree Fock ◽  
Ligand Orbital ◽  
Rhf Calculations ◽  
The Difference ◽  
Semi Empirical

The synthesis and characterization of [Cu2(L1)(3,5 prz)] (L1=1,3-Bis(2-hydroxy-3,5-chlorosalicylideneamino) propan-2-ol) 1 and of [Cu2(L2)(3,5 prz)] (L2=1,3-Bis(2-hydroxy-bromosalicylideneamino) propan-2-ol) 2 are reported. The compounds were studied by elemental analysis, infrared and electronic spectra. The structure of the Cu2(L1)(3,5 prz)] complex was determined by x-ray diffraction. The magnetochemical characteristics of these compounds were determined by temperaturedependent magnetic susceptibility measurements, revealing their antiferromagnetic coupling. The superexchange coupling constants are 210 cm−1 for 1 and 440 cm−1 for 2. The difference in the magnitude of the coupling constants was explained by the metal-ligand orbital overlaps and confirmed by ab-initio restricted Hartree-Fock (RHF) calculations. In order to determine the nature of the frontier orbitals, Extended Hückel Molecular Orbital (EHMO) calculations are also reported.

On Drift Instabilities in a Collisionless Electron-Proton Plasma from the point of view of Energy Absorption of Resonant Particles

1963 ◽  
Vol 18 (4) ◽  
pp. 446-453 ◽  
Author(s):  
Asbjørn Kildal
Keyword(s):  
Energy Absorption ◽  
Constant Electric Field ◽  
Wave Length ◽  
Collisionless Plasma ◽  
Phase Region ◽  
Point Of View ◽  
Electrostatic Waves ◽  
Transverse Current ◽  
Special Cases ◽  
A Current

The present paper is essentially devoted to the study of instabilities of electrostatic waves in a current-carrying collisionless plasma. As the underlying physical cause of the instabilities is the same as that of the LANDAU damping in an electron plasma, a detailed analysis of the latter is first given. It is shown that the damping may be considered as being due to the fact that there are more electrons in the phase-region where energy is absorbed by the particles from the field than in the phase-region where energy is given up to the field.We then proceed to the evaluation of the energy absorption A of the resonant particles, first in the absence of an external magnet field, B0 , next when the wave is propagated under an arbitrary angle with respect to B0 . When A > 0, the wave is damped, and vice-versa. Without appeal to a dispersion equation, stability criteria can thus be found, dependent on the wave frequency and wave-vector. Next some special cases are investigated and compared with the results of other authors where such results exist.As a consequence of the fact that some ions and electrons, the resonant particles, experience a constant electric field, these particles also experience a constant drift transverse to both E and B0. This drift gives rise to a transverse current which is closely related to the damping or growing of the wave. An expression for this current, averaged over one wave-length is found.

Use of Temporal Irreversibility of Symbolic Time Series for Early Detection of Extinction in Thermal Pulse Combustors

2006 ◽  
Author(s):  
Subhashis Datta ◽  
Achintya Mukhopadhyay ◽  
Dipankar Sanyal
Keyword(s):  
Time Series ◽  
Fourth Order ◽  
Time Series Data ◽  
Order System ◽  
Series Data ◽  
Thermal Pulse ◽  
Pulse Combustor ◽  
The Difference ◽  
Symbol Sequences ◽  
System Approaches

A nonlinear fourth-order dynamic model of a thermal pulse combustor has been developed. In this work, the time series data generated by solution of the fourth order system is converted into a set of symbols based on the values of pressure variables. The key step to symbolization involves transformation of the original values to a stream of discretised symbols by partitioning the range of observed values into a finite number of regions and then assigning a symbol to each measurement based on the region in which it falls. Once all the measured values are symbolized, a symbol sequence vector consisting of L successive temporal observations is defined and its relative frequency is determined. In this work, the relative frequencies of different symbol sequences are computed by scanning the time series data in forward and reverse directions. The difference between the relative frequencies obtained in forward and reverse scanning is termed as "irreversibility" of the process. It is observed that for given alphabet and word sizes, the "irreversibility" increases as the system approaches extinction. The effects of different choices of alphabet and word sizes are also considered.

A Way of Distinguishing Chaos from Random Fractal Sequences Based on the Difference in Time Reversal Symmetry

1995 ◽  
Vol 34 (Part 2, No. 7A) ◽  
pp. L863-L865 ◽  
Author(s):  
Naoki Tanaka ◽  
Hiroshi Okamoto ◽  
Masayoshi Naito
Keyword(s):  
Time Reversal ◽  
Time Reversal Symmetry ◽  
Random Fractal ◽  
The Difference

scholarly journals Patch Similarity Modulus and Difference Curvature Based Fourth-Order Partial Differential Equation for Image Denoising

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Yunjiao Bai ◽  
Quan Zhang ◽  
Hong Shangguan ◽  
Zhiguo Gui ◽  
Yi Liu ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Image Denoising ◽  
Fourth Order ◽  
Objective Evaluation ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
The Difference ◽  
Adaptively Adjusting ◽  
Difference Curvature

The traditional fourth-order nonlinear diffusion denoising model suffers the isolated speckles and the loss of fine details in the processed image. For this reason, a new fourth-order partial differential equation based on the patch similarity modulus and the difference curvature is proposed for image denoising. First, based on the intensity similarity of neighbor pixels, this paper presents a new edge indicator called patch similarity modulus, which is strongly robust to noise. Furthermore, the difference curvature which can effectively distinguish between edges and noise is incorporated into the denoising algorithm to determine the diffusion process by adaptively adjusting the size of the diffusion coefficient. The experimental results show that the proposed algorithm can not only preserve edges and texture details, but also avoid isolated speckles and staircase effect while filtering out noise. And the proposed algorithm has a better performance for the images with abundant details. Additionally, the subjective visual quality and objective evaluation index of the denoised image obtained by the proposed algorithm are higher than the ones from the related methods.

Longitudinal waves in a perpendicular collisionless plasma shock: II. Vlasov ions

1970 ◽  
Vol 4 (4) ◽  
pp. 753-760 ◽  
Author(s):  
S. Peter Gary
Keyword(s):  
Collisionless Plasma ◽  
Maximum Growth ◽  
Zero Magnetic Field ◽  
Linear Dispersion ◽  
Electrostatic Waves ◽  
Longitudinal Waves ◽  
Acoustic Instability ◽  
Ion Acoustic ◽  
Plasma Shock ◽  
Vlasov Plasma

This paper presents an analysis of the linear dispersion relation for electrostatic waves in a Vlasov plasma of unmagnetized, Maxwellian ions and magnetized, Maxwellian electrons. The electrons undergo E × B and ∇B drifts, and the electron β is small. For propagation in the perpendicular direction, maximum growth rates can be substantially larger than those of the zero magnetic field ion acoustic instability. For propagation outside a few degrees from the perpendicular the dispersion characteristics are essentially those of the ion acoustic instability.

Bio-MEMS Circular Plate Sensors Under Electrostatic Hard Excitations: Frequency Response of Superharmonic Resonance of Fourth Order

2020 ◽  
Author(s):  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Frequency Response ◽  
Circular Plate ◽  
Fourth Order ◽  
Multiple Scales ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Amplitude Frequency Response ◽  
Elastic Circular Plate ◽  
Modes Of Vibration ◽  
The Difference

Abstract This paper investigates the frequency-amplitude response of electrostatically actuated Bio-MEMS clamped circular plates under superharmonic resonance of fourth order. The system consists of an elastic circular plate parallel to a ground plate. An AC voltage between the two plates will lead to vibrations of the elastic plate. Method of Multiple Scales, and Reduced Order Model with two modes of vibration are the two methods used in this work. The two methods show similar amplitude-frequency response, with an agreement in the low amplitudes. The difference between the two methods can be seen for larger amplitudes. The effects of voltage and damping on the amplitude-frequency response are reported. The steady-state amplitudes in the resonant zone increase with the increase of voltage and with the decrease of damping.

Microstructure Of Fe-Nd-B Alloys Tailored To Approach Theoretical Coercrvtty Limits

1999 ◽  
Vol 5 (S2) ◽  
pp. 26-27
Author(s):  
Kannan M. Krishnan ◽  
Er. Girt ◽  
E. C. Nelson ◽  
G. Thomas ◽  
Ferdinand Hofer
Keyword(s):  
Magnetic Particles ◽  
Permanent Magnets ◽  
Spontaneous Magnetization ◽  
Particle Interaction ◽  
Maximum Energy ◽  
Interacting Particles ◽  
Maximum Energy Product ◽  
Energy Product ◽  
Oriented Samples ◽  
The Difference

Performance of permanent magnets for a variety of applications is often determined by the maximum energy product (BH)max. In order to obtain high (BH)max permanent magnetic materials have to have large coercivity. In theory the coercive field of ideally oriented, non-interacting, single domain, magnetic particles, assuming Kl is much bigger than K2, was shown to be He = 2K1/Ms - N Ms, where Kl and K2 are the magnetocrystalline anisotropy constants, Ms is the spontaneous magnetization and N is the demagnetization factor. For randomly oriented non-interacting particles the Stoner-Wohlfarth model predicts that the value of Hc decreases to about half. However, experimentally obtained values of the coercitive fields in permanent magnets are 3 to 10 and 2 times smaller for well oriented and randomly oriented samples, respectively. This discrepancy was attributed to inter-particle interaction and the microstructure of the permanent magnets. In order to understand the difference between the theoretically predicted and experimentally obtained results for He we prepared rapidly quenched, Nd-rich, NdxFe14B (2 < x < 150) ribbons.

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