Unperturbed Density Research Articles

Electron Transport in Configurational Model of Ferromagnetic Fulleride with Triple Orbital Degeneracy

Phenomenon of ferromagnetic ordering was for a long time associated exclusively with transition metal and rare-earth compounds. Nowadays this view is challenged by growing evidence that in molecular carbon-based systems the ferromagnetic alignment of spins can be observed as well. We have developed a microscopical model of a fulleride electronic subsystem taking into account triple orbital degeneracy of energy states within the configurational-operator approach. Using the Green function method the energy spectrum of the model has been calculated. Conditions for the ferromagnetic state stabilization have been determined. Static electrical conductivity and effective masses of current carriers in the system with orbitally degenerated energy band have been obtained. In the ground state and for low temperatures at different forms of unperturbed density of electronic states the concentration dependences of transport characteristics for less-then-half-filled lower quasiparticle subband have been calculated.

Deep and wide gaps by super Earths in low-viscosity discs

Planets can open cavities (gaps) in the protoplanetary gaseous discs in which they are born by exerting gravitational torques. Viscosity counters these torques and limits the depletion of the gaps. We present a simple one-dimensional scheme to calculate the gas density profile inside gaps by balancing the gravitational and viscous torques. By generalizing the results of Goodman & Rafikov (2001), our scheme properly accounts for the propagation of angular momentum by density waves. This method allows us to easily study low-viscosity discs, which are challenging for full hydrodynamical simulations. We complement our numerical integration by analytical equations for the gap's steady-state depth and width as a function of the planet's to star's mass ratio $\mu$, the gas disc's aspect ratio $h$, and its Shakura & Sunyaev viscosity parameter $\alpha$. Specifically, we focus on low-mass planets ($\mu<\mu_{\rm th}\equiv h^3$) and identify a new low-viscosity regime, $\alpha<h(\mu/\mu_{\rm th})^5$, in which the classical analytical scaling relations are invalid. Equivalently, this low-viscosity regime applies to every gap that is depleted by more than a factor of $(\mu_{\rm th}/\mu)^3$ relative to the unperturbed density. We show that such gaps are significantly deeper and wider than previously thought, and consequently take a longer time to reach equilibrium.

Partial local density of states from scanning gate microscopy

Scanning gate microscopy images from measurements made in the vicinity of quantum point contacts were originally interpreted in terms of current flow. Some recent work has analytically connected the local density of states to conductance changes in cases of perfect transmission, and at least qualitatively for a broader range of circumstances. In the present paper, we show analytically that in any time-reversal invariant system there are important deviations that are highly sensitive to imperfect transmission. Nevertheless, the unperturbed partial local density of states can be extracted from a weakly invasive scanning gate microscopy experiment, provided the quantum point contact is tuned anywhere on a conductance plateau. A perturbative treatment in the reflection coefficient shows just how sensitive this correspondence is to the departure from the quantized conductance value and reveals the necessity of local averaging over the tip position. It is also shown that the quality of the extracted partial local density of states decreases with increasing tip radius.

Effect of nonthermal ions on (3+1)-dimensional envelope solitary wave in magnetized PLD dusty plasma

This work investigates the envelope solitary wave (ESW) in magnetized power law distribution dusty plasma consisting of free electrons and nonthermal ions. A (3+1)-dimensional nonlinear Schr $$\ddot{o}$$ dinger equation (NLSE) through the reductive perturbation technique is derived. The nonlinear dispersion relation $$\omega =\omega (k )$$ and coefficients of NLSE are analyzed in detail by the numerical simulation method under the effect of nonthermal ions. It is indicated that the frequency increases as the number density of nonthermal ions increase. It can be seen that the frequency with higher unperturbed ion number density is larger than that with lower case. Moreover, the effects of amplitude and width on ESW are discussed with different plasma parameters. The present results can be important in understanding the characteristics of ESW for a magnetized three component plasma system.

Extreme driven ion acoustic waves

The excitation of large amplitude, strongly nonlinear ion acoustic waves from trivial equilibrium by a chirped frequency drive is discussed. Under certain conditions, after passage through the linear resonance in this system, the nonlinearity and the variation of parameters work in tandem to preserve the phase-locking with the driving wave via excursion of the excited ion acoustic wave in its parameter space, yielding controlled growth of the wave amplitude. We study these autoresonant waves via a fully nonlinear warm fluid model and predict the formation of sharply peaked (extreme) ion acoustic excitations with local ion density significantly exceeding the unperturbed plasma density. The driven wave amplitude is bound by the kinetic wave-breaking, as the local maximum fluid velocity of the wave approaches the phase velocity of the drive. The Vlasov-Poisson simulations are used to confirm the results of the fluid model, and Whitham's averaged variational principle is applied for analyzing the evolution of autoresonant ion acoustic waves.

DENSITY PERTURBATION BY ALFVÉN WAVES IN MAGNETO-PLASMA

ABSTRACT In this article, we attempt to investigate the density perturbations along magnetic field by ponderomotive effects due to inertial Alfvén waves (AWs) in auroral ionosphere. For this study, we take high-frequency inertial AWs (pump) and their nonlinear interactions with low-frequency slow modes of AWs in that region. The dynamical equations representing these wave modes are known as the Zakharov like equation, and are solved numerically. From the results presented here, we notice the density perturbations in the direction of background magnetic fields. We also find that the deepest density cavity is associated with the strongest magnetic fields. The main reason for these nonlinear structures could be the ponderomotive effects due to the pump waves. The amplitude of these density structures varies with time until the modulation instability saturates. From our results, we estimate the amplitude of most intense cavity as ∼15% of the unperturbed plasma number density n 0, which is consistent with the observations. These density structures could be the locations for particle energizations in this region.

Bending of solitons in weak and slowly varying inhomogeneous plasma

The bending of solitons in two dimensional plane is presented in the presence of weak and slowly varying inhomogeneous ion density for the propagation of ion acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using reductive perturbation technique, a modified Kadomtsev-Petviashvili equation is obtained with a chosen unperturbed ion density profile. The exact solution of the equation shows that the phase of the solitary wave gets modified by a function related to the unperturbed inhomogeneous ion density causing the soliton to bend in the two dimensional plane, while the amplitude of the soliton remains constant.

Large convective cells in the sun: a theoretical model

The geometric parameters and relationships of the horizontal and vertical velocities in a giant convective cylindrical cell were analyzed based on a continuity equation with the given vertical distribution of unperturbed gas density in the convective zone of the Sun. It has been found that the lower edge of such a convective cell must be positioned at a depth of 20 Mm in the secondary helium ionization zone. In addition, under the assumption that the plasma conductivity in the convective zone is caused by small-scale turbulence, a new stationary solution was obtained for the problem of magnetic field diffusion in the pattern of slow conductive plasma flows in scales of a convective cell.

Numerical study of density cavitations by inertial Alfvén waves

In this manuscript, we study the localization and density cavitations using inertial Alfven wave (AW) and fast AW in the auroral ionosphere. We first develop a system of equations semi-analytically for both wave modes by using two-fluid model and then solve the model equations numerically using two-dimensional pseudo-spectral approach to analyze the localized structures and cavity formation at different instant of time. The ponderomotive force associated with the pump wave changes the background density and as the inertial AWs propagate through the modified density channel it gets localized. Therefore, the inertial AW splits up into filamentary/localized structures. A low frequency fast AW traveling through these complex structures created by inertial AW, is intensified having its own filamentary structures. The filamentary structures grow with time until the instability acquires steady state. We notice that the density cavities are also accompanied by the high amplitude magnetic fields. The amplitude of the strongest density cavity is estimated as ∼0.26n 0 (n 0 is unperturbed plasma number density). We also discuss the implications of the present study in the context of auroral ionosphere.

Modulational instability of electron-acoustic waves in a plasma with Cairns–Tsallis distributed electrons

The problem of the modulational instability (MI) of electron-acoustic waves (EAWs) in a plasma with Cairns–Tsallis distributed electrons is addressed. Using the standard multiple scale method, we derive a nonlinear Schrödinger-like equation. Electron nonextensivity and nonthermality are found to significantly influence the region stability of the EAWs. In particular, it is found that the critical value kc, beyond which the instability sets in, is slightly lowered as the electrons evolve far away from their Maxwellian thermodynamic equilibrium. Electron nonthermality renders more effective and more important the influence and role of nonextensivity. Moreover, the effect of the unperturbed hot electron and cold electron number density imbalance μ on the onset of the MI is analyzed. Although both dark and bright excitations are obtained, the trend is in contrast to our earlier observations. Our results should be of relevance in wave propagation stability. Nonthermal nonextensive models may play an increasingly important role in predicting complex plasma behavior, and understanding the underlying physical processes.

Electron Acoustic Solitary Waves in Magnetized Quantum Plasma with Relativistic Degenerated Electrons

A model for the nonlinear properties of obliquely propagating electron acoustic solitary waves in a two-electron populated relativistically quantum magnetized plasma is presented. By using the standard reductive perturbation technique, the Zakharov-Kuznetsov (ZK) equation is derived and this equation gives the solitary wave solution. It is observed that the relativistic effects, the ratio of the cold to hot electron unperturbed number density and the magnetic field normalized by electron cyclotron frequency significantly influence the solitary structures.

PROPAGATION AND DISPERSION OF TRANSVERSE WAVE TRAINS IN MAGNETIC FLUX TUBES

The dispersion of small amplitude, impulsively excited wave trains propagating along a magnetic flux tube is investigated. The initial disturbance is a localized transverse displacement of the tube that excites a fast kink wave packet. The spatial and temporal evolution of the perturbed variables (density, plasma displacement, velocity, ...) is given by an analytical expression containing an integral that is computed numerically. We find that the dispersion of fast kink wave trains is more important for shorter initial disturbances (i.e. more concentrated in the longitudinal direction) and for larger density ratios (i.e. for larger contrasts of the tube density with respect to the environment density). This type of excitation generates a wave train whose signature at a fixed position along a coronal loop is a short event (duration ~ 20 s) in which the velocity and density oscillate very rapidly with typical periods of the order of a few seconds. The oscillatory period is not constant but gradually declines during the course of this event. Peak values of the velocity are of the order of 10 km/s and are accompanied by maximum density variations of the order of 10-15% the unperturbed loop density.

Models for electrostatic drift waves with density variations along magnetic field lines

Drift waves with vertical magnetic fields in gravitational ionospheres are considered where the unperturbed plasma density is enhanced in a magnetic flux tube. The gravitational field gives rise to an overall decrease of plasma density for increasing altitude. Simple models predict that drift waves with finite vertical wave vector components can increase in amplitude merely due to a conservation of energy density flux of the waves. Field‐aligned currents are some of the mechanisms that can give rise to fluctuations that are truly unstable. We suggest a self‐consistent generator or “battery” mechanism that in the polar ionospheres can give rise to magnetic field‐aligned currents even in the absence of electron precipitation. The free energy here is supplied by steady state electric fields imposed in the direction perpendicular to the magnetic field in the collisional lower parts of the ionosphere or by neutral winds that have similar effects.

Erratum: Resonant Excitation of Disk Oscillations in Deformed Disks. VI. Stability Criterion Revisited

We re-examine the excitation of a set of disk oscillations in a deformed disk by a resonant process. We assume that the disk is deformed from an axisymmetric steady state by an oscillatory deformation with frequency !D and azimuthal wavenumber mD. Then, we consider two normal mode oscillations with a set of frequencies and the azimuthal wavenumber being (!1,m1) and (!2,m2) and satisfying the resonant conditions (!1 +!2 +!D = 0 and m1 +m2 +mD = 0). These oscillations are resonantly excited ifE1E2> 0, whereE1 andE2 are the wave energies of the above two oscillations, when the deformation is maintained by external forces, or has a large amplitude compared with the oscillations. This instability condition is rather general as long as the unperturbed density and pressure vanish on the surface of the system. The possibility of applications to superhumps and negative superhumps in the superoutburst state of dwarf novae are briefly discussed.

Effective recombination coefficient and solar zenith angle effects on low-latitude D-region ionosphere evaluated from VLF signal amplitude and its time delay during X-ray solar flares

Excess solar X-ray radiation during solar flares causes an enhancement of ionization in the ionospheric D-region and hence affects sub-ionospherically propagating VLF signal amplitude and phase. In first part of the work, using the well known LWPC technique, we simulated the flare induced excess lower ionospheric electron density by amplitude perturbation method. Unperturbed D-region electron density is also obtained from simulation and compared with IRI-model results. Using these simulation results and time delay as key parameters, we calculate the effective electron recombination coefficient ($\alpha_{eff}$) at solar flare peak region. Our results match with the same obtained by other established models. In the second part, we dealt with the solar zenith angle effect on D-region during flares. We relate this VLF data with the solar X-ray data. We find that the peak of the VLF amplitude occurs later than the time of the X-ray peak for each flare. We investigate this so-called time delay ($\bigtriangleup t$). For the C-class flares we find that there is a direct correspondence between $\bigtriangleup t$ of a solar flare and the average solar zenith angle $Z$ over the signal propagation path at flare occurrence time. Now for deeper analysis, we compute the $\bigtriangleup t$ for different local diurnal time slots $DT$. We find that while the time delay is anti-correlated with the flare peak energy flux $\phi_{max}$ independent of these time slots, the goodness of fit, as measured by $reduced$-$\chi^2$, actually worsens as the day progresses. The variation of the $Z$ dependence of $reduced$-$\chi^2$ seems to follow the variation of standard deviation of $Z$ along the $T_x$-$R_x$ propagation path. In other words, for the flares having almost constant $Z$ over the path a tighter anti-correlation between $\bigtriangleup t$ and $\phi_{max}$ was observed.

Resonant Excitation of Disk Oscillations in Deformed Disks. VI. Stability Criterion Revisited

We re-examine the excitation of a set of disk oscillations in a deformed disk by a resonant process. We assume that the disk is deformed from an axisymmetric steady state by an oscillatory deformation with frequency $\omega_{\rm D}$ and azimuthal wavenumber $m_{\rm D}$. Then, we consider two normal mode oscillations with a set of frequencies and the azimuthal wavenumber being ($\omega_1, m_1$) and ($\omega_2, m_2$) and satisfying the resonant conditions ($\omega_1 + \omega_2 + \omega_{\rm D} =$ 0 and $m_1 + m_2 + m_{\rm D} =$ 0). These oscillations are resonantly excited if $E_1E_2 \gt $ 0, where $E_1$ and $E_2$ are the wave energies of the above two oscillations, when the deformation is maintained by external forces, or has a large amplitude compared with the oscillations. This instability condition is rather general as long as the unperturbed density and pressure vanish on the surface of the system. The possibility of applications to superhumps and negative superhumps in the superoutburst state of dwarf novae are briefly discussed.

Charge density mapping of strongly-correlated few-electron two-dimensional quantum dots by the scanning probe technique

We perform a numerical simulation of the mapping of charge confined in quantum dots by the scanning probe technique. We solve the few-electron Schrödinger equation with the exact diagonalization approach and evaluate the energy maps as a function of the probe position. Next, from the energy maps we try to reproduce the charge density distribution using an integral equation given by the perturbation theory. The reproduced density maps are compared with the original ones. This study covers two-dimensional quantum dots of various geometries and profiles with the one-dimensional (1D) quantum dot as a limiting case. We concentrate on large quantum dots for which strong electron–electron correlations appear. For circular dots the correlations lead to the formation of Wigner molecules that in the presence of a tip appear in the laboratory frame. The unperturbed rotationally-symmetric charge density is surprisingly well reproduced by the mapping. We find in general that the size of the confined droplet as well as the spatial extent of the charge density maxima is underestimated for a repulsive tip potential and overestimated for an attractive tip. In lower symmetry quantum dots Wigner molecules with single-electron islands nucleate for some electron numbers even in the absence of a tip. These charge densities are well resolved by the mapping. These single-electron islands appear in the laboratory frame provided that the classical point charge density distribution is unique, in the 1D limit of confinement in particular. We demonstrate that for electron systems which possess a few equivalent classical configurations the repulsive probe switches between the configurations. In consequence the charge density evades mapping by the repulsive probe.

Appearance of antiferromagnetism and superconductivity in superconducting cuprates

We represent the superconducting ceramic compounds by the single band extended Hubbard model. We use this model for solving the simultaneous presence of antiferromagnetism and the d-wave superconductivity in the Hartree–Fock (H–F) and in the coherent potential (CP) approximation, which is applied to the on-site Coulomb repulsion U.The hopping interaction used in addition to the Coulomb repulsion causes rapid expansion of the band at carrier concentrations departing from unity. This expansion shifts the d-wave superconductivity away from the half filled point reducing its occupation range approximately to the experimental range in the YBaCuO compound.The CP approximation used for the Coulomb repulsion is justified by the large ratio of Coulomb repulsion to the effective width of perturbed density of states being reduced by the hopping interaction.The experimentally observed fast disappearance of antiferromagnetism is supported in calculations by the relatively large value of the total width of unperturbed density of states and the high values of the hopping interaction.It is shown that our model is capable of describing the electron doped compounds as well.

A simple approximation for forces exerted on an AFM tip in liquid

The critical quantity in understanding imaging using an atomic force microscope is the force the sample exerts on the tip. We put forward a simple one-to-one force to water density relationship, explain exactly how it occurs, and in which circumstances it holds. We argue that two wide classes of atomic force microscope (AFM) tip should lead to at least qualitative agreement with our model and represent a significant fraction of AFM tips as currently prepared. This connection between the short-range force and the unperturbed equilibrium water density removes the need to perform simulations for each tip location, conservatively speeding up simulations by around three orders of magnitude compared to current methods that explicitly calculate the force on a tip model at each point in space.

Alfvénic tornadoes in a magnetized plasma

It is shown that three‐dimensional (3D) modified‐kinetic Alfvén waves (m‐KAWs) in a magnetized plasma can propagate in the form of Alfvénic tornadoes characterized by plasma density whirls or magnetic flux ropes carrying orbital angular momentum. By using the two‐fluid model, together with Ampère's law, we derive the wave equation for 3D m‐KAWs in a magnetoplasma with me/mi ≪ β ≪ 1, where me (mi) is the electron (ion) mass, , n0 the unperturbed plasma number density, kB the Boltzmann constant, Te(Te) the electron (ion) temperature, and B0 the strength of the ambient magnetic field. The 3D m‐KAW equation admits solutions in the form of a Laguerre‐Gauss Alfvénic vortex beam or a twisted kinetic Alfvénic wave with plasma density whirls that support the dynamics of shear Alfvénic magnetic flux ropes in plasmas.