scholarly journals Oscillatory superfluid Ekman pumping in helium II and neutron stars

2015 ◽  
Vol 783 ◽  
pp. 251-282 ◽  
Author(s):  
C. Anthony van Eysden
Keyword(s):  
Neutron Stars ◽  
Low Frequency ◽  
Line Tension ◽  
Outer Core ◽  
Oscillation Period ◽  
Analytic Solutions ◽  
Ekman Pumping ◽  
Helium Ii ◽  
Tension Parameter ◽  
Pumping Mode

The linear response of a superfluid, rotating uniformly in a cylindrical container and threaded with a large number of vortex lines, to an impulsive increase in the angular velocity of the container is investigated. At zero temperature and with perfect pinning of vortices to the top and bottom of the container, we demonstrate that the system oscillates persistently with a frequency proportional to the vortex line tension parameter to the quarter power. This low-frequency mode is generated by a secondary flow analogous to classical Ekman pumping that is periodically reversed by the vortex tension in the boundary layers. We compare analytic solutions to the two-fluid equations by Chandler & Baym (J. Low Temp. Phys., vol. 62, 1986, pp. 119–142) with the spin-up experiments by Tsakadze & Tsakadze (J. Low Temp. Phys., vol. 39, 1980, pp. 649–688) in helium II and find that the frequency agrees within a factor of four, although the experiment is not perfectly suited to the application of linear theory. We argue that this oscillatory Ekman pumping mode, and not Tkachenko modes, provides a natural explanation for the observed oscillation. In neutron stars, the oscillation period depends on the pinning interaction between neutron vortices and flux tubes in the outer core. Using a simplified pinning model, we demonstrate that strong pinning can accommodate modes with periods of days to years, which are only weakly damped by mutual friction over longer time scales.

scholarly journals 1S0 Pairing Gaps, Chemical Potentials and Entrainment Matrix in Superfluid Neutron-Star Cores for the Brussels–Montreal Functionals

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 470
Author(s):  
Valentin Allard ◽  
Nicolas Chamel
Keyword(s):  
Neutron Star ◽  
Equation Of State ◽  
Neutron Stars ◽  
Physical Meaning ◽  
Outer Core ◽  
Time Dependent ◽  
Hartree Fock ◽  
Chemical Potentials ◽  
Bogoliubov Equations ◽  
Flow Velocities

Temperature and velocity-dependent 1S0 pairing gaps, chemical potentials and entrainment matrix in dense homogeneous neutron–proton superfluid mixtures constituting the outer core of neutron stars, are determined fully self-consistently by solving numerically the time-dependent Hartree–Fock–Bogoliubov equations over the whole range of temperatures and flow velocities for which superfluidity can exist. Calculations have been made for npeμ in beta-equilibrium using the Brussels–Montreal functional BSk24. The accuracy of various approximations is assessed and the physical meaning of the different velocities and momentum densities appearing in the theory is clarified. Together with the unified equation of state published earlier, the present results provide consistent microscopic inputs for modeling superfluid neutron-star cores.

A theory for Langmuir solitons

1982 ◽  
Vol 27 (1) ◽  
pp. 95-120 ◽  
Author(s):  
N. Nagesha Rao ◽  
Ram K. Varma
Keyword(s):  
Mach Number ◽  
A Priori ◽  
Low Frequency ◽  
Analytic Solutions ◽  
Smooth Transition ◽  
Langmuir Waves ◽  
Method Of Solution ◽  
Mach Numbers ◽  
Ion Waves ◽  
Langmuir Solitons

A systematic and self-consistent analysis of the problem of Langmuir solitons in the entire range of Mach numbers (0 < M < 1) has been presented. A coupled set of nonlinear equations for the amplitude of the modulated, high-frequency Langmuir waves and the associated low-frequency ion waves is derived without using the charge neutrality condition or any a priori ordering schemes. A technique has been developed for obtaining analytic solutions of these equations where any arbitrary degree of ion nonlinearity consistent with the nonlinearity retained in the Langmuir field can be taken into account self-consistently. A class of solutions with non-zero Langmuir field intensity at the centre (ξ = 0) are found for intermediate values of the Mach number. Using these solutions, a smooth transition from single-hump solitons to the double-hump solitons with respect to the Mach number has been established through the definitions of critical and cut-off Mach numbers. Further, under appropriate limiting conditions, various solutions discussed by other authors are obtained. Sagdeev potential analyses of the solutions for the Langmuir field as well as the ion field are carried out. These analyses confirm the transition from single-hump solitons to the double-hump solitons with respect to the Mach number. The existence of many-hump solitons for higher-order nonlinearities in the low-frequency ion wave potential has been conjectured. The method of solution developed here can be applied to similar equations in other fields.

scholarly journals Vortex pinning in the superfluid core of relativistic neutron stars

2021 ◽  
Vol 503 (1) ◽  
pp. 1407-1417
Author(s):  
Aurélien Sourie ◽  
Nicolas Chamel
Keyword(s):  
Neutron Stars ◽  
Outer Core ◽  
Vortex Pinning ◽  
Global Dynamics ◽  
Mutual Friction ◽  
Dynamical Equations ◽  
General Relativistic ◽  
Superfluid Core ◽  
Relativistic Framework

ABSTRACT Our recent Newtonian treatment of the smooth-averaged mutual-friction force acting on the neutron superfluid and locally induced by the pinning of quantized neutron vortices to proton fluxoids in the outer core of superfluid neutron stars is here adapted to the general-relativistic framework. We show how the local non-relativistic motion of individual vortices can be matched to the global dynamics of the star using the fully 4D covariant Newtonian formalism of Carter & Chamel. We derive all the necessary dynamical equations for carrying out realistic simulations of superfluid rotating neutron stars in full general relativity, as required for the interpretation of pulsar frequency glitches. The role of vortex pinning on the global dynamics appears to be non-trivial.

Analytical Solution to Excited Waveform of Bias Control on Electro-Hydraulic Vibration Exciter

2010 ◽  
Vol 44-47 ◽  
pp. 1729-1733
Author(s):  
Yan Ren ◽  
Jian Ruan ◽  
Ji Yan Yi
Keyword(s):  
Analytical Solution ◽  
Low Frequency ◽  
Experimental System ◽  
Analytic Solutions ◽  
Slide Valve ◽  
Central Position ◽  
Vibration Exciter ◽  
Sinusoidal Waveform ◽  
The Mathematical Model ◽  
Single Slide

For precisely controlling the bias position of an electro-hydraulic vibration exciter, a scheme of a parallel mechanism of a two-dimensional valve (2D valve) and a servo valve is proposed. In the low frequency section, the mathematical model of the electro-hydraulic vibration exciter is simplified reasonably. A vibration central position is first analytically derived by assuming that 2D valve connected with parallel valve is equivalent to a single slide valve with neutral positive opening and the time-average flow rate through them is identical. And then the analytic solutions to excited waveforms superimposed on the bias position are further obtained. Finally, the experimental system is built to verify the theoretical analysis. The results reveal that this approximate analytical solution could describe excited waveform of bias control on electro-hydraulic vibration exciter. When the opening area of 2D valve is a constant, the bias position follows a linear relation with the throttling areas of the parallel valve which is no more than the maximum position. The excited waveform is close to the sinusoidal waveform. At the same opening area of the parallel valve, the bias position is reduced as the area coefficient of 2D valve increases. The proposed scheme not only ensures the frequency and the amplitude to be controlled independently but also the bias position to be adjusted precisely.

scholarly journals Ekman pumping in compact astrophysical bodies

1996 ◽  
Vol 312 ◽  
pp. 327-340 ◽  
Author(s):  
Mark Abney ◽  
Richard I. Epstein
Keyword(s):  
Angular Velocity ◽  
Viscous Fluid ◽  
Thin Layer ◽  
Neutron Stars ◽  
Abrupt Change ◽  
Density Stratification ◽  
Ekman Pumping ◽  
Bounding Surface ◽  
Spin Period ◽  
Astrophysical Objects

We examine the dynamics of a rotating viscous fluid following an abrupt change in the angular velocity of the solid bounding surface. We include the effects of a density stratification and compressibility which are important in astrophysical objects such as neutron stars. We confirm and extend the conclusions of previous studies that stratification restricts the Ekman pumping process to a relatively thin layer near the boundary, leaving much of the interior fluid unaffected. We find that finite compressibility further inhibits Ekman pumping by decreasing the extent of the pumped layer and by increasing the time for spin-up. The results of this paper are important for interpreting the spin period discontinuities (‘glitches’) observed in rotating neutron stars.

QUASI-STATIONARY ELECTROMAGNETIC EFFECTS IN CONDUCTORS AND SUPERCONDUCTORS IN SCHWARZSCHILD SPACE–TIME

2005 ◽  
Vol 14 (05) ◽  
pp. 817-835 ◽  
Author(s):  
B. J. AHMEDOV ◽  
F. J. FATTOYEV
Keyword(s):  
Magnetic Field ◽  
Gravitational Field ◽  
Neutron Stars ◽  
Penetration Depth ◽  
Skin Effect ◽  
Outer Core ◽  
Point Of View ◽  
Time Dependent ◽  
General Relativistic ◽  
Stationary Gravitational Field

The general principles needed to compute the effect of a stationary gravitational field on the quasistationary electromagnetic phenomena in normal conductors and superconductors are formulated from general relativistic point of view. Generalization of the skin effect, that is the general relativistic modification of the penetration depth (of the time-dependent magnetic field in the conductor) due to its relativistic coupling to the gravitational field is obtained. The effect of the gravitational field on the penetration and coherence depths in superconductors is also studied. As an illustration of the foregoing general results, we discuss their application to superconducting systems in the outer core of neutron stars. The relevance of these effects to electrodynamics of magnetized neutron stars has been shown.

The Effect of Turbulence Model on the Response of a Large Floating Wind Turbine

2017 ◽  
Author(s):  
Lene Eliassen ◽  
Erin E. Bachynski
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Fatigue Damage ◽  
Turbulence Model ◽  
Wind Turbines ◽  
Low Frequency ◽  
Turbulence Models ◽  
Line Tension ◽  
Offshore Wind ◽  
Mooring Line

The wind turbine design standards advise choosing one of two recommended turbulence models for load simulations of offshore wind turbines. The difference in fatigue loads for the two turbulence models is relatively small for bottom-fixed wind turbines, but some floating wind turbines show a higher sensitivity to the chosen turbulence model. In this study, the motions and mooring line fatigue damage of two semi-submersible floating wind turbines are investigated for three different wind speeds: 8 m/s, 14 m/s and 20 m/s, and three different wave states for each wind speed. For both concepts, the CSC 5 MW and the CSC 10 MW, the low-frequency surge response is important for the mooring line tension, and the simulations using the Kaimal turbulence model give the largest variation in tension at the surge eigenfrequency. However, using the Mann turbulence model in the load simulations give a higher response in the range of the blade passing frequency (3P). The CSC 10 MW has a higher aerodynamic thrust relative to the CSC 5 MW, and will therefore have a larger surge response at the lower frequencies than the CSC 5 MW. At the lowest wind speed, where the variation in mooring line tension at surge eigenfrequency is high, the fatigue damage is larger if the Kaimal turbulence model is applied to the load simulations. However, at the highest wind speed, using the Mann turbulence model in the simulations, give a higher mooring line fatigue damage.

scholarly journals Incommensurate Crystallization of Neutron Matter in Neutron Stars

2020 ◽  
Keyword(s):  
Neutron Star ◽  
Neutron Stars ◽  
Specific Heat ◽  
Inner Core ◽  
Surface Region ◽  
Outer Core ◽  
Neutron Matter ◽  
High Mass ◽  
The Core ◽  
Gravitational Stress

The composition of the neutron stars from its surface region, outer-core, inner-core, and to its center is still being investigated. One can only surmise on the properties of neutron stars from the spectroscopic data that may be available from time to time. A few models have suggested that the matter at the surface region of the neutron star is composed of atomic nuclei that get crushed under extremely large pressure and gravitational stress, and this leads to the creation of solid lattice with a sea of electrons, and perhaps some protons, flowing through the gaps between them. Nuclei with high mass numbers, such as ferrous, gold, platinum, uranium, may exist in the surface region or in the outer-core region. It is found that the structure of the neutron star changes very much as one goes from the surface to the core of the neutron star. The surface region is extremely hard and very smooth. Surface irregularities are hardly of the order of 5 mm, whereas the interior of the neutron star may be superfluid and composed of neutron-degenerate matter. However, the neutron star is highly compact crystalline systems, and in terrestrial materials under pressure, many examples of incommensurate phase transitions have been discovered. Consequently, the properties of incommensurate crystalline neutron star have been studied. The composition of the neutron stars in the super dense state remains uncertain in the core of the neutron star. One model describes the core as superfluid neutron-degenerate matter, mostly, composed of neutrons , and a small percentage of protons and electrons More exotic forms of matter are possible, including degenerate strange matter. It could also be incommensurate crystalline neutron matter that could be BCC or HCP. Using principles of quantum statistical mechanics, the specific heat and entropy of the incommensurate crystalline neutron star has been calculated assuming that the temperature of the star may vary between to . Two values for the temperature T that have been arbitrarily chosen for which the calculations have been done are and . The values of specific heat and entropy decrease as the temperature increases, and also, their magnitudes are very small. This is in line with the second law of thermodynamics.

Sign in / Sign up

Export Citation Format

Share Document