scholarly journals Superfluid Dynamics in Neutron Star Crusts: The Iordanskii Force and Chemical Gauge Covariance

Universe ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 28
Author(s):  
Lorenzo Gavassino ◽  
Marco Antonelli ◽  
Brynmor Haskell
Keyword(s):  
Neutron Star ◽  
Superfluid Helium ◽  
Equation Of Motion ◽  
Friction Model ◽  
Relativistic Dynamics ◽  
Fluid System ◽  
Relativistic Version ◽  
Dynamical Regimes ◽  
Gauge Covariance ◽  
Definition Of

We present a geometrical derivation of the relativistic dynamics of the superfluid inner crust of a neutron star. The resulting model is analogous to the Hall-Vinen-Bekarevich-Khalatnikov hydrodynamics for a single-component superfluid at finite temperature, but particular attention should be paid to the fact that some fraction of the neutrons is locked to the motion of the protons in nuclei. This gives rise to an ambiguity in the definition of the two currents (the normal and the superfluid one) on which the model is built, a problem that manifests itself as a chemical gauge freedom of the theory. To ensure chemical gauge covariance of the hydrodynamic model, the phenomenological equation of motion for a quantized vortex should contain an extra transverse force, that is the relativistic version of the Iordanskii force discussed in the context of superfluid Helium. Hence, we extend the mutual friction model of Langlois et al. (1998) to account for the possible presence of this Iordanskii-like force. Furthermore, we propose that a better understanding of the (still not completely settled) controversy around the presence of the Iordanskii force in superfluid Helium, as well as in neutron stars, may be achieved by considering that the different incompatible results present in the literature pertain to two, opposite, dynamical regimes of the fluid system.

scholarly journals A Superfluid Perspective on Neutron Star Dynamics

Universe ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 17
Author(s):  
Nils Andersson
Keyword(s):  
Neutron Star ◽  
Degrees Of Freedom ◽  
Temperature Scale ◽  
Fluid System ◽  
Fluid Core ◽  
State Of Matter ◽  
Entrainment Effect ◽  
Neutron Component ◽  
The Impact

As mature neutron stars are cold (on the relevant temperature scale), one has to carefully consider the state of matter in their interior. The outer kilometre or so is expected to freeze to form an elastic crust of increasingly neutron-rich nuclei, coexisting with a superfluid neutron component, while the star’s fluid core contains a mixed superfluid/superconductor. The dynamics of the star depend heavily on the parameters associated with the different phases. The presence of superfluidity brings new degrees of freedom—in essence we are dealing with a complex multi-fluid system—and additional features: bulk rotation is supported by a dense array of quantised vortices, which introduce dissipation via mutual friction, and the motion of the superfluid is affected by the so-called entrainment effect. This brief survey provides an introduction to—along with a commentary on our current understanding of—these dynamical aspects, paying particular attention to the role of entrainment, and outlines the impact of superfluidity on neutron-star seismology.

scholarly journals Theory of the deformation of aligned polyethylene

2015 ◽  
Vol 471 (2180) ◽  
pp. 20150171 ◽  
Author(s):  
A. Hammad ◽  
T. D. Swinburne ◽  
H. Hasan ◽  
S. Del Rosso ◽  
L. Iannucci ◽  
...  
Keyword(s):  
Load Transfer ◽  
Tensile Load ◽  
Equation Of Motion ◽  
Dislocation Dynamics ◽  
Viscoelastic Deformation ◽  
Transfer Length ◽  
Soliton Dynamics ◽  
Fluctuation Dissipation ◽  
Pull Out ◽  
Definition Of

Solitons are proposed as the agents of plastic and viscoelastic deformation in aligned polyethylene. Interactions between straight, parallel molecules are mapped rigorously onto the Frenkel–Kontorova model. It is shown that these molecular interactions distribute an applied load between molecules, with a characteristic transfer length equal to the soliton width. Load transfer leads to the introduction of tensile and compressive solitons at the chain ends to mark the onset of plasticity at a well-defined yield stress, which is much less than the theoretical pull-out stress. Interaction energies between solitons and an equation of motion for solitons are derived. The equation of motion is based on Langevin dynamics and the fluctuation–dissipation theorem and it leads to the rigorous definition of an effective mass for solitons. It forms the basis of a soliton dynamics in direct analogy to dislocation dynamics. Close parallels are drawn between solitons in aligned polymers and dislocations in crystals, including the configurational force on a soliton. The origins of the strain rate and temperature dependencies of the viscoelastic behaviour are discussed in terms of the formation energy of solitons. A failure mechanism is proposed involving soliton condensation under a tensile load.

Fluid system design for a superfluid helium space tanker

1989 ◽  
Author(s):  
JOHN GILLE ◽  
TIMOTHY MARTIN ◽  
GLEN MCINTOSH
Keyword(s):  
System Design ◽  
Superfluid Helium ◽  
Fluid System

scholarly journals Equation of state effects on the core-crust interface of slow rotating neutron stars

2019 ◽  
Vol 26 ◽  
pp. 120
Author(s):  
Ch. Margaritis ◽  
L. Tsaloukidis ◽  
Ch. C. Moustakidis
Keyword(s):  
Neutron Star ◽  
Equation Of State ◽  
Symmetry Energy ◽  
Transition Density ◽  
Parabolic Approximation ◽  
Transition Pressure ◽  
The Core ◽  
Nuclear Models ◽  
Definition Of

We systematically  study the symmetry energy  effects of the transition  density ntand the transition pressure Ptaround the crust-core interface of a neutron star in the framework of the dynamical and the thermodynamical method respectively. We employ both the parabolic approximation and the full expansion, for the definition of the symmetry energy. We use various theoretical  nuclear models. Firstly we derive and present an approximation for the transition pressure Ptand crustal mass Mcrust. Secondly, we explore the effects of the Equation of State (EoS) on a few astrophysical applications which are sensitive to the values of n­tand Pt. We found that the above quantities are sensitive mainly on the applied approximation for the symmetry energy (confirming previous results). Furthermore, an additional sensitivity also exists, depending on the used method (dynamical or thermodynamical). The above findings lead us to claim that the determination of the n­tand Ptmust be reliable and accurate before they are used to constrain relevant neutron star properties.

scholarly journals Kinematics, dynamics and the scale of time-II

1937 ◽  
Vol 159 (897) ◽  
pp. 171-191 ◽  
Keyword(s):  
External Force ◽  
Test Particle ◽  
Empirical Equation ◽  
Additional Term ◽  
Gravitational Effect ◽  
Equation Of Motion ◽  
Present Communication ◽  
Field Equations ◽  
Dynamical Time ◽  
Definition Of

1—In earlier investigations (Milne 1932, 1933, 1935, 1936 a, b ) the author has developed certain kinematic representations of the expanding universe. Amongst such representations is the substratum , or "smoothed-out" universe. Without appeal to the empirical laws of dynamics and gravitation, or to "field equations" or to assumed properties of geodesics in space-time, it was shown how to obtain the equation of motion of a free test-particle in the presence of a substratum, purely from the definition of a substratum. This equation of motion was then used to construct the dynamics of a particle under external force. The various dynamical quantities—mass, momentum , force, worh, energy—arose naturally from the study of a certain identity, and ttre relations between them were in many eases similar to those in the Newton-Einstein mechanics. But the equation of motion itself was formally different from the Newton-Einstein empirical equation of motion; it contained a term which could lie taken to represent the gravitational effect of the substratum on the particle; this term was Used to calculate the universal value of the "constant" of gravitation. In Part I (1937) of the present communication it was shown that in the clocks supposed to be carried by the particle-observers of the substratum are re-graduated from "kinematic" time t to a certain "dynamical" time T , and all derived measures adjusted correspondingly, then the characteristic additional term in the equation of motion disappeared and the equation of motion assumed, at least locally and for small velocities, a strictly Newtonian form. The relation between t and T was T = t 0 log ( t / t 0 ) + t 0 . (1)

scholarly journals A COMPARISON OF THE PROPER-TIME EQUATION AND THE RENORMALIZATION GROUP β-FUNCTION IN STRING THEORY

1995 ◽  
Vol 10 (21) ◽  
pp. 1565-1575
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Proper Time ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
The Other ◽  
Proportionality Factor ◽  
Yang Mills ◽  
Higher Covariant Derivative ◽  
Full Equation ◽  
Gauge Covariance ◽  
Β Function

It is known that there is a proportionality factor relating the β-function and the equations of motion viz. the Zamolodchikov metric. Usually this factor has to be obtained by other methods. The proper-time equation, on the other hand, is the full equation of motion. We explain the reasons for this and illustrate it by calculating corrections to Maxwell’s equation. The corrections are calculated to cubic order in the field strength, but are exact to all orders in derivatives. We also test the gauge covariance of the proper-time method by calculating higher (covariant) derivative corrections to the Yang-Mills equation.

scholarly journals Four-dimensional Integral Model of Dry Friction on the Example of Wheel Movement

2021 ◽  
Vol 2096 (1) ◽  
pp. 012043
Author(s):  
M S Salimov ◽  
G R Saypulaev ◽  
I V Merkuriev
Keyword(s):  
Dry Friction ◽  
Rolling Friction ◽  
Equation Of Motion ◽  
Friction Model ◽  
The Body ◽  
Integral Model ◽  
Control Torque ◽  
Padé Approximations ◽  
Pade Approximations ◽  
Dimensional Integral

Abstract A four-dimensional model of dry friction in the interaction of a solid wheel and a horizontal rough surface is investigated. It is assumed that there is no separation between the wheel and the horizontal surface. The movement of the body occurs in conditions of combined dynamics, when in addition to the sliding movement, the body participates in spinning and rolling. The equation of motion of the wheel is compiled using the Appel equation. The resulting model of sliding, spinning, and rolling friction is given for the case where the contact area is a circle. The cumbersome integral expressions were replaced by fractional-linear Pade approximations. Pade approximations accurately describe the behavior of the components of the friction model. A mathematical model is proposed that describes the simultaneous sliding, spinning and rolling of a solid wheel. The dependences of the parallel and perpendicular components of the friction force and the torque of the spinning friction were ploted with respect to the parameter that characterizes the movement of the wheel. Comparisons of the integral friction model and the model based on Pade approximations are presented. The results of the comparison showed a qualitative correspondence of the models. After obtaining the equation of motion, the simulation of motion at a constant control torque of the wheel is carried out. The graphs allow you to match the logical behavior of the wheel movement.

Experimental and Numerical Investigation on a Pressure Dependent Friction Model

2015 ◽  
Vol 639 ◽  
pp. 403-410 ◽  
Author(s):  
Fabian Zöller ◽  
Vera Sturm ◽  
Marion Merklein
Keyword(s):  
Prediction Accuracy ◽  
Fe Simulation ◽  
Friction Model ◽  
Simulation Program ◽  
Experimental Investigations ◽  
Numerical Investigations ◽  
Good Accordance ◽  
Universal Prediction ◽  
Definition Of ◽  
Cup Drawing

The objective of this paper is the investigation of the implemented pressure dependent friction model in the FE simulation program AutoForm. Since the values for the required parameters of this approach are not defined in the actual FE simulation program, this paper contributes to a first definition of these parameters. Therefore, experimental investigations with the cup drawing tests are carried out. With the support of the experimental results regarding the maximum stamping force, the model is calibrated and subsequently validated by the comparison of the sheet thicknesses of the experimental and numerical investigations. The results of this validation reveal a good accordance of simulation and reality in nearly all areas. However there are also areas in which the prediction accuracy decreases in comparison to the basic simulation. Therefore, additional investigations have to be carried out which concentrate on the modification of this pressure dependent approach towards a better universal prediction accuracy of the simulation.

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