Hydrodynamics of spin currents

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Angel Domingo Gallegos ◽  
Umut Gürsoy ◽  
Amos Yarom
Keyword(s):  
Stress Tensor ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Spin Current ◽  
Second Order ◽  
Relativistic Hydrodynamics ◽  
Hydrodynamic Equations ◽  
Spin Currents ◽  
Dynamical Spin ◽  
Good Agreement

We study relativistic hydrodynamics in the presence of a non vanishing spin potential. Using a variety of techniques we carry out an exhaustive analysis, and identify the constitutive relations for the stress tensor and spin current in such a setup, allowing us to write the hydrodynamic equations of motion to second order in derivatives. We then solve the equations of motion in a certain dynamical spin limit and in a perturbative setup and find surprisingly good agreement with measurements of global \LambdaΛ-hyperon polarization carried out at RHIC.

scholarly journals Holographic spin liquids and Lovelock Chern-Simons gravity

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
A.D. Gallegos ◽  
U. Gürsoy
Keyword(s):  
Constitutive Relations ◽  
Equations Of Motion ◽  
Spin Current ◽  
Analytic Solutions ◽  
Momentum Tensor ◽  
Spin Connection ◽  
Spin Liquids ◽  
Thermodynamic Potentials ◽  
Algebraic Constraints ◽  
Chern Simons

Abstract We explore the role of torsion as source of spin current in strongly interacting conformal fluids using holography. We establish the constitutive relations of the basic hydrodynamic variables, the energy-momentum tensor and the spin current based on the classification of the spin sources in irreducible Lorentz representations. The fluids we consider are assumed to be described by the five dimensional Lovelock-Chern-Simons gravity with independent vielbein and spin connection. We construct a hydrodynamic expansion that involves the stress tensor and the spin current and compute the corresponding one-point functions holographically. As a byproduct we find a class of interesting analytic solutions to the Lovelock-Chern-Simons gravity, including blackholes, by mapping the equations of motion into non-linear algebraic constraints for the sources. We also derive a Lee-Wald entropy formula for these blackholes in Chern-Simons theories with torsion. The blackhole solutions determine the thermodynamic potentials and the hydrodynamic constitutive relations in the corresponding fluid on the boundary. We observe novel spin induced transport in these holographic models: a dynamical version of the Barnett effect where vorticity generates a spin current and anomalous vortical transport transverse to a vector-like spin source.

Topological spin current

2017 ◽  
Author(s):  
E. Saitoh
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Spin Current ◽  
Edge State ◽  
Dimensional System ◽  
Electron Band ◽  
Electrically Conducting ◽  
Spin Currents ◽  
Surface Spin ◽  
Three Dimensional System

This chapter discusses another type of equilibrium-spin current similar to the exchange-spin current—the topological spin current. Topological spin currents are driven by topological-band structure and classified into bulk and surface topological spin currents. The former is confined onto electron-band manifolds, sometimes affecting their motions. This confinement is addressed through the standard method of combining the equations of motion and the Boltzmann equation for semi-classical electrons in a band. The latter class, on the other hand, is a surface-spin current, which is limited near surfaces of a three-dimensional system and flows along these surfaces. This type is known to appear in topological insulators, where the bulk is insulating but the surface or edge is electrically conducting due to the surface or edge state.

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

scholarly journals Anomalous spin Hall and inverse spin Hall effects in magnetic systems

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
X. R. Wang
Keyword(s):  
Hall Effect ◽  
Order Parameter ◽  
Spin Current ◽  
Spin Hall Effect ◽  
Magnetic Systems ◽  
Charge Current ◽  
Spin Currents ◽  
Tensor Quantity ◽  
Hall Effects ◽  
Spin Hall Effects

AbstractSpin current is a very important tensor quantity in spintronics. However, the well-known spin-Hall effect (SHE) can only generate a few of its components whose propagating and polarization directions are perpendicular with each other and to an applied charge current. It is highly desirable in applications to generate spin currents whose polarization can be in any possible direction. Here anomalous SHE and inverse spin-Hall effect (ISHE) in magnetic systems are predicted. Spin currents, whose polarisation and propagation are collinear or orthogonal with each other and along or perpendicular to the charge current, can be generated, depending on whether the applied charge current is along or perpendicular to the order parameter. In anomalous ISHEs, charge currents proportional to the order parameter can be along or perpendicular to the propagating or polarization directions of the spin current.

Analysis of the First Order and Slowly Varying Motions of an Axisymmetric Floating Body in Bichromatic Waves

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
João Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Drift Motion ◽  
First Order ◽  
Motion Responses ◽  
Simple Geometry ◽  
Good Agreement

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and biharmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axisymmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in biharmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

A Second Order Lagrangian Model for Irregular Ocean Waves

2005 ◽  
Vol 128 (3) ◽  
pp. 177-183 ◽  
Author(s):  
Sébastien Fouques ◽  
Harald E. Krogstad ◽  
Dag Myrhaug
Keyword(s):  
Specular Reflection ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Lagrangian Model ◽  
Lagrangian Description ◽  
Linear Wave ◽  
Irregular Solution

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

Towards a Technique for Nonlinear Modal Analysis

2012 ◽  
Author(s):  
Simon A. Neild ◽  
Andrea Cammarano ◽  
David J. Wagg
Keyword(s):  
Normal Form ◽  
Modal Analysis ◽  
Equations Of Motion ◽  
Transformation Process ◽  
Second Order ◽  
Identity Transformation ◽  
Modal Testing ◽  
System Response ◽  
Weakly Nonlinear ◽  
Nonlinear Modal Analysis

In this paper we discuss a theoretical technique for decomposing multi-degree-of-freedom weakly nonlinear systems into a simpler form — an approach which has parallels with the well know method for linear modal analysis. The key outcome is that the system resonances, both linear and nonlinear are revealed by the transformation process. For each resonance, parameters can be obtained which characterise the backbone curves, and higher harmonic components of the response. The underlying mathematical technique is based on a near identity normal form transformation. This is an established technique for analysing weakly nonlinear vibrating systems, but in this approach we use a variation of the method for systems of equations written in second-order form. This is a much more natural approach for structural dynamics where the governing equations of motion are written in this form as standard practice. In fact the first step in the method is to carry out a linear modal transformation using linear modes as would typically done for a linear system. The near identity transform is then applied as a second step in the process and one which identifies the nonlinear resonances in the system being considered. For an example system with cubic nonlinearities, we show how the resulting transformed equations can be used to obtain a time independent representation of the system response. We will discuss how the analysis can be carried out with applied forcing, and how the approximations about response frequencies, made during the near-identity transformation, affect the accuracy of the technique. In fact we show that the second-order normal form approach can actually improve the predictions of sub- and super-harmonic responses. Finally we comment on how this theoretical technique could be used as part of a modal testing approach in future work.

scholarly journals Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Coatings ◽  
2018 ◽  
Vol 8 (11) ◽  
pp. 389 ◽  
Author(s):  
Yanqing Wang ◽  
Zhiyuan Zhang
Keyword(s):  
Metal Foam ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Local Buckling ◽  
Functionally Graded ◽  
Small Scale ◽  
Refined Plate Theory ◽  
Nanoporous Metal ◽  
Non Local

In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains which vary quadratically through the thickness without considering the shear correction factor. Based on Eringen’s non-local differential constitutive relations, the equations of motion are derived from Hamilton’s principle. The analytical solutions for the buckling of FG nanoporous metal foam nanoplates are obtained via Navier’s method. Moreover, the effects of porosity distributions, porosity coefficient, small scale parameter, axial compression ratio, mode number, aspect ratio and length-to-thickness ratio on the buckling loads are discussed. In order to verify the validity of present analysis, the analytical results have been compared with other previous studies.

Morphing Continuum Theory: Incorporating the Physics of Microstructures to Capture the Transition to Turbulence Within a Boundary Layer

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Louis B. Wonnell ◽  
James Chen
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Ad Hoc ◽  
Constitutive Relations ◽  
Turbulence Models ◽  
Continuum Theory ◽  
Transition To Turbulence ◽  
Flow Turbulence ◽  
Good Agreement ◽  
Inherent Advantage

A boundary layer with Re = 106 is simulated numerically on a flat plate using morphing continuum theory. This theory introduces new terms related to microproperties of the fluid. These terms are added to a finite-volume fluid solver with appropriate boundary conditions. The success of capturing the initial disturbances leading to turbulence is shown to be a byproduct of the physical and mathematical rigor underlying the balance laws and constitutive relations introduced by morphing continuum theory (MCT). Dimensionless equations are introduced to produce the parameters driving the formation of disturbances leading to turbulence. Numerical results for the flat plate are compared with the experimental results determined by the European Research Community on Flow, Turbulence, and Combustion (ERCOFTAC) database. Experimental data show good agreement inside the boundary layer and in the bulk flow. Success in predicting conditions necessary for turbulent and transitional (T2) flows without ad hoc closure models demonstrates the theory's inherent advantage over traditional turbulence models.

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