Negative electrorheological responses of micro-polar fluids in the finite spin viscosity small spin velocity limit. I. Couette flow geometries

Negative electrorheological responses induced by micro-particle electrorotation in two-dimensional Couette flow geometries are analyzed by a set of continuum modeling field equations originating from anti-symmetric/couple stress theories in the finite spin viscosity small spin velocity (FSV) limit. Analytical solutions are obtained for the first time to express the spin velocity, linear velocity, and effective viscosity in terms of the electric field strength, driving shear rate, boundary condition selection parameter, and spin viscosity. Good agreement is achieved between the FSV theoretical predictions presented herein and the experimental measurements reported in recent literature for the effective viscosity for low driving shear rates.     

Current driven domain wall velocities exceeding the spin angular momentum transfer rate in permalloy nanowires

The velocity of domain walls driven by current in zero magnetic field is measured in permalloy nanowires using real-time resistance measurements. The domain wall velocity increases with increasing current density, reaching a maximum velocity of approximately 110 m/s when the current density in the nanowire reaches approximately 1.5 x 10(8) A/cm(2). Such high current driven domain wall velocities exceed the estimated rate at which spin angular momentum is transferred to the domain wall from the flow of spin polarized conduction electrons, suggesting that other driving mechanisms, such as linear momentum transfer, need to be taken into account.     

Correlation of spin and velocity in the homogeneous cooling state of a granular gas of rough particles

In a granular gas of rough particles the spin of a grain is correlated with its linear velocity. We develop an analytical theory to account for these correlations and compare its predictions to numerical simulations, using Direct Simulation Monte Carlo as well as Molecular Dynamics. The system is shown to relax from an arbitrary initial state to a steady-state, which is characterized by time-independent, finite correlations of spin and linear velocity. The latter are analyzed systematically for a wide range of system parameters, including the coefficients of tangential and normal restitution as well as the moment of inertia of the particles. For most parameter values the axis of rotation and the direction of linear momentum are perpendicular like in a sliced tennis ball, while parallel orientation, like in a rifled bullet, occurs only for a small range of parameters. The limit of smooth spheres is singular: any arbitrarily small roughness unavoidably causes significant translation-rotation correlations, whereas for perfectly smooth spheres the rotational degrees of freedom are completely decoupled from the dynamic evolution of the gas.     

On the evolution of higher dimensional Heisenberg continuum spin systems

We consider the evolution of a classical Heisenberg ferromagnetic spin chain in its continuum limit in higher spatial dimensions. It is shown that the evolution of a radially symmetric chain could be identified with the motion of a helical space curve as in the linear case. The resulting invariant equations for the curvature (radial energy density) and torsion (related to current density) are shown to be equivalent to a generalized nonlinear Schrödinger equation, similar to the one derived by Ruijgrok and Jurkiewicz recently. Equivalent linear equations as well as special static solutions of point singular type are obtained. Similarity solutions, a class of which belong to Riccati type, are discussed in detail. For general higher dimensions, a potentially useful formulation is presented: Under stereographic projection of the unit sphere of spin, the equation of motion takes a neater form even with the inclusion of anisotropic interactions. Classes of explicit solutions are reported in higher dimensions. Propagating spin waves, static spin waves of point singular nature and of finite energy in some cases are also discussed.     

Modulated spin waves and robust quasi-solitons in classical Heisenberg rings

We investigate the dynamical behavior of finite rings of classical spin vectors interacting via nearest-neighbor isotropic exchange in an external magnetic field. Our approach is to utilize the solutions of a continuum version of the discrete spin equations of motion (EOM) which we derive by assuming continuous modulations of spin wave solutions of the EOM for discrete spins. This continuum EOM reduces to the Landau-Lifshitz equation in a particular limiting regime. The usefulness of the continuum EOM is demonstrated by the fact that the time-evolved numerical solutions of the discrete spin EOM closely track the corresponding time-evolved solutions of the continuum equation. It is of special interest that our continuum EOM possesses soliton solutions, and we find that these characteristics are also exhibited by the corresponding solutions of the discrete EOM. The robustness of solitons is demonstrated by considering cases where initial states are truncated versions of soliton states and by numerical simulations of the discrete EOM equations when the spins are coupled to a heat bath at finite temperatures.     

Nonlinear dynamics of a continuum Heisenberg spin chain with an anisotropy and an external magnetic field

By stereographically projecting the spin vector onto a complex plane in the equations of motion for a continuum Heisenberg spin chain with an anisotropy (an easy plane and an easy axis) and an external magnetic field, the effect of the magnetic field for integrability of the system is discussed. Then, introducing an auxiliary parameter, the Lax equations for Darboux matrices are generated recursively. By choosing the constants, the Jost solutions are satisfied the corresponding Lax equations. The exact soliton solutions are investigated, then the total magnetic momentum and its z-component are obtained. These results show that the solitary waves depend essentially on two velocities which describe a spin configuration deviating from a homogeneous magnetization. The depths and widths of solitary waves vary periodically with time. The center of an inhomogeneity moves with a constant velocity, while the shape of soliton also changes with another velocity and this shape is not symmetrical with respect to the center. The total magnetic momentum and its z-component vary with time.     

Continuum modeling of micro-particle electrorotation in Couette and Poiseuille flows—The zero spin viscosity limit

A continuum mechanical model is presented to analyze the negative electrorheological responses of a particle-liquid mixture with the suspended micro-particles undergoing Quincke rotation for both Couette and Poiseuille flow geometries by combining particle electromechanics and continuum anti-symmetric/couple stress analyses in the zero spin viscosity limit. We propose a phenomenological polarization relaxation model to incorporate both the micro-particle rotation speed and macro-continuum spin velocity effects on the fluid polarization during non-equilibrium motion. Theoretical predictions of the Couette effective viscosity and Poiseuille flow rate obtained from the present continuum treatment are in good agreement with the experimental measurements reported in current literature.     

On the dynamics of a continuum spin system

For a one-dimensional system of classical spins with nearest neighbour Heisenberg interaction we derive the equation of motion for each three-dimensional spin vector. In the continuum limit where the spins lie dense on a line this set of equations reduces to a nonlinear partial differential equation. In addition to spin-wave solutions we obtain some other special solutions of this equation. In particular we find solitary waves having total energy localised in a finite region, with velocity of propagation inversely proportional to the width of this region. Solutions of still another type are shown to have a diffusive character. The stability of such solutions and the possibility of interaction of two or more solitary waves have not yet been studied.     

Direct observation of domain-wall configurations transformed by spin currents

Direct observations of current-induced domain-wall propagation by spin-polarized scanning electron microscopy are reported. Current pulses move head-to-head as well as tail-to-tail walls in submicrometer Fe20Ni80 wires in the direction of the electron flow, and a decay of the wall velocity with the number of injected current pulses is observed. High-resolution images of the domain walls reveal that the wall spin structure is transformed from a vortex to a transverse configuration with subsequent pulse injections. The change in spin structure is directly correlated with the decay of the velocity.     

The isovector spin response in a finite nucleus

A polarization propagator is evaluated in a finite nucleus by using the continuum RPA formalism and applied to the isovector spin response in a quasielastic region for a large momentum transfer.     

Natural convection with damped thermal flux in a vertical circular cylinder

Natural convection flows of an incompressible Newtonian fluid inside a circular cylinder are studied. The heat transfer process is described by a generalized fractional constitutive equation for the thermal flux-temperature gradient. Caputo time-fractional derivative operator, which provides the damping of thermal flux, is considered into the studied model.Analytical solutions to the fluid temperature, thermal flux, fluid velocity and volume flow rate are obtained with the integral transforms method (Laplace transform and finite Hankel transform).Temperature behaviors for small and large values of the time t, as well as the post-transient and transient velocity components are determined. The influence of the memory parameter (the order of the time-fractional derivative) on the temperature, thermal flux, velocity and the volume flow rate is numerically and graphically studied.     

Low temperature spin dynamics of the geometrically frustrated antiferromagnetic garnet Gd3Ga5O12

The low temperature spin dynamics of the geometrically frustrated antiferromagnet Gd 3Ga 5O (12) (GGG) have been investigated using muon spin relaxation. No evidence for static order is seen down to a temperature of 25 mK or a few percent of the Curie-Weiss temperature. Instead there is a linear decrease in the Gd spin fluctuation rate below 1 K which extrapolates to a small but finite value of 2 GHz at zero temperature. In terms of the spin fluctuations the system appears essentially to remain dynamic at low temperatures (T>0.02 K) and magnetic fields up to 1.8 T.     

The KdV-Burgers equation in speed gradient viscous continuum model

Based on the microscopic two velocity difference model, a macroscopic model called speed viscous continuum model is developed to describe traffic flow. The relative velocities are added to the motion equation, which leads to viscous effects in continuum model. The viscous continuum model overcomes the backward travel problem, which exists in many higher-order continuum models. Nonlinear analysis shows that the density fluctuation in traffic flow leads to density waves. Near the onset of instability, a small disturbance could lead to solitons described by the Korteweg-de Vries-Burgers (KdV-Burgers) equation, which is seldom found in other traffic flow models, and the soliton solution is derived.     

Interaction-driven spin precession in quantum-dot spin valves

We analyze spin-dependent transport through spin valves composed of an interacting quantum dot coupled to two ferromagnetic leads. The spin on the quantum dot and the linear conductance as a function of the relative angle theta of the leads' magnetization directions is derived to lowest order in the dot-lead coupling strength. Because of the applied bias voltage spin accumulates on the quantum dot, which for finite charging energy experiences a torque, resulting in spin precession. The latter leads to a nontrivial, interaction-dependent, theta dependence of the conductance. In particular, we find that the spin-valve effect is reduced for all theta not equal pi.     

Challenges in uncovering the origin of the proton's spin

One of the most fascinating challenges facing modern strong interaction physics is to understand the origin of the spin of the nucleon in terms of the spin and orbital angular momentum of the quarks and gluons. We review recent progress on this problem as well as some of the uncertainties associated with state of the art lattice QCD simulations. In particular, we explain the importance of the corrections associated with chiral extrapolation and finite volume corrections, especially for the term B(0) extracted from the appropriate low moment of the deeply virtual Compton scattering amplitude.     

Two-Scale Picard Stabilized Finite Volume Method for the Incompressible Flow

In this paper, we consider a two-scale stabilized finite volume method for the two-dimensional stationary incompressible flow approximated by the lowest equal-order element pair $P_1-P_1$ which does not satisfy the inf-sup condition. The two-scale method consists of solving a small non-linear system on the coarse mesh and then solving a linear Stokes equations on the fine mesh. Convergence of the optimal order in the $H^1$-norm for velocity and the $L^2$-norm for pressure is obtained. The error analysis shows there is the same convergence rate between the two-scale stabilized finite volume solution and the usual stabilized finite volume solution on a fine mesh with relation $h =\mathcal{O}(H^2)$. Numerical experiments completely confirm theoretic results. Therefore, this method presented in this paper is of practical importance in scientific computation.     

Nonlinear spin excitations in a classical Heisenberg anisotropic helimagnet

The nonlinear spin excitations in an anisotropic helimagnet in the presence of a constant magnetic field are investigated in the classical continuum limit. The helical character is introduced into the model, in analogy with the twist in a cholesteric liquid crystal. After deriving a class of spin wave solutions for the stereographic representation of the Landau-Lifshitz equation, in-plane stationary spin configurations are obtained and their stability is analysed. When the external magnetic field is along the anisotropic axis, modulational instability is observed in the spin lattice, and when the external magnetic field is normal to the anisotropic axis, the spin configurations are unstable. The perturbed spin components show fluctuations in the tail region, while the velocity and amplitude of the soliton remain unaltered.     

Microscopic imaging of slow flow and diffusion: a pulsed field gradient stimulated echo sequence combined with turbo spin echo imaging.

In this paper we present a pulse sequence that combines a displacement-encoded stimulated echo with rapid sampling of k-space by means of turbo spin echo imaging. The stimulated echo enables the use of long observation times between the two pulsed field gradients that sample q-space completely. Propagators, constructed with long observation times, could discriminate slowly flowing protons from diffusing protons, as shown in a phantom in which a plug flow with linear velocity of 50microm/s could clearly be distinguished from stationary water. As a biological application the apparent diffusion constant in longitudinal direction of a transverse image of a maize plant stem had been measured as a function of observation time. Increasing contrast in the apparent diffusion constant image with increasing observation times were caused by differences in plant tissue: although the plant stem did not take up any water, the vascular bundles, concentrated in the outer ring of the stem, could still be discerned because of their longer unrestricted diffusional pathways for water in the longitudinal direction compared to cells in the parenchymal tissue. In the xylem region of a tomato pedicel flowing water could be distinguished from a large amount of stationary water. Linear flow velocities up to 0.67 mm/s were measured with an observation time of 180 ms.     

A mathematical model for signal from spins flowing during the application of spin echo pulse sequences

Models are presented for both laminar and plug flow that predict the signal from spins flowing during the application of slice-selective spin echo pulse sequences. The models permit calculation of the total signal from a cylindrical vessel lying perpendicular to the slice and incorporate the effect of the physical displacement of the spins between successive excitations. This time-of-flight effect gives a signal which is composed of contributions from a finite number of spin populations, with each population signal weighted by the fractional volume of that spin population within the cylindrical vessel segment. The signal and fractional volume from each spin population are derived analytically for ten different spin echo pulse sequences. The models for plug and laminar flow have important application for predicting and interpreting flow effects observed in clinical images. They are shown to be useful for selecting pairs of pulse sequences that can be used to obtain digitally subtracted MR images which provide optimum contrast for flowing blood with essentially complete suppression of stationary anatomy. These models provide a means for quantitatively comparing the expected signal from flowing spins for the many techniques presently being investigated for MR angiography.