Weak Uniform Magnetic Field Research Articles

Persistent Friedel oscillations in graphene due to a weak magnetic field

Two opposite chiralities of Dirac electrons in a two-dimensional (2D) graphene sheet modify the Friedel oscillations strongly: electrostatic potential around an impurity in graphene decays much faster than in 2D electron gas. At distances $r$ much larger than the de Broglie wavelength, it decays as $1/{r}^{3}$. Here we show that a weak uniform magnetic field affects the Friedel oscillations in an anomalous way. It creates a field-dependent contribution which is dominant in a parametrically large spatial interval ${p}_{0}^{\ensuremath{-}1}\ensuremath{\lesssim}r\ensuremath{\lesssim}{k}_{F}{l}^{2}$, where $l$ is the magnetic length, ${k}_{F}$ is Fermi momentum, and ${p}_{0}^{\ensuremath{-}1}={({k}_{F}l)}^{4/3}/{k}_{F}$. Moreover, in this interval, the field-dependent oscillations do not decay with distance. The effect originates from a spin-dependent magnetic phase accumulated by the electron propagator. The obtained phase may give rise to novel interaction effects in transport and thermodynamic characteristics of graphene and graphene-based heterostructures.

On the influence of viscosity on the anisotropic dynamics of cosmological perturbations in the presence of a magnetic field

We analyse the influence that viscous effects can induce on the evolution of primordial perturbations to the isotropic universe in the presence of a weak uniform magnetic field. Previous analyses have shown that the presence of the magnetic field induces an intrinsic anisotropy in the perturbations dynamics, essentially because of the anisotropic character of the perturbed magnetic pressure. This anisotropic effect is of order unity in the perturbation amplitude, although it remains small in the linear theory when the density constraints are considered. The aim of this study is to determine the impact of viscosity, surely present in the early universe, on the growth of the perturbation anisotropy. The main merit of this study consists of demonstrating that a tiny overlapping exists in the parameter space to deal simultaneously with anisotropic features due to the magnetic field and the viscous damping of such density fluctuation. Actually, we demonstrate that the viscosity affects the value of the anisotropy, by smoothing the growing rate of the instability only when structure smaller than about 5000 solar masses are concerned. This result allows us to guarantee that the intrinsic anisotropy of the magnetized universe perturbations is not affected by the viscosity due to friction among inhomogeneous layers or compressive-like effects, and therefore, they remain good candidates for being seeds for filament formation across the universe.

Bipolar region formation in stratified two-layer turbulence

This work presents an extensive study of the previously discovered formation of bipolar flux concentrations in a two-layer model. We interpret the formation process in terms of negative effective magnetic pressure instability (NEMPI), which is a possible mechanism to explain the origin of sunspots. In our simulations, we use a Cartesian domain of isothermal stratified gas that is divided into two layers. In the lower layer, turbulence is forced with transverse nonhelical random waves, whereas in the upper layer no flow is induced. A weak uniform magnetic field is imposed in the entire domain at all times. In this study we vary the stratification by changing the gravitational acceleration, magnetic Reynolds number, strength of the imposed magnetic field, and size of the domain to investigate their influence on the formation process. Bipolar magnetic structure formation takes place over a large range of parameters. The magnetic structures become more intense for higher stratification until the density contrast becomes around $100$ across the turbulent layer. For the Reynolds numbers considered, magnetic flux concentrations are generated at magnetic Prandtl number between 0.1 and 1. The magnetic field in bipolar regions increases with higher imposed field strength until the field becomes comparable to the equipartition field strength of the turbulence. A larger horizontal extent enables the flux concentrations to become stronger and more coherent. The size of the bipolar structures turns out to be independent of the domain size. In the case of bipolar region formation, we find an exponential growth of the large-scale magnetic field, which is indicative of a hydromagnetic instability. Additionally, the flux concentrations are correlated with strong large-scale downward and converging flows. These findings imply that NEMPI is responsible for magnetic flux concentrations.

Magneto-rotational instability with the effect of cosmic rays

AbstractCosmic ray (CR) is an important component of the interstellar medium. It interacts with plasma via embedded magnetic irregularities. We study the magneto-rotational instability (MRI) in the presence of CRs. We analyse the effect of CRs including their diffusion using both linear stability analysis and MHD simulations. Two models are studied. (1) In the shearing box model, uniform initial state is adopted. Linear analysis shows that the growth rate of MRI is not sensitive to the value of CR diffusion coefficient. (2) In the differentially rotating cylinder model, the initial state is taken as a constant angular momentum polytropic disk threaded by weak uniform vertical magnetic field. Linear analysis shows that the growth rate of MRI becomes larger if the CR diffusion coefficient is larger. Both linear results are confirmed by MHD simulations.

ANALYSIS OF MAGNETOROTATIONAL INSTABILITY WITH THE EFFECT OF COSMIC-RAY DIFFUSION

We present the results obtained from linear stability analysis and 2.5-dimensional magnetohydrodynamic (MHD) simulations of the magnetorotational instability (MRI), including the effects of cosmic rays (CRs). We took into account of the CR diffusion along the magnetic field but neglect the cross-field-line diffusion. Two models are considered in this paper: shearing box model and differentially rotating cylinder model. We studied how MRI is affected by the initial CR pressure (i.e., energy) distribution. In the shearing box model, the initial state is uniform distribution. Linear analysis shows that the growth rate of MRI does not depend on the value of CR diffusion coefficient. In the differentially rotating cylinder model, the initial state is a constant angular momentum polytropic disk threaded by weak uniform vertical magnetic field. Linear analysis shows that the growth rate of MRI becomes larger if the CR diffusion coefficient is larger. Both results are confirmed by MHD simulations. The MHD simulation results show that the outward movement of matter by the growth of MRI is not impeded by the CR pressure gradient, and the centrifugal force which acts to the concentrated matter becomes larger. Consequently, the growth rate of MRI is increased. On the other hand, if the initial CR pressure is uniform, then the growth rate of the MRI barely depends on the value of the CR diffusion coefficient.

Magnetophoresis of diamagnetic microparticles in a weak magnetic field

Magnetic manipulation is a promising technique for lab-on-a-chip platforms. The magnetic approach can avoid problems associated with heat, surface charge, ionic concentration and pH level. The present paper investigates the migration of diamagnetic particles in a ferrofluid core stream that is sandwiched between two diamagnetic streams in a uniform magnetic field. The three-layer flow is expanded in a circular chamber for characterisation based on imaging of magnetic nanoparticles and fluorescent microparticles. A custom-made electromagnet generates a uniform magnetic field across the chamber. In a relatively weak uniform magnetic field, the diamagnetic particles in the ferrofluid move and spread across the chamber. Due to the magnetization gradient formed by the ferrofluid, diamagnetic particles undergo negative magnetophoresis and move towards the diamagnetic streams. The effects of magnetic field strength and the concentration of diamagnetic particles are studied in detail.

Photoactivated Colloidal Dockers for Cargo Transportation

We introduce a self-propelled colloidal hematite docker that can be steered to a small particle cargo many times its size, dock, transport the cargo to a remote location, and then release it. The self-propulsion and docking are reversible and activated by visible light. The docker can be steered either by a weak uniform magnetic field or by nanoscale tracks in a textured substrate. The light-activated motion and docking originate from osmotic/phoretic particle transport in a concentration gradient of fuel, hydrogen peroxide, induced by the photocatalytic activity of the hematite. The docking mechanism is versatile and can be applied to various materials and shapes. The hematite dockers are simple single-component particles and are synthesized in bulk quantities. This system opens up new possibilities for designing complex micrometer-size factories as well as new biomimetic systems.

THE NEGATIVE EFFECTIVE MAGNETIC PRESSURE IN STRATIFIED FORCED TURBULENCE

To understand the basic mechanism of the formation of magnetic flux concentrations, we determine by direct numerical simulations the turbulence contributions to the mean magnetic pressure in a strongly stratified isothermal layer with large plasma beta, where a weak uniform horizontal mean magnetic field is applied. The negative contribution of turbulence to the effective mean magnetic pressure is determined for strongly stratified forced turbulence over a range of values of magnetic Reynolds and Prandtl numbers. Small-scale dynamo action is shown to reduce the negative effect of turbulence on the effective mean magnetic pressure. However, the turbulence coefficients describing the negative effective magnetic pressure phenomenon are found to be converged for magnetic Reynolds numbers between 60 and 600, which is the largest value considered here. In all these models the turbulent intensity is arranged to be nearly independent of height, so the kinetic energy density decreases with height due to the decrease in density. In a second series of numerical experiments, the turbulent intensity increases with height such that the turbulent kinetic energy density is nearly independent of height. Turbulent magnetic diffusivity and turbulent pumping velocity are determined with the test-field method for both cases. The vertical profile of the turbulent magnetic diffusivity is found to agree with what is expected based on simple mixing length expressions. Turbulent pumping is shown to be down the gradient of turbulent magnetic diffusivity, but it is twice as large as expected. Corresponding numerical mean-field models are used to show that a large-scale instability can occur in both cases, provided the degree of scale separation is large enough and hence the turbulent magnetic diffusivity small enough.

Thermal diffusion in a binary fluid mixture flows due to a rotating disc of uniform high suction in presence of a weak axial magnetic field

The effect of a weak uniform axial magnetic field on separation of a binary mixture of incompressible viscous thermally and electrically conducting fluids flowing due to a rotating disc of uniform high suction is examined. Neglecting the induced electric field the equations governing the motion, temperature and concentration are solved in cylindrical polar coordinate by expanding the flow parameters as well as the temperature and the concentration in powers of suction parameter. The solution obtained for concentration distribution is plotted against the different axial distances from the disc for various values of non-dimensional parameters. It is found that the temperature gradient, axial magnetic field, Reynolds number, Schmidt number, Prandtl number and suction parameter effect the species separation significantly.

How the spheroidal deformation changes the spectra of fullerenes

The spheroidal geometry of a slightly elliptically deformed sphere was used as a possible approach to fullerenes. We are interested in the elliptically deformed fullerenes like big C240 molecule. The low-lying electronic levels are described by the Dirac equation in (2+1) dimensions. We show how a small deformation of spherical geometry evokes a shift of the electronic spectra compared to the sphere. The efiect of a weak uniform magnetic field on the electronic structure of slightly deformed fullerene molecules was also studied. We found that behavior of the electronic spectra if the magnetic field is pointed in the x direction difiers markedly from the case of the magnetic field pointed in the z direction, where z is chosen to be the symmetry axis of the fullerene. We briefly report also the C60-C240 fullerene onion.

The uniformly frustrated two-dimensional XY model in the limit of weak frustration

We consider the two-dimensional uniformly frustrated XY model in the limit of small frustration, which is equivalent to an XY system, for instance a Josephson junction array in a weak uniform magnetic field applied along a direction orthogonal to the lattice. We show that the uniform frustration (equivalently, the magnetic field) destabilizes the line of fixed points which characterize the critical behavior of the XY model for T ⩽ TKT, where TKT is the Kosterlitz–Thouless transition temperature: the system is paramagnetic at any temperature for sufficiently small frustration. We predict the critical behavior of the correlation length and of gauge-invariant magnetic susceptibilities as the frustration goes to zero. These predictions are fully confirmed by the numerical simulations.

Effect of symmetry on the electronic structure of spheroidal fullerenes in a weak uniform magnetic field

The effect of a weak uniform magnetic field on the electronic structure of slightly deformed fullerene molecules is studied within the continuum field-theory model. It is shown that fine structure of the electronic energy spectrum is very sensitive to the orientation of the magnetic field. In particular, we found that the magnetic field pointed in the $x$ direction does not influence the first electronic level whereas it causes a splitting of the second energy level. This behavior differs markedly from the case of the magnetic field pointed in the $z$ direction, where $z$ is chosen to be the symmetry axis of the fullerene.

Electronic structure of spheroidal fullerenes in a weak uniform magnetic field: A continuum field-theory model

The effect of a weak uniform magnetic field on the electronic structure of slightly deformed fullerene molecules is studied within the continuum field-theory model. It is shown how the existing fine structure of the electronic energy spectrum due to spheroidal deformation is modified in the presence of a magnetic field. Exact analytical solutions for zero-energy modes are found.

Unidirectional electrostatic waves in an inhomogeneous cold magnetized plasma in plane and cylindrical waveguides

Waves in a cold electron plasma with a nonuniform density profile in a weak uniform magnetic field are considered in the electrostatic limit. Plane and cylindrical waveguides filled with plasmas having different density profiles are investigated. The dispersion curves and eigenfunctions for the waves are obtained, and the asymmetry of the waves with respect to their propagation direction is discussed.

Calculation of effective impedance of polycrystals in weak magnetic fields

We present results for the effective surface impedance tensor (EIT) of polycrystals of metals in a weak uniform magnetic field H. The frequency region corresponds to the region in which the local impedance boundary conditions are applicable. We suppose that the resistivity tensor ρ i k ( H ) of the single crystal grains out of which the polycrystal is composed, is known up to the terms of O ( H 2 ) . For polycrystals of metals of arbitrary symmetry, the elements of the EIT can be calculated to the same order in H, even if the tensor ρ i k ( H ) is strongly anisotropic. As examples, we write down the EIT of polycrystals of (i) cubic metals, (ii) metals with ellipsoidal Fermi surfaces, and (iii) metals of tetragonal symmetry whose tensor ρ i k ( 0 ) is strongly anisotropic. Although polycrystals are metals that are isotropic on average, in the presence of a uniform magnetic field the structure of the EIT is not the same as the structure of the impedance tensor of an isotropic metal with a spherical Fermi surface. The results cannot be improved either by taking into account higher powers of H, or with respect to the anisotropy of the single crystal grains.

Initial magnetic susceptibility of ferrocolloids: The influence of chain aggregates

The behavior of a system of noninteracting chain aggregates of ferroparticles suspended in a liquid matrix and subjected to a weak uniform permanent magnetic field was studied based on the free energy functional of a monodisperse low-concentration magnetic colloid. The orientational response of a flexible chain to a weak external field showed that the model of rigid rods is applicable only for short chains (doublets and triplets) of large ferroparticles characterized by a strong magnetodipole interaction. The calculated values of the initial magnetic susceptibility of aggregated ferrofluid agree well with the computer simulation data.

Persistent current of three-dimensional spherical shells billiards

Using the semiclassical method, we analyze the persistent current of a single-ballistic three-dimensional (3D) spherical shell billiard in weak uniform magnetic field applied along the Z axis, on the basis of the independent electron model at finite temperature. Periodic orbits lying on great circular planes that share the center with spherical shells give rise to the persistent current component flowing along the latitude direction. Dependence of the current component on latitude angle, magnetic field, and Fermi wave number is demonstrated. We also compare the persistent current of a 3D spherical shell with the corresponding ones for a SO(2) rotational-symmetric chaotic 3D shell and for a completely chaotic 3D shell as well as with the one flowing through the two-dimensional ring.

Semiclassical electron motion and Novikov's conjecture

The structure of nonclosed trajectories of semiclassical electron motion in a crystal in a weak constant and uniform magnetic field of irrationality degree 3 is considered. It is proved that two cases can exist. In the first case the set of energy levels which contain nonclosed trajectories is a closed interval and any regular nonclosed trajectory lies in a finite-wide stripe and comes through it in one direction. In the other case, there is only one energy level containing nonclosed trajectories. Bibliography:5 titles.

Effect of modulation and magnetic field on the properties of two-dimensional Coulomb systems

A two-dimensional (2D) electron system in a modulation potential and a weak uniform perpendicular magnetic field is studied by a molecular-dynamics simulation method. The simulation results clearly demonstrate some interesting oscillations in the diffusion coefficient, which we interpret in terms of the orbital motion of the electrons on the modulated 2D system.

The Larmor nutation

The classical non-relativistic problem of the motion of a charged particle in an external central force field and a weak uniform magnetic field is revisited to show that the motion of the kinetic angular momentumL = r × p of the particle, in the so-called Larmor approximation, is not a simple precession but is actually a composite motion involving precession as well as a high frequency nutation. The precession-nutation motion ofL is discussed in the Larmor approximation when the Larmor-frame-orbit of the charged particle is an ellipse (or a circle) for the case of the two central forces namely the Coulomb and the Hooke-law-force, which are the only two central forces known to permit closed orbits.