External Uniform Magnetic Field Research Articles

Nonlinear wave propagation in large extra spatial dimensions and the blackbody thermal laws

Abstract Nonlinear wave propagation in large extra spatial dimensions (on and above d = 2) is investigated in the context of nonlinear electrodynamics theories that depend exclusively on the invariant F. In this vein, we consider propagating waves under the influence of external uniform electric and magnetic fields. Features related to the blackbody radiation in the presence of a background constant electric field such as the generalization of the spectral energy density distribution and the Stefan-Boltzmann law are obtained. Interestingly enough, anisotropic contributions to the frequency spectrum appear in connection to the nonlinearity of the electromagnetic field. In addition, the long wavelength regime and Wien’s displacement law in this situation are studied. The corresponding thermodynamics quantities at thermal equilibrium, such as energy, pressure, entropy, and heat capacity densities are contemplated as well.

Liquid Springs for High‐Speed Contamination‐Free Manipulation of Droplets and Solid Particles

AbstractAccurate and flexible control of droplets is essential in many industrial applications, such as water harvesting, chemical assays, and biological detection. Magnetic force‐based methods have been broadly exploited to fulfill the goals due to the advantage of non‐contact, easy control, and long‐range navigation. Nevertheless, it still suffers from some challenges, such as sample fouling, and the paradox between the droplet efficient motion and the large volume. Here a ferrofluid‐based liquid spring to achieve contamination‐free and fast droplet transportation on non‐wetting solid surfaces is proposed. The liquid spring is based on the actuation of a ferrofluid droplet in an external uniform magnetic field. The actuation enables the liquid spring to propel tiny objects, including the non‐magnetic miscible droplets and water‐repellent solid particles, with adjustable motion velocity. Furthermore, the magnetic force, applied on the ferrofluid via an additional permanent magnet, makes it possible to navigate the liquid spring in a programmable way. With the aid of the liquid spring, the single or multiple droplets/solid particles advancing, on‐demand droplets coalescence, and out‐of‐plane droplet motion are achievable.

Non-equilibrium molecular dynamics study of heat transfer parameters in two-dimensional Yukawa systems under uniform magnetic field

The present study explores the effect of a magnetic field on the thermal conductivity of two-dimensional (2D) Yukawa systems in a wide range of system parameters using the non-equilibrium molecular dynamic method (NEMD). We consider an external magnetic field with Ω=ωc/ωp≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega =\\omega _c/\\omega _p\\le 1$$\\end{document} (with Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega$$\\end{document} being the ratio of the cyclotron frequency to plasma frequency) and the coupling parameter values in the range 1≤Γ≤100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\le \\Gamma \\le 100$$\\end{document} (with Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma$$\\end{document} being the ratio of the Coulomb interaction energy at mean inter-particle distance to the thermal energy of particles). The results show that an external uniform magnetic field results in the reduction of the thermal conductivity at the considered values of the coupling parameter Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma$$\\end{document}. Additionally, we found that the effect of the magnetic field on thermal conduction is weaker at larger values of the system coupling parameter. To ensure that calculated results for the thermal conductivity are accurate and reliable, we performed a detailed investigation of the convergence of the results with respect to simulation parameters in NEMD with a strong external magnetic field. We believe that the presented results will serve as useful benchmark data for the theoretical models of (2D) Yukawa systems.

Hydrodynamic mechanism for dynamical structure formation of a system of rotating particles

Based on the hydrodynamic mechanism, which takes into account the interaction of all particles, a numerical simulation of the formation of a dynamical structure in a viscous fluid was carried out. This structure is a result of the collective dynamics of rotating particles in the fluid. It is supposed that the particles have a magnetic moment and are driven into rotation by an external variable uniform magnetic field. The results of numerical modeling of collective dynamics are presented for three initial structures that can be formed by interacting dipole particles in the absence of an external magnetic field. Such equilibrium structures are a straight chain, a closed chain, and a periodic structure in the form of a flat system of particle chains. The rotation of particles sets the surrounding fluid in motion, whose flow creates hydrodynamic forces and moments that move the particles. The collective dynamics of a system of rotating particles leads to the formation of a new dynamical structure from the original one, and this new structure has its own characteristic features for each case considered. A qualitative comparison of the results of the dynamics for a particles’ system set in motion due to the action of an external moment or an external force is carried out. The proposed hydrodynamic mechanism for the formation of a dynamical structure as a result of the collective dynamics of a rotating particles’ system can be used to control structure formation in a liquid-particle system.

Particles with magnetic dipole moment orbiting magnetized Schwarzschild black holes: Applications to orbits of hot-spots around Sgr A*

We study the circular motion of particles with magnetic dipole moment around Schwarzschild black holes immersed in external asymptotically uniform and dipolar magnetic field configurations and calculate the orbital velocity of the particles. We assume that the flares observed around supermassive black hole Sagittarius (Sgr) A* detected by the GRAVITY ESO collaboration (on May 27, July 22, and July 28, 2018) are magnetized compact objects, in particular, neutron stars (NSs) and white dwarfs (WDs). Also, we apply orbital and luminosity data from (three) flares to explore the possible role of magnetic interaction on hot spots’ dynamics. First, we found the mass range of SgrA* using the orbital data in the absence of external magnetic fields as M=(3−6.3)M⊙. It is also found that, for magnetized particles that can be in the hot spot’s orbits, the magnetic coupling parameter β has to take values less than 0.13 and 0.25 in the cases of external dipolar and uniform magnetic fields, respectively. The critical values for the surface magnetic fields, mass, and radius of magnetized NSs and WDs are found to be candidates for the hot-spot objects. Finally, we found upper and lower limits for the surface magnetic field, radius, and rotating period of the NSs and WDs, using the luminosity data of the hot spots.

Massive Dirac particles based on gapped graphene with Rosen–Morse potential in a uniform magnetic field

Abstract In this paper, we explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and the external uniform magnetic field. In order to describe the corresponding structure, we consider the propagation of electrons in graphene as relativistic fermion quasi-particles, and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation. Next, to solve and analyze the Dirac equation, we obtain the eigenvalues and eigenvectors using the Legendre differential equation. After that, we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal n and spin-orbit k. Then, the values of the energy spectrum for the ground state and the first excited state are calculated, and the wave functions and the corresponding probabilities are plotted in terms of coordinates r. In what follows, we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors K x and K y . Finally, the energy bands are plotted in terms of the wave vectors K x and K y with and without the magnetic term.

Two-dimensional open quantum system in dissipative bosonic heat bath, external magnetic field, and two time-dependent electric fields.

Non-Markovian dynamics of a charged particle in a two-dimensional harmonic oscillator linearly coupled to a neutral bosonic heat bath is investigated in an external uniform magnetic field and two perpendicular time-dependent electric fields. The analytical expressions for the time-dependent and asymptotic angular momentum are derived for the Markovian and non-Markovian dynamics. The dependence of the angular momentum on the frequency of the electric field, cyclotron frequency, collective frequency, and anisotropy of the heat bath is studied. The angular momentum (or magnetization) of a charged particle can be ruled by varying the frequency of the electric field.

Optical assembly of multi-particle arrays by opto-hydrodynamic binding of microparticles close to a one-dimensional chain of magnetic microparticles.

Two-dimensional materials possess a large number of interesting and important properties. Various methods have been developed to assemble two-dimensional aggregates. Assembly of colloidal particles can be achieved with laser-heating-induced thermal convective flow. In this paper, an opto-hydrodynamic binding method is proposed to assemble colloidal particles dispersed in a solution into multilayer structures. First, we use polystyrene (PS) microspheres to study the feasibility and characteristics of the assembly method. PS microspheres and monodispersed magnetic silica microspheres (SLEs) are dispersed in a solution to form a binary mixture system. Under the action of an external uniform magnetic field, SLEs in the solution form chains. An SLE chain is heated by a laser beam. Due to the photothermal effect, the SLE chain is heated to produce a thermal gradient, resulting in thermal convection. The thermal convection drives the PS beads to move toward the heated SLE chain and finally stably assemble into multilayer aggregates on both sides of the SLE chain. The laser power affects the speed and result of the assembly. When the laser power is constant, the degree of constraint of the PS microbeads in different layers is also different. At the same time, this method can also assemble the biological cells, and the spacing of different layers of cells can be changed by changing the electrolyte concentration of the solution. Our work provides an approach to assembling colloidal particles and cells, which has a potential application in the analysis of the collective dynamics of microparticles and microbes.

Three-dimensional nonlinear ion acoustic waves near critical density in magnetized negative ion plasmas

The nonlinear dynamics of three-dimensional ion acoustic waves near critical density in plasmas consisting of electrons, positive and negative ions in the presence of a uniform external magnetic field are investigated. In the weak nonlinear and dispersive limit, the nonlinear wave is shown to be governed by a Gardner–Zakharov–Kuznetsov (GZK) equation, which is also shown to be integrable in the sense of Painlevé only on the traveling wave frame. The invariant Painlevé analysis provides the analytical solutions in the closed form of solitary, cnoidal, double layer and bipolar structures. The Lyapunov stability analysis shows that the stationary solitary structure is always unstable due to the three-dimensional effect. Finally, the stability of one-dimensional solitary wave has been checked in the transverse direction and the regions of stability (and instability) have been separated in terms of parameters. The results are in qualitative agreement with the observations in magnetized plasmas with negative ions.

Surface wave propagation along a narrow transition layer in a slab Voigt geometry

The dispersion properties of electromagnetic surface waves, which propagate along a slab narrow transition layer separating two magnetoactive plasma uniform half spaces, are studied. Voigt geometry is considered, in which the waves propagate perpendicularly to an external uniform static magnetic field, which in turn is parallel to the interfaces between the plasmas and the transition layer. Electromagnetic power absorption within local resonances inside the transition layer is out of scope of the study. The influence of the plasma particle density profile smoothness on the surface wave dispersion properties is emphasized.

Control of a magnetizable body in a magnetic fluid droplet by the tilt of an external uniform magnetic field

We examine how the position of a magnetizable body in a magnetic fluid droplet resting on a horizontal plane can be controlled by the tilt of an external uniform magnetic field. The paper presents experiments that demonstrate the levitation of the body in a drop and uses an analytical model in which the results are obtained numerically. The impact of problem parameters, such as intensity, direction of the magnetic field, and drop volume, on the levitation height of the body is studied both theoretically and experimentally. It is discovered that there is a set of parameter values required to levitate the body. Theoretical results are in qualitative agreement with the experimentally observed levitation heights.

Use of machine learning in predicting heat transfer and entropy generation in a flat plate solar collector with twisted tape turbulator and ferrofluid under the influence of an external uniform magnetic field: A numerical study

The flat-plate solar collector is the most common and widely used model of solar collectors. This model of solar collectors is more popular than other solar collectors due to its easy installation and lower cost. It is possible to further reduce the cost and size of these systems by improving their performance. For this purpose, simultaneous application of external uniform magnetic field (MF), water-Fe3O4 ferrofluid, and twisted tape turbulator along with changing the cross-section of the serpentine absorber tube of a collector is proposed in the present research. The outlet temperature of working fluid, pressure drop of working fluid, the rate of thermal energy transferred to the flowing fluid in the collector along with the entropy production rate in the system due to fluid friction and heat transfer were considered as the performance parameters of the system. The effect of cross-section of absorber tube (circular, square, triangular), Reynolds number (Re = 500, 1000, 1500 and 2000), pitch distance of turbulator (δ = 150 mm, 200 mm and 250 mm), ferrofluid volume fraction (σ = 0, 1 %, 2 % and 4 %) and magnetic field intensity (0, 600, 900 and 1200 Gauss) on these parameters was investigated numerically using the finite volume method. In the investigations conducted in the absence of MF, collectors equipped with circular and triangular absorber tubes showed the best and worst thermal performance, respectively, while the lowest and highest total entropy production rate was associated with collectors equipped with circular and rectangular tubes, respectively. Moreover, the escalation in σ from 0 % to 4 % and under the MF effect showed an increase of 0.14 %, 8.62 %, 0.45 %, and 4.55 % in the outlet temperature, pressure drop, useful heat, and thermal entropy generation rate, respectively. While the frictional entropy generation diminished by 8.73 %. In addition, the intensification of MF intensity from 0 G to 1200 G led to enhance the outlet temperature, useful heat, and pressure drop, by almost 0.0014 %, 3.96 %, and 0.013 %, respectively at three different σ values. While total entropy generation rate reduces by 0.195 % as MF intensity increases from 0 G to 1200G. Meanwhile, the results of neural network modeling were presented as two second-order polynomial functions to predict the total entropy generation rate and useful heat under the MF effects.

Magnetohydrodynamic thermal convection in constraint-based recto-triangular cavities with CuO-water nanofluid and differential bottom-top heating

The current research explores the thermal convection of magnetohydrodynamic flow in modified and constraint-based recto-triangular thermal systems (upper part rectangular and lower part triangular) filled with copper-oxide water nanofluid. The external uniform magnetic field is applied horizontally, while the magnetic field angle γ is varied systematically. The volume/area of thermal system cavities is maintained the same while their bottom triangular portions are adjusted considering various vertex angles (Θ) of 90–270°. The cooling and heating arrangements are provided for the same lengths using the top wall and the central portion of the bottom wall, respectively. The finite element method is used to discretize and solve the dimensionless governing transport equations. The thermal and flow analyses are conducted on the backdrop of constraint-based thermal systems for varying pertinent parameters like the Rayleigh number (Ra = 103–105), Hartmann number (Ha = 0–70), magnetic field angle (γ = 0–90°) and vertex angle (Θ = 90–270°). It is revealed that the flow structure becomes more complex and asymmetric in nature at high Ra and Ha. Furthermore, the average Nu is an increasing function of Ra and Θ, whereas it is a decreasing function of Ha. The entropy plots are also generated to study the entropy generation due to magnetohydrodynamic, viscous dissipation, and thermal effects that together constitute the total entropy of the system. The constraint-based system analysis could be very helpful for the design and identification of the most efficient system for the utilized same working fluid (volume).

Quantum Hall and Shubnikov-de Haas Effects in Graphene within Non-Markovian Langevin Approach

The theory of open quantum systems is applied to study galvano-, thermo-magnetic, and magnetization phenomena in axial symmetric two-dimensional systems. Charge carriers are considered as quantum particles interacting with the environment through a one-body (mean-field) mechanism. The dynamics of charge carriers is affected by the average collision time that takes effectively into account two-body effects. The functional dependencies of the average collision time on the external uniform magnetic field, concentration and temperature are phenomenologically treated. Analytical expressions are obtained for the tensors of electric and thermal conductivity and/or resistivity. The developed theory is applied to describe the Shubnikov-de Haas oscillations and quantum Hall effect in graphene and GaAs/AlxGa1−xAs heterostructure. The dependencies of magnetization and thermal conductivity on the magnetic field are also predicted.

Magnetic field dependent thermal conductivity investigation of water based Fe3O4/CNT and Fe3O4/graphene magnetic hybrid nanofluids using a Helmholtz coil system setup

Magnetic hybrid nanofluids are making a name of themselves in mainstream application areas such as heat transfer, solar systems, acoustic applications, etc. These nanofluids are highly favorable as their ability to advance the properties of their constituent particles such as their thermophysical properties. This study aims to investigate the magnetic field dependent thermal conductivity of Fe3O4/CNT – water and Fe3O4/Graphene – water magnetic hybrid nanofluids. The thermal conductivity investigations are carried out with the 3ω method under a uniform magnetic field generated by a 3D Helmholtz coil system. Fe3O4/CNT – water and Fe3O4/Graphene – water magnetic hybrid nanofluids were purchased commercially as 20 wt% colloids. Then, the samples with 1, 2, 3, 4, and 5 wt% were prepared by diluting them with DI water. Thermal conductivity measurements were carried out for the samples under the external uniform magnetic field in the range of 0–250 G in both parallel and perpendicular directions to the temperature gradient generated by the thermal conductivity measurement probe. The results pointed out that the thermal conductivity of the samples increases as the magnetic field and particle concentration increase for both magnetic hybrid nanofluids. Additionally, it is obtained that the thermal conductivity enhancement of Fe3O4/Graphene – water is up to 3 times higher than Fe3O4/CNT – water samples. Moreover, the maximum thermal conductivity enhancement was observed as ∼12 % and ∼9 % for Fe3O4/CNT – water, and ∼51 % and ∼21 % Fe3O4/Graphene – water under external magnetic field application with parallel and perpendicular direction, respectively.

Magnetic field effect on the sedimentation process of two non-magnetic particles inside a ferrofluid

The behaviours of non-magnetic particles inside a ferrofluid have a significant effect on the performance of ferrofluid-based biosensors, such as antibody detection. The present work numerically investigates the sedimentation process of two non-magnetic spherical particles inside a ferrofluid under a uniform external magnetic field. A three-dimensional lattice Boltzmann model coupled with the bounce-back schemes is employed to simulate the corresponding flows. The present work particularly focuses on the effects of the magnetic field orientation and intensity on the sedimentation behaviours. The results show that the two particles are accelerated in a vertical magnetic field due to the reduction of drag, but decelerated in the magnetic field with the orientation of 30∘≤θ≤90∘. The inter-particle collision is encouraged by the attractive dipole force for 0∘≤θ≤45∘, resulting in an earlier occurrence of the ‘kissing’ stage, but is suppressed by the repulsive dipole force for 60∘≤θ≤90∘, leading to a postponement or even the absence of the ‘kissing’ stage. Meanwhile, it is found that the time duration of the ‘drafting’ stage decreases with the increasing of the magnetic field intensity. When the magnetic field intensity is beyond a critical value, the two particles self-assemble into a ‘dumbbell-like’ structure and the ‘tumbling’ stage will disappear during the sedimentation process. The present work demonstrates that the sedimentation behaviour of non-magnetic particles immersed in a ferrofluid can be controlled by varying the orientation and intensity of the external magnetic field, which can provide a valuable technical guidance for the industrial applications of ferrofluids.

Landau levels for a Weyl pair in a monolayer medium and thermal quantities

In this paper, we consider a Weyl pair under the effect of an external uniform magnetic field in a monolayer medium without considering any charge-charge interaction between the particles. Choosing the interaction of the particles with the magnetic field in the symmetric gauge we seek for an analytical solution of the corresponding form of a one-time fully-covariant two-body Dirac equation derived from quantum electrodynamics via the action principle. As it is usual with two-body problems, we separate the relative motion and center of mass motion coordinates. Assuming the center of mass is at rest, we derive a matrix equation in terms of the relative motion coordinates without considering any group theoretical method. This equation gives a wave equation in exactly soluble form and accordingly we obtain the spinor components and complete energy eigen-states (in closed form) for such a spinless composite structure. Our results not only give exact Landau levels for such a Weyl pair in a monolayer medium but also show the considered system behaves as a two-dimensional harmonic oscillator. Furthermore, our findings give exactly the excited states of a Weyl particle under the effect of uniform external magnetic field in a monolayer graphene sheet and there is no imprint to distinguish these modes from each other. This means that the performed experiments based on Landau levels for a monolayer graphene sheet may actually involve many-body effects. Our results provide a suitable basis to analyze the associated thermal quantities and accordingly we discuss the thermal properties by determining free energy, total energy, entropy and specific heat for the composite system in question.

Investigation of Ferrofluid Sessile Droplet Tensile Deformation in a Uniform Magnetic Field

A significant growth of research on digital microfluidics has been achieved over the past several decades, and the field is still attracting increasing attention for fulfilling relevant mechanisms and potential applications. Numerous studies have been devoted to actively manipulating droplets in a variety of fundamental and applicational scenarios. In this work, the deformation of ferromagnetic fluid droplets is studied under an external uniform magnetic field. The droplets are precisely dispersed on the bottom surface of a container assembled with polymer methacrylate (PMMA) plates. Mineral oil is applied instead of air as the surrounding medium for easy stretching and preventing water solvent evaporation in ferrofluid. The design and processing of the container are firstly carried out to observe the shape and characterize the wettability of the droplets in the immiscible mineral oil medium. Furthermore, the droplets’ deformation and the working mechanism are given under the action of the horizontal uniform magnetic field. At different magnetic field intensities, the droplet is stretched in the horizontal direction parallel to the applied field. Due to volume conservation, the dimension in the height reduces correspondingly. With the coupling effect of magnetic force, viscous force and interfacial tension, the contact angle first increases with the magnetic field and then basically remains unchanged upon magnetization saturation. Consistent with the experimental results, the numerical method clearly reveals the field coupling mechanism and the nonlinear deformation of the sessile droplet.

A Dirac-material-inspired non-linear electrodynamic model

We propose and study the properties of a non-linear electrodynamics (ED) that emerges inspired on the physics of Dirac materials. This new electrodynamic model is an extension of the one-loop corrected non-linear effective Lagrangian computed in the work of Keser et al (2022 Phys. Rev. Lett. 128 066402). In the particular regime of a strong magnetic and a weak electric field, it reduces to the photonic non-linear model worked out by Keser et al (2022 Phys. Rev. Lett. 128 066402). We pursue our investigation of the proposed model by analyzing properties of the permittivity and permeability tensors, the energy–momentum tensor and wave propagation effects in presence of a uniform magnetic background. It is shown that the ED here presented exhibits the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy, considering still the presence of a uniform external magnetic field. Our analysis is carried out within the framework of the gauge-invariant but path-dependent variables formalism. The calculation reveals a screened Coulomb-like potential with an effective electric charge that runs with the external magnetic field but, as expected for Dirac-type materials, the screening disappears whenever the external magnetic field is switched off.

Probing miniband structure and Hofstadter butterfly in gated graphene superlattices via magnetotransport

The presence of periodic modulation in graphene leads to a reconstruction of the band structure and formation of minibands. In an external uniform magnetic field, a fractal energy spectrum called Hofstadter butterfly is formed. Particularly interesting in this regard are superlattices with tunable modulation strength, such as electrostatically induced ones in graphene. We perform quantum transport modeling in gate-induced square two-dimensional superlattice in graphene and investigate the relation to the details of the band structure. At low magnetic field the dynamics of carriers reflects the semi-classical orbits which depend on the mini band structure. We theoretically model transverse magnetic focusing, a ballistic transport technique by means of which we investigate the minibands, their extent and carrier type. We find a good agreement between the focusing spectra and the mini band structures obtained from the continuum model, proving usefulness of this technique. At high magnetic field the calculated four-probe resistance fit the Hofstadter butterfly spectrum obtained for our superlattice. Our quantum transport modeling provides an insight into the mini band structures, and can be applied to other superlattice geometries.