Magnetic pseudodifferential operators represented as generalized Hofstadter-like matrices

Context. In the context of structure formation and galaxy evolution, the contribution of magnetic fields is not well understood. Feedback processes originating from active galactic nucleus (AGN) activity and star formation can be actively influenced by magnetic fields, depending on their strength and morphology. One of the best tracers of magnetic fields is polarised radio emission. Tracing this emission over a broad redshift range therefore allows an investigation of these fields and their evolution. Aims. We aim to study the nature of the faint, polarised radio source population whose source composition and redshift dependence contain information about the strength, morphology, and evolution of magnetic fields over cosmic timescales. Methods. We use a 15-pointing radio continuum L-band mosaic of the Lockman Hole, observed in full polarisation, generated from archival data of the Westerbork Synthesis Radio Telescope. The data were analysed using the rotation measure synthesis technique. We achieved a noise of 7 μJy beam−1 in polarised intensity, with a resolution of 15″. Using infrared and optical images and source catalogues, we were able to cross-identify and determine redshifts for one-third of our detected polarised sources. Results. We detected 150 polarised sources, most of which are weakly polarised with a mean fractional polarisation of 5.4%. No source was found with a fractional polarisation higher than 21%. With a total area of 6.5 deg2 and a detection threshold of 6.25σ, we find 23 polarised sources per deg2. Based on our multi-wavelength analysis, we find that our sample consists of AGN only. We find a discrepancy between archival number counts and those present in our data, which we attribute to sample variance (i.e. large-scale structures). Considering the absolute radio luminosity, we find a general trend of increased probability of detecting weak sources at low redshift and strong sources at high redshift. We attribute this trend to a selection bias. Further, we find an anti-correlation between fractional polarisation and redshift for our strong-source sample at z ≥ 0.6. Conclusions. A decrease in the fractional polarisation of strong sources with increasing redshift cannot be explained by a constant magnetic field and electron density over cosmic scales; however, the changing properties of cluster environments over cosmic time may play an important role. Disentangling these two effects requires deeper and wider polarisation observations as well as better models of the morphology and strength of cosmic magnetic fields.

The physicochemical properties of NaCl aqueous solutions in a wide range of concentrations were studied. We determined that constant magnetic fields with an induction of up to 7 T had a significant effect on the physicochemical properties of these solutions. First, we detected a decrease in pH that was dependent on the magnetic field strength both in water and in NaCl solutions. This effect was not associated with the presence of sodium cations or chlorine anions in water. Secondly, with an increase in magnetic field induction the redox potential of aqueous solutions also increased. Magnetic fields did not cause any changes in the concentration of dissolved molecular oxygen in deionized water. In this case, in aqueous solutions of NaCl under the action of a magnetic field, a concentration-dependent tendency to a decrease in the concentration of dissolved molecular oxygen is observed. Third, it was shown that under the action of a magnetic field on a NaCl solution, the rate of hydrogen peroxide generation increased with increasing NaCl concentration. Fourth, the essential role of the primary state of aqueous solutions in relation to the gas composition and gas equilibrium under magnetic influence was established. The work also evaluated the contribution of flow-mixing during sample preparation on the physicochemical properties of the solutions.

자성유체는 고액혼상유체로 뉴턴유체와 달리 자기력에 반응하는 유체이다. 본 연구에서는 금속과 유체의 특성을 겸비한 자성유체의 열전달 특성을 밀도 있게 연구함을 목적으로, 그 대상을 이중원관으로 하여 열대류현상을 고찰하기 위해 내부원관을 가열하고, 외부원관을 냉각하면서, 또한 외부에서 인가자장의 세기와 방향에 따라 자연대류 현상의 변화 및 열전달 특성을 수치해석적으로 연구하여, 실험결과와 비교 검토하였다. 자성유체의 자연대류현상은 인가자장에 따라 제어할 수 있었고, 평균 뉴셀트수를 구한 결과로서 자장을 가하지 않았을 경우와 비교해 보면 열전달은 자장을 중력방향으로 가하거나 중력과 반대방향으로 그세기를 -14 mT이상 가했을 때 증가하였고, 중력과 반대방향으로 감했을 때 감소하였다. 특히 자장의 세기가 -14 mT가 되면 열전달은 최소가 되었다. Compared with Newtonial fluids, magnetic fluids have effects on magnetic force. In this study, the purpose is to research the heat transfer characteristic of magnetic fluids which have metalic and fluid characteristics as the external pipe is being cooled and internal pipe is heated. This study found the experimental results from the study of the variety of natural convection for magnetic fluids and the characteristics of the heat transfer by using numerical analysis according to the strength and direction of the magnetic fields from being imposed from the outside. Natural convection of magnetic fluids was controlled by the impressed magnetic fields, and the result of mean nusselt number was calculated. If the impressed magnetic field is in the direction of gravity or the strength of impressed magnetic field is more than -14 mT in the opposite direction, the heat transfer is more than that without the impressed magnetic field. If the strength of impressed magnetic field is less than -14 mT in the opposite direction, it is smaller than that without the impressed magnetic field. Especially, when the strength of the magnetic field is -14 mT, the heat transfer was at the minimum.

Understanding how a magnetic field affects the interaction of magnetic nanoparticles (MNPs) with cells is fundamental to any potential downstream applications of MNPs as gene and drug delivery vehicles. Here, we present a quantitative analysis of how a pulsed magnetic field influences the manner in which MNPs interact with and penetrate across a cell monolayer. Relative to a constant magnetic field, the rate of MNP uptake and transport across cell monolayers was enhanced by a pulsed magnetic field. MNP transport across cells was significantly inhibited at low temperature under both constant and pulsed magnetic field conditions, consistent with an active mechanism (i.e., endocytosis) mediating MNP transport. Microscopic observations and biochemical analysis indicated that, in a constant magnetic field, transport of MNPs across the cells was inhibited due to the formation of large (>2 μm) magnetically induced MNP aggregates, which exceeded the size of endocytic vesicles. Thus, a pulsed magnetic field enhances the cellular uptake and transport of MNPs across cell barriers relative to a constant magnetic field by promoting accumulation while minimizing magnetically induced MNP aggregation at the cell surface.

A particle-in-cell (PIC) simulation study of the charging processes of spherical dust grains in a magnetized plasma environment is presented. Different magnetic field strengths with corresponding electron/ion gyration radii of smaller, the same or larger size than the grain radius and the plasma Debye length are examined. The magnetized plasma is created by overlapping the simulation box with a homogeneous, constant magnetic field. The charging currents are significantly reduced in the presence of a magnetic field, resulting in a more negative grain floating potential. Indeed, the most probable electron gyration radius is always smaller than that of ions in a Maxwellian plasma: however, it is demonstrated that the situation of simultaneous magnetized electron but an unmagnetized ion charging current never exists. The simulation results do not fit with a modified orbital motion limited (OML) theory approach for this situation, since the ion current is significantly reduced due to the increase of the gyration radius in the potential field of the dust grain. For very small gyration radii, the simulation results are in good agreement with a modified OML approach for both magnetized electron and ion charging currents.

In magnetic particle imaging (MPI) and magnetic particle spectroscopy (MPS) the relaxation time of the magnetization in response to externally applied magnetic fields is determined by the Brownian and Néel relaxation mechanisms. Here the authors investigate the dependence of the relaxation times on the magnetic field strength and the implications for MPI and MPS. The Fokker-Planck equation with Brownian relaxation and the Fokker-Planck equation with Néel relaxation are solved numerically for a time-varying externally applied magnetic field, including a step-function, a sinusoidally varying, and a linearly ramped magnetic field. For magnetic fields that are applied as a step function, an eigenvalue approach is used to directly calculate both the Brownian and Néel relaxation times for a range of magnetic field strengths. For Néel relaxation, the eigenvalue calculations are compared to Brown's high-barrier approximation formula. The relaxation times due to the Brownian or Néel mechanisms depend on the magnitude of the applied magnetic field. In particular, the Néel relaxation time is sensitive to the magnetic field strength, and varies by many orders of magnitude for nanoparticle properties and magnetic field strengths relevant for MPI and MPS. Therefore, the well-known zero-field relaxation times underestimate the actual relaxation times and, in particular, can underestimate the Néel relaxation time by many orders of magnitude. When only Néel relaxation is present--if the particles are embedded in a solid for instance--the authors found that there can be a strong magnetization response to a sinusoidal driving field, even if the period is much less than the zero-field relaxation time. For a ferrofluid in which both Brownian and Néel relaxation are present, only one relaxation mechanism may dominate depending on the magnetic field strength, the driving frequency (or ramp time), and the phase of the magnetization relative to the applied magnetic field. A simple treatment of Néel relaxation using the common zero-field relaxation time overestimates the relaxation time of the magnetization in situations relevant for MPI and MPS. For sinusoidally driven (or ramped) systems, whether or not a particular relaxation mechanism dominates or is even relevant depends on the magnetic field strength, the frequency (or ramp time), and the phase of the magnetization relative to the applied magnetic field.

The main properties of metallic magnetic multilayers (superlattice) of Fe/Cr type such as the type of magnetic ordering, dependence of electrical resistance on the magnetic field are defined by itinerant electrons. However, sufficiently complete theory of electron states in these multilayered metallic systems has not been developed up to now. Therefore, there are considerable difficulties, in particular, in the rigorous treatment of the mechanisms of the giant magnetoresistance and the role of intermediate nonmagnetic layers in forming the antiparallel and noncollinear magnetic structures [1]. These difficulties are mainly due to the deficit of experimental data on electron parameters. In the present paper we notice new possibilities which can be of interest in studying the propagation of elastic waves in metallic multilayers. At low temperatures the ultrasonic absorption and dependence of acoustic parameters on the magnetic field are defined by itinerant electrons. We have developed quasi-classical kinetic theory of electron magnetoacoustic effects in multilayers in the frameworks of the model of imperfect boundaries proposed in [2]. The results obtained allow us to describe the dependencies of effective elastic moduli on the magnetization and magnetic field strength. These dependencies are defined both by the parameters of electron structure and the defects of interfaces. We can estimate what of these factors is dominating.

Magnetic resonance techniques were developed in the mid-1940s to analyze the structures of chemical compounds. In the last 10 years, however, the same principles have been evolved, along with advances in magnet, computer, and display technology into one of the most exciting imaging methods available in the medical field today. Magnetic resonance imaging utilizes the property that certain nuclei when placed in a magnetic field can be stimulated into a resonance condition by external radio-frequency radiation. In recovering from this disturbance, the nuclei in turn emit rf signals (whose frequencies depend on the magnetic field strength in which the nuclei are located). To image the human body, the patient is placed in a large solenoidal magnet (field strength typically 0.5-1.5 T), and the magnetic field Is coded in various ways by the application of gradient fields, causing the protons within the volume to resonate with a range of frequencies. Relating these frequencies to positions within this volume is performed by a Fourier analysis of the signal. Reconstructed images are displayed to the user as slices of the 3-D volume being imaged.

We present a theoretical study of two- and three-dimensional massless Dirac one-component plasmas embedded in a constant uniform magnetic field. We determine the wavefunctions and Landau energy levels of a massless Dirac fermion in a constant magnetic field. On this basis we consider magnetism of Fermi fluids of massless charged particles. We show that such a three-dimensional Dirac plasma consisting of fermions with the same helicity has its own magnetic moment. We also consider the limit of strong magnetic fields and investigate the De Haas–van Alphen effect. We derive the Kubo formula for the electrical conductivity tensor of massless Dirac plasmas and consider the Shubnikov–de Haas effect. In addition, we propose a model of the static conductivity tensor and employ the matrix version of the classical method of moments to derive a Drude-like formula for the dynamic conductivity tensor for massless Dirac plasmas. We find that the electrical conductivity tensor for Dirac fermions with the right helicity is not isotropic in the plane perpendicular to the magnetic field.

A constant magnetic field can significantly improve the quality and speed of ablation by nanosecond laser pulses. These improvements are usually attributed to the confinement of laser-produced plasma by the magnetic field and specific propagation effects in the magnetized plasma. Here we report a strong influence of constant axial magnetic field on the ablation of silicon by 20-ns laser pulses at wavelength 355 nm, which results in an increase of ablation depth by a factor of 1.3 to 69 depending on laser parameters and magnitude of the magnetic field. The traditional plasma effects do not explain this result, and magneto-absorption of silicon is proposed as one of the major mechanisms of the significant enhancement of ablation.

The study of the facts and circumstances of the unaccounted use of energy resources by consumers, primarily electric energy, natural gas, hot and cold water in the practice of conducting electrical and heat engineering types of forensic examinations, is one of the most common. The initial data in forensic research in this area, namely the data of acts on the violation of the consumption of these energy resources, including information on fixing the impact on the metering device of a constant magnetic field by magnetic field effect indicator (MFEI), which in the cases under study is usually denied by the consumer as his intentional actions to create such a field. The expert task of forensic examinations in this area requires an unambiguous definition of the operation of a MFEI from a constant magnetic field with certain power characteristics, with the exclusion of other factors of influence. The most common modern designs of magnetic field impact indicators in use, which are installed by energy sales enterprises as fixing technical means of interfering with the operation of consumer metering devices when using energy resources as a result of exposure to an external constant magnetic field, are considered. The triggering mechanism of MFEI of different designs is analyzed. According to the constructive construction and principle of operation, the indicators of the influence of the magnetic field are divided into separate classification groups. Signs of atypical triggering of the MFEI are considered. Cases of activation of indicators of the impact of the magnetic field are determined, requiring a comprehensive study using research methods of various forensic specialties to establish the fact of interference in the operation of metering devices in order to unaccounted for the consumption of energy resources. Recommendations are given on the application of the method of modeling a constant magnetic field with the reproduction of the conditions for the operation of the investigated MFEI to establish the fact of interference in the operation of the meter by exposing it to an external constant magnetic field in order to unaccounted for the consumption of energy resources. The necessity of performing a check of the operable state of the MFEI in expert experience in the study of the fact of the existence of the influence of a constant magnetic field on the metering device for energy consumption is substantiated.

In previous papers, a generalization of the Weyl calculus was introduced in connection with the quantization of a particle moving in ℝ^n under the influence of a variable magnetic field B . It incorporates phase factors defined by B and reproduces the usual Weyl calculus for B = 0 . In the present article we develop the classical pseum dodifferential theory of this formalism for the standard symbol classes S^m_{ρ,δ} . Among others, we obtain properties and asymptotic developments for the magnetic symbol multiplication, existence of parametrices, boundedness and positivity results, properties of the magnetic Sobolev spaces. In the case when the vector potential A has all the derivatives of order ≥ 1 bounded, we show that the resolvent and the fractional powers of an elliptic magnetic pseudodifferential operator are also pseudodifferential. As an application, we get a limiting absorption principle and detailed spectral results for self-adjoint operators of the form H = h(Q, Π^A) , where h is an elliptic symbol, Q denotes multiplication with the variables Π^A = D − A , D is the operator of derivation and A is the vector potential corresponding to a short-range magnetic field.

A constant homogeneous magnetic field is applied to a composite system made of two scalar particles with opposite charges. Motion is described by a pair of coupled Klein-Gordon equations that are written in closed form with help of a suitable representation. The relativistic symmetry associated with the magnetic field is carefully respected. Considering eigenstates of the pseudo momentum four-vector, we separate out collective variables and obtain a 3- dimensional reduced equation, posing a nonconventional eigenvalue problem. The velocity of the system as a whole generates "motional" terms in the formulas these terms are taken into account within a manifestly covariant framework.

A highly optimized code for calculating atomic data at neutron star magnetic field strengths using a doubly self-consistent Hartree–Fock–Roothaan method

We report on the experimental observation of canard orbit and mixed mode oscillations (MMOs) in an excitable glow discharge plasma induced by an external magnetic field perturbation using a bar magnet. At a small value of magnetic field, small amplitude quasiperiodic oscillations were excited, and with the increase in the magnetic field, large amplitude oscillations were excited. Analyzing the experimental results, it seems that the magnetic field could be playing the role of noise for such nonlinear phenomena. It is observed that the noise level increases with the increase in magnetic field strength. The experimental results have also been corroborated by a numerical simulation using a FitzHugh-Nagumo like macroscopic model derived from the basic plasma equations and phenomenology, where the noise has been included to represent the internal plasma noise. This macroscopic model shows MMO in the vicinity of the canard point when an external noise is added.