Field Dependence Research Articles

Numerical solutions to Hyperbolic Maxwell quasi-variational inequalities in Bean–Kim model for type-II superconductivity

This paper is devoted to the finite element analysis for the Bean–Kim model governed by the full 3D Maxwell equations. Describing type-II superconductivity at the macroscopic level, this model leads to a challenging coupled system consisting of the Faraday equation and a hyperbolic quasi-variational inequality (QVI) of the second kind with L1-type nonlinearity, that arises explicitly from the magnetic field dependency in the critical current. With the involved Maxwell coupling in the 3D H(curl)-setting, the hyperbolic QVI character poses the primary challenge in the numerical investigation. Two mixed finite element methods based on implicit Euler and leapfrog time-stepping are proposed. On the one hand, the implicit Euler method results in a nonstandard system of curl-curl elliptic QVI with a first-order curl-type nonlinearity. Though the well-posedness of this system is guaranteed, its numerical realization is not straightforward and requires the use of a two-stage iteration process of high computational complexity. On the other hand, by approximating the electric and magnetic fields at two different time step levels, the leapfrog method turns out to be more suitable as it naturally eliminates the notorious QVI structure. More importantly, utilizing suited subdifferential and optimization techniques, we are able to prove an efficiently computable explicit formula for its exact solution in terms of the electric field, which makes its numerical computation substantially more favorable than the Euler method. As further advantages, the leapfrog method applies to broad scenarios involving low regular data of bounded variation (BV) in time for both the applied current source and the temperature distribution. Through nonstandard technical arguments tailored to the BV data, our analysis proves the conditional stability and, eventually, the uniform convergence of the proposed leapfrog method. This paper is closed by 3D numerical tests showcasing the reasonable and efficient performance of the proposed numerical solution.

Tuning critical current density properties of YBa2Cu3O y thin films under longitudinal magnetic field by using heavy-ion irradiation

We attempted to improve the critical current density J c under a longitudinal magnetic field (LMF) by using columnar defects (CDs) tilted toward the transport current, where the CDs were produced with 80 MeV Xe ions at an incident angle(s) up to φ i = 87.5° relative to the c-axis of YBa2Cu3O y thin films. The formation of CDs extending throughout the film was confirmed by cross-sectional transmission electron microscopy. The CDs tilted at φ i = 87.5° weakened the magnetic field dependence of J c under the LMF, providing a J c higher than that of the unirradiated film in a high magnetic field. This is the first study to demonstrate that CDs and/or irradiation defects contribute to flux pinning under the LMF in high-T c superconductors. In addition, the J c under LMF was sensitive to the tilt angle of the CDs: the J c was reduced by CDs tilted not only at φ i = 0°, but also at a slightly larger angle relative to the ab-plane, i.e. φ i = 85°. The introduction of CDs rather disturbs the LMF effect because of the large volume passing through the film thickness, unless the tilt angles of the CDs are within the narrow angular region effective for the LMF effect.

The dependence of the magnetism of a near-limb sunspot on height

Context. The physical parameters of the sunspot are not fully understood, especially the height dependence of the magnetic field. So far, it is also an open question as to which heights the He I 10 830 Å spectral line is formed at. Aims. Our aim is to investigate the magnetic and dynamical properties in the atmosphere above a sunspot, from the photosphere to the chromosphere. We analyzed the photospheric and chromospheric magnetic field properties of a stable sunspot in AR 12553 on June 20, 2016 using spectropolarimetric observations obtained with the GREGOR Infrared Spectrograph (GRIS) at the 1.5-meter GREGOR telescope. Methods. A spectral-line inversion technique was used to infer the magnetic field vector and Doppler velocities from the full Stokes profiles. In total, three spectral lines were inverted and the variation of the magnetic properties was qualified using the average values of the radial circles. The sunspot is located close to the solar limb, and thus this allows us to make a geometrical determination of the height of the spectral line He I 10 830 Å. Results. We find the height of helium spectral line to be 970 km above the photospheric spectral lines directly from observation at a stable sunspot. The total magnetic field strength decreases with height over the sunspot; the rates are −0.34 G km−1 for the umbra and −0.28 G km−1 for the penumbra. The inclination increases with increasing height in the umbra, but decreases in the penumbra. In the umbra, the vertical component (Bz) decreases with height, while the horizontal component (Bhor) remains almost constant. In the penumbra this is reversed, as Bz remains nearly constant over height, while Bhor decreases. We also observe fast velocities with 30 km s−1 in small chromospheric patches on the central side of the spot. Conclusions. The key parameters depending on height in the sunspot are the Bz component of the magnetic field for the umbra and the Bhor component of the magnetic field for the penumbra. The observation revealed supersonic downward velocities in and near the outer penumbra.

Representation Process of Prospective Teachers in Solving Mathematical Problems Based on Cognitive Style

This study investigates the correlation between cognitive styles and the thinking process utilized when solving mathematical problems, emphasizing the significance of aligning problem-solving strategies with problem representations. Employing a qualitative approach, the research examines two cognitive styles—Field Independent (FI) and Field Dependent (FD)—chosen based on participants' mathematical abilities. Conducted at Cenderawasih University's Mathematics Education Study Program, the study reveals that students' mathematical problem-solving proficiency remains relatively low, warranting further exploration of their thinking processes. While FI subjects demonstrate competence in aligning thinking processes with mathematical representations, particularly in structuring problem-solving steps, FD subjects exhibit limitations in articulating meaning and verbal representations. These findings underscore the importance of instructing educators not only in teaching mathematical concepts but also in guiding students to articulate problem-solving steps using verbal representations. This study highlights the need for a holistic approach to mathematical education, integrating conceptual understanding with effective problem-solving strategies tailored to individual cognitive styles.

Interplay of lattice-spin-orbital coupling and Jahn–Teller effect in noncollinear spinel Ti x Mn1−x (Fe y Co1−y )2O4: a neutron diffraction study

Local magnetostructural changes and dynamical spin fluctuations in doubly diluted spinel Ti x Mn1‒x (Fe y Co1‒y )2O4 has been reported by means of neutron diffraction and magnetization studies. Two distinct sets of compositions (i) x(Ti) = 0.20 and y(Fe) = 0.18; (ii) x(Ti) = 0.40 and y(Fe) = 0.435 have been considered for this study. The first compound of equivalent stoichiometry Ti0.20Mn0.80Fe0.36Co1.64O4 exhibits enhanced tetragonal distortion across the ferrimagnetic transition temperature T C = 258 K in comparison to the end compound MnCo2O4 (T C ∼ 180 K) with a characteristic ratio c t/√2a t of 0.99795(8) demonstrating robust lattice-spin-orbital coupling. However, in the second case Ti0.40Mn0.60Fe0.87Co1.13O4 with higher B-site compositions, the presence of Jahn–Teller ions with distinct behavior appears to counterbalance the strong tetragonal distortion thereby ceasing the lattice-spin-orbital coupling. Both the investigated systems show the coexistence of noncollinear antiferromagnetic and ferrimagnetic components in cubic and tetragonal settings. On the other hand, the dynamical ac-susceptibility, χ ac(T) reveals a cluster spin-glass state with Gabay–Toulouse (GT) like mixed phases behaviour below T C. Such dispersive behaviour appears to be sensitive to the level of octahedral substitution. Further, the field dependence of χ ac(T) follows the weak anisotropic GT-line behaviour with crossover exponent Φ lies in the range 1.38–1.52 on the H–T plane which is in contrast to the B-site Ti substituted MnCo2O4 spinel that appears to follow irreversible non-mean-field AT-line behaviour (Φ ∼ 3 + δ). Finally, the Arrott plots analysis indicates the presence of a pseudo first-order like transition (T < 20 K) which is in consonance with and zero crossover of the magnetic entropy change within the frozen spin-glass regime.

Structural, magnetic and transport properties of FeRuVZ (Z = Si, Ge) Heusler alloys: Experiment and theory

Heusler alloys based on 4d-elements are relatively less explored though they are known to host interesting electronic/magnetic properties useful for future spintronics applications. Here, we report a comparative study of the structural and magnetic properties of FeRuVSi (FRVS) and FeRuVGe (FRVG) using experimental and theoretical tools. Magneto-transport measurements have also been carried out to probe the role of magnetism on their transport behaviour. Room temperature (T) X-ray diffraction data reveals cubic crystal structure (space group No. 216) with B2 type antisite disorder between Fe and Ru sites in both the alloys. They show ferromagnetic behaviour below the Curie temperature (TC) 84 K for FeRuVSi and 57 K for FeRuVGe respectively. The field dependence of magnetization at low-T shows saturating (nearly saturating) behaviour for FRVS (FRVG). Transport measurements show metallic behaviour with a sharp reduction in the resistivity near TC. Ab-initio calculations predict nearly half metallic behaviour with ∼ 87 % and ∼ 89 % spin polarization for FRVS and FRVG in their ordered states. The inclusion of antisite disorder changes the magnetic configuration, leading to a visible decrease in the magnetic moment and spin polarization. The calculated net moment and the transport properties agree fairly well with those observed experimentally. These results confirm the importance of disorder in determining the intrinsic properties of these alloys. Such combined studies help in the identification of more novel quantum materials suitable for future spintronic applications.

Observation of the photonic Hall effect and photonic magnetoresistance in random lasers

Modulation of scattering in random lasers (RLs) by magnetic fields has attracted much attention due to its rich physical insights. We fabricate magnetic gain polymer optical fiber to generate RLs. From macroscopic experimental phenomena, with the increase of the magnetic field strength, the magnetic transverse photocurrent exists in disordered multiple scattering of RLs and the emission intensity of RLs decreases, which is the experimental observation of photonic Hall effect (PHE) and photonic magnetoresistance (PMR) in RLs. At the microscopic level, based on the field dependence theory of magnetic disorder in scattered nanoparticles and the replica symmetry breaking theory, the magnetic-induced transverse diffusion of photons reduces the scattering disorder, and then decreases the intensity fluctuation disorder of RLs. Our work establishes a connection between the above two effects and RLs, visualizes the influence of magnetic field on RL scattering at the microscopic level, which is crucial for the design of RLs.

Muon spin relaxation and emergence of disorder-induced unconventional dynamic magnetic fluctuations in Dy2Zr2O7

The disordered pyrochlore oxide Dy2Zr2O7 shows the signatures of field-induced spin freezing with remnant zero-point spin-ice entropy at 5 kOe magnetic field. We have performed zero-field and longitudinal field Muon spin relaxation (µSR) studies on Dy2Zr2O7. Our zero field studies reveal the absence of both long-range ordering and spin freezing down to 62 mK. The µSR relaxation rate exhibits a temperature-independent plateau below 4 K, indicating a dynamic ground state of fluctuating spins similar to the well-known spin ice system Dy2Ti2O7. The low-temperature spin fluctuations persist in the longitudinal field of 20 kOe as well and show unusual field dependence of the relaxation rate, which is uncommon for a spin-liquid system. Our results, combined with the previous studies do not show any evidence of spin ice or spin glass ground state, rather point to a disorder-induced dynamic magnetic ground state in the Dy2Zr2O7 material.

Students' mathematical literacy ability to solve problems using matrix material is viewed from cognitive styles.

This study aims to describe the ability of students to develop mathematical literacy by reviewing their cognitive styles. The type of research used in this study is research with a descriptive qualitative approach. The research subjects were taken from 27 students of SMK class XI TKJ in one of the schools located in Bogor District, Nganjuk Regency. The instruments used in this study were GEFT (Group Embedded Figure Test) to determine the cognitive style ability of students who would be divided into field-dependent and field-independent cognitive style groups, mathematical literacy tests, and interviews. Mathematical literacy test questions are prepared and adapted to everyday life problems. They are fully based on indicators of mathematical literacy skills that are adapted and aligned with the stages of problem-solving. The results showed that field-dependent subjects tended to formulate problems still using narrative sentences; subjects were also less able to determine their problem-solving because they still depended on the procedures that had been given and were only able to provide a brief interpretation of the final results of the solution. While field-independent subjects are able to formulate problems by using modeling, subjects are also able to determine and write down their problem-solving in an organized manner. They are able to show corrections to the final results of problem-solving.

A broad-band investigation of ferromagnetic resonance in exchange coupled permalloy/phthalocyanine bilayer heterostructures at room temperature

The phenomenon of ferromagnet/molecule interfacial electronic hybridization enables the possibility of modifying magnetic characteristics of downscaled systems for spintronic applications. Ferromagnetic resonance (FMR) at the nanoscale level through a coplanar waveguide (CPW) over a wide frequency range is a remarkably reliable technique for investigation of the magnetic heterostructure’s interfacial properties and their feasibility in applications as spintronic devices. Here, magnetron sputtering and organic molecular beam epitaxy methods are used to fabricate the following nanoscale heterostructures: permalloy (Py)/Fe phthalocyanine (Pc), Py/ZnPc, and Py/Cr. Magnetization dynamics of the bilayer heterostructures is investigated in a CPW by studying frequency dependence (5–50 GHz) of the resonance field and linewidth with parallel and perpendicular geometries of the static applied magnetic field, thereby providing insights into possible intrinsic and extrinsic sources of FMR damping. Planar Pc molecules at the Py layer interface are found to have the potential to contribute to magnetic stabilization based on calculated magnetic parameters. This is evidenced by the larger results of surface anisotropy of the Py/MPc bilayer heterostructures induced by exchange coupling interaction at room temperature as well as the lower values of damping constant.

Observation of Linear Magnetoresistance in MoO2.

Magnetoresistance, the change in resistance with applied magnetic fields, is crucial to the magnetic sensor technology. Linear magnetoresistance has been intensively studied in semimetals and semiconductors. However, the air-stable oxides with a large linear magnetoresistance are highly desirable but remain to be fully explored. In this paper, we report the direct observation of linear magnetoresistance in polycrystalline MoO2 without any sign of saturation up to 7 T under 50 K. Interestingly, the linear magnetoresistance reaches as large as 1500% under 7 T at 2 K. The linear field dependence is in great contrast to the parabolic behavior observed in single-crystal MoO2, probably due to phonon scattering near the grain boundaries. Our results pave the way to comprehending magneto-transport behavior in oxides and their potential applications in magnetic sensors.

Functional Forms for Lorentz Invariant Velocities

Lorentz invariance lies at the very heart of Einstein’s special relativity, and both the energy formula and the relative velocity formula are well-known to be invariant under a Lorentz transformation. Here, we investigate the spatial and temporal dependence of the velocity field itself u(x,t) and we pose the problem of the determination of the functional form of those velocity fields u(x,t) which are automatically invariant under a Lorentz transformation. For a single spatial dimension, we determine a first-order partial differential equation for the velocity u(x,t), which appears to be unknown in the literature, and we investigate its main consequences, including demonstrating that it is entirely consistent with many of the familiar outcomes of special relativity and deriving two new partial differential relations connecting energy and momentum that are fully compatible with the Lorentz invariant energy–momentum relations.

Effect of the global electroneutrality condition on electromigration Taylor-Aris dispersion in a microcapillary with finite Debye layer thickness.

In this work, the electromigration dispersion (EMD) due to the charged electrolytes in microchannels is considered without using the thin electrical double layer assumption. The electrokinetic flow and transport of ions are actuated within a rectangular micro-/nanochannel having a negative surface charge density under the influence of an external electric field. Due to the local variation of the conductivity and the nonvalidity of the electroneutrality condition, the local electric field varies as a function of the solute concentration, wall surface charge density, valency, and Debye layer length. The resulting electrokinetic flow due to the external electric field drives the fluid along with the charged species, where the Taylor-Aris dispersion separates the solutes into their different constituents. The local concentration dependence of the electric field leads to the formation of concentration profiles that are slightly asymmetric with respect to the standard Gaussian distribution. Including a finite Debye layer thickness has an effect on the advection of the species as well as the diffusion of the species. It is found that in cases where Debye layers are thicker, the species advects faster within the microchannel. This might give valuable insights into the nature of the EMD. Our model aims to predict the evolution of ionic concentration at all positions within the channel. A study of the higher-order statistics in skewness and kurtosis has also been conducted to obtain a better understanding of the idealized model consisting of a buffer solution.

The relative effects of direct and indirect written corrective feedback on L2 learning: The moderating role of field dependence/independence

The current study investigated the relative effects of direct and indirect written corrective feedback (WCF) on the learning of regular past tense, and the extent to which learning outcomes were related to individual variation in field dependence/independence (FDI). Fifty-nine Chinese intermediate second language (L2) learners of English were randomly assigned to two treatment groups and a control group. The two treatment groups carried out three written dictogloss tasks and received direct WCF and indirect WCF, respectively, on their erroneous use of regular past tense. The control group performed the same writing tasks but received feedback on the content of their writing. To evaluate the effect of treatment, a grammaticality judgement task and a picture description task were administered as the pretest, immediate posttest, and delayed posttest. The Group Embedded Figures Test was used to measure learners’ FDI orientation. The results showed that both treatment groups outperformed the control group on the posttests, but no significant differences were observed between the two treatment groups. In addition, the results suggested that FDI was related to learning outcomes as measured by the picture description task. Field independent learners had an overall advantage over field dependent learners, especially where indirect WCF was provided.

Unplugged Activity and Cognitive Style on The Speaking Abilities of Early Children

The ability to speak well and purposefully must be instilled in children from an early age. This is possible through the learning process at school using interesting learning methods and media according to the child's cognitive style. Because spoken language conveyed through speaking is a tool for expressing thoughts and feelings and a means of communication between humans. This will help improve children's speaking ability. This research aims to determine the differences in speaking abilities between students using the unplugged activity method and those using the beyond center and circle times (BCCT). Determine the differences in speaking ability between students with a field-dependence cognitive style and those with a field-independence cognitive style. The researcher tests the interaction between learning methods and cognitive style regarding speaking ability. This research uses an experimental design. The subjects were PGRI Jambon Kindergarten students (TK B1) and (TK B2) who studied the theme of Animals, totaling 44 children. The cognitive style was measured using a questionnaire based on the Children Embedded Figure Test (CEFT). Data analysis of relationships and interactions between variables used the two-way ANOVA test. The research results show that differences influence speaking ability between students using unplugged activity learning and BCCT. Some differences influence the student’s speaking abilities with a field-independence cognitive style and those with a field-dependence cognitive style. There is an interaction between learning methods and cognitive style regarding speaking ability.

Does the ionic distribution in the electrical double layer modify second harmonic scattering?

Surface-specific nonlinear optical techniques are ideally suited to investigate the complex structure of aqueous interfaces. For colloidal particles dispersed in aqueous solutions, interfacial properties can be retrieved with angle-resolved second harmonic scattering (AR-SHS). The mathematical framework of AR-SHS does not require a priori knowledge on the electrostatic distribution in the first few nanometers close to the interface, therefore allowing us to formulate a molecular-level description of the electrical double layer (EDL) based on the experimental data. However, farther away from the interface, an analytical form of the electrostatic potential decay is necessary to account for the distance dependence of the surface electrostatic field propagating into the solution. This requirement is especially important at low ionic strengths, where the electrostatic field is not efficiently screened by counterions. Here, we examine to what extent the analytical form of the electrostatic potential decay impacts the AR-SHS data analysis. We analyze the effect of different functions on the scattering form factors, on the integrated AR-SHS signal intensity, and on the surface parameters extracted from fitting the AR-SHS data. We find that the trends of the surface parameters remain similar regardless of the chosen function, demonstrating the robustness of our approach to establish a molecular-level picture of the EDL. At ionic strengths <10-4M for 100-nm diameter particles, a functional form that physically represents counterions packed more densely in the vicinity of the surface than in the case of the Poisson-Boltzmann distribution has the largest impact, resulting in an overestimation of the obtained surface potential.

An analytic expression for the field dependence of three-order Zernike aberrations in decentered and/or tilted optical systems

The double Zernike polynomials can describe the aperture dependence and field dependence of non-coaxial optical system aberrations simultaneously, and characterize the complex optical aberrations, which are of great value in the optical system design and alignment. In this paper, the specific analytic forms of all third-order double Zernike aberrations in decentered and/or tilted optical systems are derived based on the nodal aberration theory. This paper realizes the orthogonalization of the third-order aberrations with different aperture dependence and field dependence. The calculation process of the third-order double Zernike aberrations is presented. The ray tracing of the Cassegrain telescope verifies the analytic derivation of the double Zernike aberrations.

A phase-field model for the brittle fracture of Euler–Bernoulli beams coupling stretching and bending

Damage gradient models seek to simulate fracture mechanics by modulating the material stiffness. Within this framework, a singular scalar field representing damage is commonly utilized to globally decrease elastic energy. However, when considering structural models like beams and plates, this approach often fails to adequately capture important aspects due to the interaction between stretching and bending contributions. In this work, we propose a model for planar Euler–Bernoulli beams that incorporates the following features: firstly, we utilize two phase-field damage parameters to describe material damaging, specifically addressing the ‘erosion’ occurring above and below the original, undamaged beam; secondly, we assume a simple linear dependence of the axial stress field on the thickness coordinate, along with linear dependence on the axial force and bending moment. By appropriately identifying the constitutive response, our model effectively considers the coupling between stretching and bending induced during through-the-thickness damage, demonstrating good agreement with 2D observations.

Origin of the Apparent Electric‐Field Dependence of Electrostrictive Coefficients

AbstractElectrostrictive materials exhibit a strain that is proportional to the square of the induced polarization. In linear dielectrics where the permittivity is constant, this electromechanical strain is also proportional to the square of the electric field. However, under increasing amplitudes of the driving field, the electromechanical strain sometimes saturates; the electrostrictive coefficients therefore appear to depend on the amplitude of the electric field used to measure them. Here, a methodology showing that this apparent field dependence is a consequence of neglecting higher‐order electromechanical phenomena is presented. When these are taken into account, not only do the electrostrictive coefficients remain constant but the signs of the high‐order coefficients enable the prediction of the saturation behavior from a single measurement. This approach is illustrated on both classical and non‐classical (so‐called “giant”) electrostrictors.

Exploring magnetocaloric effect of coordination polymer based on Mn(II) and Nb(IV) by relaxation calorimetry

Magnetocaloric properties of {MnII2(imH)2(H2O)4 [NbIV(CN)8]·4H2O}n molecular magnet are reported. The coordination polymer crystallizes in the monoclinic P21/c space group and displays a magnetic second-order phase transition at Tc ≈ 24.1 K. The relaxation calorimetry measurements are analyzed in order to determine the temperature dependence of the magnetic entropy change ΔSM as well as the adiabatic temperature change ΔTad for an array of applied field changes ranging from 0 to 9 T. For μ0ΔH = 5 T the entropy change ΔSM attains the maximum value of 6.55 J K−1 mol−1 (9.5 J K−1 kg−1) at 25.5 K, while the corresponding maximum value of ΔTad amounts to 2.02 K at 25.1 K. The critical behavior of the isothermal entropy change is discussed. In particular, the analysis of the field dependence of ΔSM in terms of the power law implies that the studied compound belongs to the mean-field universality class.