Isotropic Field Research Articles

Design and implementation of a low cost isotropic electric field sensor for SAR measurements

Design and implementation of a low cost isotropic electric field sensor for SAR measurements

Isotropic tensor fields in amorphous solids: Correlation functions of displacement and strain tensor fields

Isotropic tensor fields in amorphous solids: Correlation functions of displacement and strain tensor fields

Optical Möbius strips in isotropic random non-paraxial light

Abstract The statistics of Möbius strips with various topologies, formed by the axes of polarization ellipses as they are traced along a closed circular contour of small size passing through the center of a solitary circular polarization singularity line (C-line), have been investigated both analytically and numerically in a random isotropic electromagnetic field. Found are the analytical expressions for the joint probability density function of the differential characteristics of the random isotropic electromagnetic field, which allow for the determination of the topological properties of diagrams of polarization ellipses and the normal vectors to them, as well as the optical strips that arise in the space around C-lines.

Optimization of the Electron Spectrometer Telescope geometry for the PRESET satellite through Monte Carlo simulation

The Electron Spectrometer Telescope (EST) aboard the PRESET satellite mission aims to measure the pitch angle distribution of 0.3–4 MeV electrons in the outer Van Allen belts. The PRESET satellite is planned to launch into a sun-synchronous low Earth orbit in Q2, 2026. We present comprehensive Monte Carlo simulations to optimize the design and response of the EST instrument. The EST consists of a stack of silicon strip detectors and a collimator to take pitch-angle dependent electron spectral measurements with a target angular resolution of 6° while rejecting the proton, heavy ion and gamma detection events. Various collimator designs and detector stacking configurations are investigated using the Geant4 code to deduce an optimal design and configuration. For validation of the Geant4 simulations, a benchmark test spectrometer was set up using a stack of four silicon detectors and a good agreement between the measured and simulated responses was found for a beta spectrum from a 90Sr/90Y source. The collimator design was optimized by adjusting total length, aperture size, number of view-ports and collimator materials. The optimum aperture size and the number of view-ports were determined by varying them and selecting the best cases that meet the angular resolution and the geometric factor requirements. Moreover, to address the under-utilization of the front position-sensitive detector encountered in a typical pin-hole collimator, two offset collimators with tilted axes were employed. Extensive simulations were carried out by varying the number of silicon detectors and the thickness of each detector to optimize the configuration of the silicon detector stack. An optimum thickness of the front detector was found to be 140 µm, which can minimize the perturbation counts caused by the proton detection events. For the other detectors, a stack of four 1.5 mm thick detectors was chosen to achieve a good sensitivity to low energy electrons at a tolerable complexity of the system. The angular response simulated for the optimum design of the EST showed a resolution of 5.5°, which is slightly better than the target resolution of 6°. The response matrices of the final design simulated for isotropic electron and proton fields showed a high geometric factor, which is expected to produce an average electron counting rate of 230 cps within the trapped region with a negligible contamination of the electron spectrum by protons except for a mild contamination by the 1.0–1.1 MeV protons.

Calculation of Macroscopic Effects of Quantum Gravity in General Static Isotropic Gravitational Fields

In this paper we calculated the self-interaction of the gravitational field in coordinate space by approximate method, and find the functional relationship between gravitational source and distance and self-interaction of quantum gravity. The calculation result shows that the self-interaction of quantum gravity can explain the gravitational effects of dark matter. In the solar system, the self-interaction is extremely weak, but it is enough to explain the the Pioneer anomaly.

A Comparative Study of the Hydrogen Auto-Ignition Process in Oxygen–Nitrogen and Oxygen–Water Vapor Oxidizer: Numerical Investigations in Mixture Fraction Space and 3D Forced Homogeneous Isotropic Turbulent Flow Field

In this paper, we analyze the auto-ignition process of hydrogen in a hot oxidizer stream composed of oxygen–nitrogen and oxygen–water vapor with nitrogen/water vapor mass fractions in a range of 0.1–0.9. The temperature of the oxidizer varies from 1100 K to 1500 K and the temperature of hydrogen is assumed to be 300 K. The research is performed in 1D mixture fraction space and in a forced homogeneous isotropic turbulent (HIT) flow field. In the latter case, the Large Eddy Simulation (LES) method combined with the Eulerian Stochastic Field (ESF) combustion model is applied. The results obtained in mixture fraction space aim to determine the most reactive mixture fraction, maximum flame temperature, and dependence on the scalar dissipation rate. Among others, we found that the ignition in H2-O2-H2O mixtures occurs later than in H2-O2-N2 mixtures, especially at low oxidizer temperatures. On the other hand, for a high oxidizer temperature, the ignitability of H2-O2-H2O mixtures is extended, i.e., the ignition occurs for a larger content of H2O and takes place faster. The 3D LES-ESF results show that the ignition time is virtually independent of initial conditions, e.g., randomness of an initial flow field and turbulence intensity. The latter parameter, however, strongly affects the flame evolution. It is shown that the presence of water vapor decreases ignitability and makes flames more prone to extinction.

Modeling random isotropic vector fields on the sphere: theory and application to the noise in GNSS station position time series

Modeling random isotropic vector fields on the sphere: theory and application to the noise in GNSS station position time series

Low-velocity streams inside the planetary nebula H2-18

Aims. Numerous planetary nebulae show complicated inner structures that are not obvious to explain. For one such object, we undertook a detailed 3D photoionisation and kinematical model analysis to gain a better understanding of the underlying shaping processes. Methods. We obtained 2D ARGUS/IFU spectroscopy covering the whole nebula in selected representative emission lines. We used 3D photoionisation modelling to compute images and line profiles, and a comparison of the observations with the models was performed to fine-tune the model details. This procedure predicts the approximate nebular 3D structure and kinematics. Results. We find that within a cylindrical outer nebula, there is a hidden, very dense bar-like or cylindrical inner structure. Both structures are co-axial and are inclined to the sky by 40 deg. We propose that the wide, asymmetric, one-sided plume is a flat structure attached to one end of the bar. All nebular components share the same kinematics, with an isotropic velocity field that monotonically increases with distance from the star before reaching a plateau. The relatively low velocities indicate that the observed shapes do not require particularly energetic processes, and there is no indication for the current presence of a jet. The 3D model reproduces the observed line ratios and the detailed structure of the object significantly better than previous models.

Evaluation of finite element modeling methods for predicting compression screw failure in a custom pelvic implant.

Introduction: Three-dimensional (3D)-printed custom pelvic implants have become a clinically viable option for patients undergoing pelvic cancer surgery with resection of the hip joint. However, increased clinical utilization has also necessitated improved implant durability, especially with regard to the compression screws used to secure the implant to remaining pelvic bone. This study evaluated six different finite element (FE) screw modeling methods for predicting compression screw pullout and fatigue failure in a custom pelvic implant secured to bone using nine compression screws. Methods: Three modeling methods (tied constraints (TIE), bolt load with constant force (BL-CF), and bolt load with constant length (BL-CL)) generated screw axial forces using functionality built into Abaqus FE software; while the remaining three modeling methods (isotropic pseudo-thermal field (ISO), orthotropic pseudo-thermal field (ORT), and equal-and-opposite force field (FOR)) generated screw axial forces using iterative physics-based relationships that can be implemented in any FE software. The ability of all six modeling methods to match specified screw pretension forces and predict screw pullout and fatigue failure was evaluated using an FE model of a custom pelvic implant with total hip replacement. The applied hip contact forces in the FE model were estimated at two locations in a gait cycle. For each of the nine screws in the custom implant FE model, likelihood of screw pullout failure was predicted using maximum screw axial force, while likelihood of screw fatigue failure was predicted using maximum von Mises stress. Results: The three iterative physics-based modeling methods and the non-iterative Abaqus BL-CL method produced nearly identical predictions for likelihood of screw pullout and fatigue failure, while the other two built-in Abaqus modeling methods yielded vastly different predictions. However, the Abaqus BL-CL method required the least computation time, largely because an iterative process was not needed to induce specified screw pretension forces. Of the three iterative methods, FOR required the fewest iterations and thus the least computation time. Discussion: These findings suggest that the BL-CL screw modeling method is the best option when Abaqus is used for predicting screw pullout and fatigue failure in custom pelvis prostheses, while the iterative physics-based FOR method is the best option if FE software other than Abaqus is used.

Analytical solutions considering face advance and time-dependent behavior for back-analysis of convergence measurements in deep circular tunnels under isotropic initial stress state

A methodology is presented for the back-analysis of convergence measurements in deep tunnels to determine the constitutive parameters of the surrounding rock mass. Since increasing deformations and stresses with time are due to both the face advance and the time-dependent behavior of the ground, the two effects must be considered during the excavations. To that end, an analytical solution assuming an unlined circular tunnel excavated in a homogeneous isotropic ground under an initial isotropic stress field and assuming a fractional viscoelastic plastic behavior is developed. A second closed-form solution is also derived assuming an instantaneous excavation. Additionally, combining the developed analytical solution that takes into account the progressive face advance and an empirical approach, convergences are back-analyzed based on a least-squares optimization method to calibrate the constitutive parameters of the ground. The presented methodology aims to characterize the long-term behavior of tunnels and offers the advantage of being directly applicable during the excavation phase as soon as convergence measurements are available. Finally, the method is illustrated by two case studies related to the Fréjus road tunnel and the Saint-Martin-la-Porte access gallery (SMP2).

A momentum-resolved view of polaron formation in materials

An ab-initio computational methodology for interrogating the phonon contribution to polaron formation in real materials is developed that can be directly compared to experiment. Using LiF as an example, we show that the recent ab-initio theory of Sio et al.1 makes predictions of the momentum- and branch dependent phonon amplitudes in polaron quasiparticles that are testable using ultrafast electron diffuse scattering (UEDS) and related techniques. The large electron polaron in LiF has UEDS signatures that are qualitatively similar to those expected from a simple isotropic strain field model, but the small hole polaron exhibits a profoundly anisotropic UEDS pattern that is in poor agreement with an isotropic strain field. We also show that these polaron diffuse scattering signatures are directly emblematic of the underlying polaron wavefunction. The combination of new time and momentum resolved experimental probes of nonequilibrium phonons with novel computational methods promises to complement the qualitative results obtained via model Hamiltonians with a first principles, material-specific quantitative understanding of polarons and their properties.

Multicaloric Cryocooling Using Heavy Rare-Earth Free La(Fe,Si)13-Based Compounds.

The transition toward a carbon-neutral society based on renewable energies goes hand in hand with the availability of energy-efficient technologies. Magnetocaloric cooling is a very promising refrigeration technology to fulfill this role regarding cryogenic gas liquefaction. However, the current reliance on highly resource critical, heavy rare-earth-based compounds as magnetocaloric material makes global usage unsustainable. Here, we aim to mitigate this limitation through the utilization of a multicaloric cooling concept, which uses the external stimuli of isotropic pressure and magnetic field to tailor and induce magnetostructural phase transitions associated with large caloric effects. In this study, La0.7Ce0.3Fe11.6Si1.4 is used as a nontoxic, low-cost, low-criticality multiferroic material to explore the potential, challenges, and peculiarities of multicaloric cryocooling, achieving maximum isothermal entropy changes up to -28 J (kg K)-1 in the temperature range from 190 K down to 30 K. Thus, the multicaloric cooling approach offers an additional degree of freedom to tailor the phase transition properties and may lead to energy-efficient and environmentally friendly gas liquefaction based on designed-for-purpose, noncritical multiferroic materials.

BxC Toolkit: Generating Tailored Turbulent 3D Magnetic Fields

Turbulent states are ubiquitous in plasmas, and the understanding of turbulence is fundamental in modern astrophysics. Numerical simulations, which are the state-of-the-art approach to the study of turbulence, require substantial computing resources. Recently, attention shifted to methods for generating synthetic turbulent magnetic fields, affordably creating fields with parameter-controlled characteristic features of turbulence. In this context, the BxC toolkit was developed and validated against direct numerical simulations (DNSs) of isotropic turbulent magnetic fields. Here, we demonstrate novel extensions of BxC to generate realistic turbulent magnetic fields in a fast, controlled, geometric approach. First, we perform a parameter study to determine quantitative relations between the BxC input parameters and the desired characteristic features of the turbulent power spectrum, such as the extent of the inertial range, its spectral slope, and the injection and dissipation scale. Second, we introduce in the model a set of structured background magnetic fields, B 0, as a natural and more realistic extension to the purely isotropic turbulent fields. Third, we extend the model to include anisotropic turbulence properties in the generated fields. With all these extensions combined, our tool can quickly generate any desired structured magnetic field with controlled, anisotropic turbulent fluctuations, faster by orders of magnitude with respect to DNSs. These can be used, e.g., to provide initial conditions for DNSs or easily generate synthetic data for many astrophysical settings, all at otherwise unaffordable resolutions.

Theory of the momentum source method for synthetic turbulence

The interaction between turbulence and blade leading edges is known to have a significant impact on the aerodynamic and aeroacoustic performance of propellers. In addition to directly simulating turbulence, synthetic turbulence, such as the momentum source method, has been developed as a popular method for studying this interaction process in computational fluid dynamics and computational aeroacoustics. However, it is found that for non-periodic disturbances, although the induced velocity field is divergence-free, spurious noise may be generated in the source region and contaminate simulation results. To address this issue, the present work proposes adding a correction term so that the divergence-free condition is satisfied globally and the unwanted acoustic waves are suppressed, as an extension to our previous work for time-periodic gusts [H. Jiang, Phys. Fluids 35, 096115 (2023)]. The strength of the proposed approach lies in its simplicity, flexibility, and generality. First, it derives explicit source terms, which are straightforward for numerical implementations, to generate unsteady flow fluctuations. Second, the sources can be added inside the computational domain, saving computational costs for turbulence convection and being compatible with most existing boundary conditions. Third, the proposed method can obtain analytical expressions for the needed momentum source of the Navier–Stokes equation subject to any desired isotropic or anisotropic divergence-free turbulence fields. The method has been verified by examples of synthesizing harmonic gusts, Gaussian eddies, and random turbulence. The synthetic velocity results characterized by different spectral components are directly compared to target velocity fields, verifying the proposed approach and showing its capability. Parameters that influence the distribution of added sources are systematically investigated to identify an optimal combination for different scenarios. Finally, the model is employed to evaluate the aerodynamic interaction between an incoming turbulence and a thin airfoil. The obtained results exhibit good correspondence with analytical solutions.

Dynamics of Cosmological Scalar Fields Revisited

This paper reviews the dynamics of a single isotropic and homogeneous scalar field φ(t) in the context of cosmological models. A non-standard approach to the solution of the Einstein–Klein–Gordon equations is described which uses the scalar field as the evolution parameter for cosmic dynamics. General conclusions about the qualitative behaviour of the solutions can be drawn, and examples of how to obtain explicit solutions for some cosmological models of interest are given. For arbitrary potentials, analytical results can be obtained from the slow-roll approximation by using a series expansion for the Hubble parameter H[φ], from which a quantitative estimate for the number of e-folds of expansion is obtained. This approach is illustrated with the examples of quadratic potentials and hilltop models, with special consideration of Higgs-type potentials. The GUT-scale is shown to come out of such a model quite naturally. Finally, it is discussed how to find scalar potentials giving rise to a predetermined scalar-field behaviour and the associated evolution of the scale factor.

Macroscopic Effect of Quantum Gravity in General Static Isotropic Gravitational Field

In this paper we calculated the self-interaction of the gravitational field, and analyzed the effect of the self-interactions in a general staticisotropic gravitational field using a semi classical approach. We found that the effects of the self-interaction on the gravitational field can be used to explain dark matter.

Spectral central limit theorem for additive functionals of isotropic and stationary Gaussian fields

Spectral central limit theorem for additive functionals of isotropic and stationary Gaussian fields

Inverse Compton Emission and Cooling of Relativistic Particles Accelerated at Shear Boundary Layers in Relativistic Jets

Both observational evidence and theoretical considerations from magnetohydrodynamic simulations of jets suggest that the relativistic jets of active galactic nuclei (AGN) are radially stratified, with a fast inner spine surrounded by a slower-moving outer sheath. The resulting relativistic shear layers are a prime candidate for the site of relativistic particle acceleration in the jets of AGNs and gamma-ray bursts (GRBs). In this article, we present outcomes of particle-in-cell simulations of magnetic-field generation and particle acceleration in the relativistic shear boundary layers (SBLs) of jets in AGNs and GRBs. We investigate the effects of inverse Compton cooling on relativistic particles that are accelerated in the SBLs of relativistic jets, including the self-consistent calculation of the radiation spectrum produced by inverse Compton scattering of relativistic electrons in an isotropic external soft photon field. We find that the Compton cooling can be substantial, depending on the characteristic energy (blackbody temperature and energy density) of the external radiation field. The produced Compton emission is highly anisotropic and more strongly beamed along the jet direction than the characteristic 1/Γ pattern expected from intrinsically isotropic emission in the comoving frame of an emission region moving along the jet with a bulk Lorentz factor Γ. We suggest that this may resolve the long-standing problem of the Doppler factor crisis.

The Role of Particle Inertia and Thermal Inertia in Heat Transfer in a Non-Isothermal Particle-Laden Turbulent Flow

We present an analysis of the effect of particle inertia and thermal inertia on the heat transfer in a turbulent shearless flow, where an inhomogeneous passive temperature field is advected along with inertial point particles by a homogeneous isotropic velocity field. Eulerian–Lagrangian direct numerical simulations are carried out in both one- and two-way coupling regimes and analyzed through single-point statistics. The role of particle inertia and thermal inertia is discussed by introducing a new decomposition of particle second-order moments in terms of correlations involving Lagrangian acceleration and time derivative of particles. We present how particle relaxation times mediate the level of particle velocity–temperature correlation, which gives particle contribution to the overall heat transfer. For each thermal Stokes number, a critical Stokes number is individuated. The effect of particle feedback on the attenuation or enhancement of fluid temperature variance is presented. We show that particle feedback enhances fluid temperature variance for Stokes numbers less than one and damps is for larger than one Stokes number, regardless of the thermal Stokes number, even if this effect is amplified by an increasing thermal inertia.

Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

In the current study, an ab initio derivation of the neutron self-shielding factor to solve the complex neutron transport problem of the decrease of the neutron flux as it penetrates into a material placed in an isotropic neutron field having equal flux in all directions. The theory of steady-state neutron transport was employed, starting from Stuart’s formula, to derive simple analytical formulae based on the integral cross-section parameters. The formulae could be adopted by the user according to various variables, such as the neutron flux distribution and geometry of the simulation at hand. The concluded formulae of the self-shielding factors comprise an inverted sigmoid function normalized with a weight representing the ratio between the macroscopic total and scattering cross-sections of the medium. The general convex volume geometries are reduced to a set of chord lengths, while the neutron interaction probabilities within the volume are parameterized to the epithermal and thermal neutron energies. The arguments of the inverted-sigmoid function were derived from a simplified version of neutron transport formulation. The derived analytic formulae agreed greatly with the experimental observations for different elements and geometries.