Spherical Field Research Articles

Studyof the Spin-Orbit Interaction Effects on Energy Levels and the Absorption Coefficients of Spherical Quantum Dotand Quantum Anti-Dotunderthe Magnetic Field

In this study, the energy levels of spherical quantum dot (QD) and spherical quantum anti-dot (QAD) with hydrogenic impurity in the center, in the presence of spin-orbit interaction (SOI) and weak external magnetic field have been studied. To this aim, solving the Schrodinger equation for the discussed systems by using the finite difference method, the wave functions and energies of these systems are calculated. Then the effect of the external magnetic field, system radius size and height of potential barrier on the energy levels and also the linear, nonlinear and total absorption coefficients, (ACs), of the mentioned systems are studied. Numerical results show that the SOI in both models causes a split of 2p level into two sub-levels of 2p_(1/2)and 2p_(3/2) where the low index indicates the total angular momentum J. Also, considering the electron spin, under an applied magnetic field, the 1s and 2p levels split into two sub-levels and six sub-levels, respectively. Furthermore, in this research, it is proved that energy changes are significantly different as a function of radius size and height of the potential barrier in QD and QAD models and the ACs of these systems behave differently according to the incident photon energy at the same condition.

A new approach for fractional spherical magnetic flux flows with some fractional solutions

In this paper, we construct a new approach of spherical magnetic Lorentz flux of spherical St−magnetic flows of particles by the spherical frame in S2 spherical space. Eventually, we obtain some optical conditions of spherical St−magnetic Lorentz flux by using directional spherical fields. Moreover, we determine spherical magnetic Lorentz flux for spherical vector fields. Also, we give new construction for spherical curvatures of spherical St−magnetic flows by considering Heisenberg spherical ferromagnetic spin. Finally, the magnetic flux surface is demonstrated in a static and uniform magnetic surface by using the analytical and numerical results.

UAV 3D environment obstacle avoidance trajectory planning based on improved artificial potential field method

To address the inefficiency of the traditional artificial potential field method in complex environment for obstacle avoidance, the basic potential field function of the traditional artificial potential field method is improved, and the traditional spherical potential field is proposed to be improved to ellipsoidal potential field, and the improved algorithm is compared and simulated in MATLAB. The results show that the improved artificial potential field method satisfies the UAV to have high efficiency of safety and passability in obstacle avoidance trajectory planning in complex 3D environment.

Semi-Lagrangian formulation for the advection–diffusion–absorption equation

We present a numerical method for solving advective–diffusive–absorptive problems with high values of advection and absorption. A Lagrangian approach based on the updated version of the classical Particle Finite Element Method (PFEM) is used to calculate advection, while a Eulerian strategy based on the Finite Element Method (FEM) is adopted to compute diffusion and absorption. The Eulerian FEM procedure is based on a Finite Increment Calculus (FIC) stabilized formulation recently developed by the authors. The most relevant features of each computational approach are outlined and the coupling scheme is explained. Several problems are solved to validate the method: the evolution of a localized concentration field in two dimensions (2D), the evolution of a spherical field in 3D and three benchmark problems from the literature with high absorption.

Optical fractional spherical magnetic flux flows with Heisenberg spherical Landau Lifshitz model

In this paper, we first offer the approach of spherical magnetic Lorentz flux of spherical Sα-magnetic particle flows by the spherical frame in spherical Heisenberg space Sℍ2. Eventually, we obtain some optical conditions of spherical Sα-magnetic Lorentz flux by using directional spherical fields. Moreover, we determine spherical magnetic Lorentz flux for spherical vector fields. Also, we give new construction for spherical curvatures of spherical Sα-magnetic particle flows by considering Heisenberg spherical Landau Lifshitz model. Finally, magnetic flux surface is demonstrated in a static and uniform magnetic surface by using the analytical and numerical results with Heisenberg spherical Landau Lifshitz model.

Timelike spherical magnetic [formula omitted] flux flows with Heisenberg spherical ferromagnetic spin with some solutions

In this paper, we first offer the approach of spherical magnetic Lorentz flux of spherical timelikeSN−magneticparticle by the spherical frame in S12 spherical space. Eventually, we obtain some optical conditions of spherical t-magnetic Lorentz flux by using directional spherical fields. Moreover, we determine spherical magnetic Lorentz flux for spherical vector fields. Also, we give new construction for spherical curvatures of spherical timelikeSN−magneticparticle flows by considering Heisenberg spherical ferromagnetic spin. Finally, magnetic flux surface is demonstrated in a static and uniform magnetic surface by using the analytical and numerical results.

Propagation of electromagnetic wave in gravitational field

This paper is the third part of the induction theory of gravitational field. It mainly discusses some propagation characteristics of electromagnetic wave in the space-time constructed in the first paper [Y. Yi, Phys. Essays 33, 219 (2020)]. In this paper, a new definition of the basic properties of electromagnetic wave is given at first. Second, the photoelectric effect is explained by the new electromagnetic wave properties. Then, the propagation law of electromagnetic wave in space-time is discussed. Finally, the propagation law of electromagnetic wave in axisymmetric gravitational field is analyzed. According to the analysis in this paper, the propagation path of electromagnetic wave is unique in the spherical symmetric gravitational field, while the propagation path of electromagnetic wave in the axisymmetric gravitational field is related to the wavelength. This is the difference between the induction theory of gravitational field and the existing theory, which can be used to verify the theory of gravitational field induction.

Dependence of the frequency distribution around a sphere on the voxel orientation

Microscopically small magnetic field inhomogeneities within an external static magnetic field cause a free induction decay in magnetic resonance imaging that generally exhibits two transverse components that are usually summarized to a complex entity. The Fourier transform of the complex-valued free induction decay is the purely real and positive-valued frequency distribution which allows an easy interpretation of the underlying dephasing mechanism. Typically, the frequency distribution inside a cubic voxel as caused by a spherical magnetic field inhomogeneity is determined by a histogram technique in terms of subdivision of the whole voxel into smaller subvoxels. A faster and more accurate computation is achieved by analytical expressions for the frequency distribution that are derived in this work. In contrast to the usually assumed simplified case of a spherical voxel, we also consider the tilt angles of the cubic voxel to the external magnetic field. The typical asymmetric form of the frequency distribution is reproduced and analyzed for the more realistic case of a cubic voxel. We observe a splitting of frequency distribution peaks for increasing tilt of the cubic voxel against the direction of the external magnetic field in analogy to the case for dephasing around cylindrical, vessel-like objects inside cubic voxels. These results are of value, e.g., for the analysis of susceptibility-weighted images or in quantitative susceptibility imaging since the reconstruction of these images is performed in cubic-shaped voxels.

Three-state lithography model: an enhanced mathematical approach to predict resist characteristics in grayscale lithography processes

Background: Physical modeling of grayscale lithography processes for the prediction of photoresist heights leads to complex mathematical algorithms. A promiment example is the numerical simulation of the photoresist shape after development through Dill’s equations. These grayscale lithography models exhibit accurate prediction quality but can not directly implemented into mask layout tools to simplify the layout procedure. Limited process windows, changes in the mask design, variations of the used materials or manufacturing tools lead to time-consuming and cost-intensive test procedures to adjust the photoresist model for sufficient results. Aim: The focus of this work is to enhance current grayscale lithography models for a straightforward method with the same precise prediction of remaining photoresist heights to simplify the mask layout process. Moreover, we aim for an uncomplicated optimization of the model to minimize the empirical analysis necessary for its use. Approach: Based on experimental results, we deploy a sectionally defined mathematical expression that includes the theory of Fraunhofer diffraction and illumination-dependent activation of the photo-sensitive component and its solubility in developer. Results: We produced pyramidal, spherical and chess field structures with exposure doses of 3000 and 15 , 000 J / m2 on bare silicon substrates with 100-nm resolution and on silicon substrates with anti-reflective coatings, with accuracy as fine as 20 nm. Conclusion: The proposed three-state lithography model has been verified by experimental evaluation. It is able to operate in a wide process window and can be directly implemented in existing mask layout software. This model ensures a cost-efficient and precisely controlled production of three-dimensional topographies using grayscale lithography processes.

Functional penalised basis pursuit on spheres

In this paper, we propose a unified theoretical and practical spherical approximation framework for functional inverse problems on the hypersphere. More specifically, we consider recovering spherical fields directly in the continuous domain using functional penalised basis pursuit problems with gTV regularisation terms. Our framework is compatible with various measurement types as well as non-differentiable convex cost functionals. Via a novel representer theorem, we characterise their solution sets in terms of spherical splines with sparse innovations. We use this result to derive an approximate canonical spline-based discretisation scheme, with vanishing approximation error. To solve the resulting finite-dimensional optimisation problem, we propose an efficient and provably convergent primal-dual splitting algorithm. We illustrate the versatility of our framework on real-life examples from the field of environmental sciences.

A Study on the Theoretical Calculation Method for Spherical Stress Wave Field in Linear Hardening Materials under Impact Load

基于线性硬化塑性本构模型，建立了冲击载荷作用下弹塑性球面应力波场的理论求解方法。首先，分析了冲击载荷卸载速率对球面应力波传播的影响，得到了三种不同类型的应力波传播图像；在此基础上，建立了弹性阶段、塑性加载阶段以及卸载阶段球面波动方程的理论求解方法，给出了质点位移、质点速度、应力和应变等物理量的计算方案。与已有理论方法相比，该方法考虑了不同载荷卸载速率条件下应力波的不同传播情况，并且给出了卸载阶段应力波参量计算方法，具有更广的适用范围。利用上述方法计算了恒定冲击载荷和不同指数衰减冲击载荷作用下弹塑性球面应力波场参量，在弹性阶段和塑性加载阶段，理论计算得到的物理量与已有理论方法和数值模拟结果基本吻合，在卸载阶段，已有理论方法不再适用，而本文理论计算得到的物理量与数值模拟结果基本吻合，验证了该理论方法的正确性。

High‐Resolution GRACE Monthly Spherical Harmonic Solutions

AbstractMass transport estimates based on filtered Gravity Recovery and Climate Experiment (GRACE) monthly spherical harmonic gravity field solutions generally suffer from resolution loss and signal attenuation. To develop high‐resolution solutions from GRACE Level‐1B data, this study proposes a new regularization method. Transforming spatial constraints from GRACE‐based filtered mass changes into the spectral domain and imposing them on spherical harmonics, we resolve high‐resolution gravity field solutions expressed as spherical harmonics instead of mascons. The proposed method greatly enhances the spatial resolution and signal strength of spherical harmonic solutions. Using the presented method, we have produced a time series of high‐resolution (degree 180) spherical harmonic solutions named Tongji‐RegGrace2019, which can be directly used without further smoothing. To evaluate Tongji‐RegGrace2019, we conduct the global (trend and annual amplitude) and regional comparisons (groundwater loss signals over India, hydrology signals over river basins, and ice melting signals over Greenland, Antarctica Peninsula and Patagonia) among various GRACE solutions. Our analyses show that Tongji‐RegGrace2019 agrees well with Center for Space Research and Jet Propulsion Laboratory mascon solutions in terms of signal power and spatial resolution. Over the selected areas, the correlation coefficients of mass changes between Tongji‐RegGrace2019 and mascon solutions are at least 82%. Compared to the filtered solution, higher spatial resolution and stronger signal power are achieved by Tongji‐RegGrace2019 and mascon solutions, which have the potential to retrieve signals at a smaller spatial scale. Over Patagonia Icefield, the improvement of trend estimates by Tongji‐RegGrace2019 with respect to the filtered solution is about 150%.

Characterization of interventional photoacoustic imaging (iPAI) capabilities in biological tissues.

Interventional photoacoustic imaging (iPAI) could improve ultrasound-guided minimally invasive procedures by enabling high precision needle steering, target detection, and molecular and physiologic tissue assessment. However, iPAI capabilities including visualization field, imaging depth, and spatial resolution are not well understood in biological tissues commonly encountered in clinical practice. Therefore, the potential clinical utility of iPAI remains unclear. We aim to experimentally determine iPAI capabilities in a variety of biological tissues, to assess its potential for clinical translation. We constructed an iPAI system capable of simultaneous real-time ultrasound (US) and photoacoustic imaging. This system delivers light directly into tissues using optical fiber integrated into a 16-gauge needle and detects photoacoustic signals with an external linear array ultrasound probe. iPAI's geometric visualization field, maximum imaging depth, and spatial resolution were experimentally determined in fat, muscle, kidney, and liver tissues by processing photoacoustic signal intensities of reference targets placed circumferentially around the fiber tip. The maximum detection depths of blood and indocyanine green (ICG), important common endogenous and exogenous contrast agents, respectively, were estimated in each tissue type by comparing their signal intensities with the reference target signal. iPAI could be performed in real-time concurrently with US and achieved a nearly spherical visualization field centering around the optical fiber tip in all tissues. Maximum imaging depths from the fiber tip were 54.1±1.3, 50.0±1.5, 32.7±1.1, and 16.9±1.3mm in fat, muscle, kidney, and liver tissues, respectively. Calculated maximum detection depths for blood were 41.5±3.0, 39.5±2.1, 24.4±4.0, and 8.6±2.0mm and detection depths for ICG at 0.05mg/mL concentration were 46.6±2.5, 42.6±1.4, 28.2±3.9, and 12.1±1.5mm in fat, muscle, kidney, and liver, respectively. Sub-100μm axial resolution and submillimeter lateral resolution were achieved in all tissues, and resolution did not significantly vary with distance from the fiber tip. Interventional photoacoustic imaging (iPAI) allows real-time visualization of a circumferential volume of tissue around an optical fiber tip, with submillimeter spatial resolution and tissue-dependent imaging depth. Our data strongly support further development of clinical iPAI systems as they could improve needle steering, target detection, and molecular and physiologic tissue assessment during minimally invasive procedures.

Single-hemisphere photoelectron momentum microscope with time-of-flight recording.

Photoelectron momentum microscopy is an emerging powerful method for angle-resolved photoelectron spectroscopy (ARPES), especially in combination with imaging spin filters. These instruments record kx-ky images, typically exceeding a full Brillouin zone. As energy filters, double-hemispherical or time-of-flight (ToF) devices are in use. Here, we present a new approach for momentum mapping of the full half-space, based on a large single hemispherical analyzer (path radius of 225 mm). Excitation by an unfocused He lamp yielded an energy resolution of 7.7 meV. The performance is demonstrated by k-imaging of quantum-well states in Au and Xe multilayers. The α2-aberration term (α, entrance angle in the dispersive plane) and the transit-time spread of the electrons in the spherical field are studied in a large pass-energy (6 eV-660 eV) and angular range (α up to ±7°). It is discussed how the method circumvents the preconditions of previous theoretical work on the resolution limitation due to the α2-term and the transit-time spread, being detrimental for time-resolved experiments. Thanks to k-resolved detection, both effects can be corrected numerically. We introduce a dispersive-plus-ToF hybrid mode of operation, with an imaging ToF analyzer behind the exit slit of the hemisphere. This instrument captures 3D data arrays I (EB, kx, ky), yielding a gain up to N2 in recording efficiency (N being the number of resolved time slices). A key application will be ARPES at sources with high pulse rates such as synchrotrons with 500 MHz time structure.

Existence and stability of static spherical fluid shells in a Schwarzschild-Rindler–anti–de Sitter metric

We demonstrate the existence of static stable spherical fluid shells in the Schwarzschild-Rindler-anti-de Sitter (SRAdS) spacetime where $ds^2 = f(r)dt^{2} -\frac{dr^{2}}{f(r)}-r^{2}(d\theta ^2 +\sin ^2 \theta d\phi ^2)$ with $f(r) = 1 -\frac{2Gm}{r} + 2 b r -\frac{\Lambda}{3}r^2$. This is an alternative to the well known gravastar geometry where the stability emerges due to the combination of the repulsive forces of the interior de Sitter space with the attractive forces of the exterior Schwarzschild spacetime. In the SRAdS spacetime the repulsion that leads to stability of the shell comes from a negative Rindler term while the Schwarzschild and anti-de Sitter terms are attractive. We demonstrate the existence of such stable spherical shells for three shell fluid equations of state: vacuum shell ($p=-\sigma$), stiff matter shell ($p=\sigma$) and dust shell ($p=0$) where $p$ is the shell pressure and $\sigma$ is the shell surface density. We also identify the metric parameter conditions that need to be satisfied for shell stability in each case. The vacuum stable shell solution in the SRAdS spacetime is consistent with previous studies by two of the authors that demonstrated the existence sf stable spherical scalar field domain walls in the SRAdS spacetime.

Dating of Holocene fluvial deposits in the southern Sierras Pampeanas (Argentina) by matching paleomagnetic secular variation to a geomagnetic field model

A 2-m long Holocene sedimentary sequence collected from a fluvial system located in the eastern piedmont of Sierra de Las Quijadas (San Luis, Argentina) was dated by comparing its paleomagnetic secular variation (PSV) record with the SHA.DIF.14 k time-varying spherical harmonic geomagnetic field model. Rock magnetic data suggest that the magnetic signal is mainly carried by low-coercivity magnetic minerals like magnetite. Low field magnetic susceptibility, used as a magnetic concentration parameter, shows a variation of about a factor of two along the profile. Progressive demagnetization experiments of the natural remanent magnetization show the presence of a stable magnetic component, and the Characteristic Remanent Magnetization directions are well defined (MAD <5°). The obtained magnetic inclination, declination, and the relative paleointensity (RPI) records were then compared with previously published lacustrine Holocene records from Argentina. Several common features and similar millennial-scale fluctuations are observed among the records, supporting a common geomagnetic origin. The consistency and good match among natural archives on a broader scale in different Argentinian regions suggest that the PSV records of El Chimborazo site are reliable and can thus be used to better constrain the secular variation path of the geomagnetic field in this area.

Bounded biharmonic blending of Möbius transformations for flexible omnidirectional image rectification

We propose a new method to correct distortions in equirectangular images, i.e., images that use the longitude/latitude representation to describe the full spherical field of view around a given viewpoint. We show that Möbius transformations are the correct mathematical tool to deal with the conflicting distortions in this setting: they are conformal, are able to rectify lines, perform rotations, translations and scales on the sphere and are bijective.Multiple transformations are specified through points, lines and cages on the sphere. We associate three points that uniquely define a Möbius transformation to each one of these geometric handles. Linear blend skinning with bounded biharmonic weights combine the different transformations into a single full spherical modified image. We present a collection of results in challenging settings and show that our method is more flexible and produces higher quality results when compared to previous methods.

Design of Highly Uniform Three Dimensional Spherical Magnetic Field Coils for Atomic Sensors

In this paper, three dimensional spherical magnetic field coils are proposed and optimized for atomic sensors that require highly uniform magnetic field coils within a limited volume. The design objective of the uniform coil is transformed into a nonlinear optimization model with constraints, which is solved by combining with the particle swarm optimization algorithm. Compared with the traditional cylindrical tri-axial magnetic field coil system whose volume is limited by the aspect ratio of the coil structure, the three dimensional spherical coils not only effectively reduce the volume but also provide consistent magnetic field performance in the three coordinate axis directions. It is of great significance to the miniaturization of atomic sensors. The theoretical calculation shows that the uniformity of spherical coil is improved by about 2 to 3 orders of magnitude compared with the Lee-Whiting coil and the saddle coil. The measurements show that the magnetic field uniformity of our design reached $1.5\times 10^{-4}$ along the ${z}$ -axis within a range of $\pm 0.25{R}$ . The actual magnetic field distribution is basically consistent with the theory. However, due to the limited processing and experimental conditions, the actual magnetic field uniformity is 1 to 2 orders of magnitude lower than the theory.

An optical perspective on the theory of relativity - II: Gravitational deflection of light and Shapiro time delay

By regarding a gravitational field as a special optical medium, we define its refractive index using the general form of the solution to the Einstein equation in general relativity. A generalized version of Snell's law is given by comparing the space structure of a gravitational field with that of optical medium. The applicability of Snell's law is extended from Euclidean space to a spherical symmetrical gravitational field space. Drawing upon the generalized version of Snell's law, geometrical optics are used to arrive at formulas for the gravitational deflection of light and Shapiro time delay in a spherically symmetric gravitational field. These formulas are identical to those obtained by using geodesic equations in general relativity, thus proving that a gravitational field is a special optical medium.

COMPARISON OF UAV LIDAR ODOMETRY OF ROTATING AND FIXED VELODYNE PLATFORMS

Abstract. Three-dimensional LiDAR rangefinders are increasingly integrated into unmanned aerial vehicles (UAV), due to their direct access to 3D information, their high accuracy and high refresh rate, and their tendency to be lightweight and cheaper. However, all commercial LiDARs can only offer a limited vertical resolution. To cope with this problem, a solution can be to rotate the LiDAR on an axis passing through its center, adding an additional degree of freedom and allowing more overlap, which significantly enlarges the sensor scope and allows having a complete spherical field of view (FOV). In this paper, we explore this solution in detail for drone’s context, while making comparisons between the rotating and fixed configurations for a Multi-Layers LiDAR (MLL) of type Velodyne Puck Lite. We investigate its impact on the LiDAR Odometry (LO) process by comparing the resulting trajectories with the data of the two configurations, as well as, qualitative comparisons, of the resulting maps.